Open AccessSVD-Krylov based Sparsity-preserving Techniques for Riccati-based Feedback Stabilization of Unstable Power System Models
Author(s) -
Mahtab Uddin,
Mahtab Uddin,
Md. Abdul Hakim Khan,
Md. Tanzim Hossain
Publication year - 2021
Publication title -
journal of engineering advancements
Language(s) - English
Resource type - Journals
eISSN - 2708-6437
pISSN - 2708-6429
DOI - 10.38032/jea.2021.03.002
Subject(s) - krylov subspace , singular value decomposition , mathematics , riccati equation , gramian matrix , model order reduction , control theory (sociology) , convergence (economics) , projector , projection (relational algebra) , algebraic riccati equation , generalized minimal residual method , moore–penrose pseudoinverse , mathematical optimization , computer science , algorithm , inverse , iterative method , partial differential equation , eigenvalues and eigenvectors , mathematical analysis , artificial intelligence , economic growth , control (management) , quantum mechanics , computer vision , physics , economics , geometry
We propose an efficient sparsity-preserving reduced-order modelling approach for index-1 descriptor systems extracted from large-scale power system models through two-sided projection techniques. The projectors are configured by utilizing Gramian based singular value decomposition (SVD) and Krylov subspace-based reduced-order modelling. The left projector is attained from the observability Gramian of the system by the low-rank alternating direction implicit (LR-ADI) technique and the right projector is attained by the iterative rational Krylov algorithm (IRKA). The classical LR-ADI technique is not suitable for solving Riccati equations and it demands high computation time for convergence. Besides, in most of the cases, reduced-order models achieved by the basic IRKA are not stable and the Riccati equations connected to them have no finite solution. Moreover, the conventional LR-ADI and IRKA approach not preserves the sparse form of the index-1 descriptor systems, which is an essential requirement for feasible simulations. To overcome those drawbacks, the fitting of LR-ADI and IRKA based projectors from left and right sides, respectively, desired reduced-order systems attained. So that, finite solution of low-rank Riccati equations, and corresponding feedback matrix can be executed. Using the mechanism of inverse projection, the Riccati-based optimal feedback matrix can be computed to stabilize the unstable power system models. The proposed approach will maintain minimized ℌ2 -norm of the error system for reduced-order models of the target models.