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

2.4.2.5 Phase-Locked Loop

As discussed in Section 2.4.2.4, the most salient advantage of control in an frame, i.e., the involvement of DC signals, manifests itself if the angular velocity of the frame, , equals the angular frequency of the grid voltage phasor, (Fig. 2.18). One way to achieve this goal is to force the angle to track the angle , as explained in the following.

Consider the scenario illustrated in Fig. 2.18; the frame lags the grid voltage phasor , that is, is smaller than . Therefore, the angular velocity of the frame, , must be increased, in order for the frame to reach ...