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

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.