Peak demand contract for big consumers computed based on the combination of a statistical model and a mixed integer linear programming stochastic optimization model

•Peak demand simulation with a statistical model.•Optimization model to compute peak demand contract under uncertainty.•The method considers the Expected Value and the Conditional-Value-at-Risk.•Analysis performed for a real commercial consumer. One of the main objectives of Demand Response Programs is to mitigate the effect of peak electricity demand by inducing consumers to shift or reduce their electricity consumption in peak times. In Brazil, big energy consumers should contract peak demand for the upcoming months with the utility distribution companies under a set of rules defined by the System Regulator. Based on this, the utility will have more information to reinforce the system accordingly. The challenge for consumers is to compute the best value of the peak demand contracted before the peak demand realization. One way to solve this problem is to simulate future scenarios of peak demand and optimize the value of the peak demand contracted in compliance with the current rules. In this paper, a support decision system is proposed to help consumers in this task. The proposal is divided into two parts, which are a statistical model, for estimating and simulating future scenarios of peak demand, and a stochastic optimization model, to compute the value of the peak demand contracted. In the first part, a Box & Jenkins model is used to estimate the parameters of the statistical model and to simulate it based on the historical electricity bill data. In the second part, a stochastic optimization model is applied using a convex combination of the Expected Value and Conditional Value-at-Risk, as the risk metrics for the cost uncertainty, in order to obtain the monthly values of peak demand contracted. The results achieved corroborate the importance of using an appropriate mathematical model to address the problem. To illustrate the proposed approach, a real case study for a big consumer in Brazil is presented.