An Accurate Small-Signal Model of Inverter-Dominated Islanded Microgrids using dq Reference Frame


In the islanded mode operation of a microgrid, a part of the distributed network becomes electrically separated from the main grid, while loads are supported by local sources. Such distributed energy sources (DERs) are typically power electronic based, making the full system complex to study. A method for analyzing such a complicated system is discussed in this paper. A microgrid system with two inverters working as DERs is proposed. The controllers for the inverters are designed in the dq reference frame. Nonlinear equations are derived to reflect the system dynamics. These equations are linearized around steady-state operating points to develop a state-space model of the microgrid. An averaged model is used in the derivation of the mathematical model that results in a simplified system of equations. An eigenvalue analysis is completed using the linearized model to determine the small-signal stability of the system. A simulation of the proposed microgrid system consisting of two inverter based DERs, passive loads, and a distribution line is performed. An experimental testbed is designed to investigate the system's dynamics during load perturbation. Results obtained from the simulation and hardware experiment are compared with those predicted by the mathematical model to verify its accuracy.


Electrical and Computer Engineering


National Science Foundation (U.S.)


This work was supported in part by the National Science Foundation under Award EEC-0812121 and in part by the Future Renewable Electric Energy Delivery and Management Systems Center, Raleigh, NC, USA.

Keywords and Phrases

Micro Grid; Reference Frame; Small Signal Model; Switched Energy; Mathematical Model; Inverters; Load Modeling; Microgrids; Phase Locked Loops; Equations; Voltage Measurement; Distributed Power Generation; Eigenvalues And Eigenfunctions; Invertors; Nonlinear Equations; State-Space Methods

International Standard Serial Number (ISSN)

2168-6777; 2168-6785

Document Type

Article - Journal

Document Version


File Type





© 2014 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Dec 2014