A Back-Stepping Control Method for Modular Multilevel Converters

In this article, a back-stepping method (BSM) in a-b-c reference is presented to establish the stable operating conditions for modular multilevel converter (MMC). The designed BSM utilizes arm currents, sum of submodule capacitors voltages and MMC input energy as the main variables to form the energy functions. The proposed BSM is designed by well-known dynamic MMC equations to be applicable for both single- and three-phase ones while the control of variables is also guaranteed by BSM. A virtual control input containing input energy error and its dynamics is defined in the second energy function to further enhance the appropriate transient responses of the MMC. The proposed BSM has inherent feature of the circulating current suppression control loops which helps avoiding additional control loops. Moreover, several assessments are presented to show how BSM coefficients contribute to the noticeable decrement in control variables errors of the MMC system. Experimental and simulation results prove an excellent capability of BSM for controlling MMCs compared to the conventional PI linear controller. Moreover, the BSM robustness against the variations of the MMC circuit parameters is validated.