The demand of energy is increasing due to the growing population of the world and improvements of technology. One of the best significant solution techniques to fulfill this energy demand is utilization of renewable energy sources (RESs). Modern power systems, which integrate RESs, such as wind, small hydro or solar energy sources need to carry out the uncertainty by the accessibility of demanded or injected power. Therefore, it is necessary to consider uncertainty costs in optimal power flow (OPF) problems. This paper proposed a novel hybrid meta-heuristic algorithm entitled cross entropy—cuckoo search algorithm (CE-CSA). The application of levy flights in the cuckoo search algorithm (CSA) improves the local exploitation capability while the CE method is used in the initial stage for global exploration due to its fast convergence. The effectiveness of the proposed hybrid algorithm has been demonstrated in solving the OPF problem, considering RESs and controllable loads for different stochastic scenarios in a benchmark system to minimize the total operation cost. To verify its effectiveness, its performance is compared with the most advanced and recently proposed hybrid meta-heuristic techniques. Simulation results show that the proposed algorithm can solve the OPF problems with RESs and controllable loads efficiently and can give better solutions compared to different techniques. The conventional statistical method called analysis of variance (ANOVA) test, Tukey honestly significant difference test, and Wilcoxon sign rank test are performed for comparative analysis of different techniques. The results of this test show the validation of CE-CSA compared to different optimization techniques.

中文翻译：

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混合交叉熵——用于解决可再生发电机和可控负载最优潮流的布谷鸟搜索算法

由于世界人口的增长和技术的进步，对能源的需求正在增加。满足这种能源需求的最重要的解决方案之一是利用可再生能源 (RES)。集成了 RES 的现代电力系统，例如风能、小水电或太阳能，需要通过需求或注入电力的可及性来应对不确定性。因此，有必要在最优潮流（OPF）问题中考虑不确定性成本。本文提出了一种新的混合元启发式算法，称为交叉熵——布谷鸟搜索算法（CE-CSA）。levy flights 在布谷鸟搜索算法 (CSA) 中的应用提高了局部开发能力，而 CE 方法由于其收敛速度快而在初始阶段用于全局探索。所提出的混合算法的有效性已在解决 OPF 问题中得到证明，考虑到基准系统中不同随机场景的 RES 和可控负载，以最小化总运营成本。为了验证其有效性，将其性能与最先进和最近提出的混合元启发式技术进行了比较。仿真结果表明，与其他技术相比，所提出的算法可以有效地解决RESs和可控负载的OPF问题，并且可以给出更好的解决方案。称为方差分析（ANOVA）测试的常规统计方法，为了验证其有效性，将其性能与最先进和最近提出的混合元启发式技术进行了比较。仿真结果表明，与其他技术相比，所提出的算法可以有效地解决RESs和可控负载的OPF问题，并且可以给出更好的解决方案。称为方差分析（ANOVA）测试的常规统计方法，为了验证其有效性，将其性能与最先进和最近提出的混合元启发式技术进行了比较。仿真结果表明，与其他技术相比，所提出的算法可以有效地解决RESs和可控负载的OPF问题，并且可以给出更好的解决方案。称为方差分析（ANOVA）测试的常规统计方法，T ukey honestly 显着性差异检验和 Wilcoxon 符号秩检验用于不同技术的比较分析。与不同的优化技术相比，该测试的结果显示了 CE-CSA 的有效性。