Fair and analytical allocating of transmission losses using two-step coalitional game

A fair and analytical procedure for allocating transmission losses simultaneously to individual sources and loads is presented. It is on the basis of the equivalent nodal injection currents of sources and loads. First, a two-step game is specially designed to convert the original complicated problem into two simple ones. Then, the procedure is derived mathematically by extending conceptually the coalitional game and using the Shapley value. The innovative features of the proposed procedure are that, it is directly analytical and easy to understand; It is of profound economic features; It satisfies all circuit laws and requires no assumptions; The active and reactive losses are naturally and simultaneously allocated to individual sources and loads; It takes into account accurately all interactions between sources and loads, and between P-Q flows; It is applicable for the cases of counter-flow and capacitive VAr sources; It provides both sources and loads with economic incentives. The proposed procedure gives a novel and analytical way for transmission cost fair and rational allocation in electricity markets.