Gauss-Newton Method Applied to Impedance Estimation in Grid-Connected Inverters

This work presents a methodology that employs the Gauss–Newton algorithm to perform online impedance estimation for grid-connected inverters. Conventional formulations for this class of problem typically lead to high-order nonlinear systems of equations, often of dimension 8×8. In contrast, the formulation proposed herein recasts the estimation task as a 3×3 least-squares problem, which is then solved via the Gauss–Newton method. To validate the proposed approach, a three-phase grid-connected inverter was adopted as the case study. The control system enforces three distinct active power injection levels into the grid, and the voltage, current, and phase-angle magnitudes at the point of common coupling are measured and used as inputs to the impedance estimation algorithm. Real-time validation was carried out to assess the performance of the method. The results confirm the feasibility of the proposed formulation and indicate that the approach substantially reduces the computational burden of embedded DSP-based algorithms for online grid impedance estimation.

KEYWORDS
Gauss-Newton method; grid impedance estimation; nonlinear least squares