This paper presents an optimized load frequency control (LFC) approach for interconnected power systems with conventional and renewable energy sources. A proportional integral derivative (PID) controller, tuned using particle swarm optimization (PSO) and genetic algorithm (GA) techniques, manages frequency in a thermal two-area tie-line IPS and a one-area multi-source power network. The integral time absolute error (ITAE) serves as the fitness function for optimization. Key contributions include developing sustainable power network models with renewable energy fluctuations, applying PSO and GA for robust PID tuning, and comparing controller performance under varying conditions. The PSO-PID controller shows superior frequency stability, achieving deviations of 59.97 Hz, 59.72 Hz, and 59.99 Hz for single-area multi-source, area 1, and area 2 in the two-area IPS. It outperforms the GA-PID controller in reducing undershoot, overshoot, and settling time, offering a more reliable LFC solution for interconnected power systems.

Electrical power networks consist of numerous energy control zones connected by tie-lines, with the addition of nonconventional sources resulting in considerable variations in tie-line power and frequency. Under these circumstances, a load frequency control (LFC) loop gives constancy and security to interconnected power systems (IPSs) by supplying all consumers with high-quality power at a nominal frequency and tie-line power change. This article proposes employing a proportional–integral–derivative (PID) controller to effectively control the frequency in a one-area multi-source power network comprising thermal, solar, wind, and fuel cells and in a thermal two-area tie-line IPS. The particle swarm optimization (PSO) technique was utilized to tune the PID controller parameters, with the integral time absolute error being utilized as an objective function. The efficacy and stability of the PSO-PID controller methodology were further tested in various scenarios for proposed networks. The frequency fluctuations associated with the one-area multi-source power source and with the two-area tie-line IPS’s area 1 and area 2 frequency variations were 59.98 Hz, 59.81 Hz, and 60 Hz, respectively, and, in all other investigated scenarios, they were less than that of the traditional PID controller. The results clearly show that, in terms of frequency responses, the PSO-PID controller performs better than the conventional PID controller.

The integration of nonconventional energy sources such as solar, wind, and fuel cells into electrical power networks introduces significant challenges in maintaining frequency stability and consistent tie-line power flows. These fluctuations can adversely affect the quality and reliability of power supplied to consumers. This paper addresses this issue by proposing a Proportional–Integral–Derivative (PID) controller optimized through a hybrid Particle Swarm Optimization–Artificial Hummingbird Algorithm (PSO-AHA) approach. The PID controller is tuned using the Integral Time Absolute Error (ITAE) as a fitness function to enhance control performance. The PSO-AHA-PID controller’s effectiveness is evaluated in two networks: a two-area thermal tie-line interconnected power system (IPS) and a one-area multi-source power network incorporating thermal, solar, wind, and fuel cell sources. Comparative analyses under various operational conditions, including parameter variations and load changes, demonstrate the superior performance of the PSO-AHA-PID controller over the conventional PSO-PID controller. Statistical results indicate that in the one-area multi-source network, the PSO-AHA-PID controller achieves a 76.6% reduction in overshoot, an 88.9% reduction in undershoot, and a 97.5% reduction in settling time compared to the PSO-PID controller. In the dual-area system, the PSO-AHA-PID controller reduces the overshoot by 75.2%, reduces the undershoot by 85.7%, and improves the fall time by 71.6%. These improvements provide a robust and reliable solution for enhancing the stability of interconnected power systems in the presence of diverse and variable energy sources.

The main drive system of the rolling mill often experiences torsional vibrations, which severely affect product quality, precision, and the service life of the transmission equipment. This paper investigates the torsional vibration suppression problem in the main drive system of the rolling mill, considering actuator faults, nonlinear friction, nonlinear damping, and model uncertainties. Based on the high-order fully actuated (HOFA) system approach, the main drive system of the rolling mill is transformed into a rolling mill main drive fully actuated system (RMMDFAS). Adaptive neural networks are introduced to address unknown uncertainties, and a continuous differentiable Gaussian error function is used to handle actuator faults. An adaptive neural network fault-tolerant control law for motor torque is proposed. The stability of the designed main drive torsional vibration system is rigorously proven, while maintaining the performance of the transformed states. Finally, the effectiveness and superiority of the proposed algorithm are verified through simulations.