Comprehensive Mathematical Modeling of Multilevel VSC HVDC Systems for Power System Stability Studies and Controller System Design

This paper provides a comprehensive approach for mathematical modeling of Multiterminal VSC HVDC systems. The mathematical models are developed in the Laplace Domain as it offers appropriate opportunities regarding implementation in dynamic system analysis tools and the subsequent control design process. Models for the AC and DC side of the MMC as well as for the DC network are determined. The DC network model is based on the concatenation of pi-sections and is easily extendable to Multiterminal systems. Regarding the MMC, a model for the energy storage of the submodules in the converter arms is introduced. This aims in a detailed mathematical HVDC model and applies a connection via the energy storage of submodules within the converter arms. Based on the mathematical modeling, two control strategies are provided. The first strategy controls the active power via a subordinated AC grid controller in the dq-frame and the converter energy via the DC current controller on the DC side. The second strategy controls the converter energy via an AC grid controller and the active power via a DC current controller.