Analysis of a Standalone Microgrid Stability using Generic Markov Jump Linear Systems


Recent developments to address the stability of small power systems, such as AC & DC microgrids include the use of advanced techniques that apply to Markov Jump Linear Systems (MJLSs). The system is considered to oscillate between discrete, finite operating modes, and can be represented as a Stochastic Hybrid System (SHS). Analytical solutions in terms of the moments of the power system dynamic and algebraic states were derived in previous studies. The method is validated for small systems (2 states, 2 modes). However, its scalability to larger systems remains an open question. In this paper, we apply the model to a standalone microgrid (two inverters, 36 states, 2 buses and 3 modes of operation). The resulting system statistics converge to Monte Carlo simulations. Future work will extend the application of the model to arbitrary large scale systems and will derive bounds on the statistics of the dynamic states.

Meeting Name

IEEE Power and Energy Conference at Illinois (2017: Feb. 23-24, Champaign, IL)


Electrical and Computer Engineering

Research Center/Lab(s)

Intelligent Systems Center

Keywords and Phrases

Continuous Time Systems; Hybrid Systems; Linear Systems; Markov Processes; Monte Carlo Methods; Solar Buildings; Stochastic Systems; Continuous Time Markov Chain; Markov Jump Linear Systems; Microgrid Stability; Modes Of Operation; Power System Dynamics; Small Power Systems; Stochastic Hybrid Systems; System Statistics; System Stability; Continuous Time Markov Chains

International Standard Book Number (ISBN)

978-1509055517; 978-1509055500

Document Type

Article - Conference proceedings

Document Version


File Type





© 2017 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Feb 2017