Loss allocation for radial distribution networks including DGs using Shapley value sampling estimation

This study focuses on the equitable loss allocation method for radial distribution networks integrated with distributed generators (DGs). As the traditional Shapley value method may cause a combinational explosion problem, the authors propose a sampling method for estimating the actual Shapley value. They use a stratified sampling method (SSM) to reduce the number of samples of Shapley value method with the subject to the overall equilibrium constraint. To determine the number of samples drawn from each stratum, they use the Neyman optimum allocation to minimise the variance of the sample mean. A reinforcement learning algorithm is introduced to estimate the standard deviations of the strata needed for the optimal stratified sampling. The proposed method is applied to a modified 17-bus distribution network and an actual distribution network in Zhejiang Province, People's Republic of China. The simulation results show that the proposed method can not only resolve the combinational explosion problem of Shapley value method but retain its desirable characteristics. The proposed method can dramatically reduce computational time by implementing a SSM. Therefore, the efficiency and superiority of the proposed method with regards to loss allocation are verified for radial distribution networks that include DGs.