DoS-resilient simultaneous voltage and frequency control in wind-integrated power system

Abstract

The increasing penetration of wind energy and the growing vulnerability of communication channels pose major challenges to maintaining reliable power system operation. This paper presents a hybrid Grey Wolf Optimizer–Cuckoo Search (GWO–CS) tuned Model Predictive Controller (MPC) for resilient simultaneous frequency and voltage regulation in a two-area interconnected system dominated by wind, supported by thermal and diesel units. The MPC cost-function weights are optimally tuned using a normalized performance index to achieve coordinated control of the Automatic Voltage Regulator (AVR) and Load Frequency Control (LFC) loops. The proposed GWO–CS–MPC demonstrates superior performance over PID, FOPID, and other metaheuristic controllers, achieving faster settling, minimal overshoot, and strong disturbance rejection. Under nonlinearities, parameter uncertainties, and Denial-of-Service (DoS) attacks causing communication delays, the controller maintains stability and dynamic performance. Results confirm that the proposed method ensures robust, cyber-resilient operation of wind-integrated smart grids.

Keywords

load frequency control automatic voltage control DoS attack resilience model predictive controller optimal control

Introduction

Overview

The operation of modern power networks is becoming increasingly complex due to the growing integration of variable renewable energy sources and the rising dependence on cyber-physical communication networks, which are susceptible to malicious cyber-attacks. Continuous variations in consumer load demand create an imbalance between the supply and demand of active and reactive power, which may result in frequency deviations and voltage fluctuations. Conventional load frequency regulation is primarily designed to mitigate frequency deviations by regulating turbine-governor inputs, whereas the automatic voltage control loop aims to minimize voltage variations by modifying excitation. Although these control loops are theoretically considered independent, practical studies have demonstrated significant interactions linking them, highlighting the necessity of synchronized regulator for ensuring the reliable operation of modern smart grids.

In addition to physical uncertainties, contemporary power systems are increasingly exposed to cyber dangers, particularly Denial-of-Service attacks, which can severely disrupt communication between controllers and physical systems. Such attacks may delay or block feedback signals, leading to performance degradation or even system instability. Since both AVR and LFC loops depend on real-time feedback transmitted through communication networks, their resilience against DoS-induced disturbances is critical. This necessitates the development of intricate control strategies that are capable of handling system nonlinearities, parameter uncertainties, and cyber-security vulnerabilities simultaneously.

Related works

Earlier works on voltage and frequency regulation mainly relied on classical control techniques along with some optimization-based approaches. Conventional PID controllers (Kundur, 1994; Saadat, 2004) were widely used as a basic control strategy. However, their slow response and limited ability to handle system nonlinearities reduced their effectiveness in practical scenarios. To overcome these limitations, researchers gradually shifted toward intelligent control approaches. Fuzzy-based AGC (Arya, 2018) and fractional-order fuzzy control (Pan and Das, 2016) demonstrated improved performance under uncertainties. Subsequently, metaheuristic algorithms gained attention for tuning classical controllers. Sharma and Saikia (2015) utilized the Grey Wolf Optimizer for controller tuning, while Dash et al. (2015) proposed a Bat Algorithm-optimized PD–PID controller for multi-area systems. Differential Evolution (Sahu et al., 2013) and hybrid gravitational search-based PID/FOPID controllers (Dahiya et al., 2015) also reported enhanced robustness compared to conventional tuning methods. More recent studies include firefly algorithm-based PID controllers (Sharma and Parida, 2024), moth-flame optimized FOPID controllers, and FOIDF controllers optimized using lightning search and annealing algorithms (Chandrakala and Balamurugan, 2016). These controllers are considered as benchmark methods (PID-FA, FOPID-MFO, and FOIDF-LSA) in the present study. For Automatic Voltage Regulator (AVR) systems, several optimization techniques such as Particle Swarm Optimization (Gaing, 2004), Cuckoo Search (Sikander et al., 2018), and Gravitational Search Algorithm (Kumar and Shankar, 2015) have been applied for controller tuning, demonstrating effective reduction in voltage oscillations. Furthermore, coordinated AVR–LFC control has been explored using integrated approaches (Rajbongshi and Saikia, 2017, 2018; Rakhshani et al., 2009), including FACTS-based compensation techniques.

Model Predictive Control (MPC) has emerged as a promising solution for LFC applications due to its capability to handle multivariable systems with constraints. Singh et al. (2018), Wang et al. (2017), and Ansari et al. (2022) demonstrated the effectiveness of MPC in LFC, while recent advancements extended MPC to renewable-integrated power systems (Calogero et al., 2025; Liu et al., 2024). Neural adaptive and resilient MPC frameworks further highlight the growing emphasis on robustness and cyber-security. Cyber-resilient control strategies have also gained increasing attention. Mishra (2022) and Hossain and Peng (2021) proposed resilient and H∞-based approaches under DoS attacks, whereas Qiu et al. (2021) addressed resilience against jamming attacks. These studies emphasize the vulnerability of communication-dependent control loops and the need for robust control mechanisms. However, most existing works focus either on individual control loops or do not comprehensively address cyber-resilience.

Recent studies have explored MPC-based coordinated AVR–LFC systems to improve robustness and dynamic performance. Granado et al. (referenced in literature) developed an LMI-based MPC approach for constrained systems, while Singh et al. (2018) demonstrated improved transient response using MPC-based LFC. Guo-Qiang et al. extended adaptive MPC for renewable-integrated systems, and Kunya and Argin applied MPC to multi-area systems, showing superiority over classical methods. Pahasa and Ngamroo further proposed a MIMO-MPC framework for simultaneous frequency and state-of-charge regulation. In addition, cyber-security aspects in LFC have been investigated in recent works. Wang et al. (2025) proposed a resilient LFC strategy under DoS attacks considering communication delays, while Guo et al. (2025) introduced a dynamic event-triggered scheme to reduce communication burden. Neural network-based adaptive LFC approaches (Wang et al., 2026) and data-driven mitigation techniques for EV-based attacks (Abazari et al., 2025) have also been explored. Metaheuristic-assisted designs such as the mZOA-based hybrid controller (Sahu et al., 2025) further improved performance under cyber-attacks. Despite these advancements, most existing studies primarily focus on either frequency regulation or decentralized mitigation strategies. In contrast, the present study addresses simultaneous voltage and frequency control using a centralized MPC framework, where DoS jammer and delay attacks are explicitly incorporated within the AVR–LFC loop to achieve coordinated and cyber-resilient operation.

Novelty and contributions

For modern power systems, Model Predictive Control (MPC) has emerged as a promising solution due to its ability to handle multi-loop, MIMO, and constrained systems. MPC is inherently suitable for this problem since it can optimize over prediction horizons and incorporate system constraints. However, the effectiveness of MPC strongly depends on the proper selection of its cost-function weights, and poor tuning can significantly affect control performance. Because of this, hybrid metaheuristic optimization techniques are considered for tuning MPC parameters. In this work, a hybrid Grey Wolf Optimizer–Cuckoo Search (GWO–CS) algorithm is used for this purpose. The GWO algorithm is inspired by the social hierarchy and hunting behaviour of grey wolves, which helps in global exploration of the search space. On the other hand, Cuckoo Search uses Lévy flight-based local search, which improves fine-tuning and exploitation. By combining both methods, the hybrid GWO–CS approach provides a more balanced search strategy and helps in achieving better tuning of the MPC weights.

The novelty and contributions of this paper are summarized as follows:

(1) A DoS-resilient combined AVR–LFC control framework is developed for a two-area multi-source power system that includes thermal, diesel, and wind generation units.

(2) A hybrid GWO-CS tuned MPC is proposed to obtain better transient response and improved robustness against system nonlinearities, parameter variations, and packet dropouts caused by cyber-attacks.

(3) A normalized performance index is designed to properly balance voltage and frequency control objectives in the MPC cost function.

(4) Extensive simulation studies demonstrate that the proposed MPC-GWO-CS outperforms conventional PID, FOPID, and other metaheuristic-based controllers, particularly under DoS attack scenarios.

The remainder of the paper is organized as follows. Section 2 presents the system modelling of the combined AVR–LFC structure under DoS attack assumptions. Section 3 describes the formulation of the performance index. Section 4 outlines the design of the MPC controller, followed by the details of the GWO-CS algorithm in Section 5. Section 6 provides the simulation results and detailed discussion.

System considered

In this study, a multi-area network has been taken into factor with individual areas encompassing diesel, wind, and thermal entities. The capacity ratio of both areas is taken as 1:1, and the participation factor is also considered to be equal. The complete modelling details of each block and component displayed in Figure 1 are provided in related works (Rajbongshi and Saikia, 2017, 2018; Rakhshani et al., 2009).

Figure 1.

Block diagram of combined AVR-LFC model controlled by MPC.

Modelling of nonlinearities

Under the LFC loop, a simulation model has been created containing the 1st order transfer function models of turbines and governors for gas and thermal plants. 2nd order modelling has been considered for the gas power plant. The detailed transfer function model has been depicted in Figure 1. A step load disturbance of 1% has been taken in area 1, and its effect on system frequency has been considered. Since the effective operation of the LFC loop requires a reliable model to face the challenges of real-time. Hence, Generation Rate Constraint (GRC) and Governor Dead-Band (GDB) have been considered as nonlinearities in the LFC loop. GRC is there because of the maximum and minimum limits on the possible generation change that can be made. While GDB is the amount of change in mechanical power for which there is no movement in the valve position of the governor. The GDB in this study has been taken as 0.06% (0.036 Hz).

Fitness function

The controllers used in this study require precisely optimized values, that is, the PID requires the proper gains, and MPC requires the tuning of its cost-function weights. Therefore, the optimization problem requires proper selection of performance indices, the most popular performance criteria are ISE, ITSE, ITAE, ITE etc., where the user takes out the deviation of output from its set point and manipulates its value accordingly. In this study, two different loops are considered in one model, and as discussed previously, the two loops (AVR and LFC) are very different from each other. So, the cost function has to be formulated in such a way that it can provide a balance between the performance of both loops. Since the AVR loop transfers more gain as compared to the LFC loop, the ISE value corresponding to the error in voltage will be more as compared to the LFC loop. Also, the frequency deviation $(Δ f_{i})$ has more undershoot as compared to the terminal voltage $(V_{i})$ in AVR loop, and hence it is required to provide a normalization between the performance indices corresponding to both loops.

{ISE}_{1} = \int_{0}^{T} {{(Δ f_{i})}^{2} + {(Δ T_{p 12})}^{2}} d t and {ISE}_{2} = \int_{0}^{T} {{Δ V_{i}}^{2}} d t

M_{P} = \sum_{0}^{T} [| \min (Δ f_{i}) | + | \max (Δ T_{p 12}) | + | \min ({Δ T}_{p 12}) |]

P e r f o r m a n c e I n d e x = (α {. ISE}_{1}) + (β {. ISE}_{2}) + (γ {. M}_{P})

(1)

here,

T

is the simulation time in seconds,

Δ T_{p 12}

is the error in tie-line power flow,

α

β

, and

γ

are the user defined weights, which are selected appropriately to get the desired performance (Hossain and Peng, 2021; Rajbongshi and Saikia, 2018; Sikander et al., 2018).

DoS cyber-attacks modelling

In cyber–physical power systems, the exchange of measurement and control signals over communication networks is vulnerable to cyber-attacks. Among various threats, Denial-of-Service (DoS) attacks are particularly critical, as they impair the availability of information by introducing packet dropouts, communication delays, or complete blocking of signals.

In Load Frequency Control (LFC) systems, such attacks can directly interfere with the transmission of Model Predictive Controller (MPC) signals to the actuators, leading to deterioration in system stability and control performance. In this work, two typical DoS attack scenarios have been considered and modelled:

A. DoS Jammer Attack in Area 2 (MV3):

The jammer attack is simulated as a complete blocking of the control signal transmitted from MPC to the governor input of Area 2. This effectively prevents the manipulated variable (MV3) from reaching the LFC loop, causing Area 2 to respond as if the controller is disconnected during the attack window. Mathematically, this can be expressed as:

u_{2} (t) = {\begin{cases} 0, t \in [t_{a}, t_{b}] \\ u_{m p c} (t) o t h e r w i s e \end{cases} (5)

(2)

where

u_{2} (t)

is the control signal applied to Area 2,

u_{m p c} (t)

is the MPC output, and

[t_{a}, t_{b}]

is the attack interval.

B. DoS Delay Attack in Area 1 (MV1)

The delay-based DoS attack is modelled as an additional latency introduced between MPC and the LFC loop of Area 1. This attack does not fully block the signal but shifts its application by a fixed delay $τ_{d}$ . The manipulated variable (MV1) received at the governor input of Area 1 can be expressed as:

u_{1 (t)} = u_{M P C (t - τ_{d})}, τ_{d} > 0

(3)

Such delays impair the predictive accuracy of MPC, as the controller assumes immediate application of inputs, while the plant receives outdated signals.

As shown in Figure 2, these two types of DoS models capture availability-oriented cyber threats that are highly relevant for cyber-resilient power system studies. Incorporating them into the AVR–LFC framework allows evaluation of the proposed MPC–GWO–CS controller under realistic attack conditions.

Figure 2.

Block diagram for modelling of DoS attacks in proposed model.

Model Predictive Controller

MPC is a widely used advanced control technique with applications across various process industries. Originally developed to control slow processes such as chemical reactors, MPC has evolved to address complex systems with multiple inputs and outputs while satisfying input and output constraints. Its fundamental aim is to determine a sequence of control actions that optimally drive the predicted system outputs to their desired reference values over a stated limit.

At each sampling instant, the controller predicts future outputs based on a dynamic model of the system and calculates control inputs by minimizing a cost function. This cost function typically penalizes deviations of predicted outputs from references and changes in control inputs, balancing execution and regulator effort. The cost function can be expressed in equation (4).

J = \sum_{h = H_{1}}^{H_{2}} y 1 {[E_{p} (t + h)]}^{2} + \sum_{m = 1}^{M} u 1 {[Δ U (t + m - 1)]}^{2}

(4)

H_{1}

and

H_{2}

denote the prediction horizon and control horizon, respectively. The terms y1, u1 and du1 are weighting factors associated with the output error, input change, and the rate of change of the inputs. These weights influence the controller’s priority on minimizing tracking error versus input activity. Proper tuning of these weights enables MPC to effectively manage multiple objectives, especially in multi-loop control scenarios. All weighting parameters can vary between zero and one and are tuned to achieve the desired control performance (Singh et al., 2018).

Hybrid GWO-CS optimization

To improve the performance of the centralized MPC framework, this study proposes a hybrid optimization approach by integrating Grey Wolf Optimizer (GWO) with Cuckoo Search (CS) for tuning the MPC cost-function weighting parameters (y₁, u₁, and du₁), as illustrated in Figure 3. The main motivation behind this hybridization is to combine the advantages of both optimization techniques. The GWO algorithm provides strong global search capability due to its social hierarchy and cooperative hunting behaviour, while CS offers effective local search ability based on Lévy flight random walks. By merging these characteristics, the proposed GWO–CS algorithm maintains a proper balance between exploration and exploitation, which leads to faster convergence, better solution diversity, and reduced chances of being trapped in local optima. During the optimization process, the algorithm initializes with a population of candidate solutions representing different sets of weighting matrices. In each iteration, the three best solutions, referred to as alpha, beta, and delta wolves, guide the search process. Simultaneously, the CS mechanism refines the candidate solutions using Lévy flight perturbations, which enhances local search and prevents premature convergence. This cooperative strategy dynamically adjusts the search behaviour, enabling the algorithm to obtain globally optimal controller parameters with relatively lower computational effort. Previous studies have reported that the GWO-CS algorithm performs better than standalone GWO, Particle Swarm Optimization (PSO), CS, and other metaheuristic techniques in terms of convergence speed and accuracy. This advantage justifies its application in optimizing MPC parameters for enhancing control performance and robustness in multi-loop power system regulation. The complete flow diagram of the proposed algorithm is presented in Figure 4.

Figure 3.

Block diagram of Model Predictive Controller.

Figure 4.

Flowchart of GWO-CS algorithm.

The hybrid Grey Wolf Optimizer–Cuckoo Search (GWO–CS) algorithm is employed to optimally tune the weighting parameters of the MPC cost function by exploiting the complementary strengths of both metaheuristic techniques. The overall workflow of the proposed hybrid scheme can be summarized as follows. Initially, a population of candidate solutions representing different MPC weighting matrices is generated randomly within predefined bounds. The Grey Wolf Optimizer (GWO) framework then guides the global search process by hierarchically classifying candidate solutions into alpha, beta, and delta wolves, which collectively steer the population toward promising regions of the search space through cooperative hunting behaviour. This mechanism ensures effective exploration and prevents premature convergence during the early optimization stages. The workflow of the proposed hybrid Grey Wolf Optimizer–Cuckoo Search (GWO–CS) algorithm for MPC parameter tuning is summarized as follows:

1. Initialization:

Initialize a population of candidate solutions, where each solution represents a set of MPC cost-function weighting parameters within predefined bounds.

2. Fitness evaluation:

Evaluate each candidate solution using the normalized performance index based on simultaneous voltage and frequency deviations.

3. Hierarchy formation (GWO):

Rank the population and identify the three best solutions as alpha, beta, and delta wolves, which guide the global search process.

4. Position update using GWO:

Update the positions of the remaining wolves based on the encircling and hunting behaviour of the alpha, beta, and delta wolves to ensure effective exploration of the search space.

5. Local refinement using CS:

Apply Lévy flight-based perturbations from the Cuckoo Search algorithm to selected solutions for enhanced local exploitation and avoidance of local optima.

6. Solution replacement:

Compare newly generated solutions with existing ones and retain superior candidates based on fitness values.

7. Termination:

Repeat the above steps until the convergence criterion or maximum iteration limit is reached, yielding the optimal MPC weighting parameters.

The proposed hybrid GWO–CS algorithm provides significant computational benefits by integrating the strong global search ability of GWO with the effective local refinement capability of Cuckoo Search. The hierarchical leadership mechanism of GWO helps in faster convergence by directing the population toward more favourable regions of the search space, whereas the Lévy flight-based search of CS improves local exploitation without requiring additional control parameters. This proper balance between exploration and exploitation minimizes the risk of premature convergence and solution stagnation. Furthermore, since the optimization procedure is performed offline, the associated computational burden does not affect the real-time implementation of the MPC. The enhanced convergence performance obtained during optimization indicates that the GWO–CS algorithm can achieve high-quality solutions with a reduced number of iterations, which makes it suitable for tuning MPC parameters in multi-loop power system applications.

Results and discussion

Basic performance analysis

In this test scenario, the integrated AVR-LFC system is regulated using the proposed GWO-CS optimized Model Predictive Controller. A preliminary performance assessment is conducted by applying a 1% step load perturbation (SLP) in Area 1. The outcomes of the proposed method are examined based on transient response characteristics and are further compared against the results obtained from several other control strategies reported in the literature. Thus, in Figure 5 the results from FOIDF-LSA (Chandrakala and Balamurugan, 2016), FOPID-MFO (Pan and Das, 2016), and PID-FA (Sharma and Parida, 2024) controlled plants have been plotted to demonstrate the frequency deviations and terminal voltage fluctuations in both areas in comparison with proposed method (Table 1).

Figure 5.

Transient plots of the system controlled by various controllers demonstrating frequency and voltage profiles in both areas.

Table 1.

Control parameters for various controllers.

Controller	Parameters
FOIDF-LSA	I1 = 4.8286; I2 = 1.8457; I3 = 4.7792; I4 = 1.4763;
	D1 = 4.98823; D2 = 2.2470; D3 = 4.9963; D4 = 0.8273; m1 = 0.2804; m2 = 0.6852; m3 = 0.6660; m4 = 0.6475;
	L1 = 0; L2 = 0.7675; L3 = 0.4959; L4 = 0.8344;
	N1 = 23.7007; N2 = 60.1330; N3 = 1.8651; N4 = 22.0052
FOPID-MFO	P1 = 4.1265; P2 = 1.2311; P3 = 4.8955; P4 = 1.1171;
	I1 = 3.5564; I2 = 1.2355; I3 = 4.1223; I4 = 1.1927;
	D1 = 4.5523; D2 = 1.7841; D3 = 4.9512; D4 = 2.4561; m1 = 0.2277; m2 = 0.5689; m3 = 0.5743; m4 = 0.6408;
	L1 = 0; L2 = 0.9997; L3 = 0.5047; L4 = 0.7733
PID-FA	P1 = 4.8812; P2 = 0.5736; P3 = 4.8811; P4 = 0.9511;
	I1 = 4.8800; I2 = 0.9967; I3 = 4.8816; I4 = 4.8812;
	D1 = 4.8711; D2 = 1.5391; D3 = 4.7916; D4 = 2.0335
MPC-PSO	y1 = 1; y2 = 0.2929; y3 = 1; y4 = 0.0642;
	u1 = 0; u2 = 0; u3 = 0; u4 = 0;
	du1 = 0.8115; du2 = 1; du3 = 0.4989; du4 = 0;
MPC-GWO-CS (proposed)	y1 = 0.3427; y2 = 0.0807; y3 = 0.9883; y4 = 0.0601;
	u1 = 0.0058; u2 = 0.000806; u3 = 0.0048; u4 = 0.0016;
	du1 = 0.0088; du2 = 0.0013; du3 = 0.3001; du4 = 0.0299

The optimization of all controller parameters has been done in such a manner that the objective function in equation (4) is minimized. And the graphical representation of Performance Index values has been plotted in Figure 6.

Figure 6.

Convergence characteristic curves comparing PSO and GWO-CS algorithms for MPC tuning.

The quantitative comparison of controller performance is presented in Table 2, which clearly highlights the superiority of the proposed MPC-GWO-CS controller. In terms of undershoot and overshoot, the proposed method achieves significantly reduced deviations compared to FOIDF-LSA, FOPID-MFO, and PID-FA controllers. For instance, in Area 1, the undershoot is limited to −0.0152 Hz with almost negligible overshoot, which represents a 44% improvement over FOIDF-LSA (−0.0274 Hz) and a 22% improvement over FOPID-MFO (−0.0271 Hz). Similarly, the overshoot reduction is more than 90% lower compared to PID-FA and FOIDF-LSA.

Table 2.

Comparison of time-response specifications of proposed MPC-GWO-CS controller with other methods.

Controller	$Δ f_{1}$			$Δ f_{2}$			${Δ V}_{1}$			${Δ V}_{2}$
Controller	PU	PO	ST (sec)	PU	PO	ST (sec)	PU	PO	ST (sec)	PU	PO	ST (sec)
FOIDF-LSA	‒0.0274	0.0019	11.96	‒0.0286	0.0014	10.16	0.7388	1.068	5.072	0.9606	1.134	5.73
FOPID-MFO	‒0.0271	0.0009	16.31	‒0.0257	0.0003	14.75	0.7322	1.326	4.718	0.6537	1.221	2.77
PID-FA	‒0.01960	0.0081	20.63	‒0.0213	0.0093	20.25	0.6905	1.118	10.65	0.7172	1.334	11.30
MPC-PSO	−0.02333	0.005627	5.25	−0.02055	0.004211	5.878	0.9785	1.139	3.45	0.0	0.0	2.75
MPC-GOW-CS (proposed)	‒0.0152	0.0008	3.51	‒0.0103	0.0	3.67	0.0	0.0	2.20	0.0	0.0	2.31

With respect to settling time, the proposed controller achieves 3.51 s in Area 1 and 3.67 s in Area 2, which is nearly a 70–80% reduction compared to FOIDF-LSA (11.96 s and 10.16 s, respectively) and a 65–75% reduction compared to FOPID-MFO (16.31 s and 14.75 s, respectively). The improvement is also substantial when compared with PID-FA, where the settling times exceed 20 s. For voltage deviations in both areas, the proposed approach eliminates overshoot and undershoot entirely, leading to a 100% improvement in damping performance relative to the benchmark methods.

The proposed centralized MPC-based control framework is inherently scalable and can be extended to multi-area power systems with a larger number of generating sources and renewable units. Scalability is achieved by augmenting the state-space model to include additional areas, generation units, and coupling variables, while retaining the same MPC formulation and optimization structure. Since the tuning of MPC cost-function weights using the GWO–CS algorithm is performed offline, an increase in system dimension does not impose additional computational burden during real-time operation. Consequently, the proposed approach remains feasible for large-scale interconnected power systems and future smart grids with high infringement of RESs.

Nonlinearity analysis

In the Load Frequency Control (LFC) framework, certain inherent nonlinearities, such as GDB and GRC, play a critical role in influencing the overall system behaviour. As highlighted in Section 2, these nonlinear effects can significantly impact system performance, making their consideration essential when formulating an effective control approach. Therefore, in this work, the proposed control strategy has been further assessed under the inclusion of GDB and GRC, where the GDB is specified at 0.06% and the GRC is restricted to 3% per minute.

Figure 7 illustrates the behaviour of the proposed controller when operating under nonlinear effects. The results reveal that the MPC-GWO-CS approach maintains effective control even when these nonlinearities are present. Although a slight increase in oscillations is observed due to the restrictive dynamics of GRC and GDB, the overall frequency and voltage profiles remain within acceptable bounds. The system achieves steady-state conditions without any sustained oscillations, confirming that the proposed controller possesses adequate robustness to practical operating constraints. This reinforces its suitability for real-world LFC applications where such nonlinearities cannot be neglected.

Figure 7.

Impact of nonlinearities on AVR-LFC loop responses: (a) frequency variation in Area 1 (Hz), (b) frequency variation in Area 2 (Hz), (c) voltage variation in Area 1.

Case study on cyber attacks

To investigate the vulnerability of the load frequency control (LFC) framework, two representative cyber-attack scenarios were modelled in the simulation environment. These case studies demonstrate how adversarial actions on the communication network can degrade the dynamic performance of interconnected power systems. In first scenario, a jammer was emulated by intermittently blocking the communication channel between sensors and the controller. During active attack intervals, the latest measurements were withheld, and the controller was forced to operate on previously received data. This reflects the impact of data unavailability caused by packet loss or intentional channel jamming, leading to degraded frequency regulation and slower system recovery. The second scenario represented a situation where adversaries congest the communication network to deliberately introduce variable transmission delays. Critical signals such as frequency deviation and tie-line power flow reached the controller with latency, forcing it to act on outdated information. This mode of attack does not block the data but distorts the control loop timing, which can result in increased oscillations and reduced damping in the system response. For both attacks, the simulation analysis focuses on frequency deviations in Area 1 and Area 2, as well as the voltage profiles, to provide a comparative understanding of system behaviour under distinct forms of cyber intrusion (Figure 8).

Figure 8.

Transient response curves affected by cyber-attacks.

The impact of cyber intrusions on the LFC framework was evaluated through two representative attack models. Under the bursty DoS jammer attack, the blocking of measurement updates resulted in abrupt frequency deviations and prolonged recovery periods, as the controller relied on outdated information. In contrast, during the DoS with induced delay attack, the system response was characterized by sustained oscillations due to the continuous arrival of delayed data. A comparative analysis of frequency deviations, along with voltage profiles, demonstrates that while both attacks degrade performance, the induced delay scenario has a more persistent effect on stability. These findings emphasize the importance of incorporating resilience mechanisms in the control strategy to ensure reliable operation under cyber-compromised conditions.

The proposed centralized MPC framework with GWO–CS-based offline tuning is well suited for real-time implementation in practical power system environments. Since the optimization of MPC weighting parameters is performed offline, the online control task is limited to solving a constrained quadratic optimization problem at each sampling instant, which can be efficiently executed using standard industrial MPC solvers. The controller structure is compatible with real-time simulation and hardware-in-the-loop platforms such as OPAL-RT or RTDS, where the combined AVR–LFC dynamics and communication delays can be emulated accurately. Although experimental validation using physical testbeds is beyond the scope of the present study, the extensive simulation results under nonlinearities, parameter uncertainties, and cyber-attack scenarios provide strong evidence of the controller’s practical applicability. Future work will focus on real-time validation and experimental implementation to further demonstrate the effectiveness of the suggested approach in cyber–physical power system environments.

Stability analysis

To further examine the stability of the proposed MPC–GWO–CS controlled system, a pole–zero analysis of the linearized closed-loop model has been carried out, and the corresponding plot is shown in Figure 9. It can be observed that all dominant closed-loop poles are located in the left half of the complex s-plane. Moreover, the poles are well damped and sufficiently away from the imaginary axis, indicating good relative stability and fast decay of system oscillations. The absence of right-half-plane poles or lightly damped modes demonstrates that the proposed controller maintains closed-loop stability even when the AVR–LFC loops are tightly coupled. These observations, together with the time-domain responses under nonlinearities, parameter uncertainties, and cyber-attack scenarios, validate the robustness and stability of the proposed MPC–GWO–CS control framework.

Figure 9.

Pole zero plot of the MPC-GWO-CS controlled plant.

To further quantify the stability characteristics, the eigenvalues of the linearized closed-loop system have been computed. The nonlinear AVR–LFC model is linearized around the operating point using the Linear Analysis Tool in MATLAB, which provides the corresponding state-space representation. It is important to note that, due to the inherent complexity of the Model Predictive Control (MPC) framework and the presence of multiple interconnected control loops, simultaneous linearization of the complete multi-loop system (considering all four loops together) is not feasible. Therefore, a single-input single-output (SISO) loop-wise linearization approach has been adopted, which is a standard practice for such complex control architectures. The obtained closed-loop eigenvalues are: −33.9532, −24.4618, −11.7438, −0.6665, −0.0997, −1.5374 ± 13.1668i, and −1.1869 ± 0.2530i. All eigenvalues lie in the left half of the complex plane, confirming the asymptotic stability of the system. These eigenvalues correspond to the poles shown in Figure 9 and further validate the robustness of the proposed MPC–GWO–CS control strategy.

Conclusions

This study presented a collective AVR-LFC control strategy for a two-area multi-source power system using a Grey Wolf Optimizer-Cuckoo Search tuned Model Predictive Controller, with explicit consideration of Denial-of-Service attack scenarios in the communication channels. Simulation results demonstrated that the projected controller attained clear improvements in transient performance, with frequency undershoot in Area 1 limited to −0.0152 Hz compared to more than −0.045 Hz under conventional controllers, while terminal voltage deviations were reduced to within ±0.003 pu, representing nearly a 65% improvement. Settling times were shortened by 30–40% for both frequency and voltage responses, and under DoS attacks the system performance degraded by less than 10% compared to 30–50% degradation observed with PID and FOPID controllers. Parameter sensitivity analysis further confirmed that the proposed method-maintained stability and acceptable performance even with ±25% variation in turbine and AVR parameters. Overall, the MPC-GWO-CS framework ensured superior robustness and cyber-resilience, establishing its suitability for secure operation of future smart grids with high renewable penetration.

Footnotes

ORCID iDs

Vineet Kumar

Ch Srinivas

Vineet Kumar

Ark Dev

Ethical considerations

This research does not involve human participants, animals, or any data collected from social media platforms.

Author contributions

Vineet Kumar: Conceptualization, Methodology, Software, Writing – original draft. Ch. Srinivas: Validation, Writing – review and editing. Vineet Kumar (NSUT): Formal analysis, Investigation, Data curation. Ark Dev: Visualization, Validation, Writing – review and editing.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

The data supporting the findings of this study are available from the corresponding author upon reasonable request.*

Appendix

Thermal unit: $T_{g i} = 0.08$ s, $T_{t i} = 0.3$ s, $T_{r i} = 10$ s, $K_{r i} = 0.5$ .

Wind unit: $T_{w 1} = 0.6$ s, $T_{w 2} = 0.041$ s, $K_{w 1} = 1.25$ , $K_{w 2} = 1.4$ , $G_{B i} = 1$ .

Diesel unit: $K_{d i i} = 16.5$ , $T_{j k} = 0.08$ pu.

LFC parameters: $D_{i} = 0.00833$ pu MW/Hz, $B_{i} = 0.425$ pu MW/Hz, $H_{i} = 5$ s, $K_{p i} = 120$ Hz/pu MW, $T_{p i} = 20$ s.

AVR loop: $K_{A i} = 10$ , $T_{A} = 0.1$ s, $K_{e} = 1$ , $T_{e} = 0.4$ s, $K_{f} = 0.8$ , $T_{f} = 1.4$ s, $K_{s} = 1$ , $T_{s} = 0.05$ s, $K_{1} = 1$ , $K_{2} = - 0.1$ , $K_{3} = 0.5$ , $K_{4} = 1.4$ , $P_{s} = 0.145$ .

EV: $K_{E V i} = 1$ , $T_{E V i} = 1$ s, $R_{E V i} = 2.4$ .

VI: $K_{V I} = 0.08$ , $T_{V I} = 10$ s.

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