A Quantification Index for Power Systems Transient Stability
Abstract
:1. Introduction
2. Overview of the Proposed Performance Quantification Procedure
3. Detailed Description of TSPQ Method
3.1. System Separation Module
3.2. Loss of Source Module
3.3. Damping Module
3.4. Voltage Sag Module
3.5. Stability Index R Calculation
4. IEEE 39-Bus Test System Case Study and Verification
4.1. IEEE 39-Bus Test System
4.2. Contingencies and Dispatches
4.3. TSPQ Method Results
4.3.1. Results for Dispatch D0
4.3.2. Comparison between Dispatch D0 and D1
- Group 1
- black buses: 1, 9, 12, 19, 20, 22, 30, 31, 33, 34, 35, 36, 37 and 39.
- Group 2
- green buses: 4, 5, 6, 7, 8, 10, 11, 13, 14 and 32.
- Group 3
- red buses: 2, 3, 15, 16, 17, 18, 21, 23, 24, 25, 26, 27, 28, 29 and 38.
4.3.3. Normalized Index Presentation
5. Implementation on a Real Power System
- (1)
- A total of 108 assumptive, three-phase fault contingencies with a pessimistic 10 s clearing time was applied at stations with voltages equal and above 115 kV across Maine as shown in the New England Geographic Transmission Map [22]. If any of these contingencies did not cause a criteria violation based on [11,14,15,16,17], it was removed from further consideration, to limit the data volume to only the non-trivial faults.
- (2)
- The locations where the 10 s duration three-phase contingency resulted in stability violations were re-tested by applying three-phase faults with the actual, normal clearing times (4–6 cycles range). The simulation results files were then analyzed through the TSPQ methodology and the findings are included in this report.
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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D0 (MW) | D1 (MW) | D2 (MW) | D3 (MW) | D4 (MW) | D5 (MW) | |
---|---|---|---|---|---|---|
G1 | 998 | 999.5 | 994 | 994.3 | 996.8 | 997.2 |
G2 | 573 | 573 | 573 | 573 | 673 | 673 |
G3 | 650 | 550 | 450 | 350 | 750 | 812.5 |
G4 | 632 | 632 | 632 | 632 | 732 | 790 |
G5 | 508 | 508 | 508 | 508 | 608 | 600 |
G6 | 650 | 650 | 650 | 650 | 750 | 812.5 |
G7 | 560 | 560 | 560 | 560 | 660 | 845 |
G8 | 540 | 540 | 640 | 640 | 640 | 1000 |
G9 | 830 | 933 | 933 | 933 | 930 | 1000 |
G10 | 250 | 250 | 250 | 350 | 350 | 500 |
Total MW in each dispatch | ||||||
6191 | 6195.5 | 6190 | 6190.3 | 7089.8 | 8030.2 |
Fault Location | Clearing Time (Cycles) | SS (f1) | LOS (f2) | Damping (f3) | Vsag (f4) |
---|---|---|---|---|---|
Bus2 | 1 | 0 | 0 | 0 | 0 |
Bus2 | 2 | 0 | 0 | 0 | 0 |
Bus2 | 3 | 0 | 0 | 0 | 0 |
Bus2 | 4 | 0 | 0 | 0 | 0 |
Bus2 | 5 | 0 | 0 | 0 | 0 |
Bus2 | 6 | 0 | 0 | 0 | 0 |
Bus2 | 7 | 0 | 0 | 0 | 0 |
Bus2 | 8 | 0 | 0 | 0 | 0 |
Bus2 | 9 | 0 | 0 | 0 | 0 |
Bus2 | 10 | 0 | 0 | 0 | 0 |
Bus2 | 11 | 0 | 0 | 0 | 0 |
Bus2 | 12 | 0 | 0 | 0 | 0 |
Bus2 | 13 | 0 | 0 | 0 | 0 |
Bus2 | 14 | 0 | 0 | 0 | 0.266 |
Bus2 | 15 | 0 | 0 | 0 | 0.344 |
Bus2 | 16 | 1 | N/A | N/A | N/A |
Bus2 | 17 | 1 | N/A | N/A | N/A |
Bus2 | 18 | 1 | N/A | N/A | N/A |
Bus2 | 19 | 1 | N/A | N/A | N/A |
Bus2 | 20 | 1 | N/A | N/A | N/A |
rBus2 = 5.61 |
Fault Location | Clearing Time (Cycles) | Dispatch D0 | Dispatch D1 | ||||||
---|---|---|---|---|---|---|---|---|---|
SS (f1) | LOS (f2) | Damping (f3) | Vsag (f4) | SS (f1) | LOS (f2) | Damping (f3) | Vsag (f4) | ||
Bus2 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Bus2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Bus2 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Bus2 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Bus2 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Bus2 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Bus2 | 7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Bus2 | 8 | 0 | 0 | 0 | 0.226 | 0 | 0 | 0 | 0.231 |
Bus2 | 9 | 0 | 0 | 0 | 0.281 | 0 | 0 | 0 | 0.290 |
Bus2 | 10 | 0 | 0 | 0 | 0.375 | 0 | 0 | 0 | 0.402 |
Bus2 | 11 | 1 | N/A | N/A | N/A | 1 | N/A | N/A | N/A |
Bus2 | 12 | 1 | N/A | N/A | N/A | 1 | N/A | N/A | N/A |
Bus2 | 13 | 1 | N/A | N/A | N/A | 1 | N/A | N/A | N/A |
Bus2 | 14 | 1 | N/A | N/A | N/A | 1 | N/A | N/A | N/A |
Bus2 | 15 | 1 | N/A | N/A | N/A | 1 | N/A | N/A | N/A |
Bus2 | 16 | 1 | N/A | N/A | N/A | 1 | N/A | N/A | N/A |
Bus2 | 17 | 1 | N/A | N/A | N/A | 1 | N/A | N/A | N/A |
Bus2 | 18 | 1 | N/A | N/A | N/A | 1 | N/A | N/A | N/A |
Bus2 | 19 | 1 | N/A | N/A | N/A | 1 | N/A | N/A | N/A |
Bus2 | 20 | 1 | N/A | N/A | N/A | 1 | N/A | N/A | N/A |
rBus16 = 10.882 | rBus16 = 10.923 |
Index | D0 | D1 | D2 | D3 | D4 | D5 |
---|---|---|---|---|---|---|
R | 315.404 | 319.937 | 308.417 | 295.182 | 477.585 | 780 |
Rn | 40.44% | 41.02% | 39.54% | 37.84% | 61.23% | 100% |
Index | SLL1 | SLL2 | SLL3 | SP1 |
---|---|---|---|---|
R | 22 | 26 | 21 | 21 |
Rn | 44.9% | 53.06% | 42.86% | 42.86% |
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Chen, S.; Onwuachumba, A.; Musavi, M.; Lerley, P. A Quantification Index for Power Systems Transient Stability. Energies 2017, 10, 984. https://doi.org/10.3390/en10070984
Chen S, Onwuachumba A, Musavi M, Lerley P. A Quantification Index for Power Systems Transient Stability. Energies. 2017; 10(7):984. https://doi.org/10.3390/en10070984
Chicago/Turabian StyleChen, Shengen, Amamihe Onwuachumba, Mohamad Musavi, and Paul Lerley. 2017. "A Quantification Index for Power Systems Transient Stability" Energies 10, no. 7: 984. https://doi.org/10.3390/en10070984