Cross-entropy boosted CRO-SL for optimal power flow in smart grids

C. G. Marcelino, J. Pérez-Aracil, E. F. Wanner, S. Jiménez-Fernández*, G. M.C. Leite, S. Salcedo-Sanz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Optimal power flow (OPF) is a complex, highly nonlinear, NP-hard optimization problem, in which the goal is to determine the optimal operational parameters of a power-related system (in many cases a type of smart or micro grid) which guarantee an economic and effective power dispatch. In recent years, a number of approaches based on metaheuristics algorithms have been proposed to solve OPF problems. In this paper, we propose the use of the Cross-Entropy (CE) method as a first step depth search operator to assist population-based evolutionary methods in the framework of an OPF problem. Specifically, a new variant of the Coral Reefs Optimization with Substrate Layers algorithm boosted with CE method (CE+CRO-SL) is presented in this work. We have adopted the IEEE 57-Bus System as a test scenario which, by default, has seven thermal generators for power production for the grid. We have modified this system by replacing three thermal generators with renewable source generators, in order to consider a smart grid approach with renewable energy production. The performance of CE+CRO-SL in this particular case study scenario has been compared with that of well-known techniques such as population’s methods CMA-ES and EPSO (both boosted with CE). The results obtained indicate that CE+CRO-SL showed a superior performance than the alternative techniques in terms of efficiency and accuracy. This is justified by its greater exploration capacity, since it has internally operations coming from different heuristics, thus surpassing the performance of classic methods. Moreover, in a projection analysis, the CE+CRO-SL provides a profit of millions of dollars per month in all cases tested considering the modified version of the IEEE 57-Bus smart grid system.

Original languageEnglish
Pages (from-to)6549-6572
JournalSoft computing
Issue number10
Early online date3 Mar 2023
Publication statusPublished - May 2023

Bibliographical note

Copyright © The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit

Funding Information: Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 754382. This research has been partially supported by the Spanish Ministry of Science and Innovation (MICINN), through Project Number PID2020-115454GB-C21, and by Comunidad de Madrid, PROMINT-CM project (grant No. P2018/EMT-4366).


  • Coral Reefs Optimization
  • Cross-Entropy
  • Energy efficiency
  • Energy production
  • Metaheuristics
  • Smart Grids


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