Improved Multi-Dimensional Holomorphic Embedding-Based Approximate Dynamic Programming for Stochastic Optimal Power Flow of Active Distribution Network

The optimal power flow (OPF) problem of active distribution network (ADN) is a stochastic, nonconvex, and nonlinear problem. Although several algorithms have been presented to solve this problem, most of them are difficult to obtain high-quality solutions in acceptable time. To fill this gap, this paper proposes an improved multi-dimensional holomorphic embedding (IMDHE)-based approximate dynamic programming (ADP) algorithm, which decomposes the intractable problem into tractable subproblems and then solves them successively. Compared with traditional ADP algorithms, the approximate value function is extended from the first-order function to the high-order function in the proposed algorithm. Moreover, the proposed algorithm can recursively derive the value functions order by order, instead of iteratively solving the nonconvex and nonlinear problem to obtain these value functions. In this way, both the computational accuracy and efficiency can be improved. Besides, the nonconvex and nonlinear problem for calculating the zeroth-order value function, which is the basis of the aforementioned recursive process, is decomposed from a systemscale problem into several bus-scale subproblems. This helps to further accelerate the proposed algorithm. The IMDHE-based ADP algorithm can be used for both the day-ahead and intra-day OPF problems of ADN. Numerical simulations demonstrate the effectiveness of the proposed approach.