Distributed optimal active power dispatch with energy storage units and power flow limits in smart grids

Dynamic optimal active power dispatch with energy storage units and power flow limits is an important problem in smart grids. This problem is usually described as a convex optimization model. In our model, not only the conventional equality and inequality constraints, energy storage units' constraints and power flow constraints are considered, but also the energy storage units' operational costs and the power price of the main grid are considered in the total costs. To solve this problem, a fully distributed algorithm based on the alternating direction method of multipliers (ADMM), the projected gradient method and the average consensus is proposed. The proposed algorithm can obtain the optimal output power settings of the energy storage units, distributed generators and the main grid for different demand loads with different initial states. In the proposed algorithm, firstly, the dispatch problem is decomposed into multiple subproblems on the basis of the alternating direction method of multipliers; then the subproblems can be solved according to the projected gradient method and the average consensus algorithm. In order to apply the projected gradient method, every bus is equipped with a bus agent which is responsible for information communication and the output power optimization calculation. Simulation studies demonstrate the effectiveness of the proposed algorithm.