The objective of this study is to develop an algorithm named Modified Artificial Bee Colony and Particle Swarm Optimization (MHABC-PSO) to address load frequency control (LFC) challenges in a two-area interconnected power system. The proposed MHABC-PSO algorithm is designed with two key modifications to enhance global exploration capability and improve convergence speed. Hence, a decision block is introduced in the employed bee (EB) phase incorporating a control parameter “limit” to allow each candidate solution (CS) to explore itself up to the “limit” value and boost local exploration. In addition, an introduction of a novel selection mechanism utilizing heuristic information () in EBs phase guides the onlooker bee (OB) phase to select better solutions based on success and failure history, thus promoting exploitation and reducing biased exploration. To address the efficacy of the proposed algorithm at the system level, three different two-area power systems are studied, incorporating various complexities, linearity, and non-linearity such as thermal-hydro, reheat thermal, and thermal-hydro-gas turbine configurations with HVDC link, SSSC, and CES. The algorithm is applied to optimize four objective functions (i.e. ITAE, IAE, ISAE, and ITE). The fitness function maximizes controller gains by utilizing the integral time multiplied absolute error (ITAE). Other objective functions like IAE, ISAE, and ITE are employed for a comprehensive analysis. Evaluation of MHABC-PSO effectiveness is conducted through ITAE values, peak deviations, and settling times of frequency and power deviations in different two-area systems. Results demonstrate that MHABC-PSO settles the system more quickly with zero steady-state error under step load perturbations (SLPs) of 1% and 2%. Comparative analysis with ABC, PSO, SFLA-TLBO, and OHABC-PSO using ITAE index and controller settling times shows the superiority of MHABC-PSO for LFC analysis. In conclusion, the proposed MHABC-PSO algorithm proves to be an efficient and effective solution for LFC, outperforming other algorithms in terms of the specified objective functions and exhibiting rapid convergence and optimal gains for controllers, effectively addressing LFC issues by combining exploration and exploitation techniques.

中文翻译：

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一种改进互联电力系统负载频率控制的混合优化算法

本研究的目的是开发一种名为改进人工蜂群和粒子群优化 (MHABC-PSO) 的算法，以解决两区域互连电力系统中的负载频率控制 (LFC) 挑战。所提出的 MHABC-PSO 算法在设计上进行了两个关键修改，以增强全局探索能力并提高收敛速度。因此，在雇佣蜂（EB）阶段引入了一个决策块，并结合了控制参数“限制”，以允许每个候选解决方案（CS）自我探索至“限制”值并促进局部探索。此外，在 EB 阶段引入了一种利用启发式信息 () 的新颖选择机制，引导旁观者蜂 (OB) 阶段根据成功和失败历史选择更好的解决方案，从而促进开发并减少有偏见的探索。为了解决所提出的算法在系统层面的有效性，研究了三种不同的两区域电力系统，结合了各种复杂性、线性和非线性，例如热力-水力、再热热力和热力-水力-燃气轮机配置具有 HVDC 链路、SSSC 和 CES。该算法用于优化四个目标函数（即ITAE、IAE、ISAE 和ITE）。适应度函数利用积分时间乘绝对误差 (ITAE) 来最大化控制器增益。其他目标函数如 IAE、ISAE 和 ITE 也用于综合分析。通过 ITAE 值、峰值偏差以及不同两区域系统中频率和功率偏差的稳定时间来评估 MHABC-PSO 的有效性。结果表明，在 1% 和 2% 的阶跃载荷扰动 (SLP) 下，MHABC-PSO 可以更快地稳定系统，且稳态误差为零。使用 ITAE 指数和控制器稳定时间与 ABC、PSO、SFLA-TLBO 和 OHABC-PSO 进行比较分析，表明 MHABC-PSO 在 LFC 分析中的优越性。总之，所提出的 MHABC-PSO 算法被证明是一种高效且有效的 LFC 解决方案，在指定的目标函数方面优于其他算法，并表现出快速收敛和控制器的最优增益，通过结合探索和开发技术有效解决了 LFC 问题。