Multi-terminal Direct-Current Grids: Modeling, Analysis, and Control

3.6 Small-signal Stability Analysis of AC–MTDC Grid

The modeling framework for the nonlinear dynamic simulation of the AC–MTDC grid was described in Section 3.5. However, the interaction among the state variables is often not clear from such nonlinear time-domain simulations. This insight is important in root-cause analysis of the system dynamic behavior and also for control design. Small-signal analysis in frequency-domain is very useful in this regard. A linearized model around an operating condition is required for such small-signal analysis, which is described in this section.

The set of nonlinear DAEs in (3.15–3.17) can be linearized around the equilibrium point . The steps for obtaining the equilibrium point was described in 3.5.1. The linearization is done by perturbing , , and by a small amount , , and ; expanding the equations into a Taylor series as described in Section 3.4.3; ...