On Optimistic and Pessimistic Bilevel Optimization Models for Demand Response Management

Abstract

This paper investigates bilevel optimization models for demand response management, and highlights the often overlooked consequences of a common modeling assumption in the field. That is, the overwhelming majority of existing research deals with the so-called optimistic variant of the problem where, in case of multiple optimal consumption schedules for a consumer (follower), the consumer chooses an optimal schedule that is the most favorable for the electricity retailer (leader). However, this assumption is usually illegitimate in practice; as a result, consumers may easily deviate from their expected behavior during realization, and the retailer suffers significant losses. One way out is to solve the pessimistic variant instead, where the retailer prepares for the least favorable optimal responses from the consumers. The main contribution of the paper is an exact procedure for solving the pessimistic variant of the problem. First, key properties of optimal solutions are formally proven and efficiently solvable special cases are identified. Then, a detailed investigation of the optimistic and pessimistic variants of the problem is presented. It is demonstrated that the set of optimal consumption schedules typically contains various responses that are equal for the follower, but bring radically different profits for the leader. The main procedure for solving the pessimistic variant reduces the problem to solving the optimistic variant with slightly perturbed problem data. A numerical case study shows that the optimistic solution may perform poorly in practice, while the pessimistic solution gives very close to the highest profit that can be achieved theoretically. To the best of the authors’ knowledge, this paper is the first to propose an exact solution approach for the pessimistic variant of the problem.

Stability and existence of solutions for weak bilevel optimization problems

“…As it is well known, weak nonlinear bilevel optimization problems present difficulties in their theoretical and numerical studies; see, e.g., [14,16,23,26]. Next, we give a survey on these two aspects of studies.…”

“…A numerical example was given for illustration. In [16], the authors considered the weak formulation of a bilevel electricity tariff optimization problem for demand response management. For such a problem, they provided an algorithm with numerical examples.…”

Decentralized Management of Commercial HVAC Systems

“…Then, the operator sends a feedback signal that might include other operational constraints for scheduling. An economic framework that solves a bi-level optimization problem was developed in [27]. The framework made sure that the followers/households and the retailers would benefit simultaneously, without unexpected deviations from the household side.…”

Flexibility Control in Autonomous Demand Response by Optimal Power Tracking

“…We did not use bilevel-optimized prices for the comparison of RTP to OPT because the optimistic assumption of bilevel optimization has recently been shown to be questionable [17]. Furthermore, even bilevel-optimized prices are not able to induce inner points of the consumer's flexibility region.…”