Optimal load frequency control and automatic voltage regulation in four-area interconnected power systems using FOPD-FOPIDD2 controller design with energy valley optimizer

Abstract Existing interconnected power systems (IPSs) are facing increasing challenges due to the expansion of industrial and residential sectors, alongside the integration of renewable energy sources, which result in significant fluctuations in frequency, voltage, and tie-line power threatening system stability and power quality. Automatic Voltage Regulation (AVR) and Load Frequency Control (LFC) loops aim to ensure stable and secure IPS operation by minimizing deviations in frequency, voltage, and tie-line power, thereby delivering high-quality power to consumers. Conventional controllers such as Proportional-Integral-Derivative (PID) and Fractional-Order Proportional-Integral-Derivative (FOPID) often fail to ensure robust dynamic performance under such varying conditions. To address these limitations, this study investigates the application of a cascaded set of Fractional-Order Proportional Derivative (FOPD) controller and Fractional-Order Proportional Integral Double Derivative (FOPIDD 2 ) controller optimized using the Energy Valley Optimizer (EVO) algorithm for effective control of a four-area IPS. Each area comprises five generating units: gas, thermal reheat, hydro, and two renewable sources—wind and solar photovoltaic plants. The FOPD-FOPIDD 2 controller parameters are tuned using the Energy Valley Optimizer (EVO) algorithm, with the Integral of Time multiplied by Squared Error (ITSE) serving as the fitness criterion. The performance of the EVO-FOPD-FOPIDD 2 controller in terms of voltage, frequency, and tie-line power responses is evaluated and compared with other control strategies, including Fractional-order Proportional Integral Derivative (FOPID), and Proportional Integral Derivative (PID) controllers, under a 5% step load perturbation (SLP) in each area. Comprehensive comparisons demonstrate that the proposed EVO-FOPD-FOPIDD 2 controller exhibits superior performance in stabilizing voltage, frequency, and tie-line power across all areas. Furthermore, the reliability and efficacy of the EVO-FOPD-FOPIDD 2 approach are validated through sensitivity analyses involving variations in turbine time constant and speed regulation within ± 25%. The results underscore the robustness of the EVO-FOPD-FOPIDD 2 control methodology in swiftly stabilizing deviations in terminal voltage, load frequency, and tie-line power, thereby enhancing the stability of a four-area IPS.