ModSCA MODular Simulator for Compressed Air User Manual
Contents
1. e power instantaneous power absorbed by the compressor in kW http users isy liu se johanl yalmip pmwiki php n Main HomePage 11 e energy energy consumed by the compressor kWh e flow it represents the instantaneous flow in m s provided by the compressor in FAD conditions ile Edit View Display Diagram Analysis Help B ae mu Bl O Flow rate Vsd MPC Compressor Figure 3 Vsd MPC compressor module 3 4 2 Main sub blocks Inside the folder simulator subsystems compressors there are the following sub blocks e throttle_vsd_flow slx it calculates the flow provided by the vsd Equation 6 depending on the instantaneous motor speed e throttle_vsd_power slx depending on the flow is providing the compressor and the operative pressure of the compressor the sub block implements the Equation 7 3 4 3 Data stored in the Matlab s workspace e power it represents the instantaneous power measured in kW e compressor_flow_rate it represents the instantaneous compressor flow in m3 3 at FAD conditions e energy it represents the total energy consumed by the compressor from the begin ning of the simulation until the present time It is evaluated in kWh 12 3 5 Receiver A compressed air network is made up of one or more receivers and the pipelines The vessels usually placed next to the compressors decouple the compressor production from the end user demand avoiding frequently switch from load to unlo2. a modular simulator so each element of a compressed air system is represented by a block whose internal model is not visible to the users but modifiable by them In this way the user can reproduce his compressed air system or design a new one searching the devices from the simulator library The modules already implemented emulates the mainly devices installed into the LABAC load unload compressor adjustable speed drive compressor receiver air dryer air filter network pressure reducer flow profile required by the end users and system 3 1 Compressors ModSCA can simulate two different kind of compressors a load unload compressor and an adjustable speed drive compressor Through the proper parameters setting it is possible to simulate compressors of different sizes and working point 3 2 Load Unload compressor This module simulates a load unload compressor it runs at full load as long as the outlet pressure reaches the upper activation pressure setting pmax parameter which causes the compressor goes to unload When unloaded the compressor does not deliver air but the 4 electric motor keeps on running consuming from the grid roughly 20 30 of the power this value is stored in fraction_power_unload required when it is in its load mode If the compressor keeps standing in its unload mode for several seconds set in t_on_off parameter and if maximum number of switches off per hour n_avviamenti parameter has not been al
3. air dryer 3 6 2 Main sub blocks Inside the folder simulator subsystems air_dryer there is the sub block saturated_vapour sl1x 3 6 3 Data stored in the Matlab s workspace e pressure_after_dryer for each sample time it contains pressure after the air dryer in Pag e water_vapour for each sample time it contains the amount of water vapour g m remaining in the compressed air 15 3 7 Filter The compressed air filters are used to remove particle dust and oil from compressed air The air treatment devices are necessary to provide a proper quality of compressed air and to avoid an early devices wear The air passing through the filter is subject to a pressure drop increasing with the accumulated dirt in the filter Even in the filter constantly cleaned a pressure drop of at least 300 Pa is expected In Figure 6 the filter module in reported File Edit View Display Diagram Analysis Help aS Pa ao MEON filters Filter Filter inlet pressure outlet pressure Figure 6 Air filter module The air filter module implements a pressure drop whose quantity is reported in filter_pressure_drop hence Pout Pin Ap Pag 15 where Apy is the pressure drop that occurs inside the filter filter_pressure_drop 3 7 1 Input Output signals Input signal Filter inlet pressure Pag Output signal Filter Outlet pressure Pag 3 7 2 Main sub blocks Inside the folder simulator subsys
4. blocks Each block can be easily recognized through an image of the device is emulating and through the input and output signals The Figure 1 represent the block modeling the a load unload compressor the block not receive any signal value and provide as output the power and energy consumption and the flow provided by the compressor To execute a simulation the input and output values must to be connect to the proper signals With a double click it will open a mask containing the parameters required during the simulation The parameters value can be set manually introducing the real value or modifying the corresponding value stored in the file parameters m To help the user the mask shows a brief description of the parameters and their measurement units With the right mouse button you can click Look Under Mask the blocks and sub blocks describing the mechanical electrical and physical models will appear 2 3 How to modify the model of each block ModSCA allows the user to modify the mathematical models implemented inside each block device in this way it is possible to adjust the theoretical model to the real one To modify the mathematical model of the block File Edit View Display Diagram Analysis Help aE B ENO load_unload_compressor Flow rate Load unload compressor 201 Figure 1 load unload compressor module Edit gt Unlock Library Edit gt Look Under Mask 3 Moduls ModSCA is
5. evaluate other signals Output signal e power instantaneous power absorbed by the compressor in kW e energy energy consumed by the compressor kWh e flow rate it represents the instantaneous flow in m s provided by the compressor in FAD conditions 3 2 2 Main sub blocks Inside the folder simulator subsystems compressors there are the sub block used to implement the compressor s functionalities compressor_control_1nl slx through the knowledge of the system pressure this sub block identify the compressor state load unload or off compressor_power_lnl slx it contains the implementation of the Equation 2 power_dynamics_from_loadToUnload slx it implements the dynamic of the power absorbed from the grid when the compressor switches from load to unload W Price P 1 fp e v Px fp 3 where fp represent the value contained in fraction_power_unload and v represent the velocity from load to unload whose value is stored in velocity_loadTOunload 3 2 3 Data stored in the Matlab s workspace compressor_state it contains the state of the compressor for each time sample during the simulation It can assume the value 1 2 or 3 they represent respectively the off unload and load state power it represents the instantaneous power measured in kW compressor_flow_rate it represents the instantaneous compressor flow in m s at FAD conditions energy it represents the total energy consumed by the compres
6. every second and stored in max_delta_speed kp and kr are respectively the proportional and integral gain they are stored in kp and ki K is a scaling factor in scaling factor es is the difference between the pressure set point in pressure_setpoint and the system pressure at time t while Ae t e4 1 After computing An it is possible to evaluate the motor speed at time t as follows n t n t 1 An if nmin lt n t lt Nmar n t Nmin if H t lt Nmin 5 n t Nmaz if n t gt Nmar Depending to the motor speed the flow provided by the compressor follows the dynamic Imax Imin g t See Eei nt nmin 9 6 where qmar is the maximum flow can be produced by the adjustable speed compressor stored in max_flow while qmin min_flow is the minimum flow can be provide the com pressor The absorbed compressor power depending on the flow is providing the compressor was modelled as follows P ay A2Pop T q a3 a4Pop 7 where Pop is the operative pressure of the compressor q is the flow provided by the com pressor while a1 a2 a3 a4 are parameters describing the curve P q p they are generally provided by the compressor s manufacturer File Edit View Display Diagram Analysis Help aa amp O Vsd PI Compressor 200 Figure 2 Vsd PI compressor module 3 3 1 Input Output Signals Input signal Although is not visible the module receive as input signal the pr
7. it is possible to calculate the amount of water vapour g m contained inside the air obviously this is the same quantity of water vapour after the compression process The amount of water vapour in saturated conditions comes from Handbook of thermodynamics tables and charts K R Njevi they have been reported in ModSCA inside a lookup table When the air flows inside the air dryer its temperature decreases knowing the reduced outlet air temperature and the air pressure it is possible to find through tabulated values the amount of water vapour contained in the air at that conditions the difference between the amount of water sucked in by 3The values used in ModSCA comes from the Bigino dell aria compressa 2000 14 the compressor and the water inside the air flowing out the air dryer represents the ideal amount of water inside the refrigerant The real amount of water depends on the air dryer efficiency in rendimento_air dryer the final water vapour inside the compressed air after the refrigeration process is the difference between the starting value and the real water vapour inside the refrigerant File Edit View Display Diagram Analysis Help aa aa By O air_dryer Air dryer Air dryer inlet pressure ay outlet pressure Figure 5 Air dryer module 3 6 1 Input Output signals Input signal air pressure Pag upstream the air dryer Output signal air pressure Pa downstream the
8. speed of the air inside the pipe as follows i A np a e darcy slx it implements the Equation 17 e iterazione_colebrook slx this sub block calculates the friction factor than as sumes different values as shown in the Moody diagram reported in Figure 8 The diagram can be divided into two parts the laminar and turbulent flow We assume a laminar flow when the Reynolds number is smaller than 4000 In this case the friction factor can be calculated as follows Re f S 19 18 0 1 0 09 0 08 0 07 0 06 0 05 0 04 Q x 0 03 B 3 E e 5 3 z aw g 0 02 3 oO 7 CPST i engineeringtoolbox com N Hi 0 00001 10 2345 10t 2345 102345 10 2345 107 2345 10 Reynolds Number Re Figure 8 Moody diagram If the flow is turbulent the friction factor is calculated considering the empiric equa tion of Colebrook White reported as follows 1 JD 251 F 2 log Ee RT 20 where e is the absolute roughness whose values are reported in Table 2 D the relative one and Re is the Reynolds number calculated as Equation 28 The Equa tion 20 is transcendental meaning that it is necessary to use numerical methods to find the solution We decide to use the iterative procedure proposed in Clamond Didier Efficient resolution of the Colebrook equation 2009 and following reported 19
9. the pipe s diameter v the air velocity calculated as reported in Equation 18 L the equivalent length of the pipe this value is the sum of the real length of the pipe stored 17 in pipe length and equivalent length of the curved valves gate valves etc Inside these elements concentrated losses occur through some tabulated value it is possible to describe the pressure drop inside each elements using an equivalent pipe length inside which occur the same pressure drop The values of the equivalent length used in ModSCA come from the Ingersoll Rand Company 1980 and assume the values reported in Table 1 or their interpolation Table 1 Equivalent length Ingersoll Rand Company 1980 Pipe Diameter in mm 25 40 50 80 100 125 150 Gate valve and curve 0 3m 05m 06m im 13m 16m 19m T curve and 90 curve 15m 24m 30m 48m 6m 75m 90m Gate valve half opened 5m 8m 10m 16m 20m 25m 30m 3 8 1 Input Output signals Input signal air pressure in Pag evaluated at the beginning of the pipe Moreover although is not visible the module receive another input signal the flow that passes inside the pipe This signal is not show because it isn t an input signal but a value required to evaluate other signals Output signal air pressure in Pag evaluated at the end of the pipe 3 8 2 Main sub blocks Inside the folder simulator subsystems pipe there are the following sub blocks slx e air_velocity slx this block calculate the
10. 3 3 10 1 Input Output Signals Input signal e air pressure in Pag evaluated at the before the pressure reducer e compressor power in load mode in kW e compressor flow in m s I is not visible because it isn t a real input signal but a value required to evaluate other signals Output signal energy waste in kWh 4the absolute value corresponds to the sum of the relative and ambient pressure 24 3 11 Flow profile The flow profile module Figure 11 receives as input the pressure measured upstream this block this signals is not used inside the block flow profile it was created only to give a logical sense to the final compressed air system The block has not output signals File Edit View Display Diagram Analysis Help 8A ago end user Figure 11 Module representing the flow required by the end users This module was create only to contains the vector of flows required by the end users these values are contained inside the constant flow out 25 3 12 System The block reported in Figure 12 not receive signals as input and not provide signal as output the only functionality of this block is to help the users to set parameters describing the environment surrounding the compressed air system The values is possible to set are the following pressure amb it contains the ambient pressure expressed in Pa absolute The default value is 101325 Pa T_amb it represents the temper
11. ModSCA MoODular Simulator for Compressed Air User Manual Giusi Quartarone Gianluca Sala Norma Anglani 1 ModSCA introduction This user manual has been conceived to show how to use ModSCA a new simulator for compressed air system in the following CAS developed in LABAC at the Department of Industrial and Information Engineering University of Pavia 1 1 Overview on the efficiency of compressed air systems The consumptions related to compressed air systems represent a relevant slice of the whole industrial electricity consumption Nonetheless its diligent management still does not seem to be taken into sufficient consideration only the 10 of the input energy is transferred into compressed air at the end user Moreover the research field shows scarce interest on CAS limited is the number of works focused on how to reduce the energy consumption and few dedicated softwares have been designed and made available to end users The possibility of having a simulator is of paramount importance for assisting those companies whose annual operating costs of compressed air production can account for high share of the total electricity bill for specific users The need of keeping under control how the system is working is fundamental from an energy savings point of view Moreover a superficial knowledge of the operation design and evaluation of energy requirements and critical elements of a compressed air system has highlighted the need to prov
12. Table 2 Absolute roughness Material Absolute roughness Copper and aluminium 0 001 lt e lt 0 003 Plastic materials 0 002 lt e lt 0 007 Galvanized steel 0 020 lt e lt 0 030 Steel 0 040 lt e lt 0 090 Corroded steel 0 200 lt e lt 1 000 X1 k Re 0 123968186335417556 X2 log Re 0 779397488455682028 F X2 0 2 E1 log X1 F F X2 1 X1 F F1 F 1 X1 F 0 5 E1 E1 X1 F 1 X1 F E1 1 E1 3 E2 log X1 F1 F1 X2 1 X1 F1 F2 F1 1 X1 F1 0 5 E2 E1 X1 F1 1 X1 F1 E2 1 E2 3 F3 1 251292546497022842 F2 lambda F3 F3 where k D is the relative roughness Re is the Reynolds number e pipe equivalent _length s1x it calculates the equivalent network length from Table 1 3 8 3 Data stored in the Matlab s workspace e pressure_after_pipe the vector contains the sample of the air pressure Pag after the pipe 20 3 9 Circular Network Independently of the number of installed devices and their placement two basic layouts for the distribution system exist A radial network is composed by a single line from the supply side to the points of usage On the contrary in a ring distribution system the compressed air flows in a closed loop header Two pipelines link the supply side to the point of use meaning that the total air hands out over two branches Being smaller the air mass flowing inside each line the air velocity is reduced entailing in a smaller friction against the pipe walls and reduc
13. ad mode If it happens it underlies an incorrect sizing scheme Thus a proper storage sizing becomes very important from an energy saving standpoint The module implements a pressure level variation depending on air flowing in and out the receiver p t q 1 p t de s leaks Po 14 where qe is the instantaneous flow rate provided by the compressor room this value is the FAD provided by the compressor and stored in fad parameter qusr is the instantaneous flow rate required by the users this value is the volume flow rate required by the end user expressed in FAD condition and stored in flow_out parameter and dears is the leaks flow whose value is calculated from the sub block FAD_loss slx V represents the receiver volume reported in volume_tank pp is the pressure of the FAD condition 3 5 1 Input Output signals Input signal Compressor s flow rate m s expressed in FAD condition Moreover al though is not visible the module receive another input signal the end user flow This signal is not show because it isn t a real input signal but a value required to evaluate other signals Output signal Gauge pressure inside the system Pay 3 5 2 Main sub blocks Inside the folder simulator subsystems tank there is the sub block FAD_loss slx that calculates the total mass loss of compressed air along the distribution system and converts it in volume flow rate expressed in FAD condition m s 3 5 3 Data stored in t
14. and vice versa In the first case the motor speed is reduced each ts of Anmar until the speed reaches the value zero In the other case the speed increase with the same velocity from zero to Nmin e rendimento_politropica this sub block calculates the polytropic efficiency as fol lows n 1 Npol Z k 25 k 1 where n is the polytropic coefficient and k is c Ccy In simulator subsystems air_dryer e saturated_vapour slx This sub block calculates the ideal amount of water vapour contained in the compressed air after the air dryer The block interpolates the data of the water vapour contained in one cubic meter of air at 5 bar and at 8 bar for different temperatures In simulator subsystems constants e coefficiente politropico slx Considering the air as an ideal gas the thermodynamic process inside the compressor follows a polytropic equation n 1 To h T R 26 where n is the polytropic coefficient 7 and 7 represent the air temperature re spectively before and after the compression process these two values are reported in 29 T_ref_in and T_ref_out P and P the air pressure before and after the compression process pres_ref_in and pres_ref_out From Equation 26 follows 27 e reynolds slx In fluid mechanics the Reynolds number Re is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of
15. ature in K of the inlet air of the compressor The default value is 298 15 K cp it is the specific heat at constant pressure expressed in J kg K The default value is 1005 J kg K cv it is the specific heat at constant volume expressed in J kg K The default value is 718 J kg K R_aria this parameter represents the air s constant as default this value assume the value of 287 J kg K File Edit View Display Diagram Analysis Help i CAE MLO system_parameters System parameters 172 Figure 12 System parameter module 26 4 How to set up a simulation To properly use the libraries it is firstly necessary to set their paths as follows File gt Set Path gt Add With Subfolders gt simulator The compressed air system layout we want to simulate must be reported inside a Matlab model to open this kind of file follow the instruction File gt New gt Model Now it is possible to start to reproduce the compressed air system inside the folder devices there are the modules described in sections before to simulate one of that you must open the related library copy the block and paste inside the model opened before Once reported all the blocks connect properly their input output signals Then it is necessary to set all that parameters will be used during the simulation inside the file parameters m all the simulation s parameters are reported if it is necessary you can mod
16. e obtained from dedicated graphs only for compressed air used for industrial purpose can be used the following empirical equation Tis 1 45310 4 T 110 4 35 31 The Equation 35 used in the Directive 2005 78 CE varies according to the air temperature The measurement unit is Pa s 32 B file parameters m Table 3 Constant s name Unit Default Description Variable value simulation_time s 604800 Total simulation time T Ts s 1 Sample time ts cp J kgK 1005 Constant pressure specific heat cp cv J kgK 718 Constant volume specific heat c R_aria J kgK 287 Air constant R T_amb K 293 15 Air ambient temperature Tari T_air_out K 300 15 Temperature of compressed air leaving the compressor pressure_amb Pa 101325 Ambient pressure Din U_rel 60 Relative humidity 33 Table 4 Constant s name Unit Default Description Variable value fad m s 0 043 Compressor flow provided by the compressor at fad condi tions t_on_off s 120 Time that must elapse be fore the compressor can starts again from stop mode n_avviamenti starts h 120 Maximum number of starts per hour fraction power 0 302 Percentage of rated power ab _unload sorbed by the compressor in unload mode rendimento_motore 0 9 Compressor s motor efficiency Nm rendimento_ 0 935 Compressor s gear efficiency Ngear trasmissione rendimento 0 66 Polytropic compression effi poi _politropica ciency time_
17. ed pressure drops Unfortunately the structure of simulink doesn t allow to use the same circular net work block for system with different number of loads So there were created 4 differ ent blocks the first has only one load circular_network1 slx the second has two loads circular _network2 slx the third has three loads circular _network3 slx and the fourth has four loads circular_network4 s1x Furthermore the blocks representing the end users had to be incorporated within the circular network block in order to avoid ambiguous references in the system If the number of loads is equal to n the network can be divided in n 1 parts where n 1 different flows that are our unknowns pass Since there are n 1 unknowns n 1 equations will occur These equations are one equation that describes the pressure balance and n equations that represent the mass balances In order to calculate the pressure drop in the circular network the Darcy s formula Equation 17 is implemented There are some terms that can be simplified so it can be used the first equation of the system 21 filiv Fo F falne frtiLnp10e 4 MA my i Mo tg ths thy 21 For the computation of the friction factor it is used the same procedure seen in the radial network module The sub block iterazione_colebrooke slx is incorporated within a Matlab Embedded function that solves the system 21 3 9 1 Input Output signals Input signal Inlet pressure of the network Pa Mor
18. ema Pa 650000 Pressure inside the system at po the beginning of the simulation Table 7 Constant s name Unit Default Description Variable value n saracinesche 0 Number of shutters opened _aperte n_saracinesche_ 0 Number of shutters half _mezze_aperte opened n_valvole membrana 0 Number of membrane valves n curve 0 Number of curves n_T_dritta 0 Number of T tube n_T_90 5 Number of angle pipe D_interno_tubo Im 0 05 Pipe s internal diameter D scabrezza_assoluta m 0 00005 Pipe s absolute roughness e D T_air_enduser A 293 15 Air temperature sampled near 35 the end users Table 8 Constant s name Unit Default Description Variable value flow_out m s 0 01 Flow rate required by the end qusr users at FAD conditions Table 9 Constant s name Unit Default Description Variable value filter_pressure_ Pa 20000 Filter s pressure drop Apr drop T_air_after_dryer K 298 15 Compressed air temperature after the air passes through the air dryer rendimento_air 80 Air dryer efficiency dryer 36 Table 10 Constant s name Unit Default Description Variable value kp 20 PI proportional gain kp ki 0 05 PI integral gain ki pressure_setpoint Pag 600000 Set point of the ASD Psp p_load_vsd Pag 600000 ASD load pressure p_off_vsd Pag 650000 ASD unload pressure scaling factor 2 4e 04 max_delta_speed rad s 30 4211 Maximum variation of the mo Anmax tor speed allowed dur
19. eover although is not visible the module receive another input signal the end user flow This signal is not show but it s a value required to evaluate the other signals Output signal there s no output signal 21 File Edit View Display Diagram Analysis Help pressure Circular network with 3 loads Figure 9 circular distribution system with 3 loads 3 9 2 Data stored in the Matlab s workspace e pressure_load the vector contains the sample of the air pressure Pa for each load e volume flow the vector contains the sample of the volume flow rate m s expressed in FAD condition for each load 22 3 10 Pressure reducer Higher is the air pressure inside the system bigger is the power absorbed by the compressor for this reason the pressure inside the system has to be as lower as possible Most systems have one or more critical applications that determine the minimum acceptable pressure in the system Generally the end users operative pressures are different in this cases more than one compressed air system could be necessary each of them has an own compressor room and network resulting in a higher installation and maintenance costs To reduce these costs pressure reducer are generally used pressure drops in the order of 40 of the compressor discharged pressure are not uncommon In Figure 10 is reported the pressure reducer module it emulates the pressure drop providing at the same time
20. er pmin and the maximum parameter pmax pressure levels allowed in the system The system pressure p k evaluated at time instant k can be written as p k p k 1 Ap k 1 11 Using the ideal gas law the Equation 11 can be written as reported below where qe is the instantaneous flow rate provided by the compressor room this value is the FAD provided by the compressor and stored in fad parameter qusr is the instantaneous 12 flow rate required by the users this value is the volume flow rate required by the end user expressed in FAD condition and stored in flow_out parameter V represents the receiver volume reported in volume_tank pp is the pressure of the FAD condition So at all time instants k we solve the following linear optimization problem N 1 AA X Pas n k 13 In order to solve this optimization problem the script MPC m it s needed This script contains the formulation of the problem written using YALMIP a language for advanced modelling and solution of convex and non convex optimization problems implemented as a free toolbox for MATLAB So you have to add to the Matlab path MPC m and YALMIP folder both 3 4 1 Input Output Signals Input signal Although is not visible the module receive as input signal the pressure inside the receiver This signal is not show because it isn t a real input for this module but a required value to evaluate other signals Output signal
21. essure inside the receiver This signal is not show because it isn t a real input for this module but a required value to evaluate other signals Output signal e power instantaneous power absorbed by the compressor in kW e energy energy consumed by the compressor kWh e flow it represents the instantaneous flow in m s provided by the compressor in FAD conditions 3 3 2 Main sub blocks Inside the folder simulator subsystems compressors there are the following sub blocks e compressor control _vsd_throttle slx depending on the system pressure and the pressure settings it evaluate the compressor state the number 3 represents the on mode while 1 the off mode e PI_control slx it implements the PI control to modulate the motor speed Equa tions 4 and 5 e reduction_motor_speed mdl it implements the motor speed variation when the compressor switch from load to off and vice versa 8 e throttle _vsd flow slx it calculates the flow provided by the vsd Equation 6 depending on the instantaneous motor speed throttle_vsd_power slx depending on the flow is providing the compressor and the operative pressure of the compressor the sub block implements the Equation 7 3 3 3 Data stored in the Matlab s workspace power it represents the instantaneous power measured in kW compressor_flow_rate it represents the instantaneous compressor flow in m3 s at FAD conditions energy it represents the total energy cons
22. from_off_to_on s 33 Time in unload mode before a compressor can start again fan_power AW 0 7 Power absorbed by the fun in Prun stalled inside the compressor oil_pump_power AW 0 Power absorbed by the oil Poil pump pump installed inside the com pressor velocity_ s 16 93 Time that must elapse before _loadTOunload the power absorbed from the grid passes from load to unload power T_ref_out K 358 15 Reference outlet air tempera ture without oil T_ref_in K 293 15 Reference inlet air tempera ture pres_ref_out Pag 950000 Reference outlet air pressure relative pres_ref_in Paj 100000 Reference inlet air pressure absolute pres_ref Pag 950000 Relative pressure whose temperature is T_air_compressor_out prefilter RSC Pa 0 Pressure drop caused by the _pressure_drop load unload compressor s filter prefilter_0S_ Pa 0 34 Pressure drop caused by the oil _pressure_drop separator filter Table 5 Constant s name Unit Default Description Variable value pipe length Im 0 Length of the pipe L leaks m3 s 0 Amount of air flow leakage ex qieaks pressed in FAD volume_tank m3 10 Volume of the receiver the pipe volume is evaluated and then added to this value V Table 6 Constant s name Unit Default Description Variable value pmin Pag 600000 Load pressure Pload pmax Pag 700000 Unload pressure Punload p out Pag 700000 Compressed air pressure pro vided by the compressor p iniziale_sist
23. he Matlab s workspace e tank_pressure for each sample time it contains pressure into the receiver in Pa gauge e FAD loss for each sample time it contains the volume flow rate lost along the distribution system 2FAD condition po 1 bar and To 20 C 13 File Edit View Display Diagram Analysis Help Pal oo S B ZENO receiver compressor fad Tank pressure Figure 4 Receiver module 3 6 Air dryer The air dryer removes water vapour from compressed air excessive water in compressed air either in liquid or vapour phase can cause a variety of operational problems for users of compressed air These include freezing of outdoor air lines corrosion in piping and equipment malfunctioning of pneumatic process control instruments fouling of processes and products and more Exist several type of air dryer regenerative desiccant dryers often called regens or twin tower dryers refrigerated dryers deliquescent dryers and membrane dryers The device modelled in ModSCA is a refrigerated air dryer it is refrigeration system that reduces the compressed air temperature hence the limit of water vapour saturation dew point lowering the air temperature the water starts to condensate Smaller is the output air temperature the smaller is the air moisture content Knowing the temperature of the air sucked in by the compressor and the air relative humidity this value is stored inside U_re1
24. ide this information 2 Simulator 2 1 Software s structure ModSCA needs a simulator environment this version is implemented for Matlab R2012b or following releases The folder simulator contains all the files necessary for a correct use of ModSCA The folder contains the following item e devices this folder contains files slx these are the modules emulating the main devices installed in a compressed air system The functioning of each device is mod elled inside a library block air_dryer slx circular_network slx end_user slx filter slx load_unload_compressor slx pipe slx pressure_reducer slx receiver slx system_parameters slx vsd_PI_compressor slx vsd_MPC_compressor slx e subsystems this folder contains five sub folders air_dryer compressors constants parameter pipe For more information see the Appendix A containing the blocks used to build the functionality of the library blocks e parameters m this file contains all the parameters will be used to perform the sim ulations If some parameters reported in the file are not stored in the workspace the simulation will not run correctly an error will show you during the simulation running The file suggests default values can be used if they are unknown moreover the files contains the units characterizing each value and some comments to explain what the parameter does For more details see Appendix B 2 2 Library
25. ify the default value after that you must run the file parameters m the variables will appear in your Matlab WorkSpace To modify these values it is also possible to double click on the blocks it will open a mask where it is possible to manually insert the values of the parameters required If you do not modify them they will assume the value reported inside the variable specified inside the mask Now it is possible to run the simulation as follows Simulation gt Start In order to understand how ModSCA works an easy example is proposed The ex ample LABAC slx represents model describing the compressed air system installed in our laboratory LABAC http www 3 unipv it energy labac It is composed by e load unload compressor e receiver filter e pipe network e end user 21 Edit View Display Diagram Simulation Analysis Code Jools Help O B GOD amp v maton tne 2 Power BUG B os Flow rate Tank End user pressure pressure Load unload compressor End user VariableStepDiscrete Figure 13 LABAC 28 A Sub blocks minor importance In simulator subsystems compressors e energy slx P t ts 24 where T s is the simulation time in simulation time and P t the instantaneous power absorbed by the compressor and ts the sampling period e reduction motor_speed mdl it implements the motor speed variation when the compressor switch from load to off
26. ing Ts max_speed rad s 608 4218 Maximum motor speed for an Mmax ASD min_speed rad s 225 116 Minimum motor speed for an nmin ASD max_flow m s 0 06 Maximum flow provided by an max ASD min_flow m s 0 0205 Minimum flow provided by an qmin ASD q_sc 0 0601 Coefficient p sc 1350000 Coefficient P_sc 2 4712ce 0Loefficient a_PO 0 0411 Coefficient describing relation between the flow provided by an ASD and the absorbed power a_P1 0 3124 Coefficient describing relation between the flow provided by an ASD and the absorbed power a_P2 0 0395 Coefficient describing relation between the flow provided by an ASD and the absorbed power a_P3 1 1822 Coefficient describing relation between the flow provided by an ASD and the absorbed power a_P4 0 2422 Coefficient describing relation between the flow provided by an ASD and the absorbed power a_P5 0 5426 Coefficient describing relation 37 between the flow provided by an ASD and the absorbed power Table 11 Constant s name Unit Default Description Variable value stages_number 1 reduced_pressure Pag 50000 38
27. optimal move N is generally called receding horizon parameter N At each k th instant the horizon is displaced towards the future The MPC strategy implemented in this model aims to minimize the power consumption Pas k along the prediction horizon by optimizing the motor speed The model of the power consumption is reported in Equation 7 First we introduce the constraints of a typical screw compressor Due to electrical and mechanical reasons the motor speed can vary between two thresholds Moreover the motor speed variation between two consecutive time instants is also bounded between Anmin ANmax Therefore the following constraints must be guarantee for a correct motor functioning Nmin lt n k lt Nmax k 0 8 ANmin Z n k ANmas k gt 0 where An k n k n k 1 parameter max_delta_speed and n 1 0 Moreover because the flow provided by an adjustable speed compressor can varies between two thresholds the following constraint must be fulfilled Amin lt q k lt Amaz 9 where Gmaz is the maximum flow can be produced by the adjustable speed compressor stored in max_flow while qmin min_flow is the minimum flow can be provide the com pressor Depending to the motor speed the flow provided by the compressor follows the Equation 6 10 Similarly the system pressure p k can vary between two thresholds Pmin lt p k lt Pmax 10 where Pmin and Pmax are respectively the minimum paramet
28. ready achieved then the compressor switches off When the pressure reaches the load value in pmin parameter the compressor switches in unload mode for a period whose value can be set in the parameter time_from_off_to_on After this period the compressor switches in load mode The power absorbed by the compressor in load mode is reported in the following P Pet Patong t Pian 1 where Poil pump is the power absorbed by the pump that moves the lubricant oil the value is reported in oil_pump_power Pry is the power absorbed by the fun for the air cooling fan_power and P is calculated as follows n 1 PambV n Pout _ 1 kW 2 OP Gitlin gear n 1 Pamb where Pam is the ambient pressure set in pressure_amb V is the flow provided by the compressor evaluated at FAD conditions this value is stored in fad pol Nm and Ngear represent respectively the polytropic compression efficiency the motor and gear efficiencies To set these values you have to refer to rendimento_politropica rendimento_motore and rendimento_trasmissione Pout is the relative pressure of the compressed air pro duced The parameter n represent the polytropic coefficient and is calculated by ModSCA through the Equation 26 3 2 1 Input Output signals Input signal Although is not visible the module receive as input signal the pressure inside the receiver This signal is not show because it isn t a real input for this module but a required value to
29. sor s flow at operative condition starting from the FAD conditions the first step to implement is to calculates the mass flow from the FAD as reported in Equation 32 then it is possible to convert the mass flow to volumetric flow at operative conditions The following equation allows to directly calculate the volumetric flow at operative conditions from FAD conditions 10 qeTout _ 33 O Reo 293 15K 33 Tout aNd Pout are respectively the temperature and pressure at operative conditions e filter_p_drop slx This sub block calculates the pressure drop due to the filter dust cake at each sample time The following equation allows to directly calculate the pressure drop 150 q v pa 1 e Ap 34 A pp de e3 Pa where q is the volume flow rate v is the air speed u is the dynamic viscosity of the air Pa is the air density while pp is the density of the particles A is the filter area and d is the diameter of the particles e time_load_unload_stop slx this sub block calculates each sample time the total load unload and off time of the compressor from the beginning of the simulation e viscosita_dinamica_aria slx This sub block calculates the air absolute viscosity it can can be defined as the resistance to flow encountered when one layer or plane of fluid attempts to move over another identical layer or plane of fluid at a given speed Absolute viscosity is also called dynamic viscosity The absolute viscosity can b
30. sor from the begin ning of the simulation until the present time It is evaluated in kWh load_time it represents the time in which the compressor worked in load mode It is evaluated in s unload_time it represents the time in which the compressor worked in unload mode It is evaluated in s stop time it represents the time in which the compressor was switched off It is evaluated in s 3 3 Adjustable speed compressor controlled with PI This module simulates a variable speed drive compressor it runs modulating the motor speed hence the output flow as long as the outlet pressure reaches an upper pressure setting p_off_vsd parameter which causes the compressor goes in off mode the motor starts to decrease its velocity each second the motor speed is reduce of max_delta_speed Depending on the motor speed before the stop command the compressor take some seconds to completely stop the motor When the pressure reaches the load value in p_load_vsd parameter the compressor switches in modulating mode the velocity start to increase with the same velocity When loaded the compressor modulates its velocity between a bounded range re spectively in min_speed and max_speed depending on the pressure inside the system Generally the motor speed is controlled through a PI control scheme the control law implemented is the following An min Attimar K kpAer kpkrerts 4 where Anmaz is the maximum motor speed variation allowed
31. tems parameter there is the sub block filter_p_drop slx 16 3 8 Radial Network Inside a compressed air network the air is subjected to a pressure drop due to mass losses concentrated and dynamic losses The first one depends on leaks can occur along the network the second one is due to curves junction etc in the pipes while the last one are due to frictions when the air flows inside the pipe File Edit View Display Diagram Analysis Help ty aa B O Pipe Pipe inlet pressure outlet pressure Figure 7 Radial distribution system module The dynamic losses are modeled in ModSCA through the Darcy s formula that can be used for incompressible fluids we all know that the air is a compressible fluid but it is possible to demonstrate that if the Much number is smaller than 0 3 the air can be con sidered as an incompressible fluid In fluid mechanics the Mach number is a dimensionless quantity representing the ratio of speed of an object moving through a fluid and the local speed of sound In the case considered this parameter can be calculate as follows v Ma 16 s 16 where v is the air velocity inside the pipe while c is the speed of sound The Darcy s formula is presented below pLwv ha p fp where f is the pipe s friction factor whose value is calculated inside a sub block will be 17 shown in the following and p is the air density evaluated as reported in Equation 29 D is
32. the energy wasted to increase the air pressure to levels higher than required The equation used to model the energy waste comes from D Kaya P Phelan D Chau H Sarac Energy conservation in compressed air systems 2002 File Edit View Display Diagram Analysis Help z H A e EMOR pressure_reducer system pressure z i energy waste kwh Pressure_reducer Figure 10 Pressure reducer module The total energy lost US in kWh from the beginning of the simulation can be esti mated as follows 2 US X 1 0 FR P ts 22 t 1 where F R is the ratio of the proposed power consumption to current power consumption based on maximum operating pressure it is an a dimensional value P is the power absorbed by the compressors while loaded in kW and ts is the sampling time in s The following equation can be used to estimate FR the horsepower reduction fac tor based on current and proposed operating pressures Compressed air and Gas hand 23 book 1961 Dap p p DIN 1 pap pe Die 1 Pap is the absolute discharge pressure at proposed operating pressure conditions the relative discharge pressure is reported in reduced_pressure pae is the absolute discharge pressure at current pressure conditions the relative one is reported in p_out p is the inlet pressure in pressure_amb k the specific air heat and N the number of stages stored in stages number FR 2
33. these two types of forces for given flow conditions D pa 28 u where D is the pipe s diameter p is the air density v the air velocity and u the absolute viscosity whose value is calculated in a dedicated sub block describe below In simulator subsystems parameter e air_density slx The air density can be calculated from the ideal gas law pu mRT m p 29 where p is the absolute air pressure R the air constant ant T the air temperature e fad_loss slx For each sample time it contains the volume flow rate lost along the distribution system 2 k 1 k 1 Pi PaT Pas g M C4 A p A 2 cert Bold see k 30 l d p ie ee oe 30 Where Cy is the emission coefficient A is the area of an equivalent hole p is the density of air inside the pipe while pa is the one outside the pipe p is the pressure inside the pipe while p is the one outside the pipe After computing the mass flow lost kg s we need to pass in volume flow rate expressed in FAD condition m s Mp RD P where p 100000 Pa T 293 15K for the FAD condition q 31 30 e fad to kgs slx This sub block calculates the mass flow provided by the compressor starting from the FAD Free Air Delivery it is the amount of atmospheric air free air can be sucked in by the compressor at inlet conditions p 100000 Pa T 20 C and U 0 10 q Pgs a E 32 M Rx 293 15K 32 e fad_tom3s slx This sub block calculates the compres
34. umed by the compressor from the begin ning of the simulation until the present time It is evaluated in kWh load_time_vsd it represents the time in which the compressor worked in load mode It is evaluated in s stop_time_vsd it represents the time in which the compressor was switched off It is evaluated in s 3 4 Adjustable speed compressor controlled with MPC The proposed method is based on model predictive control that is an optimal controller based on the future air demand forecasting Differently from the PI controller the MPC does not required the setting of a set point but only of a control range in which the pressure can vary As a consequence of the reduction of the pressure levels a smaller amount of energy is absorbed by the compressor and a reduction of air leaks occurs It is possible because the MPC has the ability to anticipate future events using this information to take control actions accordingly For a comprehensive implementation of this control scheme forecasting techniques need to be applied to assess end users air requirements Model predictive control is an optimal control based method to select control inputs by minimizing an objective function defined in terms of both present and predicted system variables MPC is also known as Receding Horizon Control because at the k th time it solves an op timal control problem over a finite future horizon of t 0 1 2 N 1 steps then applying only the first
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