Load Frequency Control of multi-area multi-source system with nonlinear structures using modified Grasshopper Optimization Algorithm

Nowadays, power systems are in direct contact with sources such as renewable energy sources, Electric Vehicles (EVs), distributed generation resources, etc. In other words, these sources impose additional imbalances on the system and disturb the balance between generation and consumption. Hence, this study aims to model multi-area multi-source systems with the presence of units such as thermal, hydro, diesel, and gas units, wind farms, EVs, and energy storage sources. Without a properly coordinated controller, they can expose the system to severe stress under unwanted disturbances and cause it to deviate from normal operating conditions. Therefore, after modeling the proposed system, a Proportional–Integral–Derivative (PID) controller based on a low-pass filter is presented as a widely used device in the industry. Since tuning coefficients of this controller based on trial and error were irrational, this issue turned to a frequency-based optimization problem with different operating points in unwanted operating conditions in order to have a robust design. In the previous articles, a fixed working point employed to design the controller. To cover this issue, modeling towards reality, and a wider range of unexpected conditions and events, ± 30% design uncertainty and different loading conditions are considered in this study. Then, the developed Grasshopper Optimization Algorithm (GOA) with decreasing coefficients is applied to solve it. The time-varying coefficients can properly improve the local and global search capabilities. Different scenarios based on unwanted disturbances, uncertainties, and random load changes are considered to evaluate the system and algorithm performance. Numerical results obtained by analyzing comparative criteria on time and frequency domains indicated the proposed method had over 25% better performance compared to other methods, on average. The results obtained from the frequency and time domains properly show that the settlement and overshoot and undershoot times of the system equipped with the proposed controller are less compared to other designs in the literature, and better stability has been provided in the s-plane. Also, Nyquist and Bode analyses have shown that the system can ensure optimal performance in a wide range of working points.