Intelligent ANN-Based Controller for Decentralized Power Grids’ Load Frequency Control

Abstract

In this study, the authors demonstrate the development and evaluation of an optimal frequency control controller for an interlinked two-area power system that incorporates Renewable Energy Sources (RESs). In decentralized power grids, the Load Frequency Control (LFC) system allows scheduled tie-line power as well as system frequency to be reimposed to their nominal values. Designing an advanced controller might enhance the functionality of the LFC mechanism. This article illustrates the possible impacts of converter capacitors using the new High-Voltage Direct Current (HVDC) tie-line model as well as the Inertia Emulation Technique (IET). This paper suggests a new adaptive control procedure for the expected LFC mechanism: an ANN-based (PI^λ + PI^λf) controller. The authors evaluate which control parameters are most effective using a modified version of the Quasi-Opposition-learning-based Reptile Search Algorithm (QORSA) method. Software called MATLAB/Simulink-2015 is used to create this arrangement. The use of established techniques for handling step as well as random load disturbances has enabled an evaluation of the suggested LFC architecture’s efficacy. An IET-based HVDC tie-line reduces overshoot by 100% in Areas 1 and 2 (Area 1 frequency deviation, i.e., ∆f₁, as well as Area 2 frequency deviation, i.e., ∆f₂). When considering SLD, the suggested controller outperforms the most widely used alternative settings. The IEEE-39 bus system has been changed by the addition of RESs. The IEEE-39 bus system is composed of three control areas. It is confirmed how the IEEE-39 bus system reacts to changes in frequency in Areas 1, 2, and 3. It is illustrated how to use the suggested controller in the modified IEEE-39 bus system, accompanied by real-time load variations. Recent research indicates that the suggested control method is better and more efficient due to its 100% decrease in overshoot in Areas 1 and 2 and quick response time.

1. Introduction

1.1. General Background

Contemporary electrical power system infrastructure is composed of several interconnected generating power units. One of the many factors that might result in inefficient power system operations is an imbalance between total generation as well as load demand. One challenging issue that load frequency control may help with is maintaining the prescribed levels of tie-line power as well as system frequency during both regular and irregular operating conditions. The latter problem is a significant barrier in the context of LFC and has yet to be resolved [1,2]. Recent decades have seen the publication of numerous research studies on unified LFC power networks, which supply electricity to numerous areas.

1.2. Literature Review

The literature [3] has highlighted the traditional methods used and the future challenges for frequency regulation studies. In [4], the authors discuss the frequency regulation of multi-area power plants using the LFC mechanism. The study addressed important areas of research on LFC issues in restructured power systems [5]. In a literature survey report, the present concepts and potentials of the power system, including distributed generation, were detailed [6,7]. With the help of an improved Opposition-based Sea-Horse Optimization (OSHO) technique, the FODs of optimization approaches are demonstrated and contrasted with a number of contemporary optimization procedures [8]. In the publication, LFC was analyzed using a PID controller [9]. In hybrid renewable power systems, a robust PID controller has been developed to enhance frequency deviations [10]. In the study, LFC was evaluated using a modified TID controller [11]. Arya Y. [12] controls the frequency used in modern fuzzy fractional-order FOPI-FOPDN controllers. Using a TDF-TIDF controller enhanced the load frequency controller’s performance [13]. The FOPI-FOPIDN’s parameters are improved by the use of ADIWACO, a variation of Particle Swarm Optimization (PSO) seen in the literature [14]. FO-hPID-fuzzy PID controllers and the hPSO-MSC algorithm have been applied in LFC investigations [15]. The Tri-parametric Fractional Controller (TFC) successfully tackles important issues in dual-area thermal power systems, such as cybersecurity risks as well as network latency [16]. In order to investigate the idea of LFC, research [17,18,19,20] has employed a power system that integrated conventional as well as renewable energy sources. An investigation into creating a fuzzy-logic-based controller was conducted [21,22]. The ANN-based controller was used to evaluate LFC [23,24]. Another paper examined low-SAR design [25]. This review is summarized in

Table 1. A review of AGC work.

Authors	Algorithm	Controller	Deregulation	Nonlinearity	Energy Storage Systems	Generating Units
Arya Y. [12]	ICA	Fuzzy FOPI-FOPDN	No	None	None	Three-area thermal
Sekyere Y.O.M. et al. [14]	PSO	FOPI-FOPIDN	No	GDB, GRC	None	Thermal, PV, wind
Patel and Sahu [15]	hPSO-MSC algorithm	FO-hPID-Fuzzy PID	No	GRC	None	Three-area thermal
Singh R.K. and Verma V. [24]	QOVPL algorithm	ANN-based (PIλf + PIλDN)	Yes	GDB, GRC, BD	IET	Thermal, hydro, gas, RES
Singh R. et al. [26]	QOVPL algorithm	Fuzzy-LADRC	No	GRC	EV	RES
Proposed Work	QORSA	ANN-based (PIλ + PIλf)	Yes	GRC	IET	Thermal, hydro, gas, RES, IEEE-39 bus system

.

1.3. Motivation and Research Gap

The assessment pointed out a number of research gaps that need more investigation, e.g., controlling ANN-based controllers with a large number of parameters is quite difficult. Modern situations could be too much for ANN-based PI controllers alone, underscoring the necessity for effective combinations. The control methods examined in the referenced publications have limited their broader applicability because of their exclusive focus on traditional two-area systems. Metaheuristic algorithms used in these studies often fail to find globally optimal answers. These gaps underscore the need for further comprehensive studies to surpass the limitations of ANNs, develop trustworthy controller integrations, and expand studies to encompass a range of system configurations.

Recent advancements in LFC employing fractional-order, fuzzy, and classical PID controllers are prominently highlighted in the literature review. Artificial neural network controllers are efficient in managing multi-area power systems’ nonlinearities. PI^λ as well as PI^λf controllers have advantages over integer-order controllers, such as reduced overshoot, enhanced transient response, and flexibility. A comparison of the suggested QORSA framework with metaheuristic optimization techniques (such as WOA, VPL, and salp swarm) emphasizes the latter’s better robustness and convergence. Our study introduces a parallel ANN-based (PI^λ + PI^λf) controller optimized via QORSA. Unlike previous work, this controller simultaneously leverages adaptive learning, fractional-order dynamics, and quasi-oppositional optimization to achieve faster response, improved stability, and superior performance in various deregulated power system scenarios, including PBT, BBT, CVT, and high RES penetration conditions.

1.4. Contributions

The preferred controller for a decentralized multi-source, two-area thermal power plants, hydro power plants, and gas power plants is ANN-based (PI^λ + PI^λf), and researchers are investigating it. The operation of an IET-based HVDC-linked power system is also examined through a few case studies. The proposed ANN-based adaptive fractional-order (PI^λ + PI^λf) controller, optimized using the Quasi-Oppositional Reptile Search Algorithm (QORSA), contributes not only to the improvement of Load Frequency Control (LFC) performance but also to the advancement of resilient and intelligent control strategies required for future renewable-dominated decentralized grids. Specifically:

• The proposed method enhances frequency stability under the intermittent and stochastic behavior of Renewable Energy Sources (RESs), such as wind and solar, which lack inherent inertia.
• By incorporating the Inertia Emulation Technique (IET) within the HVDC tie-line framework, the study offers a practical pathway to synthetic inertia integration, a crucial requirement in low-inertia renewable power systems.
• The intelligent ANN structure enables adaptive self-tuning of controller parameters, reducing reliance on manual retuning and improving autonomy and resilience in large-scale smart grids.
• The multi-area, multi-source configuration (thermal–hydro–gas–RES integrated IEEE-39 bus system) demonstrates the controller’s ability to maintain dynamic stability and power-sharing coordination in decentralized, deregulated energy markets.

1.5. Limitations and Possible Extensions of the Proposed Method

ANN-based (PI^λ + PI^λf) LFC controllers with IET, HVDC modeling, and QORSA have drawbacks, including computational complexity, reliance on massive datasets for training, the possibility of overfitting, and the requirement for reliable training to manage erratic power system situations, such as cyberattacks and the integration of renewable energy sources. Nonlinear dynamics, renewable intermittency, and communication delays challenge the real-world deployment of a controller and can cause instability, lower performance, and the need for adaptive or resilient control solutions. Nonlinearities, such as the fluctuating behavior of loads, necessitate more intricate modeling than what is possible with linear assumptions. Due to the latency caused by communication delays, exact real-time control is difficult and may result in oscillations or instability. The controller must efficiently integrate these varied inputs and manage grid stability due to the intermittent nature of renewable energy sources like solar as well as wind power, frequently with the aid of energy storage devices. The future holds the potential to create more sophisticated, robust, and self-tuning ANN architectures; integrate deep learning to better manage system complexity; use hybrid approaches with energy storage and microgrid technologies; and strengthen their resistance to cyberattacks using cutting-edge training techniques.

1.6. Paper Organization

The remaining portions of the article are structured as follows: the tested system is discussed. The next section provides a thorough discussion of the optimization algorithm, controller structure, as well as underlying theory. The findings and discussion parts provide the inquiry cases, corresponding results, supporting information, as well as mathematical analysis. An example of the general conclusions is provided in the last section.

2. Examined System

2.1. Experimental System Modeling

The viability of building a thermal power plant, a hydro power plant, or a gas power plant that would provide electricity to two different regions in a decentralized energy market is examined in this study. At 4000 megawatts, Area 2 has twice the power generation capability of Area 1. Area 1 can handle 2000 MW. There are 2 Generation Companies (GENCOs) as well as two Distribution Companies (DISCOs) in each area. Both of these (GENCO 1 as well as GENCO 3) rely on the thermal and gas power plants as their main source of power. A hydroelectric facility (GENCO 4) and a thermal power plant (GENCO 2) produce the energy for the first two power sectors. To establish contracts or relationships between GENCOs as well as DISCOs, the Independent System Operator (ISO) uses a bidding process. This is accomplished through a process called competitive bidding. These stations are connected using a parallel AC-HVDC tie-line system. Figure 1 [24] displays the schematic structure of the system that is being explained.

Figure 2 [24] and Figure 3 illustrate two mathematical models of the interlinked system and individual GENCOs, respectively, to illustrate the concepts in this study. In order to limit the rate of power output, thermal power systems are increasingly using Generation Rate Constraint (GRC) nonlinearity. The ANN-based (PI^λ + PI^λf) controller is employed to maintain stability over time. A modified IET-based HVDC tie-line model is used for simulation experiments in order to better comprehend the substantial influence on the system’s dynamic behavior.

2.2. Performance Index as Well as Objective Function

The governor can control frequency as well as tie-line power exchange when the active power generated and consumed are out of balance. After the power imbalance has been corrected at the producing level by establishing a new balancing point, a secondary LFC controller restores the tie-line power as well as frequency. By altering the strategy’s control parameters, the QORSA increases the LFC’s efficacy. The optimization method uses these Objective Functions (OFs) to determine the optimal controller settings.

$$\left.\begin{array}{c}O{F}_{IAE}={\int }_0^t \left(\sum \left|\mathit{\Delta }{f}_i\right|+\sum \left|\mathit{\Delta }{P}_{tie,ij}\right|\right)dt\hfill \\ O{F}_{ISE}={\int }_0^t \left(\sum \mathit{\Delta }{f}_i^2+\sum \mathit{\Delta }{P}_{tie,ij}^2\right)dt\hfill \\ O{F}_{ITAE}={\int }_0^t \left(\sum \left|\mathit{\Delta }{f}_i\right|+\sum \left|\mathit{\Delta }{P}_{tie,ij}\right|\right)\times t_{s}dt\hfill \\ O{F}_{ITSE}={\int }_0^t\left(\sum \mathit{\Delta }{f}_i^2+\sum \mathit{\Delta }{P}_{tie,ij}^2\right)\times t_{s}dt\hfill \end{array}\right\}$$

(1)

where i and j are the area numbers.

3. IET-Based AC-HVDC Tie-Line Modeling

3.1. Model Investigation of the AC-HVDC Tie-Line Utilizing IET

The inherent inertia of synchronous generators is frequently absent from RESs, especially wind and solar, which causes frequency variations to occur more quickly and significantly following disturbances. IETs simulate the inertial response of synchronous machines by regulating power converters or utilizing Energy Storage Systems (ESSs) to introduce virtual inertia into the system. By doing this, the Rate of Change of Frequency (RoCoF) is slowed down, and other control systems have more time to react. IETs can enhance the system’s transient reaction to disruptions, like load variations or generator trips, by simulating inertia, which will result in a more stable and dependable functioning. The shift to a cleaner energy mix can be facilitated by power systems accommodating increasing levels of RES penetration without sacrificing frequency stability through efficient inertia emulation. Parallel AC-HVDC transmission line topology has grown in popularity during the last few decades. This strategy lowers losses while boosting transfer capacity. This is a significant conclusion, as the LFC study’s main goal is a minimal tie-line power exchange. LFC is affected by AC-HVDC tie wires connected in parallel. The model lacks parameter computations and numerical expressions. Consequently, it employs the proper mathematical terminology to investigate an accurate HVDC model. This procedure is the same as the one utilized to create AC-HVDC models with the IET. Synchronization coefficients must be established to create an AC-HVDC tie line.

3.2. Compute the Associated Tie-Line Synchronization Coefficients

Two separate capacity areas are defined by the test system: one with a 2000 MW capacity and the other with a 4000 MW capacity. Figure 1 shows the parallel AC-HVDC tie-line system’s ends. The capacity of the AC and HVDC connect lines to transmit up to 200 MW and 600 MW of energy, respectively, is assumed. To demonstrate HVDC power electronic converters, the voltage sources E₁ < θ₁ and E₂ < θ₂ are connected in series with the reactances X₁ and X₂. The bus voltages for the first and the second areas are denoted by the symbols V₁ < θ₁ and V₂ < θ₂, respectively. Figure 4 uses these components to illustrate an electrical equivalent circuit. Power flow over both AC and HVDC tie-lines must be linearized using Equations (2) and (3).

$$\mathit{\Delta }{P}_{tie,AC}={\displaystyle \frac{2\pi T_{tie,AC}}{s}}(\mathit{\Delta }{f}_1-\mathit{\Delta }{f}_2)$$

(2)

$$\mathit{\Delta }{P}_{tie,DC}={\displaystyle \frac{2\pi T_{tie,DC}}{s}}(\mathit{\Delta }{f}_1-\mathit{\Delta }{f}_2)$$

(3)

For AC and HVDC, the matching coefficients for tie-line synchronization are T_tie,AC and T_tie,DC.

$$T_{t\dot{ie},AC}={\displaystyle \frac{P_{AC,max}}{P_{\mathrm{rated}}}}\mathrm{c}\mathrm{o}\mathrm{s}({\delta }_1-{\delta }_2)$$

(4)

$$T_{\mathrm{tie},DC}={\displaystyle \frac{T_{DC1}\times T_{DC2}}{T_{DC1}+T_{DC2}}}$$

(5)

where

$$T_{DC1}={\displaystyle \frac{P_{DC,max}}{P_{\mathrm{rated},1}}}\mathrm{c}\mathrm{o}\mathrm{s}({\delta }_1-{\theta }_1),T_{DC2}={\displaystyle \frac{P_{DC,max}}{P_{ratid,2}}}\mathrm{c}\mathrm{o}\mathrm{s}({\delta }_2-{\theta }_2)$$

To determine the synchronization coefficient, a 50% loaded AC tie-line is assumed.

$$\mathrm{s}\mathrm{i}\mathrm{n}({\delta }_1-{\delta }_2)={\displaystyle \frac{P_{\mathrm{tie},AC}}{P_{AC,\max }}}={\displaystyle \frac{100}{200}}=0.5;({\delta }_1-{\delta }_2)={30}^{\circ }$$

$$T_{\mathrm{tie},AC}=0.0867$$

(6)

The coefficient for the fifty percent loaded HVDC tie-line synchronization, for instance, was calculated as follows:

$$\mathrm{s}\mathrm{i}\mathrm{n}({\delta }_1-{\theta }_1)=\mathrm{s}\mathrm{i}\mathrm{n}({\delta }_2-{\theta }_2)={\displaystyle \frac{P_{tie,DC}}{P_{DC,max}}}={\displaystyle \frac{300}{600}}=0.5$$

Since the claimed capabilities of the two areas are equal,

T_DC1 = 0.2598; T_DC2 = 0.1299

$$T_{t\dot{ie},DC}={\displaystyle \frac{T_{DC1}\times T_{DC2}}{T_{DC1}+T_{DC2}}}=0.0866$$

(7)

Coefficients for HVDC tie-line synchronization can be computed for various loading conditions.

3.3. Using HVDC Tie-Lines with the IET

The HVDC converters’ DC capacitors allow for frequency variations. For LFC, this article depicts one type of strategy. The charging equation may be demonstrated to work with a DC capacitor (C_DC) that has a rated capacity of S_DC and an operating voltage of V_DC.

$$n{C}_{DC}{V}_{DC}^{\circ }{\displaystyle \frac{d}{dt}}\mathsf{\Delta }{V}_{DC}=P_{in}-P_{\mathrm{out} }=P_{\mathrm{tie}, DC}$$

(8)

This is the linearized expression (8) per unit:

$$\left({\displaystyle \frac{n{C}_{DC}}{S_{DC}}}\right)V_{DC}^{\circ }{\displaystyle \frac{d}{dt}}\mathit{\Delta }{V}_{DC}=\mathit{\Delta }{P}_{\mathrm{tie},DC}$$

(9)

The swing Equation (10) for the synchronous machine is used rather than the capacitor charging equation.

$$\left({\displaystyle \frac{2H}{f_o}}\right){\displaystyle \frac{d}{dt}}(\mathit{\Delta }f)=\mathit{\Delta }{P}_m-\mathit{\Delta }{P}_e=\mathit{\Delta }{P}_{SM}$$

(10)

The use of Equations (9) and (10) can articulate it.

$$\left({\displaystyle \frac{n{C}_{DC}}{S_{DC}}}\right)V_{DC}^{\circ }{\displaystyle \frac{d}{dt}}\mathit{\Delta }{V}_{DC}=\left({\displaystyle \frac{2H}{f_0}}\right){\displaystyle \frac{d}{dt}}(\mathit{\Delta }f)$$

(11)

It is possible to obtain the voltage fluctuation formula in (11) by applying the Laplace transformation.

$$\mathit{\Delta }{V}_{DC}\left(s\right)=\left({\displaystyle \frac{2Hs}{n{C}_{DC}{f}_o{\left(V_{DC}^{\circ }\right)}^2}}\right)\mathit{\Delta }f\left(s\right)$$

(12)

The relationship between charging voltage variation and frequency is explained by this equation. Multiplying the tie-line current by the observed voltage yields the power-reference signal. The HVDC tie-line load condition can be used to assign the value “I”. Because of the 50% loading, “I” is set to 0.5. In Figure 5 [24], the IET for the transferring function simulation is further explained.

4. Deregulation for Proposed LFC

ISO uses competitive bidding to determine the supply–demand relationship in the current decentralized electricity markets, and the highest bidders will consult and submit offers to both GENCO and DISCO [27]. The parties will use A DISCO Participation Matrix (DPM) to conduct LFC investigations, with the CPF for the applicable GENCO contract provided in each DPM entry. Each testing area has two DISCOs and two GENCOs. For example, using the DPM:

$$DPM=\left[\begin{array}{cccc}cp{f}_{11}& cp{f}_{12}& cp{f}_{13}& cp{f}_{14}\\ cp{f}_{21}& cp{f}_{22}& cp{f}_{23}& cp{f}_{24}\\ cp{f}_{31}& cp{f}_{32}& cp{f}_{33}& cp{f}_{34}\\ cp{f}_{41}& cp{f}_{42}& cp{f}_{43}& cp{f}_{44}\end{array}\right]$$

(13)

A DPM is composed of GENCO rows and DISCO columns. Consequently, deliberate delegations of jurisdictional authority are known as

$$\mathit{\Delta }{P}_{\mathrm{tie},sch}=P_E-P_I$$

(14)

P_E minus P_I is the quantity of electricity exported or electricity exported less electricity imported. The following is another way to express the tie-line:

$$\mathit{\Delta }{P}_{\mathrm{tie}, \mathrm{error}}=\mathit{\Delta }{P}_{\mathrm{tie}, \mathrm{act}}-\mathit{\Delta }{P}_{\mathrm{tie},sch}$$

(15)

The actual tie-line power due to AC-IET technology for HVDC tie-lines is as follows:

$$\mathit{\Delta }{P}_{\mathrm{tie}, \mathrm{act}}=(\mathit{\Delta }{P}_{\mathrm{tie}, \mathrm{DC}}-\mathit{\Delta }{P}_{\mathrm{IET},1}-a_{12}\mathit{\Delta }{P}_{\mathrm{IET}, 2})+\mathit{\Delta }{P}_{\mathrm{tie}, \mathrm{AC}}$$

(16)

The resulting Area Control Error (ACE) is described using the following equation, which serves as a reference for the input from the controllers:

$$ACE=B_i\mathit{\Delta }{f}_i+\mathit{\Delta }{P}_{\mathrm{tie}, \mathrm{error}}$$

(17)

Unrestricted trades include bilateral, poolco-based, as well as hybrid transactions. As demand changes, the local PBT power plants adjust. Together, the associated GENCOs created the BBT load-type switch. PBT and BBT types can be combined to examine a variety of situations more thoroughly.

5. Techniques for Controller and Optimization Proposed

5.1. The (PI^λ + PI^λf) Controller Based on ANN

Biological neural networks and Artificial Neural Networks (ANNs), a subclass of specialized data-handling networks, are intended to function similarly. In a typical configuration, the neurons act in tandem to complete their jobs. This structure is packed with neurons. In an artificial neural network, two neurons form “connecting links”, which interconnect the other neurons. Because of their assigned significance, these interconnected nodes stand in for the particular data that makes up the input signal. Changing the weight by backpropagation is the only way to solve this challenging problem. An ANN-based closed-loop (PI^λ + PI^λf) controller is shown in Figure 6, which includes this distinctive feature.

The authors make an effort to minimize the inaccuracy of their work because it could be interpreted as a result of the discrepancy between the actual and projected rates of outlier occurrences. To find out the optimal (PI^λ + PI^λf) gains for the system (the ANN has output), the neural network’s connection weights can be iteratively updated using the backpropagation technique. The only way to achieve this is to significantly reduce the speed. The ANN can produce results even if it has not been trained. The neural network’s parameters are taught to the controller via the backpropagation technique. The study employs a three-layer ANN trained using the backpropagation algorithm, where connection weights are iteratively optimized using a suitable learning rate and inertia terms. The tuning of these parameters directly influences error minimization, controller adaptability, and frequency stability in the power system, leading to faster settling times, reduced overshoot, and improved dynamic performance.

Table 2. Summary of Performance Impact.

Parameter	Role in ANN Training	Effect on System Performance
Number of layers (3)	Defines the model’s ability to map nonlinear relationships	More layers → higher learning capacity, but risk of overfitting
Learning rate (η)	Controls weight update magnitude	Too low: slow learning; too high: instability
Backpropagation	Optimization algorithm	Reduces frequency error and settling time
Hidden neurons	Determine feature extraction capability	More neurons improve accuracy but increase computational cost

shows the summary of the performance of the ANN.

5.2. Backpropagation Algorithm

To improve the (PI^λ + PI^λf) controller parameters, a backpropagation technique is employed [28]. Figure 7 depicts a flowchart of the backpropagation algorithm functions which are as follows:

⮚

Step 1: ACE, ∆f, as well as ∆f_ref are used to incorporate the output of the final model into the ANN (Figure 2). A bias input of 1 will result in the proper operation of the system. It is necessary to initialize the weights of the output layer (W⁽³⁾_qj(0)) as well as the hidden layer (W⁽²⁾_ji(0)) using inertia coefficients and learning rate coefficients, respectively.

⮚

Step 2: ∆f(k) and ∆f_ref are used to generate the efficiency index function E(k). To take into consideration the system’s ∆f, the authors set ∆f_ref to zero when creating this scenario.

⮚

Step 3: The authors establish the weights for the hidden layer (W⁽³⁾_qj(0)) as well as the output layer (W⁽²⁾_ji(0)).

⮚

Step 4: The most recent weighting variables (W⁽²⁾_ji(k), W⁽³⁾_qj(k)) and the activation function are used to compute the neural network’s output. With the parameters of a (PI^λ + PI^λf) controller, the ANN yields the most efficient result.

⮚

Step 5: Whether the contract’s conditions (the number of epochs) have been met is confirmed. If this condition is not satisfied, k = k + 1 will be used in step 2.

5.3. The Suggested Adaptive (PI^λ + PI^λf) Controller

Cascade and fractional order are two common controller design types. There are benefits and drawbacks to any concept. Outlining the general advantages of specific architectures is the aim of this article by applying concepts of adaptive and fractional-order policy. In this study, a novel controller configuration—ANN-based (PI^λ + PI^λf)—was used. A few case studies have shown positive results. Some of the fundamental research was incorporated into the construction of this controller.

Allowing for the selection of fractional-order integrators increases the transient response by substituting it with a fractional-order integrator, thereby further improving the simple integral controller. The formula is PI^λ + PI^λf:

$$G_{P{I}^{\lambda }+P{I}^{\lambda f}}=K_{P_i}+{\displaystyle \frac{K_{I_i}}{s^{{\lambda }_i}}}+ K_{P_{if}}+{\displaystyle \frac{K_{I_{if}}}{s^{{\lambda }_{if}}}}$$

(18)

The integral and proportional gains are represented by the symbols K_Ii and K_Pi, respectively. Here, “i” stands for the “ith” area. The order of an integrator is represented by λ. The main advantages of using the ANN-based (PI^λ + PI^λf) controller over traditional fuzzy or PID-based controllers are that it is very fast, produces no overshoots, and produces smooth waveforms. Every parameter’s range is set between 0 and 2. The range for λ is between 0 and 1.5 [19]. Fractional order controllers, such as Fractional Order PI (FOPI) controllers, to tune their fractional orders (λ, λf) use time domain performance criteria and frequency domain restrictions. Gain crossover frequency, phase margin, sensitivity, and complementary sensitivity are among these requirements in the frequency domain; in the time domain, they include integral performance criteria such as ITSE. Although the particular system and control goal will determine how sensitive the system’s performance is to variations in λ and λf, fractional-order controllers often provide more flexibility and the possibility of better performance than integer-order controllers do.

The controllers used in LFC research may be diverse. All controllers, no matter how different, have advantages as well as disadvantages. For the LFC mechanism, a (PI^λ + PI^λf) controller and an input-scaled ANN-based cascading FOPI controller are combined in a new parallel branching manner. ANN-based controllers manage complicated nonlinear systems effectively. Since their inception in the AGC of power systems, fractional-order PI^λf (FOPI^λf) controllers have garnered attention in recent years. Compared to an integral-order classical PI^λ, a fractional-order controller has a number of advantages, including a greater degrees of freedom, adjustable parameters, a wider range of slopes, etc. By allocating the controller’s movable weights, the optimal control activity can also be identified. More encouraging results are obtained when the adaptive control mechanism is included. Figure 8 depicts the intricate controller mechanism. The controller section performance is given below:

• The controller has been tested under various deregulated scenarios—Poolco-Based (PBT), Bilateral-Based (BBT), and Contract Violation-based (CVT)—each introducing unpredictable load changes and renewable energy fluctuations.
• The system consistently maintained frequency stability, minimal overshoot, and fast settling time, indicating strong resilience to parameter uncertainties and load variations that mimic real-world behavior.
• In practice, Renewable Energy Sources (RESs) like solar and wind exhibit intermittent and unpredictable outputs. The study incorporated this uncertainty (fluctuating between 0.005 p.u. and 0.003 p.u.), and the controller adapted effectively using the ANN’s self-learning and adaptive gain-tuning ability, ensuring frequency restoration even under dynamic renewable penetration levels.
• Unlike conventional PI or PID controllers, which require manual retuning for new operating points, the ANN-based controller automatically updates control parameters through continuous learning. This makes it durable in evolving grid conditions, such as varying generation mixes, grid topology changes, or demand surges.

5.4. Optimization Technique

The field of LFC has used a wide variety of optimization algorithms to systematically tune controller characteristics. In this study, the parameters of the suggested ANN-based (PI^λ + PI^λf) controller are optimized using a novel optimization framework called the Quasi-Oppositional Reptile Search Algorithm (QORSA). The literature contains a wealth of metaheuristic techniques for many engineering problems and LFC. This includes a relatively recent metaheuristic method, the Reptile Search Algorithm (RSA). Its high exploitation and exploration properties have been proven among other well-known algorithms. Standard metaheuristic algorithms are surpassed by the RSA in solving a wide range of benchmark functions and difficult engineering problems. Using the quasi-opposite population, the research indicates a high probability of obtaining optimal solutions. In order to achieve a faster rate of convergence towards a global optimal solution, RSA has been improved by integrating quasi-opposition-based learning technologies. Avoiding the local optimum solution’s trap is also beneficial. In order to develop the proposed algorithm, some preparatory research was performed. Drawing inspiration from the cooperative hunting and social activities of crocodiles, the Reptile Search Algorithm (RSA) is a population-based, gradient-free metaheuristic [29]. It contains two stages: an exploration phase that simulates encircling prey, as well as an exploitation phase that reflects focused hunting behavior. Both phases are intended to effectively converge to the global optimum.

The quasi-oppositional learning approach is used to improve the convergence rate as well as search capabilities even further. By producing quasi-opposite solutions for every member of the population, this method enhances the algorithm’s capacity to evade local minima and speeds up overall convergence. Figure 9 shows the steps in the proposed QORSA [26] procedure.

6. Results and Discussion

A few case studies that utilize the new controller are examined in this paper, along with an explanation of the IET-defined HVDC tie-line. The models discussed in the preceding part and the MATLAB/Simulink environment were used to create this configuration. Four independent analyses make up the full analysis: discussion topics include (i) justification for the suggested controller; (ii) impact of an IET-based HVDC tie-line on frequency regulation (BBT), along with sensitivity analysis as well as stability analysis; (iii) contract violation; and (iv) survey of relevant literature. The QORSA ensures excellent performance in every scenario.

6.1. Case Study 1: Justification for the Suggested Controller

The case study is based on the uncontrolled environment of the PBT type and the two-area structure of Section 2. The authors only need to look at Equation (19) to identify the PBT-DPM of interest. Each GENCO is supposed to contribute about the same amount to load variations in its service areas.

$$DPM=\left[\begin{array}{cccc}0.5& 0.5& 0& 0\\ 0.5& 0.5& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]$$

(19)

Fuzzy FOPI, ANN-based PI^λDN, FOPI, fuzzy (PI^λf + PI^λDN), and the suggested adaptive control controller are utilized to record the dynamic performance of the system. With the help of the QORSA,

Table 3. QORSA optimal controller gain values.

Control Parameters	FOPI		Fuzzy FOPI		Fuzzy (PIλ + PIλDN)		ANN-Based PIλDN		Proposed Controller
	A1	A2	A1	A2	A1	A2	A1	A2	A1	A2
KPi	0.0234	0.1847	0.1284	0.5526	1.2568	0.5394	0.3972	0.0749	0.1307	0.0081
KIi	0.1237	0.5842	0.2493	0.1102	1.4335	0.4831	0.1864	0.1435	0.0261	0.0111
KDi	-	-	-	-	1.9104	0.9105	0.0815	0.0047	-	-
KfPi	-	-	-	-	1.6359	1.1047	-	-	0.0824	0.0179
KfIi	-	-	-	-	0.8917	1.0048	-	-	0.0205	0.0014
Ni	-	-	-	-	61.438	62.382	17.218	27.283	-	-
λi	0.48901	-	-	-	1.1891	1.1824	1.4182	1.8327	0.2914	0.0150
λfi	-	0.5934	1.5226	1.4452	0.4605	1.5627	-	-	0.0370	0.2901
K1i	-	-	0.0971	0.1724	0.8790	1.7628	-	-	-	-
K2i	-	-	0.3875	0.0271	0.6864	0.5435	-	-	-	-
w1	-	-	-	-	1.9852	0.5789	0.0896	0.1408	0.1958	0.0022
w2	-	-	-	-	0.8649	1.4072	0.0182	0.1989	0.3147	0.2920

below displays the control settings for each of the controllers in question. Frequency as well as tie-line power are affected by the Step-change in Load Demand (SLD), as seen in Figure 10a–c.

A ±5% error tolerance is used when calculating the settling time. The ability of the suggested controller to effectively generate the required enhanced transient responsiveness is demonstrated by this kind of proof. In terms of error reduction and rising time, QORSA outperforms VPL and WOA. Figure 10d uses the numbers from Table 5 to display the OF against the number of iterations. When adaptive control is used with the suggested controller, improvements become apparent. Table 4 provides a comprehensive study of undershoot, overshoot, as well as settling time.

Table 4. Step-change in load demand for calculating the system’s response.

Controllers		∆f1			∆f2			∆P12			OF
		OS	US(−ve)	TS	OS	US(-ve)	TS	OS	US(−ve)	TS
FOPI		0.057	0.055	99.5	0.028	0.0284	99.59	0.013	0.01281	99.97	4.51
Fuzzy FOPI		0.026	0.028	99.7	0.009	0.0201	99.98	0.005	0.00882	99.92	1.13
Fuzzy (PIλ + PIλDN)		0.005	0.015	6.08	0.003	0.0096	6.360	0.000	0.00319	6.801	9.52 × 10−5
ANN-based PIλDN		0.001	0.012	18.1	0.025	0.0068	11.20	0.000	0.00322	97.02	6.47 × 10−2
Proposed controller	IAE	0.001	0.013	16.1	0.001	0.0088	18.01	0.000	0.00375	38.94	7.18 × 10−2
	ISE	0.001	0.007	22.2	0.000	0.0034	19.01	0.000	0.00145	37.90	6.22 × 10−2
	ITAE	0.039	0.015	12.1	0.040	0.011	17.02	0.039	0.04825	41.31	0.781
	ITSE	0.000	0.012	9.01	0.000	0.0065	13.82	0.000	0.00196	32.75	7.02 × 10−2

Table 4. Step-change in load demand for calculating the system’s response.

Controllers		∆f1			∆f2			∆P12			OF
		OS	US(−ve)	TS	OS	US(-ve)	TS	OS	US(−ve)	TS
FOPI		0.057	0.055	99.5	0.028	0.0284	99.59	0.013	0.01281	99.97	4.51
Fuzzy FOPI		0.026	0.028	99.7	0.009	0.0201	99.98	0.005	0.00882	99.92	1.13
Fuzzy (PIλ + PIλDN)		0.005	0.015	6.08	0.003	0.0096	6.360	0.000	0.00319	6.801	9.52 × 10−5
ANN-based PIλDN		0.001	0.012	18.1	0.025	0.0068	11.20	0.000	0.00322	97.02	6.47 × 10−2
Proposed controller	IAE	0.001	0.013	16.1	0.001	0.0088	18.01	0.000	0.00375	38.94	7.18 × 10−2
	ISE	0.001	0.007	22.2	0.000	0.0034	19.01	0.000	0.00145	37.90	6.22 × 10−2
	ITAE	0.039	0.015	12.1	0.040	0.011	17.02	0.039	0.04825	41.31	0.781
	ITSE	0.000	0.012	9.01	0.000	0.0065	13.82	0.000	0.00196	32.75	7.02 × 10−2

Table 5. Ideal gain values are altered by step load demand.

Gains	WAO		VPL		QORSA
					IAE		ISE		ITAE		ITSE
	Area 1	Area 2	Area 1	Area 2	Area 1	Area 2	Area 1	Area 2	Area 1	Area 2	Area 1	Area 2
KPi	0.38	0.58	0.75	0.801	0.542	0.451	1.464	0.48	0.502	0.661	0.321	0.381
KIi	0.73	0.86	0.73	0.802	0.085	0.687	0.038	0.62	0.025	0.090	0.110	0.043
KfPi	0.95	0.93	0.85	0.896	0.221	0.914	0.143	0.08	0.143	0.066	0.131	0.032
KfIi	0.65	0.97	0.63	0.912	0.038	0.296	0.221	0.05	0.181	0.014	0.161	0.011
λi	0.96	0.76	0.60	0.100	1.374	1.235	1.572	1.81	1.351	1.791	0.131	0.241
λfi	0.97	0.78	0.62	0.102	1.381	1.240	1.580	1.82	1.359	1.799	1.132	0.249
w1	0.48	0.53	0.45	0.083	0.418	0.597	0.981	0.85	0.441	0.141	0.131	0.181
w2	0.32	0.37	0.22	0.347	0.641	0.848	1.464	0.63	0.286	0.450	0.341	0.075

Table 5. Ideal gain values are altered by step load demand.

Gains	WAO		VPL		QORSA
					IAE		ISE		ITAE		ITSE
	Area 1	Area 2	Area 1	Area 2	Area 1	Area 2	Area 1	Area 2	Area 1	Area 2	Area 1	Area 2
KPi	0.38	0.58	0.75	0.801	0.542	0.451	1.464	0.48	0.502	0.661	0.321	0.381
KIi	0.73	0.86	0.73	0.802	0.085	0.687	0.038	0.62	0.025	0.090	0.110	0.043
KfPi	0.95	0.93	0.85	0.896	0.221	0.914	0.143	0.08	0.143	0.066	0.131	0.032
KfIi	0.65	0.97	0.63	0.912	0.038	0.296	0.221	0.05	0.181	0.014	0.161	0.011
λi	0.96	0.76	0.60	0.100	1.374	1.235	1.572	1.81	1.351	1.791	0.131	0.241
λfi	0.97	0.78	0.62	0.102	1.381	1.240	1.580	1.82	1.359	1.799	1.132	0.249
w1	0.48	0.53	0.45	0.083	0.418	0.597	0.981	0.85	0.441	0.141	0.131	0.181
w2	0.32	0.37	0.22	0.347	0.641	0.848	1.464	0.63	0.286	0.450	0.341	0.075

Furthermore, according to Equation (1), Objective Functions (OFs) can be separated into four different categories: IAE, ISE, ITAE, and ITSE. A system’s reaction using all four OFs is displayed in Figure 11a–c. For different OFs, QORSA’s evaluation results of the suggested controller’s control parameters are shown in Table 5. The effectiveness of the suggested controller as well as the system concerning all OFs is shown by the numerical data in Table 4. Following the adoption of ITSE, additional developments in OS, US, as well as TS were seen. ITSE is therefore given more consideration as the primary optimization objective. In this study, the deregulation of the decentralized PBT type is of interest to the authors. Due to its exclusive impact on Area 1, the load shift was similarly distributed among all GENCOs (Figure 11d).

The optimal parameters identified by QORSA significantly enhanced the SLD scenario using the proposed controller. The authors assessed the system’s reaction to the chaotic load variations depicted in Figure 12a using the same optimal settings from Table 3. Figure 12b–d show how the system reacts dynamically to a random load disturbance. The adaptive controller that is suggested performs better than the alternatives.

6.2. Case Study 2: Impact of an IET-Based HVDC Tie-Line on Frequency Regulation (BBT), Along with Sensitivity Analysis and Stability Analysis

A DC capacitor is frequently seen in HVDC converters. Such capacitors aid in frequency regulation. In order to meet IET criteria, this article examines how changing the HVDC tie-line could affect the test setup’s LFC.

The remaining 30% of the load shift in Area 1 is caused by the gas turbine system, and 70% is caused by the thermal power system (GENCO 1). Similarly, hydropower accounts for 40% and thermal power in Area 2 accounts for 60%. Considering the SLD of 0.01 p.u., both sections are compared to the original case study. In the context of BBT, DPMs can be represented by the following Equation (20).

$$DPM=\left[\begin{array}{c}0.2 0.1 0.2 0.1\\ 0.4 0.3 0.4 0.3\\ 0.3 0.2 0.2 0.1\\ 0.1 0.4 0.2 0.5\end{array}\right]$$

(20)

In the first case, the dynamic responsiveness of the proposed system is investigated with the help of an Alternating Current (AC) tie-line. In Scenario 2, the AC tie-line is eventually replaced with a parallel HVDC tie-line that uses AC-IET technology.

Table 6. QORSA’s optimal gain values in different scenarios, with and without an IET-based HVDC.

Control Parameters	Scenario 1		Scenario 2		Scenario 3		Scenario 4
	Area 1	Area 2	Area 1	Area 2	Area 1	Area 2	Area 1	Area 2
KPi	0.1152	0.2441	0.2764	0.0195	0.0690	0.2235	0.4268	0.3817
KIi	0.0417	0.6758	0.0052	0.1642	0.0961	0.8452	0.0259	0.5947
KfPi	0.8839	0.8944	0.8179	0.8454	0.8298	0.8123	0.8179	0.8219
KfIi	0.7487	0.7682	0.7431	0.7528	0.7437	0.7546	0.8245	0.8346
λi	1.6547	1.7891	0.9748	0.8724	1.1219	1.4217	0.7965	0.6645
λfi	1.6782	1.7936	0.9812	0.8819	1.1429	1.4481	0.8150	0.6814
w1	0.1854	0.2437	0.0912	0.2939	0.4932	0.3464	0.7916	0.8431
w2	0.5641	0.7145	0.1675	0.5627	0.1452	0.1459	0.5949	0.3319

shows an investigation’s ideal control parameters. Figure 13a,b display the system’s frequency deviation response for each of the two conceivable outcomes. The results show that undershoot is reduced by 49.52% and 59.04%, respectively, when an IET-based HVDC tie-line is used.

Table 7. Evaluating hypotheses’ efficacy with as well as without an IET-based HVDC tie-line.

Performance		Scenario 1	Scenario 2	Improvement (%)	Scenario 3	Scenario 4	Improvement (%)
OS	∆f1	0.00424	0.00000	100	0.000298	0.000261	12.41
	∆f2	0.00126	0.00000	100	0.000140	0.000120	14.28
US (−ve)	∆f1	0.04917	0.02014	59.04	0.019615	0.01172	40.24
	∆f2	0.044281	0.02235	49.52	0.099116	0.046018	53.40
Ts	∆f1	9.1633	7.4912	18.24	22.62	21.38	5.48
	∆f2	10.2546	8.8520	13.67	23.68	21.33	9.92
OF		0.02031	0.0084	58.64	0.0033	0.0026	21.21

displays these numerical comparisons. The GENCOs’ answer is shown in Figure 13c, and a similar scenario is shown in Figure 13d. Additionally, the authors perform a sensitivity analysis on Scenario 2 to determine how vulnerable it is to changes in the system’s properties. The authors assess the suggested controller’s QORSA-optimized stability by changing the input parameters by ± twenty-five percent of their usual range. A sensitivity study requires the following parameters: the hydro system’s transient droop (T_R and T_RH) parameters, the gas turbine parameters (X, Y, b_g, as well as c_g), the time constant (T_PSi), the power system gain (K_PSi), the thermal turbine constant (T_Ti), and the thermal governor time constant (T_Gi) (see Appendix A). There is a range of 3% to 10% in GRC. Figure 14 displays several GRC values for the tie-line, Area 1, as well as Area 2 frequency deviation. For each GRC, the ideal controller gain values are displayed in Table 9.

The robustness of the proposed ANN-based (PI^λ + PI^λf) controller is shown by the numerical analysis, which is shown in Table 8. As seen in Figure 15, the perturbation has no discernible effect on the system’s closed-loop stability.

Table 8. Investigation of the system’s susceptibility to notable modifications in input parameters.

Change% in Parameter		+25% of Nominal			−25% of Nominal
Parameter		Ts	U.S (−Ve)	O.S.	Ts	U.S (−Ve)	O.S.
TG1	∆f1	15.2234	0.02112	0.0000	14.2941	0.02112	0.0000
	∆f2	15.1562	0.02820	0.0000	14.7182	0.02881	0.0000
	∆Ptie,error	18.6829	0.00000	0.0282	18.6829	0.00000	0.0281
TG2	∆f1	15.3190	0.02104	0.0000	14.1192	0.02103	0.0000
	∆f2	15.4185	0.02892	0.0000	14.3409	0.02889	0.0000
	∆Ptie,error	18.8957	0.00000	0.0282	18.8912	0.00000	0.0282
Tt	∆f1	15.9120	0.02103	0.0000	14.4571	0.02103	0.0000
	∆f2	15.6206	0.02785	0.0000	14.3690	0.02869	0.0000
	∆Ptie,error	18.7647	0.00000	0.0282	18.8734	0.00000	0.0281
TRH	∆f1	15.5729	0.01957	0.0000	14.6724	0.01942	0.0000
	∆f2	15.3482	0.02830	0.0000	14.3782	0.02829	0.0000
	∆Ptie,error	18.6492	0.00000	0.0282	18.6825	0.00000	0.0283
KPS1	∆f1	15.6437	0.02118	0.0000	14.8252	0.02118	0.0000
	∆f2	15.2881	0.02941	0.0000	14.9432	0.02899	0.0000
	∆Ptie,error	18.7690	0.00000	0.0283	18.4622	0.00000	0.0282
TPS1	∆f1	15.5720	0.02135	0.0000	14.7823	0.02092	0.0000
	∆f2	15.6843	0.02884	0.0000	14.4689	0.02889	0.0000
	∆Ptie,error	18.9170	0.00000	0.0283	18.9762	0.00000	0.0282
KPS2	∆f1	15.4857	0.02179	0.0000	14.8755	0.02182	0.0000
	∆f2	15.3049	0.02966	0.0000	14.5373	0.02987	0.0000
	∆Ptie,error	18.9786	0.00000	0.0295	18.3284	0.00000	0.0295
TPS2	∆f1	15.6958	0.02104	0.0000	14.9822	0.02034	0.0000
	∆f2	15.8552	0.02848	0.0000	14.2039	0.02849	0.0000
	∆Ptie,error	18.2384	0.00000	0.0283	18.3748	0.00000	0.0280
TGH	∆f1	15.2874	0.02995	0.0000	14.8729	0.02098	0.0000
	∆f2	15.3276	0.02819	0.0000	14.1278	0.02801	0.0000
	∆Ptie,error	18.4764	0.00000	0.0284	18.3984	0.00000	0.0281
TR	∆f1	15.3746	0.02134	0.0000	14.3948	0.02036	0.0000
	∆f2	15.3981	0.02949	0.0000	14.2837	0.02911	0.0000
	∆Ptie,error	18.7384	0.00000	0.0286	18.4748	0.00000	0.0281
cg	∆f1	15.0372	0.02148	0.0000	14.6562	0.02177	0.0000
	∆f2	15.1348	0.02832	0.0000	14.1457	0.02826	0.0000
	∆Ptie,error	18.3394	0.00000	0.0287	18.2376	0.00000	0.0282
bg	∆f1	15.3287	0.02112	0.0000	14.0924	0.02046	0.0000
	∆f2	15.3893	0.02889	0.0000	14.1396	0.02889	0.0000
	∆Ptie,error	18.9227	0.00000	0.0284	18.1318	0.00000	0.0282
X	∆f1	15.3920	0.01962	0.0000	14.4829	0.02057	0.0000
	∆f2	15.3891	0.02892	0.0000	14.1813	0.02861	0.0000
	∆Ptie,error	18.4734	0.00000	0.0283	18.1570	0.00000	0.0281
Y	∆f1	15.4024	0.02189	0.0000	14.5385	0.02052	0.0000
	∆f2	15.3076	0.02824	0.0000	14.2489	0.02835	0.0000
	∆Ptie,error	18.4280	0.00000	0.0285	18.4829	0.00000	0.0284

Table 8. Investigation of the system’s susceptibility to notable modifications in input parameters.

Change% in Parameter		+25% of Nominal			−25% of Nominal
Parameter		Ts	U.S (−Ve)	O.S.	Ts	U.S (−Ve)	O.S.
TG1	∆f1	15.2234	0.02112	0.0000	14.2941	0.02112	0.0000
	∆f2	15.1562	0.02820	0.0000	14.7182	0.02881	0.0000
	∆Ptie,error	18.6829	0.00000	0.0282	18.6829	0.00000	0.0281
TG2	∆f1	15.3190	0.02104	0.0000	14.1192	0.02103	0.0000
	∆f2	15.4185	0.02892	0.0000	14.3409	0.02889	0.0000
	∆Ptie,error	18.8957	0.00000	0.0282	18.8912	0.00000	0.0282
Tt	∆f1	15.9120	0.02103	0.0000	14.4571	0.02103	0.0000
	∆f2	15.6206	0.02785	0.0000	14.3690	0.02869	0.0000
	∆Ptie,error	18.7647	0.00000	0.0282	18.8734	0.00000	0.0281
TRH	∆f1	15.5729	0.01957	0.0000	14.6724	0.01942	0.0000
	∆f2	15.3482	0.02830	0.0000	14.3782	0.02829	0.0000
	∆Ptie,error	18.6492	0.00000	0.0282	18.6825	0.00000	0.0283
KPS1	∆f1	15.6437	0.02118	0.0000	14.8252	0.02118	0.0000
	∆f2	15.2881	0.02941	0.0000	14.9432	0.02899	0.0000
	∆Ptie,error	18.7690	0.00000	0.0283	18.4622	0.00000	0.0282
TPS1	∆f1	15.5720	0.02135	0.0000	14.7823	0.02092	0.0000
	∆f2	15.6843	0.02884	0.0000	14.4689	0.02889	0.0000
	∆Ptie,error	18.9170	0.00000	0.0283	18.9762	0.00000	0.0282
KPS2	∆f1	15.4857	0.02179	0.0000	14.8755	0.02182	0.0000
	∆f2	15.3049	0.02966	0.0000	14.5373	0.02987	0.0000
	∆Ptie,error	18.9786	0.00000	0.0295	18.3284	0.00000	0.0295
TPS2	∆f1	15.6958	0.02104	0.0000	14.9822	0.02034	0.0000
	∆f2	15.8552	0.02848	0.0000	14.2039	0.02849	0.0000
	∆Ptie,error	18.2384	0.00000	0.0283	18.3748	0.00000	0.0280
TGH	∆f1	15.2874	0.02995	0.0000	14.8729	0.02098	0.0000
	∆f2	15.3276	0.02819	0.0000	14.1278	0.02801	0.0000
	∆Ptie,error	18.4764	0.00000	0.0284	18.3984	0.00000	0.0281
TR	∆f1	15.3746	0.02134	0.0000	14.3948	0.02036	0.0000
	∆f2	15.3981	0.02949	0.0000	14.2837	0.02911	0.0000
	∆Ptie,error	18.7384	0.00000	0.0286	18.4748	0.00000	0.0281
cg	∆f1	15.0372	0.02148	0.0000	14.6562	0.02177	0.0000
	∆f2	15.1348	0.02832	0.0000	14.1457	0.02826	0.0000
	∆Ptie,error	18.3394	0.00000	0.0287	18.2376	0.00000	0.0282
bg	∆f1	15.3287	0.02112	0.0000	14.0924	0.02046	0.0000
	∆f2	15.3893	0.02889	0.0000	14.1396	0.02889	0.0000
	∆Ptie,error	18.9227	0.00000	0.0284	18.1318	0.00000	0.0282
X	∆f1	15.3920	0.01962	0.0000	14.4829	0.02057	0.0000
	∆f2	15.3891	0.02892	0.0000	14.1813	0.02861	0.0000
	∆Ptie,error	18.4734	0.00000	0.0283	18.1570	0.00000	0.0281
Y	∆f1	15.4024	0.02189	0.0000	14.5385	0.02052	0.0000
	∆f2	15.3076	0.02824	0.0000	14.2489	0.02835	0.0000
	∆Ptie,error	18.4280	0.00000	0.0285	18.4829	0.00000	0.0284

Table 9. Optimal controller gain values for different GRCs.

Control Parameters	Proposed GRC 3%		GRC 5%		GRC 7.5%		GRC 9.9%
	Area 1	Area 2	Area 1	Area 2	Area 1	Area 2	Area 1	Area 2
KPi	0.1307	0.0081	0.9063	0.2015	0.0508	0.2402	0.0941	0.4213
KIi	0.0261	0.0111	0.2047	0.3515	0.1860	0.3020	0.0464	0.3337
KfPi	0.0824	0.0179	0.2108	0.3741	0.3290	0.0186	0.1975	0.0820
KfIi	0.0205	0.0014	0.0222	0.3895	0.0132	0.0086	0.0486	0.0030
λi	0.2914	0.0150	0.1209	0.1764	0.0594	0.2041	0.0252	0.2907
λfi	0.0370	0.2901	0.1217	0.1904	0.1430	0.1299	0.1382	0.4655
w1	0.1958	0.0022	0.3113	0.2506	0.1852	0.2540	0.4900	0.0985
w2	0.3147	0.2920	0.1282	0.6165	0.0612	0.0899	0.2860	0.1207

Table 9. Optimal controller gain values for different GRCs.

Control Parameters	Proposed GRC 3%		GRC 5%		GRC 7.5%		GRC 9.9%
	Area 1	Area 2	Area 1	Area 2	Area 1	Area 2	Area 1	Area 2
KPi	0.1307	0.0081	0.9063	0.2015	0.0508	0.2402	0.0941	0.4213
KIi	0.0261	0.0111	0.2047	0.3515	0.1860	0.3020	0.0464	0.3337
KfPi	0.0824	0.0179	0.2108	0.3741	0.3290	0.0186	0.1975	0.0820
KfIi	0.0205	0.0014	0.0222	0.3895	0.0132	0.0086	0.0486	0.0030
λi	0.2914	0.0150	0.1209	0.1764	0.0594	0.2041	0.0252	0.2907
λfi	0.0370	0.2901	0.1217	0.1904	0.1430	0.1299	0.1382	0.4655
w1	0.1958	0.0022	0.3113	0.2506	0.1852	0.2540	0.4900	0.0985
w2	0.3147	0.2920	0.1282	0.6165	0.0612	0.0899	0.2860	0.1207

6.3. Case Study 3: Contract Violation

DISCOs typically try to use their position for more significant goals when they break contracts. In certain areas, all emergency power would be supplied by the GENCOs. The Area 1 DISCOs are presumably asking for a 0.05 p.u. increase over the section’s base rate (0.01 + 0.005). Production at both GENCOs has been modified to meet client demands. From 10 s to 20 s, the RES runs and adds 0.005 p.u. to the simulation. Following that, RESs will supply any extra power required during this time, while conventional sources will once more supply the predetermined amount of power. After the experiment’s 20 s, the generation is expected to drop from 0.005 p.u. to 0.003 p.u. Due to the uncertainty of the RESs, the remaining 0.002 p.u. will be divided evenly between GENCOs 1 and 2 during this period. Both Scenarios 3 and 4—with and without the HVDC connecting line—are analyzed. RESs with intermittent output, however, are noticeably less transiently reactive than HVDC tie-lines based on IET. Both the frequency response as well as the GENCOs’ reaction to this hypothetical situation are depicted in Figure 16. The high load variations and different levels of RES penetration for 5%, 10%, 15%, and 25% are displayed in Figure 17.

6.4. Case Study 4: Survey of Relevant Literature

Additionally, by examining previous studies, the efficacy of the suggested QORSA-optimized controllers based on ANN-based (PI^λ + PI^λf) controllers is evaluated [30]. A salp swarm was used to optimize the PIDF (1 + FOD) controller that the authors employed in their research. The suggested LFC approach may be employed in place of a salp swarm-optimized PIDF (1 + FOD) controller to restore the system’s original frequency response.

Figure 18 shows the system’s dynamic response. The numerical study’s findings, which are shown in

Table 10. Comparing the proposed controller to [30].

Performance Terms		Reference [30]	Proposed Controller	Improvement (%)
OS	∆f1	0.003266	0.0000000	100
	∆f2	0.002076	0.0000000	100
	∆P12	0.000821	0.0000000	100
US (−Ve)	∆f1	0.011600	0.0114429	1.35
	∆f2	0.004970	0.00548245	−10.31
	∆P12	0.004721	0.00233316	50.57
Ts	∆f1	9.0973	7.02252	22.80
	∆f2	16.8061	8.51215	49.35
	∆P12	19.2226	9.43779	50.90
OF		0.0002435	0.0001542	36.67

, demonstrate that the recommended controller enhanced the transient behavior. This demonstrates the adaptability of the suggested controller to various types of testing equipment.

The two-area thermal power plant, hydro power plant, and gas power plant test system in a decentralized setting was modeled using the previously described findings and debates. An IET-based HVDC tie-line reduces overshoot by 100% (Area 2 frequency deviation, such as ∆f₂) and 100% (Area 1 frequency deviation, such as ∆f₁). On the other hand, the findings show that the IET-based HVDC tie-line preserves the power system’s nominal values admirably. In the context of Poolco-Based Transactions (PBTs), Bilateral-Based Transactions (BBTs), as well as Contract Violation-based Transactions (CVTs), all of the major GENCOs actively participate in the decentralized power system. When SLD is considered, the suggested controller outperforms the most widely used alternative settings. The IEEE-39 bus system is modified with the addition of RESs [31]. The three control regions that comprise the IEEE-39 bus system are seen in Figure 19. Figure 20 shows how the IEEE-39 bus system responds to changes in frequency in Areas 1, 2, and 3. Using the proposed ANN-based (PI^λ + PI^λf) controller in the modified IEEE-39 bus system with real-time load variations is demonstrated in this example.

7. Conclusions

This research presents a new control setup for the suggested LFC technique in a decentralized two-area power system that uses RESs. The authors have examined the impact of the redesigned HVDC tie-line on the system under test. In order to determine the individual parameters of the suggested controller based on the ITSE performance index, the research used the efficient QORSA technique, which significantly improved the controller’s overall performance as well as system stability. The stability and overall precision control performance of the tested system are improved using a novel ANN-based (PI^λ + PI^λf) controller. Even random load disturbances can be resisted by the ideal parameters produced by the QORSA approach. Every potential deregulation scenario, including PBT, BBT, as well as CVT, has been validated by this study. By contrasting the controller’s performance with recently published work, it has also been verified that the suggested control technique enhances performance. The recommended controller fared better than the other controllers in the comparison because of its benefits, which included better noise reduction and faster rejection of disturbances. The QORSA is a popular technique for control setting optimization that is successful in lowering the Figure of Demerit (FOD). The key findings of the proposed method are:

• By adopting an IET-based HVDC tie-line, undershoot is reduced by 49.52% and 59.04%, respectively, according to the results.
• With an IET-based HVDC tie-line, overshoot is reduced by 100% in Areas 1 and 2 (frequency in Area 2, i.e., ∆f2, as well as frequency in Area 1, i.e., ∆f1).
• However, the results show that the IET-based HVDC tie-line performs admirably in preserving the power system’s nominal values.
• Lastly, a modified three-area IEEE-39 bus system is used to test the compatibility of the suggested controller, which has been tweaked by QORSA. In the IEEE-39 bus test system, the controller demonstrates effectiveness in handling real-time load variations.

In light of the growing number of problems with modern power systems, this work aimed to examine the effectiveness, efficiency, as well as versatility of the proposed QORSA-optimized ANN-based (PI^λ + PI^λf) controllers for LFC mechanisms. The growing popularity of electric cars, energy storage systems, as well as smart grid ideas may improve this research in the future.