Learning without Data: Physics-Informed Neural Networks for Fast Time-Domain Simulation

Abstract

In order to drastically reduce the heavy computational burden associated with time-domain simulations, this paper introduces a Physics-Informed Neural Network (PINN) to directly learn the solutions of power system dynamics. In contrast to the limitations of classical model order reduction approaches, commonly used to accelerate time-domain simulations, PINNs can universally approximate any continuous function with an arbitrary degree of accuracy. One of the novelties of this paper is that we avoid the need for any training data. We achieve this by incorporating the governing differential equations and an implicit Runge-Kutta (RK) integration scheme directly into the training process of the PINN; through this approach, PINNs can predict the trajectory of a dynamical power system at any discrete time step. The resulting Runge-Kutta-based physics-informed neural networks (RK-PINNs) can yield up to 100 times faster evaluations of the dynamics compared to standard time-domain simulations. We demonstrate the methodology on a single-machine infinite bus system governed by the swing equation. We show that RK-PINNs can accurately and quickly predict the solution trajectories.

Time-Series Machine Learning Techniques for Modeling and Identification of Mechatronic Systems with Friction: A Review and Real Application

“…The functions present in both discretization schemes are replaced with neural networks and the networks are trained using the regular loss of typical neural networks (i.e., the MSE between the actual u and predicted û at each time step). This approach was discussed in following papers [69][70][71] and used to model the nonconservative forces in the dynamic equation of an inverted pendulum in [11]. PINNs are usually implemented with feedforward neural networks because they are faster to train.…”

A Frequency Domain Approach to Predict Power System Transients

“…Recently, physics-Informed Neural Networks have been proposed in [22] to learn solutions that satisfy equations from implicit Runge-Kutta (RK) integration. This approach has been applied to power system swing dynamics in [18]. Since RK method is the weighted sum of ODE solutions in discretized intervals, its accuracy decreases sharply when predicting trajectories with large oscillations for a longer horizon (e.g., larger than 1 second), as illustrated in Fig.…”

“…The proposed method using Fourier Neural Operator (FNO) is compared with Physics-Informed Neural Networks (PINN) and deep neural network (DNN). The parameters for PINN is the same as [18] where the case study is also a singlemachine infinite bus system. The DNN have a dense structure and seven layers.…”

“…More importantly, since the majority of trajectory used in training is stable, the learned networks fail predict unstable behaviors. Physics informed neural networks that directly attempt to solve the ODEs have been proposed as an alternative [18], but it does not currently scale beyond small networks.…”