Modeling of the Modular Multilevel Converters Based on the State-Plane Analysis and $\Sigma\Delta$ Coordinate Transformation

Because of its simple modular structure and easy voltage scaling, the modular multilevel converter (MMC) is deemed the most suitable for high-voltage power conversion using relatively low-voltage devices. In most practices, the volume of the capacitors is more than 50% of the total module size. Hence, methods of reducing circulating energy and the size of the capacitor bank have been widely pursued. Even though a significant progress has been made toward reducing the capacitor voltage ripple, there is a lack of an effective modeling tool that enables a more systemic approach to address control strategies for system optimization. This paper proposes a method of modeling and control based on the state trajectory analysis and offers graphical visualization of the power throughput and circulating energy. Furthermore, through a coordinate transformation, a simple equivalent circuit model is developed leading to the establishment of the two control laws that enable maximum power throughput with minimum circulating energy.