Voltage and Reactive Power Estimation for Contingency Analysis

1. Voltage and Reactive Power Estimation for Contingency Analysis Pablo A. Ruiz ECE Department, University of Illinois Power Affiliates Program Annual Review May 11, 2007

2. Outline • Motivation • Sensitivities and linear approximations • Equipment limits impacts and piecewise linear approximations • Numerical studies • Summary and Work in Progress

3. Contingency Analysis • Operational reliability is assessed using contingency analysis • A power flow is solved for each post-contingency scenario • Contingencies typically include line and generator outages

4. Computational Approaches • Approximate power flow solutions are acceptable in a variety of studies • Full Newton power flows are computationally expensive • Fast decoupled power flow is a very useful tool in these cases • Sensitivities (distribution factors) are used to obtain the approximations without iterations

5. Voltage and Reactive Power Sensitivity-based Methods • The Q-V relations are believed to be eminently nonlinear • The original implementation [Ilić 86] yielded errors of about 30% • Assumptions: FDPF, constant current injections • These assumptions have been relaxed in various studies, but the errors remain relatively large

6. Impacts of Equipment Limits • The approximation methods in the literature do not account for equipment limits • Following a contingency, the voltage control devices change their settings • Whenever a device reaches a control limit, the voltage cannot be controlled • Ignoring this issue leads to errors in voltage and reactive flow approximations

7. Reactive Generation Limits • If , then • If , then

8. Objective Approximate the post-contingency voltage and reactive power generation at bus i, and , and the reactive power flow through line i-k, , exclusively using information from the base case power flow.

9. Linear Approximations Linearly parameterize the occurrence of the contingency using K:let all specified variables and parameters be linear functions of K post-contingency pre-contingency

10. Linear Parameterization Example Load and generation outage at bus k

11. Linear Approximations Using Taylor series expansion

12. Sensitivities

13. Sensitivities w.r.t. power flows • All specified variables remain constant • There are 4 flows to be specified, hence we need 4 additional degrees of freedom • The outage of the two fictitious generators simulates the original line outage

14. Line 2-3 Outage in 7-bus System -5.2 specified line flows -5.4 -5.6 specified line admittance -5.8 1.0 0.0 0.2 0.4 0.6 0.8

15. Impacts of Equipment Limits 20 10 40 20 0 1.10 1.05 1.00 1.0 0.0 0.2 0.4 0.6 0.8

16. Piecewise Linear Approximations We only use first order information available from the pre-contingency power flow 20 error 10 40 error 20 0 1.0 0.0 0.2 0.4 0.6 0.8

17. Flow Diagram

18. Approximation Algorithm Characteristics • All types of contingencies can be handled • The FDPF assumptions are not made, but the method is flexible to allow their incorporation • Post-contingency generation redispatch is taken into account • Equipment limits are explicitly considered

19. Numerical Results: IEEE 14 Bus • Error: • 37% to 97% reduction in mean error with respect to the results reported in the literature

20. Numerical Results: IEEE 57 Bus 39% to 92% reduction in mean error with respect to the results reported in the literature

21. Summary and Work in Progress • We have discussed the computation of voltage and reactive power flow sensitivities and their application to contingency studies • Using piecewise linear estimates we have captured the effect of equipment limits • Equipment limits may have a significant impact in post-contingency voltages and reactive flows • We are working on the detection of high estimation errors