Microgrids are power distribution systems that are small where total generation capacity is similar to the total demand. Examples may be found in isolated villages, military bases that may or may not be connected to the surrounding power grid, and vehicles ranging from automobiles to satellites to ships. DC microgrids have also been proposed for residential applications, where a single house would be a complete system, and for telecommunications power systems. Microgrids are an enabling technology for widespread deployment of renewable energy, such as solar and wind systems. This project will apply emerging control theory concepts to microgrid stability analysis. Previous researchers have usually assumed that all loads and sources have some ability to be controlled, but in practical systems, most loads change randomly, and renewable resources are subject to weather variations. The random events could cause the microgrid to become unstable and shut down. Microgrids are essential to the expansion of renewable energy due to the distributed nature of renewable energy generation, and the improved stability analysis from this project is needed to give system operators confidence in their proper operation.
The objective of this project is to analyze ac and dc microgrids using advanced techniques that apply to generic impulsive Markov jump linear systems. A Markov jump linear system (MJLS) is a system that jumps instantaneously among a set of linear dynamical systems according to a Markov process. More generically, the transitions in the discrete state could be accompanied by impulses in the continuous-time states, forming an impulsive MJLS. This is a good description for the small-signal characteristics of a microgrid. Unfortunately, generic stability results for an impulsive MJLS are few. In this project, stability results for the subset of impulsive MJLS that appropriately describes microgrids will be derived. Suitable models for both ac and dc microgrids will be derived and analyzed. The results will be parameterized by controller gains and other characteristics that are within the purview of the system designer, so that stability may be guaranteed by design. Both the discrete state, which evolves randomly, and the continuous state, which is deterministic, will be considered simultaneously. The approach will be validated with simulations and experiments. Two example microgrids, one ac and one dc, will be studied to demonstrate the ability to compose an appropriate nonlinear model, to convert it to a set of small-signal models, and to map it into the impulsive MJLS framework. The proposed impulsive MJLS study will be applicable to other dynamical systems, such as networked control systems, that fit a similar framework. Similarly, demonstrating the application of impulsive MJLS methods to microgrids may stimulate research within the power community on other applications that fit a similar structure, such as the load on a voltage regulator module (VRM).
