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A continuous-time dynamic model of a network of wind turbines (induction generators) and capacitors connected to a distant bus is developed and implemented in Matlab code in order to study the stability properties of the system. One particular configuration and parameters of the network were provided by Southern California Edison to represent a local wind farm, where voltage instability had been observed and methods to prevent it were being considered. The mathematical model consists of a system of ordinary differential equations and algebraic relations. The implementation provides an efficient method for simulating the model, and bifurcations can be observed which lead to unstable steady states. As an example, the precise role of the compensating capacitors in stability is studied. This model and the associated analytic techniques are prototypical tools which can be used to efficiently determine the causes of voltage instability and its prevention.