Riccati-based feedback stabilization for unstable Power system models

In this article, the objective is mainly focused on finding optimal control for the large-scale sparse unstable power system models using optimal feedback matrix achieved by the Riccati-based feedback stabilization process. Our aim is to solve the Continuous-time Algebraic Riccati Equations (CAREs) governed from large-scale unstable power system models, which are of index-1 descriptor systems with a sparse pattern. We propose the projection-based Rational Krylov Subspace Method (RKSM) for the computation of the solution of the CAREs, the novelties of RKSM are sparsity-preserving techniques and the implementation of time convenient recursive adaptive shift parameters. We modify the machine-independent Alternating Direction Implicit (ADI) technique based nested iterative Kleinman-Newton (KN) method and adjust this to solve the CAREs governed from large-scale sparse unstable power system models. We compare the results achieved by the Kleinman-Newton method with that of using the RKSM. The applicability and adaptability of the proposed methods are justified through the Brazilian Inter-Connected Power System (BIPS) models and their transient behaviors are comparatively analyzed by both tabular and graphical approaches.