Green retailer : a stochastic bi-level approach to support investment decisions in sustainable energy systems

This paper presents a bi-level approach to support retailers in making investment decisions in renewable-based systems to provide clean electricity. The proposed model captures the strategic nature of the problem and combines capacity sizing decisions for installed technologies with pricing decisions regarding the electricity tariffs to offer to a reference end-user, representative of a class of residential prosumers. The interaction between retailer and end-user is modeled using the Stackelberg game framework, with the former acting as a leader and the latter as follower. The reaction of the follower to the electricity tariff affects the retailer's profit, which is calculated as the difference between the revenue generated from selling electricity and the total investment, operation and management costs. To account for uncertainty in wholesale electricity prices, renewable resource availability and electricity request, the upper-level problem is formulated as a two-stage stochastic programming model. First-stage decisions refer to the sizing of installed technologies and electricity tariffs, whereas second-stage decisions refer to the operation and management of the designed system. The model also incorporates a safety measure to control the average profit that can be achieved in a given percentage of worst-case situations, thus providing a contingency against unforeseen changes. At the lower level, the follower reacts to the offered tariffs by defining the procurement plan in terms of energy to purchase from the retailer or potential competitors, with the final aim of minimizing the expected value of the electricity bill. A tailored approach that exploits the specific problem structure is designed to solve the proposed formulation and extensively tested on a realistic case study. The numerical results demonstrate the efficiency of the proposed approach and validate the significance of explicitly dealing with the uncertainty and the importance of incorporating a safety measure.