Calculations of Static Voltage Stability Margin of Power Systems under N-1 Contingency using Holomorphic Embedding Method

Abstract

A calculation technique for the static voltage stability margin (SVSM) of power system under <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> -1 contingency based on the fast and flexible holomorphic embedding (FFHE) method is proposed. It can also obtain the approximate analytic function between the post <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> -1 contingency SVSM and the pre-contingency SVSM. Using the contingency parameter as an embedded variable, the relationship between the SVSM under an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> -1 contingency and the pre-contingency SVSM is approximately described as a polynomial. By constructing the FFHE matrix equation, the values of state variables at the pre-contingency static voltage stability limit point are taken as the 0th order coefficients. The FFHE matrix equation is solved to obtain the higher order coefficients from the lower order coefficients step by step, thereby the power series expression of each bus voltage and the SVSM with respect to the contingency parameter can be obtained. The proposed method is applied to the IEEE 39-bus system, and the obtained post-contingency SVSM is compared with the result of optimal power flow (OPF) method to verify the high accuracy of the proposed method.