Consensus-Based Energy Management in Smart Grid With Transmission Losses and Directed Communication

This paper investigates the problem of distributed energy management for both generation and demand side in smart grid. Different from existing works, we formulate a social welfare maximization problem for a more practical scenario by taking transmission losses into account. The formulated problem is non-convex due to the non-convexity of the power balance equality constraint caused by the transmission losses. To solve the problem, we first transform the equality constraint into an inequality constraint and obtain a new convex optimization problem. We then derive a sufficient condition to guarantee that the new problem has the same solution as the original one. Because of the coupling in the constraint, Lagrange duality method is adopted to decompose the problem. Considering the general communication topology among generators and demands, i.e., directed connected topology, we design a consensus-based algorithm to solve the problem in a distributed way. We also prove the convergence and optimality of the proposed algorithm, under which the social welfare maximization is achieved. Extensive simulations validate the theoretical results and demonstrate the effectiveness of the proposed algorithm.