Consider that the grid-side converter of DFIG always operates at unity power factor, i.e. Qr= 0, the reactive power Qg is equal to the stator reactive power Qs, i.e. Qg=Qs. In the steady state analysis, in accordance with the expressions of stator power and the rotor power, it can be proved that Pr=-sPs, and Pg=Ps/(1-s). Accordingly, the real and reactive powers equations and the torque equation can be rewritten as
Xs ds X
2H- = Te - Tm = WdsIqs + WqsIds ) " Tm = "-fU^r ~ (25)
Finally, the equations (17-18), (21-22), (23-25) constitute the 3rd order simplified practical DFIG model.
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