Swing equation in power systems: Approximate analytical solution and bifurcation curve estimate

The swing equation plays a central role in the model and analysis of power system dynamics, including small-signal stability and transient stability. As it has the same form as that in a variety of different disciplines, such as the forced pendulum in mechanics, the classical mechanistic description of superconducting Josephson junctions in physics, and the classical second-order phase-locking loop in electronics, it has aroused general interest in science and engineering. In this paper, its approximate solution of the limit cycle is obtained by means of the incremental harmonic balance (IHB) method. It is found that the trouble of a more distorted limit cycle when the parameters are closer to the homoclinic bifurcation curve can be easily solved by incorporating higher order harmonics in the IHB method. In this way, we can predict the homoclinic bifurcation curve perfectly. In addition, the method is extended to study a generalized swing equation including excitation voltage dynamics.