Xi Zhang, Chi Kong Wong University of Macau. IEEE 2011 Electrical Power and Energy Conference

Transcription

1 Xi Zhang, Chi Kong Wong University of Macau

2 Contents Introduc-on Index Formula?on & Comparison Simula?on Results and Discussion Conclusion

3 Introduc-on Voltage stability problem is one of the major concerns in power system Damage of voltage collapse several blackouts (Japan, USA, France) 2003 North- East USA blackout : leading to 80% load loss in New York affec?ng 55 million people in 8 states causing great economic losses

4 Introduc-on Voltage stability analysis (sta?c) Stable: high V & low I Sta-c view point Transfer limit Collapse point Sta?c load Unstable: low V & high I voltage stability index (VSI) Transfer limit P-V curves Voltage collapse

5 Introduc-on Voltage stability analysis (dynamic) Dynamic problem by nature Example: induction motor disturbance s Q V P e s Another stable point Voltage collapse Transfer limit P e s Motor stalling Voltage collapse occurs before transfer limit Network and motor P-V curve P Transfer limit Voltage collapse

6 Introduc-on Though transfer limit is not the collapse point, it is s?ll cri?cal and is iden?fied by VSI. Voltage stability index (VSI) Derived under sta?c load Load increase: P & Q in propor?on Sta?c load: constant Z, I, P P & Q in propor?on Dynamic load: restore power Q sharply, P Objec?ve Sta?c VSIs are compared under dynamic load

7 Contents Introduc?on Index Formula-on & Comparison Simula?on Results and Discussion Conclusion

8 Index Formula-on & Comparison Four line VSIs Line index FVSI L mn LVSI LQP Sta?c load Power flow Indicate transfer limit of a line

9 Index Formula-on & Comparison Fast Voltage Stability Index (FVSI) Sending end Receiving end FVSI<1 1 Transfer limit Two bus system quadra?c equa?on of discriminant larger than 0

10 Index Formula-on & Comparison Line Stability Index (L mn ) Sending end Receiving end Two bus system quadra?c equa?on of discriminant larger than 0 L mn <1 1 Transfer limit

11 Index Formula-on & Comparison On Line Stability Index (LVSI) Sending end Receiving end Two bus system quadra?c equa?on of discriminant larger than 0 LVSI<1 1 Transfer limit

12 Index Formula-on & Comparison Line Stability Factor (LQP) Sending end Receiving end Two bus system quadra?c equa?on of discriminant larger than 0 LQP<1 1 Transfer limit

13 Index Formula-on & Comparison Comparison of FVSI, L mn, LVSI and LQP FVSI L mn

14 Index Formula-on & Comparison Comparison of FVSI, L mn, LVSI and LQP Index Formulation FVSI (simplified) FVSI L mn LVSI LQP Rela?ve variables Q V Z X Q V δ Z X R Q V δ X θ P V δ R θ P Q V X LQP best for dynamic loads Q P Q & P Sta?c load: constant Z, I, P P & Q in propor?on Dynamic load: restore power Q sharply, P

15 Index Formula-on & Comparison Comparison of FVSI, L mn, LVSI and LQP Index Formula?on Assump?ons FVSI (simplified) FVSI δ=0 no large for heavy load lines L mn LVSI no no When θ-δ 90, cos(θ-δ) 0, in the denominator LQP Critical value: 1 transfer limit R/X<<1 always satisfied

16 Contents Introduc?on Index Formula?on & Comparison Simula-on Results and Discussion Conclusion

17 Simula-on Results and Discussion Power system for case study 39 buses 34 lines 10 generators 19 load buses Dynamic load: induc?on motor motor stalling voltage collapse IEEE 39 bus system

18 Simula-on Results and Discussion Case 1 (motor stalls before transfer limit) Motor at bus 24 stalls first 6.61s VSIs reach 1.0 first on line 2423 aler 10s IEEE 39 bus system sta?c load increase at all buses induc?on motor: 40%

19 Simula-on Results and Discussion Case 1 (motor stalls before transfer limit) VSIs on line 2423 & slip of bus 24 VSIs reach 1.0 Transfer limit Motor stalling (voltage collapse) Before transfer limit FVSI L mn LQP is larger than others

20 Simula-on Results and Discussion Case 1 (motor stalls before transfer limit) Motor stalling (voltage collapse) Close to collapse limit: P injected to 24 Q injected to 24 stop V 24 V angle difference as P

21 Simula-on Results and Discussion Case 1 (motor stalls before transfer limit) LVSI for a healthy line 1617 When θ-δ 90, cos(θ-δ) 0, in the denominator LVSI reaches 1.0 at 3.2s Voltage collapse at 6.6s Mis- iden?fy

22 Simula-on Results and Discussion Case 2 (motor stalls aler transfer limit) Motor at bus 28 stalls first s VSIs reach 1.0 first on line 2829 before 101s IEEE 39 bus system sta?c load increase at bus 28 induc?on motor: 40%

23 Simula-on Results and Discussion Case 2 (motor stalls aler transfer limit) VSIs on line 2829 & slip of bus 28 VSIs reach 1.0 Transfer limit Motor stalling (voltage collapse) ABer transfer limit FVSI L mn Simplified FVSI small δ is large LQP reaches 1 earlier than others

24 Simula-on Results and Discussion Case 2 (motor stalls aler transfer limit) Motor stalling (voltage collapse) Close to collapse limit: P injected to 28 Q injected to 28 stop V 28 δ when P fail to restore

25 Contents Introduc?on Index Formula?on & Comparison Simula?on Results and Discussion Conclusion

26 Conclusion Comparison of 4 line VSIs FVSI, L mn, LVSI and LQP under dynamic load is discussed FVSI and L mn are equivalent simplified FVSI & LVSI have limita?ons LQP perform beoer under dynamic load FVSI and L mn directly involve Q LVSI directly involve P LQP directly involves Q & P Useful to choose Proper index for dynamic voltage collapse predic?on

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