Recursive versus nonrecursive Richardson algorithms: systematic overview, unified frameworks and application to electric grid power quality monitoring

Sufficiently accurate, fast and computationally efficient solution of the system of linear equations is required in many estimation problems. Richardson iteration is one of the main solvers for linear equations, which provides optimization possibilities for time critical and accuracy critical applic...

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Published in:	Automatika Vol. 63; no. 2; pp. 328 - 337
Main Author:	Stotsky, Alexander
Format:	Journal Article Paper
Language:	English
Published:	Ljubljana Taylor & Francis 03.04.2022 Taylor & Francis Ltd KoREMA - Hrvatsko društvo za komunikacije,računarstvo, elektroniku, mjerenja i automatiku Taylor & Francis Group
Subjects:	Algorithms Automation & Control Systems Computational efficiency Computing time Convergence Decomposition Electric power grids Electric power systems Engineering frequency inverses iterative method Iterative methods Linear equations matrix Monitoring Newton-Schulz matrix inversion algorithms Optimization Parameter estimation power power quality monitoring quality monitoring Richardson algorithms Robotics and automation Robotik och automation
ISSN:	0005-1144, 1848-3380
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Abstract	Sufficiently accurate, fast and computationally efficient solution of the system of linear equations is required in many estimation problems. Richardson iteration is one of the main solvers for linear equations, which provides optimization possibilities for time critical and accuracy critical applications. Convergence rate improvement and reduction of the computational complexity of the Richardson iteration are the most important problems in the area. The introduction of Newton-Schulz iterations is the efficient way for convergence rate improvement and the paper starts with systematic overview of the high-order Newton-Schulz matrix inversion algorithms. In addition, the unified framework for recursive computationally efficient convergence accelerators and error models for a number of combinations of Richardson and Newton-Schulz iterations is developed. A new nonrecursive parameter estimation concept is introduced and compared in this paper with recursive estimation. Recursive and nonrecursive Richardson algorithms together with the standard LU decomposition method were applied to the electric grid power quality monitoring problem. The algorithms were tested for the detection of the sag and swell signatures in the voltage and current signals on real data in three-phase power system. Nonrecursive Richardson algorithms which save close to half of the computational time compared to LU decomposition method were recommended for power quality monitoring applications.
AbstractList	Sufficiently accurate, fast and computationally efficient solution of the system of linear equations is required in many estimation problems. Richardson iteration is one of the main solvers for linear equations, which provides optimization possibilities for time critical and accuracy critical applications. Convergence rate improvement and reduction of the computational complexity of the Richardson iteration are the most important problems in the area. The introduction of Newton–Schulz iterations is the efficient way for convergence rate improvement and the paper starts with systematic overview of the high-order Newton–Schulz matrix inversion algorithms. In addition, the unified framework for recursive computationally efficient convergence accelerators and error models for a number of combinations of Richardson and Newton–Schulz iterations is developed. A new nonrecursive parameter estimation concept is introduced and compared in this paper with recursive estimation. Recursive and nonrecursive Richardson algorithms together with the standard LU decomposition method were applied to the electric grid power quality monitoring problem. The algorithms were tested for the detection of the sag and swell signatures in the voltage and current signals on real data in three-phase power system. Nonrecursive Richardson algorithms which save close to half of the computational time compared to LU decomposition method were recommended for power quality monitoring applications.
Author	Stotsky, Alexander
Author_xml	– sequence: 1 givenname: Alexander surname: Stotsky fullname: Stotsky, Alexander email: alexander.stotsky@chalmers.se, alexander.stotsky@telia.com organization: Chalmers University and University of Gothenburg
BackLink	https://gup.ub.gu.se/publication/314253$$DView record from Swedish Publication Index (Göteborgs universitet) https://research.chalmers.se/publication/528911$$DView record from Swedish Publication Index (Chalmers tekniska högskola)
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SubjectTerms	Algorithms Automation & Control Systems Computational efficiency Computing time Convergence Decomposition Electric power grids Electric power systems Engineering frequency inverses iterative method Iterative methods Linear equations matrix Monitoring Newton-Schulz matrix inversion algorithms Optimization Parameter estimation power power quality monitoring quality monitoring Richardson algorithms Robotics and automation Robotik och automation
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Title	Recursive versus nonrecursive Richardson algorithms: systematic overview, unified frameworks and application to electric grid power quality monitoring
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