First order Markov chain approximation of microgrid renewable generators covariance matrix

Smart grids present interesting challenges as we integrate renewable energy sources and allow for customer participation in the decision making. A key to smart grids is getting information from the grid in real time and especially at the distribution level beyond the substation, which we refer to as the microgrid. This paper presents a distributed state estimation algorithm for microgrids with distributed renewable energy generation. We use a factor graph approach to model the microgrid network with renewable generators. The renewable generators are correlated resulting in many loops in the factor graph. This presents a problem when using distributed algorithms such as belief propagation. To limit the number of loops in the factor graph, we approximate the correlation among the renewable generators using a Markov chain approach. The algorithm is sub-optimal, but has low complexity using a greedy approach and Cholesky factorization. We present a simple microgrid example with renewable generators and show through simulations that our approximate solution gives performance close to the optimal solution.