Cell-Based VSC Analysis Methodology: From Graph Laplacian to Converter Degrees of Freedom

The cell-based class of Voltage Source Converter (VSC) topologies, including Modular Multilevel Converter (MMC), are being considerably employed through the power system to interconnect heterogeneous electrical systems. Their versatility to play with the converter topology is widely exploited to accommodate several terminals and ports according with the specific application. One of the most challenging, and fundamental, question to comprehend the behavior of each topology concerns the definition of the so-called degrees of freedom (DOFs). The topology-geometry of the converter circuit is strongly characterizing its intrinsic DOFs; however, it is not yet considered a methodology to assess them in a generalized approach. For instance, the well-known Clarke transformation, to achieve the electrical DOFs, is only valid for a star-based system topology. Therefore, topology changes might lead to different, and not evident, converter DOFs. With respect to this, the main purpose of the article is to present a systematic methodology, scalable to every cell-based converter topology, to assess their electrical DOFs and the inherent ports affinities. The method lies in the topology-graph Laplacian spectral analysis, which indicates the structural normal modes at the converter points of connections. The analysis is then validated experimentally.