Multivariable control of modular multilevel converters with convergence and safety guarantees

TL;DR

The paper tackles safe, convergent current control for modular multilevel converters (MMCs) in multivariable settings where bilinear dynamics and input constraints hinder conventional decoupled control. It introduces a static state-feedback controller synthesized via linear matrix inequalities (LMIs) using a physics-informed linear MMC model and an LPV formulation, ensuring zero tracking error and constraint satisfaction within an invariant domain $\mathbb{S}_x$. The control law $u = K_x \bar{x} + K_w w$ guarantees asymptotic convergence of the current tracking error and preserves safe operation of the total arm voltage, with $K_x = Y Z^{-1}$ and $K_w = \Gamma - K_x \Pi$ derived from the LOT framework. Validation spans simulations on both averaged and linear MMC models and experimental tests on a scaled AC/AC MMC prototype, showing accurate current tracking, decoupled phase currents at their target frequencies, and robust safety margins without requiring a PLL, highlighting the method’s practicality for AC/AC MMCs used in ultra-fast charging.

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.

Figures (11)

• Figure 1: Schematic of a three-phase bidirectional direct AC/AC MMC topology with full-bridge submodules as presented in Pereira2021ExampleACAC.
• Figure 2: Typical hierarchical control scheme of CCSs, as in Du2018MMCBook, for MMCs connected to the grid and a medium frequency transformer (MFT).
• Figure 3: Block diagram of the proposed MMC's Current Control
• Figure 4: Simulation results from scenario (i): (a) Trajectory of the grid current, (b) trajectory of the output current, (c) FFT analysis of grid current, and (d) FFT analysis output current.
• Figure 5: Simulation results from scenario (i): (a) Error of the grid current $e^g_m$, (b) Error of the output current $e^z_m$, (c) FFT analysis of grid current error, and (d) FFT analysis output current error.

Theorems & Definitions (5)

• Theorem 4.2: Controller Synthesis
• Remark 4.3
• Remark 4.4
• Definition 4.5: MMC Safe Operation
• Theorem 4.6: MMC Stability