Transmission cost-sharing in multi-supplier power grid

Ever-increasing energy consumption and growing penetration of renewable energy sources stimulate the development of new power grid models and architectures. Since the decentralization of power grids causes the unreliability of power supply, it is crucial to switch to a production-oriented consumption in order to provide the stability of a grid. Power flows in a grid are distributed according to Kirchhoff's laws and use multiple parallel lines in circuitous routes. Once the profile of energy injections and withdrawals is fixed, the values of load current flows can be defined over the network. Generally, it is not possible to directly determine the accordance between the energy contracts and the loop flows that contribute to the total congestion in network links. In this work, we describe a multi-supplier power grid model. Then we formulate a nonlinear minimization problem which solution gives a flow distribution fulfilling Kirchhoff's laws. Finally, we introduce a cost-sharing technique for finding individual transmission costs.