Cross Entropy Covariance Matrix Adaptation Evolution Strategy for Solving the Bi-Level Bidding Optimization Problem in Local Energy Markets

Abstract

The increased penetration of renewables in power distribution networks has motivated significant interest in local energy systems. One of the main goals of local energy markets is to promote the participation of small consumers in energy transactions. Such transactions in local energy markets can be modeled as a bi-level optimization problem in which players (e.g., consumers, prosumers, or producers) at the upper level try to maximize their profits, whereas a market mechanism at the lower level maximizes the energy transacted. However, the strategic bidding in local energy markets is a complex NP-hard problem, due to its inherently nonlinear and discontinued characteristics. Thus, this article proposes the application of a hybridized Cross Entropy Covariance Matrix Adaptation Evolution Strategy (CE-CMAES) to tackle such a complex bi-level problem. The proposed CE-CMAES uses cross entropy for global exploration of search space and covariance matrix adaptation evolution strategy for local exploitation. The CE-CMAES prevents premature convergence while efficiently exploring the search space, thanks to its adaptive step-size mechanism. The performance of the algorithm is tested through simulation in a practical distribution system with renewable energy penetration. The comparative analysis shows that CE-CMAES achieves superior results concerning overall cost, mean fitness, and Ranking Index (i.e., a metric used in the competition for evaluation) compared with state-of-the-art algorithms. Wilcoxon Signed-Rank Statistical test is also applied, demonstrating that CE-CMAES results are statistically different and superior from the other tested algorithms.

Metaheuristic Optimization Algorithms Comparison Adopted for the Profit Maximization of Electricity Market Participants

“…LEMs address this issue by providing a platform for prosumers, consumers, and producers to actively engage in energy trading [5]. The energy dealings in LEMs can be termed as a bi-level optimization problem, with all participants want to maximize their profits by refining their bidding strategies [6].…”

“…The optimization challenge within local electricity markets presents a multifaceted problem that can be approached and resolved through various perspectives and methodologies. One common formulation involves framing the participation of stakeholders in LEMs as a bi-level optimization problem [6]. Despite diverse assumptions, adaptations, and hybrid algorithmic approaches, attaining optimal or near-optimal solutions remains a significant hurdle within this domain.…”

“…The problem is conceptualized as a multi-period bi-level optimization challenge, wherein competitive agents at the upper-level aim to maximize their profits (referred to as a multileader problem) [10]. The bids or offers made by these agents influence the market clearing price determined at the lower-level problem (a single-follower problem), establishing a significant interdependence among their decisions [6].…”