Computationally Efficient Optimal Control for Unstable Power System Models

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 (...

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Bibliographic Details
Published in:Mathematical problems in engineering 2021-10, Vol.2021, p.1-17
Main Authors: Uddin, Mahtab, Uddin, M. Monir, Hakim Khan, Md. Abdul
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Control systems
Control theory
Eigenvalues
Engineering
Iterative methods
Mathematical models
Mathematical problems
Microelectromechanical systems
Newton methods
Optimal control
Parameter modification
Riccati equation
Sparsity
Subspace methods
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2021/8071869