Pricing mechanism based on losses using grid topology

The currently used pricing mechanisms for the network costs in the domestic sector do not give incentives to lower the stress on the grid. In this paper, we present a novel pricing mechanism for the grid costs based on the losses caused by the transport of energy in the low voltage (LV) grid. The mechanism is based on the Shapley value. In a first step, we derive the Shapley value based on the given locations of the households in the grid. As the locations influence the prices heavily, we present a second mechanism by averaging the Shapley value over all permutations of households. This leads to a contribution to the costs as if the household is on an average location. We show that this value can be calculated efficiently by an explicit expression if the households are connected to a single cable. Furthermore, we present an approximation for this value which may be useful for extensions to LV grids of a different topology.