Bilinear Quadratic Feedback Control of Modular Multilevel Converters

The present paper introduces the formulation and development of a bilinear quadratic control algorithm for Modular Multilevel Converter (MMCs), with a specific emphasis on achieving internal energy stabilization and balance within the converter. A bilinear average model of the MMC is employed, enabling the separation between the DC voltage and the voltage generated by submodules. The algorithm proposed in this study is formulated using bilinear theory and is founded on quadratic feedback control principles. The stability of the suggested controller is scrutinized using a meticulous mathematical approach based on Lyapunov theory. Subsequently, the theoretical findings are assessed using a comprehensive MMC switching model implemented in Matlab Simscape Electrical. The utilization of a phase-shift PWM technique, accompanied by a sorting algorithm, is considered in the study. Additionally, a comparison between the proposed bilinear controller and a standard PI controller is conducted. The outcomes demonstrate that the proposed controller effectively facilitates the regulation of circulating and AC currents, along with managing the internal energy of MMCs. Consequently, this achievement makes a noteworthy contribution to the field, as it introduces an innovative bilinear control approach capable of stabilizing all the state variables of MMCs converters using a single control law.