Ties between classical energy based Lyapunov functions in nonlinear circuits and power systems

Lyapunov and energy-based stability analysis for estimating regions of attraction for stable equilibria in power system models has a very long history. The author provides tutorial background on the development of such energy analysis with the goal of establishing connections between the types of energy functions employed in power systems and classical energy based Lyapunov functions in circuits. The main result shows that the dynamic model used in such power system stability analyses has a nonlinear circuit analogy. In this analogy, the power system Lyapunov function is simply stored energy in the circuit. Conditions for existence of a closed-form expression for energy then correspond to reciprocity in the analogous circuit. Nonzero transfer conductances in the power system model appear as nonreciprocal inductance terms in the circuit analogy. Addition of parasitic terms to resolve ill-defined trajectories also has a simple analogy in the circuit model