Mixed Iterative Adaptive Dynamic Programming for Optimal Battery Energy Control in Smart Residential Microgrids

In this paper, a novel mixed iterative adaptive dynamic programming (ADP) algorithm is developed to solve the optimal battery energy management and control problem in smart residential microgrid systems. Based on the data of the load and electricity rate, two iterations are constructed, which are P-iteration and V-iteration, respectively. The V-iteration is implemented based on value iteration, which aims to obtain the iterative control law sequence in each period. The P-iteration is implemented based on policy iteration, which updates the iterative value function according to the iterative control law sequence. Properties of the developed mixed iterative ADP algorithm are analyzed. It is shown that the iterative value function is monotonically nonincreasing and converges to the solution of the Bellman equation. In each iteration, it is proven that the performance index function is finite under the iterative control law sequence. Finally, numerical results and comparisons are given to illustrate the performance of the developed algorithm.