Non-unique equilibria in wind turbine models

Accurate dynamic models of wind turbine generators are extremely important for assessing the effect of wind generation on power system dynamic performance. The paper considers a generic model for doubly-fed induction generator (type-3) wind turbines. It is shown that two of its modules, those associated with converter control and pitch control, duplicate an integrator that seeks to drive frequency error to zero. As a consequence of these duplicate integrators, the set of equations describing steady-state conditions is under-determined. Equilibria define a 1-manifold (curve) rather than the usual point solutions. It is shown that if the duplicated integrators are switched in unison, then pre- and post-disturbance equilibria will coincide. However if switching of the duplicated integrators is not coordinated, then post-disturbance transients will generically settle to a steady-state that differs from pre-disturbance conditions. These conclusions are illustrated using a standard WECC test case.