A Data-Driven Method for Microgrid System Identification: Physically Consistent Sparse Identification of Nonlinear Dynamics

TL;DR

MGs with DER variability and low inertia challenge accurate system identification for frequency control. The paper introduces Physically Consistent SINDy ($PC\text{-}SINDy$) that builds an analytically designed function library from DER dynamics and identifies the true governing equations directly from PMU data via sparse regression, without requiring network or DER parameters. Key contributions include analytical candidate functions for grid-forming and grid-following converters, a practical identification workflow using PMU measurements, and a case study on a 4-bus MG showing accurate one-step-ahead frequency predictions under large disturbances and noisy, low-sampling data, outperforming an intuitive library SINDy. The work enables interpretable, online-capable models for MG frequency regulation across untested scenarios and topology changes.

Abstract

Microgrids (MGs) play a crucial role in utilizing distributed energy resources (DERs) like solar and wind power, enhancing the sustainability and flexibility of modern power systems. However, the inherent variability in MG topology, power flow, and DER operating modes poses significant challenges to the accurate system identification of MGs, which is crucial for designing robust control strategies and ensuring MG stability. This paper proposes a Physically Consistent Sparse Identification of Nonlinear Dynamics (PC-SINDy) method for accurate MG system identification. By leveraging an analytically derived library of candidate functions, PC-SINDy extracts accurate dynamic models using only phasor measurement unit (PMU) data. Simulations on a 4-bus system demonstrate that PC-SINDy can reliably and accurately predict frequency trajectories under large disturbances, including scenarios not encountered during the identification/training phase, even when using noisy, low-sampled PMU data.

Figures (5)

• Figure 1: (a) Droop control of GFM converters and (b) three-phase PLL diagrams of GFL converters.
• Figure 2: Flowchart of the PC-SINDy-based Identification method for the true physical system.
• Figure 3: The 4-bus MG.
• Figure 4: Comparison between analytical $\Xi$ and SINDy-estimated $\hat{\Xi}$ using low-quality measurements.
• Figure 5: Prediction of the GFM frequency $f_1$ and the GFL frequency $f_2$ following \ref{['equ:sindy-pred']} with the proposed analytical library and intuitive library nandakumar2023.