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

TL;DR

This work addresses the challenge of modeling low-inertia power grids with physically meaningful gradients for control. It compares PINNs, NODEs, and Differentiable Programming (DP) on the SMIB benchmark for trajectory prediction, parameter identification, and LQR synthesis. The study finds that NODE offers strong extrapolation by capturing the vector field, DP enables fast convergence in parameter identification and delivers near-optimal closed-loop stability, and NODE can act as a surrogate when governing equations are unavailable. These findings guide the choice of differentiable modeling tools for robust, control-oriented identification and regulation in low-inertia grids.

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.

Figures (7)

• Figure 1: Single machine infinite bus (SMIB) system.
• Figure 2: Comparison of predicted trajectories for rotor angle $\delta$ (top) and angular velocity $\omega$ (bottom) in the stable scenario. The shaded region ($t>10 s$) indicates the extrapolation horizon.
• Figure 3: Comparison of predicted trajectories for rotor angle $\delta$ (top) and angular velocity $\omega$ (bottom) in the oscillating scenario. The shaded region ($t>10 s$) indicates the extrapolation horizon.
• Figure 4: Predicted trajectories of NODE for rotor angle $\delta$ (top) and angular velocity $\omega$ (bottom) in the oscillatory scenario with $5\%$ noise.
• Figure 5: Convergence behavior of PINN in parameter estimation for inertia $\theta_M$ (top) and damping coefficient $\theta_D$ (bottom) with respect to data loss weight $\lambda_d$. Higher values of $\lambda_d$ accelerate the convergence to the true values.