A Matrix Representation of a Markov Jump Linear System Applied to a Standalone Microgrid

The analysis of microgrid stability requires an adequate modeling of the randomness in the disturbances affecting the system. For a microgrid operating in a standalone mode, abrupt disturbances are generated when local power sources and loads are switched on and off. Novel methods include the representation of microgrids as Stochastic Hybrid Systems. In this frame, continuous variations in the dynamic and algebraic states as well as discrete, random and abrupt effects are conjointly modeled. The purpose of this study is to present a detailed procedure to derive a matrix representation of a Markov Jump Linear System as a special case of the general stochastic hybrid system framework and apply it to an inverter-based microgrid. Numerical results in terms of the conditional moments of the stochastic model are presented and discussed.