Nyquist stability analysis of a VSC-HVDC system using a distributed parameter DC-cable model

In this paper a two terminal VSC-HVDC system embedded in a strong grid ACenvironment is considered, emphasizing modeling, controllers design and small-signal stability analysis. Traditionally, DC cables are most often modeled by Π-sections, and when using them for higher frequencies or in case of transmission over long distances, approximation accuracy aspects must be considered. Here, a distributed parameter cable model, based on the damped wave equation, is used to overcome this limitation. It is shown that the VSC-HVDC system can be described by a forward transfer function cascaded with a feedback loop. The first transfer function will be different, due to which input and output variables that are considered but is in all realistic cases stable. The feedback loop, where the forward path is a rational function and the return path is a dissipative infinite dimensional system, remains the same in all cases. The stability is then analyzed, using the Nyquist criterion, in a straight forward manner. Numerical examples are given by MATLAB.