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Multi-terminal Direct-Current Grids: Modeling, Analysis, and Control by Nilanjan Chaudhuri, Balarko Chaudhuri, Rajat Majumder, Amirnaser Yazdani

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2.4.2.5 Phase-Locked Loop

As discussed in Section 2.4.2.4, the most salient advantage of control in an c02-math-0504 frame, i.e., the involvement of DC signals, manifests itself if the angular velocity of the c02-math-0505 frame, c02-math-0506, equals the angular frequency of the grid voltage phasor, c02-math-0507 (Fig. 2.18). One way to achieve this goal is to force the angle c02-math-0508 to track the angle c02-math-0509, as explained in the following.

Consider the scenario illustrated in Fig. 2.18; the c02-math-0510 frame lags the grid voltage phasor c02-math-0511, that is, c02-math-0512 is smaller than . Therefore, the angular velocity of the frame, , must be increased, in order for the frame to reach ...

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