Computing leastcore allocations for firm-energy rights: a mixed integer programming procedure

Abstract

The Firm energy of generation plants is a critical component in some electricity markets. It is usually calculated by the regulator and sets a cap to the amount a plant can trade in capacity markets (or auctions), in order to avoid free-riding behaviors. Firm energy is a systemic property and, in case of hydro plants, a synergy is observed whenever a cooperative operation occurs, i.e., the firm energy of a system is greater than the sum of the individual plants. In this case an interesting problem is how to allocate the synergic benefits in a fair way. It is shown in this work that this criterion is equivalent to the calculation of the core of a cooperative game. The objective of this work is to investigate the application of different allocation methods of firm energy rights among hydro plants using a game-theoretic framework. However, calculating the core constraints for realistic systems is a large scale linear-programming problem. This work discusses alternatives to the calculating the core constraints, presenting a MIP model, discussing its limitations and future approaches. These methods are based on the constraints relaxation to handle the difficulty caused by its exponential growth with the number of constraints in the problem with the increase in the agent's number. Applications are illustrated with examples from the Brazilian system.The Firm energy of generation plants is a critical component in some electricity markets. It is usually calculated by the regulator and sets a cap to the amount a plant can trade in capacity markets (or auctions), in order to avoid free-riding behaviors. Firm energy is a systemic property and, in case of hydro plants, a synergy is observed whenever a cooperative operation occurs, i.e., the firm energy of a system is greater than the sum of the individual plants. In this case an interesting problem is how to allocate the synergic benefits in a fair way. It is shown in this work that this criterion is equivalent to the calculation of the core of a cooperative game. The objective of this work is to investigate the application of different allocation methods of firm energy rights among hydro plants using a game-theoretic framework. However, calculating the core constraints for realistic systems is a large scale linear-programming problem. This work discusses alternatives to the calculating the core constraints, presenting a MIP model, discussing its limitations and future approaches. These methods are based on the constraints relaxation to handle the difficulty caused by its exponential growth with the number of constraints in the problem with the increase in the agent's number. Applications are illustrated with examples from the Brazilian system.