Matrix Method to Linearization and State Space Representation of Power Systems Containing Doubly Fed Induction Machines Operating as Wind Generators

The control design using modern control theory requires the representation of the system in state space. In electric power systems, besides the control design, the state space representation makes possible the prediction about the system transient stability through the model matrices analysis. However, power systems dynamic models consist of differential and algebraic nonlinear equations and, for large power systems, these models are too complex making difficult the controllers design and the stability analysis. The model linearization allows the application of the linear control theory in a linearized model, and the transient stability analysis through the model state matrix eigen values positioning evaluation. Some works have showed linearization and state space representation methods for power systems containing synchronous machines. This work presents methods for power systems containing doubly fed induction generators, which have an increasing penetration in power systems, mainly in Europe, operating as wind generators.