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This paper proposes a new methodology for allocation of transmission losses to participants of an energy market. The methodology begins by first determining the contribution of each generator to the current flow in each line/load of the transmission network using a proportional sharing technique. The losses incurred by each generator while supplying a particular load is then calculated by tracing the load currents back to the respective generators by using the aforesaid technique a second time. The method is based on a solved load flow and is easily understood and implemented. Since it is based on current distributions rather than power distributions, the proposed method is intuitively more reasonable for allocating losses. Also, since the losses are determined in a more `direct' manner making use of only reasonable assumptions, the fairness of the method is evident to the reader. In the paper, the method is demonstrated using several test systems and its performance is illustrated by comparing it with the performance of other popular methods.