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

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.