Loss Allocation for Weakly Meshed Distribution System Using Analytical Formulation of Shapley Value

A practical loss allocation method should consider size, distance from source, and network usage of its' participants. The power flow pattern in distribution network has changed over a period due to increased integration of distributed generation (DG) and hence, the equivalent distance and usage of network have changed for the conventional distribution network. The regulators require a fair and robust model for loss allocation which should be able to discriminate between the contributions of multiple participants. The loss allocation techniques proposed earlier in the literature either require additional quantities over and above power flow solution or are specifically developed only for radial distribution networks. This paper presents a cooperative game approach which provides stable solution integrated with appropriate penalties or rewards to participants. The proposed method provides an analytical solution which is solved using Shapley value for radial as well as weakly meshed distribution network. The memory and computational burden with the Shapley value have been overcome by a final analytical formula that satisfies the axioms of fairness. The use of the method is straightforward without any assumptions and requires only network data and power flow solution. The results are illustrated using different scenarios of DG output levels and network topologies and compared with other methods to establish its effectiveness.