$\tau$-Value Based Approach for Loss Allocation in Radial and Weakly Meshed Distribution Networks With Distributed Generation

Based on
$\tau$
-value concept of cooperative game theory, this paper presents a technique for efficient loss allocation in radial and weakly meshed distribution network (DN). The application of
$\tau$
-value concept requires the quasi-balanced condition to be satisfied by the game. Therefore, with suitable mathematical derivations, it is demonstrated that a DN having only load or only distributed generation (DG) satisfies the necessary quasi-balanced condition. Then, a two-step method to allocate the network losses among loads and DGs is presented. Further, the intensive computational burden involved in
$\tau$
-value method limits its applicability to practical DN. Therefore, by suitable mathematical analysis, computational complexity associated with
$\tau$
-value method is reduced. The proposed method is tested on a few possible scenarios of loading, DG penetration, DG location, and X/R ratio in radial and weakly meshed DNs. The results obtained by the proposed
$\tau$
-value, conventional
$\tau$
-value, Shapley value and branch current decomposition method are compared based on the attributes of fair and efficient loss allocation.