Robust Secondary Controller for Enhanced Frequency Regulation of Hybrid Integrated Power System

Abstract

This present article examines the frequency control of a dual-area interconnected hybrid power system that integrates conventional as well as non-conventional sources with additional support from electric vehicles. The complicated, non-linear behavior of the system adds to the grid’s already high level of complexity. To navigate this complex environment, it becomes essential to develop a resilient controller. In this respect, a robust secondary controller is developed to handle the problem. The controller is developed while taking into account the intricate design of the contemporary power system. An extensive comparison between well-established controllers is presented to verify the efficacy of the proposed controller. An AI-based optimization technique, namely, COVID-19, is employed to obtain optimal values for different parameters of the controller. This work also investigates the effect of the FACTS device as a static synchronous series compensator (SSSC) on the dynamics of the system. Moreover, it also investigates the role of electric vehicles (EVs) and an SSSC on system stability. Further, the developed system is subjected to significant load variations and intermittent solar and wind disturbances to check the response of the optimal controller under dynamic conditions. The results demonstrate that the proposed controller reactions successfully handle system disturbances, highlighting the strength of the proposed controller design. Lastly, a case study on an IEEE-39 bus system is carried out to check the optimality of the proposed secondary controller.

1. Introduction

Addressing the increasing global energy demand requires integrating different generating units through existing transmission lines. Managing such an expansive interconnected power system amid growing size, complexity, and unpredictable disruptions poses a formidable task for power system engineers. Further, the unpredictability and randomness of load demand may lead the system dynamics to deviate unexpectedly. Hence, ensuring effective load frequency control (LFC) is paramount to maintaining these dynamics within limits [1,2]. Inadequate LFC systems for massive interconnected power systems can compromise system responses, potentially leading to instability. Therefore, this article aims to establish an LFC system in a hybrid power system (HPS), addressing these critical concerns.

1.1. Related Literature

Elgerd et al. [3] pioneered the initial endeavor in load frequency control (LFC) within a multi-area power system (MAPS). Saika and team [4] further applied the principles introduced by [3] to investigate LFC challenges across multiple MAPSs. The study published by [5] extensively delved into employing MA thermal systems for LFC operations, emphasizing the incorporation of system non-linearities essential for practical implementation. The inclusion of specific non-linearities, such as the generation rate constraint (GRC) and governor dead band (GDB), has been a focus. Thermal and hydro units currently stand as primary sources of power. Ref. [6] showcased the LFC problem, emphasizing hydro units with applicable GRC. Meanwhile, investigations by [7] explored LFC concerns caused by system non-linearities. The introduction of time delay, along with GRC and GDB, for MAPS is shown in [8]. The discussions in [3,4,5,6,7,8] predominantly centered on LFC problems within non-renewable sources. However, factors like population surges and increased industrialization have strained existing power systems. With fossil fuel reserves depleting rapidly, researchers advocate integrating renewable energy-based units into the current setup [9,10]. Renewable sources, notably wind and solar energy, known for their eco-friendliness and escalating performance, hold prominence in LFC analyses [11]. The authors in [12] extensively examined the role of renewable energy sources (RESs) in effective frequency control. Frequency mitigation in wind systems is demonstrated in [13]. Farooq et al. [14] explored the utilization of solar thermal systems (STSs) for LFC in MAPS. From the above literature, limited authors have presented studies on MAPSs with renewable sources and system non-linearities. Hence, this awaits further investigation.

Conventional transportation vehicles and thermal power plants contribute significantly to harmful carbon emissions, affecting the atmosphere. Electric vehicles (EVs) offer a promising alternative to mitigate these emissions, as highlighted in [15]. Their widespread adoption not only aids in grid frequency regulation but also reduces the load on traditional power generating units, as discussed in [16]. Another study [17] emphasizes the significance of EVs and their capacity management within MAPSs. The use of EVs in frequency regulation with emission depletion abilities is shown by the authors in [18]. A MAPS with optimal EV location is reported in [19] The existing literature underscores the evolving research landscape concerning EV integration into the current power system.

Energy security is a pivotal aspect of a nation’s development. Establishing connections among diverse networks aims to lower the overall cost of power while simultaneously enhancing the reliability and security of these systems. Employing technologies like FACT devices serves the purpose of bolstering system stability and optimizing the efficiency of the existing infrastructure. In this respect, the authors aim to utilize one of the FACT devices in an already existing MAPS.

The inclusion of system non-linearities adds realism to the power system but introduces undesired oscillations. Furthermore, the unpredictable fluctuations in wind speed and load demand contribute to uncertainty within the system. To mitigate the impact of these oscillations and uncertainties, the implementation of a robust controller becomes essential to alleviate disruptive influences [20,21]. In this respect, the authors aim to investigate an advanced multistage controlling strategy in an MAPS, as multistage controllers have been very effective in handling the above-mentioned hindrances [20,21].

The effective performance of the controller hinges upon securing the most suitable gain values to ensure stable operation. Optimal adjustment of these gains is critical for efficient functioning of MAPSs. Attaining the best possible values for these gains is vital to maintain stability within the controller’s operation. Employing suitable optimization methods is a key approach to achieve this goal, with meta-heuristic-based optimization techniques proving highly effective. In this regard, the authors have made an attempt to employ a novel COVID-19-based optimization technique in power system studies, as the COVID-19 technique performed exceptionally well on different test functions when compared with already established optimization techniques [22]. The controller gains’ resilience, initially obtained under normal conditions, undergo validation using a robustness test, a method well-documented in the existing literature. Numerous studies have been employed to assess various controllers. Additionally, the identified optimal controller gains must exhibit robustness when subjected to such changes.

1.2. Motivation

The analysis underscores that in traditional power systems, managing LFC seems relatively straightforward due to disruptions being limited to the load side. However, the surging prominence of solar and wind energy emphasizes the pressing requirement to integrate the mentioned sources into power systems. Of particular interest are electric vehicles (EVs). FACTSs are crucial components within today’s power systems. As renewable sources multiply, system complexity increases, rendering the system more reliable yet simultaneously introducing uncertainties. Consequently, controlling the system is a formidable challenge, with classical regulators falling short in delivering satisfactory performance. In such a scenario, a robust controller becomes imperative for optimal functionality within the dynamics and control of regulated environments. This study endeavors to establish an effective method for frequency control in an EV-centered MAPS, leveraging FACTS devices for secondary frequency control, employing a novel COVID-19-based optimization technique.

1.3. Contribution

The primary contributions of the current study involve:

• The application of a novel COVID-19-based optimization technique for controller gain optimization.
• This article illustrates the preliminary application of a double-derivative-based multistage controlling action for concurrent regulation of frequency and tie-line power.
• The EVs are integrated with both areas of a hybrid power system for enhancing the dynamic stability.
• Finally, the effect of an SSSC as an FACT device in addition to EVs for frequency stability is also presented.

1.4. Objectives

Based on the preceding conversation, the aims pursued in the current study are as follows:

• To assess the effectiveness of the COVID-19 algorithm in handling objective function convergence in an MAPS by comparing it with orthodox optimization methods.
• Develop and validate a resilient double-derivative-based multistage control strategy. This approach, in contrast to the typical control techniques outlined in prior research, intends to increase the operating efficiency of the integrated power system by controlling frequency and tie-line power simultaneously. Then, confirm its effectiveness through empirical validation, being sure to distinguish it from already recognized control techniques.
• Use realistic situations such as random load deviations and renewables’ intermittent nature to test the robustness of the optimized controller gains of the robust optimal controller developed.
• To evaluate the impact on system performance with inclusion of modern electric vehicles (EVs) and the static synchronous series compensator (SSSC) device. The goal is to assess how these contemporary technologies improve system performance in general and frequency stability in particular.

2. Modeling of the System and Electric Vehicle

2.1. Multi-Area Power System (MAPS)

For our analysis, we have chosen a multi-area power system (MAPS) that is unbalanced. Here, two areas are considered, where area 1 incorporates a conventional thermal plant (CTP), solar thermal systems (STSs), and electric vehicles (EVs). The participation factor being 60 percent from CTP, 30 percent from STS and 10 percent from EVs. The second area comprises a CTP, wind turbine systems (WTSs), and EVs. The participation factor is 60 percent from the CTP, 30 percent from the WTSs, and 10 percent from EVs. The major participation is given to the CTP considering the practical scenario, as the majority of electricity is being produced by them. The aim of incorporating these renewables and EVs into the developed system is to bring current trends into the power system. As the number of EVs increases, harmonics are introduced into the system, possibly resulting in problems with power quality, an erroneous depiction of the system’s dynamic responsiveness, and the need for more complicated harmonic mitigation for practical uses. Figure 1 shows the developed MAPS model for investigation. The thermal plants in both areas are equipped with non-linearites like a GRC rate of 3% per minute and GDB rate of 0.06%. This is to exhibit the practicality in the developed MAPS and preserve realism. All the simulations and execution of codes (optimization technique) are performed in a MATLAB Simulink platform. A 1:2 capacity ratio has been considered between the two areas. The fundamental system specifications (transfer function parameters of the system as well as generation sources) were taken from references [4,14]. Our study focuses on minimizing an objective function via the integral squared error (ISE), as defined in Equation (1).

$$ISE=\underset{0}{\overset{T}{\int }}(\Delta f_i^2+\Delta P_{tiei-j}^2)dt,i=1,2$$

(1)

2.2. Electric Vehicles (EVs)

The simulation model utilized for EVs in the current analysis is depicted in Figure 2. Within this model, the responsibility of handling power interchange between the grid and the EV battery lies with the battery charger. An important aspect of EVs in grid integration is their ability to adapt batteries for frequency mitigation. The incorporation of EVs into the grid involves the utilization of bi-directional power electronic converters (BPECs).

Potential scenarios can happen where EVs unexpectedly disengage from the gird, thereby causing unsatisfactory frequency outcomes that are detrimental to the power system. To mitigate such risks, the frequency is constrained within ±10 mHz. The performance of an EV is intricately linked to its charging/discharging behavior, which significantly affects the regulatory duty assigned to the EV [16]. EVs involved in regulatory operations usually need a significant amount of time to recharge their batteries to the desired capacity. Any power imbalance is divided into two segments, as all power-generating units, EVs included, play a role in regulation. Part of the regulatory task is shared among all sources in a specific area, while the rest is managed by the battery charger module (BCM). The droop coefficient value, denoted as $R_{EV}$, is specified as 2.4 Hz/MW. The largest and least power outputs are expressed as $P_{AG}^{max}$ and $P_{AG}^{min}$, respectively, as given in (2) and (3).

$$P_{AG}^{max}=+({\displaystyle \frac{1}{N_{EV}}})(\Delta P_{EVi})$$

(2)

$$P_{AG}^{min}=-({\displaystyle \frac{1}{N_{EV}}})(\Delta P_{EVi})$$

(3)

3. Multistage Proportional–Integral–Double Derivative (MSPIDD) Controller

To establish an efficacious secondary controller for a contemporary power system, certain criteria need to be met:

• Capable of responding efficiently to fluctuations in load.
• Resilient in the face of uncertainties related to renewable energy sources.
• Adaptable to diverse situations through flexible tuning mechanisms.

Due to the straightforward design, consistent operation, and efficient performance at an affordable price, the traditional PID controller and its many control structures continue to be a popular choice among academics. The PID controller is notable as being the most extensively used control method in industrial settings. It is a reliable and simple to understand controller that can provide excellent control outcomes even when a process or plant has a variety of dynamic variables. PID controllers, as the name suggests, operate in three different modes: proportional, integral, and derivative, allowing for flexible functioning. The intricacy of achieving the best state can occasionally be a problem with the traditional PID arrangement though. The intrinsic balance that exists among the integral and derivative components is the cause of this problem.

The problem may be remedied by increasing the controller’s integral component, which reduces the steady-state error. However, this method may cause unfavorable system behavior while it is in use. Moreover, achieving optimal performance is sometimes made more difficult by the complex balance between the integral and derivative gains necessary in a PID controller’s design.

As an illustration, enhancing the integral gain to mitigate steady-state error leads to an unfavorable reaction during the system’s transient phase. Ideally, the integral component must exclusively function within the steady-state segment of the response, serving to minimize or eliminate steady-state error. This objective can be accomplished through the utilization of a multistage PID controller configuration, incorporating an initial PD controller stage followed by a subsequent PI controller stage. The performance can be further improved by adding the derivative component in the second stage, thereby leading to an MSPIDD controller, as depicted in Figure 3. The controller receives the area control error (ACE) as its input. On the other hand, the ‘O’ symbolizes the regulated output from the controller, which is subsequently supplied to the plant under its control. The optimization of MSPIDD controller gains is achieved through the utilization of the COVID-19 technique. The objective is to minimize the ISE value as defined in (1), while adhering to the constraints outlined in Equation (4).

$$\begin{array}{c}\hfill K_p^{min}\le K_p\le K_p^{max}\\ \hfill K_i^{min}\le K_i\le K_i^{max}\\ \hfill K_d^{min}\le K_d\le K_d^{max}\\ \hfill N_i^{min}\le N_i\le N_i^{max}\end{array}$$

(4)

where $K_p$, $K_i$, and $K_d$ are the respective gains of the MSPIDD controller and N is its filter coefficient. The optimization range for gains is set between 0 and 1, while the range set for N is 1 to 100.

4. COVID-19 Optimization Algorithm

This part outlines the approach behind the COVID-19 algorithm. The COVID-19 algorithm is formulated based on identified containment factors. The succeeding subsections elaborate on the attributes to be estimated within the framework of the COVID-19 technique.

4.1. Initial Population

The starting point involves a starting population comprising ‘n’ individuals (rows) and ‘p’ parameters (columns). Within this population, there exists one impacted individual known as patient zero (PZ). The assumption is PZ transmits infection to a portion of the population. Initially, a stochastic process is employed to contaminate specific people within this population. Subsequently, a matrix $x(n,p)$ is generated utilizing (5).

$$x(n,p)=L_l+random(n,p)\times \{U_l-L_l\}.$$

(5)

The solution’s upper and lower limits, denoted as $L_l$ and $U_l$, respectively, are contingent upon the specific problem parameters. Consequently, normalizing the starting matrix becomes imperative for subsequent calculations, given the variability in these upper and lower limits. The normalization process for the starting matrix $x(n,p)$, accomplished through (6), yields the matrix $x_{norm}(n,p)$:

$$x_{norm}(n,p)={\displaystyle \frac{x(n,p)-min\left(x\right)}{max\left(x\right)-min\left(x\right)}}.$$

(6)

4.2. Containment Factors (CFs)

The CFs revolve around the infection transmission dynamics of COVID-19. These CFs primarily involve (a) practicing social distancing (SD), (b) utilizing masks, and (c) computing the antibody rate. Following PZ’s infection spread within the population, an assessment of the containment factors is conducted for each individual. The subsequent section delves into a mathematical representation of each CF.

4.2.1. Social Distancing (SD)

In the context of COVID-19 infection, isolating an impacted person from the broader population is crucial to curtail the infection spread. This study adopts a comparable strategy following the initial infection. Each individual undergoes evaluation for the social distancing (SD) factor. A matrix dedicated to SD is constructed, illustrating the parameter distances within the population. Simplistically, the distance (D) can be computed using the formula displayed in (7).

$$Distance\left(\mathit{D}\right)=i-j;i\ne j.$$

(7)

The $x_{norm}(n,p)$, as defined in (6), serves as the basis for computing the SD factor. The SD matrix (9) is constructed using $x_{norm}(n,p)$. This SD matrix delineates parameter distances, featuring dimensions of n × j × p.

$$\begin{array}{c}{x}_{norm}(n,p)\end{array}=\left[\begin{array}{cccc}{x}_{norm11}& x_{norm12}& \dots & x_{norm1p}\\ x_{norm21}& x_{norm22}& \dots & x_{norm2p}\\ |& |& |& |& |\\ x_{normn1}& x_{normn2}& \dots & x_{normnp}.\end{array}\right]$$

(8)

$$SD(n,j,p)=\{x_{norm}(n,p)-x_{norm}(j,p)\};j=1:n,n\ne j.$$

(9)

When an individual breaches SD norms and comes into near proximity to an impacted person, there is a heightened risk of infection, represented as the infection rate (IR). The IR is influenced by the SD factor; as the SD factor increases, the IR decreases. The threshold distance (TD) defines the proximity below which infection transmission can occur due to SD violations. Adhering to World Health Organization (WHO) guidelines, the practical TD value is standardized between 0 and 1, wherein 0 signifies the lowest TD value and 1 indicates the maximum (6 feet). In this study, $\rho SD$ denotes the social distancing probability, representing the normalized practical distance, within the range 0 to 1. Figure 4 provides a visual representation illustrating the influence of SD on the infection rate (IR).

4.2.2. Use of Masks

Surgical masks are effective in obstructing the dissemination of respiratory droplets, offering increased protection against the spread of diseases. Upon exposure to COVID-19 through contacts (where SD is less than TD), individuals become susceptible to infection at a rate denoted as µR. The calculation for µR is determined based on $R_0$, as indicated in (10).

$$\mu R={\displaystyle \frac{R_0}{T_{infection}}}.$$

(10)

Therefore, (DPR) linked to mask utilization within an ‘n × p’ population can be expressed as (11):

$$DPR(p,j,n)=\mu R\{1-SD(n,j,p\left)\right\}.$$

(11)

Suppose a group consistently adheres to wearing masks. Denoting ${\eta }_m$ as the effectiveness in impeding COVID-19 spread, the collective infectious spread and recovery rates can be assessed through Figure 5. The schematic is represented in Figure 5, the equation for (DPR), articulated in (11), is further adapted to define the MIR (12):

$$MIR(p,j,n)=\mu \times R\{1-SD(n,j,p)\}-\{SD(n,j,p)+{\eta }_m{x}_{norm}(n,p)\}.$$

(12)

Let $\rho M$ represent mask usage probability, indicating the normalized measure within the range of 0 to 1. If an individual exhibits SD and MIR values higher than $\left(\rho SD\right)$ and $\left(\rho M\right)$, respectively, they are considered susceptible to reinfection. Subsequently, the individuals undergo evaluation for AR, assessed through the following AR factor.

4.2.3. Antibody Rate (AR)

Earlier research showed the utilization of T-immune cell responses to combat influenza. In the current model, we examine the capability of T-immune cells to suppress COVID-19. Within this study, the AR within population $x_{norm}(n,p)$ (6) is computed according to (13):

$$AR(n,j,p)=x_{norm}(n,p)\{r(1-{\displaystyle \frac{x_{norm}(j,p)}{K}})-(c+1)\}.$$

(13)

Figure 6 illustrates the process of T-cells eliminating infected cells within the human body. Represented on a scale from 0 to 1, $\rho AR$ signifies an individual’s antibody rate probability. A value of 0 designates the minimum infection-cell killing rate through an individual’s immune response, while a value of 1 represents the maximum infection-cell killing rate. Consequently, individuals surpassing the $\rho AR$ threshold are deemed recovered. Among the recovered population, the individual boasting the largest AR value is regarded as the healthiest. The said technique was developed by the authors in [22]. Their work developed the optimization technique based on the coronavirus infection. The flowchart detailing the COVID-19 algorithm is presented in Figure 7.

4.3. Validation of COVID-19 Technique

The validation of the COVID-19 technique involves a comparative analysis with other reputed optimization methods to determine its efficacy. A similar MAPS with a PID controller as a secondary controller is considered for each optimization technique while evaluating the system performance (convergence). The optimization techniques chosen for comparison are arithmetic optimization algorithm (AOA) [23], magnetotacti bacteria optimization (MBO) [24], grey wolf optimization (GWO) [25], and satin bowerbird optimization (SBO) [26]. The MAPS, integrated with a PID controller, is individually simulated using each specified optimization technique, and the resulting convergence curve is documented and displayed in Figure 8. The characteristics presented in Figure 8 clearly indicate that COVID-19 exhibits superior performance with improved convergence features and the lowest ISE value, serving as the objective function for system optimization. Consequently, the COVID-19 algorithm was implemented for further optimization.

5. Result and Discussion

The study employs the MATLAB Simulink software (2018) to simulate the MAPS and execute optimization codes. It specifically addresses the concurrent control of system dynamics, including frequency and tie-line power. In this system, a 1 percent disturbance is introduced to area 1 at time t = 1 s for nominal system conditions. Throughout the analysis, the objective function is the ISE (integral square error).

5.1. Secondary Controller Selection

This results part focuses on choosing the most effective secondary controller from various options for mitigating frequency fluctuations in an MAPS. The controllers under consideration—PID, MSPID, and the newly proposed MSPIDD—are individually evaluated. The COVID-19 technique is employed to adjust the gains of these controllers, aiming to minimize the integral square error (ISE), serving as the primary objective in this study. Simulations of the MAPS are conducted with above-mentioned controllers. The system dynamics are obtained and depicted in Figure 9. Upon analyzing Figure 9, it becomes evident that the proposed MSPIDD controller exhibits superior performance, showcasing the optimal handling of the MAPS dynamics.

The MSPIDD controller introduced effectively minimizes system deviations, significantly reducing overshoots and undershoots compared to both PID and MSPID. It ensures that system fluctuations converge swiftly to zero steady-state values. Additionally, the MSPIDD demonstrates rapid damping of responses when compared to PID and MSPIDD strategies.

Moreover,

Table 1. Controller ISE values.

Controller	ISE Value (Objective Function)
PID	0.00090
MSPID	8.016 × 10−5
MSPIDD	2.980 × 10−5

shows the achieved ISE values for each controller, clearly indicating that the MSPIDD controller exhibits the lowest ISE, a highly favorable outcome for power system stability. Notably, a smaller ISE signifies superior overall system performance, underscoring the minimal system deviations achieved by the MSPIDD controller. Additionally, the entries in

Table 2. Inferences from Figure 9.

Parameter	Controller	HU	HO	RST
$\Delta f_1$	PID	−0.0238	0.0129	18.1
	MSPID	−0.0095	0.0068	16.2
	MSPIDD	−0.0051	0.0029	7.05
$\Delta f_2$	PID	−0.0106	0.0003	23.2
	MSPID	−0.0039	0.0023	16.3
	MSPIDD	−0.0014	0.0006	8.96
$\Delta P_{tie}$	PID	−0.0009	0.0013	20.3
	MSPID	−0.0042	0.0027	17.6
	MSPIDD	−0.0021	0.0011	11.9

for the recorded values of highest overshoot (HO), highest undershoot (HU), and response settling time (RST) further validate the superiority of the MSPIDD controller among the compared secondary control methods.

5.2. Resilience of the Controller to Uneven Load Disruptions

In a practical power system, the uncertain nature of load demand necessitates the incorporation of practical considerations into the developed MAPS. To emulate this unpredictability, random load disturbances (RLDs) are introduced in area 1, as illustrated in Figure 10a. The system’s performance is evalutaed under these conditions, considering the MSPIDD secondary controller. Simulations of the RLP-integrated MAPS are conducted, and the resulting system responses are visible in Figure 10b–d. Notably, the evaluation of these responses underscores the superior effectiveness of the proposed MSPIDD controller in handling random disturbances and maintaining the system dynamics under stable limits.

5.3. Influence of EVs in MAPS

In contemporary times, EVs are increasingly utilized as conventional energy sources rapidly diminish. The swift characteristics of EVs have notably enhanced power system dynamics, showing their positive impact. To determine the performance of EVs within the MAPS, one quantity of EVs is linked independently to each control area. Simulation of the MAPS integrated with EVs is conducted, and the corresponding outcomes are obtained and illustrated in the accompanying Figure 11. Figure 11 illustrates a contrast in the system dynamics observed in both areas against the nominal system responses (depicted in Figure 9), where EVs are not linked. The responses clearly indicate that EVs contribute significantly to enhancing various system characteristics, with a notable impact on system stability in particular. Moreover, the undershoot, overshoot, and settling time in Figure 11 substantiate the superior performance achieved with the incorporation of EVs in the system. This enhanced performance is attributed to the supportive role of EVs as energy storage devices, effectively addressing high-frequency elements present in the MAPS.

5.4. Impact of Static Synchronous Series Compensator (SSSC) FACTS Device

The SSSC functions as a series flexible AC transmission system (FACTS) device, and is employed for regulating the system dynamics. Its primary purpose is to mitigate oscillations within the system. The transfer function model of the SSSC utilized in the current study is depicted in Figure 12.

The MAPS is augmented with a static synchronous series compensator (SSSC), as illustrated in Figure 1. The optimization of the MSPIDD controller parameters is once again conducted using the COVID-19 algorithm. The transfer function model of the SSSC is considered. The SSSC parameters are referenced from [27], where $T_1=0.2587$, $T_2=0.2481$, $K_{SSSC}=0.2035$, and $T_{SSSC}=0.03$ s. The dynamic responses of the MAPS are obtained and displayed in Figure 13. The obtained responses are contrasted with those of the standard system in the absence of the SSSC. Evidently, the integration of the SSSC as an FACT device in the MAPS results in significantly improved performance. The conducted analysis underscores the positive impact of incorporating FACTS devices in the present MAPS, leading to enhanced performance in terms of oscillation depletion, overshoot reduction, and settling time enhancement. This supports the recommendation to include an SSSC in MAPSs to enhance overall system performance.

5.5. Combined Impact of EV and SSSC as FACTS Device in MAPS

This investigation involves the integration of both an FACTS device (SSSC) and electric vehicle (EV) into the MAPS. The investigation is carried out in the presence of an optimal MSPIDD controller. The same complete setup along with the position of the EV and SSSC can be seen in Figure 1. The optimization of the MSPIDD controller parameters, viz., $K_p$, $K_i$, $K_d$, and the filter coefficient (N), are again conducted using the COVID-19 technique. The dynamic response achieved for the mentioned combination (both EV and SSSC included) is depicted in Figure 14. Upon critically analyzing Figure 14, it becomes evident that the LFC system exhibits its most favorable performance when incorporating the combination of EV and SSSC. This is attributed to the effective mitigation of high-frequency components within the power system by EVs and SSSCs, consequently leading to a reduction in the regulation processes typically handled by generation components. They both improve the stability of the MAPS, which is clearly visible in Figure 14.

5.6. Sensitivity Evaluation (SE)

An SE is utilized to evaluate the robustness of the MSPIDD controller gains when the system parameters undergo variations, deviating from their nominal state. The SE process involves monitoring the dynamic behavior of the MAPS. In order to execute the SE, the MAPS is subjected to uneven solar input, as depicted in Figure 15a, along with variations in wind inputs, illustrated in Figure 16a.

The MSPIDD controller gains are adjusted for each modified situation. The system responses obtained with the newly adjusted controller gains for each altered scenario are referred to as real-time responses (blue dotted). In contrast, the responses obtained with the previously adjusted MSPIDD controller gains under the nominal system conditions are labeled offline responses (black color).

The recorded results pertaining to solar variations are shown in Figure 15b–d, whereas the responses associated with changes in wind speed are illustrated in Figure 16b–d. A comprehensive examination of Figure 15 and Figure 16 underscores the robustness of the suggested MSPIDD controller, evident in the similarity of responses to those obtained under nominal conditions. Hence, the optimized gains for the proposed MSPIDD controller eliminate the necessity for further tuning when the system parameters undergo variations.

5.7. Case Study on IEEE-39 Bus System

This section inspects a practical power system modeled as the IEEE-39 standard bus system to assess the efficiency of the MSPIDD controller. Figure 17 demonstrates a schematic representation of the system, which incorporates 10 generators, 12 transformers, 34 transmission lines, and 19 loads. The test system is split into three distinct areas. The test system’s characteristic values are cited from [28]. The system’s non-linearities and the features of the regulation are also taken into account. One generator (G1, G8, and G5) is assigned to manage the load frequency control (LFC) function for each region. There is just one disruption introduced in area 1. The effectiveness of the MSPIDD controller is contrasted to that of the MSPID and PID controllers in this IEEE test system, the same as in Section 5.1. In Figure 18, the dynamic reactions are displayed. Figure 18’s analysis shows that the proposed controller performs at its best since system deviations are much decreased, which enhances the power system’s dynamic stability. Further, the characteristic values like highest overshoot, highest undershoot, and settling of responses from Figure 18 are reported in

Table 3. Characteristic analysis of Figure 18.

Parameter	Controller	HU	HU	RST
$\Delta f_1$	PID	−0.01913	0.00099	20.89
	MSPID	−0.0148	3.2 × 10−5	18.44
	MSPIDD	−0.01091	0.0002845	11.47
$\Delta f_2$	PID	−0.0074	6.488 × 10−5	25.32
	MSPID	−0.0040	1.337 × 10−5	22.51
	MSPIDD	−0.0029	0.000105	16.39
$\Delta f_3$	PID	−0.0061	7.51 × 10−5	24.43
	MSPID	−0.003501	1.532 × 10−5	23.12
	MSPIDD	−0.00261	0.00011	17.21
$\Delta P_{tie12}$	PID	−0.0013	1.12 × 10−5	31.86
	MSPID	−0.00071	3.31 × 10−7	29.3
	MSPIDD	−0.00051	2.289 × 10−5	19.66
$\Delta P_{tie23}$	PID	−1.12 × 10−5	0.0013	32.21
	MSPID	−3.286 × 10−7	0.00071	30.75
	MSPIDD	−2.29 × 10−5	0.00051	22.12
$\Delta P_{tie13}$	PID	−0.0061	6.51 × 10−5	28.46
	MSPID	−0.0037	9.32 × 10−6	26.32
	MSPIDD	−0.0026	0.00013	18.44

. These values show the better outcome in suppressing the system deviations with the proposed secondary controller, as the responses for MSPIDD are much improved against the other considered established controllers.

6. Conclusions

Here are the conclusion drawn from this study.

• The study shows that the COVID-19-based algorithm performs better than conventional optimization techniques in attaining precise stability and control while successfully handling the objective function convergence in MAPS.
• By controlling frequency and tie-line power at the same time, the proposed MSPIDD secondary controller greatly improves the integrated power system’s operational efficiency while maintaining the stability limits.
• Strong resilience against sporadic renewable energy sources and unpredictable load variances is demonstrated by the MSPIDD controller. It successfully upholds performance and stability, demonstrating its capacity to manage practical operating circumstances and maximize controller benefits. The resilient performance of the proposed MSPIDD controller is further demonstrated in the case study on the IEEE-39 bus system.
• The inclusion of contemporary electric vehicles (EVs) and an SSSC as an FACTS device further enhances the overall performance of the system, especially with regard to frequency stability. This is owing to the reason that EVs provide flexible load management and storage of energy, while SSSCs improve the power flow control and stability, hence providing efficacious control of the integrated power system.