PINNSim: A Simulator for Power System Dynamics based on Physics-Informed Neural Networks

TL;DR

PINNSim addresses the computational bottleneck of time-domain power-system simulations by learning single dynamic components with Physics-Informed Neural Networks and coupling them through a scalable root-finding process. The approach enables substantially larger time steps than traditional trapezoidal integration while preserving accuracy, demonstrated on a 9-bus system. Key contributions include a voltage parametrisation scheme, PINN-based component solvers, and a Newton-type coupling mechanism that preserves current balance across buses. The proposed framework promises significant speedups for large-scale power-system dynamics, with parallelizable computations and modular training of components enabling scalability to complex networks.

Abstract

The dynamic behaviour of a power system can be described by a system of differential-algebraic equations. Time-domain simulations are used to simulate the evolution of these dynamics. They often require the use of small time step sizes and therefore become computationally expensive. To accelerate these simulations, we propose a simulator - PINNSim - that allows to take significantly larger time steps. It is based on Physics-Informed Neural Networks (PINNs) for the solution of the dynamics of single components in the power system. To resolve their interaction we employ a scalable root-finding algorithm. We demonstrate PINNSim on a 9-bus system and show the increased time step size compared to a trapezoidal integration rule. We discuss key characteristics of PINNSim and important steps for developing PINNSim into a fully fledged simulator. As such, it could offer the opportunity for significantly increasing time step sizes and thereby accelerating time-domain simulations.

Figures (6)

• Figure 1: Structure of the that govern the power system dynamics with current injections $\Bar{\bm{i}}^C$ from the components, e.g., generators and loads, and current flows in the network $\Bar{\bm{i}}^N$. Adapted from sauer_power_1998.
• Figure 2: The panels show the simulated trajectories of the frequency deviation at machine 2 $\Delta \omega_2$ with a trapezoidal and PINNSim time stepping scheme for two time step sizes. The markers indicate the values at the time steps. The curves within a time step stem from the prediction of the PINNs for PINNSim and from a quadratic interpolation for the trapezoidal integration. The ground truth stems from a highly accurate integration scheme.
• Figure 3: Comparison of the maximum error of $\Delta \omega_2$ over a trajectory of $2.4s$ for a range of time step sizes $\Delta t$.
• Figure 4: Maximum error for single time step predictions of different length $\Delta t$ starting from 200 different initial conditions. Comparison between the trapezoidal rule and PINNSim with different voltage scheme orders ($r$) and number of query points $s$. Larger $r$ and $s$, both improve the accuracy of PINNSim.
• Figure 5: Error characteristics of the PINN for machine 2 on a test dataset. Both plots show the same results but on a logarithmic x-axis (left) and a linear x-axis (right) to highlight the accuracy of PINNs over large time steps.