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The cost allocation problem faced by an operator of an electricity network, where the fixed cost of the network has to be allocated among its users is discussed. Usage-based methods, such as the postage stamp rate method and the MW-mile method, are easy to understand and compute, but may yield cost allocations for which some transactions are subsidising others. Formally, this is equivalent to allocations outside of the core of the corresponding co-operative cost game. The main contribution of this paper is to present a method, similar to a well known method for computing the nucleolus of a cooperative game, by which several usage-based methods may be combined to produce allocations that are in, or as close as possible to, the core. Simulation results are conducted using two test systems.