This paper proposes a novel, reliable, and effective hybrid approach based on the integration of the firefly algorithm (FA) and the adaptive particularly tunable fuzzy particle swarm optimization (APT-FPSO) method to address reactive power dispatch (RPD) problem, a crucial optimization problem in the operation of power systems. Similar to many other original meta-heuristic optimization techniques, the standard FA suffers from some severe drawbacks, most importantly being easily trapped into a locally optimal solution. In order to tackle these difficulties, in the current study, an improved version of fuzzy-based particle swarm optimization is utilized in the internal structure of the original FA. The developed hybrid approach, which is capable of avoiding premature convergence of the original FA by enhancing exploration and exploitation procedures, is employed to determine the optimum control variables (i.e., the voltage of generation buses, tap positions of tap-changer transformers, and reactive power output of shunt compensators) through optimizing three distinct objective functions consisting of total transmission real power loss, the voltage magnitude deviations as well as voltage stability index. To validate the accuracy and competency of the proposed hybrid approach, it is firstly used for solving several benchmark optimization functions and then applied to three test systems at different scales, consisting of IEEE 30-bus, IEEE 57-bus, and IEEE 118-bus power systems, for solving the RPD problem. Eventually, the results of the presented hybrid method will be compared to those obtained by other implemented swarm intelligence-based approaches. The statistical analysis of this research substantiates the robustness and effectiveness of the developed algorithm to handle sophisticated optimization problems, particularly the RPD problem.

本文提出了一种新颖，可靠，有效的混合方法，该方法基于萤火虫算法（FA）和自适应特别可调的模糊粒子群优化（APT-FPSO）方法的集成，以解决无功功率分配（RPD）问题，这一关键问题电力系统运行中的优化问题。类似于许多其他原始的元启发式优化技术，标准FA遭受一些严重的缺点，最重要的是很容易陷入局部最优解决方案中。为了解决这些困难，在当前研究中，在原始FA的内部结构中使用了基于模糊粒子群优化的改进版本。所开发的混合方法能够通过增强勘探和开发程序来避免原始FA的过早收敛，通过优化三个不同的目标函数来确定最优控制变量（例如，发电母线的电压，分接开关变压器的分接位置和并联补偿器的无功功率输出），该目标函数包括总传输有功损耗，电压幅值偏差以及电压稳定性指标。为了验证所提出的混合方法的准确性和竞争力，首先将其用于解决几种基准优化功能，然后将其应用于三个不同规模的测试系统，包括IEEE 30总线，IEEE 57总线和IEEE 118总线。电力系统，用于解决RPD问题。最终，将所提出的混合方法的结果与通过其他已实施的基于群体智能的方法所获得的结果进行比较。