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.