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Doubly-fed wind turbine has no concept of power angle? Why is the power angle characteristic of doubly-fed wind turbine more special than that of synchronous motor?
The question you asked is very deep, and my doctoral thesis is devoted to this issue, hehe.

Doubly-fed is a power electronic interface, and its power angle is essentially different from that of synchronous motor. The power angle of the synchronous machine is determined by the mechanical angle, which is basically uncontrollable and can only swing slowly. The power angle of doubly-fed power converter is modulated by power electronic converter, which can be controlled quickly. The magnitude of the internal potential is the same as above. Mathematically speaking, the power angle of synchronous machine is a slow dynamic state variable, while the power angle of doubly-fed machine is basically a fast dynamic intermediate variable.