ABSTRACT
The simulation of continuous-time algebraic Riccati equations (CARE) derived from the very large power system models is a highly laborious task and most cases infeasible due to the sophisticated structural ingredients. The computation is very time costly and the rate of convergence can be severely affected in the direct solvers. To overcome those adversities, an iterative approach Rational Krylov Subspace Method (RKSM) is introduced to deal with those large-scale CAREs. The solutions of those CAREs and hence the optimal feedback matrices can be efficiently explored by the RKSM approach to stabilize the power system models of unstable categories. In this approach, shift parameters play a vital role in the convergence of the computations and size of the solution spaces. The goal of the work is to investigate the effect of different types of shift parameters on the stabilization process. To attain the mentioned objective, a modified version of the iterative RKSM algorithm is proposed by employing two types of shift parameters, namely, the adaptive ADI shifts and heuristic shifts. Qualitative discussions for the outcomes for those shift parameters are narrated by tabular and figurative methods.
Keywords: Shift parameter, RKSM, Riccati equation, Feedback stabilization, and Power system model.
Citation: Uddin M, Uddin MM, and Khan MAH. (2021). Effect of shift parameters in rational Krylov subspace method for solving Riccati equations arise from power system models, Int. J. Mat. Math. Sci., 3(2), 43-49. https://doi.org/10.34104/ijmms.021.043049
