The Sine–Cosine algorithm (SCA) is efficient but faces challenges in exploitative abilities, slow convergence, and exploration–exploitation balance. This study proposes a novel optimization method, the learning-based sine–cosine algorithm (L-SCA), to solve the optimal power flow (OPF) problem. The basic SCA has been modified with a learning phase operator inspired by TLBO. The SCA handles global exploration, while the learner phase of teaching–learning based optimization (TLBO) offers strong local search capabilities, which can be utilized to enhance the solution neighborhood space provided by the SCA technique. The L-SCA and original SCA algorithms address OPF in IEEE 57-bus, Algerian 59-bus, and IEEE 118-bus power systems, considering twelve cases with a focus on cost savings, voltage stability, voltage profile, emissions, and power losses. The comparative study shows that the proposed L-SCA consistently outperforms standard SCA and other reported methods in all cases for varied-scale standard test systems as well as for a practical power system, within reasonable execution times. For instance, L-SCA in the Algerian 59-bus system cut fuel costs by around 13.13% compared to initial case, equating to annual savings of $2.2 million, while in the IEEE-118 bus system, power loss is significantly reduced to 17.881 MW, marking an 86.5% reduction compared to the base case.

正弦余弦算法（SCA）虽然高效，但面临开发能力、收敛速度慢以及探索-开发平衡方面的挑战。本研究提出了一种新颖的优化方法，即基于学习的正弦余弦算法（L-SCA）来解决最优潮流（OPF）问题。受 TLBO 启发，使用学习阶段运算符对基本 SCA 进行了修改。 SCA 处理全局探索，而基于教学的优化 (TLBO) 的学习者阶段提供强大的局部搜索功能，可用于增强 SCA 技术提供的解决方案邻域空间。 L-SCA 和原始 SCA 算法解决了 IEEE 57 总线、阿尔及利亚 59 总线和 IEEE 118 总线电力系统中的 OPF 问题，考虑了 12 种情况，重点关注成本节约、电压稳定性、电压分布、排放和功率损耗。比较研究表明，对于各种规模的标准测试系统以及实际电力系统，在合理的执行时间内，所提出的 L-SCA 始终优于标准 SCA 和其他报告的方法。例如，阿尔及利亚 59 路总线系统中的 L-SCA 与初始情况相比，燃料成本降低了约 13.13%，相当于每年节省 220 万美元，而在 IEEE-118 总线系统中，功率损耗显着降低至 17.881 MW ，与基本情况相比减少了 86.5%。