A Reliable Model Based on Lagrangian Constrained Optimization to Calculate the Cost of Breaching the Bilateral Contracts in an Electricity Market System

In the current model of the electricity market, buyers and sellers of the market conclude bilateral contracts. Then prior to consumption day, with respect to the capability of the market, the exact and final amount of energy required for each consumer is determined. Any energy consumption in excess of the amount specified by the contract is supplied by the energy available to the market manager, and the amount is determined by the market manager. Also, overproduction of producers is purchased at a fixed price determined by the market manager. Obviously, this can be unfair to buyers, sellers, or even both groups. In this paper, a new mechanism based on the Lagrange multipliers method is proposed to determine the share of the difference between the actual consumption amount and what is stated in the contract. This mechanism introduces a criterion by which the excess consumption amount of each buyer will be associated by the extra production of sellers proportional to what is accepted on their mutual contracts (minimizing the sum of squared errors). Therefore, the price to be paid will be determined according to the sum of amounts mentioned in the contracts, which seems to be fairer.