Multivariable control of modular multilevel converters with convergence and safety guarantees

TL;DR

This paper introduces a multivariable control design for modular multilevel converters that guarantees stability, safety, and constraint satisfaction through a linear matrix inequality approach, improving current regulation in complex AC/AC configurations.

Contribution

It presents a physics-informed linear model and a linear matrix inequality-based controller synthesis method for MMCs, ensuring convergence and safety guarantees.

Findings

Controller guarantees stable and safe operation.

Effective current regulation demonstrated in simulations.

Successful prototype testing for EV charging applications.

Abstract

Well-designed current control is a key factor in ensuring the efficient and safe operation of modular multilevel converters (MMCs). Even though this control problem involves multiple control objectives, conventional current control schemes are comprised of independently designed decoupled controllers, e.g., proportional-integral (PI) or proportional-resonant (PR). Due to the bilinearity of the MMC dynamics, tuning PI and PR controllers so that good performance and constraint satisfaction are guaranteed is quite challenging. This challenge becomes more relevant in an AC/AC MMC configuration due to the complexity of tracking the single-phase sinusoidal components of the MMC output. In this paper, we propose a method to design a multivariable controller, i.e., a static feedback gain, to regulate the MMC currents. We use a physics-informed transformation to model the MMC dynamics linearly and synthesise the proposed controller. We use this linear model to formulate a linear matrix inequality that computes a feedback gain that guarantees safe and effective operation, including (i) limited tracking error, (ii) stability, and (iii) meeting all constraints. To test the efficacy of our method, we examine its performance in a direct AC/AC MMC simulated in Simulink/PLECS and in a scaled-down AC/AC MMC prototype to investigate the ultra-fast charging of electric vehicles.