xi#zhang,#chi#kong#wong# university#of#macau · xi#zhang,#chi#kong#wong# university#of#macau. ieee...

IEEE 2011 Electrical Power and Energy Conference

Xi Zhang, Chi Kong Wong University of Macau


Contents �

Introduc-on

Index Formula?on & Comparison

Simula?on Results and Discussion

Conclusion �


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


Introduc-on� Voltage stability analysis (sta?c)

Transfer limit �

Collapse point�

Stable: high V & low I�

Unstable: low V & high I�

Sta-c view point �

voltage stability index (VSI) �

Transfer limit �

Voltage collapse �

Sta?c load �

P-V curves�


P

Introduc-on� Voltage stability analysis (dynamic)

Network and motor P-V curve�

Dynamic problem by nature �

Example: induction motor �

disturbance� s� Q� V�

Pe s � Another stable point �

Pe s � Motor stalling�Transfer limit�

Voltage collapse�

Transfer limit �

Voltage collapse�

Voltage collapse occurs

before transfer limit�


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

Objec?ve Sta?c VSIs are compared under dynamic load �

Sta?c load: constant Z, I, P�

Dynamic load: restore power �

P & Q in propor?on �

Q sharply, P — �


Contents �

Introduc?on

Index Formula-on & Comparison


Conclusion �


Index Formula-on & Comparison� Four line VSIs

Line index�

FVSI� Lmn � LVSI� LQP�

Power flow �Sta?c load �Indicate

transfer limit of a line�


Index Formula-on & Comparison� Fast Voltage Stability Index (FVSI)

Two bus system�

Sending end �

Receiving end �

quadra?c equa?on of �

discriminant larger than 0�

FVSI<1� Transfer limit �1 �


Index Formula-on & Comparison� Line Stability Index (Lmn)

Two bus system�

Sending end �

Receiving end �



Lmn<1�Transfer

limit �1 �


Index Formula-on & Comparison� On Line Stability Index (LVSI)

Two bus system�

Sending end �

Receiving end �



LVSI<1� Transfer limit �1 �


Index Formula-on & Comparison� Line Stability Factor (LQP)

Two bus system�

Sending end �

Receiving end �



LQP<1� Transfer limit �1 �


Index Formula-on & Comparison� Comparison of FVSI, Lmn, LVSI and LQP

FVSI�

Lmn �



Index �FVSI�

(simplified) �FVSI� Lmn � LVSI� LQP�

Formulation �

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 �

Q � P � Q & P �

Sta?c load: constant Z, I, P�

Dynamic load: restore power �

P & Q in propor?on �

Q sharply, P — �

LQP best for dynamic loads �



Index � Formula?on � Assump?ons�

FVSI�(simplified) �

δ=0�

FVSI� no �

Lmn � no �

LVSI� no �

LQP� R/X<<1�

Critical value: 1 � transfer limit�

always satisfied �

large for heavy load lines �

When θ-δ 90°, cos(θ-δ) 0, in the denominator �


Contents �

Introduc?on


Simula-on Results and Discussion

Conclusion �


Simula-on Results and Discussion� Power system for case study�

IEEE 39 bus system�

39 buses 34 lines�

10 generators 19 load buses �

Dynamic load: induc?on motor

motor stalling voltage collapse


Simula-on Results and Discussion� Case 1 (motor stalls before transfer limit) �


sta?c load increase at all

buses

VSIs reach 1.0 first on line 2423 aler 10s �

Motor at bus 24 stalls first

6.61s�

induc?on motor: 40%



Motor stalling (voltage collapse) �

VSIs reach 1.0

Transfer limit�

Before

transfer limit�

VSIs on line 2423 & slip of bus 24 �

FVSI Lmn �

LQP is larger than others �




P injected to 24�

Q injected to 24 stop �

V 24 �

V angle difference as P�

Close to collapse limit: �



LVSI for a healthy line 1617�

LVSI reaches 1.0 at 3.2s �

When θ-δ 90°, cos(θ-δ) 0, in the denominator �

Voltage collapse at 6.6s �

Mis-‐iden?fy�


Simula-on Results and Discussion� Case 2 (motor stalls aler transfer limit) �


sta?c load increase at bus 28

VSIs reach 1.0 first on line 2829

before 101s �

Motor at bus 28 stalls first 101.06s�

induc?on motor: 40%



VSIs on line 2829 & slip of bus 28 �

ABer

transfer limit�

FVSI Lmn �


LQP reaches 1 earlier than others �

VSIs reach 1.0

Transfer limit�

Simplified FVSI small δ is large�




P injected to 28�

Q injected to 28 stop �

V 28 �

δ when P fail to restore �

Close to collapse limit: �


Contents �

Introduc?on



Conclusion �


Conclusion � Comparison of 4 line VSIs FVSI, Lmn, LVSI and LQP under dynamic load is discussed FVSI and Lmn are equivalent simplified FVSI & LVSI have limita?ons LQP perform beoer under dynamic load

• FVSI and Lmn directly involve Q • LVSI directly involve P • LQP directly involves Q & P

Useful to choose Proper index for dynamic voltage collapse predic?on �

xi#zhang,#chi#kong#wong# university#of#macau · xi#zhang,#chi#kong#wong# university#of#macau. ieee...

Documents