Calculation of static voltage stability margin under N-1 contingency based on holomorphic embedding and Pade approximation methods

Abstract

A calculation technique for the static voltage stability margin (SVSM) under N-1 contingency based on the fast and flexible holomorphic embedding (FFHE) and Pade approximation (PA) methods is proposed. The technique can also obtain the approximate analytic function between the post N-1 contingency SVSM and the pre-contingency SVSM. Using the contingency parameter as an embedded variable, the relationship between the post N-1 contingency SVSM and the pre-contingency SVSM is approximately described in the form of power series. 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 post N-1 contingency SVSM is obtained. In addition, by using the PA method, the approximate rational fraction expression of the post-contingency SVSM which can improve the convergence and accuracy of the power series can be obtained. Test results for the IEEE 39-bus system and an actual 1559-bus power grid demonstrate that the proposed method to calculate the post-contingency SVSM has high accuracy and strong robustness compared with the optimal power flow and continuation power flow methods. The average relative errors of the proposed method in the two cases are 0.58155% and 1.0862%. The strong robustness is reflected in the fact that there is no need to repeatedly select the initial value for calculation under different contingencies.