Large-scale power system small signal stability analysis based on matrix exponential

A new method for small signal stability analysis of large-scale power system is presented in this paper. The task of the eigenvalue analysis method which is the most common method used in the small signal stability analysis is to obtain the eigenvalue of the state matrix. However, it is very difficulty for the exiting mathematic method to solve the eigenvalue of the studied system when the orders of system reaches thousands or more. In this paper, the numerical solution of matrix exponential by employing the precise time-step integration and the numerical curve of the trace of matrix exponential are used to solve the linearization and high-order state matrix of system. For the numerical curve of the trace, the impact of the positive real part of eigenvalues will be extended of the corresponding period while the impact of the negative real part of eigenvalues will be diluted. The mode parameters, such as frequency, damp, can be obtained by using the HHT method to analyze the sections divided according to time-domain characteristics the numerical curve. Then the small signal stability is analyzed by employing the mode parameters. The results carried out on the 16 machine-68 buses test system show that the proposed method is effective for the small signal stability analysis for the large power system. The analysis process is shown in Figure 1.