Approximation of faulted power system trjectories via averaging

The theory of averaging for autonomous systems is used to obtain simple approximate models from the nonlinear swing equation representation for electric power system dynamics. These models can be useful in the study of mid-term dynamics. The linearity of the simplified models makes them ideal for rapid numerical integration. It is shown that the new representation is approximately valid when the system is far from a stable operating point. The small parameter of the averaging method is taken as the reciprocal of the synchronous frequency. A numerical example is given to illustrate the nature of the approximation.