Physics-Informed Neural Networks: Solving & Discovering Charge Dynamics in Gaseous High Voltage Insulation - Exploring the use of PINNs for Forward and Inverse Problems within Charge Dynamics in Air Insulation

Abstract

Abstract The development of efficient high-voltage equipment is imperative for minimizing greenhouse gas emissions and saving costs within the energy system. Effective insulation plays a pivotal role in such development and requires an understanding of the performance of gaseous insulators, such as air, under high-voltage stress. Electric discharges and charge transport in gases are modeled using systems of partially differentiable equations (PDEs) and their solutions are traditionally approximated numerically with discretizing methods such as the finite element method (FEM). However, such methods have significant shortcomings including difficulty handling high-dimensional problems, non-smooth behaviors, and inverse problems with hidden physics. An emerging, mesh-free alternative to numerical methods is physics-informed neural networks (PINNs). PINNs solve PDEs using a neural network with the PDE and associated constraints embedded into the network’s loss function and are easily extended to inverse problems. Initial experiments with PINNs for the forward problems related to electric discharges and charge dynamics have shown promising advantages compared to FEM but failed to model strongly non-uniform functions and coupled equations within the domain. This thesis contributes to this research by showing how a variety of performance-enhancing techniques can address the weaknesses of previous works, improving accuracy and enabling the modeling of steeper gradients and coupled PDEs. Additionally, it demonstrates how PINNs can be used to solve inverse problems related to discharge and charge dynamics, discovering both unknown parameters and distributions.