Iterative Methods for Nonlinear Systems Applied to Grid Impedance Estimation: A Comparative Study

Abstract

In this work, a comparative study is presented to evaluate the performance of iterative methods to solve nonlinear systems applied to grid impedance estimation. The iterative methods of Newton-Raphson, Potra-Pták, and Chun were embedded in the control system of a three-phase inverter supported by a photovoltaic plant connected to the grid. The adopted impedance estimation technique consists of successive variation of the power injected into the grid, more precisely, at three different levels. The voltage and current amplitudes at the point of common coupling~(PCC) are monitored and serve as input for the iterative methods, which, after processing them, provide an estimate of the grid impedance. To compare the performance between the methods, the following merit figures were listed: execution time, number of iterations required to deliver the estimates, percentage error, efficiency index, computational efficiency, computational efficiency index, and stability of the iterative method. The results presented were obtained through real-time simulations. From that, it was possible to conclude about the method with the best performance, thus contributing to greater assertiveness on the part of designers when choosing the most efficient iterative method to be embedded in a microcontroller for grid impedance estimation purposes.

Keywords

• Chun method
• comparative analysis
• grid impedance estimation,
• iterative methods
• Newton-Raphson method
• Potra-Pták method