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The influence of wind turbine generators (WTGs) on power system dynamic performance is becoming increasingly important as wind generation grows. The dynamic behavior of WTGs should therefore be thoroughly understood. The paper analyzes dynamic models of type-3 WTGs, and in particular the WECC generic model. The behavior of such models is governed by interactions between the continuous dynamics of state variables, and discrete events associated with limits. It is shown that these interactions can be quite complex, and may lead to switching deadlock that prevents continuation of the trajectory. Switching hysteresis is proposed for eliminating deadlock situations. Various type-3 WTG models include control blocks that duplicate integrators. It is shown that this leads to non-uniqueness in the conditions governing steady-state, and may result in pre- and post-disturbance equilibria not coinciding. It also gives rise to a zero eigenvalue in the linearized WTG model.