Integrated mathematical model for uniform purchase prices on multi-zonal power exchanges

•A new model is presented for unified purchase prices on European power exchanges.•The model applies explicit income-expense balance to execute the clearing.•This is the first working UPP model without special iterative heuristics.•The integrated approach facilitates the optimization and later developments. Electricity market integration is an important aspect of the planned Internal Energy Market in Europe. Day-ahead power exchanges (PXs) are going to be merged into a unified trading platform with a single clearing algorithm. This algorithm – called EUPHEMIA – practically handles an innovative hybrid of currently operating PXs: it includes elements that are new or have never been used together. As a result, difficulties arise during the mathematical formulation of several components. The officially described calculation of uniform purchase prices for demand bids across different price regions is one of the most complicated issues. It can be straightforwardly implemented only in non-convex mixed integer programs (MIPs) which are extremely hard to solve. This paper presents a new formulation to incorporate these prices into the usual and computationally efficient convex MIP model of European PXs. Benefits and limitations of the proposal are discussed and also demonstrated with numerical tests.