Sharing congestion management costs among system operators using the Shapley value

With energy generation becoming increasingly decentralized, the need for congestion management across grid voltage levels is also increasing. To enable fair sharing of congestion costs among grid operators, these costs must be allocated to congested grid elements. We propose using the Shapley value for this purpose. The Shapley value is a cooperative game theory concept that was developed to share a total surplus generated by a coalition of players between the players based on their marginal contributions to the coalition. We apply this concept to share the costs of congestion management between grid elements based on their contributions to overall congestion management costs. To reduce the computational complexity of the Shapley value, we introduce two novel simplification approaches and compare them to existing methods using a numerical example based on CIGRE benchmark grids. The first method exploits the fact that the characteristic function for the congestion costs is obtained from an optimal power flow computation (i.e., a constrained optimization problem). It utilizes knowledge about which constraints are non-binding in the optimization to derive the values of related coalitions without calculating them. The second method takes advantage of the fact that the congestion management cost-allocation game is monotone and derives the values of coalitions based on this property. Both methods are implemented and compared to sampling. Using the first method, we are able to reduce computational complexity to less than 20% of that of the original problem while maintaining exact results. Our second approach is not dependent on detailed knowledge of the underlying optimization problem and can reduce the computational time by almost half with exact results and much further when compromising precision. While the methods are presented through an application example, they can be applied to other games with similar properties.