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PLECS - User Manual

1. Parameters Name L1 E Width E ja Inductance 0 001 El Initial current O E OK Cancel Help Apply Figure 2 4 Inductor dialog box Of greater importance are the parameters that determine for example the inductance of an inductor the capacity of an capacitor or the voltage of a DC voltage source If you want the name and selected parameters to be displayed in the schematic you must check the little button on the right side of the edit field For reasons of clarity we prefer to display only the most important pa rameters of a component Units Like Simulink PLECS does not know anything about units It is your respon sibility that variables are scaled correctly For power electronics we recom mend the use of SI quantities However if you want to employ PLECS for the simulation of power systems it may be more appropriate to work with per unit quantities For every component enter the values according to the schematic in Fig 2 1 In the dialog boxes of the inductor and the capacitor you can additionally set the initial current resp the initial voltage Please leave both values at zero A Simple Passive Network Signals Up to now our electrical circuit lacks a connection with the Simulink envi ronment You will notice this from the fact that the PLECS block in Simulink does not have inputs or outputs In order to add inputs and outputs we must copy the respective port blocks
2. 15 LICONSA RET E ek 17 Student Version e 17 Full Versi n 2000 AA E ee te 17 How to Use This Manual o 18 1 Introduction 19 Concepts of PLECS crara cti a ae 19 Integration into Simulink 19 Ideal Switches 20 Contents 2 Getting Started 23 Where to Find PLECS o o 002 eee eee eee 23 A Simple Passive Network 23 Components at ta 24 Connections iran ta at 25 Component Properties 26 BAS cut A Sati at cog a tete 26 e RA Bete la ND ee eRe eR Nahe Sale 27 Adding More Measurements 0020005 27 Importing Signals ratas at 28 Buck Converter umi dee da a BA aa ek 28 SWITCHES nava tee ch Be e SS anes NA 29 Gate Signals 2028 i a e lea AE aes 29 Using PLECS 31 Configuring PLECS 0 00000 ee ee ee eee 31 Creating a New Circuit e 32 Using the Component Browser 0 0000 eee uae 33 Components naneo a oe a ee da a a 34 Specifying Component Parameters 34 Displaying Parameters in the Schematic 34 Changing Component Names 0 000 eee 35 Changing the Orientation of Components 35 Getting Component Help 0 0 00 000 35 Libraries aa tena we ee hee La eS tk oe a aa 36 Creating a New Library 36 Creating a Library Reference
3. o 36 Updating a Library Reference 37 Breaking a Library Reference 37 Connections dada o e is eek 38 WALES 4 o ANNA ia ta ta dad A 38 Contents A AI gh BA bow amp amp Albee dee ee hase 38 Creating Branches 0 0 0 pee eee ens 39 Annotations A es oe ene ee aa 39 SUDCIFCUIES enans Goede 4 4 e E Se a ee eel Sa ae 40 Creating a Subcircuit by Adding the Subcircuit Block 40 Creating a Subcircuit by Grouping Existing Blocks 40 Arranging Subcircuit Terminals 41 Resizing a Subcircuit Block 41 Placing the Subcircuit Label 42 Masking Subcircuits s iome eena ee e a a a a E E E A a aS 43 Mask Icons nuria 43 Mask Parameters eee eee eee 45 Mask Probe Signals eee eee ee 46 Mask Documentation o o e 47 Unprotecting Masked Subcircuits 48 Circuit Browser lt 6 ya ote a Be Se ee e ee 49 Showing Masked Subcircuits 0 2000005 49 PLECS Probe users ELA AAA RR ER eee ee ES 50 Copying aProbe 51 Controlling Access to Circuits and Subcircuits 52 Encrypting Circuits and Subcircuits 52 Exporting Circuits for the PLECS Viewer 53 Circuit Simulation Parameters o o 54 Working Principle of PLECS
4. 216 Op AMPS 4 6 3044 A A AS A e a ar ok 218 OPAM pra o a a aa nl ee eh 218 Limited Op AMD ue ee EE Se aa 219 Converters fos cess tata ae TA ia oe a hal ee ke este 220 Diode Rectifier 2 2 o o ee 220 Thyristor Rectifier Inverter o 222 2 Level IGBT Converter o o 224 3 Level IGBT Converter o o 226 2 Level MOSFET Converter o o 228 2 Level Converter 2 o o e 230 3 Level Converter 2 o o e 231 3 Phase Transformers o eee eee eee 232 2 Winding 3 Phase Transformers 232 3 Winding 3 Phase Transformers 235 Thermal ls ls wie aa eSB A RS OSS Ree eee eee a ew denen 238 Heat Sink 20234 oe SSeS SSS eA AS BRE eee 238 Controlled Temperature 240 Constant Temperature 2 0 pee ee ee 241 Controlled Heat FloWw o o e eee 242 Constant Heat Flow o o 243 Thermometer e 244 Heat Flow Meter o e e e 245 Thermal Resistor o eee ee 246 Thermal Capacitor 0 0 ee ee eee 247 Thermal Ground 0 0 0 eee eee eee 249 Ambient Temperature aoaaa aa 250 Thermal Port ae aire nd e e eee al eee a 251 Modulators A e a ho ott eee ek 252 Symmetrical PWM e ea a 252 Contents 10 Sawtooth PWM 2 aaa ee 255 Symmet
5. 0044 91 2 Winding Mutual Inductance 004 93 3 Winding Mutual Inductance 95 Pi Section Line ama ds 97 Nonlinca a a aaa 99 Saturable Inductor o oo 99 Variable Inductor oo e a 101 Variable Resistor with Variable Series Inductor 103 Variable Resistor with Constant Series Inductor 105 Saturable Capacitor imita ww WE RN a e y 107 Variable Capacitor ee 109 Variable Resistor with Variable Parallel Capacitor 111 Variable Resistor with Constant Parallel Capacitor 113 Saturable Transformers o o 00 eee eee 115 Switches uo ae st te ae aes Dea ea oe oe ames ate ate NaN 117 SW ete Bia ie aie eae Geng teen eG ae Se eae 117 Double Switch scoopet akedi ee 118 Triple SWCD e 119 Breaker ansus ea rr ad a a Oe feels 120 Set Reset Switch o ee 121 Didde ira gerner OER a eS A AED as 123 Diode with Reverse Recovery o 125 Zener Diod criar Aaa ada 128 THiS uva aa a A A O da 130 ET latas 132 IGBT a id ak on ea ee oe eo da ay 134 IGBT with Diode 20d So Be he ee Be eS 136 MOSEET o vata seactgpie E RRO a 138 MOSFET with Diode o e eee eee 140 TRA ES Bette a o aint ns att Ran ohare tas 142 Machines rn a A ne ee E 144 Contents Induction Machine o o o e eee 144 Squirrel Cage Induction Machine 149 Induction Machi
6. C3 fa Width E z Initial voltage C OK Cancel Help Apply 109 6 Block Reference Width The width of the electrical ports resp the number of variable capacitors represented by the component Initial voltage The initial voltage of the capacitor at simulation start in volts V This parameter may either be a scalar or a vector with the width of the compo nent The positive pole is marked with a The initial voltage default is 0 Probe Signals Capacitor voltage The voltage measured across the capacitor in volts V A positive voltage is measured when the potential at the terminal marked with is greater than the potential at the unmarked terminal 110 Variable Resistor with Variable Parallel Capacitor Variable Resistor with Variable Parallel Capacitor Purpose Variable resistor with variable parallel capacitor Library Nonlinear Description This component models a variable resistor with a variable capacitor connected in parallel The resistance and capacitance are determined by the continuous signals fed into the inputs of the component The current through this compo nent is determined by the equation v d 1 d d Therefore the control signal for the capacitor is a vector twice as wide as the width of the component It contains both the momentary capacitance values and their derivatives with respect to time C1 C2 Cn 401 C2 4C It is the responsibility of the
7. Negative carrier flipped Negative carrier shifted Modulation index Switching function 257 6 Block Reference 258 Parameters and Dialog Box The figures below illustrate the different Regular Sampling methods offered by this block With double edge sampling left figure the modulation index is updated at the carrier tips and zero crossings With single edge sampling right figure the modulation index is updated only at the outer tips Double edge sampling Single edge sampling o Modulation index 1 1114 4 1 f Switching function o E Block Parameters Symmetrical PWM 3 Level 2j x m Symmetrical PWM 3 Level mask Three level PWM generator with two symmetrical triangular carriers The input m is the modulation index with a range of 1 1 The switching function s outputs either 1 0 or 1 If the input is a vector the output is also a vector of the same width m Parameters Sampling Natural carrier starts with 0 bad Carrier frequency 1000 Negative carrier Flipped zl Cancel Help Apply Symmetrical PVVM 3 Level Sampling Select a sampling method If you select Natural Sampling the carrier signal may begin with 0 or 1 at simulation start The Regular Sampling method lets you choose between double edge and single edge sam
8. m y Lm 0 0 Lm 3 0 if asia Baa const is assumed to be constant at all saturation levels The equivalent magnetizing flux Ym in an isotropic machine is defined as Wn Wat W m For flux linkages Ym far below the transition flux Yr the relationship be tween flux and current is almost linear and determined by the unsaturated magnetizing inductance Lo For large flux linkages the relationship is gov erned by the saturated magnetizing inductance Lm sat Vr defines the knee of the transition between unsaturated and saturated main flux inductance The tightness of the transition is defined with the form factor fr If you do not have detailed information about the saturation characteristic of your machine fr 1is a good starting value The function plsaturation Lm0 Lmsat PsiT fT Salient Pole Synchronous Machine Parameters and Dialog Box plots the main flux vs current curve and the magnetizing inductance vs cur rent curve for the parameters specified The model accounts for steady state cross saturation i e the steady state magnetizing inductances along the d axis and q axis are functions of the cur rents in both axes In the implementation the stator currents the field cur rent and the main flux linkage are chosen as state variables With this type of model the representation of dynamic cross saturation can be neglected with out affecting the machine s performance The computation of the time deriva tive
9. 1 _ 7 1 ici Rs Lis La we Weg Ris i CA ANY i XS Usd Lm d axis 1 7 isq Rs Lis Lir w Ved Ria me oe YY YY C Z Us q Im Vv q axis 155 6 Block Reference 156 The rotor flux is defined as poor Via F Lir trad T Lm isa Tv ita gt I Vig Lir tra Lm isq a j The electrical system of the machine model is implemented with state variable equations that are derived from the equivalent circuit in the stationary ref erence frame The value of the main flux inductance L is not constant but depends on the main flux linkage Ym as illustrated in the Ym im diagram For Pad m sat IP di L IP di L m 0 flux linkages far below the transition flux Yr the relationship between flux and current is almost linear and determined by the unsaturated magnetizing inductance Lm 0 For large flux linkages the relationship is governed by the saturated magnetizing inductance Lom sat Vr defines the knee of the transi tion between unsaturated and saturated main flux inductance The tightness of the transition is defined with the form factor fr If you do not have detailed information about the saturation characteristic of your machine fr lisa good starting value The function plsaturation Lm0 Lmsat PsiT fT plots the main flux vs current curve and the magnetizing inductance vs cur rent curve for the parameters specified The model accounts for steady state cross saturation i e the steady st
10. 2 Level IGBT Converter Purpose Library Description Parameters and Dialog Boxes Three phase two level IGBT converter Converters Implements a three phase two level IGBT converter with reverse diodes The gate input is a vector of three signals one per leg The upper IGBT con nected to the positive dc level is on if the corresponding gate signal is posi tive The lower IGBT is on if the gate signal is negative If the gate signal is zero both IGBTs in the leg are switched off You can choose between two different converter models e The basic 2 Level IGBT Converter is modeled using the component IGBT with Diode see page 136 PLECS needs only six internal switches to rep resent this converter so the simulation is faster compared to the detailed converter No electrical parameters can be entered but the thermal losses may be specified e The Detailed 2 Level IGBT Converter is based on individual IGBT see page 134 and Diode see page 123 components In this model you may specify all electrical and thermal parameters separately for the IGBTs and the diodes The electrical circuit for the converter is shown below iY ie tk tk atk A For a description of the parameters see the documentation of the IGBT with Diode on page 186 the IGBT on page 134 and the Diode on page 123 2 Level IGBT Converter Probe Signals Block parameters E le x r2 Level IGBT Conv
11. Note The Switched Reluctance Machine models can only be simulated with the Continuous State Space Method The machine flux linkage is modeled as a nonlinear function of the stator cur rent and rotor angle i 0 accounting for both the magnetization characteris tic of the iron and the variable air gap Y 0i E sat dWV di L 185 6 Block Reference 186 In the unaligned rotor position the flux linkage is approximated as a linear function Pali Luci In the aligned rotor position the flux linkage is a nonlinear function of the sta tor current Vali Wear 1 e7 Loari where La Lsat K Viat For intermediate rotor positions the flux linkage is written as a weighted sum of these two extremes V t 0 Vali f A Vali Vad using the weighting function HO 5 500s x le ar where N is the number of rotor poles N is the number of stator poles and x 0 Ns 2 1 is the index of the stator phase Electrical System aw Y 7 R i 00 aes MM h id ol The terminal voltage of a stator phase is determined by the equation O O e O dt i dt dt The electromagnetic torque produced by one phase is the derivative of the co energy with respect to the rotor angle 2 W i 0 di The total torque T of the machine is given by the sum of the individual phase torques T i 9 Switched Reluctance Machine Mechanical System Roto
12. plecsclear rehash toolboxcache only for MATLAB version 6 0 or higher in the MATLAB command line Mac OS X Linux Solaris e If applicable unzip with gunzip filename tar gz e Untar with tar xf filename tar in a directory of your choice This will create a new sub directory named plecs containing the required files Installing PLECS e Copy the license file license dat into the just created directory named plecs See section Licensing on page 17 for more information There is no license dat file for the student version e In MATLAB add the new directory plecs and the subdirectory demos to your search path Use the Path Browser under the menu item File gt Set Path gt Add Folder Alternatively edit directly the file pathdef m in the directory matlabroot toolbox local If you do not have file system per mission to modify the file pathdef m add the commands addpath plecs_directory addpath plecs_directory demos to the file matlab startup m In case the file does not exist create an empty file startup m in the subdirectory matlab of your home direc tory e If you previously had installed an older version of PLECS execute plecsclear rehash toolboxcache only for MATLAB version 6 0 or higher in the MATLAB command line Configuring PLECS For information about setting global configuration options for PLECS see Configuring PLECS on page 31 Installing Dif
13. mary side To model a transformer without saturation enter 1 as the magne tizing current values and the desired magnetizing inductance Lm as the flux 235 6 Block Reference values A stiff Simulink solver is recommended if the iron losses are not negli gible i e Rfe is not infinite esi Hot bay atx an Dia og Ydy Transformer mask link Box This component implements a three winding three phase transformer in star delta star connection with a three leg or five leg core The secondary side may be of type d1 d3 d5 d7 d9 or d11 the tertiary side may be of type y0 y2 y4 d6 d8 or d10 depending on the specified phase lag The core saturation characteristic is piece wise linear To model a transformer without saturation enter 1 as magn current values and the magnetization inductance as flux values amp stiff solver is recommended if Rfe is not infinite Parameters Name Ydy Trafo E Leakage inductance L1 L2 L3 No of core legs 3 or 5 2e 3 1e 3 1e 3 Ef 3 ja Winding resistance A1 R2 R3 Phase lag degree angle2 angle3 611 J oq E No tums n n2 n3 Initial current wdg 1 ila i1b itc n074 fE 1000 F Magnetizing current values Initial current wdg 2 i2a 2b 1 z 00 F Magnetizing flux values Initial curent wda 3 i3a i3b 3c io 3 ooo El Core loss resistance Afe inf zf OK Cancel Help Apply Leakage inductance A three element
14. Apply No of turns A vector containing the number of turns of the primary winding n4 the secondary winding na and the tertiary winding nz if applicable Magnetizing current values A vector of positive current values in amperes A defining the piece wise linear saturation characteristic of the transformer legs The current values must be positive and strictly monotonic increasing At least one value is required Magnetizing flux values A vector of positive flux values in Vs defining the piece wise linear satura tion characteristic The flux values must be positive and strictly monotonic increasing The number of flux values must match the number of current values Core loss resistance An equivalent resistance Rf representing the iron losses in the trans former core The value in ohms 2 is referred to the primary side Initial current A vector containing the initial currents on the primary side the sec ondary side 2 and the tertiary side i3 if applicable The currents are given in amperes A and considered positive if flowing into the trans former at the marked terminals The default is 0 O 0 116 Switch Switch Purpose Ideal single switch Library Switches Description This Switch provides an ideal short or open circuit between its two electrical terminals The switch is open when the gate input signal is zero otherwise o_o closed Dep at ag ala and Dialog EET Box Ideal on off swit
15. Cancel Help Apply Expression The expression applied to the input signal in C language syntax Input width The width of the input signal The default is 2 Probe Signals Input The input signal Output The output signal 206 Gate Function Gate Function Purpose Apply a relational or logical expression to a gate signal Library Signals amp Systems Description The Gate Function block applies a relational or logical expression specified in C language syntax to its input The input may be a scalar or vectorized gate EN signal the output is always a scalar gate signal The expression may consist of one or more of the following components e u the input of the block If the input is vectorized u i or u i repre sents the ith element of the vector To access the first element enter u 1 u 1 or u alone e Brackets e Numeric constants e Relational operators gt lt gt lt e Logical operators 88 e MATLAB workspace variables The Gate Function icon can be distinguished from the Compare Function by the brown instead of a green input terminal Parameters lolx and Dialog ene Box Function block for processing gate signals TParameters Name GateFen E Expression ult amp amp u 2 F Input width jz k OK Cancel Help Apply Expression The expression applied to the input signal in C language syntax Input width The widt
16. If you copy a Thermal Port block into the schematic of a subcircuit a terminal will be created on the subcircuit block The name of the port block will appear as the terminal label If you choose to hide the block name by unselecting the show button in the dialog box the terminal label will also disappear Terminals can be moved around the edges of the subcircuit by holding down the Shift key or by using the middle mouse button Note Thermal Port blocks cannot be placed in top level circuits nor may they be used in schematics that contain Ambient Temperature blocks see page 250 Block parameters ES gt Thermal Port Provide a thermal port for a subcircuit Parameters Name Fon O h OK Cancel Help Apply 251 6 Block Reference 252 Symmetrical PWM Purpose Library Description PWM generator with symmetrical triangular carrier Extras Modulators 2 level PWM generator with a symmetrical triangular carrier The input m is the modulation index with a linear range of 1 1 The switching function s outputs either 1 or 1 If the modulation index is a vector the switching func tion is also a vector of the same width The block can be used to control the 2 Level IGBT Converter see page 224 or the ideal 2 Level Converter see page 230 In these cases the modulation index must have a width of 3 according to the number of inverter legs The block offers different sampling me
17. Parameters and Dialog Box or inverter The inputs of the block are a logical enable signal a ramp signal vy produced e g by a PLL and the firing angle alpha If the Double pulses option is checked each thyristor receives two pulses one when the firing angle is reached and a second when the next thyristor is fired JBlock Parameters 6 Pulse Generator ax 6 Pulse Generator mask This block generates the pulses used to fire the thyristors of a 6 pulse converter Inputs are a logical enable signal a ramp signal phi produced e g by a PLL and the firing angle alpha If the Double pulses option is checked each thyristor receives two pulses one when the firing angle is reached and a second when the next thyristor is fired Parameters Pulse width radians pi 3 F Double pulses Cancel Help Apply Pulse width The width of the firing pulses in radians with respect to one period of fun damental frequency Double pulses Enables a second firing pulse for each thyristor 2 Pulse Generator 2 Pulse Generator Purpose Generate firing pulses for an H bridge thyristor converter Library Extras Modulators Description This block generates the pulses used to fire the thyristors of an H bridge rec tifier The inputs of the block are a logical enable signal a ramp signal y pro enable duced e g by a PLL and the firing angle alpha phi alpha Dialog Box aixi
18. Systems and connect its output to the switch By default the gate signal evaluates to false if the corresponding Simulink sig nal is zero and else to true Therefore the switch will close upon a non zero signal and open when the signal goes back to zero File Edit View Simulation Format iste L 25e 3 Figure 2 9 Electrical part of buck converter By now you should be able to model the electrical part of the buck converter as shown in Fig 2 9 For the buck converter we will implement a hysteresis type control that keeps the capacitor voltage roughly in a 0 2 V band around 6 V To make things a bit more interesting we apply a step change from 12 V down to 8V to the input voltage during the simulation Jr Scope lt 2 gt File Edit View Simulation Format Tools Help 185 P BP B E ve_ref Figure 2 10 Simulation of buck converter with hysteresis control Using PLECS The user interface of PLECS very closely resembles that of Simulink Circuits are built using the same simple click and drag procedures that you use to build a model This chapter explains those aspects of PLECS that either are unique to PLECS or work differently from Simulink Configuring PLECS PLECS reads global configuration parameters from a file called plecscon fig m The file is located in the installation directory of PLECS For more in formation see Installing PLECS on page 11 Edit the file plecsc
19. This transformer models three coupled windings on the same core The magnetization inductance Lm and the core loss resistance Am are modeled as linear elements Their values are referred to the primary side Parameters Name Linear Trafo3 E Leakage inductance L1 L2 L3 0 01 0 001 0 001 Ei Winding resistance R1 R2 R3 1011 No tums n n2 n3 1012 F Magnetization inductance Lm E El Core loss resistance Am inf al Initial current i1 12 13 oo 4 OK Cancel Help apply Core loss resistance An equivalent resistance Rm representing the iron losses in the trans former core The value in ohms 9 is referred to the primary side Initial current A three element vector containing the initial currents on the primary side i the secondary side 2 and the tertiary side 3 in amperes A The cur rents are considered positive if flowing into the transformer at the marked terminals The default is 0 O 0 92 2 Winding Mutual Inductance 2 Winding Mutual Inductance Purpose Magnetic coupling between two windings Library Passive Components Description This component implements a magnetic coupling between two separate wind ings For both windings the self inductance and resistance are specified in dividually The mutual inductance and resistance are modeled as linear ele ments The electrical circuit for this component is given below i
20. V This parameter may either be a scalar or a vector with the width of the compo nent The positive pole is marked with a The initial voltage default is 0 Probe Signals Capacitor voltage The voltage measured across the capacitor A positive voltage is measured when the potential at the terminal marked with is greater than the potential at the unmarked terminal 86 Transformer Transformer Purpose Ideal transformer Library Passive Components Description This component represents a transformer with two or more ideally coupled windings At all windings w the voltage v across the winding divided by the corresponding number of turns n is the same V1 v2 U3 ny n2 n3 The currents of all windings multiplied with the corresponding number of turns add up to zero 0 ii ni tie ng ig ngt In the transformer symbol the first primary side winding is marked with a little circle The orientation of the other windings is indicated by a dot To change the orientation of a specific winding w make the corresponding num ber of turns nuy negative Parameters lala and Dialog Transformer Box Ideal transformer TParameters Name Tr3 E Width E El Number of windings 1 2 Fal Number of turns A SS OK Cancel Help Apply Width The width of the electrical ports resp the number of ideal transformers represented by the component 87 6 Block Re
21. i e Rfe is not infinite Block parameters oj xj Yy Transformer mask link This component implements a two winding three phase transformer in star star connection with a three leg or five leg core The type may be Yy0 Yy2 Yy4 Yy6 Yy8 or Yy10 depending on the phase lag of the secondary side The core saturation characteristic is piece wise linear To model a transformer without saturation enter 1 as magn current values and the magnetization inductance as flux values amp stiff solver is recommended if Rfe is not infinite Parameters Name Yy Trafo a Leakage inductance L1 L2 Core loss resistance Rfe 2e 3 1e 3 F inf B Winding resistance A1 R2 No of core legs 3 or 5 51 ja 3 No of turns n1 n2 Phase lag of secondary side degree 101 F 0 E Magnetizing current values Initial current wdg 1 ila i1b itc E 3 woo E Magnetizing flux values Initial current wdg 2 i2a i2b i2c fo ao 4 OK Cancel Help Apply Leakage inductance A two element vector containing the leakage inductance of the primary side L and the secondary side Lz The inductivity is given in henries H Winding resistance A two element vector containing the resistance of the primary winding R and the secondary winding R2 in ohms Q No of turns A two element vector containing the number of turns of the primary wind ing n and the secondary winding nz Magnetiz
22. in Nm The vectorized output signal of width 3 contains the rotational speed wm in rad s the mechanical rotor position th in rad the electrical torque Te in Nm Parameters Name PMSM E Stator resistance A Number of pole pairs p 3 E z Stator inductance Ld Lag Initial rotor speed wm le 2 1e 2 ic 0 E Flux induced by magnet Phi Initial rotor position thm0 0 2 F 0 E Inertia J Initial stator current isa0 isb0 1e 3 F 00 E Friction coefficient F fo OK Cancel Help Apply Stator resistance Armature or stator resistance R in Q Stator inductance A two element vector containing the combined stator leakage and magne tizing inductance La is referred to the d axis and L to the q axis of the rotor The values are in henries H Flux induced by magnets Constant flux linkage y in Vs induced by the magnets in the stator wind ings Inertia Combined rotor and load inertia J in Nms 173 6 Block Reference Inputs and Outputs 174 Friction coefficient Viscous friction F in Nms Number of pole pairs Number of pole pairs p Initial rotor speed Initial mechanical rotor speed wm in radians per second s Initial rotor position Initial mechanical rotor angle 0m o in radians Initial stator currents A two element vector containing the initial stator currents is a o and is b 0 of phase a and b in amperes A Mechanical torque The
23. shift register is subtracted from the accumulator The output of the block is the current accumulator value divided by the number of samples Note This block is only available for Matlab 7 0 or newer E Block Parameters Discrete Mean Yalue y 21xj Discrete Mean Value mask Computes the mean value of a periodic signal The input signal is sampled with the sample time specified The fundamental frequency f of the averaging window is calculated as f 1 4 sample time number of samples The initial condition describes the input signal before simulation start It can either be a scalar or a vector matching the number of samples m Parameters Initial condition 0 Sample time 0 01 Number of samples 10 Cancel Help Apply Initial condition The initial condition describes the input signal before simulation start This parameter may either be a scalar or a vector matching the number of samples The default is 0 Sample time The time interval between samples Discrete Mean Value Number of samples The number of samples used to calculate the mean value 275 6 Block Reference 276 Discrete RMS Value Purpose Library Description Parameters and Dialog Box Calculate the root mean square RMS value of the input signal Extras Discrete Analysis This block calculates the RMS value of a periodic input signal based on dis crete samples The sample time and the numbe
24. 1 6 5 7 0 7 3 Microsoft Windows Y Y Y Y Y Mac OS X Y Y Linux Y Y Y Solaris Y Y Y The various platforms and MATLAB versions require different install pack ages Table 2 indicates which package is required in your case The packages can be found in the root directory of the PLECS CD ROM Microsoft Windows e Unzip the appropriate package file in a directory of your choice either with pkzip d filename zip Before You Begin 12 Table 2 Install packages Platform MATLAB Version Package File Microsoft Windows 5 3 7 3 plecs 1 5 0_pc_r11 zip MacOSX 6 5 7 3 plecs 1 5 0_mac_r13 tar Solaris 6 1 7 3 plecs 1 5 0 sol _r12p1 tar 6 1 6 5 plecs 1 5 0_glx_r12p1 tar Linux 32 7 0 7 3 plecs 1 5 0_glx_r14 tar Linux 64 7 1 7 3 plecs 1 5 0 a64 r14p3 tar or with WinZIP This will create a new sub directory named plecs con taining the required files If you use WinZIP make sure that Use Folder Names is checked in the Extract menu Copy the license file license dat into the just created directory named plecs See section Licensing on page 17 for more information There is no license dat file for the student version In MATLAB add the new directory plecs and the subdirectory demos to your search path using the Path Browser The Path Browser is found under the menu item File gt Set Path gt Add Folder If you previously had installed an older version of PLECS execute
25. 5 fa 2 E Armature inductance La Friction coefficient F 0 01 0 f Field resistance Rf Initial rotor speed wm 200 mi 0 fE Field inductance Lf Initial armature current a0 100 F 0 a Field armature mutual inductance Laf Initial field current iff 2 m o E OK Cancel Help Apply Armature inductance Field winding inductance L in henries H Field armature mutual inductance Field armature mutual inductance L f in henries H Inertia Combined rotor and load inertia J in Nms Friction coefficient Viscous friction F in Nms Number of pole pairs Number of pole pairs p Initial rotor speed Initial mechanical speed wm o in radians per second s71 Initial armature current Initial current ia y in the armature winding in amperes A Initial field current Initial current if o in the field winding in amperes A 176 DC Machine Inputs and Mechanical torque Outputs The input signal Tm represents the mechanical torque at the rotor shaft in Nm The output vector m contains the following 2 signals 1 Rotor speed The rotational speed wm of the rotor in radians per second s71 2 Electrical torque The electrical torque T of the machine in Nm 177 6 Block Reference Brushless DC Machine Purpose Detailed model of a brushless DC machine excited by permanent magnets Library Machines Description A brushless DC machine is a type of permanent magnet
26. Box back to Simulink or from a subcircuit to the parent circuit If you copy an out put block into a schematic an output terminal will be created on the corre sponding subsystem block The name of the output block will appear as the terminal label If you choose to hide the block name by unselecting the show button in the dialog box the terminal name will also disappear The Continu ous Output block can be distinguished from the Gate Output block see page 194 by the green instead of a brown input terminal Output Blocks in a Top Level Circuit If an output block for a continuous or gate signal is placed in a top level cir cuit a unique number is assigned to the block In Simulink the relative posi tion of the corresponding input terminals is determined by the order of block numbers You may change the block number in order to change the relative terminal position Output Blocks in a Subcircuit If placed in a subcircuit the outputs are not identified by numbers since termi nals on subcircuit blocks can be freely positioned Which terminal corresponds to which output block can be seen from the block name In order to move an unconnected terminal with the mouse around the edges of a subsystem hold down the Shift key or use the middle mouse button Width The width of the output signal The default is 1 Port number The terminal number of the output block This parameter appears only if the block is placed in a top level circuit C
27. Dialog E lectrical Ground Box Provide an electrical ground connection Parameters Name Ground fi Width E E OK Cancel Help Apply Width The width of the ground port The default is 1 201 6 Block Reference 202 Subcircuit Purpose Library Description E Dialog Box Represent a circuit within another circuit Signals amp Systems A subcircuit block represents a circuit within another circuit In order to create a subcircuit copy the subcircuit block from the library into your schematic You can then open the subcircuit block and copy components into the subcircuit s window The input output and electrical terminals on the block icon correspond to the input output and electrical port blocks in the subcircuit s schematic If the block names are not hidden they appear as terminal labels on the subcircuit block You can move unconnected terminals with the mouse around the edges of the subcircuit by holding down the Shift key or using the middle mouse button You can create a dialog box for your Subcircuit by masking the block Continuous Function Continuous Function Purpose Apply an arithmetic expression to a continuous signal Library Signals amp Systems Description The Continuous Function block applies an arithmetic expression specified in C language syntax to its input The input may be a scalar or vectorized contin fu p uous signal the out
28. Inductance per unit length The series line inductance L per unit length If the length is specified in meters m the unit of L is henries per meter H m Resistance per unit length The series line resistance R per unit length If the length is specified in meters m the unit of R is ohms per meter Q m Capacitance per unit length The capacitance C between the line conductors per unit length If the length is specified in meters m the unit of C is farads per meter F m 97 6 Block Reference 98 block parameters ix rPi section line Single phase pi section transmission line Parameters Name Linel E Inductance per unit length 2e 3 ja Resistance per unit length 0 1 m Capacitance per unit length 10e 9 mj Conductance per unit length fo E Length 100 mi Number of pi sections BO O l le OK Cancel Help Apply Conductance per unit length The conductance G between the line conductors per unit length If the length is specified in meters m the unit of G is siemens per meter S m Length The length of the line The unit of l must match the units L R C and G are based on Number of pi sections Number of sections used to model the transmission line The default is 3 Saturable Inductor Saturable Inductor Purpose Saturable inductor Library Nonlinear Description This component provide
29. Inductor see page 105 e the Variable Resistor with Variable Parallel Capacitor see page 111 and e the Variable Resistor with Constant Parallel Capacitor see page 113 Heat Sinks and Subcircuits 64 By default if you place a subcircuit on a heat sink the heat sink tempera ture is propagated recursively into all subschematics of the subcircuit and all thermal losses dissipated in all subschematics flow into the heat sink In some cases this is not desirable The implicit propagation mechanism is disabled if a subschematic contains one or more heat sinks or the Ambient Temperature block see page 250 This latter block provides a thermal connection to the heat sink enclosing the par ent subcircuit block Y Z Ambient D f u 1 vacio vac R ror VE vZ Cathode As an example the figure above shows the subschematic of the Diode with Re verse Recovery see page 125 By default this diode model would only dissi pate the ohmic losses from the three resistors and the conduction losses of the Heat Sinks and Subcircuits internal ideal diode However the losses from the reverse recovery current in jected by the current source would be neglected because current sources and also voltage sources do not dissipate thermal losses The Diode with Reverse Recovery therefore uses a Controlled Heat Flow block see page 242 to inject the electrical power loss into t
30. Inputs and Outputs Probe Signals Same as for the Induction Machine with slip ring rotor see page 144 Same as for the Induction Machine with slip ring rotor see page 144 Most probe signals for the Induction Machine with slip ring rotor see page 144 are also available with this squirrel cage machine Only the following probe signal is different Rotor currents The rotor currents i and i q in the stationary reference frame in A re ferred to the stator side 151 6 Block Reference 152 Induction Machine with Open Stator Windings Purpose Library Description Non saturable induction machine with squirrel cage rotor and open stator windings Machines This model of a squirrel cage induction machine can only be used with the continuous state space method The machine model is based on a stationary reference frame Clarke transformation A sophisticated implementation of the Clarke transformation facilitates the connection of external inductances in series with the stator windings The machine operates as a motor or generator the sign of the mechanical torque determines the mode of operation positive for motoring negative for generating All electrical variables and parameters are viewed from the sta tor side In the component icon the positive terminal of phase a of the stator windings is marked with a dot In order to inspect the implementation please select the component in your circuit and c
31. Parameters Name M3 ul Number of windings fa El Inductance 1211 121 11 250 001 Fat Initial current 000 Fj OK Cancel Help Apply Number of windings The number of ideal inductors represented by the component Inductance The inductance in henries H All finite positive and negative values are accepted including 0 If the parameter is a scalar or a vector no coupling exists between the windings In order to model a magnetic coupling between the windings a square matrix must be entered The size n of the matrix corresponds to the number of windings L is the self inductance of the internal inductor and M the mutual inductance 83 6 Block Reference la san d v2 M21 La gt es Man a2 Un Mn Mp2 re Ln fin Initial current The initial current in the windings at simulation start in amperes A This parameter may either be a scalar or a vector corresponding to the number of windings The direction of the initial current inside the com ponent is from the positive to the negative terminal The default of the initial current is 0 Probe Signals Winding i current The current flowing through winding i The direction of a positive current corresponds to the small arrow in the component symbol 84 Capacitor Capacitor Purpose Library Description ia ge dE Parameters and Dialog Box Ideal capacitor Passive Components This component provides one or more ideal capacitor
32. Rost Lrr 3 RL fo O K UL Parameters Block parameters o a nd Dia log Diode with Reverse Recovery mask B ox This model of a power diode includes the reverse recovery effect Only two of the three parameters trr Irrm and Orr must be specified The undefined parameter should be set to 0 otherwise the value for rr is ignored The parameter Lrr can be arbitrarily set to a very small value e g 10 pH Parameters Name rd E Forward voltage Vf Reverse recovery time tr Po aires k On resistance Ron Peak recovery current Irrm poo fs Off resistance Roff Reverse recovery charge Orr jnt Pate 9 mj Continuous forward current f0 Lrr fis pa framo E Current slope at turn off dir dt Pones m Forward voltage Additional de voltage V in volts V between anode and cathode when the diode is conducting The default is 0 On resistance The resistance Ro of the conducting device in ohms 9 The default is 0 126 Diode with Reverse Recovery Probe Signals References Off resistance The resistance Rog of the blocking device in ohms Q The default is inf Continuous forward current The continuous forward current It under test conditions Current slope at turn off The turn off current slope d dt under test conditions Reverse recovery time The turn off time t under test conditions Peak recovery current The absolute peak value of the reverse current J under tes
33. Sawtooth PWM 3 Level 2 x Sawtooth PWM 3 Level mask Three level PWM generator with two sawtooth carriers The input m is the modulation index with a range of 1 1 The switching function s outputs either 1 O or 1 If the input is a vector the output is also a vector of the same width m Parameters Sampling regular zi Ramp falling y Carrier frequency frooo Sampling Choose between Natural and Regular Sampling Ramp Choose between rising and falling ramps in the carrier signal Carrier frequency The frequency f of the carrier signal 261 6 Block Reference 262 3 Phase Overmodulation Purpose Library Description Extend the linear range of the modulation index for three phase converters Extras Modulators For three phase signals this block extends the linear range of the modulation index from 1 1 to 1 154 1 154 by adding a zero sequence offset This block may be used for the control of three phase converters without neutral point connection such as the 2 Level IGBT Converter see page 224 The figures below illustrates the working principle of the 3 Phase Overmodu lation block in conjunction with the Symmetrical PWM see page 252 Original modulation indices Offset Corrected modulation indices Resulting pulses 3 Phase Overmodulation Dialog Box Block Parameters 3 Phase Overmodulatio
34. Source generates a constant voltage between its two electrical terminals The voltage is considered positive at the terminal marked with a E Note A voltage source must not be short circuited or connected in parallel to a capacitor or any other voltage source Parc lola and Dialog rDC Voltage Source Box Generate a constant voltage TParameters Name Vode E Width E E Voltage E E DK Cancel Help Apply Width The width of the component The default is 1 Voltage The magnitude of the constant voltage in volts V This parameter may either be a scalar or a vector with the width of the component The default value is 1 Probe Signals Source voltage The source voltage in volts V 71 6 Block Reference 72 AC Voltage Source Purpose Library Description Parameters and Dialog Box Generate a sinusoidal voltage Sources amp Meters The AC Voltage Source generates a sinusoidal voltage between its two electri cal terminals The voltage is considered positive at the terminal marked with a The momentary voltage v is determined by the equation v A sin w t y where t is the simulation time Note A voltage source must not be short circuited or connected in parallel to a capacitor or any other voltage source AE PAC Voltage Source Generate a sinusoidal voltage Parameters Name V_ac HE Width E E Amplitude E z
35. Turn on loss therm la jal Turn offloss therm la El OK Cancel Help Apply Width The width of the component This affects both the width of the electrical ports and the width of the gate input signals The default is 1 Initial conductivity Initial conduction state of the switch The switch is initially open if the parameter evaluates to zero otherwise closed This parameter may either be a scalar or a vector with the width of the component The default value is 0 121 6 Block Reference Probe Signals 122 The following parameters define the thermal behavior of the component For more information see chapter Thermal Modeling on page 59 On state voltage drop therm A 2 D function von i T defining the voltage drop in volts V that is used for calculating the thermal conduction losses The default is meaning no thermal conduction losses Turn on loss therm Turn off loss therm 3 D functions Eon Upre ipost T and Eor Upost ipre T defining the total ther mal losses dissipated during a switching transition in joule J The de fault is meaning no thermal turn on resp turn off losses Switch conductivity Conduction state of the switch The signal outputs 0 if the switch is open and 1 if it is closed Switch conduction loss Continuous thermal conduction losses in watt W Only defined if the com ponent is placed on a heat sink Switch switching loss Inst
36. a PLECS circuit and a subcircuit see page 202 If you copy an Electrical Port block into the schematic of a subcircuit a terminal will be created on the subcir cuit block The name of the port block will appear as the terminal label If you choose to hide the block name by unselecting the show button in the dialog box the terminal label will also disappear Unconnected terminals can be moved around the edges of the subcircuit by holding down the Shift key or by using the middle mouse button Note Since you cannot make electrical connections in Simulink PLECS does not permit to place electrical port blocks into top level circuits lol rElectrical Port Provide an electrical port for a subcircuit TParameters Name Portl E Width E ja OK Cancel Help Apply 195 6 Block Reference 196 Continuous Mux Purpose Combine several continuous signals into a vector Library Signals amp Systems Description This multiplexer combines several continuous signals into a vectorized signal The input signals may be scalars or vectors In the block icon the first input is marked with a dot When you change the number of inputs all signals will be disconnected from the block If you want to combine gate signals use the Gate Mux block see page 197 The Continuous Mux icon can be distinguished from the Gate Mux by green instead of brown terminals Parameters and Dialog Box all
37. and considered positive if flowing into the transformer The default is 0 O 0 3 Winding 3 Phase Transformers 3 Winding 3 Phase Transformers Purpose Three phase transformers in Ydy and Ydz connection Library 3 Phase Transformers Description This group of components implements three winding three phase transform ers with a three leg or five leg core The transformer core is assumed symmet rical i e all phases have the same parameters The primary winding is in star connection with an accessible neutral point and the secondary winding is in delta connection Depending on the chosen component the tertiary winding is wired either in star y or zig zag z connection The phase angle difference between the primary and the secondary side must be an odd integer multiple of 30 If the tertiary winding is in star connection the phase lag against the primary side must be an integer multiple of 60 If it is in zig zag connection the phase lag can be chosen arbitrarily The wind ings of the secondary and tertiary side are allocated to the transformer legs according to the phase lags Please note that the phase to phase voltage of delta windings is by a factor of 1 V3 lower than the voltage of star or delta windings if the number of turns are equal i i 2 iQ i m The core saturation characteristic of the transformer legs is piece wise linear The magnetizing current im and flux Ym value pairs are referred to the pri
38. angle can only be varied in steps of 60 Initial currents wdg 1 A vector containing the initial currents on the primary side i 11 and iic The currents are given in amperes A and considered positive if flow ing into the transformer The default is 0 O 0 Initial currents wdg 2 A vector containing the initial currents on the secondary side i2 and iz The currents are given in amperes A and considered positive if flowing into the transformer The default is 0 O 0 Initial currents wdg 3 A vector containing the initial currents on the tertiary side iz 31 and i3 The currents are given in amperes A and considered positive if flow ing into the transformer The default is 0 0 0 237 6 Block Reference Heat Sink Purpose Library Description Parameters and Dialog Box Model an idealized heat sink Thermal The Heat Sink absorbs the thermal losses dissipated by the components within its boundaries At the same time it defines an isotherm environment and propagates its temperature to the components which it encloses To change the size of a Heat Sink select it then drag one of its selection handles With the parameter Number of terminals you can add and remove thermal connectors to the heat sink in order to connect it to an external thermal net work The connectors can be dragged along the edge of the heat sink with the mouse by holding down the Shift key or using the middle mouse button In order
39. circuited or connected in series to an inductor or any other current source Pele FAC Current Source Generate a sinusoidal current Parameters Name Lac HE Width E E Amplitude E zi Frequency rad sec 2pi 50 fal Phase rad fo El DK Cancel Help Apply Width The width of the component The default is 1 Each of the following parameters may either be a scalar or a vector with the width of the component AC Current Source Amplitude The amplitude A of the current in amperes A The default is 1 Frequency The angular frequency w in s71 The default is 2 pi 50 which corre sponds to 50 Hz Phase The phase shift y in radians The default is 0 Probe Signals Source current The source current in amperes A 77 6 Block Reference Voltmeter Purpose Library Description Parameters and Dialog Box Probe Signals 78 Output the measured voltage Sources amp Meters The Voltmeter measures the voltage between its two electrical terminals and provides it as a continuous signal at the output of the component A positive voltage is measured when the potential at the terminal marked with a is greater than at the unmarked one The output signal can be made accessible in Simulink with a Continuous Output block see page 192 or by dragging the component into the dialog box of a Probe block Note The Voltmeter is ideal i e it h
40. conditions for switch components in the component dia log See for example the Thyristor see page 130 16 Licensing Licensing Student Version The free Student Version is offered as a special service to the student commu nity It permits you to simulate models containing no more than one PLECS block This PLECS block in turn may contain no more than six state variables and six switches The Student Version may be used in conjunction with courses at a degree granting institution only If you are using the software at a company or gov ernment lab as an instructor at a university for research or for commercial or industrial purposes you must acquire a commercial resp academic license A splash screen reminds you of these license terms once in each MATLAB ses sion the first time you use PLECS Full Version License File When you install the full version of PLECS you must have a valid license file license dat This file will be sent to you by email when you purchase a li cense for PLECS Copy the file license dat into the directory where you have installed PLECS If the license file is not present or contains invalid data you will still be able to open or save models containing PLECS circuits However you cannot mod ify a circuit or run a simulation Note PLECS scans the license file only once when the module is loaded by MATLAB Therefore if you reinstall the license file you need to clear the PLECS module before
41. containing the resistance of the primary winding R and the secondary winding R2 in ohms Q Winding ratio The ratio n1 n2 between the number of turns of the primary and sec ondary winding Magnetization inductance The magnetization inductance Lm in henries H The value is referred to the primary side 89 6 Block Reference ttockeparametera ix rLinear 2 Winding Transformer mask link This transformer models two coupled windings on the same core The magnetization inductance Lm and the core loss resistance Am are modeled as linear elements Their values are referred to the primary side Parameters Name Linear Trafo2 E Leakage inductance L1 L2 Y Winding resistance R1 R2 101 Jar Winding ratio n1 4n2 10 Ef Magnetization inductance Lm E El Core loss resistance Am inf al Initial current i1 12 10 0 E OK Cancel Help apply Core loss resistance An equivalent resistance Rm representing the iron losses in the trans former core The value in ohms 9 is referred to the primary side Initial current A two element vector containing the initial currents on the primary side i and the secondary side 2 in amperes A The currents are considered positive if flowing into the transformer at the marked terminals The de fault is 0 0 90 linear 3 Winding Transformer Linear 3 Winding Transformer Purpose Library Descript
42. copied block This is due to the fact that a Probe block can only monitor components from a circuit residing in the same Simulink model see the note above 51 3 Using PLECS 52 Controlling Access to Circuits and Subcircuits PLECS allows you to control user access to individual subcircuits or to com plete circuits In particular you can prevent a user from viewing or modifying a schematic while still allowing the user to simulate a circuit To change the access settings of a circuit open the permissions dialog box by choosing Circuit permissions from the File menu To change the settings of a subcircuit choose Subcircuit permissions from the Edit menu or from the block s context menu You can grant or deny the following privileges e The View privilege controls whether a user can view the schematic of a cir cuit or subcircuit e The Modify privilege controls whether a user can modify the schematic of a circuit or subcircuit For a subcircuit it also controls whether the mask definition may be modified If you apply access restrictions you will be asked for a password to prevent an unauthorized person from lifting these restrictions The access settings can only be changed again if the correct password is provided Encrypting Circuits and Subcircuits When PLECS saves a circuit with access restrictions to the Simulink model file it encrypts the respective sections to protect the circuit description from unauthorized
43. either by voltages and currents in the system or by external gate signals Buck Converter File Edit View Simulation Format Tools Help f int PLEC Sout 4 Circuit Pulse Generator Time offset 0 Figure 2 7 RLC network with a pulsed voltage source i 25 mH src TIN DONA gt Usre 7X 2204F ve 22 Figure 2 8 Schematic of buck converter Switches In the buck converter outlined in Fig 2 8 we will model the transistor as an entirely controllable switch and bear in mind that it may conduct current only in one direction We also need a free wheeling diode The diode is a switch that closes as the voltage across it becomes positive and opens as the current through it becomes negative Both the diode an the switch can be found in the library Switches All components in this library are based on ideal switches that have zero on resistance and infinite off resistance They open and close instantaneously In some components like the diode you may add a forward voltage or a non zero on resistance If you are unsure about these values leave them to zero Gate Signals As mentioned above we must use gate signals instead of continuous signals for controlling switches In order to control the switch in our buck converter 29 2 Gettin g Started 30 we import a gate signal from Simulink by means of the gate block Gate1 from the library Signals amp
44. from the library Signals amp Systems into the schematic In our case we want to access in Simulink the voltage measured by the voltmeter Therefore we need the Out1 block that exports a continuous signal into the parent system Signals in PLECS correspond to the connections between Simulink blocks They provide unidirectional information interchange between components and with Simulink Unlike Simulink PLECS distinguishes two kinds of signals Continuous signals displayed in green are used to control voltage and current sources Voltmeters and ammeters also deliver continuous signals In contrast gate signals are used exclusively for controlling switches They are displayed in brown Connect the output of the voltmeter with the input of the port block In Simulink connect a Scope to the output of the PLECS block and start the simulation In order to see something of the more interesting part of the sim ulation you probably need to set the stop time to 0 1 By this time you should have something like Fig 2 5 and Fig 2 6 on your screen File Edit View Simulation Format Tools Help File Edit View Simulation Format L1 L 0 01 PLECS Ove Circuit Figure 2 5 Complete model Adding More Measurements If you want to measure other quantities in the circuit simply add the required voltmeters and ammeters The measured signals can b
45. input signal The default is 1 Initial conductivity Initial conduction state of the breaker The breaker is initially open if the parameter evaluates to zero otherwise closed This parameter may either be a scalar or a vector with the width of the component The default value is 0 Breaker current The current through the component in amperes A A positive current flows from the left to the right terminal in the above breaker icon Breaker conductivity Conduction state of the internal switch The signal outputs 0 if the breaker is open and 1 if it is closed Set Reset Switch Set Reset Switch Purpose Ideal switch with RS flipflop behavior Library Switches Description This component provides an ideal short or open circuit between its two elec trical terminals The switch closes when the closing gate signal the upper in ot a put in the component icon becomes non zero It opens when the opening gate signal the lower input becomes non zero The Set Reset Switch provides the basis for all other switches and power semiconductor models in PLECS Parameters Block parameters TS and Dialog SetReset Switch Box Ideal on off switch with RS fipflop behavior The switch closes when the closing gate signal becomes non zero and opens when a non zero opening gate signal is applied Parameters Name Es Width fi Ja Initial conductivity II B On state voltage drop therm la Ei
46. input signal T represents the mechanical torque at the rotor shaft in Nm The output vector m contains the following 3 signals 1 Rotor speed The rotational speed wm of the rotor in radians per second s71 2 Rotor position The mechanical rotor angle 6 in radians 3 Electrical torque The electrical torque T of the machine in Nm DC Machine DC Machine Purpose Library Description Parameters and Dialog Box Simple model of DC machine Machines The machine operates as a motor or generator the sign of the mechanical torque determines the mode of operation positive for motoring negative for generating In the component icon the positive poles of armature and field winding are marked with dots Electrical System Electromagnetic torque Te Lag te ta Induced voltage of the armature winding Ea Lag te Wm Mechanical System 1 Wm Te Fwm Tm J Armature resistance Armature winding resistance Ra in ohms Q Armature inductance Armature winding inductance L in henries H Field resistance Field winding resistance Rf in ohms Q 175 6 Block Reference lala rDC Machine mask The input signal Tm represents the mechanical torque in Nm The vectorized output signal of width 2 contains the rotational speed wm in rad s and the electrical torque Te in Nm Parameters Name DCM E Armature resistance Ra Inertia J 0
47. instantaneous power losses This is illustrated in the figure below The curves show the simplified current and voltage wave forms and the dissipated power during one switching cycle of an IGBT in an inverter leg E gt In other simulation programs the computation of switching losses is usually challenging because it requires very detailed and accurate semiconductor mod els Furthermore very small simulation time steps are needed since the du ration of an individual switching transition is in the order of a few hundred nanoseconds In PLECS this problem is bypassed by using the fact that for a given circuit the current and voltage waveforms during the transition and therefore the to tal loss energy are principally a function of the pre and post switching condi tions and the device temperature E Eon Vpro post T E Eoft posts tpres T These functions are defined by the parameters Turn on loss therm and Turn off loss therm as 3D look up tables in form of structs with three in dex vectors v i T and an output array E You can omit any of the index vectors if the switching loss does not depend on the corresponding variable The number of dimensions of the output ta ble must correspond to the number of index vectors and the dimensions must be in the above order If you do not specify any index vector the output ta ble must be a scalar In this case you can also specify the voltage directly as a scal
48. inverting and inverting input with a specified gain The resulting voltage is applied between the output and ground terminal Output and ground are electrically isolated from the inputs If you want to build a linear amplifier the output voltage must somehow be fed back to the inverting input The demo models plOpAmps and plActiveLowPass demonstrate different applications with op amps cla rOp Amp mask Ideal op amp with finite gain Parameters Name Op Amp E Open loop gain E te DK Cancel Help Apply Open loop gain The voltage gain of the Op Amp The default is 1e6 Limited Op Amp Limited Op Amp Purpose Ideal operational amplifier with finite gain and limited output voltage Library Op Amps Description This component amplifies a voltage between the non inverting and invert ing input with a specified gain taking into account the specified output voltage limits The resulting voltage is applied between the output and ground terminal Output and ground are electrically isolated from the inputs If you want to build a linear amplifier the output voltage must somehow be fed back to the inverting input The demo model p10pAmps shows a possible application of the Limited Op Amp Parameters 1512 a nd Dia log rLimited Op Amp mask Box Ideal op amp with finite gain and limited output voltage Parameters Name Lim Op Amp E Open lo
49. is 1 Source current The source current in amperes A DC Current Source DC Current Source Purpose Generate a constant current Library Sources amp Meters Description The DC Current Source generates a constant current between its two electri cal terminals The direction of a positive current through the component is marked with an arrow Note A current source must not be open circuited or connected in series to an inductor or any other current source sat aa pag Pele an 1a og DC Current Source Box Generate a constant current TParameters Name I_de E Width E jal Current E jan DK Cancel Help Apply Width The width of the component The default is 1 Current The magnitude of the constant current in amperes A This parameter may either be a scalar or a vector with the width of the component The default value is 1 Probe Signals Source current The source current in amperes A 75 6 Block Reference 76 AC Current Source Purpose Library Description Parameters and Dialog Box Generate a sinusoidal current Sources amp Meters The AC Current Source generates a sinusoidal current between its two elec trical terminals The direction of a positive current is marked with an arrow The momentary current is determined by the equation i A sin w t y where t is the simulation time Note A current source must not be open
50. is 1 Initial position Initial position of the switch The switch is initially in the middle position if the parameter evaluates to zero For values greater than zero it is in the lower position for values less than zero it is in the upper position This parameter may either be a scalar or a vector with the width of the compo nent The default value is 0 Probe Signals Switch position State of the internal switches The signal outputs 0 if the switch is in the middle position 1 if it is in the lower position and 1 if it is in the upper position 119 6 Block Reference 120 Breaker Purpose Library Description an Parameters and Dialog Box Probe Signals Ideal AC circuit breaker Switches This component provides an ideal short or open circuit between its two elec trical terminals The switch closes when the controlling gate signal becomes non zero It opens when both the gate signal and the current are zero There fore this circuit breaker can be used to interrupt inductive AC currents lola Breaker Ideal circuit breaker for inductive AC currents The switch closes upon a non zero gate signal Itopens when the gate signal is zero and the current tries to reverse pParameters Name En Width fi El Initial conductivity pc OK Cancel Help Apply Width The width of the component This affects both the width of the electrical ports and the width of the gate
51. is conducting Device conduction loss Continuous thermal conduction losses in watt W Only defined if the com ponent is placed on a heat sink Device switching loss Instantaneous thermal switching losses in joule J Only defined if the component is placed on a heat sink 137 6 Block Reference MOSFET Purpose Ideal MOSFET with or without on resistance Library Switches Description The Metal Oxide Semiconductor Field Effect Transistor is a semiconductor switch that is controlled via the external gate It conducts a current from drain to source or vice versa only if the gate signal is not zero E Parameters lxI and Dialog MOSFET Box The MOSFET is closed while a non zero gate signal is applied It conducts current in both directions Parameters Name MOSFET a Width fi ja On resistance Ron re D Initial conductivity es On state voltage drop therm la jal Turn on loss therm la jal Turn offloss therm la El OK Cancel Help Apply Width The width of the component This affects both the width of the electrical ports and the width of the gate input signal The default is 1 Each of the following parameters may either be a scalar or a vector with the width of the component 138 MOSFET Probe Signals On resistance The resistance Ron of the conducting device in ohms Q The default is 0 Initial conductivity Initial c
52. is greater than the potential at the unmarked terminal Saturation level The saturation level indicates which sector of the piece wise linear charac teristic is currently applied During linear operation i e operation in the first sector the saturation level is 0 The saturation level is negative for negative charge and voltage values 108 Variable Capacitor Variable Capacitor Purpose Variable capacitor Library Nonlinear Description This component models a variable capacitor The capacitance is determined A Parameters and Dialog Box by the continuous signal fed into the input of the component The current through a variable capacitance is determined by the equation d d d i gC CeCe Ye Therefore the control signal is a vector twice as wide as the width of the com ponent It contains both the momentary capacitance values and their deriva tives with respect to time C1 C2 Cn 401 4C2 4C It is the respon sibility of the user to provide the correct derivatives The momentary capaci tance may not be set to zero Note e The variable capacitor is based on a current controlled voltage source It may therefore not be connected in parallel with other voltage sources or capaci tors e The control signal for the momentary capacitance values must be continuous Discontinuous changes will produce non physical results Pele rVarCapacitor Variable capacitor rParameters Name
53. it closes if the voltage between anode and cathode is positive and a positive gate signal is applied It opens if the current becomes zero or if the gate signal becomes negative Block parameters oj xj GTO The GTO closes upon a positive voltage between anode and cathode and a positive gate signal It opens when the current tries to reverse or a negative gate signal is applied pParameters Name pro Width On state voltage drop therm fi Jl mi Forward voltage Vf Turn on loss therm Pp el lr On resistance Ron Turn off loss therm pc ell Initial conductivity es OK Cancel Help Apply Width The width of the component This affects both the width of the electrical ports and the width of the gate input signal The default is 1 Each of the following parameters may either be a scalar or a vector with the width of the component Forward voltage Additional dc voltage V in volts V between anode and cathode when the GTO is conducting The default is 0 On resistance The resistance Ron of the conducting device in ohms Q The default is 0 GTO Probe Signals Initial conductivity Initial conduction state of the GTO The GTO is initially blocking if the parameter evaluates to zero otherwise it is conducting The following parameters define the thermal behavior of the component For more information see chapter Thermal Modeling on page 59 On state voltage dro
54. level inverter bridges Library Extras Modulators Description This block generates a blanking time for 3 level inverter bridges so that the turn on of one switch is delayed with respect to the turn off of the other switch in the same inverter leg The input s is a switching function generated by a 3 level modulator such as the Symmetrical PWM 3 Level generator see page 257 The values of the output s are either 1 0 5 0 0 5 or 1 If the input is a vector the output is also a vector of the same width Parameters aixi a nd D ia log Blanking Time 3 Level mask Box This block generates a blanking time for 3 level inverter bridges so that the turn on of one switch is delayed with respect to the turn off of another switch in the inverter leg The input s is a switching function generated by a 3 level modulator The values of the output s are either 1 0 5 0 0 5 or 1 If the input is a vector the output is also a vector of the same width Parameters Delay time fi De 6 Cancel Help Apply Delay time The delay in seconds s between the turn off of one switch and the turn on of another switch in an inverter leg 265 6 Block Reference 266 6 Pulse Generator Purpose Generate firing pulses for a three phase thyristor converter Library Extras Modulators Description This block generates the pulses used to fire the thyristors of a 6 pulse rectifier enable phi alpha
55. loss therm la a Turn off loss therm la E OK Cancel Help Apply Any MATLAB constant variable or expression that evaluates to an accept able result can be used to specify the value of a parameter Parameter ex pressions are evaluated when you start a simulation or update the Simulink model In case an error occurs during evaluation of the parameters an error dialog appears and the corresponding component is highlighted Displaying Parameters in the Schematic You can cause PLECS to display any component parameter beneath the block icon in the schematic You specify the parameters to be displayed using the check boxes next to the edit fields in the dialog box Components Changing Component Names The component name is also entered in the dialog box All component names in the same schematic must be unique and must contain at least one non space character Trailing spaces are removed from the names Changing the Orientation of Components You can change the orientation of a component by choosing one of these com mands from the Format menu e The Rotate command rotates a component clockwise 90 degrees Ctrl R e The Flip left right command flips a component horizontally Ctrl F e The Flip up down command flips a component vertically Ctrl D Note Unlike in Simulink flipping a component is not equivalent to rotating it 180 degrees Getting Component Help Use the Help button in the
56. more than three identical values 1D Look Up Table Vector of output values f x The vector containing the output values f x This vector must be the same size as the input vector Probe Signals Input The block input signal Output The block output signal 213 6 Block Reference 214 2D Look Up Table Purpose Library Description 2D f u Table Parameters and Dialog Box Output an approximated two dimensional function using intrapola tion extrapolation Signals amp Systems The 2D Look Up Table block maps two continuous input signals to a continu ous output signal You define the mapping function by specifying two vectors of input values and a matrix of output values The input vector x corresponds to the rows of the output matrix the input vector y to the columns The output value is interpolated or extrapolated from the block parameters using the technique described for the 1D Look Up Table block see page 212 zix r2D Look Up Table Output an approximated two dimensional function using interpolation extrapolation Parameters Name PD Table E Vector of input values x In 2 jal Vector of input values y 2 Bi Matrix of output values f x y zsa oo l OK Cancel Help Apply Vector of input values x The vector of input values x This vector must be the same size as the number of rows in the output matrix and monotonically incr
57. o 54 Diode Turn On Threshold Voltage 55 Continuous State Space Method 55 Discrete State Space Method 55 Contents 4 Thermal Modeling Heat Sink Concept ioc BSA Se oe et Re Se SS eee ted da Implementation naaa a Thermal Loss Dissipation e Semiconductor Losses 2 0 0 0 Ohmic Losses coma a RR Pio EEE SSS eS Heat Sinks and Subcircuits 0 0 02 000 000004 Command Line Interface Reading Parameters of Components 080000 Setting Parameters of Components 0 20005 Other CLIcommands 0 002 eee ee ene Example yess cc es es ae eee BB Ek de a te til al be ee ea Block Reference Sources amp Meters evocar eee ae ERE OE EH a Controlled Voltage Source DC Voltage Source ee ee AC Voltage Source 2 2 eee Controlled Current Source o oo eee DC Current Source a AC Current Source e VoltmMe ter 20 a a Ammieter NN Passive Components Resisto ura A ee a aa Inductor i i a det iratis al id eee aa As Mutual Inductor ic ee or eg id a ae Pee a CAPaGltOn wv ivevawd srt a ee RRA RIERA Sada Transformer 5 203 404 fre Soe oe heer BOE ER AS eS Linear 2 Winding Transformer 0045 59 59 60 60 60 64 64 67 67 67 68 68 Contents Linear 3 Winding Transformer
58. of the electrical ports and the width of the gate input signal The default is 1 Initial conductivity Initial conduction state of the device The device is initially blocking if the parameter evaluates to zero otherwise it is conducting This parameter may either be a scalar or a vector with the width of the component The default value is 0 136 IGBT with Diode The following parameters define the thermal behavior of the component For more information see chapter Thermal Modeling on page 59 On state voltage drop therm A 2 D function von i T defining the voltage drop in volts V that is used for calculating the thermal conduction losses The default is meaning no thermal conduction losses Turn on loss therm Turn off loss therm 3 D functions Eon Upre ipost T and Eor Upost ipre T defining the total ther mal losses dissipated during a switching transition in joule J The de fault is meaning no thermal turn on resp turn off losses Probe Signals Device voltage The voltage measured between collector cathode and emitter anode The device voltage can never be negative Device current The current through the device The current is positive if it flows through the IGBT from collector to emitter and negative if it flows through the diode from anode to cathode Device conductivity Conduction state of the internal switch The signal outputs 0 when the device is blocking and 1 when it
59. of the main flux inductance is not required Electro Mechanical System Electromagnetic torque a a Te gt 2 Pp isq Wa Usd Ya Mechanical System Mechanical rotor speed wm 1 Um Te Fwy Im dim 5 la Fi n Ta Stator resistance Armature or stator winding resistance R in ohms 9 Stator leakage inductance Armature or stator leakage inductance L in henries H Unsaturated magnetizing inductance A two element vector containing the unsaturated stator magnetizing in ductance Lm a o and Lm q 0 of the d axis and the q axis The values in hen ries H are referred to the stator side Saturated magnetizing inductance The saturated stator magnetizing inductance Lyd sat along the d axis in H If no saturation is to be modeled set Lim dsat Lm a o Magnetizing flux at saturation transition Transition flux linkage Yr in Vs defining the knee between unsaturated and saturated main flux inductance 163 6 Block Reference 164 Block parameters 51 xj Salient Pole Synchronous Machine mask signal of width S contains the rotational speed wm in rad s the mechanical rotor position th in rad Poo Stator leakage inductance Lis ee Unsat magn inductance Lmd0 Lmq0 e s 1e 3 Ej Saturated magn inductance Lmdsat ee s Magn flux at sat transition PsiT Pe dd Tightness of sat transition fT fi El Field resistance Rf pa ooo Field leakage inductance Lif Pe
60. path within the circuit For adding components to this list simply select them in the schematic editor and drag them into the probe edi tor The new components are appended at the bottom of the list You can re order the components by using the Up Down and Remove buttons Available signals The list box on the right side shows the available probe signals for the selected component Use the check boxes next to the signal names in order to enable or disable individual signals You can simultane ously edit the signal states of several components provided that the compo PLECS Probe nents have the same type In order to select multiple components hold the Shift or Ctrl key while clicking on a list entry The output of the Probe block is a vector signal consisting of all enabled probe signals If no probe signal is enabled a warning message will be printed to the command window and the block will output a scalar zero Note The Probe block must be in the same Simulink model as the Circuit block whose components you want to monitor In addition a Probe block only accepts components from one single Circuit block at a time Copying a Probe When you copy a Probe block within the same Simulink model the component list and the states of the individual probe signals are duplicated You can edit the copied Probe block independently from the original When you copy a Probe block into a different Simulink model all data is cleared from the
61. saturation transition Form factor fr defining the tightness of the transition between unsatu rated and saturated main flux inductance The default is 1 Viscous friction F in Nms Saturable Induction Machine Number of pole pairs Number of pole pairs p Initial rotor speed Initial mechanical rotor speed wm o in s Initial rotor position Initial mechanical rotor angle 0 9 in radians If m is an integer multiple of 27 p the stator windings are aligned with the rotor windings at simula tion start Initial stator currents A two element vector containing the initial stator currents is a and is b 0 of phases a and b in amperes A Initial stator flux A two element vector containing the initial stator flux Y y and Y 0 in the stationary reference frame in Vs Inputs and Mechanical torque Outputs The input signal T represents the mechanical torque at the rotor shaft in Nm The output vector m contains the following 3 signals 1 Rotational speed The rotational speed wm of the rotor in radians per second s71 2 Rotor position The mechanical rotor angle 6 in radians 3 Electrical torque The electrical torque T of the machine in Nm Probe Signals Stator phase currents The three phase stator winding currents isa is and is c in A Currents flowing into the machine are considered positive Rotor phase currents The three phase rotor winding currents i a 1 and ijo in A referred to th
62. stator currents A two element vector containing the initial stator currents ay and ipo of phase a and b in amperes A Mechanical torque The input signal T represents the mechanical torque at the rotor shaft in Nm The output vector m contains the following 6 signals 1 Rotor speed The rotational speed wm of the rotor in radians per second s71 2 Rotor position The mechanical rotor angle 6 in radians 3 Electrical torque The electrical torque T of the machine in Nm 4 6 Back EMF voltages The back EMF voltages ea ep e in volts V D Hanselman Brushless permanent magnet motor design 2nd ed The Writers Collective Mar 2003 P Pillay R Krishnan Modeling simulation and analysis of permanent magnet motor drives Part 11 The brushless DC motor drive IEEE Trans on Ind App Vol 25 No 2 Mar Apr 1989 Switched Reluctance Machine Switched Reluctance Machine Purpose Detailed model of a switched reluctance machine with open windings Library Machines Description These components represent analytical models of three common switched re luctance machine types three phase 6 4 SRM four phase 8 6 SRM and five phase 10 8 SRM The machines operate as motor or generator the sign of the mechanical torque determines the mode of operation positive for motoring negative for generating In the component icon the positive terminals of the stator wind ings are marked with a dot
63. the changes can become effective You can do this by en tering plecsclear at the MATLAB command prompt 17 Before You Begin Network Licensing If you purchase one or more concurrent licenses for PLECS the license server program FLEXIm is employed to control access to PLECS FLEXIm is a prod uct of Macrovision Corporation The license sent to you must be installed on the license server This file contains information that identifies the computer running the license manager and specifies the number of concurrent licenses you have purchased On the client computer s you need to use a text editor to create the license file license dat in the PLECS directory with the following content SERVER hostname ANY USE_SERVER where hostname is the name of the computer running the license manager PLECS tries to obtain a license from the server the first time you load a model or library containing a PLECS circuit If the license is not granted either because the server is down or unreachable or because the licensed num ber of concurrent users is already reached PLECS will fall back to an un licensed mode In this mode you cannot modify a circuit or run a simulation saving a model is still possible In order to retry to obtain a license you first need to close all models including the PLECS library Once granted a li cense is returned to the server when you close the last model containing a PLECS circuit If the connection t
64. the component The output signal can be made accessible in Simulink with a Continuous Output block see page 192 or by dragging the component into the dialog box of a Probe block Block parameters 5 xj r Thermometer Output the measured temperature pParameters OK Cancel Help Apply Measured temperature The measured temperature in kelvin K Heat Flow Meter Heat Flow Meter Purpose Output the measured heat flow Library Thermal Description The Heat Flow Meter measures the heat flow through the component and pro Dialog Box Probe Signals vides it as a continuous signal at the output The direction of a positive heat flow is indicated by the small arrow at one of the thermal ports The output signal can be made accessible in Simulink with a Continuous Output block see page 192 or by dragging the component into the dialog box of a Probe block Block parameters 5 xj HeatFloweter Output the measured heat flow pParameters Name keo o OK Cancel Help Apply Measured heat flow The measured heat flow in watts W 245 6 Block Reference 246 Thermal Resistor Purpose Library Description oa myo Parameters and Dialog Box Ideal thermal resistor Thermal This component provides an ideal one dimensional thermal resistor between its two thermal ports See section Configuring PLECS in chapter Using PLECS fo
65. the input is a vector the output is also a vector of the same width m Parameters Sampling rein S d Ramp falling Carrier frequency frooo Cancel Help Apply Sampling Choose between Natural and Regular Sampling Ramp Choose between rising and falling ramps in the carrier signal Carrier frequency The frequency f of the carrier signal Symmetrical PVVM 3 Level Symmetrical PWM 3 Level Purpose 3 level PWM generator with symmetrical triangular carrier Library Extras Modulators Description 3 level PWM generator with two symmetrical triangular carriers The input m is the modulation index with a linear range of 1 1 The switching function s outputs either 1 0 or 1 If the modulation index is a vector the switching function is also a vector of the same width The block can be used to control the 3 Level IGBT Converter see page 226 or the ideal 3 Level Converter see page 231 In these cases the modulation index must have a width of 3 according to the number of inverter legs The figures below illustrate the Natural Sampling method In the left figure the negative carrier signal is obtained by flipping the positive carrier verti cally around the time axis In the right figure the positive carrier is verti cally shifted to construct the negative carrier The latter technique reduces the switching frequency and hence the semiconductor stress in three phase converters
66. the piece wise linear charac teristic is currently applied During linear operation i e operation in the first sector the saturation level is 0 The saturation level is negative for negative flux and current values Variable Inductor Variable Inductor Purpose Library Description Parameters and Dialog Box Variable inductor Nonlinear This component models a variable inductor The inductance is determined by the continuous signal fed into the input of the component The voltage across a variable inductance is determined by the equation d do d Therefore the control signal is a vector twice as wide as the width of the com ponent It contains both the momentary inductance values and their deriva tives with respect to time L L Ln L1 L Ln It is the respon sibility of the user to provide the correct derivatives The momentary induc tance may not be set to zero U Note e The variable inductor is based on a voltage controlled current source It may therefore not be connected in series with other current sources or inductors e The control signal for the momentary inductance values must be continuous Discontinuous changes will produce non physical results lala Variable inductor Variable inductor Parameters Name L3 fa Width E z Initial current C OK Cancel Help Apply 101 6 Block Reference Width The width of the electrical p
67. the thermal behavior of the component For more information see chapter Thermal Modeling on page 59 On state voltage drop therm A 2 D function von T defining the voltage drop in volts V that is used for calculating the thermal conduction losses The default is meaning the voltage drop is calculated as von Vi Ron 1 Turn on loss therm Turn off loss therm 3 D functions Eon Upre ipost T and Eos Vpost ipre T defining the total ther mal losses dissipated during a switching transition in joule J The de fault is meaning no thermal turn on resp turn off losses Thyristor voltage The voltage measured between anode and cathode Thyristor current The current through the thyristor flowing from anode to cathode Thyristor conductivity Conduction state of the internal switch The signal outputs 0 when the thyristor is blocking and 1 when it is conducting Thyristor conduction loss Continuous thermal conduction losses in watt W Only defined if the com ponent is placed on a heat sink Thyristor switching loss Instantaneous thermal switching losses in joule J Only defined if the component is placed on a heat sink 131 6 Block Reference 132 GTO Purpose Library Description 7 Parameters and Dialog Box Ideal GTO with or without forward voltage and on resistance Switches The Gate Turn Off Thyristor can also be switched off via the gate Like a nor mal thyristor
68. toggle instantaneously between a closed and an open circuit This approach which is implemented in PLECS has two major advantages Firstly it yields systems that are linear between two switching instants Sec ondly to handle discontinuities at the switching instants only two integration steps are required Both speed up the simulation considerably Concepts of PLECS You should use ideal switches as the basis for all power electronic components Switches can be controlled externally or internally or by a combination of both External in this context means that the control signal does not directly depend on voltages or currents in the circuit Instead this signal is supplied by the overlaying control system Examples for externally controlled switches are breakers and half bridges of voltage source inverters Internal control variables are voltages or currents that can be measured in the circuit The simplest example of a purely internally controlled switch is a diode A diode is switched on by a positive voltage and off by a negative cur rent Power electronic components such as thyristors GTOs and IGBTs oper ate according to a logical combination of external and internal switching con ditions Sometimes other non linear components like a saturable inductor may also be approximated as piece wise linear They can be assembled by combining lin ear elements and switches True nonlinearities however must be modeled by voltage controlle
69. user to provide the correct derivatives The momen tary capacitance and the resistance may not be set to zero Note e This component is based on a current controlled voltage source It may there fore not be connected in parallel with other voltage sources or capacitors e The control signal for the momentary capacitance values must be continuous Discontinuous changes will produce non physical results dah espa lla and Dia og VarResistoWarlapacitor 7 Box Variable capacitor with variable parallel resistor Parameters Name RCI E Width E z Initial voltage oO O bB OK Cancel Help Apply 111 6 Block Reference Width The width of the electrical ports resp the number of resistors capacitors represented by the component Initial voltage The initial voltage of the capacitor at simulation start in volts V This parameter may either be a scalar or a vector with the width of the compo nent The positive pole is marked with a The initial voltage default is 0 Probe Signals Capacitor voltage The voltage measured across the capacitor in volts V A positive voltage is measured when the potential at the terminal marked with is greater than the potential at the unmarked terminal 112 Variable Resistor with Constant Parallel Capacitor Variable Resistor with Constant Parallel Capacitor Purpose Variable resistor with constant parallel capacitor Libra
70. zero gate signal is applied The device can conduct current only from collector to emitter rParameters Name eno o O Width On state voltage drop therm fi df Ei Forward voltage Vf Turn on loss therm lc eri On resistance Ron Turn offloss therm pc elt Initial conductivity es OK Cancel Help Apply Width The width of the component This affects both the width of the electrical ports and the width of the gate input signal The default is 1 Each of the following parameters may either be a scalar or a vector with the width of the component Forward voltage Additional dc voltage V in volts V between collector and emitter when the IGBT is conducting The default is 0 On resistance The resistance Ron of the conducting device in ohms Q The default is 0 IGBT Initial conductivity Initial conduction state of the IGBT The IGBT is initially blocking if the parameter evaluates to zero otherwise it is conducting The following parameters define the thermal behavior of the component For more information see chapter Thermal Modeling on page 59 On state voltage drop therm A 2 D function von T defining the voltage drop in volts V that is used for calculating the thermal conduction losses The default is meaning the voltage drop is calculated as von Vs Ron 1 Turn on loss therm Turn off loss therm 3 D functions Eon Upre ipost T and E
71. 2 Pulse Generator mask This block generates the pulses used to fire the thyristors of an H bridge converter Inputs are a logical enable signal a ramp signal phi produced e g by a PLL and the firing angle alpha E Cancel Help Apply 267 6 Block Reference 268 3 Phase To Stationary Reference Frame Purpose Library Description ab gt cB Dialog Box Transform a three phase signal into the stationary reference frame Extras Transformations This block transforms a three phase signal za x e into a two dimensional vector ya ys in the stationary reference frame 2 1 1 La Ya 3 3 3 PA EP 1 a v3 v3 E Any zero sequence component in the three phase signals is discarded E Block Parameters 3ph gt SRF 3 Ax Transformation 3ph gt SRF mask Transforms a three phase signal into a two dimensional vector in the stationary reference frame a b c gt alpha beta Cancel Help Apply Stationary Reference Frame To 3 Phase Stationary Reference Frame To 3 Phase Purpose Transform a vector into a three phase signal Library Extras Transformations Description This block transforms a two dimensional vector xa xg in the stationary refer ence frame into a three phase signal ya yp ye ap E 1 0 Ya 1 v3 Ta ey 2 2 E LB Ye 1 V3 2 The resulting three phase signal does not have any zero sequence component Dialog Box azi Transformation SRF gt 3ph mask Trans
72. Continuous Multiplexer Combine multiple continuous signals into one vector Parameters Name CMux E Number of inputs ES DK Cancel Help Apply Number of inputs This parameters allows you to specify the number and width of the input signals You can choose between the following formats for this parameter Scalar A scalar specifies the number of scalar inputs to the block If this format is used the block accepts only signals with a width of 1 Vector The length of the vector determines the number of inputs Each element specifies the width of the corresponding input signal Gate Mux Gate Mux Purpose Library Description I Parameters and Dialog Box Combine several gate signals into a vector Signals amp Systems This multiplexer combines several gate signals into a vectorized signal The input signals may be scalars or vectors In the block icon the first input is marked with a dot When you change the number of inputs all signals will be disconnected from the block If you want to combine continuous signals use the Continuous Mux block see page 196 The Gate Mux icon can be distinguished from the Continuous Mux by brown instead of green terminals aioli Gate Multiplexer Combine multiple gate signals into one vector Parameters Name GMux E Number of inputs BO O tk OK Cancel Help Apply Number of inputs This parameters allow
73. FET turn off loss therm Diode turn off loss therm MOSFET turn off loss herm la tf i m Diode forward voltage p E OK Cancel Help Apply OK Cancel Help Apply 2 Level MOSFET Converter For a description of the parameters see the documentation of the MOSFET with Diode on page 140 the MOSFET on page 138 and the Diode on page 123 Probe Signals The two level MOSFET converters provide five or ten probe signals each a vector containing the appropriate quantities of the individual devices voltage current conductivity conduction loss and switching loss The vector elements are ordered top to bottom left to right a a b b c c 229 6 Block Reference 230 2 Level Converter Purpose Library Description Dialog Box Ideal three phase two level converter Converters Implements a three phase two level converter with ideal bi positional switches The converter is modeled using the Double Switch component see page 118 The gate input is a vector of three signals one per leg The phase output is connected to the positive dc level upon a positive gate signal and else to the negative dc level The electrical circuit for the converter is shown below e AE rldeal 2 Level Converter mask This block implements an ideal three phase two level converter The gate input is a vector of three signals one per leg The AC side terminal i
74. Icon Drawing Commands The available drawing commands are described below If you enter more than one command the graphic objects are drawn in the order in which the com mands appear In case an error occurs during evaluation of the commands PLECS displays three question marks in the mask icon Note Unlike with Simulink masks the PLECS drawing commands do not have access to variables defined in the mask or base workspace Text text text displays a text in the center of the icon text x y text fontsize places the text at the coordinates x and y The optional argument fontsize allows you to specify the font size The displayed text does not rotate or flip together with the icon It is always displayed from left to right and it is centered both horizontally and vertically at its position Line line xvec yvec plots the vector yvec against the vector xvec Both vectors must have the same length The vectors may contain NaN and inf values When NaNs or infs are encountered the line is interrupted and continued at the next point that is not NaN or inf Patch patch xvec yvec draws a solid polygon whose vertices are specified by the vectors xvec and yvec Both vectors must have the same length Circle circle x y r draws a circle at the coordinates x and y with the radius r Image image xvec yvec imread filename on reads an image from the file filename in the MATLAB path and displa
75. Mechanical rotor speed 1 on T Po Ta im 3 Te Fum Tu Mechanical and electrical rotor angle m Wm be p Om LT T Simple Brushless DC Machine mask Simple three phase brushless DC machine with trapezoidal back EMF The input signal Tm represents the mechanical torque in Nm The vectorized output signal of width 6 contains the rotational speed wm in rad s the mechanical rotor position th in rad the electrical torque Te in Nm the back EMF voltages Parameters Name Eimple BLDG E Back EMF constant K_E Number of pole pairs p pes Gf y Combined stator and mutual inductance L M Initial rotor speed wm0 pisze s c E Stator resistance R Initial rotor angle thm0 ae llc lei kes Inertia J Initial stator currents a0 b0 fi 1e 7 fo 0 E Friction coefficient F pees SCS OK Cancel Help ay Back EMF constant The back EMF constant Ky in Vs 183 6 Block Reference Inputs and Outputs References 184 Stator resistance The stator resistance R in ohms Q Stator inductance The stator inductance L M in henries H Inertia Combined rotor and load inertia J in Nms Friction coefficient Viscous friction F in Nms Number of pole pairs Number of pole pairs p Initial rotor speed Initial mechanical speed wm o in radians per second s Initial rotor angle Initial mechanical rotor angle 0mo in radians Initial
76. O gt Ln fin In order to model a magnetic coupling between the internal inductors en ter a square matrix The size n of the matrix corresponds to the width of the component L is the self inductance of the internal inductor and M j the mutual inductance d Vi Ly Mi 2 nue Min ail d v2 Mz Log Man 2 v M M pate di n n 1 n 2 n den Initial current The initial current through the inductor at simulation start in amperes A This parameter may either be a scalar or a vector with the width of the component The direction of a positive initial current is indicated by a small arrow in the component symbol The default of the initial current is 0 Probe Signals Inductor current The current flowing through the inductor The direction of a positive cur rent corresponds to the small arrow in the component symbol 82 Mutual Inductor Mutual Inductor Purpose Mutual inductor Library Passive Components Description This component provides two or more coupled inductors Electrically it is equivalent with a vectorized Inductor see page 81 In contrast to the vec torized Inductor this component displays the individual inductors in the schematic as separate windings In the symbol of the mutual inductor the positive terminal of winding 1 is marked with a little circle The positive terminals of all other windings are marked with dots ag iat ake cla an Dia og rMutinductor Box Mutual inductor
77. Oxide Semiconductor Field Effect Transistor has an in tegrated anti parallel diode The diode is usually included in power MOSFET r L packages Dialog Box zix ridea MOSFET with Diode MOSFET with integrated anti parallel diode pParameters Name hosFET2 E Width a On resistance Ron Es Initial conductivity pc ts On state voltage drop therm la fa Turn on loss therm la a Turn off loss therm la mi OK Cancel Help Apply Width The width of the component This affects both the width of the electrical ports and the width of the gate input signal The default is 1 Initial conductivity Initial conduction state of the device The device is initially blocking if the parameter evaluates to zero otherwise it is conducting This parameter 140 MOSFET with Diode may either be a scalar or a vector with the width of the component The default value is 0 The following parameters define the thermal behavior of the component For more information see chapter Thermal Modeling on page 59 On state voltage drop therm A 2 D function von T defining the voltage drop in volts V that is used for calculating the thermal conduction losses The default is meaning no thermal conduction losses Turn on loss therm Turn off loss therm 3 D functions Eon Upre ipost T and Eos Upost ipre T defining the total ther mal losses dissi
78. Pe Tightness of sat transistion fT fi zf Field resistance Rf fet Field leakage inductance Lif ke 4 a Damper resistance Rkd Rkq1 Rkqg2 All parameters and electrical quantities are referred to the stator side Parameters Name fm Round Rotor mu Stator resistance Rs Damper leakage ind Ukd Ukq1 Ukg2 fne s Te 4 2e 3 Pi Inertia J fes m Friction coefficient F pc tk Number of pole pairs p fi zf Initial rotor speed wm0 Brprao fa Initial rotor position thm0 pc eld Initial stator currents isa isbO foo E Initial field damper current 1f0 ikq1 foo E Initial stator flux Psisd0 Psisq0 re 2 3 2 8e 3 4 feo E OK Cancel Help ay Initial field damper current A two element vector containing the initial currents 7 in the field wind ing and ij 9 in one of the damper windings in amperes A referred to the stator side Same as for the Salient Pole Synchronous Machine see page 161 Most probe signals for the Salient Pole Synchronous Machine see page 161 are also available with this machine Only the following probe signal is differ ent Round Rotor Synchronous Machine Damper currents ie ae fy oe The damper currents i 4 ik al and i in the stationary reference frame in A referred to the stator side References K A Corzine B T Kuhn S D Sudhoff H J Hegner An improved method for incorporating magnetic satu
79. Piece wise Linear Electrical Circuit Simulation PLECS _ Circuit simulation at system level User Manual Version 1 5 How to Contact Plexim 41 44 445 24 10 Phone 41 44 445 24 11 Fax Plexim GmbH Mail Technoparkstrasse 1 8005 Zurich Switzerland info plexim com Email http www plexim com Web PLECS User Manual 2002 2007 by Plexim GmbH The software PLECS described in this manual is furnished under a license agreement The software may be used or copied only under the terms of the license agreement No part of this manual may be photocopied or reproduced in any form without prior written consent from Plexim GmbH PLECS has been developed under license of ETH Zurich PLECS is a registered trademark of Plexim GmbH MATLAB and Simulink are registered trademarks of The MathWorks Inc Other product or brand names are trademarks or registered trademarks of their respective holders Contents Contents 10 Before You Begin 11 Installing PLECS aaa 11 Microsoft Windows o e e eee 11 Mac OS X Linux Solaris o o 12 Configuring PLECS o 13 Installing Different PLECS Versions in Parallel 13 What s New in Version lb o e 14 What s New in Version l4 o o eee eee eee 14 What s New in Version 13 o o 15 What s New in Version 1 2 o o
80. This component is based on a voltage controlled current source It may there fore not be connected in series with other current sources or inductors e The control signal for the momentary inductance values must be continuous Discontinuous changes will produce non physical results zix Variable resistor inductor Variable inductor with variable series resistance Parameters Name RLI E Width E z Initial current oO O B OK Cancel Help Apply 103 6 Block Reference Width The width of the electrical ports resp the number of resistors inductors represented by the component Initial current The initial current through the component at simulation start in amperes A This parameter may either be a scalar or a vector with the width of the component The direction of a positive initial current is indicated by a small arrow in the component symbol The default of the initial current is 0 Probe Signals Inductor current The current flowing through the inductor in amperes A The direction of a positive current corresponds to the small arrow at one of the terminals 104 Variable Resistor with Constant Series Inductor Variable Resistor with Constant Series Inductor Purpose Variable resistor with constant series inductor Library Nonlinear Description This component models a variable resistor with a constant inductor connected in series The resistance is determined by t
81. access Exporting Circuits for the PLECS Viewer Exporting Circuits for the PLECS Viewer The PLECS Viewer enables you to share your circuit models with users that do not have a license for PLECS The PLECS Viewer is available for free and allows a user to simulate and optionally view but not modify a circuit model provided that it bears a special signature In particular the PLECS Viewer does not permit changing a component parameter nor is it possible to specify parameters as variables from the MATLAB workspace In order to export a circuit for use with the PLECS Viewer choose Export for PLECS Viewer from the File menu If the Simulink model has unsaved changes you will be asked to save them before you can proceed Afterwards a dialog allows you to specify a filename for the Viewer version of the model PLECS will then automatically copy the current model to the specified export file replace component parameters that access the MATLAB workspace with their actual values break any links to component libraries and sign it for use with the Viewer The original model itself remains unchanged Note An exported circuit can not be changed by anyone not even by its cre ator It is therefore advisable that you keep the original model for later use and that you choose export filenames that are easily distinguished from the origi nal 53 3 Using PLECS Circuit Simulation Parameters PLECS allows you to specify vari
82. ace Simulink objects in a PLECS schematic and vice versa since both programs do not share the same Graphical User Interface Connections The unconnected electrical terminals of a component are marked with little hollow circles If we bring the pointer close to such a terminal the pointer shape changes from an arrow to a cross We now can drag a connection to an other component by holding the left mouse button down When we approach another terminal or an existing connection the pointer shape changes into a double cross As soon as we release the mouse button an electrical connection will be created For drawing a branch connection place the pointer on an existing connection where you want the branch to start With the right mouse button or with the left mouse button while holding down the Ctrl key you can create a connec tion from there to the desired destination Note PLECS does not allow you to create a connection between two points that already are connected via another path 25 2 Getin g Started 26 Component Properties A double click on a component opens a dialog box in which you can set the name of the component and its parameters Each component is identified by a unique name which is chosen automatically You may change it as you wish The name is intended only for documentation purposes and does not affect the simulation Fig 2 4 shows the dialog box for an inductor ala rlnductor Ideal inductor
83. alue Mask parameters appear on the dialog box as edit fields in the order they ap pear in the prompt list You can add or remove parameters or change their order by using the four buttons to the left of the prompt list Variable Scope PLECS associates a local variable workspace with each masked subcircuit that has one or more mask parameters defined Components in the underlying schematics can only access variables that are defined in this mask workspace 45 3 Using PLECS 46 Mask Editor Components Machines IM1 q oj xj Icon Parameters Probes Documentation Prompt Variable Stator leakage inductance Lls Delete Rotor resistance Rr Rr Rotor leakage inductance Llr Llr Up Magnetizing inductance Lm Down gt Variable Rs Initalization commands isd0 is0 1 a isq0 1sqri S s0 1 2 is0 2 imd0 psisdq0 1 Us isdO Lm img psisdqO 2 Ls isq0 Lm OK Cancel Unmask Help Apply Initialization Commands The mask initialization commands are evaluated in the mask workspace when a simulation is started You can enter any valid MATLAB expression con sisting of MATLAB functions operators and variables defined in the mask workspace Variables defined in the base workspace cannot be accessed Mask Probe Signals The Probes pane enables you to define the probe signals that the masked subcircuit will provide to the PLECS Probe Mask probe signals
84. ameters Name fD Table E Vector of input values x 2 mj Vector of input values y In 2 Ei Vector of input values y In 2 El SD array of output values f x y z fag n2 84 156 75p J OK Cancel Help Apply Vector of input values x The vector of input values x This vector must be the same size as the size of the first dimension in the output array and monotonically increasing It should not contain more than three identical values Vector of input values y The vector of input values y This vector must be the same size as the size of the second dimension in the output array and monotonically increasing It should not contain more than three identical values 3D Look Up Table Vector of input values z The vector of input values z This vector must be the same size as the size of the third dimension in the output array and monotonically increasing It should not contain more than three identical values 3D array of output values f x y z The array containing the output values f x y z The dimensions must match the size of the input vectors Probe Signals Input x The block input signal z Input y The block input signal y Input z The block input signal z Output The block output signal 217 6 Block Reference 218 Op Amp Purpose Library Description Parameters and Dialog Box Ideal Op Amp with finite gain Op Amps This Op Amp amplifies a voltage between the non
85. an be connected using wire branches All points connected by a wire or wire branches have the same electrical po tential The schematic editor does not allow to create wire loops i e connect two points that already have the same potential Signals Signals are similar to Simulink signals in that they represent a directed flow of values from the output of one component to the input of one or several other components Values can be either scalars or vectors The width of a sig nal is determined at the time you draw the connection You can only draw a signal between an output and an input that have the same width and type i e continuous signal or gate signal see below Continuous Signals Continuous signals are drawn in green color They represent signals that change continuously in time Continuous signals are used e g to control volt age or current sources or to measure voltages or currents in a circuit Gate Signals Gate signals are drawn in brown color They represent signals that change at discrete instants in time and are used to control switches Gate signals can either be imported from Simulink by placing a Gate Input component in the top level schematic of a circuit Or they can be generated from continuous sig nals using the Compare Function block see page 205 Annotations If you generate a gate signal by comparing one ore more continuous signals PLECS automatically generates the necessary zero crossing signals
86. ance Rz 0 01 a Forward voltage Vf 0 9 F Forward resistance Rf 0 01 E OK Cancel Help Apply Zener voltage Breakdown voltage V in reverse direction in volts V If the diode is re verse conducting the voltage drop across the diode is determined by this Zener voltage plus the voltage across the Zener resistance Zener resistance The resistance R in ohms Q if the diode is reverse conducting Forward voltage Additional dc voltage V in volts V between anode and cathode when the diode is forward conducting The default is 0 Zener Diode Probe Signals On resistance The resistance Rf of the forward conducting device in ohms Q The de fault is 0 Diode voltage The voltage measured between anode and cathode Diode current The current through the diode flowing from anode to cathode Forward conductivity Conduction state of the positive internal switch The signal outputs 1 when the diode is conducting in forward direction and 0 otherwise Reverse conductivity Conduction state of the negative internal switch The signal outputs 1 when the diode is conducting in reverse direction and 0 otherwise 129 6 Block Reference 130 Thyristor Purpose Library Description 3 Parameters and Dialog Box Ideal thyristor with or without forward voltage and on resistance Switches The Thyristor can conduct current only in one direction like the diode In ad dition to
87. antaneous thermal switching losses in joule J Only defined if the component is placed on a heat sink Diode Diode Purpose Library Description Parameters and Dialog Box Ideal diode with or without forward voltage and on resistance Switches The Diode is a semiconductor device controlled only by the voltage across it and the current through the device The Diode model is basically an ideal switch that closes if the voltage between anode and cathode becomes positive and opens again if the current through the component becomes zero In addi tion to the ideal switch a forward voltage and an on resistance may be speci fied If unsure set both values to 0 all Diode The diode closes upon a positive voltage between anode and cathode It opens when the current tries to reverse pParameters Name Po o o E Width fi fa Forward voltage Vf pc ke On resistance Ron es On state voltage drop therm la E Turn on loss therm la fa Turn offloss therm la fa OK Cancel Help Apply Width The width of the component The default is 1 Each of the following parameters may either be a scalar or a vector with the width of the component 123 6 Block Reference Probe Signals 124 Forward voltage Additional de voltage V in volts V between anode and cathode when the diode is conducting The default is 0 On resistance The resistance R
88. appear in the probe editor in the order they appear in the mask signal list You can add or remove signals or change their order by using the four buttons to the left of the signal list Mask probe signals are defined as vectors of probe signals from components below the subcircuit mask For this reason the controls in the lower half of the dialog are identical to those of the probe editor In order to define a mask signal select the signal in the list and then drag the desired components into the dialog window The new components are added to the bottom of the list Masking Subcircuits Mask Editor Components Machines IM1 oj xj Icon Parameters Probes Documentation Mask signals Add Stator phase currents Rotor currents dq Stator flux dq Delete Maqnetizing flux dq Rotor flux dq Rotational speed Rotor position Down Electrical torque xl Signal name stator phase currents Probed components Component signals Up a Mi Measured current Ammeter isb in IM1 Down Ammeter isc in IML Remove OK Cancel Unmask Help Apply of probed components Next select the components one by one and enable the desired component signals in the list on the right side by using the check boxes Mask Documentation The Documentation pane enables you to define the descriptive text that is displayed in the dialog box of the masked subcircuit Mask Type The mask type is a strin
89. ar rather than as a struct with a single scalar field A setting of 0 or means no switching losses 62 Thermal Loss Dissipation Eon v 100 200 300 Eon i 13 23 32 50 Eon T 25 125 Eon E le 3 0 083 0 167 0 250 0 567 0 167 0 333 0 500 1 133 0 250 0 500 0 750 1 700 Eon E 2 le 3 0 167 0 333 0 500 1 133 0 333 0 667 1 000 2 267 0 500 1 000 1 500 3 400 v V 100 0 i A Note Due to the instantaneous nature of the switching transitions the dissi pated thermal energy cannot be consumed electrically by the device This must be taken into account when you use the thermal losses for estimating the effi ciency of a circuit Semiconductor components that implement this loss model are e the Diode see page 123 e the Thyristor see page 130 e the GTO see page 132 e the IGBT see page 134 e the IGBT with Diode see page 136 e the MOSFET see page 138 e the MOSFET with Diode see page 140 and e the TRIAC see page 142 In addition the Set Reset Switch see page 121 is also included in this group to enable you to build your own semiconductor models 63 A thermal Modeling Ohmic Losses Ohmic losses are calculated as i R resp u R They are dissipated by the following components e the Resistor see page 80 e the Variable Resistor with Variable Series Inductor see page 103 e the Variable Resistor with Constant Series
90. arameters and Dialog Box Magnetic coupling between three windings Passive Components This component implements a magnetic coupling between three separate windings For all windings the self inductance and resistance are specified in dividually The mutual inductance and resistance are modeled as linear ele ments The electrical circuit for this component is given below t1 Li Lm Ri Rm L2a Lm R2a Rm i2 NANA A 3 DORA ao E La 3 La3 Lm R3 Rm i3 Rm DONA lt o In the symbol of the mutual inductance the primary winding is marked with a little circle The secondary and tertiary windings are marked with dots Self inductance A three element vector containing the self inductance for the primary winding L the secondary winding L and the tertiary winding L3 The inductivity is given in henries H Winding resistance A three element vector containing the self resistance of the primary wind ing R the secondary winding Ra and the tertiary winding R3 in ohms Q Mutual inductance The mutual inductance Lm in henries H Mutual resistance The mutual resistance Rm in ohms Q 95 6 Block Reference stock parameters ix 3 Winding Mutual Inductance mask Implements a magnetic coupling between three windings Parameters Name Mutual Ind 3 E Self inductance L1 L2 L3 0 002 0 002 0 002 ya Winding resistance A1 R2 R3 222 E M
91. as an infinite internal resistance Hence if multiple voltmeters are connected in series the voltage across an individual voltmeter is undefined This produces a run time error Likewise if switches connected in series are all in open position the voltages across the individual switches are not properly defined Although this does not produce a run time error it may lead to unexpected simulation results zox Voltmeter Output the measured voltage Parameters Name Yml E Width E El DK Cancel Help Apply Width The width of the component This affects both the width of the electrical ports and the width of the output signal The default is 1 Measured voltage The measured voltage in volts V Ammeter Ammeter Purpose Library Description Parameters and Dialog Box Probe Signals Output the measured current Sources amp Meters The Ammeter measures the current through the component and provides it as a continuous signal at the output The direction of a positive current is indi cated by the small arrow at one of the electrical terminals The output signal can be made accessible in Simulink with a Continuous Output block see page 192 or by dragging the component into the dialog box of a Probe block Note The Ammeter is ideal i e it has zero internal resistance Hence if mul tiple ammeters are connected in parallel the current through an individual am meter is undefin
92. ase three level IGBT converter with neutral point clamping The gate inputis a vector of three signals one per leg The topmost IGBT is turned on for gate signals gt 1 the second IGBT for signals 0 Block parameters 5 xj Detailed SLevel IGBT Converter mask This block implements a three phase three level IGBT converter with neutral point clamping The gate input is a vector of three signals one per leg The topmost IGBT is turned on for gate signals 1 the second IGBT for signals 0 the third one for signals 0 and the lowest one for signals lt 1 Gate signal values of 1 0 and 1 connect the phase output to the positive neutral and the third one for signals lt 0 and the lowest one negative de level for signals lt 1 Gate signal values of 1 0 and 1 connect the phase output to the positive Parameters neutral and negative dc level Name PetalednS LevelniGBT Corn a pParameters Name IGBT forward voltage Diode forward voltage 2 LeveniG8 TinGonv E p C g mi IGBT on resistance Diode on resistance IGBT on state voltage drop therm la la IGBT turn on loss therm la B M A IGBT on state voltage drop therm Diode on state voltage drop therm la dp Bi IGBT turn off loss therm IGBT turn on loss therm Diode turn on loss therm 5 fo 4 fi E Clamping diode on state voltage drop therm IGBT turn off loss therm Diode tu
93. ate magnetizing inductances along the d axis and q axis are functions of the cur rents in both axes In the implementation the stator currents and the main Saturable Induction Machine Parameters and Dialog Box flux linkage are chosen as state variables With this type of model the repre sentation of dynamic cross saturation can be neglected without affecting the machine s performance The computation of the time derivative of the main flux inductance is not required In order to inspect the implementation please select the component in your circuit and choose Look under mask from the Edit menu If you want to make changes you must first choose Break library link and then Unpro tect both from the Edit menu Electro Mechanical System Electromagnetic torque 3 Te 2 Pp isq Ysa z isd Vs q Mechanical System Mechanical rotor speed wm 1 m T Fum Tn J W PWm Mechanical rotor angle 0m Bon Wm 0 phm Stator resistance Stator winding resistance R in ohms Q Stator leakage inductance Stator leakage inductance Lis in henries H Rotor resistance Rotor winding resistance R in ohms Q referred to the stator side Rotor leakage inductance Rotor leakage inductance Li in henries H referred to the stator side Unsaturated magnetizing inductance Unsaturated main flux inductance Lo in henries H referred to the sta tor side 157 6 Block Reference 158 Block paramet
94. bcircuit block is resized automatically in order to accommodate the new terminal You can move a terminal to another free slot on the border by dragging it with the center mouse button While you hold down the mouse button a circle shows the free slot nearest to the mouse pointer When you release the mouse button the terminal is moved The figures below show a Subcircuit block before during and after moving a terminal E O pj Port Port Subcircuit Subcir cuit Subcircuit Notice how the shape of the cursor changes to crosshairs as you move it into the capture radius of the terminal When you press and hold down the center mouse button the cursor shape changes to a pointing hand Resizing a Subcircuit Block To change the size of a Subcircuit block select it then drag one of its selection handles While you hold down the mouse button a dashed rectangle shows the new size When you release the mouse button the block is resized The minimum size of a Subcircuit block is limited by the number of terminals on each side The figures below show a Subcircuit block before during and after resizing SL Subir cuit Subir cuit 41 3 Using PLECS 42 Notice how the terminals on the right edge of the Subcircuit block are shifted after you release the mouse button in order to fit into the new frame The block height cannot be reduced further because the terminals cannot be shifted any closer Placing the Subcircuit La
95. bel The label of a Subcircuit block can be placed at any of the following nine po sitions at the middle of the four edges at the four corners or in the center of the block To change the placement of the label drag it to a new location While you hold down the mouse button a dashed rectangle shows the new po sition When you release the mouse button the label is moved Masking Subcircuits Masking Subcircuits Masking a subcircuit allows you to create a custom user interface for a Subcir cuit block that hides the underlying schematic making it appear as an atomic component with its own icon and dialog box Many of the components in the PLECS component library are in fact masked subcircuits To mask a subcircuit select the Subcircuit block then choose Mask subcir cuit from the Edit menu or from the block s context menu The mask editor appears The mask editor consists of four tabbed panes that are described in detail below Mask Icon The Icon pane enables you to create icons that show descriptive text or labels graphics and images Mask Editor Components Machines IM1 Gg oj x Icon Parameters Probes Documentation Drawing commands circle 0 0 18 circle 0 0 25 line 25 28 10 10 circle 26 5 13 5 5 E Icon frame Invisible x Icon transparency Transparent z OK Cancel Unmask Help Apply 43 3 Using PLECS 44 Mask
96. c This parameter should be scalar if the input signal is a vector 279 6 Block Reference 280 Discrete Total Harmonic Distortion Purpose Library Description signal THO f Parameters and Dialog Box Calculate the total harmonic distortion THD of the input signal Extras Discrete Analysis This block calculates the total harmonic distortion of a periodic input signal based on discrete samples The sample time and the number of samples can be specified The THD is defined as X U 2 _Tp2_ T72 THD v gt 2 gt Us Yo Ui Ui Ui where U is the RMS value of the vth harmonic of the input signal and U ms is its overall RMS value The fundamental frequency f of the running window is 1 sample time x number of samples f Note This block is only available for Matlab 7 0 or newer Block Parameters Discrete Total Harmonic Distortion 2 xi Discrete Total Harmonic Distortion mask Computes the total harmonic distortion THD of a periodic signal The THD is defined as the RMS value of the harmonics divided by the RMS value of the fundamental frequency The input signal is sampled with the sample time specified The fundamental frequency f1 of the input signal is determined by Al 1 sample time number of samples m Parameters Sample time 0 01 Number of samples 10 Cancel Help Apply Sample time The time interval between samples Discrete Total Ha
97. ce 226 3 Level IGBT Converter Purpose Library Description Three phase three level neutral point clamped IGBT converter Converters Implements a three phase three level IGBT converter with neutral point clamping The gate input is a vector of three signals one per leg The top most IGBT connected to the positive dc level is turned on if the correspond ing gate signal is gt 1 and the second IGBT if the signal is gt 0 The third IGBT is turned on for signals lt 0 and the lowest one for signals lt 1 Gate signal values of 1 0 and 1 connect the phase output to the positive neu tral and negative dc level By applying a non zero signal at the inhibit input marked with x you can turn off all IGBTs You can choose between two different converter models e The basic 3 Level IGBT Converter is modeled using the component IGBT with Diode see page 136 No parameters can be entered e The Detailed 3 Level IGBT Converter is based on individual IGBT see page 134 and Diode see page 123 components In this model you may specify forward voltages and on resistances separately for the IGBTs and the diodes The electrical circuit for the converter is shown below o 4 3 Level IGBT Converter Parameters and Dialog Boxes Probe Signals lock parameters ue TE SLevel IGBT Converter mask This block implements a three ph
98. ch The switch is open when the gate signal is zero otherwise itis closed pParameters Name Eo Width fi El Initial conductivity pc OK Cancel Help Apply Width The width of the component This affects both the width of the electrical ports and the width of the gate input signal The default is 1 Initial conductivity Initial conduction state of the switch The switch is initially open if the parameter evaluates to zero otherwise closed This parameter may either be a scalar or a vector with the width of the component The default value is 0 Probe Signals Switch conductivity Conduction state of the switch The signal outputs 0 if the switch is open and 1 if it is closed 117 6 Block Reference 118 Double Switch Purpose Ideal changeover switch Library Switches Description This changeover switch provides an ideal short or open circuit If the gate in put signal is zero the switch is in the upper position For all other values the Poe de switch is in the lower position a Parameters and Dialog Box Probe Signals lola Double Switch Ideal changeover switch When the gate signal is zero the switch connects to the port indicated in the icon Otherwise it connects to the opposite port Parameters Name Eo ff Width fi jal Initial position pc le OK Cancel Help Apply Width The width of the component This affects both the wi
99. cogging torque Toog of the machine in Nm 5 7 Back EMF voltages The back EMF voltages ea ep e in volts V References D Hanselman Brushless permanent magnet motor design 2nd ed The Writers Collective Mar 2003 P Pillay R Krishnan Modeling simulation and analysis of permanent magnet motor drives Part 11 The brushless DC motor drive IEEE Trans on Ind App Vol 25 No 2 Mar Apr 1989 181 6 Block Reference Simple Brushless DC Machine Purpose Simple model of a brushless DC machine excited by permanent magnets Library Machines Description The Simple Brushless DC Machine is a model of a permanent magnet syn chronous machine with trapezoidal back EMF The machine operates as a motor or generator the sign of the mechanical torque determines the mode of operation positive for motoring negative for generating In the component icon phase a of the stator winding is marked with a dot Electrical System i R L cs EN YYA de ey YYY de fay OPN ae The back EMF voltages are determined by a shape function ke and the me chanical rotor speed wm The shape function is an ideal trapezoidal function scaled with the back EMF constant Keg x Oe Wm Kea Oe Wm N a oy 5n 6 T 182 Simple Brushless DC Machine Parameters and Dialog Box Electromechanical System The electromagnetic torque is To 5 Koala z a b c Mechanical System
100. d current sources or vice versa Their characteristics must be computed in an external feedback loop Since this method reduces the per formance you should employ it as little as possible 21 1 Introduction 22 Getting Started Let us have a quick tour and see how PLECS is used Our aim is to show the essential elements of PLECS in real applications without regarding all the de tails rules and exceptions At this stage we are not trying to be complete We want to get you as soon as possible to the point where you can set up useful applications Many of the details are not necessary at the beginning and can be studied later Where to Find PLECS To access PLECS you simply need to enter plecslib in the MATLAB com mand line This will bring up a Simulink model that contains a generic PLECS block named Circuit and various component libraries In the li braries you find electrical components from which you can create your cir cuits Alternatively you may access the PLECS toolbox by opening it in the Simulink library browser A Simple Passive Network The only way to become familiar with a new program is by using it For this reason we are presenting here two example circuits that you can reconstruct on your computer The examples are based on each other since the features of PLECS will be explained step by step The first electrical system we are going to model is a simple RLC network as shown in Fig 2 1 A capaci
101. dialog box to get online help about the component 35 3 Using PLECS 36 Libraries Libraries enable you to ensure that the custom components or masked sub circuits used in your circuit are always up to date Or the other way round if you are developing your own custom components you can use a library to ensure that changes you make to your component models are automatically propagated to a user s circuit upon loading Creating a New Library To create a new component library open the PLECS Extras library and copy the PLECS Library block into a Simulink model or library The Simulink model must be named i e saved before you can copy components from the component library Creating a Library Reference When you copy a library component either into a circuit schematic or into another or even the same component library PLECS automatically creates a reference component rather than a full copy You can modify the parameters of the reference component but you cannot mask it or if it is already masked edit the mask You can recognize a library reference by the string link dis played next to the mask type in the dialog box or by the string Link dis played in the title bar of the underlying schematic windows The reference component links to the library component by its full path i e the Simulink path of the PLECS Library block and the path of the compo nent within the component library as they are in effect at t
102. dth of the electrical ports and the width of the gate input signal The default is 1 Initial position Initial position of the switch The switch is initially in the upper position if the parameter evaluates to zero For all other values it is in the lower position This parameter may either be a scalar or a vector with the width of the component The default value is 0 Switch position State of the internal switches The signal outputs 0 if the switch is in the upper position and 1 if it is in the lower position Triple Switch Triple Switch Purpose Ideal changeover switch Library Switches Description This changeover switch provides an ideal short or open circuit The switch position drawn in the icon applies if the gate input signal is zero For values 0 greater than zero the switch is the lower position For values less than zero it o is in the upper position Parameters atx and Dialog Tipe Switch Box Ideal changeover switch When the gate signal is zero the switch connects to the middle port as indicated in the icon For values greater than zero the switch connects to the portin direction of the input arrow For values less than zero it connects to the opposite port Parameters Name Initial position pc OK Cancel Help Apply Width The width of the component This affects both the width of the electrical ports and the width of the gate input signal The default
103. duces the ef fect of reverse recovery This effect can be observed when a forward biased diode is rapidly turned off It takes some time until the excess charge stored in the diode during conduction is removed During this time the diode rep resents a short circuit instead of an open circuit and a negative current can flow through the diode The diode finally turns off when the charge is swept out by the reverse current and lost by internal recombination The following figure illustrates the relationship between the diode parameters and the turn off current waveform Iro and dI dt denote the continuous for ward current and the rated turn off current slope under test conditions The turn off time t is defined as the period between the zero crossing of the cur rent and the instant when it becomes equal to 10 of the maximum reverse current Irm The reverse recovery charge is denoted Q Only two out of the three parameters t r I rm and Qrr need to be specified since they are linked geometrically The remaining parameter should be set to 0 If all three param eters are given Q is ignored The equivalent circuit of the diode model is shown below It is composed of a resistance and inductance and a controlled current source which is linearly dependent on the inductor voltage The values of these internal elements are automatically calculated from the diode parameters 125 6 Block Reference Ron
104. e Integrator block see page 209 57 3 Using PLECS 58 Thermal Modeling Thermal management is an important aspect of power electronic systems and is becoming more critical with increasing demands for higher packaging and power density PLECS enables you to include the thermal design with the electronics design at an early stage in order to provide a cooling solution suit able for each particular application Heat Sink Concept The core component of the thermal library is an idealized heat sink depicted as a dashed box in the figure below A heat sink absorbs the thermal losses dissipated by the components within its boundaries At the same time a heat sink defines an isotherm environment and propagates its temperature to the components which it encloses 1 ma i A A Pos i Brake i rr i H Resistor H BH N gt Las P E Summ H E i H 9 H H y Brake i i H IN Chopper i A TA A ae HEA AKA AKA Diode Module GBT Module Heat conduction from one heat sink to another or to an ambient temperature is modeled with lumped thermal resistances and capacitances that are con A thermal Modeling nected to the heat sinks This approach allows you to control the level of de tail of the thermal model Implementation Each heat sink has an intrinsic thermal capacitance versus the thermal
105. e click on the Components block in the PLECS library opens the com ponent browser window shown below You can navigate through the compo nent library either by clicking on the list entries on the left side of the win dow Alternatively you can double click on the icons on the right side Components 5 xj File Edit View Format Components 3 Phase Transformers iba Converters e Machines l Nonlinear Op Amps E Passive Components Sources amp Meters Passive Components Nonlinear Signals Systems Sources amp Meters Switches q Thermal E Switches Signals 4 Systems Converters SPhase Transformers Drag the components you need from the component browser into the schematic editor Note You cannot place Simulink blocks in a PLECS schematic or PLECS com ponents in a Simulink model since both programs do not share the same Graph ical User Interface 33 3 Using PLECS 34 Components Specifying Component Parameters Every component has a dialog box to view and modify the component parame ters The dialog box appears when you double click on the component icon Block parameters TES Diode The diode closes upon a positive voltage between anode and cathode It opens when the current tries to reverse Parameters Name Width fi fa Forward voltage Vf pc tk kewl On resistance Ron ee On state voltage drop therm la ja Turn on
106. e exported to Simulink with additional port blocks Alternatively you can bundle the measured sig nals into a vector by using the multiplexer for continuous signals CMux 27 2 Gettin g Started IEJES 0 0 02 0 04 0 06 0 08 0 1 Time offset 0 Figure 2 6 Simulation result from the library Signals amp Systems Before you can connect the blocks you need to set the parameter Width in the dialog boxes of the multiplexer and the port block to the desired value Importing Signals You have already learned how to export signals from the electrical circuit to Simulink via the output block In the same manner you can also import sig nals from Simulink into your circuit usually to control sources Let us see how the capacitor in our example charges and discharges if we ap ply a pulsed voltage In the schematic we replace the DC voltage source by a controlled one Copy the input block In1 into the schematic and connect it to the voltage source The PLECS block in Simulink now also has an input terminal Any Simulink signal that you connect to this terminal will be trans lated into a voltage in the electrical circuit In Fig 2 7 we used a pulse gener ator with a period of 0 04 sec and an amplitude of 10 Buck Converter 28 In the next example we will introduce the concept of ideal switches which distinguishes PLECS from other simulation programs It will be shown how switches are controlled i e
107. e name of Circuit1 plecsedit get mdl Circuit1 CircuitModel returns the circuit simulation method of Circuiti plecsedit get mdl1 Circuit1 R1 returns the parameters of component R1 in circuit Circuit1 plecsedit set mdl Circuit1 R1 R 2 sets the resistance of component R1 in circuit Circuit1 to 2 Block Reference 6 Block Reference 70 Controlled Voltage Source Purpose Library Description Parameters and Dialog Box Probe Signals Generate a variable voltage Sources amp Meters The Controlled Voltage Source generates a variable voltage between its two electrical terminals The voltage is considered positive at the terminal marked with a The momentary voltage is determined by the continuous signal fed into the input of the component Note A voltage source must not be short circuited or connected in parallel to a capacitor or any other voltage source lla Controlled Voltage Source Generate a variable voltage TParameters Name v E Width DO O tk ee OK Cancel Help Apply Width The width of the component This affects both the width of the electrical ports and the width of the input signal The default is 1 Source voltage The source voltage in volts V DC Voltage Source DC Voltage Source Purpose Generate a constant voltage Library Sources amp Meters Description The DC Voltage
108. e of the components listed below Arithmetic and relational operators as well as mathematical functions may only be applied on continuous signals Logical operators may only be ap plied on the results of comparisons e u the input of the block If the input is vectorized u i or u i repre sents the ith element of the vector To access the first element enter u 1 u 1 or u alone e Brackets e Numeric constants e Arithmetic operators e Relational operators gt lt gt lt e Logical operators amp amp e Mathematical functions abs acos asin atan atan2 cos cosh exp log log10 pow sgn sin sinh sqrt tan and tanh e MATLAB workspace variables The Compare Function icon can be distinguished from the Gate Function see page 207 by the green instead of a brown input terminal Note This block is intended for compound components that contain internally and or externally controlled switches It is for expert use only The block shall not be used to implement controllers like a hysteresis type control since this may lead to unexpected simulation results Controllers should always be imple mented directly in Simulink 205 6 Block Reference Parameters zix and Dialog E ompare function Box Function block for generating gate signals from continuous signals Parameters Name CmpFen E Expression u t gt ul2 ja Input width jz O te OK
109. e stator side Currents flowing into the machine are considered positive Stator flux dq The stator flux linkages Y and Y in the stationary reference frame in Vs Magnetizing flux dq The magnetizing flux linkages Ym and V in the stationary reference frame in Vs 159 6 Block Reference Rotor flux dq The rotor flux linkages Y and Y in the stationary reference frame in Vs referred to the stator side Rotational speed The rotational speed wm of the rotor in radians per second s71 Rotor position The mechanical rotor angle 6 in radians Electrical torque The electrical torque T of the machine in Nm References K A Corzine B T Kuhn S D Sudhoff H J Hegner An improved method for incorporating magnetic saturation in the Q D synchronous ma chine model IEEE Transactions on Energy Conversion Vol 13 No 3 Sept 1998 E Levi A unified approach to main flux saturation modelling in D Q axis models of induction machines IEEE Transactions on Energy Conver sion Vol 10 No 3 Sept 1995 E Levi Impact of cross saturation on accuracy of saturated induction ma chine models IEEE Transactions on Energy Conversion Vol 12 No 3 Sept 1997 160 Salient Pole Synchronous Machine Salient Pole Synchronous Machine Purpose Salient pole synchronous machine with main flux saturation Library Machines Description The Salient Pole Synchronous Machine models main flux
110. easing It should not contain more than three identical values Vector of input values y The vector of input values y This vector must be the same size as the number of columns in the output matrix and monotonically increasing It should not contain more than three identical values Matrix of output values f x y The matrix containing the output values f x y The number of rows and columns must match the size of the input vectors 2D Look Up Table Probe Signals Input x The block input signal z Input y The block input signal y Output The block output signal 215 6 Block Reference 216 3D Look Up Table Purpose Library Description OaD Table Parameters and Dialog Box Output an approximated three dimensional function using intrapola tion extrapolation Signals amp Systems The 3D Look Up Table block maps three continuous input signals to a contin uous output signal You define the mapping function by specifying three vec tors of input values and an array of output values The input vectors x y and z correspond to the first second and third dimension of the output array The output value is interpolated or extrapolated from the block parameters using the technique described for the 1D Look Up Table block see page 212 Block parameters 151 x 8D Look Up Table Output an approximated three dimensional function using interpolation extrapolation Par
111. ed This produces a run time error Likewise if switches connected in parallel are all in closed position the current through the individual switches is not properly defined Although this does not produce a run time error it may lead to unexpected simulation results ala r mmeter Dutput the measured current TParameters Name Amt E Width E jar OK Cancel Help Apply Width The width of the component This affects both the width of the electrical ports and the width of the output signal The default is 1 Measured current The measured current in amperes A 79 6 Block Reference 80 Resistor Purpose Library Description ep SAA o Parameters and Dialog Box Ideal resistor Passive Components This component provides an ideal resistor between its two electrical terminals See section Configuring PLECS in chapter Using PLECS for information on how to change the graphical representation of resistors Note Like all other parameters of PLECS components the resistance cannot be changed during the simulation lla rResistor Ideal resistor Parameters Name R1 E Width E jal Resistance E jan OK Cancel Help Apply Width The width of the electrical ports resp the number of ideal resistors repre sented by the component Resistance The resistance in ohms Q All positive and negative values are accepted
112. eg core The transformer core is assumed symmetri z cal i e all phases have the same parameters Depending on the chosen com ponent the windings are wired in star Y or delta D connection on the pri mary side On the secondary side the windings are either in star y delta d 7 or zig zag z connection Star and zig zag windings have an accessible neutral point The phase angle difference between the primary and the secondary side can be chosen For Yy and Dd connections the phase lag must be an integer mul gt tiple of 60 For Yd and Dy connections the phase lag must be an odd integer multiple of 30 The phase lag of zig zag windings can be chosen arbitrarily The windings of the secondary side are allocated to the transformer legs ac cording to the phase lag Please note that the phase to phase voltage of delta gt a windings is by a factor of 1 v3 lower than the voltage of star or delta wind ings if the number of turns are equal 1 0 1 0 1 6 in The core saturation characteristic of the transformer legs is piece wise linear The magnetizing current im and flux Ym value pairs are referred to the pri mary side To model a transformer without saturation enter 1 as the magne tizing current values and the desired magnetizing inductance Lm as the flux 232 2 Winding 3 Phase Transformers Parameters and Dialog Box values A stiff Simulink solver is recommended if the iron losses are not negli gible
113. eluctance torque caused by the non constant stator in ductance dL To 5 heaie gt ap iz x a b c The cogging torque is again expressed as a fourier series of the electrical rotor angle Teog Be Y Ton cos n0 Tn sin n0 n Mechanical System Mechanical rotor speed 1 Wm 7 Te Tog 9c Fun Tm Mechanical and electrical rotor angle Om Wm 0 p Om 179 6 Block Reference Parameters and Dialog Box 180 Block parameters la x Brushless DC Machine mask Detailed three phase brushless DC machine The input signal Tm represents the mechanical torque in Nm The vectorized output signal of width 7 contains the rotational speed wm in rad s the mechanical rotor position th in rad the electrical torque Te in Nm the cogging torque Tcog in Nm the back EMF voltages The back EMF voltages the stator inductance and the cogging torque are modeled as fourier series in function of the electrical rotor position Parameters Name Boo TTT Back EMF shape coefficients Ken Cogging torque coefficients Tsn 00000 E p ma Back EMF shape coefficients Ksn Inertia J pararme 0190 1 50 mj Pe 3 mf Stator resistance R Friction coefficient F pcs ho2 mi Stator inductance constant LO M Number of pole pairs p poo EE Stator inductance coefficients Len Initial rotor speed wm0 PO O Stator inductance coefficients Lsn Initial rotor angle
114. emperature difference be tween its two thermal connectors or between the thermal connector and the thermal reference The temperature difference is considered positive if the ter minal marked with a has a higher temperature The momentary tempera ture difference is determined by the continuous signal fed into the input of the component Block parameters 5 xj Controlled Temperature Generate a variable temperature pParameters Name A OK Cancel Help Apply Temperature The temperature difference in kelvin K Constant Temperature Constant Temperature Purpose Generate a constant temperature Library Thermal Description The Constant Temperature generates a constant temperature difference be tween its two thermal connectors or between the thermal connector and the thermal reference The temperature difference is considered positive if the ter minal marked with a has a higher temperature Dialog Box lx Constant Temperature Generate a constant temperature Parameters Name RE Temperature Pc ec OK Cancel Help Apply Temperature The temperature difference generated by the component in kelvin K The default is 0 Probe Signals Temperature The temperature difference in kelvin K 241 6 Block Reference 242 Controlled Heat Flow Purpose Library Description Dialog Box Probe Signals Generate a control
115. ener Diode see page 128 New function block 3D Look Up Table see page 216 What s New in Version 1 4 The following list describes new features and enhancements added in PLECS 1 4 since version 1 3 New saturable machine models Saturable Induction Machine see page 155 Salient Pole Synchronous Machine see page 161 Round Rotor Syn chronous Machine see page 167 An advanced behavioral reverse recovery diode model see page 125 Define custom probe signals for masked subcircuits See Masking subcir cuits on page 43 Library references enable you to ensure that your models always use the most current version of custom components from the library See Libraries on page 36 Additional signal blocks e g the Constant Block see page 211 the 1D Look Up Table see page 212 and the 2D Look Up Table see page 214 el What s New in Version 1 3 What s New in Version 1 3 The following list describes new features and enhancements added in PLECS 1 3 since version 1 2 New machine models Brushless DC Machine see page 178 Switched Re luctance Machine see page 185 Additional power semiconductor models MOSFET see page 138 MOSFET with Diode see page 140 2 Level MOSFET Converter see page 228 TRIAC see page 142 Advanced models for nonlinear passive components e g the Variable Resis tor with Variable Series Inductor see page 103 or the Saturable Capacitor see page 107 New componen
116. erature v Von i T This function is defined by the parameter On state voltage therm as a 2D look up table in form of a struct with two index vectors i T and an output matrix v 50 40 30 Von i 0 0 5 15 35 50 a Von T 25 125 Em Von v 0 0 8 1 3 1 7 2 3 2 7 20 00 6 1 1 1 6 2 6 3 21 v V You can omit any of the index vectors if the voltage does not depend on the corresponding variable The number of dimensions of the output table must correspond to the number of index vectors If you do not specify any index vector the output table must be a scalar In this case you can also specify the voltage directly as a scalar rather than as a struct with a single scalar field A setting of O means no conduction losses If you specify an empty matrix the default will be used i e the losses are calculated from the electrical device parameters Note Unless you specify the default losses the dissipated thermal power does not correspond to the electrical power that is consumed by the device This must be taken into account when you use the thermal losses for estimating the efficiency of a circuit Switching Losses Switching losses occur because the transitions from on state to off state and vice versa do not occur instantaneously During the transition interval both 61 4 Thermal Modeling the current through and the voltage across the device are substantially larger than zero which leads to large
117. erited from the Simulink model Refine factor This parameter controls the internal step size which PLECS uses to discretize the state space equations The discretization time step At in the equations above is thus calculated as the sample time divided by the refine factor The refine factor must be a positive integer The default is 1 Choosing a refine factor larger than 1 allows you to use a sample time that is convenient for your discrete controller while at the same time taking into account the usually faster dynamics of the electrical system ZC step size This parameter is used by the Switch Manager when a non sampled event usually the zero crossing of a current or voltage is detected It controls the relative size of a step taken across the event The default is 1e 9 Tolerances The error tolerances are used to check whether the state vari ables are consistent after a switching event The defaults are 1e 3 for the rel ative tolerance and 1e 6 for the absolute tolerance 56 Circuit Simulation Parameters Note The discrete method cannot be used with circuits that contain direct non linear feedbacks because in conjunction with Tustin s method this would lead to algebraic loops This applies for instance to the standard models for the induction machine and the two synchronous machines with wound rotor For these machines the li brary contains discretizable equivalents in which the feedback loops have been broken using th
118. ers 5 x Saturable Induction Machine mask the rotational speed wm in rad s the mechanical rotor position th in rad the electrical torque Te in Nm Three phase induction machine The input signal Tm represents the mechanical torque in Nm The vectorized output signal of width 3 contains All parameters and electrical quantities are referred to the stator side Parameters Name Stator resistance Rs pa Stator leakage inductance Us Pe 3 m Rotor resistance Ar ps Rotor leakage inductance Ur Pe 3 E Unsaturated magn inductance Lm0 froe s zh Saturated magn inductance Lmsat f 0e 3 pa Magn flux at sat transition PsiT pl Tightness of sat transition fT A E Eaturable IM E Inertia J P3 Friction coefficient F II Number of pole pairs p pc el Initial rotor speed wm0 DA Initial rotor position thm0 EY Initial stator currents isa0 isb0 foo fa Initial stator flux PsisdO Psisq0 oo 7 ES e al Saturated magnetizing inductance Saturated main flux inductance L sa in henries H referred to the stator side If you do not want to model saturation set Lm sat Lm o Magnetizing flux at saturation transition Transition flux linkage Yr in Vs defining the knee between unsaturated and saturated main flux inductance Inertia Combined rotor and load inertia J in Nms Friction coefficient Tightness of
119. erter mask This block implements a three phase two lewel IGBT converter The gate inputis a vector of three signals one per leg The upper IGBT is turned on with a positive the lower one with a negative gate signal Parameters Name B LevelnIGBTinGonv E Device on state voltage drop therm la aj Device turn on loss therm fo m Device turn off loss therm A OK Cancel Help y Block parameters oxi rDetailed 2 Level IGBT Converter mask This block implements a three phase two level IGBT converter The gate input is a vector of three signals one per leg The upper IGBT is turned on with a positive the lower one with a negative gate signal Parameters Name Petalledin2 LeveniGB TC IGBT forward voltage Diode forward voltage p zp al IGBT on resistance Diode on resistance Pp ld IGBT on state voltage drop therm Diode on state voltage drop therm es IGBT turn on loss therm Diode turn on loss therm Df IGBT turn off loss therm Diode turn off loss therm po ll el OK Cancel Help Apply The two level IGBT converters provide five or ten probe signals each a vector containing the appropriate quantities of the individual devices voltage cur rent conductivity conduction loss and switching loss The vector elements are ordered top to bottom left to right a a b b c c 225 6 Block Referen
120. es A Same as for the Induction Machine with slip ring rotor see page 144 Most probe signals for the Induction Machine with slip ring rotor see page 144 are also available with this machine Only the following probe signal is different Rotor currents The rotor currents i and i in the stationary reference frame in A re ferred to the stator side Saturable Induction Machine Saturable Induction Machine Purpose Description Induction machine with slip ring rotor and main flux saturation The Saturable Induction Machine models main flux saturation by means of a continuous function The model is implemented with machine equations in the stationary reference frame Clarke transformation Since the machine terminals have current source characteristic no external inductors may be connected They must be included in the leakage inductances This machine model can be used with both the continuous and the discrete state space method To facilitate the discretization of the model the Integrator block see page 209 is used which allows non linear feedback in the circuit The machine operates as a motor or generator the sign of the mechanical torque determines the mode of operation positive for motoring negative for generating All electrical variables and parameters are viewed from the sta tor side In the component icon phase a of the stator and rotor winding is marked with a dot Electrical System
121. esponding output signal 199 6 Block Reference 200 Wire Mux Purpose Library Description Parameters and Dialog Box Combine several wires into a bus or vice versa Signals amp Systems This multiplexer combines several individual wires into a wire bus The indi vidual wires may themselves be buses In the block icon the first individual wire is marked with a dot When you change the number of wires all wires will be disconnected from the block sox rWire Multiplexer Combine multiple wires into one bus or vice versa Parameters Name WMux E Width 3 El OK Cancel Help Apply Width This parameters allows you to specify the number and or width of the indi vidual wires You can choose between the following formats for this param eter Scalar A scalar specifies the number of individual wires each having a width of 1 Vector The length of the vector determines the number of individual wires Each element specifies the width of the corresponding individual wire Electrical Ground Electrical Ground Purpose Provide an electrical ground connection Library Signals amp Systems Description The ground block implements an electrical connection to the ground 2 Note PLECS does not require a circuit to be grounded at one or more points The ground block just provides a convenient means to connect distant points to a common potential Parameters x and
122. ference Number of windings A two element vector w wa containing the number of windings on the primary side w and on the secondary side wz The default is 1 1 which represents a two winding transformer with opposite windings Number of turns A row vector specifying the number of turns for each winding The vector length must match the total number of primary and secondary side wind ings First all primary side windings are specified followed by the specifi cations for all secondary side windings 88 linear 2 Winding Transformer Linear 2 Winding Transformer Purpose Library Description CQ Parameters and Dialog Box Two winding transformer Passive Components This transformer models two coupled windings on the same core The magne tization inductance Lm and the core loss resistance Rm are modeled as linear elements Their values are referred to the primary side A stiff solver is rec ommended if Rm is not infinite The electrical circuit for this component is given below ii Li R La Ra i2 ANA YY o WAITS Lm Rm n In the transformer symbol the primary side winding is marked with a little circle The secondary side winding is marked with a dot Leakage inductance A two element vector containing the leakage inductance of the primary side L and the secondary side Lz The inductivity is given in henries H Winding resistance A two element vector
123. ferent PLECS Versions in Parallel If you want to keep different versions of PLECS installed in parallel on one computer you must ensure that only one version is on your MATLAB path at any time during a MATLAB session Otherwise loss of data may occur Be fore changing the MATLAB path be sure to clear the currently loaded PLECS module by entering plecsclear at the MATLAB command prompt As an ad ditional precaution you should restart MATLAB after the change 13 Before You Begin 14 What s New in Version 1 5 The following list describes new features and enhancements added in PLECS 1 5 since version 1 4 The Thermal library enables you to include the thermal design with the electronics design of your power circuit See Thermal Modeling on page 59 The PLECS Viewer lets you share your circuit models with users that do not have a license for PLECS See Exporting Circuits for the PLECS Viewer on page 53 The simulation parameter Refine factor of the Discrete State Space Method allows you to simulate the discretized circuit model with a smaller time step than the Simulink model See Circuit Simulation Parameters on page 54 Enhanced three phase transformer models for three leg and five leg trans formers including saturation 2 Winding 3 Phase Transformer see page 232 3 Winding 3 Phase Transformer see page 235 New machine model Simple Brushless DC Machine see page 182 New semiconductor model Z
124. ff losses Probe Signals TRIAC voltage The voltage measured between the terminals TRIAC current The current flowing through the device to the terminal with the gate TRIAC conductivity Conduction state of the internal switch The signal outputs 0 when the TRIAC is blocking and 1 when it is conducting TRIAC conduction loss Continuous thermal conduction losses in watt W Only defined if the com ponent is placed on a heat sink TRIAC switching loss Instantaneous thermal switching losses in joule J Only defined if the component is placed on a heat sink 143 6 Block Reference 144 Induction Machine Purpose Library Description Non saturable induction machine with slip ring rotor Machines This model of a slip ring induction machine can only be used with the continu ous state space method If you want to use the discrete state space method or if you need to take saturation into account please use the Saturable Induction Machine see page 155 The machine model is based on a stationary reference frame Clarke transfor mation A sophisticated implementation of the Clarke transformation facil itates the connection of external inductances in series with the stator wind ings However external inductors cannot be connected to the rotor windings due to the current sources in the model In this case external inductors must be included in the leakage inductance of the rotor The machine operates as a motor o
125. forms a two dimensional vector in the stationary reference frame into a three phase signal alpha beta gt a b c Cancel Help Apply 269 6 Block Reference Stationary To Rotating Reference Frame Purpose Library Description Dialog Box 270 Transform a vector from the stationary to a rotating reference frame Extras Transformations This block transforms a two dimensional vector xa xg in the stationary refer ence frame into a vector ya yq in a rotating reference frame The first input is the vector za 15 The second input is the angle y between the rotating and the stationary frame y is given in radians Ya cosw it sinwy t Ley Yq sinwt coswyt LB Transformation SRF gt RAF mask Transforms a two dimensional vector from the stationary into a rotating reference frame The angle in radians between the rotating and the stationary frame is determined by the second input alpha beta phi gt d q Cancel Help Apply Rotating To Stationary Reference Frame Rotating To Stationary Reference Frame Purpose Library Description Dialog Box Transform a vector from a rotating to the stationary reference frame Extras Transformations This block transforms a two dimensional vector xq xq from a rotating refer ence frame into a vector ya ys in the stationary reference frame The first in put of the block is the vector 4 x4 The second input is the angle
126. g used only for purposes of documentation PLECS displays this string in the dialog box and appends mask in order to differ entiate masked subcircuits from built in components Mask Description The mask description is informative text that is displayed in the dialog box in the frame under the mask type Long lines of text are automatically wrapped 47 3 Using PLECS 48 Mask Editor Components Machines IM1 E Of xj Icon Parameters Probes Me Mask type Equirrel cage Induction Machine Mask description Three phase squirrel cage induction machine The input signal Tm represents the mechanical torque in Nm The vectorized output signal of width 3 contains the rotational speed wm in rad s the mechanical rotor position th in rad the electrical torque Te in Nm All parameters and electrical quantities are referred to the stator side OK Cancel Unmask Help Apply to fit into the dialog box You can force line breaks by using the Enter or Re turn key Unprotecting Masked Subcircuits If you define a mask icon for a Subcircuit block PLECS automatically protects the block and the underlying schematic You can no longer resize the Subcir cuit block or modify the sub schematic The purpose of this protection is to prevent the user from making unintentional changes that might render the icon useless If you want to change a masked Subcircuit block you can unprotect
127. h of the input signal The default is 2 207 6 Block Reference 208 Probe Signals Input The input signal Output The output signal Integrator Integrator Purpose Library Description re Parameters and Dialog Box Probe Signals Integrate a continuous signal Signals amp Systems The Integrator block outputs the integral of its continuous input signal at the current time step Simulation with the Continuous State Space Method When simulated with the continuous method the input signal is simply passed on to the Simulink solver along with the derivatives of the electrical states Simulation with the Discrete State Space Method When simulated with the discrete method the input signal is integrated within PLECS using the Forward Euler method Pree rIntegrator Integration of the input signal Parameters Name Integrator E Width E Ei Initial condition oO O B OK Cancel Help Apply Width The width of the input and output signal The default is 1 Initial condition The initial condition of the integrator State The internal state of the integrator 209 6 Block Reference e e Fourier Series Purpose Calculate a fourier series Library Signals amp Systems Description The Fourier Series block calculates the series y ao 5 an cos nx bn sin nx Fourier a Series lle as a function of the continuo
128. hase Rotating Reference Frame To 3 Phase Purpose Transform a vector in a rotating reference frame into a three phase signal Library Extras Transformations Description This block transforms a two dimensional vector xq xq in a rotating reference frame into a three phase signal ya yb yc The first input of the block is the dq vector xq zq The second input is the rotation angle y of the rotating refer cP ence frame y is given in radians Ya cos Y siny La y cos p 120 sin pp 120 Tq Ye cos p 120 sin y 120 The resulting three phase signal does not have any zero sequence component Dialog Box ax Transformation RRF gt 3ph mask Transforms a two dimensional vector in a rotating reference frame into a three phase signal The rotation angle in radians of the rotating reference frame is determined by the second input d q phi gt a b c Cancel Help Apply 273 6 Block Reference 274 Discrete Mean Value Purpose Calculate the running mean value of the input signal Library Extras Discrete Analysis Description This block calculates the running mean of the input signal based on discrete signal mean f Parameters and Dialog Box samples The sample time and the number of samples can be specified The block is implemented with a shift register and an accumulator The sample entering the shift register is added to the accumulator the sample exiting the
129. he continuous signal fed into the input of the component Note This component is based on a voltage controlled current source It may therefore not be connected in series with other current sources or inductors Parameters ola nd Dialog a Variable resistor Box Variable resistor with constant series inductance TParameters Name aL2 E Width E jar Inductance 1e 3 JA Initial current fo z OK Cancel Help Apply Width The width of the electrical ports resp the number of resistors inductors represented by the component Inductance The inductance in henries H All finite positive and negative values are accepted excluding 0 The default is 1e 3 If the parameter is a scalar all internal inductors have the same induc tance To specify the inductances individually in a vectorized component 105 6 Block Reference use a vector L L2 Ln The length n of the vector must correspond to the parameter Width Initial current The initial current through the component at simulation start in amperes A This parameter may either be a scalar or a vector with the width of the component The direction of a positive initial current is indicated by a small arrow in the component symbol The default of the initial current is O Probe Signals Inductor current The current flowing through the inductor in amperes A The direction of a positive current corresponds to the small arro
130. he thermal model via the Ambient Temperature block The power loss is calculated by multiplying the device voltage and the device current 65 4 Thermal Modeling 66 Command Line Interface PLECS offers a Command Line Interface CLI to access component and cir cuit parameters directly from the MATLAB command line The command for the CLI is plecsedit cmd parameterl parameter2 where cmd is one of the following commands get set version hostid Reading Parameters of Components The command plecsedit get componentPath parameter returns the value of parameter of the PLECS component indicated by the com ponentPath as a string If parameter is omitted a cell aray with all available parameters is returned Setting Parameters of Components plecsedit set componentPath parameter value sets the value of parameter of the PLECS component indicated by the compo nentPath to value 5 Command Line Interface 68 Other CLI commands Examples The command plecsedit version returns the PLECS version information as a string and plecsedit hostid returns a struct with hostid and MATLAB license information Some examples for using the command line interface plecsedit get mdl Circuit1 returns the parameters of Circuit1 in the simulink model mal plecsedit get mdl Circuit1 Name returns th
131. he time the copy is made If PLECS is unable to resolve a library reference it highlights the reference component and issues an error message You can fix an unresolved library reference in two ways e Delete the reference component and make a new copy of the library compo nent e Add the directory that contains the required Simulink model to the MAT LAB path and reload the circuit Libraries Updating a Library Reference Library references are only resolved upon loading of a circuit If you make changes to a library component you will need to close and reload all circuits that reference this component in order to propagate the changes Breaking a Library Reference You can break the link between a library reference and the library component The reference then becomes a simple copy of the library component changes to the library component no longer affect the copy In order to break the link between a reference and its library component se lect the reference component then choose Break library link from the Edit menu or from the component s context menu 37 3 Using PLECS 38 Connections Connections define the relationship and interaction between components PLECS knows different connection types that are explained in this section Wires Wires are ideal electrical connections between two points They are drawn in black color A wire can connect one electrical port with another Several elec trical ports c
132. hoose Look under mask from the Edit menu Electrical System i 1 w Y isa Rs Las Lir DA Ria td Ml AA SAA e NY Usd Lm d axis w y isa Rs Lis Lir H ra Rig dq pe CN MM 2 o Us q Lm q axis Induction Machine with Open Stator Windings 1s 0 Rs Us 0 Lis 0 axis The rotor flux is computed as Y a Lir ika Lm isa iha Op A Vig Lir tiq UN Lm isa sx tea The three phase voltages Usa Us p and vs across the individual stator wind ings are transformed into dq0 quantities 2 1 1 Us d 3 73 Usa 1 Al Us q 0 J J Urb 1 1 1 Us 0 3 3 3 Ur Likewise the stator currents in the stationary reference frame are trans formed back into three phase currents isa 1 0 1 isd 1 V3 x isb 5 3 7 1 s q 1 3 Us c 3 3 1 s 0 Electro Mechanical System Electromagnetic torque 3 ya sy amp To zP Im isa iza isa ie Mechanical System Mechanical rotor speed wm 1 Un 5 J Te Fwm Tm 153 6 Block Reference 154 Parameters Inputs and Outputs Probe Signals W pwm Mechanical rotor angle 0m m Wm 0 phm Most parameters for the Induction Machine with slip ring rotor see page 144 are also applicable for this machine Only the following parameter differs Initial stator currents A three element vector containing the initial stator currents is a 0 is b o and is co Of phase a b and c in amper
133. i Frequency rad sec 2pi 50 fal Phase rad fo El DK Cancel Help Apply Width The width of the component The default is 1 Each of the following parameters may either be a scalar or a vector with the width of the component AC Voltage Source Amplitude The amplitude A of the voltage in volts V The default is 1 Frequency The angular frequency w in s71 The default is 2 pi 50 which corre sponds to 50 Hz Phase The phase shift y in radians The default is 0 Probe Signals Source voltage The source voltage in volts V 73 6 Block Reference 74 Controlled Current Source Purpose Library Description Parameters and Dialog Box Probe Signals Generate a variable current Sources amp Meters The Controlled Current Source generates a variable current between its two electrical terminals The direction of a positive current through the component is marked with an arrow The momentary current is determined by the contin uous signal fed into the input of the component Note A current source must not be open circuited or connected in series to an inductor or any other current source lla Controlled Current Source Generate a variable current Parameters Name i E Width it tk ee OK Cancel Help Apply Width The width of the component This affects both the width of the electrical ports and the width of the input signal The default
134. i Ly Lm Ri Rnm L Lm R2 Rm la am aan ee gt E Em 1 1 e o In the symbol of the mutual inductance the primary winding is marked with a little circle The secondary winding is marked with a dot Parameters Self inductance and Dialog A two element vector containing the self inductance for the primary wind Box ing L and the secondary winding Ly The inductivity is given in henries H Winding resistance A two element vector containing the self resistance of the primary winding R and the secondary winding R in ohms Q Mutual inductance The mutual inductance L in henries H Mutual resistance The mutual resistance Rm in ohms Q 93 6 Block Reference Block parameters ll x 2 Winding Mutual Inductance mask Implements a magnetic coupling between two windings p Parameters gt Name Mutual Ind 2 E Self inductance L1 L2 foana o Winding resistance A1 R2 2 2 E Mutual inductance Lm foo o Mutual resistance Am E El Initial current i1 i2 10 0 E OK Cancel Help Apply Initial current A two element vector containing the initial currents on the primary side i and the secondary side i2 in amperes A The direction of positive cur rents is indicated by little arrows in the component symbol The default value is 0 0 94 3 Winding Mutual Inductance 3 Winding Mutual Inductance Purpose Library Description P
135. ia Combined rotor and load inertia J in Nms Friction coefficient Viscous friction F in Nms Number of pole pairs Number of pole pairs p Initial rotor speed Initial mechanical speed wm o in radians per second s71 Initial rotor position Initial mechanical rotor angle 0 9 in radians If m is an integer multiple of 27 p the d axis is aligned with phase a of the stator windings at simula tion start Initial stator currents A two element vector containing the initial stator currents is a o and is b 0 of phase a and b in amperes A Initial field current Initial current 7 o in the field winding in amperes A referred to the sta tor side Initial stator flux A two element vector containing the initial stator flux Y 4 o and Y qo in the rotor reference frame in Vs Inputs and Mechanical torque Outputs The input signal T represents the mechanical torque at the rotor shaft in Nm The output vector m contains the following 3 signals 1 Rotational speed The rotational speed wm of the rotor in radians per second s71 2 Rotor position The mechanical rotor angle 6 in radians 3 Electrical torque The electrical torque T of the machine in Nm 165 6 Block Reference Probe Signals Stator phase currents The three phase stator winding currents isa is and is in A Currents flowing into the machine are considered positive Field currents The excitation current i in A referred to the sta
136. ier frequency The frequency f of the triangular carrier signal 254 Sawtooth PVM Sawtooth PWM Purpose Library Description PWM generator with sawtooth carrier Extras Modulators 2 level PWM generator with a sawtooth carrier The input m is the modula tion index with a linear range of 1 1 The switching function s outputs ei ther 1 or 1 If the modulation index is a vector the switching function is also a vector of the same width The block can be used to control the 2 Level IGBT Converter see page 224 or the ideal 2 Level Converter see page 230 In these cases the modulation index must have a width of 3 to match the number of inverter legs The following figures illustrate different sampling methods offered by the modulator block In the figure on the left Natural Sampling is used The right figure shows Regular Sampling i e the modulation index is updated at the vertical flanks of the carrier In both figures carrier signals with falling ramps are employed Natural Sampling Regular Sampling Modulation index 1 f Switching function o l 255 6 Block Reference Parameters and Dialog Box 256 E Block Parameters Sawtooth PWM 2 x Sawtooth PWM mask Two level PWM generator with a sawtooth carrier The input m is the modulation index with a range of 1 1 The switching function s outputs either 1 or 1 If
137. including O and inf co The default is 1 If the parameter is a scalar all internal resistors have the same resis tance To specify individually the resistances in a vectorized component use a vector R R2 Rn The length n of the vector must correspond to the width of the component Inductor Inductor Purpose Library Description eT ss Parameters and Dialog Box Ideal inductor Passive Components This component provides one or multiple ideal inductors between its two elec trical terminals If the component is vectorized a magnetic coupling can be specified between the internal inductors Inductors may be switched in series only if their momentary currents are equal Pele rInductor Ideal inductor TParameters Name L1 E Width E zi Inductance 0 001 ln Initial current E B OK Cancel Help Apply Width The width of the electrical ports resp the number of ideal inductors repre sented by the component Inductance The inductance in henries H All finite positive and negative values are accepted including 0 The default is 0 001 If the parameter is a scalar all internal inductors have the same induc tance To specify individually the inductances in a vectorized component use a vector L L2 Ln The length n of the vector must correspond to the parameter Width 81 6 Block Reference pa a 20 ee UVa 0 La ESA 0 tiz Un 0
138. ing current values A vector of positive current values in amperes A defining the piece wise linear saturation characteristic of the transformer legs The current values must be positive and strictly monotonic increasing At least one value is required 233 6 Block Reference 234 Magnetizing flux values A vector of positive flux values in Vs defining the piece wise linear satura tion characteristic The flux values must be positive and strictly monotonic increasing The number of flux values must match the number of current values Core loss resistance An equivalent resistance Ry representing the iron losses in the trans former core The value in ohms 2 is referred to the primary side No of core legs The number of legs of the transformer core This value may either be 3 or 5 Phase lag of secondary side The phase angle between the primary side and the secondary side in de grees Unless the secondary side is in zig zag connection the angle can only be varied in steps of 60 Initial currents wdg 1 A vector containing the initial currents on the primary side 1 a 11 p and if the winding has a neutral point i1 lt The currents are given in amperes A and considered positive if flowing into the transformer The default is 0 O 0 Initial currents wdg 2 A vector containing the initial currents on the secondary side i2 12 1 and if the winding has a neutral point i The currents are given in amperes A
139. ing detection capability For this reason the continuous method can only be used with a variable step solver In general the default solver of Simulink ode45 is recommended However your choice of circuit parameters may lead to stiff differential equations e g if you have large resistors connected in series with inductors In this case you should choose one of Simulink s stiff solvers Discrete State Space Method When simulating a circuit with the discrete method PLECS transforms the circuit into a discrete state space model with fixed time steps The continuous state space equations are discretized using the bilinear transformation also 55 3 Using PLECS known as Tustin s method The integration of the state variables is thus re placed with a simple update rule Xn AdXn 1 Ba un F u 1 At At ae ie ecm We Me ype 1 Fa 1 Fa 1 Ba 34 Ali 2 2 where At is the discretization time step With line commutated power electronic devices such as diodes and thyristors the natural switching instants will generally not coincide with a time step of the discretized circuit model The Switch Manager detects such non sampled events and uses an interpolation scheme to ensure that the state variables are always consistent with the switch positions Options Sample time This parameter determines the rate with which Simulink samples the circuit A setting of auto or 1 means that the sample time is inh
140. ion Parameters and Dialog Box Three winding transformer Passive Components This transformer models three coupled windings on the same core The mag netization inductance Lm and the core loss resistance Rm are modeled as lin ear elements Their values are referred to the primary side A stiff solver is recommended if Rm is not infinite The electrical circuit for this component is given below ii L R Lo Ra i2 YYY A DRAN lt o o la Rm m3 L3 R3 13 A YY lt o o In the transformer symbol the primary side winding is marked with a little circle The secondary winding is marked with a dot at the outside terminal the tertiary winding with a dot at the inside terminal Leakage inductance A three element vector containing the leakage inductance of the primary side L the secondary side Lo and the tertiary side L3 The inductivity is given in henries H Winding resistance A three element vector containing the resistance of the primary winding R the secondary winding Ra and the tertiary winding R in ohms Q No of turns A three element vector containing the number of turns of the primary winding n the secondary winding n and the tertiary winding na Magnetization inductance The magnetization inductance Lm in henries H The value is referred to the primary side 91 6 Block Reference olock parameters ix rLinear 3 Winding Transformer mask link
141. ircuit Simulation Parameters switches and the currents and voltages measured in the circuit and decides whether a switching action is necessary If any switching occurs a new set of state space matrices is calculated on the fly Diode Turn On Threshold Voltage This parameter globally controls the turn on behavior of line commutated de vices such as diodes thyristors GTOs and similar semiconductors A diode starts conducting as soon as the voltage across it becomes larger than the sum of the forward voltage and the threshold voltage Similar conditions apply to the other line commutated devices The default value for this parameter is 1e 3 For most applications the threshold voltage could also be set to zero How ever in certain cases it is necessary to set this parameter to a small positive value to prevent line commutated devices from bouncing Bouncing occurs if a switch receives an opening command and a closing command repeatedly in subsequent simulation steps or even within the same simulation step Such a situation can arise in large stiff systems that contain many interconnected switches Continuous State Space Method When simulating a circuit with the continuous method PLECS employs the Simulink solver to solve the differential equation and integrate the state vari ables The Switch Manager communicates with the solver in order to ensure that switching occurs at the correct time This is done with Simulink s zero cross
142. iscrete Fourier transform of a periodic input signal based on discrete samples The sample time the number of samples and the harmonic order s can be specified The fundamental frequency f of the run ning window is 1 sample time x number of samples f The outputs of the block are the magnitude and phase angle of the specified harmonics If you specify more than one harmonic the outputs will be vectors with the corresponding width Alternatively you can specify a single harmonic and feed a vector signal into the block Note This block is only available for Matlab 7 0 or newer Block Parameters Discrete Fourier 2 x m Discrete Fourier Transform mask Performes a discrete Fourier transform of the input signal The fundamental frequency f1 of the averaging window is calculated as f 1 4 sample time number of samples The outputs contain the magnitude and phase in radians of the specified harmonics Their width corresponds to the harmonic orders specified Parameters Sample time 0 01 Number of samples 10 Harmonic orders n 01 2 Cancel Help Apply Discrete Fourier Transform Sample time The time interval between samples Number of samples The number of samples used to calculate the Fourier transform Harmonic orders n A scalar or vector specifying the harmonic component s you are interested in Enter 0 for the de component 1 for the fundamental component et
143. it by choosing Unprotect from the Edit menu or from the block s context menu You can later protect it again by choosing Protect from the same menus Circuit Browser Circuit Browser The Circuit Browser enables you to navigate a circuit diagram hierarchically To display the Circuit Browser select Show circuit browser from the Cir cuit browser options submenu of the View menu of the schematic editor JP CIGRE HVDC benchmark model File Edit View Simulation Format 3ph measurement 3ph measurementl id rect 75 deg 84 deg L 596 8e 3 R25 R25 AC system SCR 2 5 AC system SCR 2 5 Lower inverter Lower rectifier Upper inverter Upper rectifier vdSy0 transformer vdSy0 transformeri a amp AC system SCR 2 5 84 deg pulses rect The editor window splits into two panes The left pane shows a tree structured view of the circuit hierarchy The right pane displays the schematic of the selected sub circuit The first entry in the tree view corresponds to the top level schematic of your circuit A or sign next to a name indicates that the corresponding schematic contains one or more subcircuits By double clicking on the entry you can expand or collapse the list of these subcircuits To view the schematic of any sub circuit listed in the tree view select the entry by clicking on it Showing Masked Subcircuits By default the Circuit Browser does not list masked subcircuits Yo
144. l probably need computer simulations During the design phase this is usually the only way to predict how the system will behave under normal and faulty operating conditions For the simulation of purely electrical circuits there is a number of power ful programs available They allow the user to enter circuits as netlists or schematics However incorporating complex control structures requires a pro found knowledge of the specific program With some programs the integration of controls is extremely difficult The program Simulink is ideally suited for the simulation of controls There fore Simulink is also a convenient tool for the design of closed loop controlled Introduction 20 electrical systems Unfortunately it is rather difficult to model electrical cir cuits directly in Simulink because Simulink does not accept schematics or netlists If you want to do it you have to represent the circuits by mathemat ical formulae which must be set up anew for every change in the circuit This process takes a lot of time and is prone to errors PLECS is a toolbox that enhances Simulink with the capability to simulate electrical circuits directly You can simply enter a circuit as a schematic of electrical components At Simulink block level the circuit is then represented as a subsystem so you can build controls and other non electrical elements around it and take full advantage of the Simulink environment With PLECS you can arbitra
145. led heat flow Thermal The Controlled Heat Flow generates a variable heat flow between the two thermal ports The direction of a positive heat flow through the component is marked with an arrow The momentary heat flow is determined by the con tinuous signal fed into the input of the component Block parameters ioj xj Controlled Heat Flow Generate a variable heat flow pParameters Name A OK Cancel Help Apply Heat flow The heat flow in watts W Constant Heat Flow Constant Heat Flow Purpose Generate a constant heat flow Library Thermal Description The Constant Heat Flow generates a constant heat flow between the two ther mal ports The direction of a positive heat flow through the component is marked with an arrow Parameters and Dialog Box Probe Signals Pele rConstant Heat Flow Generate a constant heat flow Parameters Name Heat flow Po OK Cancel Help Apply Heat flow The magnitude of the heat flow in watts W The default is 1 Heat flow The heat flow in watts W 243 6 Block Reference 244 Thermometer Purpose Output the measured temperature Library Thermal Description The Thermometer measures the temperature difference between its two ther o gt Dialog Box Probe Signals mal ports or between the thermal port and thermal reference and provides it as a continuous signal at the output of
146. n 263 6 Block Reference 264 Blanking Time Purpose Library Description Parameters and Dialog Box Generate a commutation delay for 2 level inverter bridges Extras Modulators This block generates a blanking time for 2 level inverter bridges so that the turn on of one switch is delayed with respect to the turn off of the other switch in the same inverter leg The input s is a switching function generated by a 2 level modulator such as the Symmetrical PWM generator see page 252 The values of the output s are either 1 upper switch turned on 0 both switches off or 1 lower switch on If the input is a vector the output is also a vector of the same width 5 Block Parameters Blanking Time 2 x Blanking Time mask This block generates a blanking time for two level inverter bridges so that the turn on of one switch is delayed with respect to the turn off of the other switch in the inverter leg The input s is a switching function generated by a 2 level modulator The values of the output s are either 1 0 or 1 If the input is a vector the output is also a vector of the same width m Parameters Delay time 10e 6 Cancel Help Apply Delay time The delay in seconds s between the turn off of one switch and the turn on of the other switch in an inverter leg Blanking Time 3 Level Blanking Time 3 Level Purpose Generate a commutation delay for 3
147. n Since the machine ter minals have current source characteristic no external inductors may be con nected They must be included in the leakage inductances The machine can be used with both the continuous and the discrete state space method The machine operates as a motor or generator the sign of the mechanical torque determines the mode of operation positive for motoring negative for generating All electrical variables and parameters are viewed from the sta tor side In the component icon phase a of the stator winding and the positive pole of the field winding are marked with a dot In order to inspect the implementation please select the component in your circuit and choose Look under mask from the Edit menu If you want to make changes you must first choose Break library link and then Unpro tect both from the Edit menu Electrical System I rd 1 a k a R Wm Ya Lik d ES ta S C NY Va o Stator flux linkages a J I Wa Lis ia Lma ia Ug ika _ 1 Wa Lis tq Em ig T bg T ika 167 6 Block Reference J I il al wm Y Lie et Red A tq Rs an d Lis ks a LAA o vq Lm q o q axis The electrical system of the machine model is implemented with state variable equations that are derived from the equivalent circuit in the rotor reference frame The value of the main flux inductance Lm is not constant but depends on the main flux linkage Ym as ill
148. ne with Open Stator Windings 152 Saturable Induction Machine ooo o 155 Salient Pole Synchronous Machine 161 Round Rotor Synchronous Machine 167 Permanent Magnet Synchronous Machine 172 DC Machine gt tr sec e OR RARE 8 a ea ata 175 Brushless DC Machine 00002 ee eee 178 Simple Brushless DC Machine 004 182 Switched Reluctance Machine ooo oo 185 Signals amp Systems a 189 Continuous Input 189 Gate Input yh ees a ee al od ty 191 Continuous Output 192 Gate Output a SOE A 194 Electrical Port 24555504244 85 A Mee eR a 195 Continvious MUx soni eee AA RRR ee eS 196 Gate Mu osese a Phi AO de ME homens aed sel eh aise GEO feels 197 Continuous Demux ee 198 Gate Demuk vce Ge a ol are a ARE hae 199 Wire Mux ices 6 BRAD R RS OR a Ee ies 200 Electrical Ground o ee 201 SUBCIPCUIE esas ca deter SSS MAE Cake A Gt Gla el 202 Continuous Function 0 0 000 eee eee 203 Compare Function 0 2 0 a 205 Gate Function sanae e eS we Re eS 207 Inte sra ias a eR ROR ES AOE 209 Fourier Series 2 e e 210 Constant A Ae ee cote et dal oa te 211 1D Look Up Table 2 20 0 0 0000 2 e eee eee 212 Contents 2D Look Up Table 214 3D Look Up Table
149. ng the compo nent MOSFET with Diode see page 140 PLECS needs only six internal switches to simulate this converter Only the on resistances of the MOS FETs can be entered e The Detailed 2 Level MOSFET Converter is based on individual MOSFET see page 138 and Diode see page 123 components In this model you may specify forward voltages and on resistances separately for the MOSFETs and diodes block parameters ES 2 Level MOSFET Converter mask This block implements a three phase two level MOSFET converter The gate inputis a vector of three signals one per leg The upper MOSFET is turned on with a positive the lower one with a negative gate signal Block parameters 5 xi Detailed 2 Level MOSFET Converter mask This block implements a three phase two level MOSFET converter The gate inputis a vector of three signals one per leg The upper MOSFET is turned on with a positive the lower one with a negative gate signal Parameters Parameters Ens Name Petaledn2 Levelin OSFETInConw i P LevelnMOSFETINCONY E MOSFET on resistance Diode on resistance MOSFET on resistance Ron pc tec kel MOSFET on state voltage drop therm A M MOSFET on state voltage drop therm Diode on state voltage drop therm la la fa fo B MOSFET turn on loss therm Diode turn on loss therm MOSFET turn on loss therm MR m Heee J jal i B MOS
150. o Damper resistance Rkd Rkq fne 2 20 21 mj The input signal Tm represents the mechanical torque in Nm The vectorized output All parameters and electrical quantities are referred to the stator side Parameters Name fm Salient Pole E Stator resistance Rs Damper leakage inductance Ukd Ukq ce a 1e S E Inertia J fes J Friction coefficient F T Number of pole pairs p fs E Initial rotor speed wm0 Prprsorts fa Initial rotor position thmO pc Z m Initial stator currents isa0 isb0 jeo mj Initial field current if0 pc tk Initial stator flux Psisd0 Psisq0 foo el ENE Tightness of saturation transition Form factor fr defining the tightness of the transition between unsatu rated and saturated main flux inductance The default is 1 Field resistance d axis field winding resistance R in ohms 9 referred to the stator side Field leakage inductance d axis field winding leakage inductance L in henries H referred to the stator side Damper resistance A two element vector containing the damper winding resistance R q and k Of the d axis and the q axis The values in ohms Q are referred to Salient Pole Synchronous Machine the stator side Damper leakage inductance A two element vector containing the damper winding leakage inductance Lika and Lik q of the d axis and the q axis The values in henries H are referred to the stator side Inert
151. o Upost ipre T defining the total ther mal losses dissipated during a switching transition in joule J The de fault is meaning no thermal turn on resp turn off losses Probe Signals IGBT voltage The voltage measured between collector and emitter IGBT current The current through the IGBT flowing from collector to emitter IGBT conductivity Conduction state of the internal switch The signal outputs 0 when the IGBT is blocking and 1 when it is conducting IGBT conduction loss Continuous thermal conduction losses in watt W Only defined if the com ponent is placed on a heat sink IGBT switching loss Instantaneous thermal switching losses in joule J Only defined if the component is placed on a heat sink 135 6 Block Reference IGBT with Diode Purpose Ideal IGBT with ideal anti parallel diode Library Switches Description This model of an Insulated Gate Bipolar Transistor has an integrated anti parallel diode The diode is usually required in AC applications such as volt 5 age source inverters Dialog Box zix rideal IGBT with Diode IGBT with integrated anti parallel diode for AC applications Parameters Name cetz E Width fi Ei Initial conductivity pc tk tl On state voltage drop therm la jal Turn on loss therm la Ei Turn offloss therm la El OK Cancel Help Apply Width The width of the component This affects both the width
152. o the license server is lost after you have obtained a license PLECS will temporarily switch to the unlicensed mode Upon successful recon nection to the server PLECS will switch back to normal operation How to Use This Manual 18 In this manual we presume that you are already familiar with Simulink If you are new to both Simulink and PLECS you should get to know Simulink first Not only because you cannot use PLECS without it Also the user in terface of PLECS resembles Simulink so if you know Simulink you will intu itively be able to use PLECS Introduction PLECS stands for Piece wise Linear Electrical Circuit Simulation It is a tool box for the fast simulation of electrical circuits within the Simulink environ ment It is specially designed for power electronics systems but is also a pow erful tool for any combined simulation of electrical circuits and controls Concepts of PLECS This chapter introduces the two basic concepts underlying PLECS i e its in tegration in Simulink and the use of ideal switches You need to understand these concepts in order to take full advantage of the features of PLECS Integration into Simulink Many electrical systems consist of an electrical circuit and controllers Take power electronic systems as an example where high power semiconductor valves are switched on and off according to sophisticated control schemes If you want to study the behavior of such systems thoroughly you wil
153. oltage measured across the capacitor in volts V A positive voltage is measured when the potential at the terminal marked with is greater than the potential at the unmarked terminal 114 Saturable Transformers Saturable Transformers Purpose Library Description Parameters and Dialog Box Single phase transformers with two or three windings and core saturation Nonlinear These transformers model two or three coupled windings on the same core i i 2 iQ i m The core saturation characteristic is piece wise linear The magnetizing cur rent im and flux Ym value pairs are referred to the primary side To model a transformer without saturation enter 1 as the magnetizing current values and the desired magnetizing inductance Lm as the flux values A stiff Simulink solver is recommended if the iron losses are not negligible i e Rf is not infi nite In the transformer symbol the primary side winding is marked with a little circle The secondary winding is marked with a dot at the outside terminal the tertiary winding with a dot at the inside terminal Leakage inductance A vector containing the leakage inductance of the primary side L4 the sec ondary side L and if applicable the tertiary side L3 The inductivity is given in henries H Winding resistance A vector containing the resistance of the primary winding R the sec ondary winding R and if applicable the tertiary winding R in ohm
154. on loss and switching loss The vector elements are ordered ac cording to the natural sequence of commutation 221 6 Block Reference 222 Thyristor Rectifier Inverter Purpose Library Description Parameters and Dialog Boxes Probe Signals Three phase thyristor rectifier inverter Converters Implements a three phase rectifier or inverter based on the Thyristor model see page 130 The gate input is a vector of six signals ordered according to the natural sequence of commutation This sequence corresponds to the num bering of the thyristors in the electrical circuits below The rectifier is shown on the left side the inverter on the right e o o MU MU Es Poa Thy Thys ZN Thys Thy Thye Thy ao oa bo 4 e ob co oc Lf HE Lf ra le Thy a Thys ZN Thys Thy Thys Thys o o For a description of the parameters see the documentation of the Thyristor on page 130 The thyristor converters provide five probe signals each a vector containing the appropriate quantities of the six individual thyristors voltage current conduction loss and switching loss The vector elements are ordered according to the natural sequence of commutation Thyristor Rectifier Inverter Block parameters Block parameters istorinRectifier yristorininverter i 223 6 Block Reference 224
155. on of the conducting device in ohms Q The default is 0 The following parameters define the thermal behavior of the component For more information see chapter Thermal Modeling on page 59 On state voltage drop therm A 2 D function von T defining the voltage drop in volts V that is used for calculating the thermal conduction losses The default is meaning the voltage drop is calculated as von Vi Ron 1 Turn on loss therm Turn off loss therm 3 D functions Eon Upre ipost T and Eos Vpost ipre T defining the total ther mal losses dissipated during a switching transition in joule J The de fault is meaning no thermal turn on resp turn off losses Diode voltage The voltage measured between anode and cathode Diode current The current through the diode flowing from anode to cathode Diode conductivity Conduction state of the internal switch The signal outputs 0 when the diode is blocking and 1 when it is conducting Diode conduction loss Continuous thermal conduction losses in watt W Only defined if the com ponent is placed on a heat sink Diode switching loss Instantaneous thermal switching losses in joule J Only defined if the component is placed on a heat sink Diode with Reverse Recovery Diode with Reverse Recovery Purpose Behavioral model of a diode with reverse recovery Library Switches Description This component is a behavioral model of a diode which repro
156. onduction state of the MOSFET The MOSFET is initially blocking if the parameter evaluates to zero otherwise it is conducting The following parameters define the thermal behavior of the component For more information see chapter Thermal Modeling on page 59 On state voltage drop therm A 2 D function von i T defining the voltage drop in volts V that is used for calculating the thermal conduction losses The default is meaning the voltage drop is calculated as Von Ron 2 Turn on loss therm Turn off loss therm 3 D functions Eon Upre ipost T and Eos Upost ipre T defining the total ther mal losses dissipated during a switching transition in joule J The de fault is meaning no thermal turn on resp turn off losses MOSFET voltage The voltage measured between drain and source MOSFET current The current through the MOSFET flowing from drain to source MOSFET conductivity Conduction state of the internal switch The signal outputs 0 when the MOSFET is blocking and 1 when it is conducting MOSFET conduction loss Continuous thermal conduction losses in watt W Only defined if the com ponent is placed on a heat sink MOSET switching loss Instantaneous thermal switching losses in joule J Only defined if the component is placed on a heat sink 139 6 Block Reference MOSFET with Diode Purpose Ideal MOSFET with ideal anti parallel diode Library Switches Description This model of a Metal
157. onfig m to configure PLECS Type edit plecsconfig at the MATLAB command prompt It contains entries in the form config parameter value Change the values in these lines to your needs The parameter drawANSI sets whether resistors and capacitors are drawn in DIN 0 or ANSI 1 style Table 3 1 shows the different component represen tation for both settings Note You may also copy the file plecsconfig m to your MATLAB home di rectory to your working directory or anywhere else on your MATLAB path if you want to configure PLECS per user To find the path to the currently active configuration file type which plecsconfig at the MATLAB command prompt 3 Using PLECS Table 3 1 Components Drawn in DIN or ANSI format DIN 0 ANSI 1 te ANo i T Creating a New Circuit Open the PLECS library by typing plecslib at the MATLAB command prompt On Windows you can also use the Simulink library browser and click on the entry PLECS Copy the Circuit block from the PLECS library into your Simulink model then double click the block to open the schematic editor E Library plecslib lol xj File Edit View Format Help DISES teel PLECS PLECS b Circuit Probe Probe Circuit amy a Le Components PLECS PLECS Library 1 5 Copyright 2002 2006 Plexim GmbH under license from ETH Zurich Ready 100 Locked h 32 Using the Component Browser Using the Component Browser A doubl
158. ontinuous Output Block parameters 193 6 Block Reference 194 Gate Output Purpose Library Description Parameters and Dialog Box Create an output terminal for a gate signal Signals amp Systems Gate outputs are used to feed discontinuous gate signals from a PLECS cir cuit back to Simulink or from a subcircuit to the parent circuit If you copy an output block into a schematic an output terminal will be created on the cor responding subsystem block The name of the output block will appear as the terminal label If you choose to hide the block name by unselecting the show button in the dialog box the terminal label will also disappear The Gate Out put block can be distinguished from the Continuous Output block see page 192 by the brown instead of a green input terminal zix Gate Outport Provide a gate output port for a circuit or subcircuit Parameters Name GateDutl E Width E E Port number PM DK Cancel Help Apply Width The width of the output signal The default is 1 Port number The terminal number of the output block This parameter appears only if the block is placed in a top level circuit Electrical Port Electrical Port Purpose Library Description Ce Dialog Box Provide an electrical port for a subcircuit Signals amp Systems Electrical ports are used to establish electrical connections between
159. op gain 1e6 af Output voltage limits min Ymax t1010 nl OK Cancel Help Apply Open loop gain The voltage gain of the amplifier if operating in linear mode The default is 1e6 Output voltage limits A two element vector containing the minimum and maximum output volt age Vmin and Vmax in volts V The default is 10 10 219 6 Block Reference 220 Diode Rectifier Purpose Library Description Parameters and Dialog Box Three phase diode rectifier Converters Implements a three phase rectifier based on the Diode model see page 123 The electrical circuit for the rectifier is given below Z Di D3 Z Ds act b Ce ooo Cc gt ZN Da De Z Da o Block parameters jol x Diode Rectifier mask This block implements a three phase diode rectifier Parameters Name Pioden ectifier E Diode forward voltage Vf pc tk Diode on resistance Ron pc ke tt Diode on state voltage drop therm la fa Diode turn on loss therm la fal Diode turn off loss therm la fal OK Cancel Help Apply For a description of the parameters see the documentation of the Diode on page 123 Diode Rectifier Probe Signals The Diode Rectifier provides five probe signals each a vector containing the appropriate quantities of the six individual diodes voltage current conduc tivity conducti
160. orts resp the number of variable inductors represented by the component Initial current The initial current through the inductor at simulation start in amperes A This parameter may either be a scalar or a vector with the width of the component The direction of a positive initial current is indicated by a small arrow in the component symbol The default of the initial current is 0 Probe Signals Inductor current The current flowing through the inductor in amperes A The direction of a positive current corresponds to the small arrow at one of the terminals 102 Variable Resistor with Variable Series Inductor Variable Resistor with Variable Series Inductor Purpose Library Description Parameters and Dialog Box Variable resistor with variable series inductor Nonlinear This component models a variable resistor with a variable inductor connected in series The resistance and inductance are determined by the continuous sig nals fed into the inputs of the component The voltage across this component is determined by the equation y Rit Led n 52 iti i Therefore the control signal for the inductor is a vector twice as wide as the width of the component It contains both the momentary inductance values and their derivatives with respect to time L L Ln L1 L Ln It is the responsibility of the user to provide the correct derivatives The momen tary inductance may not be set to zero Note e
161. ous simulation options such as the method used for simulating a circuit and related parameters To open the param eter dialog select PLECS parameters from the Simulation menu of the schematic editor Working Principle of PLECS PLECS is based on a piece wise linear state space approach A circuit con taining only linear components can be described mathematically by one set of time invariant equations x Ax Bu y Cx Du where x is the state variable vector with the inductor currents and capacitor voltages and u is the input vector with the source voltages and currents The output vector y contains voltages and currents measured in the circuit If a circuit consists not only of linear components but also of one or more ideal switches every combination of switch positions i e open closed is described by a different set of matrices The basic working principle of PLECS is outlined in the figure below When you start a simulation PLECS analyzes your circuit schematic and builds the state space model for the initial switch positions i e in general all open During the simulation the Switch Manager monitors the gate signals of the S a E measure continuous Ta e Es ments inputs B A A c m TEE o lo Cc a lo gt Di E a 5 ate I 9 3 inputs Y PLECS S function A 54 C
162. p therm A 2 D function von T defining the voltage drop in volts V that is used for calculating the thermal conduction losses The default is meaning the voltage drop is calculated as von Vs Ron 1 Turn on loss therm Turn off loss therm 3 D functions Eon Upre ipost T and Eo Upost ipre T defining the total ther mal losses dissipated during a switching transition in joule J The de fault is meaning no thermal turn on resp turn off losses GTO voltage The voltage measured between anode and cathode GTO current The current through the GTO flowing from anode to cathode GTO conductivity Conduction state of the internal switch The signal outputs 0 when the GTO is blocking and 1 when it is conducting GTO conduction loss Continuous thermal conduction losses in watt W Only defined if the com ponent is placed on a heat sink GTO switching loss Instantaneous thermal switching losses in joule J Only defined if the component is placed on a heat sink 133 6 Block Reference 134 IGBT Purpose Library Description A Parameters and Dialog Box Ideal IGBT with or without forward voltage and on resistance Switches The Insulated Gate Bipolar Transistor is a semiconductor switch that is con trolled via the external gate It conducts a current from collector to emitter only if the gate signal is not zero Block parameters 5 oj xj IGBT The IGBT is closed while a non
163. pated during a switching transition in joule J The de fault is meaning no thermal turn on resp turn off losses Probe Signals Device voltage The voltage measured between drain and source The device voltage can never be negative Device current The current through the device The current is positive if it flows through the MOSFET from drain to source and negative if it flows through the diode from source to drain Device conductivity Conduction state of the internal switch The signal outputs 0 when the device is blocking and 1 when it is conducting Device conduction loss Continuous thermal conduction losses in watt W Only defined if the com ponent is placed on a heat sink Device switching loss Instantaneous thermal switching losses in joule J Only defined if the component is placed on a heat sink 141 6 Block Reference 142 TRIAC Purpose Library Description xs Parameters and Dialog Box Ideal TRIAC with or without forward voltage and on resistance Switches The TRIAC can conduct current in both directions It is built using two anti parallel thyristors see page 130 and controlled by an external gate signal The TRIAC is modeled by two ideal switches that close if the voltage is pos itive and a non zero gate signal is applied The conducting switch remains closed until the current becomes zero A TRIAC cannot be switched off via the gate ox TRIAG The triac is a semicond
164. pecifies the number of scalar outputs If this format is used all output signals have a width of 1 Vector The length of the vector determines the number of outputs Each element specifies the width of the corresponding output signal Gate Demux Gate Demux Purpose Split a vectorized gate signal Library Signals amp Systems Description This demultiplexer extracts the components of a gate input signal and outputs them as separate signals The output signals may be scalars or vectors In the block icon the first output is marked with a dot When you change the num ber of outputs all signals will be disconnected from the block If you want to split vectorized continuous signals use the Continuous Demux block see page 198 The Gate Demux icon can be distinguished from the Continuous Mux by brown instead of green terminals arameters lola and Dialog 3 Gate Demultiplexer Box Split vectorized gate signal into smaller vectors Parameters Name GDemux fa Number of outputs fa E OK Cancel Help Apply Number of outputs This parameters allows you to specify the number and width of the output signals You can choose between the following formats for this parameter Scalar A scalar specifies the number of scalar outputs If this format is used all output signals have a width of 1 Vector The length of the vector determines the number of outputs Each element specifies the width of the corr
165. pling Carrier frequency The frequency f of the triangular carrier signals Negative carrier Select the phase shift between the negative and positive carrier signals The negative carrier may be constructed from the positive carrier either by flipping or shifting 259 6 Block Reference 260 Sawtooth PWM 3 Level Purpose Library Description 3 level PWM generator with sawtooth carrier Extras Modulators 3 level PWM generator with a sawtooth carrier The input m is the modula tion index with a linear range of 1 1 The switching function s outputs ei ther 1 0 or 1 If the modulation index is a vector the switching function is also a vector of the same width The block can be used to control the 3 Level IGBT Converter see page 226 or the ideal 3 Level Converter see page 231 In these cases the modulation index must have a width of 3 to match the number of inverter legs The figures below illustrate different sampling methods offered by the modula tor block In the left figure Natural Sampling is used The right figure shows Regular Sampling i e the modulation index is updated at the vertical flanks of the carrier In both figures carrier signals with rising ramps are employed Natural sampling Regular sampling Modulation index 1 f Switching function Sawtooth PWM 3 Level Parameters and Dialog Box i Block Parameters
166. put is always a scalar continuous signal The expression may consist of one or more of the following components e u the input of the block If the input is vectorized u i or u i repre sents the ith element of the vector To access the first element enter u 1 u 1 or u alone e Brackets e Numeric constants e Arithmetic operators e Mathematical functions abs acos asin atan atan2 cos cosh exp log log10 pow sgn sin sinh sqrt tan and tanh e MATLAB workspace variables Parameters aii d Di l Block parameters 5 xi an 1a og Continuous function 7 Box Function block for processing continuous signals Parameters Name Fen H Expression ult Pul2 ja Input width 2 E OK Cancel Help Apply Expression The expression applied to the input signal in C language syntax Input width The width of the input signal The default is 2 203 6 Block Reference 204 Probe Signals Input The input signal Output The output signal Compare Function Compare Function Purpose Library Description Apply a compare expression to a continuous signal Signals amp Systems The Compare Function block generates a gate signal from a continuous signal by means of relational operators The input may be a scalar or vectorized con tinuous signal the output is always a scalar gate signal The expression has C language syntax and may consist of one or mor
167. r generator the sign of the mechanical torque determines the mode of operation positive for motoring negative for generating All electrical variables and parameters are viewed from the sta tor side In the component icon phase a of the stator and rotor windings is marked with a dot In order to inspect the implementation please select the component in your circuit and choose Look under mask from the Edit menu If you want to make changes you must first choose Break library link and then Unpro tect both from the Edit menu Electrical System w Ww isa Rs Lis Lir tna Ria ia az MNM OMA Y as de Usd Lm Und d axis Induction Machine 7 aa 1 isq Fes Lis Li ES Ya Rig tg ts SOON ONDA a ey Us q Lm Wa q axis The rotor flux is computed as row Vid Lir trd ga Lm isa T ira Oop a Vr Lir Yat Lm isq us ig The three phase voltages vs ap and vs pc at the stator terminals are trans formed into dq quantities 2 1 Usd 3 3 Us ab v E 0 vV s q V3 r bc Likewise the stator currents in the stationary reference frame are trans formed back into three phase currents tga 1 0 2 1 V3 i s d s b TQ Ta i 1 3 ts q c Ta 2 Similar equations apply to the voltages and currents at the rotor terminals with 0 being the electrical rotor position ae 2 cosg cos 6 2 v ERa 3 r ab Ua 3 sin sin 0 22 Vea ira cos 0 sin O i ip cos 0 4 sin 6 22 Pi i
168. r information on how to change the graphical representation of thermal resistors ola gt Thermal Resistor Thermal resistor Parameters Name Pith E Thermal resistance fi El OK Cancel Help Apply Thermal resistance The resistance in K W All positive and negative values are accepted in cluding O and inf co The default is 1 Thermal Capacitor Thermal Capacitor Purpose Library Description age 0 oO LI hull Parameters and Dialog Box Ideal thermal capacitor Thermal This component provides an ideal thermal capacitance between its two ther mal ports or between the thermal port and the thermal reference See section Configuring PLECS in chapter Using PLECS for information on how to change the graphical representation of thermal capacitors Block parameters 5 xj Thermal Capacitor Thermal capacitor Parameters Name bm o Thermal capacitance fi mi Initial temperature DIN k OK Cancel Help Apply Capacitance The value of the capacitor in farads F All finite positive and negative values are accepted including 0 The default is 1 Initial temperature The initial temperature difference between the thermal ports or between the thermal port and thermal reference at simulation start in kelvins K The default is 0 247 6 Block Reference Probe Signals Temperature The temperature diffe
169. r of samples can be specified The fundamental frequency f of the running window is _ 1 sample time x number of samples The Discrete RMS Value block is implemented with the Discrete Mean Value block see page 274 Note This block is only available for Matlab 7 0 or newer Block Parameters Discrete RMS Value 21xj Discrete RMS Value mask Computes the root mean square value of a periodic signal The input signal is sampled with the sample time specified The fundamental frequency f1 of the running window is calculated as Al 1 sample time number of samples The initial condition describes the input signal before simulation start It can either be a scalar or a vector matching the number of samples Parameters Initial condition 0 Sample time Joo Number of samples 10 Cancel Help Apply Initial condition The initial condition describes the input signal before simulation start This parameter may either be a scalar or a vector matching the number of samples The default is 0 Discrete RMS Value Sample time The time interval between samples Number of samples The number of samples used to calculate the RMS value 277 6 Block Reference Discrete Fourier Transform Purpose Library Description Parameters and Dialog Box 278 Perform a discrete Fourier transform of the input signal Extras Discrete Analysis This block calculates the d
170. r own reusable components For more information see Masking Subcircuits on page 48 You can create a subcircuit in two ways e Add a Subcircuit block to your schematic then open that block and add the blocks it contains to the subcircuit e Select a number of blocks then group those blocks into a subcircuit Creating a Subcircuit by Adding the Subcircuit Block To create a new subcircuit first add a Subcircuit block to the schematic then add the elements that make up the subcircuit 1 Copy the Subcircuit block from the Signals amp Systems library into your schematic 2 Double click on the Subcircuit block in order to open it 3 In the empty Subcircuit window build the subcircuit Use the different ter minal blocks i e Inports Outports and the Electrical Port to configure the interface of the subcircuit Creating a Subcircuit by Grouping Existing Blocks If a schematic already contains the blocks you want to convert to a subcircuit you can create the subcircuit by grouping those blocks 1 Select the blocks and connections that you want to include in the subcircuit within a bounding box 2 Choose Create subcircuit from the Edit menu PLECS replaces the se lected blocks with a Subcircuit block Subcircuits Arranging Subcircuit Terminals When you add a terminal block to a subcircuit schematic a corresponding ter minal appears at a free slot on the border of the Subcircuit block If necessary the Su
171. r speed d 1 w To Fw Tm dt J Rotor angle d 0 w dt Parameters 5d Dial la a a og 6 4 Switched Reluctance Machine mask Box Switched reluctance machine with four rotor poles and six stator poles The input signal Tm represents the mechanical torque in Nm The vectorized output signal of width 6 contains the rotational speed wm in rad s the mechanical rotor position th in rad the electrical torque Te in Nm the flux linkages in the individual stator phases Parameters Name Br gt Stator resistance R Inertia J os poe J Unaligned inductance Lu Friction coefficient F Peres a poo Gf Initial aligned inductance La Initial rotor speed w0 pees PO J Saturated aligned inductance Lsat Initial rotor angle thO pes ip q Aligned saturation flux linkage Psisat Initial stator currents a0 ib0 ic0 pess Jpo a y OK Cancel Help Apply Stator resistance Stator resistance R in ohms Q Unaligned stator inductance Stator inductance L in the unaligned rotor position in henries H Initial aligned stator inductance Initial stator inductance L in the aligned rotor position in henries H Saturated aligned stator inductance Saturated stator inductance Lsat in the aligned rotor position in henries H 187 6 Block Reference Inputs and Outputs References 188 Aligned saturation flux linkage Flux linkage Va at which
172. r speed wm 1 eee A Po Ta J Om Um Parameters Most parameters for the Salient Pole Synchronous Machine see page 161 are and Dialog also applicable to this round rotor machine The following parameters are dif Box ferent Unsaturated magnetizing inductance The unsaturated magnetizing inductance Lm The value in henries H is referred to the stator side Saturated magnetizing inductance The saturated magnetizing inductance Ly sat in H If no saturation is to be modeled set Lm sat Lm o Damper resistance A three element vector containing the damper winding resistance Rj q Ri q and Rj 2 of the d axis and the q axis The values in ohms Q are referred to the stator side Damper leakage inductance A three element vector containing the damper winding leakage inductance Lika Eix q1 and Lik of the d axis and the q axis The values in henries H are referred to the stator side 169 6 Block Reference 170 Inputs and Outputs Probe Signals Block parameters 5 xj Round Rotor Synchronous Machine mask The input signal Tm represents the mechanical torque in Nm The vectorized output signal of width 3 contains the rotational speed wm in rad s the mechanical rotor position th in rad the electrical torque Te in Nm eso Stator leakage inductance Lis A Unsat magn inductance Lm0 Bs uO Saturated magn inductance Lmsat ee s z Magn flux at sat transition PsiT
173. ration in the Q D synchronous ma chine model IEEE Transactions on Energy Conversion Vol 13 No 3 Sept 1998 E Levi Modelling of magnetic saturation in smooth air gap synchronous machines IEEE Transactions on Energy Conversion Vol 12 No 2 March 1997 E Levi Impact of cross saturation on accuracy of saturated synchronous machine models IEEE Transactions on Energy Conversion Vol 15 No 2 June 2000 171 6 Block Reference 172 Permanent Magnet Synchronous Machine Purpose Synchronous machine excited by permanent magnets Library Machines Description This machine is modeled in the rotor reference frame The machine operates as a motor or generator the sign of the mechanical torque determines the mode of operation positive for motoring negative for generating All elec trical variables and parameters are viewed from the stator side In the compo nent icon phase a is marked with a dot Electrical System Dio ld Rs m Pa 7 C F Ly Va La o d axis i R Wm Pd q e Vq Ly f o q axis Stator flux linkages Pa Lata Pa Lala On Electromagnetic torque 3 f To 3P paty Yq ia Permanent Magnet Synchronous Machine Parameters and Dialog Box Mechanical System Mechanical rotor speed wm ee ee S Wm 5 e Wm tm J Om Wm alo rPermanent Magnet Synchronous Machine mask The input signal Tm represents the mechanical torque
174. re cos 22 sin 22 di 145 6 Block Reference 146 Parameters and Dialog Box Electro Mechanical System Electromagnetic torque 3 2 a v g Te Dim is q ita 15 4 iha Mechanical System Mechanical rotor speed wm 1 Wm 7 Te Fwm Tm W Pm Mechanical rotor angle 8m On Wm 0 P Om OT T rInduction Machine mask Three phase induction machine The input signal Tm represents the mechanical torque in Nm The vectorized output signal of width 3 contains the rotational speed wm in rad s the mechanical rotor position th in rad the electrical torque Te in Nm All parameters and electrical quantities are referred to the stator side Parameters Name fra 1 a Stator resistance Rs Friction coefficient F E Stator leakage inductance Us Number of pole pairs p poe i DN Rotor resistance Rr Initial rotor speed wm0 bs le Rotor leakage inductance Ur Initial rotor position thm0 pes Sp m Magnetizing inductance Lm Initial stator currents isa0 isb0 fes fot es Inertia J Initial stator flux psisdO psisq0 Pr if fe OK Cancel Help apiy Induction Machine Stator resistance Stator winding resistance R in ohms Q Stator leakage inductance Stator leakage inductance Ls in henries H Rotor resistance Rotor winding resistance R in ohms Q referred to the stator side Rotor leakage inductance Rotor leakage ind
175. ree phase rotor winding currents ii a ipp and i lt in A referred to the stator side Currents flowing into the machine are considered positive Stator flux dq The stator flux linkages Y q and Y in the stationary reference frame in Vs p3 Ysa T Lis tsa T Lm isa T a A Wa Vs q Lis ls q T Lm isa Tv lea Magnetizing flux dq The magnetizing flux linkages Ym and V in the stationary reference frame in Vs Wind Lm lza T ina Uma Lm leg a Rotor flux dq The rotor flux linkages Y and Y in the stationary reference frame in Vs l Rotational speed The rotational speed wm of the rotor in radians per second s71 Rotor position The mechanical rotor angle 0m in radians Electrical torque The electrical torque T of the machine in Nm Squirrel Cage Induction Machine Squirrel Cage Induction Machine Purpose Library Description Non saturable induction machine with squirrel cage rotor Machines This model of a squirrel cage induction machine can only be used with the continuous state space method If you want to use the discrete state space method or if you need to take saturation into account please use the Sat urable Induction Machine see page 155 and short circuit the rotor terminals The machine model is based on a stationary reference frame Clarke transfor mation A sophisticated implementation of the Clarke transformation facil itates the connection of e
176. refer ence node All thermal losses absorbed by the heat sink flow into this capaci tance and therefore raise the heat sink temperature Heat exchange with the environment occurs via the external connectors H ay _ i O gt DF7O gt 0 Thermal L l Heatsink losses temperature HeatSink You may set the intrinsic capacitance to zero but then you must connect the heat sink either to an external thermal capacitance or to a fixed temperature i e the Constant Temperature block see page 241 or the Controlled Tempera ture block see page 240 Thermal Loss Dissipation There are two classes of intrinsic components that dissipate thermal losses semiconductor switches and ohmic resistors Semiconductor Losses Power semiconductors dissipate losses due to their non ideal nature These losses can be classified as conduction losses and switching losses For com pleteness the blocking losses due to leakage currents need to be mentioned but these can usually be neglected Conduction Losses The conduction losses can be computed in a straightforward manner as the product of the device current and the device voltage By default the on state voltage is calculated from the electrical device parameters as v V Ron 1 60 Thermal Loss Dissipation However PLECS also allows you to specify the on state voltage used for the loss calculation as an arbitrary function of the device current and the device temp
177. rence measured across the capacitance A positive value is measured when the temperature at the terminal marked with is greater than the temperature at the unmarked terminal 248 Thermal Ground Thermal Ground Purpose Provide a connection to the thermal reference Library Thermal Description The Thermal Ground implements a connection to the thermal reference a Dialog Box ala Thermal Ground Provide a thermal ground connection pParameters Name fran OK Cancel Help Apply 249 6 Block Reference 250 Ambient Temperature Purpose Provide a connection to the ambient temperature Library Thermal Description The Ambient Temperature is only useful in subcircuits When placed in a sub V Dialog Box circuit it provides a thermal connection to the heat sink that encloses the subcircuit For more information see section Heat Sinks and Subcircuits on page 64 Note Ambient Temperature blocks may not be used in schematics that con tain Thermal Port blocks see page 251 AE Ambient Temperature Connect to ambient temperature pParameters Name ambient oK Cancel Help Apply Thermal Port Thermal Port Purpose Library Description Ca Dialog Box Provide a thermal port for a subcircuit Thermal Thermal ports are used to establish thermal connections between a PLECS circuit and a subcircuit see page 202
178. rical PWM 3 LeveD ooo eee 257 Sawtooth PWM 3 Level o oo e 260 3 Phase Overmodulati0O o o 262 Blanking Time m y ta o a Poe 8 264 Blanking Time 3 Level o o 265 6 Pulse Generator o 266 2 Pulse Generator o e 267 Transformati0ns e a aae a BEATA ee ee 268 3 Phase To Stationary Reference Frame 268 Stationary Reference Frame To 3 Phase 269 Stationary To Rotating Reference Frame 270 Rotating To Stationary Reference Frame 271 3 Phase To Rotating Reference Frame 272 Rotating Reference Frame To 38 Phase 273 Discrete Analysis aoreet eee aaa ko Pea nt 274 Discrete Mean Value o o 274 Discrete RMS Value o eee eee 276 Discrete Fourier Transform o 278 Discrete Total Harmonic Distortion 280 Control Blocks 020440000 dt a A ee 282 AMC A A 282 Before You Begin Installing PLECS Installing PLECS on your system is pretty easy You do not need to have sys tem administrator permissions Since PLECS requires MATLAB and Simulink make sure these programs are installed on your system Table 1 shows the platforms and MATLAB versions that are currently supported by PLECS Table 1 System requirements Platform MATLAB Version 5 3 6 0 6
179. rily assemble circuits from library components or you can use your own elements The list of library components includes various voltage and current sources meters passive components switches and complex components such as electrical machines Sources meters and switches form the interface between the electrical circuit and the control sys tem The inputs of the Simulink subsystem that represents the circuit are the commands for controlled sources and switches The outputs provide the mea surements taken by volt and ammeters The concept of integration into Simulink has the advantage that only the part of the system in which electrical units are of interest needs to be modeled as an electrical circuit The simulation of all non electrical parts can be done in Simulink Although PLECS also provides some signal processing features these should be used as little as possible It is Simulink that has its strengths in this field Ideal Switches Most circuit simulation programs model switches as highly nonlinear ele ments Due to steep voltage and current flanks the simulation becomes slow when switches are toggled In the simplest case a switch is modeled as a vari able resistance between 0 an co In other cases it is represented by a sophisti cated semiconductor model When we simulate complex power electronic systems however the processes during switching are of little interest Here it is more appropriate to use ideal switches that
180. rmonic Distortion Number of samples The number of samples used to calculate the THD 281 6 Block Reference 282 Timer Purpose Library Description Parameters and Dialog Box Generate a piece wise constant signal Extras Control Blocks The Timer block generates a signal that changes at discrete instants and is otherwise constant You can use the Timer block e g in order to control switches such as circuit breakers Note This block is only available for Matlab 7 0 or newer Timer mask Generates a piece wise constant signal The output changes at the specified time values Before the first time value is reached the output is zero m Parameters Time values jn 233 5 Output values In 1250 Cancel Help Apply Time values A vector containing the transition times This vector must have the same length as the vector of output values Before the first transition time the output is zero Output values A vector containing the output values corresponding to the transition times This vector must have the same length as the vector of time values
181. rn off loss therm la c i El OK Cancel Help Apply la Bi Clamping diode turn on loss therm la B Clamping diode turn off loss therm a OK Cancel Help sy For a description of the parameters see the documentation of the IGBT with Diode on page 136 the IGBT on page 134 and the Diode on page 123 The three level IGBT converters provide 30 probe signals grouped by leg Each signal is a vector containing the appropriate quantities of the individ ual devices voltage current conductivity conduction loss and switching loss The vector elements are ordered top to bottom For the Detailed 3 Level IGBT Converter the diode probe signal vectors are in the order anti parallel diodes top to bottom clamping diodes top to bottom 227 6 Block Reference 228 2 Level MOSFET Converter Purpose Library Description Parameters and Dialog Boxes Three phase two level MOSFET converter Converters Implements a three phase two level MOSFET converter with reverse diodes The gate input is a vector of three signals one per leg The upper MOSFET connected to the positive dc level is on if the corresponding gate signal is posi tive The lower MOSFET is on if the gate signal is negative If the gate signal is zero both MOSFETs in the leg are switched off You can choose between two different converter models e The basic 2 Level MOSFET Converter is modeled usi
182. ry Nonlinear Description This component models a variable resistor with a constant capacitor connected in parallel The resistance is determined by the continuous signal fed into the input of the component It may not be set to zero Note This component is based on a current controlled voltage source It may therefore not be connected in parallel with other voltage sources or capacitors alg es ba PSE an la og rVarResistorConstCapacitor Box Variable resistor with constant parallel capacitor Parameters Name RC2 E Width E z Capacitance 100 6 al Initial voltage fo z OK Cancel Help Apply Width The width of the electrical ports resp the number of resistors capacitors represented by the component Capacitance The value of the capacitor in farads F All finite positive and negative values are accepted excluding 0 The default is 100e 6 If the parameter is a scalar all internal capacitors have the same value To specify the capacitances individually in a vectorized component use a vector C1 C2 C The length n of the vector must correspond to the parameter Width 113 6 Block Reference Initial voltage The initial voltage of the capacitor at simulation start in volts V This parameter may either be a scalar or a vector with the width of the compo nent The positive pole is marked with a The initial voltage default is 0 Probe Signals Capacitor voltage The v
183. s Q 115 6 Block Reference AE lola 12 inding Transformer mask link gt r3Winding Transformer mask link This transformer models two coupled windings on the same core This transformer models three coupled windings on the same core The The piece wise linear core saturation characteristic is referred to piece wise linear core saturation characteristic is referred to the primary the primary side To model a transformer without saturation enter side To model a transformer without saturation enter 1 as magn 1 as magn current values and the magnetization inductance as current values and the magnetization inductance as flux values A stiff flux values A stiff solver is recommended if Rfe is not infinite solver is recommended if Rfe is not infinite Parameters Parameters Name Name Saturable Trafo2 Saturable Trafo3 E Leakage inductance L1 L2 Magnetizing flux values Leakage inductance L1 L2 L3 Magnetizing flux values 0 01 0 001 Fr 0 1 0 2 j 0 01 0 001 0 001 E 0 1 0 2 F Winding resistance R1 R2 Core loss resistance Rfe Winding resistance R1 R2 R3 Core loss resistance Rfe fot int ja n011 m int E No of turns n1 n2 Initial current i1 i2 No turns n1 n2 n3 Initial current i1 i2 i3 n01 m oo E n013 Fi 000 El Magnetizing current values Magnetizing current values 1 10 1 10 E DK Cancel Help Apply OK Cancel Help
184. s connected to the positive terminal upon a positive gate signal and else to the negative terminal Parameters Name 2LevelConveter E DK Cancel Help Apply 3 Level Converter 3 Level Converter Purpose Ideal three phase three level converter Library Converters Description Implements a three phase three level converter with ideal switches The con verter is modeled using the Triple Switch component see page 119 The gate input is a vector of three signals one per leg The phase output is connected to the positive neutral and negative dc level according to the sign of the cor responding gate signal The electrical circuit for the converter is shown below e a o bo E o 0 Co A e O Dialog Box lx rldeal 3 Level Converter mask This block implements an ideal three phase three level converter The gate input is a vector of three signals one per leg The AC side terminal is connected to the positive neutral and negative terminals according to the sign of the gate signal Parameters Name 3LevelConveter E DK Cancel Help Apply 231 6 Block Reference 2 Winding 3 Phase Transformers Purpose Three phase transformers in Yy Yd Yz Dy Dd and Dz connection Library 3 Phase Transformers Description This group of components implements two winding three phase transformers with a three leg or five l
185. s a saturable inductor between its two electrical termi nals The inductor has a symmetrical piece wise linear saturation characteris Man tic defined by positive current flux pairs Y YO PO WL j i 1 i 2 i8 i Parameters Current values and Dialog A vector of positive current values i in amperes A defining the piece wise Box linear saturation characteristic The current values must be positive and strictly monotonic increasing At least one value is required Flux values A vector of positive flux values Y in Vs defining the piece wise linear satu ration characteristic The flux values must be positive and strictly mono tonic increasing The number of flux values must match the number of current values Initial current The initial current through the inductor at simulation start in A The di rection of a positive initial current is indicated by a small arrow at one of the terminals The initial current default is 0 99 6 Block Reference 100 AE rSatlnductor Saturable inductor Parameters Name L2 fil Current values 0 1 fal Flux values 10 0 01 l Initial current O d OK Cancel Help Apply Probe Signals Inductor current The current flowing through the inductor in amperes A The direction of a positive current corresponds to the small arrow at one of the terminals Saturation level The saturation level indicates which sector of
186. s between its two electri cal terminals If the component is vectorized a coupling can be modeled be tween the internal capacitors Capacitors may be switched in parallel only if their momentary voltages are equal See section Configuring PLECS in chapter Using PLECS for information on how to change the graphical representation of capacitors AE Capacitor Ideal capacitor Parameters Name cl HF Width E El Capacitance 100e 6 ll Initial voltage C OK Cancel Help Apply Width The width of the electrical ports resp the number of ideal capacitors rep resented by the component Capacitance The value of the capacitor in farads F All finite positive and negative values are accepted including 0 The default is 100e 6 If the parameter is a scalar all internal capacitors have the same value To specify individually the capacitances in a vectorized component use a vector C1 C2 Cn The length n of the vector must correspond to the parameter Width 85 6 Block Reference d at V2 Fa a eee sx iO in 0 0 aa Cn Lun In order to model a coupling between the internal capacitors enter a square matrix The size n of the matrix corresponds to the width of the component j C C sis GO a 11 1 1 2 ln ae U1 d 12 Ca1 Ca EE Con a U2 i C C C dy n n l n 2 n dt vn Initial voltage The initial voltage of the capacitor at simulation start in volts
187. s you to specify the number and width of the input signals You can choose between the following formats for this parameter Scalar A scalar specifies the number of scalar inputs to the block If this format is used the block accepts only signals with a width of 1 Vector The length of the vector determines the number of inputs Each element specifies the width of the corresponding input signal 197 6 Block Reference 198 Continuous Demux Purpose Library Description Parameters and Dialog Box Split a vectorized continuous signal Signals amp Systems This demultiplexer extracts the components of a continuous input signal and outputs them as separate signals The output signals may be scalars or vectors In the block icon the first output is marked with a dot When you change the number of outputs all signals will be disconnected from the block If you want to split a vectorized gate signal use the Gate Demux block see page 199 The Continuous Demux icon can be distinguished from the Gate Mux by green instead of brown terminals lol Continuous Demultiplexer Split vectorized continuous signal into smaller vectors Parameters Name CDemux E Number of outputs ES k DK Cancel Help Apply Number of outputs This parameters allows you to specify the number and width of the output signals You can choose between the following formats for this parameter Scalar A scalar s
188. saturation by means of a continuous function The model is implemented with machine equations in the rotor reference frame Park transformation Since the machine ter minals have current source characteristic no external inductors may be con nected They must be included in the leakage inductances The machine can be used with both the continuous and the discrete state space method The machine operates as a motor or generator the sign of the mechanical torque determines the mode of operation positive for motoring negative for generating All electrical variables and parameters are viewed from the sta tor side In the component icon phase a of the stator winding and the positive pole of the field winding are marked with a dot Electrical System 1 1 ty d i 1 kd k ia Rs Wm Yq Lig Ly E YY e CI Va Lm d o d axis um Y 1 ig Rs O Las Lika Rea tka o E YY COD 3 Vq Lm q q axis 161 6 Block Reference 162 Stator flux linkages Wa Lisia Ema ia it ika Wy Lista Lm q ig ika The electrical system of the machine model is implemented with state variable equations that are derived from the equivalent circuit in the rotor reference frame The value of the main flux inductances Lm and Lm q are not constant but depend on the main flux linkage Ym as illustrated in the Ym im diagram In this machine model the anisotropic factor Eh m sat IP di L P di L m 0
189. so that Simulink can determine the precise time at which the value of the gate signal changes On the other hand a gate signal imported from Simulink is taken as is the origin of the signal is responsible for the zero crossing signal gen eration Note The Simulink blocks Signal Generator Signal Builder and Repeating Sequence should not be used as sources for gate signals These blocks do not use zero crossing detection to ensure that a simulation step is taken at the in stant when a discontinuity occurs Creating Branches For drawing a branch connection place the pointer on an existing connection or node where you want the branch to start With the right mouse button or with the left mouse button while holding down the Ctrl key you can create a connection from there to the desired destination Annotations Like in Simulink you can annotate circuits with text labels Create an anno tation by double clicking in an unoccupied area of your PLECS circuit and start typing You can move an annotation by selecting and dragging it with the mouse Choose Text alignment from the Format menu to change the text alignment of the annotation 39 3 Using PLECS 40 Subcircuits In analogy to Simulink subsystems subcircuits allow you to simplify a circuit diagram by establishing a hierarchy where a Subcircuit block is on one layer and the elements that make up the subcircuit are on another Subcircuits also enable you to create you
190. synchronous machine in which the back electromotive force EMF is not sinusoidal but has a more or less trapezoidal shape Additionally the variation of the stator inductance with the rotor position is not necessarily sinusoidal The machine operates as a motor or generator the sign of the mechanical torque determines the mode of operation positive for motoring negative for generating In the component icon phase a of the stator winding is marked with a dot Electrical System ia R La 0e ee MAYA t3 YYY C3 A YYY E The back EMF voltages are determined by a shape function ke and the me chanical rotor speed wm The shape function in turn is expressed as a fourier series of the electrical rotor angle 0 x Oe Wm Kea Oe Wm ke a 00 Y Ken cos n0 Ks n sin n0 n 27 2mn ke blbe 2 Kem cos nbe 37 Ks nsin n0 37 ke c 0 5 Ken cos n0 ls Ks n sin n0 a i 3 3 n 178 Brushless DC Machine The stator self inductance is also expressed as a fourier series of the electrical rotor angle The mutual inductance M between the stator phases is assumed to be constant Since the stator windings are star connected the mutual in ductance can simply be subtracted from the self inductance La 0 Lo M Len cos n0 Ls n sin n0 Electromechanical System The electromagnetic torque is a superposition of the torque caused by the per manent magnet and a r
191. t conditions Reverse recovery charge The reverse recovery charge Q r under test conditions If both t and Tim are specified this parameter is ignored Lrr This inductance acts as a probe measuring the di dt It should be set to a very small value The default is 10e 10 Diode voltage The voltage measured between anode and cathode Diode current The current through the diode flowing from anode to cathode Diode conductivity Conduction state of the internal switch The signal outputs 0 when the diode is blocking and 1 when it is conducting A Courtay MAST power diode and thyristor models including automatic parameter extraction SABER User Group Meeting Brighton UK Sept 1995 127 6 Block Reference 128 Zener Diode Purpose Library Description Parameters and Dialog Box Zener diode with controlled reverse breakdown voltage Switches The Zener diode is a type of diode that permits current to flow in forward di rection like a normal diode see page 123 but also in reverse direction if the voltage is larger than the rated breakdown or Zener voltage Zener diodes are widely used to regulate the voltage across a circuit ixi Zener Diode mask flink In forward operation the component behaves like a normal diode In reverse direction a current will flow if the voltage is larger than the Zener voltage Parameters Name zi E Zener voltage Vz 56 Mi Zener resist
192. the diode it can be controlled by an external gate signal The thyris tor is modeled by an ideal switch that closes if the voltage between anode and cathode is positive and a non zero gate signal is applied The switch remains closed until the current becomes zero A thyristor cannot be switched off via the gate Block parameters ioj xj cThyristor The thyristor closes upon a positive voltage between anode and cathode and a non zero gate signal It opens when the current tries to reverse pParameters Name f ny E Width On state voltage drop therm fi Jl ml Forward voltage Vf Turn on loss therm p dJi JE On resistance Ron Turn off loss therm p Jl El Initial conductivity p fz OK Cancel Help Apply Width The width of the component This affects both the width of the electrical ports and the width of the gate input signal The default is 1 Each of the following parameters may either be a scalar or a vector with the width of the component Forward voltage Additional dc voltage V in volts V between anode and cathode when the thyristor is conducting The default is 0 Thyristor Probe Signals On resistance The resistance Ron of the conducting device in ohms Q The default is 0 Initial conductivity Initial conduction state of the thyristor The thyristor is initially blocking if the parameter evaluates to zero otherwise it is conducting The following parameters define
193. the stator saturates in the aligned position in Vs Inertia Combined rotor and load inertia J in Nms Friction coefficient Viscous friction F in Nms Initial rotor speed Initial mechanical speed wm o in radians per second s Initial rotor angle Initial mechanical rotor angle 0m o in radians Initial stator currents A three element vector containing the initial stator currents iao ipo and ico Of phases a b and c in amperes A Mechanical torque The input signal T represents the mechanical torque at the rotor shaft in Nm The output vector m contains the following 7 signals 1 Rotor speed The rotational speed wm of the rotor in radians per second s71 2 Rotor position The mechanical rotor angle 0m in radians 3 Electrical torque The electrical torque T of the machine in Nm 4 6 Flux linkages The flux linkages in the individual phases of the machine in Vs D A Torrey J A Lang Modelling a nonlinear variable reluctance motor drive IEE Proceedings Vol 137 Pt B No 5 Sept 1990 D A Torrey X M Niu E J Unkauf Analytical modelling of variable reluctance machine magnetisation characteristic IEE Proceedings Elec tric Power Applications Vol 142 No 1 Jan 1995 Continuous Input Continuous Input Purpose Create an input terminal for a continuous signal Library Signals amp Systems Description Continuous inputs are used to feed continuous signals from Simulink in
194. thm0 pc Z E _ Cogging torque coefficients Ten Initial stator currents fa ib0 ph or OK Cancel Help Apply Back EMF shape coefficients Fourier coefficients Ken and K s n of the back EMF shape function ke a 0 in volts per second Vs Stator resistance The stator resistance R in ohms Q Stator inductance The constant inductance Lo M and the fourier coefficients Len Ds of the phase a inductance L 0 in henries H Cogging torque coefficients Fourier coefficients T T of the cogging torque T lt og 0 in Nm Inertia Combined rotor and load inertia J in Nms Brushless DC Machine Friction coefficient Viscous friction F in Nms Number of pole pairs Number of pole pairs p Initial rotor speed Initial mechanical speed wm o in radians per second s71 Initial rotor angle Initial mechanical rotor angle 0m y in radians Initial stator currents A two element vector containing the initial stator currents ay and ipo of phase a and b in amperes A Inputs and Mechanical torque Outputs The input signal Tm represents the mechanical torque at the rotor shaft in Nm The output vector m contains the following 7 signals 1 Rotor speed The rotational speed wm of the rotor in radians per second s71 2 Rotor position The mechanical rotor angle 6 in radians 3 Electrical torque The electrical torque T of the machine in Nm 4 Cogging torque The
195. thods for the modulation index The fig ure below illustrates Natural Sampling Natural Sampling Modulation index o Switching function o The following figures illustrate the different Regular Sampling methods In the figure on the left double edge sampling is used i e the modulation in dex is updated at both tips of the triangular carrier In the right figure single Symmetrical PVM edge sampling is employed Here the modulation index is updated only at the upper tips of the carrier Double edge sampling Single edge sampling o Modulation index 1 1 f 7 1 f Switching function o Parameters 21x a nd D Ia log m Symmetrical PWM mask Box PWM generator with a symmetrical triangular carrier The input m is the modulation index with a range of 1 1 The switching function s outputs either 1 or 1 If the input is a vector the output is also a vector of the same width m Parameters Sampling Natural carrier starts with 0 y Carrier frequency 1000 Cancel Help Apply Sampling Select a sampling method If you select Natural Sampling the carrier signal may begin with 0 or 1 at simulation start The Regular Sampling method lets you choose between double edge or single edge sampling 253 6 Block Reference Carr
196. to a PLECS circuit or from a circuit into a subcircuit If you copy an input block I t into a schematic an input terminal will be created on the corresponding sub system block The name of the input block will appear as the terminal label If you choose to hide the block name by unselecting the show button in the di alog box the terminal label will also disappear The Continuous Input block can be distinguished from the Gate Input block see page 191 by the green instead of a brown output terminal Input Blocks in a Top Level Circuit If an input block for a continuous or gate signal is placed in a top level circuit a unique number is assigned to the block In Simulink the relative position of the corresponding input terminals is determined by the order of block num bers You may change the block number in order to change the relative termi nal position Input Blocks in a Subcircuit If placed in a subcircuit the inputs are not identified by numbers since the ter minals of the subcircuit can be freely positioned Which terminal corresponds to which input block can only be seen from the block name In order to move an unconnected terminal with the mouse around the edges of a subsystem hold down the Shift key or use the middle mouse button Parameters Width and Dialog The width of the input signal The default is 1 Box Port number The terminal number of the input block This parameter appears only if the block is placed in a top le
197. to remove a thermal connector disconnect it then reduce the Number of terminals PLECS will not allow you to remove connected terminals For additional information see chapter Thermal Modeling on page 59 Block parameters 154 xj rHeat Sink The Heat Sink absorbs the thermal losses dissipated by the components within its boundaries At the same time it defines an isotherm environment and propagates its temperature to the components which it encloses Parameters Name Heat Sink E Number of terminals p ja Thermal capacitance fi ja Initial temperature es OK Cancel Help Apply Number of terminals This parameter allows you to change the number of external thermal con nectors of a heat sink The default is 0 Heat Sink Thermal capacitance The value of the internal thermal capacitance in J K The default is 1 If the capacitance is set to zero the heat sink must be connected to an ex ternal thermal capacitance or to a fixed temperature Initial temperature The initial heat sink temperature in degrees Celsius C The default is 0 Probe Signals Temperature The heat sink temperature in degrees Celsius C 239 6 Block Reference 240 Controlled Temperature Purpose Library Description Parameters and Dialog Box Probe Signals Generate a variable temperature Thermal The Controlled Temperature generates a variable t
198. tor is charged by a DC voltage source via an RL branch and its voltage is monitored with a voltmeter 2 Getin g Started 24 10mH 100 ENANA T C 10V 1004F vc Figure 2 1 Simple RLC network In order to enter the circuit in PLECS we have to open a new Simulink model Into the model window we copy the block Circuit from the PLECS library by dragging it with the mouse Our Simulink model should now look like Fig 2 2 File Edit View Simulation Format Tools Help PLECS Circuit Figure 2 2 Simulink model Components A double click on the PLECS block will open an empty schematic window with a menu bar quite similar to the one of a Simulink window The components required for our circuit must be copied into this window from the components libraries Like in Simulink this is done by dragging them with the mouse If you want to copy components within the same window hold down the Ctrl control key or use the right mouse button After you have copied all components the schematic window should look like Fig 2 3 If not move the components with the left mouse button To rotate selected components press Ctrl R to flip them horizontally press Ctrl F All these functions can also be accessed via the menu bar A Simple Passive Network File Edit View Simulation Format Figure 2 3 PLECS schematic Note You cannot pl
199. tor side Damper currents The damper currents i q and i q in the stationary reference frame in A Stator flux dq The stator flux linkages Y q and Y in the stationary reference frame in Vs Magnetizing flux dq The magnetizing flux linkages Ym and Ym q in the stationary reference frame in Vs Rotational speed The rotational speed wm of the rotor in radians per second s71 Rotor position The mechanical rotor angle 6 in radians Electrical torque The electrical torque T of the machine in Nm References K A Corzine B T Kuhn S D Sudhoff H J Hegner An improved method for incorporating magnetic saturation in the Q D synchronous ma chine model IEEE Transactions on Energy Conversion Vol 13 No 3 Sept 1998 E Levi Saturation modelling in D Q axis models of salient pole syn chronous machines IEEE Transactions on Energy Conversion Vol 14 No 1 March 1999 E Levi Impact of cross saturation on accuracy of saturated synchronous machine models IEEE Transactions on Energy Conversion Vol 15 No 2 June 2000 166 Round Rotor Synchronous Machine Round Rotor Synchronous Machine Purpose Smooth air gap synchronous machine with main flux saturation Library Machines Description The Round Rotor Synchronous Machine models main flux saturation by means of a continuous function The model is implemented with machine equations in the rotor reference frame Park transformatio
200. ts with variable number of coupled windings Mutual Induc tor see page 83 and Ideal Transformer see page 87 All switches can now be vectorized e g the Circuit Breaker see page 120 Command Line Interface CLI See Command Line Interface on page 67 What s New in Version 1 2 The following list describes new features and enhancements added in PLECS 1 2 since Version 1 1 Fixed time step simulations circuit discretization See section Circuit Simulation Parameters on page 54 Possibility to encrypt and password protect PLECS circuits See section Controlling Access to Circuits and Subcircuits on page 52 Automatic creation of subcircuits See section Subcircuits on page 40 Vectorized electrical wires See the Wire Mux component see page 200 Most intrinsic components can be used with vectorized wires Additional blocks and components in the PLECS library e g the Electri cal Ground see page 201 the Integrator see page 209 discretizable ma chines Many enhanced components in the PLECS library e g the Inductor see page 81 Configure the graphical representation of resistors and capacitors See sec tion Configuring PLECS on page 31 15 Before You Begin e Possibility to change the placement of subcircuit labels See section Placing the Subcircuit Label on page 42 e Annotations in circuits See section Annotations on page 39 e Specify the initial
201. u can change this behavior by selecting Show masked subcircuits from the Cir cuit browser options submenu of the View menu of the schematic editor 49 3 Using PLECS 50 PLECS Probe PLECS p Probe The PLECS Probe enables you to monitor various quantities in a circuit Most intrinsic components provide one or more probe signals that describe their cur rent state input or output signals For instance an inductor provides a probe signal that monitors the inductor current the probe signals of a diode are the diode voltage current and conduction state In order to use the PLECS Probe drag the Probe block from the library into the Simulink model that contains the circuit which you want to probe Double click the icon to open the probe editor window r Probed circuit Circuit in plBuck Converter r Probed components r Available signals Up IGBT IGBT in Circuit IGBT voltage Diode D in Circuit IGBTcurrent Down Inductor L in Circuit re Capacitor C in Circuit JE IGBT conductivity Remove This window contains the following information Probed circuit The text box across the top shows the name of the circuit that you are probing and its path i e the Simulink system containing the Cir cuit block Probed components The list box on the left side shows the components that you have selected for probing The components are identified by their type name and
202. uctance Li in henries H referred to the stator side Magnetizing inductance Magnetizing inductance Lm in henries H referred to the stator side Inertia Combined rotor and load inertia J in Nms Friction coefficient Viscous friction F in Nms Number of pole pairs Number of pole pairs p Initial rotor speed Initial mechanical rotor speed wm o in s Initial rotor position Initial mechanical rotor angle 0 9 in radians If 0m is an integer multiple of 27 p the stator windings are aligned with the rotor windings at simula tion start Initial stator currents A two element vector containing the initial stator currents is a and is b 0 of phases a and b in amperes A Initial stator flux A two element vector containing the initial stator flux Y 4 o and Y in the stationary reference frame in Vs Inputs and Mechanical torque Outputs The input signal Tm represents the mechanical torque at the rotor shaft in Nm The output vector m contains the following 3 signals 1 Rotational speed The rotational speed wm of the rotor in radians per second s71 2 Rotor position The mechanical rotor angle 0 in radians 147 6 Block Reference Probe Signals 148 3 Electrical torque The electrical torque T of the machine in Nm Stator phase currents The three phase stator winding currents isa is and is in A Currents flowing into the machine are considered positive Rotor phase currents The th
203. uctor device that behaves like a circuit breaker rParameters Name frac SR Width On state voltage drop therm fi Jl El Forward voltage Vf Turn on loss therm p fo Ei On resistance Ron Turn off loss therm p Jl E Initial conductivity p OK Cancel Help Apply Width The width of the component The default is 1 Each of the following parameters may either be a scalar or a vector with the width of the component Forward voltage Additional dc voltage V in volts V when one of the thyristors is conduct ing The default is 0 On resistance The resistance Ron of the conducting device in ohms Q The default is 0 TRIAC Initial conductivity Initial conduction state of the TRIAC The TRIAC is initially blocking if the parameter evaluates to zero otherwise it is conducting The following parameters define the thermal behavior of the component For more information see chapter Thermal Modeling on page 59 On state voltage drop therm A 2 D function von T defining the voltage drop in volts V that is used for calculating the thermal conduction losses The default is meaning the voltage drop is calculated as von Vs Ron 1 Turn on loss therm Turn off loss therm 3 D functions Eon Upre ipost T and Eo Upost ipre T defining the total ther mal losses dissipated during a switching transition in joule J The de fault is meaning no thermal turn on resp turn o
204. us input signal z Parameters lx and Dialog e rFourier Series Box Dutput the fourier series y a0 2 sum an cos n x bn sin r x Parameters Name Fourier E Fourier coefficient a0 E El Fourier coefficients an fo El Fourier coefficients bn 10 E DK Cancel Help Apply Fourier coefficients The coefficients ao an and bn of the fourier series The vectors a and bn must have the same length Probe Signals Input The input signal Output The output signal 210 Constant Constant Purpose Library Description EZ Parameters and Dialog Box Probe Signals Output a constant signal Signals amp Systems The Constant block outputs a constant signal Block parameters 5 x Constant Outputs a constant signal Parameters Name Fonstant E Width fi fa Value IA _ OK Cancel Help Apply Width The width of the component The default is 1 Value The constant value This parameter may either be a scalar or a vector with the width of the component The default value is 1 Output The constant signal 211 6 Block Reference 212 1D Look Up Table Purpose Library Description ip Table Parameters and Dialog Box Output an approximated one dimensional function using intrapola tion extrapolation Signals amp Systems The 1D Look Up Table block maps a continuous input signal to a continuous outp
205. ustrated in the W i diagram For flux linkages Ym far below the transition flux Yr the relationship between flux and current is almost linear and determined by the unsaturated magnetizing inductance Lm o For large flux linkages the relationship is governed by the saturated magnetizing inductance Ly sat Ur defines the knee of the transi tion between unsaturated and saturated main flux inductance The tightness of the transition is defined with the form factor fr If you do not have detailed information about the saturation characteristic of your machine fr lisa good starting value The function plsaturation Lm0 Lmsat PsiT fT plots the main flux vs current curve and the magnetizing inductance vs cur rent curve for the parameters specified The model accounts for steady state cross saturation i e the steady state magnetizing inductances along the d axis and q axis are functions of the cur rents in both axes In the implementation the stator currents the field cur rent and the main flux linkage are chosen as state variables With this type of model the representation of dynamic cross saturation can be neglected with out affecting the machine s performance The computation of the time deriva tive of the main flux inductance is not required Electro Mechanical System Electromagnetic torque Oe To 9 Pp isa Ya s d Ya 168 Round Rotor Synchronous Machine i Mechanical System Mechanical roto
206. ut signal You define the mapping function by specifying a vector of in put values and a vector of output values If the input signal lies within the range of the input vector the output value is calculated by linear interpolation between the appropriate two points If the input signal is out of bounds the block extrapolates using the first or last two points Step transitions are achieved by repeating an input value with different out put values If the input signal exactly matches the input value of such a dis continuity the output signal will be the output value of the mapping function that is first encountered when moving away from the origin If the discontinu ity is at input value 0 the output signal will be the average of the two output values This behavior can be overridden by defining three output values for the same input value in this case the middle output value will be chosen Use the 2D Look Up Table block see page 214 to map two continuous input signals to a continuous output signal AE 71D Look Up Table Output an approximated one dimensional function using interpolation extrapolation pParameters Name fiD Table Vector of input values x 2 fat Vector of output values f x In 2 E OK Cancel Help Apply Vector of input values x The vector of input values x This vector must be the same size as the out put vector and monotonically increasing It should not contain
207. utual inductance Lm PY Mutual resistance Am E El Initial current i1 i2 13 foo 4 OK Cancel Help Apply Initial current A three element vector containing the initial currents on the primary side i1 the secondary side 2 and the tertiary side i3 in amperes A The di rection of positive currents is indicated by little arrows in the component symbol The default value is 0 0 0 96 Pi Section Line Pi Section Line Purpose Library Description 7 Parameters and Dialog Box Single phase pi section transmission line Passive Components The Pi Section Line implements a single phase transmission line with param eters lumped in pi sections A transmission line is characterized by a uniform distribution of inductance resistance capacitance and conductance along the line However in many cases these distributed parameters can be approximated by cascading multiple pi sections with discrete components The figure below illustrates the electri cal circuit used for the line model L R L R L R 7 MA YY eee YY IS v Q Let 1 be the length of the line and n the number of pi sections representing the line The inductance L the resistance R the capacitance C and the con ductance G of the discrete elements can then be calculated from their per unit length counterparts L R C and G using the following equations l L I R LU C Leo G lg n n n n
208. vector containing the leakage inductance of the primary side L the secondary side L gt and the tertiary side L3 The inductivity is given in henries H Winding resistance A three element vector containing the resistance of the primary winding R the secondary winding R and the tertiary winding Rs in ohms 0 No of turns A three element vector containing the number of turns of the primary winding n the secondary winding n s and the tertiary winding na Magnetizing current values A vector of positive current values in amperes A defining the piece wise linear saturation characteristic of the transformer legs The current values 236 3 Winding 3 Phase Transformers must be positive and strictly monotonic increasing At least one value is required Magnetizing flux values A vector of positive flux values in Vs defining the piece wise linear satura tion characteristic The flux values must be positive and strictly monotonic increasing The number of flux values must match the number of current values Core loss resistance An equivalent resistance Ry representing the iron losses in the trans former core The value in ohms Q is referred to the primary side No of core legs The number of legs of the transformer core This value may either be 3 or 5 Phase lag of secondary side The phase angle between the primary side and the secondary side in de grees Unless the secondary side is in zig zag connection the
209. vel circuit 189 6 Block Reference Block parameters 190 Gate Input Gate Input Purpose Library Description eb Parameters and Dialog Box Create an input terminal for a gate signal Signals amp Systems Gate inputs are used to feed gate signals from Simulink into a PLECS circuit or from a circuit into a subcircuit If you copy an input block into a schematic an input terminal will be created on the corresponding subsystem block The name of the input block will appear as the terminal label If you choose to hide the block name by unselecting the show button in the dialog box the ter minal label will also disappear The Gate Input block can be distinguished from the Continuous Input block see page 189 by the brown instead of a green output terminal sox Gate Inport Provide a gate input port for a circuit or subcircuit Parameters Name Gatel E Width E E Port number 2 EH DK Cancel Help Apply Width The width of the input signal The default is 1 Port number The terminal number of the input block This parameter appears only if the block is placed in a top level circuit 191 6 Block Reference 192 Continuous Output Purpose Create an output terminal for a continuous signal Library Signals amp Systems Description Continuous outputs are used to feed continuous signals from a PLECS circuit x1 Parameters and Dialog
210. w at one of the terminals 106 Saturable Capacitor Saturable Capacitor Purpose Saturable capacitor Library Nonlinear Description This component provides a saturable capacitor between its two electrical ter R minals The capacitor has a symmetrical piece wise linear saturation charac T teristic defined by positive voltage charge pairs Parameters and Dialog Box zix rSatCapacitor Saturable capacitor Parameters Name C2 fa Voltage values 101 El Charge values to 0 01 E Initial voltage C OK Cancel Help Apply Voltage values A vector of positive voltage values in volts V defining the piece wise lin ear saturation characteristic The voltage values must be positive and strictly monotonic increasing At least one value is required Charge values A vector of positive charge values in As defining the piece wise linear sat uration characteristic The charge values must be positive and strictly monotonic increasing The number of charge values must match the num ber of voltage values Initial voltage The initial voltage across the capacitor at simulation start in volts V The positive pole is marked with a The initial voltage default is 0 107 6 Block Reference Probe Signals Capacitor voltage The voltage measured across the capacitor in volts V A positive voltage is measured when the potential at the terminal marked with
211. xternal inductances in series with the stator wind ings The machine operates as a motor or generator the sign of the mechanical torque determines the mode of operation positive for motoring negative for generating All electrical variables and parameters are viewed from the sta tor side In the component icon phase a of the stator winding is marked with a dot In order to inspect the implementation please select the component in your circuit and choose Look under mask from the Edit menu Electrical System isa Rs Lis Li ij k q Ya d axis The rotor flux is computed as Fot I Yra Lir trd T Lm is a T ika _ ply Vig Lir trg T Lm isq 7 Es irq 149 6 Block Reference 150 rw wl 7 z isq Rs Lis Lir r d Bra Ta gt YYY DARA E ca a re Us q Lm q axis The three phase voltages vs ap and vs pc at the stator terminals are trans formed into dq quantities 1 3 Us ab 2 v a O IN V3 Ur bc Likewise the stator currents in the stationary reference frame are trans formed back into three phase currents isa 1 0 2 L i Bo tsb 72 7 2 1 3 re ts c T2 72 Electro Mechanical System Electromagnetic torque 3 54K ee To zP Lm isa iza id tka Mechanical System Mechanical rotor speed wm 1 m 5 To Fum Tm W PUm Mechanical rotor angle 0m m Wm 0 phm SquirrelCage Induction Machine Parameters
212. y between the rotating and the stationary frame y is given in radians Yo cosw it sinwjt La YB sinw t coswyt Ta Transformation RRF gt SRF mask Transforms a two dimensional vector from a rotating into the stationary reference frame The angle in radians between the rotating and the stationary frame is determined by the second input d q phi gt alpha beta Cancel Help Apply 271 6 Block Reference 3 Phase To Rotating Reference Frame Purpose Library Description ab dq f Dialog Box 272 Transform a three phase signal into a rotating reference frame Extras Transformations This block transforms a three phase signal za x e into a two dimensional vector ya ya in a rotating reference frame The first input is the three phase signal The second input is the rotation angle y of the rotating reference frame y is given in radians T cos p sin Y La Ya 2 3 cos p 120 sin y 120 xp Yq cos p 120 sin y 120 Te Any zero sequence component in the three phase signals is discarded EJ Block Parameters 3ph gt RRF 2 x m Transformation 3ph gt RAF mask Transforms a three phase signal into a two dimensional vector in a rotating reference frame The rotation angle in radians of the rotating reference frame is determined by the second input a b c phi gt d q Cancel Help Apply Rotating Reference Frame To 3 P
213. ys it on the mask icon The two element vectors xvec and yvec specify the minimum and maximum coordinates of the image s extent Use the optional flag on to indicate that the image data should rotate or flip together with the mask icon By default this is set to off and the im age data remains stationary Masking Subcircuits Mask Icon Coordinates All coordinates used by the mask drawing commands are expressed in pixels The origin of the coordinate system is always the center of the block icon it is moved when the block is resized Use the icon frame and or the terminal locations as reference points in order to position graphic elements Both the frame and the terminals snap to a grid of 10 by 10 pixels Mask Icon Properties Icon frame The icon frame is the rectangle that encloses the block You can choose to show or hide the frame by setting the Icon frame property to Visi ble or Invisible Icon transparency The icon can be set to Opaque or Transparent either hiding or showing the terminal labels underneath the icon Mask Parameters The Parameters pane enables you to define the parameters that will appear in the dialog box of the masked subcircuit Prompts and Associated Variables Mask parameters are defined by a prompt and a variable name The prompt provides information that helps the user identify the purpose of a parameter The variable name specifies the variable that is to store the parameter v

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