Designing electricity tariffs in the retail market: A stochastic bi-level approach

This paper presents a stochastic bi-level approach for tariff design in the electricity market where the leader is represented by a retailer and the follower by a residential prosumager, i.e. a consumer equipped with an energy system consisting of photovoltaic panels and a battery storage device. Both players solve an optimization problem subject to uncertainty in market prices, weather-related variables and electricity demand. To account for the retailer’s attitude towards risk, the upper level problem includes a safety measure to maximize. The model allows to determine a dynamic pricing scheme with time-variant rates delivering the average profit that can be gained in a given percentage of unfavorable realizations of the uncertain parameters and the optimal load pattern that minimizes the expected prosumager's electricity bill. The stochastic bi-level problem is reformulated as a single level model and different approaches to deal with the lower level problem and the non linearity in the objective function are analyzed and empirically investigated. A large number of numerical experiments have been carried out on real test cases. The results have shown the efficacy of the proposed approach as a tool to define pricing schemes that reflect the retailer's risk attitude underlining the importance of explicitly dealing with uncertainty.