  In this paper we investigate how the equilibrium characteristics of
conventional power systems may change with an increase in wind penetration. We
first derive a differential-algebraic model of a power system network
consisting of synchronous generators, loads and a wind power plant modeled by a
wind turbine and a doubly-fed induction generator (DFIG). The models of these
three components are coupled via nonlinear power flow equations. In contrast to
the traditional approach for solving the power flows via iterative methods that
often lead to only local solutions, we apply a recently developed
parameter-homotopy based numerical continuation algorithm to compute all
possible solutions. The method solves the power flow equations over multiple
values of the wind penetration level with far less computational effort instead
of solving them at each value individually. We observe that depending on the
penetration limit and the setpoint value for the magnitude of the wind bus
voltage, the system may exhibit several undesired or even unstable equilibria.
We illustrate these results through a detailed simulation of a 5-machine power
system model with wind injection, and highlight how the solutions may be
helpful for small-signal stability assessment.
