Multivariable control of ac/ac modular multilevel converters under square wave operation using Fourier expansion

Nowadays, modular multilevel converters (MMCs) with AC voltage output, i.e., AC/AC MMCs, have emerged as a promising alternative for grid-connected applications. Among them, MMCs operating under square waves, i.e., AC/SQR MMCs, present a unique advantage, i.e., having lower pulsating power and fewer modules. However, tracking nonlinear periodic references, i.e., the square-shaped signals, imposes some challenges when designing the MMC controller. This paper proposes a multivariable controller, i.e., static feedback gain, designed to regulate the currents of the AC/SQR MMC. To address the nonlinear dynamics resulting from square-shaped signals, we use the Fourier expansion to create a linear model of the system. Employing the obtained model, a linear matrix inequality (LMI) is solved for synthesizing a controller that guarantees exponential convergence and constraint satisfaction inside a domain of attraction. Simulation validation is conducted on a high-fidelity model built on Simulink/PLECS of a downscaled MMC prototype dedicated to ultra-fast charging of electric vehicles. Finally, we show the efficacy of the controller in keeping low pulsating power, i.e., 44.4% lower than the AC/AC MMCs.