determine current transformer suitability using emtp models
Contents
1. 1 001 1 0008 2 as 5 1 0006 D 9 1 0004 S e 1 0002 1 0 20 40 60 80 100 120 140 160 Percent Rated Primary Current 2 5 P 2 gt iz gt 2 c gt 1 5 ci i c e 1 Un 2 e lt 0 5 N cd K 0 0 20 40 60 80 100 120 140 160 Percent Rated Primary Current B 5 APPENDIX C EXAMINE X R SATURATION AND BURDEN EFFECTS Use the ATPDraw circuit shown in Figure C 1 to simulate CT response to changes in saturation and burden The source represents system voltage Adjust X R with the RLC element connected to the source Appendix A describes the CT which is modeled as a saturable transformer component Set the CT secondary burden using the RLC element connected to the transformer d 2 System Burden Figure C 1 Test Circuit ATPDraw Enter all of the component data and review the ATP Settings command under the ATP menu item in ATPDraw Use the Make File command under ATP menu item to create the following text file for ATP input C Generated by ATPDRAW August Thursday 19 1999 C A Bonneville Power Administration program C Programmed by H idalen at SEfAS NORWAY 1994 98 ALLOW EVEN PLOT FREQUENCY C Miscellaneous Data Card dT gt lt Tmax gt lt Xopt gt lt Copt gt 000018 09 60 60 500 50 1 1 1 0 0 1 0 C 1 2 3 4 5 6 7 8 C 34567890123456789012345678901234567890123456789012345678901232. D alude oe d d 1 1 3 i cre 1 Figure 21 CT Saturation Effects 22 and 20 Calculations Appendix E Power System and Digital Relay Models describes the ATPDraw circuit and Mathcad calculations used in this example CONCLUSIONS 1 ATP ATPDraw TOP and Mathcad are effective inexpensive tools for power system transient analysis and relay simulation ATP is very effective for modeling particular power systems and equipment configurations 2 You can construct an effective C class CT model from excitation curve data The model is limited to a frequency response of a few kilohertz and does not include hysteresis or remnant flux 3 You can derive an accurate relay model from public information such as conference papers and instruction manuals Use the model to understand relay transient performance in your system to improve applications and settings REFERENCES 1 2 3 4 2 6 7 3 9 10 Stanley Zocholl and D W Smaha Current Transformer Concepts Proceedings of the 46 Annual Georgia Tech Protective Relay Conference Atlanta GA April 29 May 1 1992 Stanley E Zocholl Jeff Roberts and Gabriel Benmouyal Selecting CTs to Optimize Relay Performance Proceedings of the 23 Annual Western Protective Relay Conference Spokane WA Octo
3. Mk mam omn MCA E 9 T La db db e L w MAJ M Canaus Figure E 2 A Portion of the Mathcad Display File Copyright SEL 1999 All rights reserved Printed in USA 991007 E 10
4. Create a filter index if and apply full cycle cosine filter CF to current and voltage vectors linterp if RS 1 S RS 1 imr 2 PAL 2 dd g RS 1 k k 0 CF la if VA if IB CF Ib if VB CK Vb if IC C Ie if VC CK Ve if Create a complex vector index iv and form a complex vector quantities at 90 degree intervals iv RS4 1 S IAcpx IA RS VAopx VA tj VA RS IBepx cpx from filtered IB j IB iv iv iv 4 4 4 VBepx VB iom RS IC RS VCcpx VC MS RS 4 4 4 Calculate sequence currents and voltages 2 2 Cy T ee ees 3 3 IQ ZERO ZERO VAcpx VBcpx I 5 ONE IAopx IBcpx ONE VAcpx VBcpx VCepx D TWO TAcpx IBepx TWO VBepx VCepx Create polarizing voltages for impedance calculations ii RS 1 RS 17 ii RS 17 S 31 VPOLVa V ME VPOLVa Vl VPOLVa 111 111 32 32 VPOLVb a VPOLVa VPOLVc a VPOLVa continued on next page E 6 continued from previous page Calculate phase to phase impedances Rel VAcpx VBepx VPOLVa VPOLVb rr S Re 1 4 aIL TAcpx IBepx
5. 001 0 130912 31 2538 0011 0 143192 34 0012 0 15527 37 1111 0013 0 167126 39 0014 0 178746 42 0015 0 190111 45 0016 0 201206 48 0017 0 212015 50 0010 0 222523 53 0019 0 232714 55 002 0 242575 58 118 0021 0 252091 60 0022 0 261249 62 1999 9087 2564 2068 9628 7576 4917 1611 7621 291 7441 4094 6149 Type 8 BUR24018 gt PRI SRC Type 8 Figure B 3 TOP CSV Text File Output B 2 The Mathcad file that processes the primary and secondary data 15 listed below Import data from an external file into matrix Data Data C BUR24018 CSV men Count rows of matrix Data and create an index 1 as a row pointer 1 0 rows Data 1 Create time vector t and calculate the data time step At Data Create current vector Isec and Ipri from imported data Isec lt DataS pri Plot The data from ATP consists of 3 cycles each at 5 10 20 60 100 and 150 rated primary current The functions below calculate RCF and PACF using the middle cycle of the 3 cycle tests 4000 2000 Ipri 0 2000 4000 0 160 Create index of middle cycle endpoints Create functions k y and g y to calculate the beginning and ending row index points of the middle cycle continued on next page B 3 Ky oaj D 2 60 At gy 60 continued from previous page
6. Create function RMS to calculate the rms value of the middle cycle of current I determined by RMS I Y rms 0 for je g Y rms 60 rms RMSc 4 ms Calculate the number of data points per quarter cycle 111 4 60 At r ceil Create function PA to calculate the phase angle difference in seconds between Ipri and Isec at middle cycle points lt 0 for je 2 g Y e Ipri w j pri Iscc lt Isec Isec i ee j arg arg sce 180 60 T lt mean pa Calculate the rms value of secondary current Isec at the middle cycle points y RM5sec RMS Isec y Calculate the rms value of primary current Ipri at the middle cycle points y lt 5 1 Calculate the phase angle difference in seconds between Ipri Isec at the middle cycle points y PA Calculate the ratio correction factor RCF at each middle cycle point y The calculation assumes a 1200 5 CT RMSpri RMSsec 240 continued on next page B 4 continued from previous page Calculate the percent primary current at each middle cycle point y The calculation assumes a 1200 5 CT This quantity is used as the independent variable x axis for graphing 100 PCTIpri 1200 Graph and secondary phase angle minutes
7. FF 121984 10000 10000 4 20009 RECOV gt SEC 4 SEC 8 50000 RECOV PRI SRC 8 0 20 0 Time mS 60 80 100 Figure C 2 Simulation Results in File Save As menu item Import the CSV text file into Mathcad The Mathcad file that processes the data is listed below data CA RECOV CSV data i 0 r 1 t data 07 lt V PE data _ lt I cea data _ lt l pri data At t to 1 gt 2 gt 3 gt Count rows of matrix Data Create an index as a row pointer Calculate the data time step At continued on next page Import data from an external file into matrix Data Create time vector secondary Voltage vector V sec current vectors from imported data continued from previous page Create a function VTA to calculate the Volt Time Area of the V secondary voltage curve X VTA x gt coo At j j 0 VT VTA i Create functions k y and g y to calculate the beginning and ending cycle index points for the RMS calculation Ky oaj D 2 60 At gy tel 60 Create function RMS to calculate the rms value of one cycle of current determined by cycle count Y RMS I Y rmse 0 for je k Y g Y rms
8. RMS 3 90504 CF 2 7198 1000 4 FF 1 5095 Ej i 2000 BUR24018 SEC Type 8 BUR24018 gt PRI SRC Type 8 0 100 200 JUU Time mS 5000 Figure 5 Primary and Secondary Current in TOP save the TOP active window containing the CT primary and secondary currents shown in Figure 5 as a CSV text file using the File Save As menu item Read the CSV text file into Mathcad and calculate the RCF and PACF Figure 6 shows calculated RCF and PACF The maximum ratio error is 0 09 percent indicating that this CT could be used in a metering application You can easily change the ATPDraw circuit to include other burdens and connections For example you could model wye connected CTs under unbalanced load to see how the size of a common neutral wire affects accuracy Appendix B Calculate CT Accuracy describes the ATPDraw circuit and Mathcad calculations used in this example 1 001 1 0008 1 0006 1 0004 Correction Factor 1 0002 Phase Angle Secondary Lead Minutes Percent Fated Primary Cumrent Figure 6 Calculated RCF and PACF THE EFFECTS OF X R CT CLASS AND BURDEN ON CT SATURATION AND RECOVERY TIMES The criterion to avoid CT saturation 2 1s R Where X R the X R ratio of the primary fault circuit Ir the maximum fault current in pe
9. z VPOLVb 00001 Rel 1 Z 011 IBepx ICcpx VPOLVb VPOLVs 00001 Rd VCcpx VAcpx VPOLVe VPOLVa 1 ACepx VPOLV VPOLVa 00001 Calculate phase to ground impedances Re VPOLVa 8 E A U a Re CI Z o1L IAcpx 3 k0 I0 VPOLV 00001 Re VB CPX VPOLV Re I IBepx 3 k0 I0 VPOLVR 00001 Re VPOLVS MCG Rd I Z 01 1 3 k0 I0 VPOLVS 00001 Calculate negative sequence impedance Rd V2 2 1 Z aL p 00001 22 1V Calculate zero sequence impedance Iz 10 E 00001 Figure E 2 below which extends over several pages shows a portion of the Mathcad display file Example plots show simulated relay response to saturated CT secondary currents calculated by ATP E 7 dala tumigas ZB ua d PA iD TJA 2 3 60 cdi 3397 OL ES 516 Import dala tom an extemal file eo mabnx dala Creato 10 enber complex data in polar farm Enter the value al Ihe transmessian lina Enter the posite sequence line angle Erter the zero guirit bine angie Erter the number of samples par cycle of the digital relay Call refererste fle background calculations B Reference NNP RAT witch T Pref mc E 8 ERE ee mom m ay EE HAL
10. 10 1 1 1 0 0 1 0 1 2 3 4 5 6 7 8 345678901234567890123456789012345678901234567890123456789012345678901234567890 BRANCH lt n 1 gt lt 2 gt lt refl gt lt ref2 gt lt gt lt gt lt gt lt n 1 gt lt 2 gt lt refl gt lt ref2 gt lt gt lt A gt lt B gt lt Leng gt lt gt lt gt 0 TRANSFORMER TX0001 1 INCLUDE C WINDOWS DESKTOP WPRC CT1200 SAT240RD PCH 1 00015 576 240 2PRI 1 0E 7 l PRI 1 00E7 0 SWITCH lt n 1 gt lt 2 gt lt Tclose gt lt Top Tde gt lt Vf CLOP gt lt type gt SECI MEASURING 1 SOURCE lt 1 gt lt gt lt Ampl gt lt Freq gt lt Phase T0 gt lt Al gt lt gt lt TSTART gt lt TSTOP gt 14XX0001 0 707 1 60 1 l BLANK BRANCH BLANK SWITCH BLANK SOURCE BLANK OUTPUT BLANK PLOT BEGIN NEW DATA CASE BLANK A 4 Send the file to ATP with the run ATP command under the ATP menu in ATPDraw Examine the output with the graphical postprocessor TOP and record the secondary excitation voltage versus the RMS excitation current Repeat this process for every data point in the excitation curve Plot the secondary excitation voltage versus the RMS excitation current to test the model Figure A 5 shows the ATP output pl4 file in TOP The source in ATP was set for a peak of 707 1 V or 500 RMS From the file SA7240 atp at 500 V the secondary excitation current should be 0 12 A RMS TOP calculates the RMS cu
11. 6253 100 f A 2 58757 Magnitude 00 Time mS Figure D 2 Simulation Results in TOP Save the TOP active window containing the currents and voltage as a CSV text file using the File Save As menu item Import the CSV text file into Mathcad The Mathcad file that processes the data is listed below Import data from an external file into matrix Data Data C RECOV CSV Count rows of matrix Data R rows Data 1 66599 Create an index 1 as a row pointer 1 0 Create time vector and current vector from imported data and calculate the data time step At IR At U to Enter the number of samples per cycle of the relay RS 16 Calculate the number of samples to create an averaging LP filter with a cutoff frequency at 1 2 the sampling frequency 2 LPW floor 60 At RS I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I lt 0 gt t Data I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I continued on next page I I D 2 continued from previous page Averaging filter LPW 1 gt IR LPW k S LPW LP a 1 R k 0 Calculate L
12. Transmission line impedance on either side of the fault e Fault switch e Fault impedance Dampening resistance to prevent numerical oscillation e Voltage transformers resistor dividers e Current transformers e CT secondary lead and burden impedances Digital Relay Model The digital relay model is derived from public information conference papers and manufacturer instruction manuals The digital relay model includes e Anti alias low pass filter cutoff slightly above one half sampling frequency e Sampling function e Full cycle cosine filter e Sample to vector converter e Sequence current and voltage calculation e Polarizing voltage calculation e Phase distance calculation e Ground distance calculation Negative sequence impedance calculation e impedance calculation Appendix E Power System and Digital Relay Models describes the ATPDraw circuit and Mathcad calculations used in this example Figure 17 shows the effects of CT saturation during a phase to phase to ground fault at 15 percent of the line length applied at 7 cycles into the simulation Force saturation by increasing CT burden to 4 Ohms Open the line breaker after 5 cycles Pimp Li E Figure 17 Saturated B and C Phase CT Secondary Current Phase to Phase to Ground Fault After analog filtering sampling and digital filtering the CT secondary current appears as shown in Figure 18 i
13. but you can use any ATP line model Split the line into two elements one on either side of the fault Appendix A Develop A 1200 5 CT Model describes the CTs which are modeled as saturable transformer components The CT secondaries are wye connected and grounded at the relay The CT leads and relay elements are modeled as resistances but you can change them to include reactances Attach shunt RLC elements to the circuit breakers to dampen numerical oscillation E 1 Figure E 1 Small System Model in ATPDraw Enter all of the component data and review the ATP Settings command under the ATP menu item in ATPDraw Use the Make File command under the ATP menu item to create the following text file for ATP input E 2 C Generated by ATPDRAW September Wednesday 1 1999 C A Bonneville Power Administration program C Programmed by H H idalen at SEfAS NORWAY 1994 98 ALLOW EVEN PLOT FREQUENCY C Miscellaneous Data Card C dT gt lt Tmax gt lt Xopt gt lt Copt gt 000002 2833 60 60 500 250 1 1 1 0 0 1 0 C 1 2 3 4 5 6 7 8 C 345678901234567890123456789012345678901234567890123456789012345678901234567890 BRANCH C lt n 1 gt lt 2 gt lt refl gt lt ref2 gt lt R gt lt gt lt gt lt n 1 gt lt 2 gt lt refl gt lt ref2 gt lt gt lt A gt lt B gt lt Leng gt lt gt lt gt 0 C Sending Source Impedance 5IVSA 3 681 24 515 52VSB 819 7 757 5315 VSBC
14. lt Copt gt 000018 2 60 60 500 50 1 1 1 0 0 1 0 1 2 3 4 5 6 7 8 C 345678901234567890123456789012345678901234567890123456789012345678901234567890 BRANCH lt n 1 gt lt n 2 gt lt refl gt lt ref2 gt lt gt lt L gt lt gt lt n 1 gt lt n 2 gt lt refl gt lt ref2 gt lt R gt lt A gt lt gt lt Leng gt lt gt lt gt 0 TRANSFORMER TX0001 3 1SEC 576 240 2SWI 1 0E 6 1 SEC 5 3 PRI SRC 39 4 5 3 SWITCH lt n 1 gt lt 2 gt lt Tclose gt lt Top Tde gt lt Vf CLOP gt lt type gt SWI 1 100 10000 0 SOURCE lt n 1 gt lt gt lt Ampl gt lt Freq gt lt Phase TO gt lt Al gt lt gt lt TSTART gt lt TSTOP gt 14SRC 0 120000 60 85 24 40333 20 BLANK BRANCH BLANK SWITCH BLANK SOURCE SEC BLANK OUTPUT BLANK PLOT BEGIN NEW DATA CASE BLANK I I INCLUDE C WINDOWS DESKTOP WPRC CT1200 SAT240 PCH D 1 Send the file to ATP with the run ATP command under the ATP menu in ATPDraw Examine the output with the graphical postprocessor TOP and plot the secondary current as shown in Figure D 2 RECOV SEC Type 8 Max 169 81 in 109 274 150 Avg 51 578 Abs 169 81 RMS 65
15. simulation Burden voltage at time step Plot VTA n as n changes from 0 to the end of the simulation and compare the result to the rating voltage of 800 volts for a C800 CT The voltage in Figure 8 shows slight saturation after 5 cycles when the accumulated volt time area shown in Figure 9 approaches 1 000 volts Recall that CT ratio accuracy will be within 10 percent at the CT rating voltage The criterion to avoid CT saturation will maintain this accuracy cir VIA LETT Figure 9 Accumulated Volt Time Area Now consider a C800 CT Figure 7 operating at its rating voltage 100 amps secondary 8 Ohm burden Using the same technique plot the secondary voltage and accumulated volt time area in Figure 10 Vote PLAGE REA AG OV SLAVE ALE SEL SE SEL A 00V VM M M V LLL M NL Figure 10 C800 CT at Rated Voltage Note in Figure 10 that the CT is operating in saturation but the ratio correction factor in Table 1 shows the CT accuracy is within its rating limits after one cycle and below two percent error after four cycles Table 1 CT RCF at Rated Voltage Finally consider the C800 CT in Figure 7 now with a secondary burden of 4 Ohms The magnitude of the primary current is selected to give 65 amps secondary operating the CT well below its rating voltage after the dc transient subsides The dc offset in the primary current drives the CT into saturation In Figure 11 the CT
16. transient modeling Different computer operating systems use different versions of the program Version ATPMING works very well with MS Windows 95 and 98 ATP is free to licensed users who meet the requirements of the ATP users group Most utilities consultants and manufacturers easily meet these requirements Licensing information is available on the World Wide Web at Attp www ee mtu edu atp index html Once licensed simply download the program from a password protected site on the World Wide Web ATPDraw ATPDraw is a graphical mouse driven preprocessor to ATP on the MS Windows platform and uses a Standard Windows layout Users build a picture of an electric circuit by selecting components from menus and using dialog boxes to enter component values and ATP parameters ATPDraw then creates the ATP input file and runs ATP Basic ATP model development is much easier in this environment particularly for new users You can download ATPDraw for Windows free of charge from the ftp server ftp ee mtu edu user Anonymous password your e mail address The Bonneville Power Administration USA and SINTEF Energy Research Norway own the proprietary rights TOP written and supported by Electrotek Concepts Inc is a graphical postprocessor for transient data TOP will graph ATP output files pl4 and allow users to save the data in different formats including COMTRADE and comma separated variable CSV text files This program is the bridg
17. 1 1993 BIOGRAPHY Ralph W Folkers received his B S and M S in Electrical Engineering from Iowa State University He joined Iowa Public Service in 1978 specializing in substation operations and design electric metering and system protection In 1998 he joined the Research and Development Group of Schweitzer Engineering Laboratories as a power engineer Mr Folkers has been a registered Professional Engineer in the State of Iowa since 1979 He has authored several technical papers and presentations on power engineering APPENDIX A DEVELOP A 1200 5 CT MODEL Use the data in Figure A 1 to develop and test a 1200 5 CT model in ATP me Characteristics A E V alta Bi dH mtb 347 8 bill at Jr HAUT eo J M 1111 VA 0 0024 Ohms Turn 75 Al iV 1 785 Es Turn Knee 0 01 100 Secondary E Amps Figure A 1 CT Characteristics Calculate secondary resistance Rs Rs 0 0024 240 Rs 0 576 Q Calculate secondary voltage V at the knee of the excitation curve 1 875 240 428 4 V Create a file SAT240 atp with current voltage pairs selected from the 1200 5 secondary excitation curve Select a point at the lower end of the curve several points at and just above the knee of the curve and a point at the upper end of the curve Send this file to ATP to create a punch file SAT240 pch contai
18. 16 samples per cycle or 960 samples per second The analog low pass filter is set at a cutoff frequency of 540 Hz to limit signal aliasing After sampling by the A D converter the relay converts the current samples to complex vectors by Icpx I j 1 4 Where Icpx complex current at sample 5 the most recent sample of current at sample s n the number of samples per cycle I n4 the sample of current take 1 4 cycle in the past The relay then compares the absolute values of the complex currents to the 50 element setting to determine if the element should operate Figure 14 shows the relay response to the saturated current from Figure 12 Calculated Current asap aed 30 Setting Figure 14 Relay Response to Saturated CT Secondary Current In this example saturation initially reduces the relay magnitude response by one half a reduction that may affect relay performance in different ways For example a high set instantaneous 50 element could pick up for one cycle and then drop out for one to two cycles A time delayed overcurrent element could respond up to three cycles late This example demonstrates that you can model saturated CTs and relay elements to better understand relay performance during transient events Appendix D Examine Overcurrent Element Response to Saturated CT Secondary Current describes the ATPDraw circuit and Mathcad calculation
19. 45678901234567890 BRANCH lt n 1 gt lt n 2 gt lt refl gt lt ref2 gt lt gt lt L gt lt gt lt n 1 gt lt n 2 gt lt refl gt lt ref2 gt lt R gt lt A gt lt gt lt Leng gt lt gt lt gt 0 TRANSFORMER TX0001 3 INCLUDE C WINDOWS DESKTOP WPRC CT1200 SAT240 PCH 1SEC 576 240 2SWI 1 0E 6 1s SEC 4 3 PRI SRC 39 4 5 3 SWITCH C lt n 1 gt lt 2 gt lt Tclose gt lt Top Tde gt lt Vf CLOP gt lt type gt SWI PRI 1 10 10000 0 SOURCE lt 1 gt lt gt lt Ampl gt lt Freq gt lt Phase TO gt lt Al gt lt gt lt TSTART gt lt TSTOP gt 14SRC 0 100000 60 85 24 20 BLANK BRANCH BLANK SWITCH BLANK SOURCE SEC BLANK OUTPUT BLANK PLOT BEGIN NEW DATA CASE BLANK C 1 Send the file to ATP with the run ATP command under the ATP menu in ATPDraw Examine the output with the graphical postprocessor TOP and plot the secondary burden voltage secondary burden current and primary current as shown in Figure C 2 Notice that the secondary quantities appear very small because of the plot vertical scale Save the TOP active window containing the currents and voltage as a CSV text file using the Voltage V 0000 RECOV gt SEC 4 f Max 642 902 500 930 ib Avg 192 497 Abs 642 902 RMS 234 813 20000 CF dr
20. 60 1 2 1 rms RMS arms Create an index of simulation time in integer cycles u 1 floor max t 60 Calculate the CT ratio correction factor 1 RMS 1 coc ti 22407 RMS I prj ii Create a cycle pointer X 1 ii Ratio correction factor at the end of each cycle 0 1 2 3 4 5 stack B RCE 1 2487 1 8881 1 3119 1 1109 1 0594 continued on next page C 3 continued from previous page 4 APPENDIX D EXAMINE OVERCURRENT ELEMENT RESPONSE TO SATURATED CT SECONDARY CURRENT Use the ATPDraw circuit shown in Figure D 1 to simulate CT response to changes in X R saturation and burden The source represents system voltage Adjust X R with the RLC element connected to the source Appendix A Develop A 1200 5 CT Model describes the CT which is modeled as a saturable transformer component Set the CT secondary burden using the RLC element connected to the transformer 2 Sushem MER LC Burden Figure 0 1 Test Circuit ATPDraw Enter all of the component data and review the ATP Settings command under the ATP menu item in ATPDraw Use the Make File command under the ATP menu item to create the following text file for ATP input C Generated by ATPDRAW August Friday 20 1999 C A Bonneville Power Administration program C Programmed by H H idalen at SEfAS NORWAY 1994 98 ALLOW EVEN PLOT FREQUENCY C Miscellaneous Data Card dT gt lt Tmax gt lt Xopt gt
21. C Line Impedance Sending Side 5IVSLA FA 7 363 49 03 52VSLB 1 639 15 514 53VSLC VSBA 1 9 2 VSBB 1 9 2 VSBC 1 9 2 Three Phase Fault Impedance FSWA FN 1 0E 6 3 FSWB FN 1 0E 6 3 FSWC FN 1 0E 6 3 C Line Impedance Receiving Side 51FA VRLA 29 45 196 21 52FB VRLB 6 555 62 055 53FC VRLC C Ground Fault Impedance FN 1 0E 6 0 C Receiving Source Impedance 51RBA VRA 3 681 24 515 52RBB VRB 819 Ff SF 53RBC RBA 1 9 2 RBB 1 9 2 1 9 2 Dampening Resistance VSSWA 4 00E5 0 VSSWB 4 00E5 0 VSSWC 4 00E5 0 C Dampening Resistance VRSWA 4 00E5 0 VRSWB 4 00E5 0 VRSWC 4 00E5 0 C Phase C Current Transformer TRANSFORMER TX0001 3 INCLUDE C WINDOWS DESKTOP WPRC CT600 SAT120 PCH 1SCC 288 120 2VSBC CTC 1 0E 6 I C Phase B Current Transformer TRANSFORMER TX0002 3 INCLUDE C WINDOWS DESKTOP WPRC CT600 SAT120 PCH 1SCB 288 120 2VSBB 1 0E 6 ly continued on next page E 3 C Phase A Current Transformer TRANSFORMER 1SCA 2VSBA SECC SECB SECA C Phase SECC C Phase SECB C Phase SECA C Phase VSECB VSBB C Phase VSECA VSBA C Phase VSECC VSBC SWITCH C lt I n 2 gt lt Tclose gt lt Top Tde gt lt CTA CTB CTC RBA RBB RBC SECN 288 CTA SCC SCB SECN SCA C Relay Resistance 4 Relay Resistance 4 A Relay Resistance 4 B Voltage Transformer 100 VSECB 2 00 5 A Voltage Transformer 100 VSECA 2 00
22. DETERMINE CURRENT TRANSFORMER SUITABILITY USING EMTP MODELS Ralph Folkers Schweitzer Engineering Laboratories Inc Pullman WA USA ABSTRACT Current transformer CT and relay modeling are practical tools to evaluate protection equipment performance This paper demonstrates the use of a set of software tools Electromagnetic Transients Program EMTP The Output Processor TOP and Mathcad to model transient events in the power system as well as relay response to those events The paper provides step by step instructions for using these tools to better understand and protect power systems Specifically in this paper we 1 Model CTs using EMTP to visualize transient events 2 Transfer EMTP output into Mathcad to examine CT accuracy burden effects saturation and subsidence 3 Model digital relays in Mathcad to show the effects of CT saturation on overcurrent distance and directional element operation making relay response to transient events easier to understand INTRODUCTION Older existing or spare equipment is often used in new construction or retrofit projects Changing system conditions can cause existing and spare equipment to operate outside of its intended rating To effectively evaluate equipment suitability you must have the tools to determine power transformer or circuit breaker CT performance in a protection scheme The Alternative Transients Program ATP version of EMTP is an inexpensive powerful tool f
23. E5 C Voltage Transformer 100 VSECC 2 00E5 VSSWA VSSWB VSSWC VRSWA VRSWB VRSWC C Sending Circuit Breaker VSSWA VSSWB VSSWC VSLA l VSLB l VSLC l C Receiving Circuit Breaker VRLA VRLB VRLC C Fault FSWA FSWB FSWC SOURCE VRSWA VRSWB VRSWC Switch continued from previous page TX0003 INCLUDE C WINDOWS DESKTOP WPRC CT600 SAT120 PCH 001 1 0E 6 NS 1 10 FB 117 117 I5 Ie 120 Iz gt lt Vf CLOP gt lt type 01 01 01 01 01 lt n 1 gt lt gt lt Ampl gt lt Freq gt lt 0 gt lt C Sending Source 14VSA 0 189500 60 14VSB 0 189500 60 14VSC 0 189500 60 C Receiving Source 14VRA 0 189500 60 14VRB 0 189500 60 14VRC 0 189500 60 BLANK BRANCH BLANK SWITCH BLANK SOURCE BLANK OUTPUT BLANK PLOT BEGIN NEW DATA CASE BLANK 120 120 30 150 90 A1 MEASURING MEASURING MEASURING MEASURING MEASURING MEASURING T1 TSTART TSTOP 1 1 1 1 1 1 P LE gt E 4 Send the file to ATP with the run ATP command under the ATP menu in ATPDraw Examine the output with the graphical postprocessor TOP and plot secondary currents and voltages from the sending end Save the TOP active window containing the currents and voltage as a CSV text file using the File Save As menu item I
24. P filtered current 1 lt I LP 11 66 99 Calculate the number of relay samples available in data and create an index 5 as a row pointer Ss floor t 6085 s 0 S Create a vector Ja representing the sampled relay values interp r RS 60 Create a filter index if and apply a full cycle cosine filter IF to vector if Z RS 1 5 RS 1 gt COS RS k 0 Create a vector index iv and form vector current Icpx from 90 degree interval filtered quantities iv 1 5 2 k if RS 1 k 1 j TE 4 continued next page D 3 m Iv cles continued from previous page Calculated Current Magnitude Saturated Secondary Current 1 0625 r 1 1 E Ch wy ch Ch 1 Graph the absolute value of complex quantity and value of sampled D 4 APPENDIX E POWER SYSTEM AND DIGITAL RELAY MODELS Use the ATPDraw circuit shown in Figure E 1 to simulate CT response in a two bus power system The system quantities are 8 19 177 57 Positive sequence line impedance Zo 36 81 3245 15 Zero sequence line impedance Zs 0 1 ZL Positive and zero sequence source impedances Vp 189500 Peak source voltage V sena leads Vreceive by 30 This example uses mutually coupled RL elements for lines and sources
25. a 9 9 25 9 5 g 75 1 7 E 8 75 0 Cycles Calculated Current Magnitude Saturated Secondary Current 50 Element Setting Figure 16 Subsidence Current 7 5 to 10 Cycles The one half cycle cosine filtered current drops below 0 5 amps at t 2 8 6 cycles or 0 75 cycles after the breaker opens The unfiltered CT secondary current and low pass filtered CT secondary 13 current decay over time dropping below 0 5 amps at approximately 10 cycles or 3 cycles after the breaker opens A low set 50BF relay that picks up on dc will have a very long dropout time An induction cup electromechanical relay designed for breaker failure applications will drop out in 1 25 cycles In this example the CT secondary burden is resistive to give the most subsidence current Investigate subsidence by varying burden magnitude burden angle and circuit breaker opening time Appendix D Examine Overcurrent Element Response to Saturated CT Secondary Current describes the ATPDraw circuit and Mathcad calculations used in this example SATURATED SECONDARY CURRENT AND ITS EFFECTS ON DISTANCE AND DIRECTIONAL ELEMENT PERFORMANCE ATP Power System Model Use a more detailed ATP system model to examine the effects of saturated CT secondary current on distance and directional elements As a minimum include the following elements in the ATP model as shown in Figure E 1 e Sending and receiving sources e Source impedances e Line circuit breakers e
26. ber 15 17 1996 J Esztergalyos S Sambasivan J P Gosalia and R Ryan ATP Simulator of Low Impedance Bus Differential Protection Proceedings of the 50 Annual Relay Engineers Conference Texas A amp M University College Station Texas April 7 9 1997 E O Schweitzer III and Jeff Roberts Distance Relay Element Design Proceedings of the 46 Annual Relay Engineers Conference Texas A amp M University College Station Texas April 12 14 1993 Stanley E Zocholl and Gabriel Benmouyal How Microprocessor Relays Respond to Harmonics Saturation and Other Wave Distortions Proceedings of the 24 Annual Western Protective Relay Conference Spokane WA October 21 23 1997 E O Schweitzer III and Daqing Hou Filtering for Protective Relays Proceedings of the 47 Annual Georgia Tech Protective Relay Conference Atlanta GA April 28 30 1993 Alternative Transients Program ATP Rule Book Copyright 1987 1988 by Canadian American EMTP User Group L szl Prikler and Hans Kr Hgidalen ATPDraw for Windows 3 1x 95 NT version 1 0 User s Manual SINTEF Energy Research Trondheim Norway October 15 1998 IEEE C57 13 1993 Standard Requirements for Instrument Transformers Joseph B Mooney Charlie Henville and Frank P Plumptre Computer Based Relay Models Simplify Relay Application Studies Proceedings of the 20 Annual Western Protective Relay Conference Spokane WA October 19 2
27. e between ATP and Mathcad You can download TOP free of charge from the Electrotek website at Attp www electrotek com Mathcad 7 Professional Mathcad worksheets process the CT transient data generated by ATP The Mathcad desktop interface uses mathematical equations similar to those seen in textbooks Concepts are easy to see and understand although the same results can be achieved in other programs such as MATLAB Mathcad 7 Professional is available from Mathsoft Inc CONSTRUCTING A CT MODEL USING ATP This section demonstrates CT modeling using the ATP Saturable Transformer Component shown in Figure 1 BUS1 1 1 Low Voltage Winding 1 LP RP IDEAL RS LS 2 BUS1 2 High Voltage Winding 2 BUS2 1 BUS2 2 Figure 1 ATP Saturable Transformer Component To model the CT use the CT accuracy class ratio secondary winding resistance and excitation curve Some manufacturers provide the ratio and phase angle correction curves which are useful while testing the model Accuracy class indicates the CT relay accuracy can be calculated adequately 9 This paper considers only C class CTs Using the step by step instructions in Appendix A Develop a 1200 5 CT Model create the CT model in ATP as follows 1 Model the CT secondary on Winding 1 of the saturable transformer component Figure 1 2 On Winding 2 set resistor RS equal to zero Set inductor LS which must have a value greater than zero equa
28. l to 10E 6 Set LP equal to zero since a C class CT secondary leakage reactance is very small 4 Setresistor RP equal to the CT secondary winding resistance Add separate circuit components to model lead resistance and burden resistance 5 Set magnetizing resistance RMAG to infinity since RMAG is very large Enter a 0 in the ATP model for infinite RMAG 6 Select seven to ten excitation current versus voltage points from the CT excitation curve to include saturation in the model 7 Convert these current versus voltage points to current versus flux points using the ATP supporting routine SATURA 8 Create the CT model in ATPDraw Figure 2 9 Test the model by recreating the CT excitation curve using the ATPDraw circuit shown in Figure 2 Figure 2 CT Excitation Test Circuit in ATPDraw Figure 3 shows the results of three excitation curve tests using three four and nine points to model saturation The nine point model gives the best results of the three Volts Original Points 9 Point Model 4 Point Model tic 3 Point Model Figure 3 Comparison of CT Models with Different Numbers of Excitation Points Always test the CT model Mistakes appear as ratio errors and irregularities in the excitation curve Use the model only after it has been tested In ATP saturation is a piecewise linear model that can be unstable in certain conditions Picking too many points on the excitation curve or se
29. lecting a time step that is too large can cause high frequency oscillations in the output Appendix A Develop a 1200 5 CT Model describes the development of a 1200 5 C800 CT model using nine points from the excitation curve SECONDARY BURDEN AND CONNECTION EFFECTS ON RCF AND PACF Increasing CT burden increases induced secondary voltage and exciting current causing ratio and phase angle errors ina CT Since C class CT accuracy can be calculated accurately use ATP to examine the effects of secondary burden at different primary current levels Appendix B Calculate CT Accuracy describes the ATPDraw circuit and Mathcad calculations in the following example This example uses a 1200 5 class C800 CT model in the ATPDraw circuit in Figure 4 The six sources turn on and off in sequence to apply 5 10 20 60 100 and 150 rated current Each source is on for three cycles 2 Burden Gode i 3E Figure 4 Accuracy Test Circuit in ATPDraw The CT secondary resistor in Figure 4 is a standard burden 1 8 1 62 j0 784 This burden is equivalent to 1 800 feet of No 10 AWG Figure 5 shows the ATP output of primary and secondary current in the graphical postprocessor TOP The secondary quantities appear very small because of the plot vertical scale Notice the six increasing levels of primary current BUR24018 gt SEC Type 8 Max 10 5868 2000 ana 10 8909
30. mary Current Current Current Source 3 s ue me os _ Figure B 2 shows the CT primary and secondary current in the graphical postprocessor TOP Notice that the secondary quantities appear very small because of the plot vertical scale Save the TOP active window containing the CT primary and secondary currents as a CSV text file in TOP using the File Save As menu item Magnitude Mag BUR24018 gt SEC Type 8 Max 10 5868 um 2 2000 Ne 0 6209 RMS 3 90504 1000 FF 1 0095 1000 2000 BUR24018 gt SEC 8 BUR24018 PRI SRC 8 100 Time mS 500 Figure B 3 shows the beginning of the CSV text file created by TOP The file columns are listed in the first line as Figure B 2 Primary and Secondary Current in TOP 1 Time in seconds 2 CT secondary current 3 CT primary current Delete the first text row so Mathcad can read the numerical data BUR24018 SEC 0 0 000181417 5 20417e 15 0001 0 0141828 3 0002 0 0274833 6 39525 0003 0 0407447 9 58151 0004 0 0539482 12 7542 0005 0 067075 15 0006 0 0801065 19 0406 0007 0 0930242 22 1454 0008 0 10581 25 2188 0009 0 118445 28
31. mport the CSV text file into Mathcad The Mathcad file shown below processes the data and is a reference for the Mathcad file that displays the data Count rows of matrix Data m e 291 deg Z A B el R rows data 1 men Create an index 1 as a row pointer 1 0 rows data 1 Create time vector t from imported data and calculate the data time step At t 2 data 0 Ati t to Calculate the number of samples to create an averaging LP filter with at cutoff frequency at 1 2 the sampling frequency RS LPW floor 60 ACRS Averaging filter LPW 1 1 a LPW k 5 LPW LK C a i 14 R k 0 Create an index 11 for the LP filtered quantities ij LPW R Calculate filtered quantities ia LPdata gt ii ya SEP dad 6 ib z LP data 2 ii vb LP data ii LP data ii vc LP data ii You Calculate the number of samples available in the data and create an index s as a row pointer S floor t 60 RS 0 5 continued on next page E 5 continued from previous page Create vectors representing sampled current and voltages in the relay 4 5 5 t ib linterp t ic RS 60 zs um Ib lt i2 linterp linterp 1 linterp t vb is RS 60 uc 5 60 i RS 60 S S S TE
32. ning the current flux pairs that define the CT characteristic used in the transformer model saturation branch Use ATPDraw to create the circuit diagram Figure A 2 The drawing is saved in a circuit adp file Enter component values by clicking with the mouse on the component to open a BEGIN NEW DATA CASE 1 SATURATION 60 001 01 0 4 40 0 9999 l PUNCH SAT240 pch BLANK LINE BEGIN NEW DATA CASE BLANK LINE ENDING ALL CASES 2 C 345678901234567890123456789012345678901234567890 3 E 6 1 0 9 90 428 500 600 700 780 800 927 C lt gt Cards punched by support routine on C 60 001 C C C 01 04 0 1 12 40 0 9999 Ww rn LE 41421356E 02 36733089 02 31694552E 01 5046597E 01 89134128E 01 41310866E 01 61072569E 01 5998771E 01 43968011 01 9999 CO Co n9 9 CO 6 1 9 90 428 500 600 700 780 800 927 3 618619E 02 37618619 01 60556410 00 87565899 00 25079079 00 62592259 00 92602803 00 00105439 00 47747177E 00 0 14 Jun 99 15 37 55 lt gt dialog box Figure A 2 CT Test Circuit in ATPDraw A 2 The circuit has four components a voltage source on the transformer secondary a current probe the saturable transformer model and a primary resisto
33. or evaluating CT performance This paper briefly describes ATP software provides instructions for constructing a CT model using ATP and presents a method of modeling relay response by using the CT model as input to digital relay models in Mathcad The paper uses the CT and relay models to demonstrate e Secondary burden and connection effects on Ratio Correction Factor RCF and Phase Angle Connection Factor PACF to answer the question When can a relay accuracy class CT be used for metering e The effects of X R CT class and burden on CT saturation and recovery times e Saturated secondary current reduction and its effects on overcurrent inverse time overcurrent and breaker failure element pickup e The effect of CT subsidence current on breaker failure element dropout time e Saturated secondary current and its effects on distance and directional element performance Examples in this paper show methods of analysis rather than illustrating the performance of particular CTs or relays Appendices A through E provide ATPDraw circuits and detailed Mathcad calculations used in these examples SOFTWARE ATP The choice of power system transient analysis software is a matter of suitability cost and individual preference Cost can range from 0 to 15 000 We chose the four programs used in the following work for their power availability and reasonable price The ATP version of EMTP is the basic software tool for electric system
34. r Figure A 3 shows the saturable transformer model LP RP IDEAL RS LS BUS1 1 N1 N2 BUS1 2 Low Voltage Winding 1 High Voltage Winding 2 BUS2 1 BUS2 2 Figure A 3 ATP Saturable Transformer Model Use the low voltage winding as the CT secondary The values required by ATPDraw in the saturable transformer attributes dialog box are in Table A 1 Table A 1 Saturable Transformer Attributes Values in ATPDraw Flux Wb turn in MB at steady state Resistance in magnetizing branch in Ohm 0 infinite resistance VRS 1 Rated voltage kV in secondary winding N2 RMS 0 Nonlinear characteristic flag Current Flux characteristic must be entered Figure A 4 shows how the saturation characteristic file SAT240 pch is entered as an INCLUDE file in the component characteristic dialog box A 3 Comper APO 4 E Fie Animae Eome Fipe Figure A 4 Saturable Transformer Characteristic Dialog Box in ATPDraw Enter all of the component data and review the ATP Settings command under the ATP menu item in ATPDraw Use the Make File command under the ATP menu item to create the following text file for ATP input C Generated by ATPDRAW July Monday 19 1999 C A Bonneville Power Administration program C Programmed by H H idalen at SEfAS NORWAY 1994 98 ALLOW EVEN PLOT FREQUENCY C Miscellaneous Data Card C dT gt lt Tmax gt lt Xopt gt lt Copt gt 000002 05 60 60 500
35. r unit of CT rating Z the CT burden in per unit of standard burden As an example consider a transmission line with an impedance angle of 85 24 X R 12 anda 1200 5 C800 CT The maximum fault current 1s four times the rated CT current The criterion 1s satisfied when Z5 is less than or equal to 0 38 per unit of the standard 8 Ohm burden or 3 08 Ohms Use the circuit shown in Figure 7 to model this example Burden 2 System Figure 7 Test Circuit ATPDraw Figure 8 shows the voltage developed across the CT secondary during the simulation 100 Volts L5 I HT SERRA Cycles 2 Figure 8 CT Burden Voltage During an Asymmetrical Fault The equation that describes the volt time area under the voltage wave produced by asymmetrical fault current is 0 lt 5 12 as t Kod 7 L Where B I Zg L R Saturated flux density Number of turns Core cross sectional area Power system frequency Magnitude of secondary current Secondary burden impedance Time constant of the primary fault circuit The CT is at the point of saturation The same quantity is calculated from the simulation voltage by Where VTA n W At n VTA n At Volt time area at time step Power system frequency Simulation time step duration Number of the time step in the
36. recovers from saturation when the peak of the volt time area drops below approximately 1000 volts dri Figure 11 CT Recovery From Saturation Use these techniques to calculate actual CT class and performance For example a C400 CT may actually be just below a C800 rating Calculate the accuracy under different burdens or use ATP to model CT performance under load and offset fault current at a particular point in your system Appendix C Examine X R Saturation and Burden Effects describes the ATPDraw circuit and Mathcad calculations used in this example SATURATED SECONDARY CURRENT REDUCTION AND ITS EFFECTS ON OVERCURRENT ELEMENT PICKUP Saturation reduces the magnitude of CT secondary current from its ideal value as shown in Figure 12 a Sec rulary PES CIR Figure 12 CT Primary and Secondary Current During Saturation You can calculate the effect of this reduction on digital relay overcurrent elements if you know the relay parameters Consider the digital relay block diagram in Figure 13 M lt P XT Mathcad A D Full Cycle 50 Element 50 Element Setting Figure 13 Digital Relay Block Diagram The following example demonstrates a digital overcurrent relay response to saturated CT secondary current Assume a sample rate of
37. rrent as 0 120022 A CT240C95 SEC4 Type 8 Max 0 174973 in 0 1750062 Avg 0 111163 Abs 0 175062 0 1 RMS 0 120022 CF 1 45858 FF 1 0797 UN VI VIV 0 10 20 30 40 50 Time mS Magnitude Mag Figure A 5 ATP Output pl4 File in TOP Figure A 6 shows the RMS secondary excitation current from ATP plotted along with the current voltage points selected from the CT characteristic curve a Volts ai CO Pomte Modal Figure 6 Original and Calculated Secondary Excitation Current A 5 APPENDIX B CALCULATE CT ACCURACY Use the 1200 5 CT model from Appendix A in the test circuit Figure B 1 with a known burden B 1 8 1 62 j0 784 ATPDraw supports Windows cut and paste functions Copy transformer graphical element in the circuit of Appendix A and paste it into the new drawing Transformer data CTR etc will be included in the operation 2 Burden i 3E Figure B 1 CT Accuracy Test Circuit in ATPDraw Table B 1 shows the setup of the current sources for the accuracy test Each source is turned on for three cycles and then turned off The six sources operate in sequence The data required by each source element also includes frequency 60 Hz and phase angle 0 degrees Table B 1 Current Source Setup Percent RMS Peak Full Primary Pri
38. s in this example THE EFFECT OF CT SUBSIDENCE CURRENT ON BREAKER FAILURE ELEMENT DROPOUT TIME Subsidence current is the current that flows through a CT burden after the line breaker opens Subsidence current may affect the dropout time of breaker failure overcurrent element 5OBF If the SOBF element is picked up beyond the breaker failure time delay other breakers must trip to isolate the failed breaker CT subsidence current keeps the 50BF element asserted longer than necessary and may contribute to a false breaker failure operation in tightly coordinated systems Model CT subsidence current with the relay elements shown in Figure 13 Since a fast dropout overcurrent element is used for breaker failure applications replace the full cycle cosine filter with a one half cycle cosine filter Open the power system circuit breaker while the CT is saturated to see the most subsidence current Figure 15 shows the same system as in Figure 12 using a one half cycle cosine filter HN LL LLL 50 40 20 Amps LN 20 Calculated Current Magnitude TH Saturated Secondary Current Element Setting Figure 15 Subsidence Current Figure 16 shows the model results between 7 5 and 10 cycles Notice the subsidence current and the relay response Lit At tt ty T 1 MEN EE stats ames cl mam E 0 _ joe mmm bbb 5 T7135 a 8 25
39. y H dia x E HI Figure 18 Filtered Secondary Current Phase to Phase to Ground Fault Saturation causes the relay to under reach as shown in Figure 19 Without saturation the relay calculates the ideal B phase to C phase impedance MBC 0 936 Ohm at 1 375 cycles after fault inception 4 With saturation the relay calculates MBC 2 09 Ohms at 1 375 cycles after fault inception At 5 cycles after fault inception with the B and C phase CTs still slightly saturated the relay calculates 1 Ohm xl i ml m af E 1 Ll la D 7 MEC Figure 19 Phase to Phase Impedance Calculation During CT Saturation The phase angle calculated by the relay remains close to the actual phase angle as the CT recovers from saturation as shown in Figure 20 i i C m L 8 4 4 17 E H E F i Ii 1 in ll CA m SEE Phams OE Figure 20 CT Phase Angle During Saturation Figure 21 shows the effects of CT saturation on Z2 and ZO calculations These directional elements are very secure Notice that ZO has a brief positive excursion Security counters in the directional logic ensure that the calculation has stabilized before allowing a directional determination 16 F i 1 l
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