Real-Time Reactive Power Distribution in Microgrids by Dynamic Programing

In this paper a new real-time optimization method for reactive power distribution in microgrids is proposed. The method enables location of a globally optimal distribution of reactive power under normal operating conditions. The method exploits the typical compact structure of microgrids to obtain a solution by parts, using the dynamic programming method and Bellman equation. The proposed solution method is based on the fact that the microgrid is designed with a central feeder line to which clusters of generators and loads are connected, and is suitable for microgrids with ring topologies as well as radial ones. The optimization problem is formulated with the cluster reactive powers as free variables, and the solution space is spanned by the cluster reactive power outputs. The optimal solution is then constructed by efficiently scanning the entire solution space, by scanning every possible combination of reactive powers, by means of dynamic programming. Since every single step involves a one-dimensional problem, the complexity of the solution is only linear with the number of clusters, and as a result, a globally optimal solution may be obtained in real time. The paper includes the results of two test-case networks.