Neural Lyapunov stability analysis of shipboard DC power systems

A shipboard DC power system typically has higher hosting capabilities for power electronics (PE) devices and pulsive loads (PLs) due to its compactness and efficiency. With a high penetration of PE and PL devices, a DC system's dynamics are characterized by high-order nonlinearity, which is distorted by large-signal disturbances. Existing works have studied ad hoc Lyapunov functions to analyze transient stability. Nonetheless, the conservativeness grows rapidly with the increase of modeling complexity due to the stringent function structure. We propose a neural network (NN)-based method to approach the problem. The proposed method leverages the Converse Lyapunov Theorem and the Universal Approximation Theorem such that if a Lyapunov function exists, an NN with sufficiently large scale would be able to approximate it. We train the neural Lyapunov function by minimizing an empirical Lyapunov risk defined over randomly sampled state trajectories. Our method is validated through simulations based on a motivating shipboard DC power system example. Simulation results demonstrate that the method effectively characterizes a broad and reliable stability region.