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

Abstract

Based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\tau$</tex-math></inline-formula> -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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\tau$</tex-math></inline-formula> -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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\tau$</tex-math></inline-formula> -value method limits its applicability to practical DN. Therefore, by suitable mathematical analysis, computational complexity associated with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\tau$</tex-math></inline-formula> -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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\tau$</tex-math></inline-formula> -value, conventional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\tau$</tex-math></inline-formula> -value, Shapley value and branch current decomposition method are compared based on the attributes of fair and efficient loss allocation.