High-Speed EMT Modeling of MMCs With Arbitrary Multiport Submodule Structures Using Generalized Norton Equivalents

In order to improve features, such as fault current blocking and capacitor voltage balancing, modular multilevel converter (MMC) topologies incorporating multiport submodules (SMs) are being considered as candidates for HVdc transmission applications. This paper presents high-speed and accurate electromagnetic transient (EMT) models for MMCs composed of such multiport SMs. The approach uses the Schur's complement technique to recursively eliminate internal nodes of the converter structure to create a multiport Norton equivalent that connects to the external network. Thus, the final admittance matrix seen by the EMT solver has a dimension orders of magnitude smaller than that of the unreduced structure. As with previously developed approaches for MMCs with single-port SMs, all internal information, such as individual SM capacitor voltages, is preserved and can be output by the program if needed. This increases the bookkeeping effort, but the overall reduction in matrix size more than compensates for any resulting time penalty. Approximately two to three orders of magnitude speedup over a straightforward implementation in an EMT program is achieved.