Multivariable Control Design for Grid-Forming Inverters With Decoupled Active and Reactive Power Loops

Abstract

Grid-forming inverters (GFMIs) are recognized as a prominent driver toward achieving renewable energy-rich power grids. Unlike grid-following inverters (GFLIs), which are controlled as current sources, GFMIs are controlled as voltage sources. In GFMIs, dynamic control of the magnitude ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$V_{\mathrm{c}}$</tex-math></inline-formula> ) and angle ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\theta$</tex-math></inline-formula> ) of the point of common coupling (PCC) voltage is used to achieve active ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P$</tex-math></inline-formula> ) and reactive ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> ) power transfer across a line. However, independent control of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> via <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$V_{\mathrm{c}}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\theta$</tex-math></inline-formula> becomes challenging due to the coupling between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> loops. The coupling becomes severe as the resistance-to-reactance ratio of the grid impedance and the power angle between the GFMI and the grid voltages are increased. This article proposes a novel multivariable controller to completely decouple <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> loops in GFMIs. The proposed multivariable controller could be designed based on the prevalent control structures for GFMIs such as droop controller, swing equation-based virtual synchronous generator (VSG) controller, zero steady-state error reactive power controller, and fixed steady-state error reactive power controller. The additional cross-channel decoupling controllers in the proposed multivariable controller provide superior decoupling action over the existing decoupling methods, such as the virtual inductor-based method. An <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> -based method is adopted to tune the proposed multivariable controller parameters, where the straightforward formulation of the desired closed-loop dynamics based on the open-loop system is clearly shown. The decoupling performance of the controller is experimentally validated extensively. The experimental results show that the proposed controller results in superior performance over the prevalent decoupling methods, such as the virtual-inductor decoupling method.