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Neural Operators for Power Systems: A Physics-Informed Framework for Modeling Power System Components

Ioannis Karampinis, Petros Ellinas, Johanna Vorwerk, Spyros Chatzivasileiadis

TL;DR

The work introduces Physics-Informed DeepONets to surrogate non-autonomous power-system components, enabling direct trajectory predictions from initial states and time-varying inputs without step-by-step integration. By embedding physics residuals into the training loss, PI-DeepONets achieve robust generalization with substantially reduced data needs. Across a 4th-order synchronous-machine case study, PI-DeepONets outperform PINNs in accuracy and offer over 30x inference speedups, making real-time simulation and digital-twin applications feasible. The approach supports scalable, physics-aware dynamic simulations and provides practical guidance for dataset generation, architecture choices, and training strategies for neural-operator surrogates in power systems.

Abstract

Modern power systems require fast and accurate dynamic simulations for stability assessment, digital twins, and real-time control, but classical ODE solvers are often too slow for large-scale or online applications. We propose a neural-operator framework for surrogate modeling of power system components, using Deep Operator Networks (DeepONets) to learn mappings from system states and time-varying inputs to full trajectories without step-by-step integration. To enhance generalization and data efficiency, we introduce Physics-Informed DeepONets (PI-DeepONets), which embed the residuals of governing equations into the training loss. Our results show that DeepONets, and especially PI-DeepONets, achieve accurate predictions under diverse scenarios, providing over 30 times speedup compared to high-order ODE solvers. Benchmarking against Physics-Informed Neural Networks (PINNs) highlights superior stability and scalability. Our results demonstrate neural operators as a promising path toward real-time, physics-aware simulation of power system dynamics.

Neural Operators for Power Systems: A Physics-Informed Framework for Modeling Power System Components

TL;DR

The work introduces Physics-Informed DeepONets to surrogate non-autonomous power-system components, enabling direct trajectory predictions from initial states and time-varying inputs without step-by-step integration. By embedding physics residuals into the training loss, PI-DeepONets achieve robust generalization with substantially reduced data needs. Across a 4th-order synchronous-machine case study, PI-DeepONets outperform PINNs in accuracy and offer over 30x inference speedups, making real-time simulation and digital-twin applications feasible. The approach supports scalable, physics-aware dynamic simulations and provides practical guidance for dataset generation, architecture choices, and training strategies for neural-operator surrogates in power systems.

Abstract

Modern power systems require fast and accurate dynamic simulations for stability assessment, digital twins, and real-time control, but classical ODE solvers are often too slow for large-scale or online applications. We propose a neural-operator framework for surrogate modeling of power system components, using Deep Operator Networks (DeepONets) to learn mappings from system states and time-varying inputs to full trajectories without step-by-step integration. To enhance generalization and data efficiency, we introduce Physics-Informed DeepONets (PI-DeepONets), which embed the residuals of governing equations into the training loss. Our results show that DeepONets, and especially PI-DeepONets, achieve accurate predictions under diverse scenarios, providing over 30 times speedup compared to high-order ODE solvers. Benchmarking against Physics-Informed Neural Networks (PINNs) highlights superior stability and scalability. Our results demonstrate neural operators as a promising path toward real-time, physics-aware simulation of power system dynamics.

Paper Structure

This paper contains 26 sections, 12 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Deep Neural Operators for Time-Varying Input Dynamical Systems
  3. Problem Formulation
  4. Classical Ordinary Differential Equations Solvers
  5. Deep Operator Network
  6. Branch Net
  7. Trunk Net
  8. Training the Solution Operator DeepONet
  9. A Training Pipeline for DeepONets
  10. Setting up the ODEs with the Time-Varying Input
  11. Dataset Generation
  12. Deep Operator Neural Network (DeepONet) Architecture
  13. Training of DeepONet
  14. Testing: Performance Assessment of DeepONet
  15. Accuracy
  16. ...and 11 more sections

Figures (4)

  • Figure 1: Traditional Unstacked DeepONet architecture
  • Figure 2: Stacked-N DeepONet architecture
  • Figure 3: Illustration of three trajectories from the test dataset showing the rotor angle $\delta$ and speed $\omega$ obtained from the reference ODE solver, the PI-DeepONet surrogates, and the single PINN model. The corresponding time-varying external voltage magnitude $V_s$ and phase $\theta_{vs}$ are shown in the lower panels.
  • Figure 4: Comparison of the absolute error (AE) over time among the three surrogate models, illustrating their relative accuracy and temporal stability.