Critical Eigenvalues Calculation In Power Systems

With the growing of power grids, large-capacity generators constantly put into operation, rapid and High Magnification excitation system is widely used. Low-frequency oscillations in large interconnected power system occurs from time to time.It has become a threat to network security. From the early 1980s, low frequency oscillation occurred in many power systems. With the implement of Power Transmission from West China to East and the national network project, low-frequency oscillation has a growing trend. In order to effectively prevent the low-frequency oscillation, to improve the stability of small signal stability, at first, we must quickly and accurately calculate the modes of low frequency oscillation in power system.The analysis of Eigenvalue is the most widely used method in small signal stability, eigenvalue methods base on modern control theory, which describe the Power system as a general control system of standard linear state equation. The QR algorithm is the most traditional eigenvalue calculation method .It has good numerical stability, high accuracy and can able to calculate the full matrix eigenvalue for small-scale matrix (<1000) rapid. Modern power systems increase, the controller is getting more complicated, in some studies of oscillation, as regional oscillation, the modeling for large dynamic elements makes the state matrix dimension as high as several thousand, even thousands, then traditional QR method is not effective.Eigenvalues ordered in decreasing real parts in large-scale power systems, i.e. critical eigenvalues, are directly computed by explicitly restarted Arnoldi method with Chebyshev acceleration (CA), where an ellipse containing unwanted eigenvalues is constructed and the Chebyshev polynomial is adopted to acquire a restart vector. Chebyshev ellipse is important to this method. So I introduce a new method which named AA method that improved CA method in determining the parameters of Chebyshev ellipse. Than I design a program in MATLAB. The calculation of a 1000 matrix proves the AA method's efficiency.The 36-node system of state matrix derived using C language from PSASP and calculate using the improved method in MATLAB.Then I compare the results of the improved method ,QR algorithm in MATLAB,the two methods in PSASP.The results show that the algorithm can be calculated accurately and effectively the critical eigenvalue and is suitable for large-scale power system analysis.