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.