Particle Swarm Optimization for Computing Nash and Stackelberg Equilibria in Energy Markets

Interactions among stakeholders in deregulated markets lead to complex interdependent optimization problems. The present study is motivated by load control programs in energy markets and more precisely by using the power supply interruption as a tool for reducing consumers’ demand voluntarily, also...

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Bibliographic Details
Published in:Operations Research Forum 2020-09, Vol.1 (3), p.20, Article 20
Main Authors: Vrahatis, Michael N., Kontogiorgos, Panagiotis, Papavassilopoulos, George P.
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Business and Management
Consumers
Decision making
Demand side management
Deregulation
Energy industry
Energy management
Equilibrium
Game theory
Games
Heuristic methods
Lagrange multiplier
Math Applications in Computer Science
Mathematical analysis
Mathematical and Computational Engineering
Mathematical programming
Operations Research/Decision Theory
Optimization
Original Research
Particle swarm optimization
Stakeholders
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Summary:Interactions among stakeholders in deregulated markets lead to complex interdependent optimization problems. The present study is motivated by load control programs in energy markets and more precisely by using the power supply interruption as a tool for reducing consumers’ demand voluntarily, also known as voluntary load curtailment programs. The problem is formulated as a Stackelberg game, specifically, as a bilevel optimization problem that belongs to the mathematical programs with equilibrium constraints. In this game, a player that acts as leader determines the actions of the players that act as followers and play a Nash game among them through a subsidy program. The corresponding equilibria need to be found and the presence of nonconvex functions makes the use of metaheuristic algorithms attractive. An extension of particle swarm optimization is proposed for solving such problems based on the unified particle swarm optimization that is a variation of the plain particle swarm optimization algorithm. The proposed algorithm is tested by solving some examples of the formulated games in order to study its efficiency and the interactions between the stakeholders of the market.
ISSN:2662-2556
2662-2556
DOI:10.1007/s43069-020-00021-4