Nyquist Stability Analysis of an AC-Grid Connected VSC-HVDC System Using a Distributed Parameter DC Cable Model

In this paper, a two-terminal VSC-HVDC system embedded in a weak grid ac environment is considered, emphasizing modeling, controller design, and small-signal stability analysis. Traditionally, the dc cable is modeled by Pi-sections, implying that care has to be taken when using the model for higher frequencies or in cases of higher cable impedance density, such as submarine cables. Here, a distributed parameter cable model is used to overcome this problem. The VSC-HVDC system can be described as two cascaded blocks. The first block is a transfer function that will differ depending on what input and output variables are considered, but which is in all realistic cases stable. The second block is a feedback loop, where the forward path is a rational function and the return path is a dissipative infinite dimensional function, remaining the same in all cases. The stability is then analyzed, using the Nyquist criterion, in a straightforward manner. Numerical examples are given by the use of MATLAB. The result is that if the VSC-HVDC system using a single Pi-section cable model is stable, so is the VSC-HVDC system using a distributed parameter cable model.