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Voltage and Reactive Power Estimation for Contingency Analysis. Pablo A. Ruiz ECE Department, University of Illinois. Power Affiliates Program Annual Review May 11, 2007. Outline. Motivation Sensitivities and linear approximations
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Voltage and Reactive Power Estimation for Contingency Analysis Pablo A. Ruiz ECE Department, University of Illinois Power Affiliates Program Annual Review May 11, 2007
Outline • Motivation • Sensitivities and linear approximations • Equipment limits impacts and piecewise linear approximations • Numerical studies • Summary and Work in Progress
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
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
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
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
Reactive Generation Limits • If , then • If , then
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.
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
Linear Parameterization Example Load and generation outage at bus k
Linear Approximations Using Taylor series expansion
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
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
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
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
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
Numerical Results: IEEE 14 Bus • Error: • 37% to 97% reduction in mean error with respect to the results reported in the literature
Numerical Results: IEEE 57 Bus 39% to 92% reduction in mean error with respect to the results reported in the literature
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