Study of the existence of energy functions for power systems with losses

It is shown that there is no general energy function for multimachine power systems with losses. It is also shown that under the condition of small losses, there does exist an energy function (defined in a compact set of the state space) which can be incorporated into direct methods for the stability analysis of power systems with losses. One implication of the results is that any general procedure attempting to construct an energy function for power systems with losses must include a step serving to check the existence of an energy function. This step would essentially play the same kind of role as the Lyapunov equation plays in determining the stability of an equilibrium point. The results confirm current practice in the area of direct analysis of power system stability for using numerical energy functions