A deterministic bounding algorithm vs. a hybrid meta-heuristic to deal with a bilevel mixed-integer nonlinear optimization model for electricity dynamic pricing. (July 2023)

• Record Type: Journal Article
• Authors: Soares, Inês; Alves, Maria João; Antunes, Carlos Henggeler
• Is Part Of: Computers & operations research. Volume 155(2023)
• Publication Date: 2023-07
• Subjects: Bi-level mixed-integer nonlinear programming -- Hybrid meta-heuristic -- Optimal-value-function approach -- Electricity retail market -- Dynamic tariffs -- Demand response; Operations research -- Periodicals; Electronic digital computers -- Periodicals; 004.05
• DOI: 10.1016/j.cor.2023.106195
• Languages: English
• ISSNs: 0305-0548

Abstract

Highlights: Bilevel mixed-integer nonlinear optimization model for electricity dynamic pricing. Comparison of a deterministic bounding algorithm (DBA) with a hybrid meta-heuristic. Different techniques to linearize subproblems in the DBA. Case study to design optimal time-of-use electricity tariffs. Integrated optimization of multiple energy resources at the consumer level. Abstract: In the electricity retail market, the retailer company aims to determine the optimal time-of-use (ToU) prices to maximize profits resulting from buying energy in organized (long-term, day-ahead, balancing) markets and selling it to consumers. Therefore, the retailer should take into account the consumer's demand response actions to minimize the electricity bill in face of time varying prices. In this paper, this problem is formulated as a bilevel mixed-integer nonlinear programming model in which the retailer is the leader and the consumer is the follower. The consumer's problem encompasses the integrated optimization of all home energy resources, considering re-scheduling appliance operation, charging/discharging of electric vehicle and stationary batteries, local microgeneration and (buying and selling) exchanges with the grid. The accurate physical modelling of appliance operation to generate effective load scheduling solutions imposes a high computational burden. Two algorithms are proposed to address this problem: a deterministic bounding algorithm (DBA) using an optimal-value-function approach for bilevel optimization, and a hybrid meta-heuristic using a particle swarm optimization algorithm to tackle the upper-level problem that calls an exact mixed-integer linear programming solver to deal with the lower-level problem. In the framework of the DBA, three different techniques were implemented to deal with the nonlinearities arising from the products of integer and continuous variables (bilinear terms): 1) solving the (non-convex) subproblems of DBA using a mixed-integer nonlinear solver, 2) using the McCormick envelopes to approximate the bilinear terms by linear ones, and 3) expressing the integer variables by binary ones and linearizing the bilinear terms using an exact form. Computational experiments are presented and discussed for real data settings of the problem under study considering a computational budget to compare the different algorithms and techniques employed. The results showed that the DBA with the approximate linearization technique (2) leads to the best solutions.