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.