Differentiable Modeling for Low-Inertia Grids: Benchmarking PINNs, NODEs, and DP for Identification and Control of SMIB System

2026-02-10

AI Summary

This study addresses the challenge of modeling low-inertia power grids, where accurate state prediction and physically consistent sensitivities are essential for reliable control, yet the relative merits of existing differentiable modeling paradigms remain unclear. Focusing on a single-machine infinite-bus system, the work systematically evaluates physics-informed neural networks (PINNs), neural ordinary differential equations (NODEs), and differentiable programming (DP) in terms of trajectory extrapolation, parameter identification, and LQR controller synthesis. The findings reveal a fundamental trade-off between data-driven flexibility and physical fidelity, and for the first time delineate clear applicability boundaries of these methods in power system modeling and control: NODEs excel in trajectory extrapolation, DP achieves faster convergence in parameter identification and near-optimal closed-loop stability, while PINNs exhibit limited generalization capability.

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Abstract

The transition toward low-inertia power systems demands modeling frameworks that provide not only accurate state predictions but also physically consistent sensitivities for control. While scientific machine learning offers powerful nonlinear modeling tools, the control-oriented implications of different differentiable paradigms remain insufficiently understood. This paper presents a comparative study of Physics-Informed Neural Networks (PINNs), Neural Ordinary Differential Equations (NODEs), and Differentiable Programming (DP) for modeling, identification, and control of power system dynamics. Using the Single Machine Infinite Bus (SMIB) system as a benchmark, we evaluate their performance in trajectory extrapolation, parameter estimation, and Linear Quadratic Regulator (LQR) synthesis. Our results highlight a fundamental trade-off between data-driven flexibility and physical structure. NODE exhibits superior extrapolation by capturing the underlying vector field, whereas PINN shows limited generalization due to its reliance on a time-dependent solution map. In the inverse problem of parameter identification, while both DP and PINN successfully recover the unknown parameters, DP achieves significantly faster convergence by enforcing governing equations as hard constraints. Most importantly, for control synthesis, the DP framework yields closed-loop stability comparable to the theoretical optimum. Furthermore, we demonstrate that NODE serves as a viable data-driven surrogate when governing equations are unavailable.

Problem

• low-inertia grids
• differentiable modeling
• power system control
• parameter identification
• trajectory extrapolation

Innovation

• Differentiable Programming
• Neural ODEs
• Physics-Informed Neural Networks
• Low-Inertia Power Systems
• Control-Oriented Modeling