A stochastic programming optimization framework to design an energy system and face market stages

The design-operation optimization problem for an electricity retailer involves decisions about i) sizes of the energy conversion units and ii) operation in the Day-Ahead market (DA) and Balancing Market (BM), under uncertain renewables. A three-stage Stochastic Programming (SP) model is required to entirely formulate the design-operation optimization problem and maximize the retailer’s profit. The first and second stage decisions, taken before the realization of stochastic scenarios, refer to investments and to the energy purchased in the DA market, respectively. The third stage decision, affected by stochastic scenarios, refers to the energy exchanged in the BM. This work conducts numerical experiments on the second and third stages, evaluated in typical winter and summer days, to preliminary attain an optimal operation solution. A novel method is proposed that generates stochastic scenarios of solar irradiance by k-means clustering and defines their conditional probabilities to account for the relationships between consecutive days of the DA and BM stages in the numerical experiments. The goal is to achieve, by the SP optimization model, reliable outcomes that are comparable to those obtained by a utopic approach with a perfect knowledge of future scenarios. The SP optimization provides a solution that is maximum 1% far from the utopic approach. On the other hand, the solution assessed on a large set of historical scenarios differs approximately only 1 to 9% from that evaluated by the restricted set of representative scenarios. Defining the scenario probability as cluster frequency, as usually done in the literature, would lead to worse results.