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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| Vydáno v: | Automatika Ročník 63; číslo 2; s. 328 - 337 |
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| Hlavní autor: | |
| Médium: | Journal Article Paper |
| Jazyk: | angličtina |
| Vydáno: |
Ljubljana
Taylor & Francis
03.04.2022
Taylor & Francis Ltd KoREMA - Hrvatsko društvo za komunikacije,računarstvo, elektroniku, mjerenja i automatiku Taylor & Francis Group |
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| 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. |
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| 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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| Cites_doi | 10.1007/s00009-016-0833-2 10.1016/j.ifacol.2020.12.847 10.1002/zamm.19330130111 10.1137/1.9781611971484 10.1177/0959651814553964 10.1016/j.laa.2015.07.010 10.1214/aoms/1177731489 10.1007/s12190-018-01229-8 10.1002/zamm.19870670712 10.1002/047134608X.W1046 10.1007/s40313-018-0385-8 10.1016/0024-3795(91)90385-A 10.1007/s12190-013-0743-4 10.1016/j.egyr.2020.07.027 10.1007/BF02243566 10.1016/0022-247X(67)90036-4 10.1109/CDC.2015.7402847 10.1090/S0025-5718-66-99922-4 10.1109/TPWRD.2007.893185 |
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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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