Power grid parameter estimation involves the estimation of unknown parameters, such as inertia and damping coefficients, using observed dynamics. In this work, we present a comparison of data-driven algorithms for the power grid parameter estimation problem. First, we propose a new algorithm to solve the parameter estimation problem based on the Sparse Identification of Nonlinear Dynamics (SINDy) approach, which uses linear regression to infer the parameters that best describe the observed data. We then compare its performance against two benchmark algorithms, namely, the unscented Kalman filter (UKF) approach and the physics-informed neural networks (PINN) approach. We perform extensive simulations on IEEE bus systems to examine the performance of the aforementioned algorithms. Our results show that the SINDy algorithm outperforms the PINN and UKF algorithms in being able to accurately estimate the power grid parameters over a wide range of system parameters (including high and low inertia systems). Moreover, it is extremely efficient computationally and so takes significantly less time than the PINN algorithm, thus making it suitable for real-time parameter estimation.
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