Development of an eigenvalue estimation method (Mode Coupling Method) for small signal stability analysis of power system

Abstract

AbstractAn eigenvalue estimation method for small signal stability analysis of electric power systems is proposed. The method, called the Mode Coupling Method, is used to estimate efficiently the nonlinear change of the eigenvalue with respect to the change of parameter. The eigenvalue sensitivity analysis method, which has been used to estimate the change of the eigenvalue, is a method of linear estimation of the change of the eigenvalue. However, the eigenvalue frequently shows a strong nonlinear change, and therefore the calculation efficiency and speed were insufficient in the conventional method. In the Mode Coupling Method, the most important modes and those most related to the major mode under consideration are first selected. Next, these two or more selected modes are coupled and the new eigenvalues of the coupled matrix are calculated, providing good estimation of the new eigenvalues. The size of the coupled matrix is very small. We can consider mutual interaction between important modes. Thus, this is a powerful method in which nonlinear estimation of eigenvalues is possible. When the QR method is used, the calculation time for eigenvalue analysis is proportional to the third power of the size of the matrix. The size of the matrix used for the mode coupling method is approximately 1/6 of the original value. Therefore, the computing time for eigenvalue estimation becomes less than 1% of the original computing time. The computational accuracy of the proposed method is verified with the IEEJ EAST30 standard power system model. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 174(1): 10–16, 2011; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/ eej.21037