《A Combined TSA-SPA Algorithm for Computing》.pdf

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 1, FEBRUARY 2013 149 A Combined TSA-SPA Algorithm for Computing Most Sensitive Eigenvalues in Large-Scale Power Systems C. Y. Chung, Senior Member, IEEE, and Bo Dai, Member, IEEE Abstract—A novel algorithm (TSA-SPA) that combines the The traditional full-eigenvalue computation methods such as Two-Sided Arnoldi method (TSA) and the Sensitive Pole Algo- QR/QZ methods are inefficient when applied to modern large- rithm (SPA) is proposed in this paper for calculation of the most scale power systems because they require high computational sensitive eigenvalues to control parameters in large power systems. memory for solving high dimensional problems [18]. Moreover, In the proposed method, first, with the shift-invert transformation precondition, TSA builds two Krylov subspaces and obtains a re- normally, only a few dominant eigenvalues are of interest to duced matrix of a much smaller scale, which contains eigenvalues system operators; it is unnecessary and impractical to compute close to the chosen shift point. Second, SPA is adopted to realize all eigenvalues of the system. the most sensitive eigenvalue computation. TSA-SPA can find the Selective eigenvalue algorithms of subspace methods, e.g., most sensitive eigenvalues of interest, with satisfactory reliability subspace iteration, Lanczos method and Arnoldi method, are and convergence, in a specified frequency domain. With proper selection of sizes of Krylov subspace and the reduced matrix, the commonly adopted for computation of eig