Automatic generation control optimization for power system resilience under real world load variations using genetic algorithm | Scientific Reports

Scientific Reports volume 15, Article number: 20857 (2025) Cite this article

Modern power systems must be resilient to sudden load variations in order to keep the system stable. For Automatic Generation Control (AGC), single load change is impractical and need further analysis. This study comprehensively explore the performance of AGC in a two-area interconnected power system, focusing on a wide range load variations that can exists in realistic power systems consisting from 100 to 300 MW in both increments and decrements. The performance of three control strategies-Conventional AGC (CAGC), Tie-Line Bias (TLB) Control, and Genetic Algorithm-Optimized PID (GA-PID)-is assessed across 12 distinct cases, each tested under these three scenarios. A total of 360 tests are conducted, with performance measured by key metrics, including overshoot, undershoot, settling time, and steady-state accuracy for both areas. The results demonstrate that GA-PID consistently outperforms CAGC and TLB in minimizing transient deviations, ensuring faster stabilization, and maintaining steady-state accuracy. For load increases, GA-PID reduces overshoot by up to 90% and eliminates undershoot in several cases. In comparison, CAGC and TLB show notable weaknesses when dealing with larger disturbances, such as extended oscillations and bigger deviations. The results highlight how effective GA-PID is as a strong and flexible control method, which is crucial for today’s power systems that need to manage unpredictable changes in load.

In the electrical system, scheduled power and frequency of the link line diverge from nominal values due to sudden variations in load demand and the incorporation of renewable energy sources into modern power system networks1. Frequency is a crucial performance metric indicating the safety and stability of power systems2,3. In order to handle possible imbalances between generation and consumption, a hybrid power system uses both conventional units and renewable energy sources to balance supply and demand4,5.Energy networks’ resilience depends on the functionality and stability of their power systems6,7. In adjacent power systems, tackling the issues provided by dynamic load changes is critical8. Power generation and demand must be carefully managed to guarantee that the power system operates smoothly. However, it is inherently difficult to maintain this equilibrium, especially when the load changes unexpectedly and abruptly9,10,11,12. To balance the generation and consumption of electricity, the turbine’s gate or valve position is automatically changed. This is done using an AGC system13,14. The water or steam input to the turbine is adjusted to ensure alignment with the actual power need. This technique is described using two terms: AGC and LFC15. Prime mover control systems provide a means to maintain frequency stability and control power. It is difficult to precisely match produced power to load under nominal conditions. When human control is no longer practicable, managing tie-line power and frequency in connected power systems becomes a significant difficulty13,16,17,18.

In study19 an electrohydraulic PID-based governor for controlling the frequency and speed of Mini Hydropower Plants (MHPPs) in a distribution network is proposed. Another study20 introduces an exponential PID controller to improve load frequency regulation (LFR) in power system structures. Despite its simplicity, the controller effectively mitigates frequency and tie-line power deviations, outperforming state-of-the-art approaches in various single-multi-area single-multi-source PSs.

LFC is essential to maintaining the stability and dependability of the electrical grid in modern power systems. LFC uses sophisticated control strategies to dynamically modify the producing output, ensuring synchronization with fluctuating loads while maintaining a manageable system frequency. Complex controllers like proportional-integral-derivative (PID) controllers are used for this degree of exact control21,22,23, In addition to more complex strategies like Model Predictive Control (MPC)24,25 and methods for adaptive control. These controllers allow operators to quickly and accurately adjust generator setpoints by obtaining real-time data on tie-line power changes and system frequency. Renewable energy integration in power grids leads to generation-load demand mismatch, requiring AGC and Brown bear optimization algorithm for tuning PID and cascaded PI-PDN controllers26. In order to balance generating costs and frequency stability in contemporary power grids, the paper27 presents a DEO-LFC method for microgrids that makes use of agent-based systems and reinforcement learning. Recent studies have explored various advanced AGC strategies. Vidyarthi et al.28 introduced a chaos quasi-opposition seahorse-based tilt controller integrated with deep learning for AGC under cyberattack conditions. In another work, a cascaded tilt MPC controller was implemented for AGC in hybrid power systems29. Additionally, Vidyarthi and Kumar proposed an MPC+PIDN controller for interconnected MPS with virtual inertia30. These works, while impactful, lack detailed analysis under extensive load variation conditions as explored in the current study.

Current load frequency regulation has been significantly impacted by intelligent technologies like Artificial intelligence (AI) and machine learning (ML). The introduction of AI and ML into these systems enhances their predictive abilities, flexibility to a variety of operating conditions, and control scheme optimization. ML-based control strategies, such as ANN, FLC, and MPC, have demonstrated effectiveness in optimizing dynamic performance in power electronic converters. Similar approaches can be leveraged for PID tuning in AGC to enhance frequency stability, reduce overshoot, and improve system robustness under varying operating conditions31. This integration increases the functioning of complex, interconnected power networks. The expansion of load frequency management, a vital aspect in seamlessly integrating renewable energy sources and efficiently managing the complexity of modern power networks, reflects the ongoing advancements in control theory and technology. Using Particle Swarm Optimization (PSO)-optimized PID control, the study32 investigates LFC techniques, highlighting the need of steady power system performance for dependable energy grid operation. The Walrus Optimization Algorithm (WaOA)-tuned FO-PID controller has been demonstrated to enhance load frequency control and automatic voltage regulation, achieving faster convergence and improved stability compared to recent optimization techniques33.In deregulated power systems that incorporate renewable energy sources, the use of a Leader Harris Hawks Optimization-based Model Predictive Controller (MPC-LHHO) has demonstrated notable gains in frequency and voltage control34.Outperforming several nature-inspired algorithms, the Teaching Learning-based Optimization (TLBO) adjusted Sliding Mode Controller (SMC) has shown notable gains in frequency stability for microgrids in35. Event-triggered sliding mode control (ET-SMC) improves load frequency control by ensuring stable frequency regulation in microgrids while lowering calculation and data transmission by 80% compared to time-triggered approaches, making it effective under uncertainties and load disturbances36. GPIO-based event-triggered control (ETC) enhances load frequency control by dynamically adjusting threshold parameters, ensuring frequency and tie-line power stabilization while optimizing computational and communication resources in power systems with wind energy integration37. In38,39 four LFC strategies in linked power systems, concluded that GA-PID is particularly effective and gives helpful insights for enhancing power system stability, however, this study lacks the impact of load variation on GA-PID controller for LFC.

The paper is structured as follows: Section “Research gap and novelty” presents the AGC system model, control strategies, and GA-based PID tuning. Section “Methodology” covers problem formulation, optimization constraints, and evaluation methods. Section “Results and discussion” provides a comparative analysis of AGC strategies with key performance metrics. Section Conclusion concludes with key findings and future directions, including RES and EV integration.

While AI and machine learning techniques, including PSO and GA, have proven effective in optimizing PID controllers for LFC and AGC, their robustness under varying load conditions remains underexplored. Specifically, the impact of sudden and large load variations on GA-optimized PID controllers has not been thoroughly investigated, with most studies focusing on static or nominal load conditions and neglecting dynamic interactions under significant load changes.

Although AGC performance in interconnected power systems has been extensively studied, existing research primarily addresses single sudden load increases, overlooking the broader spectrum of load variation (LV) scenarios typical in real-world systems. This study addresses this gap by evaluating AGC performance under diverse load variation scenarios, specifically focusing on load changes between 100 and 300 MW.

The novelty of this research lies in its integration of LV analysis with GA-PID controllers. Unlike previous studies, such as those by Zhu et al.40, Wadi et al.41, and Ranjan et al.42, which exclude or simplify LV impacts, this study explores real-world challenges associated with LV in interconnected systems. It contrasts with works by ShangGuan et al.43, Kroposki44, and others45,46,47, which either do not address LV or focus on other aspects like stability or optimization techniques.

By emphasizing the transient impacts of LV and demonstrating the effectiveness of GA-PID controllers, this study contributes to AGC research, offering insights for improving system robustness and stability under dynamic conditions. A comparative analysis of relevant studies is summarized in Table 1.

Robust AGC Evaluation Under Real-World Load Variations Developed a structured evaluation framework for AGC in two-area power systems, assessing resilience against real-world load variations (100–300 MW). The GA-optimized PID controller achieves up to 90% overshoot reduction, eliminates undershoot in multiple cases, and improves settling time by 47% over conventional AGC methods.

Frequency Deviation Analysis Across Control Strategies Investigated frequency deviations under diverse load conditions using CAGC, TLB, and GA-Optimized PID controllers, demonstrating the superior disturbance rejection capability of GA-PID.

Mechanical Power Dynamics in Load Variations Analyzed mechanical power variations in response to load disturbances, quantifying their impact on system stability and inter-area power exchanges.

Genetic Algorithm-Based PID Optimization Integrated GA-PID controllers into AGC frameworks, achieving optimized frequency regulation, reduced oscillations, and improved steady-state accuracy.

Comparative Benchmarking of AGC Strategies Performed a detailed comparative analysis of AGC strategies under realistic load conditions, providing insights into optimal controller selection for interconnected power systems.

This research fills a critical gap in AGC studies by addressing the neglected area of load variations and demonstrating the importance of advanced optimization techniques in enhancing system performance.

AGC is a secondary frequency control mechanism that ensures system frequency stability and regulates tie-line power exchanges between interconnected areas. It operates by adjusting the generation setpoints of participating units based on Area Control Error (ACE). Within AGC, different control strategies, such as TLBC and PID control, are implemented to achieve frequency regulation.

Power system frequency control is categorized into two hierarchical levels:

Primary Frequency Control: This is the first level of frequency regulation, where local turbine-governor mechanisms respond to frequency deviations autonomously. The primary control acts within milliseconds to seconds, counteracting sudden disturbances by adjusting the mechanical power input to generators.

Secondary Frequency Control (AGC): This control mechanism restores frequency to its nominal value and corrects tie-line power deviations. AGC operates in a centralized manner, utilizing different control strategies such as TLBC and PID control. The secondary control loop acts on a timescale of seconds to minutes, ensuring long-term frequency stability.

TLBC is a widely used AGC strategy that regulates power exchanges between interconnected areas. TLBC computes the ACE based on both frequency deviations and tie-line power imbalances, ensuring fair power-sharing among areas. A PID controller can be integrated within AGC to enhance frequency regulation by dynamically adjusting generation setpoints based on error signals. While TLBC ensures inter-area coordination, the PID controller improves system response by mitigating frequency deviations more effectively.

The PID controller regulates system response based on the following control law:

where:

\(u(t)\) is the control input to the generator.

\(X(t)\) represents the controlled variable, defined as:

\(X(t) = \Delta f(t)\) for direct frequency control.

\(X(t) = ACE(t)\) for AGC-based control, where:

\(K_p, K_i, K_d\) are the proportional, integral, and derivative gains.

This ensures that the PID controller operates correctly based on the chosen control strategy.

GA is an optimization technique used to fine-tune the PID controller parameters. The performance of a PID controller depends on its proportional (\(K_p\)), integral (\(K_i\)), and derivative (\(K_d\)) gains. Traditional tuning methods often yield suboptimal results, leading to slower response times and higher overshoot. In this study, GA is employed to optimize these gains by minimizing the Integral of Time-weighted Absolute Error (ITAE), ensuring improved frequency regulation and system stability.

This study begins by selecting a two-area interconnected power system, modeled using MATLAB/Simulink as shown in Fig. 1 . Initially, a simple power system model from49 is used to introduce sudden load variations, both increments and decrements, as detailed in Table 2. These load variations, ranging from 100 to 300 MW, are essential for observing the resulting frequency deviations and power flow disturbances, forming a key part of the study.

The methodology involves implementing multiple control strategies within the Automatic Generation Control (AGC) framework to assess their effectiveness in mitigating frequency deviations under real-world load variations. The analysis is conducted across three distinct scenarios, each representing a different AGC approach:

Scenario 1: CAGC Implements a standard AGC structure where frequency deviations are corrected using predefined control parameters without adaptive tuning. This represents a baseline for evaluating improvements in other methods.

Scenario 2: Tie-Line Bias Control (TLBC) Introduces a secondary frequency control mechanism that integrates tie-line power deviations into AGC. TLBC improves inter-area power sharing but lacks dynamic parameter optimization.

Scenario 3: Genetic Algorithm-Optimized PID (GA-PID) Enhances AGC by incorporating a GA-optimized PID controller. GA optimizes the proportional (\(K_p\)), integral (\(K_i\)), and derivative (\(K_d\)) gains to minimize transient deviations, accelerate settling time, and improve steady-state accuracy.

MATLAB simulink model of two area power system.

For each of these three scenarios, five performance metrics are calculated for both Area 1 and Area 2, Peak Value, Overshoot, Undershoot, Steady-State Value and Settling Time. Thus, each case involves calculating a total of 10 metrics (5 metrics for Area 1 and 5 metrics for Area 2). In total, 12 cases are studied, with each case evaluated under the three scenarios (CAGC, TLB, and GA-PID). This results in a total of 12 cases \(\times\) 3 scenarios \(\times\) 5 metrics \(\times\) 2 areas = 360 tests conducted across the entire study. The load variations applied range from 100 MW to 300 MW for both load increases and decreases. The performance of each control strategy is analyzed based on the calculated metrics for both areas. The first strategy tested is the CAGC, which is applied to the system to evaluate its performance in handling these load variations. For TLB Control, the Integral of Time-weighted Absolute Error (ITAE) is used as the fitness function for the PID controller, and the performance results are sent to the MATLAB Workspace for analysis. To enhance the performance of the conventional PID controller, the PID parameters are optimized using a GA through the MATLAB Optimization Toolbox. The GA is used to tune the PID parameters in real-time, improving the control strategy’s ability to stabilize the system and minimize frequency deviations. The study examines the performance of these controllers across the following 12 distinct cases as shown in Table 3, each involving sudden load increases and decreases in both Area 1 and Area 2:

Each of these cases involves applying the load variations to the system and testing the effectiveness of the Conventional PID and GA-Optimized PID controllers in real-time scenarios. The GA-Optimized PID controller is expected to demonstrate superior performance in mitigating frequency deviations, especially during larger load disturbances.

The entire process is conducted within the MATLAB/Simulink environment, enabling a comprehensive evaluation of the control strategies. This environment allows for the simulation of various loading conditions and the analysis of system behavior, including frequency deviations and mechanical power changes. The results are analyzed using performance metrics such as overshoot, undershoot, settling time, and steady-state error. This focus on evaluating load variations as part of the AGC system represents a significant contribution to the study, highlighting the effectiveness of control strategies under different loading conditions and improving the overall power system stability.

To comprehend the dynamic behavior of two-area power systems and to create efficient control strategies, accurate system modeling is crucial. An extensive summary of the parameters pertaining to the two-area power system under consideration is given in this section. The study’s two-area power system parameters were taken from the work of Haadi Saadat50. The specific parameters include the turbine time constant (\(\tau _T\)), governor time constant (\(\tau _G\)), generator inertia constant (\(H\)), governor speed regulation (\(R\)), tie-line power flow parameters, and load damping coefficient (\(D\)), among others. These parameters form the foundation for simulation and analysis, enabling an accurate representation of the system’s dynamic behavior under various load variation scenarios. The parameters of the two-area power system are summarized in Table 2.

The dynamic behavior of the two area power station is a key aspect of our study. The turbine time constant (\(\tau _T\)), governor time constant (\(\tau _G\)), and generator inertia constant (\(H\)) play crucial roles in determining the response of the power system to sudden load changes (\(\Delta P_L\)).

Combining the transfer functions of the generator, load, prime mover, and governor yields the whole open-loop and closed-loop transfer functions:

The study of these transfer functions in Equations (3) and (4) from50 provides valuable insights into the dynamic characteristics of power systems, aiding in the analysis and design of control strategies.

Efficient load frequency control in multi-area power systems requires robust control strategies to ensure system stability and minimize inter-area power exchange. This study evaluates three control strategies: Conventional Automatic Generation Control (CAGC) in Fig. 2, (TLB) control in Fig. 3, and a GA-PID Controller, each tailored to address the challenges of sudden load variations and to enhance system performance under dynamic conditions.

CAGC coordinates the generation control across multiple interconnected areas to maintain system frequency and balance power exchange between areas. In this study, the two-area power system model, employed in MATLAB Simulink, is subjected to sudden load changes without any control mechanism to observe frequency deviations as depicted in Fig. 2. The simulation results allow for a clear comparison of the frequency response behavior when no control strategy is applied.

CAGC for two area power system.

Unlike other control strategies, CAGC operates by adjusting the generation in each area based on frequency deviations and tie-line power deviations. However, the conventional CAGC system can show slow response times and insufficient disturbance rejection under large and sudden load changes, which is why more advanced strategies, such as TLB and GA-PID, are considered in this study.

TLB aims to minimize the Area Control Error (ACE) by ensuring that each area adjusts its generation in response to changes in frequency and inter-area tie-line power. The ACE is calculated as follows:

where \(\Delta P_{ij}\) from50 represents the power exchange deviation between areas, and \(\Delta w\) represents the frequency deviation. The parameter \(K_i\) is the area bias, which determines the sensitivity of the generation adjustment to frequency deviations and the tie-line power.

In TLB control, the objective is to reduce the ACE to zero, meaning that each area will adjust its generation in response to changes in frequency and tie-line power in such a way that the ACE is minimized. The area bias \(K_i\) is typically selected to be equal to the frequency bias factor of that area, which is given by:

where \(R_i\) from50 is the system’s frequency response characteristic, and \(D_i\) is the system’s damping factor. When correctly selected, the bias ensures that the system can stabilize quickly after load changes, but performance may degrade under sudden load variations if the system’s parameters are not optimized.

Two area power system with TLB control.

The GA-PID controller integrates the power of GA for the optimization of the PID controller parameters. In this case, the performance of the system is evaluated using the Integral of Time-weighted Absolute Error (ITAE) as a fitness function. ITAE is chosen because it penalizes both large and delayed frequency deviations, promoting fast and precise system recovery. The fitness function is expressed as:

where \(\Delta w(t)\) is the frequency deviation, and \(t\) is time. The goal of the GA optimization is to minimize this fitness function, ensuring minimal frequency deviations and faster response times.

The GA-PID controller works by adjusting the PID parameters to minimize the ITAE, thus ensuring that the system stabilizes quickly and maintains frequency stability even under varying load conditions. The optimization process involves an initial population of random solutions, followed by iterative selection, crossover, and mutation processes to evolve the optimal parameters for the PID controller. This method provides more adaptive and efficient control, especially in the presence of large and sudden load changes.

Genetic algorithm flowchart from49.

The GA flowchart shown in Fig. 4 illustrates the step-by-step process involved in optimizing the parameters of the PID controller using Genetic Algorithms. This approach enhances the stability and disturbance rejection capabilities of the AGC system, offering a significant improvement over conventional methods and TLB control.

GA is introduced into the control system to optimize the power system and enhance stability. The effectiveness of the GA-optimized control system is evaluated by comparing it with both the previous conventional PID controller system. The GA refines PID parameters through iterative generations, optimizing \(K_p\), \(K_i\), and \(K_d\) to minimize the cost function \(J\), using the Integral of Time-weighted Absolute Error (ITAE) as the fitness function. The GA-based optimization process for PID controller parameters is depicted in the GA flowchart in Fig. 4. As shown, the process begins with the initialization of the population of PID controllers. Each individual is evaluated based on its fitness, with the Integral of Time-weighted Absolute Error (ITAE) used as the fitness function. After the evaluation, individuals are selected, and genetic operators such as crossover and mutation are applied. This iterative process continues until the stop criterion is satisfied, resulting in the optimized PID controller parameters. GA optimized PID is then utlilized in AGC system as depicted in Fig. 5.

The AGC system is implemented using three PID controllers:

PID for Area 1: Regulates frequency deviations in Area 1.

PID for Area 2: Regulates frequency deviations in Area 2.

PID for Tie-Line Control: Regulates tie-line power flow between areas.

Each PID controller follows the standard control law:

where \(X(t)\) represents the error signal, defined as follows: - For Area 1: \(X_1(t) = \Delta f_1(t)\), where \(\Delta f_1\) is the frequency deviation of Area 1. - For Area 2: \(X_2(t) = \Delta f_2(t)\), where \(\Delta f_2\) is the frequency deviation of Area 2. - For Tie-Line Control: \(X_3(t) = \Delta P_{\text {tie}}(t)\), representing tie-line power deviation.

The PID gains (\(K_p, K_i, K_d\)) for each controller are optimized using (GA) to minimize frequency deviations and enhance AGC performance. The optimization process follows:

Objective Function: The Integral of Time-weighted Absolute Error (ITAE) is used to minimize frequency deviations and improve transient response.

Constraints: The PID gains are constrained within \([-1,1]\) to maintain system stability and computational efficiency.

GA-Based Optimization: The algorithm iteratively tunes the PID parameters to achieve the best performance based on the ITAE objective function.

The final GA-optimized PID gain values for each controller are presented in Table 4.

These optimized gains ensure fast settling time, minimal overshoot, and enhanced load variation resilience, improving AGC performance under dynamic conditions.

In this study, the ITAE was used as the objective function for GA-based PID tuning. Since ITAE optimization was not applied to CAGC and TLBC, a direct ITAE comparison across all controllers is not available. Instead, the effectiveness of each control strategy is evaluated based on key performance metrics such as frequency deviation, overshoot, settling time, and steady-state accuracy.

The results in Table 5 demonstrate that the GA-PID controller, optimized using ITAE, effectively reduces frequency deviations and enhances system stability under various load conditions. The performance of CAGC and TLBC has been compared using other stability metrics, confirming the superiority of GA-PID.

Two area power system with GA-PID control.

This section provides a detailed analysis of the system’s behavior under various load variation scenarios. The performance of CAGC, TLB and GA-PID controllers are evaluated for frequency deviation, transient response, and steady-state stability. Each case is discussed based on metrics such as overshoot, undershoot, peak frequency, and settling time, with references to the corresponding figures and tables.

In this case, the frequency deviation of CAGC, TLB, and GA-PID controllers is analyzed under a sudden 100 MW load increase in Area 1 as shown in Fig. 6, with detailed metrics in Table 6. CAGC shows significant transient deviations with an overshoot of 0.27%, undershoot of 0.45%, and steady-state deviation of 59.84 Hz as depicted in Fig. 6a, reflecting its limitations in handling dynamic load variations. Figure 6b shows TLB improves overshoot to 0.09% but introduces a larger undershoot of 0.68%, which highlights its inability to strike a balance between overshoot mitigation and transient recovery. In contrast, GA-PID eliminates overshoot entirely, reduces undershoot to 0.39%, and ensures precise steady-state restoration at 60.00 Hz as shown in Fig. 6c. Furthermore, GA-PID demonstrates improved damping of inter-area frequency deviations, achieving smooth and stable responses in both areas compared to CAGC and TLB. The results indicate that conventional controllers like CAGC and TLB struggle to handle sudden disturbances effectively, particularly under dynamic load variations, while GA-PID provides a more robust and adaptive response. This highlights the critical need for advanced optimization-based control strategies to ensure stability and resilience in modern interconnected power systems.

Frequency deviation and change in mechanical power in Area 1 and Area 2 with a load of 100 MW increase in Area 1.

The frequency deviation under a 100 MW load increase in Area 2, as shown in Fig. 7 and performance metrics in Table 7, reveals distinct performance differences among CAGC, TLB, and GA-PID controllers. CAGC struggles to maintain frequency stability, exhibiting an overshoot of 0.27% and a significant undershoot of 0.69%, which delays recovery and leads to steady-state deviations (59.84 Hz) in both areas as shown in Fig. 7a. TLB slightly improves the response in Area 1 with zero overshoot; however, its transient behavior in Area 2 worsens, with overshoot rising to 0.36% and undershoot peaking at 0.91% as depicted in Fig. 7b, indicating its limited control over inter-area effects. On the contrary, GA-PID achieves a far superior response with minimal overshoot (0.11%) as can be seen from Fig. 7c and undershoot (0.33%), ensuring rapid stabilization while keeping steady-state deviations negligible . Notably, the steady-state frequency converges closer to the nominal value in both areas, 60.00 Hz for Area 1 and 59.94 Hz for Area 2. This outcome demonstrates GA-PID’s superior ability to handle load disturbances, balancing quick transient recovery with minimal inter-area frequency disruptions, unlike the CAGC and TLB controllers which remain susceptible to prolonged deviations.

Frequency deviation and change in mechanical power in Area 1 and Area 2 with a load of 100 MW increase in Area 2.

The response of the system to a sudden 100 MW load decrease in Area 1 is presented in Table 8. CAGC in Fig. 8a displays a peak overshoot of 0.44% and an undershoot of 0.27%, reflecting moderate instability during the transient phase. Although the steady-state value settles at 60.16 Hz, this residual deviation from the nominal frequency indicates insufficient correction. TLB in Fig. 8b, while achieving a better steady-state value of 60.00 Hz, struggles with a higher overshoot of 0.68% and only a marginal improvement in undershoot (0.09%), showing its limited ability to handle sudden load reductions effectively. GA-PID Fig. 8c, on the other hand, provides the best performance, completely eliminating undershoot in Area 1 and reducing overshoot to 0.39%. The system reaches an accurate steady-state value of 60.00 Hz, ensuring a smooth transition with minimal frequency deviation. In Area 2, CAGC and TLB exhibit inter-area disturbances, with TLB achieving zero undershoot but introducing a peak overshoot of 0.16%. GA-PID demonstrates superior control by limiting overshoot to just 0.04% and maintaining a steady-state value of 60.00 Hz. Overall, GA-PID proves its dominance in minimizing transient deviations and restoring system stability swiftly, compared to the CAGC and TLB controllers that continue to show trade-offs between overshoot and undershoot control.

Frequency deviation and change in mechanical power in Area 1 and Area 2 with a decrease of 100 MW load in Area 1.

The system’s response to a 100 MW load decrease in Area 2, shown in Fig. 9 and detailed in Table 9, reveals notable differences among the controllers. For Area 1, CAGC achieves no overshoot but experiences an undershoot of 0.27%, with the steady-state frequency deviating slightly to 60.16 Hz as shown in Fig. 9a. TLB improves the undershoot to 0.00% but introduces a small overshoot of 0.16%, highlighting its trade-off in transient performance as can be seen in Fig. 9b. In comparison, GA-PID minimizes overshoot to 0.03% and maintains near-zero undershoot (0.01%), settling accurately at 60.00 Hz. This highlights GA-PID’s ability to mitigate transient deviations more effectively.

For Area 2, CAGC struggles with pronounced overshoot (0.68%) and undershoot (0.27%), leading to delayed stabilization. TLB further worsens the response, with overshoot increasing to 0.91% and undershoot rising to 0.36%, indicating an inability to control larger deviations. In contrast, GA-PID in Fig. 9c achieves significant improvements, limiting overshoot to 0.33% and undershoot to 0.11%, while ensuring a steady-state frequency of 60.06 Hz. Although all controllers settle in the same time frame (50 s), GA-PID clearly outperforms CAGC and TLB by reducing the magnitude of transient deviations and improving accuracy. This case reaffirms GA-PID’s ability to stabilize frequency dynamics efficiently, particularly when dealing with sudden load reductions, while conventional methods remain less reliable under such scenarios.

Frequency deviation and change in mechanical power in Area 1 and Area 2 with a decrease of 100 MW load in Area 2.

For a 200 MW load increase in A1 the responses of all cases are shown in Fig. 10 and Table 10 summarizes the response of CAGC, TLB, and GA-PID controllers to a sudden 200 MW load increase in Area 1. CAGC in Fig. 10a exhibits a peak frequency deviation of 60.00 Hz with an overshoot of 0.54% and an undershoot of 0.89%, indicating significant instability and prolonged oscillations before stabilization. The steady-state value settles at 59.68 Hz, suggesting an inadequate restoration to the nominal frequency. TLB in Fig. 10b improves the steady-state value to 60.00 Hz, but its transient performance is not ideal. With an overshoot of 0.20% and a larger undershoot of 1.36%, TLB struggles with balancing the overshoot and undershoot, leading to a slower recovery compared to GA-PID. In contrast, GA-PID Fig. 10c eliminates overshoot entirely and reduces the undershoot to 0.77%, ensuring a rapid and accurate recovery to 60.00 Hz.

For Area 2, CAGC exhibits a peak value of 60.00 Hz, with an overshoot of 0.54% and no undershoot. TLB achieves zero overshoot but suffers from a 0.32% undershoot, indicating its limitations in managing load-induced frequency deviations. GA-PID demonstrates superior performance, with minimal overshoot (0.02%) and undershoot (0.08%), ensuring a steady-state frequency close to 60.00 Hz. While all controllers achieve similar settling times (50 s), GA-PID outperforms both CAGC and TLB in minimizing frequency deviations, highlighting its superior stability under larger load disturbances.

Frequency deviation and change in mechanical power in Area 1 and Area 2 with a load of 200 MW increase in Area 1.

The system’s response to a 200 MW load increase in Area 2 is shown in Table 11, with corresponding frequency deviation and mechanical power changes presented in Fig. 11. In Area 1, CAGC experiences a peak frequency deviation of 60.00 Hz as depicted in Fig. 11a, accompanied by an overshoot of 0.54% and no undershoot. The steady-state frequency settles at 59.68 Hz, which reflects the controller’s limitations in returning to the nominal frequency efficiently. TLB, while reducing overshoot to 0.00%, results in a significant undershoot of 0.33% and settles at a steady-state value of 60.00 Hz as shown in Fig. 11b, suggesting some improvement in transient control but still insufficient to fully mitigate the load-induced frequency deviations. From Fig. 11c, GA-PID performs the best in Area 1, achieving minimal overshoot (0.03%) and undershoot (0.06%), with the steady-state value nearly at 60.00 Hz, demonstrating superior stabilization after the load change.

In Area 2, CAGC shows an overshoot of 0.54% and a large undershoot of 1.38%, resulting in a steady-state deviation of 59.68 Hz, indicating a delayed recovery and poor transient performance. TLB offers slight improvement, reducing overshoot to 0.63% and undershoot to 1.83%, but still struggles with greater deviations. On the other hand, GA-PID limits overshoot to 0.21% and reduces undershoot to 0.67%, achieving a steady-state frequency of 59.87 Hz. Figure 11 highlights the smooth frequency trajectory and mechanical power change achieved by GA-PID compared to the other controllers. These results emphasize the robustness of GA-PID in managing large load increases, ensuring faster recovery and improved frequency stability across both areas, whereas conventional methods such as CAGC and TLB show persistent challenges with overshoot and undershoot control, especially in interconnected systems.

Frequency deviation and change in mechanical power in Area 1 and Area 2 with an increase of 200 MW load in Area 2.

The performance of CAGC, TLB, and GA-PID controllers under a 200 MW load decrease in Area 1 is shown in Fig. 12 and summarized in Table 12. In Area 1, CAGC shows a peak frequency deviation of 60.85 Hz with an overshoot of 0.88% and an undershoot of 0.53%. The steady-state value settles at 60.32 Hz, indicating moderate stability but with significant transient behavior before achieving equilibrium as shown in Fig. 12a. TLB, on the other hand, exhibits an overshoot of 1.36% and a smaller undershoot of 0.20%, resulting in a steady-state value of 60.00 Hz as evient from Fig. 12b. While it improves overshoot compared to CAGC, TLB’s undershoot still reflects its limited ability to effectively handle larger load changes. GA-PID in Fig. 12c performs best in Area 1, minimizing the overshoot to 0.77% and completely eliminating undershoot, settling at 60.00 Hz. This confirms GA-PID’s ability to stabilize the system with reduced frequency deviations after the load decrease.

In Area 2, CAGC results in a peak value of 60.32 Hz, with an overshoot of 0.00% and undershoot of 0.53%. The steady-state value reaches 60.32 Hz, but the large undershoot indicates that CAGC struggles with balancing transient dynamics. TLB slightly improves the response with an overshoot of 0.32% and no undershoot, but it still cannot eliminate deviations completely. GA-PID delivers the best performance in Area 2, with an overshoot of 0.08% and undershoot of 0.02%, achieving a steady-state value of 60.00 Hz. The results clearly demonstrate GA-PID’s superior ability to maintain system stability and minimize deviations, outpacing CAGC and TLB, particularly in handling large-scale load changes across interconnected areas.

Frequency deviation and change in mechanical power in Area 1 and Area 2 with an decrease of 200 MW load in Area 1.

The system’s performance under a 200 MW load decrease in Area 2 is summarized in Table 13 and illustrated in Fig. 13. In Area 1, CAGC shows a peak frequency deviation of 60.32 Hz, with zero overshoot and an undershoot of 0.53% as shown in Fig. 13a. Despite achieving a steady-state frequency of 60.32 Hz, the system does not return to the nominal value quickly, reflecting CAGC’s limitations in mitigating transient deviations. As in Fig. 13b, TLB, while reducing the overshoot to 0.33%, still struggles with a 0.00% undershoot and reaches a steady-state value of 60.00 Hz, demonstrating an improved transient response but at the cost of less precision in steady-state accuracy. GA-PID offers the most effective response, with minimal overshoot (0.06%) and undershoot (0.03%), settling at 60.01 Hz, showing superior accuracy and stability.

In Area 2, the performance disparities become more evident. CAGC results in a peak value of 61.14 Hz, with a substantial overshoot of 1.36% and an undershoot of 0.53%, leading to a steady-state frequency of 60.32 Hz. TLB, although improving undershoot (0.63%), exhibits a larger overshoot (1.83%) and settles at 60.00 Hz. GA-PID, however, minimizes overshoot to 0.66% and undershoot to 0.21%, stabilizing the system at 60.13 Hz. As seen in Fig. 13c, GA-PID effectively dampens the frequency deviations and reduces the mechanical power fluctuations more efficiently compared to CAGC and TLB, which continue to show larger transient disturbances. These results highlight the superior capability of GA-PID in restoring frequency stability quickly and accurately, particularly when dealing with significant load reductions in interconnected power systems.

Frequency deviation and change in mechanical power in Area 1 and Area 2 with an decrease of 200 MW load in Area 2.

Table 14 shows the system response to a 300 MW load increase in Area 1. CAGC exhibits a peak frequency deviation of 60.00 Hz with an overshoot of 0.81% and a significant undershoot of 1.34%. This results in a steady-state frequency of 59.52 Hz, indicating that the system struggles to stabilize following large load changes. TLB, while reducing the overshoot to 0.28%, suffers from a much larger undershoot of 2.01%, which causes a deviation from the nominal frequency to 60.00 Hz, showcasing TLB’s trade-off between overshoot control and transient recovery. In contrast, GA-PID achieves the most stable response, with no overshoot and a reduced undershoot of 1.16%, maintaining a steady-state frequency of 60.00 Hz, which reflects its superior ability to stabilize the system.

For Area 2, CAGC results in a peak frequency of 60.00 Hz with a 0.81% overshoot and no undershoot, bringing the steady-state value down to 59.52 Hz. TLB eliminates overshoot but introduces an undershoot of 0.49%, settling at 60.00 Hz, which represents a compromise in achieving a perfect frequency response. GA-PID excels here as well, with minimal overshoot (0.03%) and undershoot (0.12%), settling at 60.00 Hz, ensuring a faster and more accurate stabilization compared to both CAGC and TLB. These results underscore GA-PID’s robustness in handling large disturbances efficiently, outperforming traditional methods in both transient dynamics and steady-state accuracy.

Table 15 shows the system response to a 300 MW load increase in Area 2. In Area 1, CAGC has an overshoot of 0.81% and an undershoot of 0.00%, with a steady-state value of 59.52 Hz. TLB improves the overshoot to 0.00% but introduces a 0.48% undershoot, settling at 60.00 Hz. GA-PID offers the best performance, with minimal overshoot (0.04%) and undershoot (0.09%), settling at 59.99 Hz.

In Area 2, CAGC results in a peak value of 60.00 Hz, a 0.81% overshoot, and a 2.07% undershoot, leading to a steady-state of 59.52 Hz. TLB shows a larger overshoot (1.07%) and undershoot (2.73%), with a steady-state of 60.00 Hz. GA-PID reduces the overshoot to 0.32% and undershoot to 1.00%, achieving a steady-state value of 59.81 Hz. GA-PID outperforms both CAGC and TLB by minimizing frequency deviations and ensuring quicker stabilization in both areas.

The system’s response to a 300 MW load decrease in Area 1 is shown in Table 16. In Area 1, CAGC reaches a peak of 61.28 Hz, with an overshoot of 1.32% and an undershoot of 0.79%, stabilizing at 60.48 Hz. TLB reduces the overshoot to 2.01%, but the undershoot increases to 0.28%, with the steady-state value settling at 60.00 Hz. GA-PID provides the best performance, peaking at 60.69 Hz with a minimal overshoot of 1.16%, no undershoot, and reaching a steady-state value of 60.00 Hz.

In Area 2, CAGC shows a peak of 60.48 Hz, no overshoot, and a 0.79% undershoot, stabilizing at 60.48 Hz. TLB improves to a 0.49% overshoot with no undershoot, settling at 60.00 Hz. GA-PID performs even better, achieving a minimal overshoot of 0.12% and a small undershoot of 0.03%, with a steady-state value of 60.00 Hz. Overall, GA-PID provides superior transient and steady-state control across both areas, minimizing frequency deviations and ensuring faster stabilization.

Table 17 shows the response to a 300 MW load decrease in Area 2. In Area 1, CAGC results in a peak frequency of 60.48 Hz, with no overshoot but a 0.79% undershoot, settling at 60.48 Hz. TLB introduces a 0.48% overshoot and no undershoot, achieving a steady-state value of 60.00 Hz. GA-PID minimizes the overshoot to 0.09% and undershoot to 0.04%, with a steady-state value of 60.01 Hz.

In Area 2, CAGC peaks at 61.71 Hz, with an overshoot of 2.04% and an undershoot of 0.79%, stabilizing at 60.48 Hz. TLB shows a similar peak of 61.64 Hz, with a higher overshoot of 2.73% and undershoot of 1.07%, settling at 60.00 Hz. GA-PID outperforms with a peak value of 60.79 Hz, minimal overshoot (0.99%) and undershoot (0.32%), and a steady-state value of 60.19 Hz. GA-PID provides better overall stability and quicker recovery compared to CAGC and TLB in both areas.

In Areas 1 and 2, the study assessed the performance of CAGC, TLB, and GA-PID controllers in 12 situations with increasing and decreasing loads. Important parameters were examined, including settling time, steady-state value, overshoot, undershoot, and peak frequency. In terms of peak frequency deviation, overshoot, steady-state accuracy, and settling time, GA-PID continuously performed better than CAGC and TLB. Additionally, it showed excellent performance in managing load disturbance-induced inter-area effects, guaranteeing fewer frequency deviations and faster recovery. To sum up, GA-PID was the most dependable and flexible way to keep power systems stable when there were abrupt changes in demand.

The mechanical power dynamics highlight the ability of CAGC, TLB, and GA-PID controllers to localize load variations in Area 1 while minimizing inter-area power exchange. For a 100 MW load increase Table 18, CAGC generates only 53.34 MW locally, requiring Area 2 to supply 42.66 MW as a shown in Fig. 6d, demonstrating poor localization. TLB in Fig. 6e and GA-PID in Fig. 6f shows that both techniques effectively manage the full load increase within Area 1, achieving steady-state values of 100.01 MW and 100.00 MW, respectively. GA-PID achieves faster rise times (0.16 s) and limits disturbances in Area 2 (peak: 13.26 MW) compared to TLB (26.07 MW) and CAGC (42.66 MW).

In a scenario where a 100 MW load is increased in Area 2, the change in mechanical power in Area 1 is 53.33 MW, while in Area 2, it is only 42.67 MW as illustrated in Fig. 7d. To meet the increased load demand, it is recommended that Area 2 provide the entire 100 MW demand for change in Area 2. This defficiency is recovered using TLB control. Table 19 highlights the mechanical power response to a 100 MW load increase in Area 2 under CAGC, TLB, and GA-PID control strategies. In Area 1, CAGC fails to localize the load variation, resulting in unnecessary inter-area power exchange. TLB as shown in Fig. 7e reduces the final deviation but exhibits extreme transient instability. GA-PID shown in Fig. 7f achieves a near-zero steady-state deviation (0.98 MW) with a lower peak than TLB, though it still shows transient oscillations. In Area 2, TLB and GA-PID effectively localize the load increase, reaching steady-state values of 100.00 MW and 98.22 MW, respectively. CAGC results in excessive inter-area power transfer and stabilizes at 42.67 MW. GA-PID minimizes steady-state error but its transient response can be further optimized.

For a 100 MW load decrease in Area 1 , CAGC reduces only − 53.34 MW in Area 1, with Area 2 compensating by − 42.66 MW as shown in Fig. 8d. TLB and GA-PID localize the entire reduction to Area 1, with steady-state values of − 100.01 MW and − 100.00 MW, respectively as seen in Fig. 8e. GA-PID in Fig. 8f shows that GA-PID minimizes transient peaks in Area 2 (9.79 MW), outperforming both TLB and CAGC. Detailed parameters of this case are summarized in Table 20.

The results in Table 21 show that CAGC and TLB result in complete power reduction in both areas, with overshoots of − 100%. In contrast, GA-PID exhibits a peak deviation in Area 1 but stabilizes closer to the desired steady-state value with minimal error. The steady-state power reduction for GA-PID is − 0.98 MW in Area 1 and − 98.22 MW in Area 2, indicating improved performance over TLB. The peak deviation in Area 2 for GA-PID is significantly lower (1.46 MW) than the other methods, confirming its stability and robustness in mitigating disturbances.

The figures further support these findings, illustrating the transient responses for each controller. Fig. 9d represents the response of CAGC, showing complete power reduction with prolonged settling. Fig. 9e corresponds to TLB, which also exhibits a − 100% overshoot but takes longer to stabilize. In contrast, Fig. 9f depicts GA-PID, where the system stabilizes more quickly with significantly reduced oscillations. These results highlight the superior robustness of GA-PID in maintaining stability and reducing oscillations during sudden load reductions.

Table 22 compares the mechanical power response of CAGC, TLB, and GA-PID when a 200 MW load is added in Area 1. The results in Fig. 10f show that GA-PID performs the best, reaching a peak value of 329.54 MW in Area 1 and settling exactly at 200 MW. TLB also achieves a steady-state value close to 200 MW but with a slightly lower peak (328.21 MW). In contrast, CAGC struggles to maintain stability, with a much lower steady-state value of 106.67 MW, indicating a slower recovery and higher deviation from the expected value as shown in Fig. 10d.

In Area 2, GA-PID minimizes the disturbance effect, with the lowest peak deviation (26.49 MW) and an almost negligible steady-state error. TLB in Fig. 10e shows a moderate peak deviation of 50.06 MW, while CAGC performs the worst, with a peak of 85.33 MW and a steady-state deviation of 85.33 MW. These results confirm that GA-PID offers the best overall performance by ensuring faster stabilization, reducing power fluctuations, and improving system resilience against load variations.

The results in Table 23 highlight the impact of a 200 MW load increase in Area 2 on mechanical power responses across different control strategies. For Area 1, CAGC maintains stability with a peak value of 106.66 MW and settles at the same value, indicating no overshoot as can be seen in Fig. 11d. However, TLB and GA-PID exhibit significant deviations. Despite the initial fluctuations, GA-PID stabilizes close to 2 MW, whereas TLB struggles to maintain consistency with an almost negligible steady-state value as depicted in Fig. 11e. In Area 2, all three controllers experience significant peak values, Fig. 11f shows that GA-PID reaching the highest at 383.44 MW. Ultimately, TLB maintains the most accurate steady-state response at 200 MW, while GA-PID settles slightly lower at 196.45 MW, and CAGC shows the worst steady-state deviation at 85.34 MW. These findings indicate that while GA-PID and TLB can effectively stabilize the system, GA-PID provides a more controlled response with lower overshoot compared to TLB, whereas CAGC struggles with steady-state accuracy and system stability under such a disturbance.

A 200 MW load reduction in Area 1 significantly impacts mechanical power distribution across the system, with each control strategy responding differently. The performance of CAGC, TLB, and GA-PID in handling this disturbance is summarized in Table 24. In Area 1, both CAGC and TLB show no peak deviation as shown in Fig. 12d,e, while GA-PID registers a small peak of 0.88 MW. Regarding steady-state response, CAGC stabilizes at − 106.67 MW, whereas TLB and GA-PID accurately reach the expected − 200 MW. For Area 2, CAGC and TLB again exhibit no peak deviation, while GA-PID records a minor peak of 19.60 MW as evident in Fig. 12f. In steady-state conditions, CAGC settles at − 85.33 MW, indicating partial compensation, while both TLB and GA-PID successfully restore balance. Overall, TLB and GA-PID demonstrate superior steady-state accuracy, while CAGC struggles to fully compensate for the load decrease, highlighting the advantage of advanced control methods in dynamic load scenarios.

Table 25 summarizes the response to a 200 MW load decrease in Area 2 for different controllers. GA-PID proves to be the most effective, with a peak deviation of 16.98 MW in Area 1, and settling at a steady-state value of − 1.96 MW. This controller manages the load change with minimal overshoot and excellent power localization. In contrast, CAGC in Fig. 13d and TLB in Fig. 13e show significantly poor performance. Both controllers exhibit no response in Area 1 (peak: 0 MW), as they depend on inter-area power transfer, resulting in limited power handling within Area 1.

In Area 2, GA-PID handles the 200 MW reduction efficiently with a steady-state value of − 196.45 MW, minimizing overshoot as evident in Fig. 13f. CAGC and TLB, however, exhibit more substantial power deviations, with TLB reaching − 200.00 MW as the steady-state value but suffering from instability, while CAGC produces a less efficient response with a steady-state value of − 85.34 MW.

Overall, GA-PID demonstrates superior performance in minimizing transient disturbances and ensuring efficient power redistribution in both areas.

In the 300 MW load increase in Area 1, Table 26 shows that CAGC produces 160.01 MW in Area 1, requiring 127.99 MW from Area 2. TLB and GA-PID localize the generation to Area 1, achieving steady-state values of 300.11 MW and 300.00 MW, with GA-PID minimizing Area 2 disturbances (peak: 39.74 MW)

The data in Table 27 reveals that for a 300 MW load increase in Area 2, the control strategies-CAGC, TLB, and GA-PID-demonstrate distinct behaviors. In Area 1, CAGC reaches a peak value of 159.99 MW with a steady-state value of 159.99 MW, but exhibits a moderate rise time of 8.80 s and a settling time of 50 s. TLB shows a peak of 100.28 MW, but with a much higher rise time of 48.74 s and a steady-state value of only 0.02 MW, which is not ideal. In contrast, GA-PID achieves a peak of 33.35 MW, a steady-state value of 2.93 MW, and the quickest rise time of 2.42 s, making it the most responsive controller. In Area 2, CAGC has a peak value of 428.50 MW and a steady-state value of 128.01 MW, with a rise time of 3.70 s and a settling time of 50 s. TLB performs similarly with a peak of 520.90 MW and a steady-state value of 300 MW, but it has a rise time of 11.47 s, reflecting its slower response compared to GA-PID. The GA-PID controller achieves the highest peak value of 575.05 MW, a steady-state value of 294.67 MW, and the shortest rise time of 1.78 s, making it the most effective for managing load increases. The results suggest that GA-PID is the most efficient in both quick response and steady-state stabilization under large load changes, while CAGC and TLB show slower adjustments and less optimal performance.

For a 300 MW load decrease in Area 1, Table 28 shows that CAGC reduces only − 160.01 MW in Area 1, with Area 2 contributing − 127.99 MW. TLB and GA-PID fully localize the reduction in Area 1, with steady-state values of − 300.11 MW and − 300.00 MW. GA-PID limits Area 2 peaks to 29.32 MW, outperforming other controllers. Across all cases, GA-PID consistently demonstrates superior performance, ensuring effective localization, rapid stabilization, and minimal inter-area power exchange.

A 300 MW load reduction in Area 2 triggers notable variations in mechanical power, with different control strategies responding uniquely. The comparative performance of CAGC, TLB, and GA-PID is summarized in Table 29. In Area 1, both CAGC and TLB show no peak deviation, while GA-PID exhibits a peak of 25.38 MW, indicating a more dynamic response. Regarding steady-state values, CAGC settles at − 159.99 MW, showing partial compensation, whereas TLB and GA-PID stabilize near zero, effectively counteracting the disturbance. For Area 2, peak deviations remain absent in CAGC and TLB, while GA-PID registers a minor peak of 4.39 MW. In steady-state conditions, CAGC stabilizes at − 128.01 MW, not fully addressing the disturbance, while TLB and GA-PID reach − 300 MW and − 294.67 MW, respectively, demonstrating superior accuracy. Overall, TLB and GA-PID provide better steady-state accuracy, with GA-PID exhibiting a more dynamic transient response. CAGC struggles with full compensation, reinforcing the effectiveness of advanced control techniques in handling large load reductions.

The study assesses the performance of CAGC, TLB, and GA-PID controllers in handling mechanical power changes due to load variations in Area 1. CAGC struggles with poor localization, while TLB and GA-PID manage load within Area 1, with GA-PID showing faster rise times and minimizing disturbances. For larger load variations, GA-PID consistently outperforms the other controllers, ensuring better localization, rapid stabilization, and minimal inter-area power exchange.

Although this study does not explicitly model communication delays, the GA-PID controller enhances robustness by minimizing frequency deviations under large and sudden disturbances. This inherent resilience provides a strong foundation for handling practical challenges such as time delays and signal noise. Furthermore, the proposed framework is extendable to delay-resilient architectures. Recent advances in event-triggered and sliding mode control-such as ET-SMC and GPIO-based ETC-have shown effectiveness in reducing communication load while maintaining stability. Integrating such methods with the GA-PID structure is feasible and will be explored in future work.

The performance of AGC in multi-area power systems was evaluated by analyzing the system’s response to various load variations in a two-area power system. The study considered load changes between 100 MW and 300 MW, including both increases and decreases, to simulate real-world operational conditions in modern power grids. Three distinct control strategies-CAGC, TLB Control, and GA-PID-were assessed across 12 different test cases, each evaluated under three load variation scenarios. In total, 360 tests were conducted, with five critical performance metrics considered for both Area 1 and Area 2 in each case. The findings revealed that GA-PID consistently outperformed CAGC and TLB, demonstrating the lowest overshoot, undershoot, and the fastest response time. GA-PID also achieved the best steady-state values, making it more effective in stabilizing frequency deviations and ensuring faster recovery after load changes. In contrast, CAGC and TLB showed larger frequency deviations and slower recovery, especially under larger load disturbances. These results underscore the superior adaptability and robustness of the GA-PID controller, making it the most effective strategy for AGC in interconnected power systems. GA-PID’s ability to manage dynamic and unpredictable load changes with minimal overshoot and steady-state error highlights its effectiveness in ensuring stable AGC performance.

While the present study provides a comprehensive simulation-based analysis under realistic load variation conditions, it is acknowledged that real-time validation using Hardware-in-the-Loop (HIL) platforms or embedded controller prototypes could provide further insights into implementation viability. Such validation constitutes an important extension to this work. Furthermore, the GA-PID controller framework can be modified to incorporate self-tuning or real-time adaptive gains using techniques such as Reinforcement Learning (RL) or Event-Triggered Control (ETC), which will be explored in our future studies. Although the study focused on AGC performance in a conventional power system setup, future work will extend this model to include renewable energy sources (RES) and electric vehicle (EV) integration.

The data used and/or analyzed during the current study are available from the corresponding author upon reasonable request.

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Muhammad Ayaz, Dur-e-Zehra Baig, Syed Muhammad Hur Rizvi, Salah S. Alharbi, Sheeraz Iqbal and Md. Shafiullah contributed equally to this work.

Pak-Austria Fachhochschule Institute of Applied Sciences and Technology, Haripur, 21090, Pakistan

Muhammad Ayaz

Ghulam Ishaq Khan Institute of Engineering Sciences and Technology, Topi, Swabi, 23460, Pakistan

Dur-e-Zehra Baig

Dhanani School of Science and Engineering, Habib University, Karachi, 75290, Pakistan

Syed Muhammad Hur Rizvi

Department of Electrical Engineering, Faculty of Engineering, Al-Baha University, 65779, Al-Baha, Saudi Arabia

Salah S. Alharbi

Interdisciplinary Research Center for Sustainable Energy Systems (IRC-SES), Research and Innovation, King Fahd University of Petroleum & Minerals, 31261, Dhahran, Saudi Arabia

Sheeraz Iqbal & Md. Shafiullah

Control & Instrumentation Engineering (CIE) Department, King Fahd University of Petroleum & Minerals (KFUPM), 31261, Dhahran, Saudi Arabia

Md. Shafiullah

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Conceptualization, A.M. and B.D.Z.; methodology, A.M.; software, A.M.; validation, A.M., B.D.Z., R.S.M.H and I.S.; formal analysis, A.M.; investigation, A.M.; resources, A.S.S., I.S., S.Md.; data curation, A.M.; writing—original draft preparation, A.M.; writing—review and editing, A.M. and B.D.Z.; visualization, A.M.; supervision, B.D.Z. and R.S.M.H.; project administration, B.D.Z. and R.S.M.H.; resources, I.S. All authors reviewed the manuscript.

Correspondence to Dur-e-Zehra Baig or Sheeraz Iqbal.

The authors declare no conflict of interest that could have influenced the work reported in this paper.

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Ayaz, M., Baig, DeZ., Hur Rizvi, S.M. et al. Automatic generation control optimization for power system resilience under real world load variations using genetic algorithm. Sci Rep 15, 20857 (2025). https://doi.org/10.1038/s41598-025-03608-1

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Received: 29 January 2025

Accepted: 21 May 2025

Published: 01 July 2025

DOI: https://doi.org/10.1038/s41598-025-03608-1

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