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In this article, the focus is mainly on gaining the optimal control for theunstable power system models and stabilizing them through the Riccati-basedfeedback stabilization process with sparsity-preserving techniques. We are tofind the solution of the Continuous-time Algebraic Riccati Equations (CAREs)governed from the unstable power system models derived from the BrazilianInter-Connected Power System (BIPS) models, which are large-scale sparseindex-1 descriptor systems. We propose the projection-based Rational KrylovSubspace Method (RKSM) for the iterative computation of the solution of theCAREs. The novelties of RKSM are sparsity-preserving computations and theimplementation of time-convenient adaptive shift parameters. We modify theLow-Rank Cholesky-Factor integrated Alternating Direction Implicit (LRCF-ADI)technique based nested iterative Kleinman-Newton (KN) method to a sparse formand adjust this to solve the desired CAREs. We compare the results achieved bythe Kleinman-Newton method with that of using the RKSM. The applicability andadaptability of the proposed techniques are justified numerically with MATLABsimulations. Transient behaviors of the target models are investigated forcomparative analysis through the tabular and graphical approaches.

Computationally efficient optimal control for unstable power system models