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.
G. Mpembele and J. W. Kimball, "Analysis of a Standalone Microgrid Stability using Generic Markov Jump Linear Systems," Proceedings of the IEEE Power and Energy Conference at Illinois (2017, Champaign, IL), Institute of Electrical and Electronics Engineers (IEEE), Feb 2017.
The definitive version is available at https://doi.org/10.1109/PECI.2017.7935737
IEEE Power and Energy Conference at Illinois (2017: Feb. 23-24, Champaign, IL)
Electrical and Computer Engineering
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)
Article - Conference proceedings
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01 Feb 2017