The stability control of nominal frequency and terminal voltage in an interconnected power system (IPS) is always a challenging task for researchers. The load variation or any disturbance affects the active and reactive power demands, which badly influence the normal working of IPS. In order to maintain frequency and terminal voltage at rated values, controllers are installed at generating stations to keep these parameters within the prescribed limits by varying the active and reactive power demands. This is accomplished by load frequency control (LFC) and automatic voltage regulator (AVR) loops, which are coupled to each other. Due to the complexity of the combined AVR-LFC model, the simultaneous control of frequency and terminal voltage in an IPS requires an intelligent control strategy. The performance of IPS solely depends upon the working of the controllers. This work presents the exploration of control methodology based on a proportional integral–proportional derivative (PI-PD) controller with combined LFC-AVR in a multi-area IPS. The PI-PD controller was tuned with recently developed nature-inspired computation algorithms including the Archimedes optimization algorithm (AOA), learner performance-based behavior optimization (LPBO), and modified particle swarm optimization (MPSO). In the earlier part of this work, the proposed methodology was applied to a two-area IPS, and the output responses of LPBO-PI-PD, AOA-PI-PD, and MPSO-PI-PD control schemes were compared with an existing nonlinear threshold-accepting algorithm-based PID (NLTA-PID) controller. After achieving satisfactory results in the two-area IPS, the proposed scheme was examined in a three-area IPS with combined AVR and LFC. Finally, the reliability and efficacy of the proposed methodology was investigated on a three-area IPS with LFC-AVR with variations in the system parameters over a range of  ± 50%. The simulation results and a comprehensive comparison between the controllers clearly demonstrates that the proposed control schemes including LPBO-PI-PD, AOA-PI-PD, and MPSO-PI-PD are very reliable, and they can effectively stabilize the frequency and terminal voltage in a multi-area IPS with combined LFC and AVR.

The increasing expansion of the industrial and domestic sectors, combined with the integration of renewable energy sources, has led to an overload of the existing interconnected power systems, which in turn has led to significant bottlenecks. This confluence of factors manifests itself in severe frequency, voltage and tie-line power issues, highlighting the urgent need for intelligent control mechanisms. Automatic voltage regulation (AVR) and load frequency control (LFC) are key components that ensure the supply of high-quality energy to consumers while maintaining the nominal frequency, voltage and power deviations in the grid. These measures are essential to ensure the stability and safety of the IPS under these challenging conditions. This research addresses the control strategies for a four-area sophisticated IPS. The complexity of the system, which includes five generation units in each area, including gas, thermal reheating, hydropower and two renewable energy sources (wind and photovoltaic), requires a careful study of the control methods. In particular, the inclusion of various non-linear factors, such as the governor dead band (GDB), generation rate constraint (GRC) and boiler dynamics (BD) in each of the four areas, increases the realism of the study. In this context, a recently introduced meta-heuristic algorithm, the One-to-One-based Optimizer (OOBO), was used to determine the optimal parameters of the proportional-integral-proportional-derivative (PI-PD) controller. The tuning process involves using the integral of time multiplied by the squared error value (ITSE) as the error criterion for evaluating the fitness function. In the study, the voltage, frequency and power performance of the OOBO PI-PD controller is evaluated and compared with alternative control methods, namely Proportional-Integral-Derivative (PID), Integral-Proportional (I-P) and Integral-Proportional-Derivative (I-PD) controllers, all of which are tuned with OOBO. Under the influence of a 5% load step load perturbation (SLP), comprehensive comparisons show the superior performance of the OOBO PI-PD controller, which shows better responses in all areas. Furthermore, the reliability and effectiveness of the OOBO PI-PD method are validated by a sensitivity analysis that considers simultaneous variations of the turbine time constant and speed control within a range of ±25%. The results highlight the robustness of the OOBO-PI-PD control strategy and demonstrate its ability to effectively stabilize variations in terminal voltage, load frequency and tie-line power with a significantly shorter settling time within the complicated dynamics of a four-area IPS with nonlinearities.

The ball and balancer system is a popular research platform for studying underactuated mechanical systems and developing control algorithms. It is a well-known two-dimensional balancing problem that has been addressed by a variety of controllers. This research work proposes two controllers that are proportional integral derivative-second derivative-proportional integrator (${\mathrm{PIDD}}^2$-PI) controller and tilt integral derivative with filter (TID-F) controller in a multivariate, electromechanical, and nonlinear under-actuated ball and balancer system. Integral Time Absolute Error (ITAE) is an objective function used for designing controllers because of its ability to be more sensitive to overshooting as well as reduced settling time and steady-state error. As part of the analysis, four metaheuristic optimization algorithms are compared in the optimization of proposed control strategies for cascaded control of the ball and balancer system. The algorithms are the Grey Wolf optimization algorithm (GWO), Cuckoo Search algorithm (CSA), Gradient Base Optimization (GBO), and Whale Optimization Algorithm (WOA). The effectiveness of proposed controllers ${\mathrm{PIDD}}^2$-PI and TID-F is investigated to be better in terms of transient time response than proportional integral derivative (PID), proportional integral-derivative (PI-D), proportional integral-proportional derivative (PI-PD) and proportional integral derivative-second derivative-proportional derivative (${\mathrm{PIDD}}^2$-PD). Moreover, these two proposed controllers have also been compared with recently published work. During the analysis, it is shown that the proposed control strategies exhibit significantly greater robustness and dynamic responsiveness compared to other structural controllers. The proposed controller WOA-${\mathrm{PIDD}}^2$-PI reduced the 73.38% settling time and 88.16% rise time compared to classical PID. The other proposed controller GWO-TID-F reduced 58.06% the settling time and 26.96% rise time compared to classical PID. These results show that proposed controllers are particularly distinguished in terms of rise time, settling time, maximum overshoot, and set-point tracking.