Reactive power limit of wind farm with doubly-fed induction generators and its asymmetric P-Q dependence

• A RPL model of DFIG independent of initial reactive power setting is proposed. • The RPL model of wind farm decided by the PCC voltage is proposed. • It is newly found that the upper/lower RPL of the wind farm is not symmetrical. • Relation of active power and the RPL is newly described by a quadric function. The existing reactive power limit models of doubly-fed induction generators ignore the relation among wind speed, rotor speed, and active power output. Furthermore, they are decided by stator voltage and reactive power setting, but the former is uncontrollable, and the latter is different from the maximum/minimum reactive power. The reactive power limit of wind farm with doubly-fed induction generators and collectors is important to power system dispatch, but has not been studied. In this paper, iterative solution to reactive power limit model of the doubly-fed induction generator is proposed, with the novelty of correspondence of wind speed to active power, not using simplified slip power, and independent of the reactive power setting. By alternatively solving the reactive power limits of the doubly-fed induction generators and power flow of the collectors, the reactive power limit of wind farm is proposed, which is based on the voltage at the point of common coupling instead of the stator voltage. It is found that with the same wind speed and grid voltage, the upper/lower reactive power limit of wind farm is asymmetrical. Dependence of active power on the reactive power limit is newly described by a quadric function. Simulation results give the reactive power limit of the doubly-fed induction generators and wind farm, compare the active power at the upper/lower reactive power limit, and verify the impacts of the voltage at the point of common coupling and wind speed on the dependence of active power on the reactive power limit.