Designing time-of-use tariffs in electricity retail markets using a bi-level model – Estimating bounds when the lower level problem cannot be exactly solved

Abstract

Time-of-use tariffs are a pricing strategy for a product or service in which the supplier establishes time-differentiated prices. Dynamic (e.g., day-ahead) time-differentiated electricity prices can contribute to increase the retailer's profit, allow end-users to reduce the consumption costs and enhance grid efficiency.The electricity retailer and the consumer are hierarchically related. The interaction between them can be modeled by a bi-level (BL) optimization model – the retailer is the upper level decision maker and the consumer is the lower level decision maker. The retailer and the consumer have different and conflicting goals: the retailer establishes the pricing scheme to sell electricity to consumers to maximize his profit; the consumer reacts to these prices by determining the operation of the controllable loads in order to minimize the discomfort and the electricity bill.In this work, a BL optimization model incorporating shiftable, interruptible and thermostatic loads is proposed. The upper level problem is tackled by a particle swarm optimization algorithm while the lower level problem is solved by an exact mixed-integer programming solver. The inclusion of the thermostatic load in the lower level problem imposes a much higher computational burden. Therefore, it may not be possible to find the optimal lower level solution, and a sub-optimal lower level solution is infeasible to the BL problem. Considering a computational budget, this work proposes an approach to compute good quality estimates of bounds for the upper level objective function, providing the leader further information and allowing him to make sounder decisions in an adequate time frame.