Reduced-Order Small-Signal Model of Microgrid Systems

TLDR

The study aims to develop a reduced‑order small‑signal model for microgrid systems that operates in both grid‑tied and islanded modes. Nonlinear dq‑frame equations were linearized around stable operating points, the resulting high‑order state matrix was reduced via singular perturbation by retaining slow states and discarding fast ones, and the simplified model’s step responses were validated against hardware test data. When applied to a modified IEEE‑37 bus microgrid, the reduced‑order model accurately captured dynamic responses in grid‑tied, islanded, and transition scenarios.

Abstract

The objective of this study was to develop a reduce-dorder small-signal model of a microgrid system capable of operating in both the grid-tied and the islanded conditions. The nonlinear equations of the proposed system were derived in the dq reference frame and then linearized around stable operating points to construct a small-signal model. The high-order state matrix was then reduced using the singular perturbation technique. The dynamic equations were divided into two groups based on the small-signal model parameters ε. The "slow" states, which dominated the system's dynamics, were preserved, whereas the "fast" states were eliminated. Step responses of the model were compared to the experimental results from a hardware test to assess their accuracy and similarity to the full-order system. The proposed reduced-order model was applied to a modified IEEE-37 bus grid-tied microgrid system to evaluate system's dynamic response in grid-tied mode, islanded mode, and transition from grid-tied to islanded mode.