Iterative algorithm for finding equilibrium prices in a spatial electricity market

We consider a restructured electricity market divided in zones, where sell bids and purchase bids are presented by generating companies and customers respectively. The Market Operator has to fix the zonal prices as well as to decide the energy quantity to be accepted for each bid, in order to maximize the social surplus, while taking into account transmission constraints among zones. The market equilibrium is the result of the interactions among power producers, consumers and the Market Operator: this process generates a list of accepted purchase and sell quantities, clearing zonal prices and power flows among zones. In the auction scheme introduced in [1] for the Italian market (see also [2]), if the price declared in a sell bid in zone k is higher than the price fixed by the Market Operator in that zone, then the offered energy is not accepted, while the whole offered volume is accepted if the bid price is lower than the zonal price. Purchase bids are treated analogously. If the bid price is exactly equal to the zonal price, then any energy volume between zero and the maximum offered quantity can be accepted by the Market Operator. In this paper we consider a modified auction scheme where all bids participate to the auction, with the exception of sell bids with price greater than the zonal price and purchase bids with price less than the zonal price: for all other bids, any energy volume between zero and the maximum offered quantity can be accepted by the Market Operator. With this modified auction, an algorithm is proposed, based on the Nelder and Mead simplex method, in order to find the global maximum of the social surplus function.