# $H_{\infty}$-Control of Grid-Connected Converters: Design, Objectives and Decentralized Stability Certificates

## TL;DR

This paper introduces an $H_{
abla}$-control framework for power converters in modern grids, enabling systematic, robust, and decentralized stability assurance amidst variable conditions, supported by simulations and real-time tests.

## Contribution

It presents a novel $H_{
abla}$-control design method with decentralized stability certificates for grid-connected converters, improving robustness and stability guarantees.

## Key findings

- Systematic $H_{
abla}$-control design for converters.
- Decentralized stability criterion based on small gain theorem.
- Validated effectiveness through nonlinear and real-time simulations.

## Abstract

The modern power system features high penetration of power converters due to the development of renewables, HVDC, etc. Currently, the controller design and parameter tuning of power converters heavily rely on rich engineering experience and extrapolation from a single converter system, which may lead to inferior performance or even instabilities under variable grid conditions. In this paper, we propose an $H_{\infty}$-control design framework to provide a systematic way for the robust and optimal control design of power converters. We discuss how to choose weighting functions to achieve anticipated and robust performance with regards to multiple control objectives. Further, we show that by a proper choice of the weighting functions, the converter can be conveniently specified as grid-forming or grid-following in terms of small-signal dynamics. Moreover, this paper first proposes a decentralized stability criterion based on the small gain theorem, which enables us to guarantee the global small-signal stability of a multi-converter system through local control design of the power converters. We provide high-fidelity nonlinear simulations and hardware-in-the-loop (HIL) real-time simulations to illustrate the effectiveness of our method.