Computationally efficient optimal control for unstable power system models

TL;DR

This paper presents a computationally efficient method for stabilizing unstable large-scale power system models using Riccati-based feedback and sparsity-preserving techniques, with novel projection-based algorithms and adaptive parameters.

Contribution

It introduces a projection-based Rational Krylov Subspace Method with sparsity preservation and adaptive shifts for solving CAREs in large-scale unstable power systems, improving computational efficiency.

Findings

RKSM effectively computes CARE solutions for large sparse systems.

Proposed methods outperform traditional Kleinman-Newton in efficiency.

Numerical simulations validate the stability and transient behavior improvements.

Abstract

In this article, the focus is mainly on gaining the optimal control for the unstable power system models and stabilizing them through the Riccati-based feedback stabilization process with sparsity-preserving techniques. We are to find the solution of the Continuous-time Algebraic Riccati Equations (CAREs) governed from the unstable power system models derived from the Brazilian Inter-Connected Power System (BIPS) models, which are large-scale sparse index-1 descriptor systems. We propose the projection-based Rational Krylov Subspace Method (RKSM) for the iterative computation of the solution of the CAREs. The novelties of RKSM are sparsity-preserving computations and the implementation of time-convenient adaptive shift parameters. We modify the Low-Rank Cholesky-Factor integrated Alternating Direction Implicit (LRCF-ADI) technique based nested iterative Kleinman-Newton (KN) method to a sparse form and adjust this to solve the desired CAREs. We compare the results achieved by the Kleinman-Newton method with that of using the RKSM. The applicability and adaptability of the proposed techniques are justified numerically with MATLAB simulations. Transient behaviors of the target models are investigated for comparative analysis through the tabular and graphical approaches.