Distributed Model-free Control in Low Voltage Distribution Networks: A Mean Field Approach

In order to tackle to the rising difficulties on modeling and information acquisition in modern low voltage distribution networks (LVDN), a model-free distributed approach to seek the approximate optimal control trajectory of users is proposed. The proposed approach employs Mean Field Theory to simplify information acquisition, which reduces communication burden. Besides, Hamilton-Jacob-Bellman (HJB) equation is introduced, to make users figure out their control trajectory individually by solving a personalized partial differential equation. Different from classical HJB applications, the system dimension is reduced by a broadcast signal, which relieves the computation burden. The case study is done with a 103 nodes realistic LVDN, with a benchmark done by centralized optimization algorithm under ideal conditions, which proves the effectiveness of the proposed approach.