-Synthesis-Based Generalized Robust Framework for Grid-Following and Grid-Forming Inverters

Abstract

Grid-following and grid-forming inverters are integral components of microgrids and for integration of renewable energy sources with the grid. For grid following (GFL) inverters, which need to emulate controllable current sources, a significant challenge is to address the large uncertainty of the grid impedance. For grid forming (GFM) inverters, which need to emulate a controllable voltage source, large uncertainty due to varying loads has to be addressed. This article presents a generalized control framework by leveraging the voltage-current duality in the plant dynamic model of GFL and GFM inverters. The modeling of uncertainties is also generalized under the control framework by quantifying the uncertainties in grid impedance parameters and the uncertainties in equivalent loading parameters for GFL and GFM inverters, respectively. Based on the generalized control framework, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\mu}$</tex-math></inline-formula> -synthesis-based robust control design methodology is proposed for both GFL and GFM inverters. The control objectives, while designing the proposed optimal controllers, are reference tracking, disturbance rejection, and harmonic compensation capability with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${i})$</tex-math></inline-formula> sufficient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${LCL}$</tex-math></inline-formula> resonance damping under large variations of grid impedance uncertainty for GFL inverters and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${ii})$</tex-math></inline-formula> with enhanced dynamic response under large variations of equivalent loading uncertainty for GFM inverters. A combined system-in-the-loop, controller hardware-in-the-loop, and power hardware-in-the-loop based experimental validation on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {10}$</tex-math></inline-formula> -kVA microgrid system with two physical inverter systems is conducted in order to evaluate the efficacy and viability of the proposed controllers.