Development of energy function algorithm for improving the stability assessment criterion of power systems

Until now, only few techniques may be considered to make complete analysis for the stability problem of interconnected nonlinear power systems. Most of the conventional methods are only investigations to know whether the power system is stable or not when a given accident disturbance is cleared. Also, the knowledge of the detailed behavior of the machines during the transient period has been bridged. For this and many other significant reasons, we increasingly need a criterion that has the capability to give a complete answer for the prediction of stability or instability problem. The ordinary scalar or vector Lyapunov function methodology must be developed when the transfer conductance should be taken into consideration. In this paper, a set of energy functions is derived for the whole power system based on the construction of the first integrals of the motion for all machines. Moreover, the corresponding state variables are referred to the center of inertia of the overall power system instead of relative rotor angle reference. According to this technique, a transient energy function is generated, in more symmetric form for both multi- and single-machine power system. The critical energy value at the stability boundary is determined by using the lowest unstable equilibrium point algorithm. A single machine power system is used to realize numerically the proposed criterion for obtaining more accurate transient energy function