Markov Jump Linear System Analysis Of Microgrid Stability


In a typical microgrid, the power generation capacity is similar to the maximum total load. The low inertia of the system provides little margin for error in the power balance, both active and reactive, and requires rapid control response to load changes. In the present work, a microgrid is modeled as a Markov jump linear system (MJLS). An MJLS is a dynamic system with continuous states governed by one of a set of linear systems, and a continuous-time Markov process that determines which linear system is active. When the discrete state of the Markov process changes, there is a 'jump' in the dynamics of the continuous states. In addition, the jump may be impulsive. The present work first explores impulsive MJLS stability. Conservative bounds on the expected value of the state are determined from a combination of the Markov process parameters, the dynamics of each linear system, and the magnitude of the impulses. Then the microgrid model is cast into the MJLS framework and stability analysis is performed. The conclusions are verified with detailed simulations.

Meeting Name

American Control Conference (2014: Jun. 4-6, Portland, OR)


Electrical and Computer Engineering


National Science Foundation (U.S.)


This project was supported in part by the FREEDM Systems Center, funded by the National Science Foundation under award EEC-0812121.

Keywords and Phrases

Electric Power Distribution; Linear Systems; Almost Sure Stability; Continuous-Time Markov Process; Markov Jump Linear Systems; Micro Grid; Microgrid Modeling; Microgrid Stability; Power Generation Capacities; Stability Analysis; Markov Processes; Markov Jump Linear System; Microgrid; Microgrids; Stability Analysis; Switches; Power System Stability; Markov Processes; Linear Systems; Eigenvalues And Eigenfunctions; Power System Dynamic Stability; Continuous Time Systems; Discrete Time Systems; Distributed Power Generation; Linear Systems; Power Generation Control

International Standard Book Number (ISBN)

978-1479932726; 978-1479932740

International Standard Serial Number (ISSN)

0743-1619; 2378-5861

Document Type

Article - Conference proceedings

Document Version


File Type





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

Publication Date

01 Jun 2014