ECE 6323 HW Soln 2 - 2024_Final (2)

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Apr 3, 2024

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Georgia Institute of Technology School of Electrical and Computer Engineering ECE6323 Power System Protection - Spring 2024 Homework Assignment #2 Solution Problem P1 (20 Points): (Objectives: become familiar with the COMTRADE standard, computation of frequency and computation of phasors). A relay has recorded the voltage and current of one phase at a certain location of a power system. The captured data have been stored in COMTRADE format in the file. The COMTRADE files are provided with the names: Homework_02_Spring22.cfg and Homework_02_Spring22.dat. For your convenience, the data are in ASCII format. 1. Write a computer program to read the data of the voltage and current. For this purpose, consult the IEEE Std C37-111-1999 that describes the COMTRADE format. 2. What is the sampling rate of the data? The sampling rate is 9600 samples/sec. 3. Graph the sample values of the voltage over the entire data record. Figure 1. Graph of the voltage waveform plotted in Matlab

Figure 2. Graph of the voltage: Upper trace: over the entire data record, Lower trace: Zoom-in view plotted in WinXFM Station: Use Case 01: ECE6323Homework02 IED: Recording Start: January 24, 2022 - 00:25:52.000000 Trigger Time: January 24, 2022 - 00:25:52.000000 90.53 kV -90.53 kV VoltageAtTLBUS1PhaseAN 0.000 s 0.682 s 1.365 s 2.047 s 2.729 s 3.411 s 4.094 s 4.776 s 5.45 Station: Use Case 01: ECE6323Homework02 IED: Recording Start: January 24, 2022 - 00:25:52.000000 Trigger Time: January 24, 2022 - 00:25:52.000000 89.59 kV -89.66 kV VoltageAtTLBUS1PhaseAN 2.421 s 2.512 s 2.603 s 2.694 s 2.785 s 2.875 s 2.966 s 3.057 s 3.148 s

4. Compute and graph the frequency of the voltage over the entire data record. Use one cycle sliding window. Figure 3. Graph of the frequency of the voltage over a sliding window of one cycle in Matlab Figure 4. Graph of the frequency of the voltage over a sliding window of one cycle in WinXFM Station: Use Case 01: ECE6323Homework02 IED: Recording Start: January 24, 2022 - 00:25:52.000000 Trigger Time: January 24, 2022 - 00:25:52.000000 60.06 Hz 59.94 Hz FrequencyFromVoltage = FREQ(VoltageAtTLBUS1PhaseAN,60.0) 0.175 s 0.825 s 1.475 s 2.125 s 2.775 s 3.425 s 4.075 s 4.725 s 5.375 s

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5. Compute and graph the magnitude of the fundamental frequency voltage phasor over the entire data record. Use one cycle sliding window. Figure 5. Graph of the magnitude of the voltage over a sliding window of one cycle in Matlab Figure 6. Graph of the magnitude of the voltage over a sliding window of one cycle in WinXFM Station: Use Case 01: ECE6323Homework02 IED: Recording Start: January 24, 2022 - 00:25:52.000000 Trigger Time: January 24, 2022 - 00:25:52.000000 64.01 kV 59.02 kV VoltageMagnitude = RMS(VoltageAtTLBUS1PhaseAN,60.0) 0.175 s 0.825 s 1.475 s 2.125 s 2.775 s 3.425 s 4.075 s 4.725 s 5.375

6. Compute and graph the phase angle of the fundamental frequency voltage phasor over the entire data record. Use one cycle sliding window. Figure 7. Graph of the phase angle of the voltage over a sliding window of one cycle in Matlab Figure 8. Graph of the phase angle of the voltage over a sliding window of one cycle in WinXFM Station: Use Case 01: ECE6323Homework02 IED: Recording Start: January 24, 2022 - 00:25:52.000000 Trigger Time: January 24, 2022 - 00:25:52.000000 39.52 Degrees 26.90 Degrees PhaseOfVoltage = PHASE(VoltageAtTLBUS1PhaseAN,60.0,1) 0.175 s 0.825 s 1.475 s 2.125 s 2.775 s 3.425 s 4.075 s 4.725 s 5.375

7. Repeat 3 through 6 for the current. Figure 9. Graph of the current waveform plotted in Matlab

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Figure 10. Graph of the current: Upper trace: over the entire data record, Lower trace: Zoom-in view plotted in WinXFM Station: Use Case 01: ECE6323Homework02 IED: Recording Start: January 24, 2022 - 00:25:52.000000 Trigger Time: January 24, 2022 - 00:25:52.000000 174.4 A -174.3 A CurrentAtTLBUS1PhaseALineX 0.175 s 0.825 s 1.475 s 2.125 s 2.775 s 3.425 s 4.075 s 4.725 s 5.375 Station: Use Case 01: ECE6323Homework02 IED: Recording Start: January 24, 2022 - 00:25:52.000000 Trigger Time: January 24, 2022 - 00:25:52.000000 172.5 A -172.6 A CurrentAtTLBUS1PhaseALineX 2.949 s 2.972 s 2.995 s 3.019 s 3.042 s 3.065 s 3.088 s 3.111 s 3.134

Figure 11. Graph of the frequency of the current over a sliding window of one cycle in Matlab Figure 12. Graph of the frequency of the current over a sliding window of one cycle in WinXFM Station: Use Case 01: ECE6323Homework02 IED: Recording Start: January 24, 2022 - 00:25:52.000000 Trigger Time: January 24, 2022 - 00:25:52.000000 60.06 Hz 59.94 Hz FrequencyFromCurrent = FREQ(CurrentAtTLBUS1PhaseALineX,60.0) 62.54 ms 0.728 s 1.394 s 2.060 s 2.726 s 3.392 s 4.058 s 4.724 s 5.39

Figure 13. Graph of the magnitude of the current over a sliding window of one cycle in Matlab Figure 14. Graph of the magnitude of the current over a sliding window of one cycle in WinXFM Station: Use Case 01: ECE6323Homework02 IED: Recording Start: January 24, 2022 - 00:25:52.000000 Trigger Time: January 24, 2022 - 00:25:52.000000 123.4 A 113.6 A CurrentMagnitude = RMS(CurrentAtTLBUS1PhaseALineX,60.0) 62.54 ms 0.728 s 1.394 s 2.060 s 2.726 s 3.392 s 4.058 s 4.724 s 5.39

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Figure 15. Graph of the phase angle of the current over a sliding window of one cycle in Matlab Figure 16. Graph of the phase angle of the current over a sliding window of one cycle in WinXFM Station: Use Case 01: ECE6323Homework02 IED: Recording Start: January 24, 2022 - 00:25:52.000000 Trigger Time: January 24, 2022 - 00:25:52.000000 -163.2 Degrees -175.9 Degrees PhaseOfCurrentPhasor = PHASE(CurrentAtTLBUS1PhaseALineX,60.0,1) 62.54 ms 0.728 s 1.394 s 2.060 s 2.726 s 3.392 s 4.058 s 4.724 s 5.390

Here is what to do for each iteration: where , k is the index of the data point in the COMTRADE file, k = 1: length of the data set N is the number of samples per cycle. In this case, N = 160 samples/cycle After step 4, the frequency, amplitude, and phase angle are all calculated. Generate the plots with the calculated results. 0 0 2 f w p = 0 60 f Hz =

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