Mohamed Mohamed Ahmed Ebrahim, Jagatheesan K, Anand B
Electrical Engineering Department, Faculty of Engineering at Shoubra, Benha University, Cairo, Egypt.
Department of Electrical and Electronics Engineering, Paavai Engineering College, Namakkal, Tamilnadu, India.
Sci Rep. 2023 Aug 28;13(1):14084. doi: 10.1038/s41598-023-41024-5.
This article presents frequency regulation of an interconnected three-area power system (Thermal + Wind + Hydro). Fractional Order PID (FOPID) and Proportional-Integral-Derivative (PID) controllers are applied as subsidiary regulators to control the electrical power interconnected system at the time of sudden load variation. To accomplish this study, Genetic Algorithm (GA), Grey Wolf Optimizer (GWO), Sine Cosine Inspired Algorithm (SCIA) and Atom Search Inspired Algorithm (ASIA) are implemented to optimize the secondary regulators' gains (PID and FOPID) by considering various cost functions such as Integral Absolute Error (IAE), Integral Time Absolute Error (ITAE), Integral Square Error (ISE), and Integral Time Square Error (ITSE). Performance analysis in this work is conducted using various cost functions based on GA, GWO, SCIA and ASIA. The comparative analysis of the attained results reveals that GWO-PID and ASIA-PID settle at (83.83 s) and (30.31 s), respectively and ASIA-FOPID at (25.12 s). The controllers based on ITSE as a cost function outperform the comptrollers with other cost functions (ISE, IAE and ITAE). In addition, the ISE-based GA-PID and SCIA-PID settle at (113.92 s) and (35.1 s), respectively and SCIA-FOPID at (24.78 s). The ISE-based regulators yield improved response equated to other cost functions (ITSE, IAE and ITAE) optimized controllers. The robustness test also is carried out to validate the effectiveness of the proposed optimization techniques by changing the system parameters within ± 25% and ± 50% from their nominal values as well as changing the load pattern.
本文介绍了一个互联三区域电力系统（火电+风电+水电）的频率调节。分数阶比例积分微分（FOPID）控制器和比例积分微分（PID）控制器被用作辅助调节器，以在突然负载变化时控制电力互联系统。为完成这项研究，实施了遗传算法（GA）、灰狼优化算法（GWO）、正弦余弦启发算法（SCIA）和原子搜索启发算法（ASIA），通过考虑各种成本函数，如积分绝对误差（IAE）、积分时间绝对误差（ITAE）、积分平方误差（ISE）和积分时间平方误差（ITSE），来优化二次调节器的增益（PID和FOPID）。这项工作中的性能分析是使用基于GA、GWO、SCIA和ASIA的各种成本函数进行的。对所得结果的比较分析表明，GWO-PID和ASIA-PID分别在（83.83秒）和（30.31秒）达到稳定，ASIA-FOPID在（25.12秒）达到稳定。以ITSE为成本函数的控制器优于具有其他成本函数（ISE、IAE和ITAE）的控制器。此外，基于ISE的GA-PID和SCIA-PID分别在（113.92秒）和（35.1秒）达到稳定，SCIA-FOPID在（24.78秒）达到稳定。与其他成本函数（ITSE、IAE和ITAE）优化的控制器相比，基于ISE的调节器产生了更好的响应。还进行了鲁棒性测试，通过将系统参数在其标称值的±25%和±50%范围内变化以及改变负载模式来验证所提出优化技术的有效性。
