Load frequency regulation of interconnected muli-source multi-area power system with penetration of electric vehicles aggregator model

The recent widespread installation of renewable energy sources in place of fossil fuel, along with the substitution of electric vehicles, has given rise to several integration difficulties. Due to their intermittent nature, these systems are generally supplied through variable power generators. The control architecture of such connected systems focuses especially on minimizing frequency deviations and tie-line power fluctuations. In this paper, a cascaded proportional integral-proportional derivative (PI-PD) controller is proposed based on a chaotic butterfly optimization algorithm (CBOA) for parametric determination. The suggested controller and optimization approach is tested on a two-area power network, consisting of multiple renewable energy systems and electric vehicles while considering different load and frequency fluctuations. The proposed algorithm is evaluated based on four performance features. Its superiority is demonstrated by comparing it with recent optimization-algorithms-tuned controllers such as artificial rabbit algorithm 1 + PD, chaos game algorithm 1 + PI, dragonfly search algorithm, fractional order PID, and firefly algorithm PID. The acquired results validate the efficient performance of the proposed methodology by mitigating the frequency and tie-line power variations. Moreover, it exhibits robustness and enhanced stability of the system throughout a broad range of parameters.


Literature review
In recent years, the global energy demand is increasing due to the installation of new industries and increased population.Conventional energy resources like oil, gas, and coal are decreasing with time.Looking at this problem, the world is inclining towards renewable energy sources (RES) solutions which are non-depletable and available every day.The international energy agency (IEA) report highlighted the utilization of renewable energy to 29% in 2021.These resources are reliable and generate efficient amounts of energy.However, net-zero emission of carbon is planned to meet by 2050 [1].By lowering greenhouse gas emissions, RES helps to create a sustainable environment.The incorporation of RESs, primarily photovoltaic, wind power, small hydro, fuel cells, and biomass has resulted in a major dynamic characteristic shift in power systems over the last decade because of their technical and economic importance [2,3].Moreover, the use of plug-in electric vehicles (PEV) is anticipated to increase soon due to their low cost of charging, lowering carbon emissions, lack of noise pollution, and consequently environmentally friendly design.Nowadays, PEVs are linked to the power grid, making it possible to transfer electricity between customers and the generator as efficiently as possible.
Frequency fluctuations are introduced in the system by the incorporation of RESs into an electrical network.The output power and frequency of RESs are impacted due to varied weather conditions.Therefore, due to the varying nature of RESs, frequency regulation is a challenge without using cutting-edge control technology.An automatic generation control (AGC) is the control system that helps to keep the tieline power and the frequency at their nominal values under disturbed conditions.It mainly consists of two control parts, i.e., load frequency control (LFC) and automatic voltage regulator (AVR) [4].With an AVR, steady voltage is provided for smooth power flow during varying load conditions.On the other side, LFC's primary goals are to regulate each area frequency within predetermined limits and adapt the tie line power flow by shifting load requirements [5,6].The formation of the power grid is in such a way that it has several areas, where each area is connected to other areas through transmission lines.The main job of RESs is to fulfill their energy demand and to control the power flow within the connecting areas.The most important concern with the integration of RESs is that the output of the grid must show minimal frequency deviation and it should be free from the restriction of load changes.Moreover, the frequency on both sides of the demand and supply should be kept in balance [7].Several approaches and controllers like classical, optimal, adaptive, centralized/decentralized have been developed to control the frequency variations.In addition to them, various soft computing techniques have also been proposed containing different heuristic/metaheuristic optimization-based controllers, fuzzy-based controllers, sliding mode control, etc. [8].A more sophisticated type of PID controller is the fractional order PID controller [9], which resolves the LFC problem but still lacks precision in the control area.Several modified fuzzy-based controllers are used in literature to address LFC adaptive type-2 controller in [10], cascaded fuzzy with filter (CF-FOIDF) in [11], fuzzy PID with GWO optimization in [12], and fuzzy-based optimized PI controller is employed in [13] to manage the disturbance and regulate the LFC problem by online update, however, fuzzy parameters did not contain detailed mathematical description.
Different genetic algorithms with evolutionary programming, including cuckoo search [14], particle swarm optimization [15], artificial bee colony [16], firefly algorithm [17], and grasshopper algorithm [18], etc. are used to address the LFC problem.Although these algorithms appear to be effective in addressing the LFC problem, they are sluggish in their convergence speed by local minimum trapping during the search.Additionally, these controllers are employed to enhance the PID controller's closed-loop performance.For LFC, an ABC optimized-based PID controller has been developed [19].A multiverse optimization technique is used to build PID plus double-derivative (PID + DD) for LFC, where the extra derivative has added oscillation to the frequency response.
Using the dragonfly search technique to make the tunable parameters as efficient as possible, the notion of a FOPID controller is introduced in [20].In 2014, Grey Wolf Optimization (GWO), a novel optimization technique, was introduced [21].The method imitates the grey wolf social structure and hunting methods.This algorithm uses their hunting approach to identify and track prey (solution).Researchers employed the GWO approach to estimate the PI controller values for a power system problem [22].The GWO approach was utilized in [23] to solve a nonlinear optimization problem.In [24], a grouped GWO technique is suggested to adjust the PID controller parameters of a wind turbine.For the solution of nonlinear discontinuous economic dispatch issues with various equality and inequality restrictions, a hybrid GWO approach has been proposed [25].A different kind of fractional-based tilt integral-derivative (TID) is created in [26] using an upgraded particle swarm optimization (PSO) technique to enhance the system frequency.The design of an optimum controller (OP) for a multi-area deregulated environment is discussed in [27], taking into account an energy storage device that has shown to work optimally in non-linear states.Many researchers in the field of LFC also employed Model Predictive Control (MPC) [28], this method can reduce frequency oscillation since it uses real-time prediction based on previously collected sampled data error.The PI plus MPC-based two area system with PV and thermal is reported in [29], where the findings are encouraged by the addition of a PI controller which exterminates steadystate error.The idea of scheduling the derivative gains for an interrelated power network using MPC-based PI gain is also introduced in [30][31][32].Additionally [30][31][32] introduces the concept of scheduling the derivative gains for an integrated power system utilizing MPC-based PI gain scheduling a selftuning fuzzy control algorithm, and a lightning search-based variable structure design.To lessen frequency fluctuation, an FLC-based LFC with a high wind turbine penetration is presented in [33].The sliding mode controller (SMC) [34], which has excellent precision to reduce frequency oscillations, is also utilized to handle nonlinear issues.An internal model controller (IMC) [35] is a method for tuning the controller that was created generally and can meet the requirements for achieving stability and performance.However, the primary flaw is its slow response time to load disturbances.Additionally, certain methods, such as hybrid ALO pattern search, are very effective at minimizing frequency disturbance [36].
The irregular nature of wind and photovoltaic (PV) energy has compelled the power system to employ various technologies and techniques to be more adaptable and effective in mitigating the variations in load and generation.In order to maintain system stability, energy storage systems (ESSs) are built-in to address issues with power unbalance and frequency deviation [37][38][39].They can be employed as loads or generators, which lowers generation/demand fluctuations and enhance load frequency response.However, the primary and secondary control loops are used to control the minor and major fluctuations of frequency correspondingly that need to maintain tie-line power in compliance with the power reserve [40].In recent years, as the use of EV has grown, the idea of vehicle-to-grid has emerged.PEVs are the future of transportation and are gaining popularity.When the predicted power output from RES is not being produced, EV batteries are used to isolate system generation power from load requirements [41].
The effects of plug-in EV penetration on the LFC system are examined in [42].The primary LFC is significantly impacted by the PEVs, and they have the potential to improve it.The primary LFC is envisioned to be assisted by the PEVs in [43].Reference [44] examines the effects of PEV charging and discharging on the LFC in the power system of Great Britain and it is presented as an initial order transfer function.Plug-in EVs are reportedly offered as a strategy for thermal plants to help regulate load frequency [45].Moreover, in a power system with EV, the time delay margin of the load frequency management system is estimated in [46].The LFC system's stability is significantly impacted by the time delay.Maintenance of frequency fluctuations via plug-in EVs using multiarea thermal systems is examined in [47].According to [48,49], the Modified Harmony Search Algorithm is used in conjunction with conventional fuzzy sets and systems of type-2 to adjust the PI controller in a microgrid with plug-in EVs.
Further to the above discussion, the response of the different controllers implies that conventional and noncascaded control strategies have difficulty minimizing the system's uncertainty.Hence, there is room for improvement in the cascaded structure to enhance the overall controlling capability of the cascaded design.However, the complexity becomes more severe with the integration of RESs into the power system.A cascaded formation design has been presented to address system stability to enhance the controller's optimal performance.A newly developed swarm intelligence (SI) method, the butterfly optimization algorithm (BOA), mimics the natural food-seeking behavior of butterflies with modification via chaotic maps and has been used for the optimization of the parameters [21].In this paper, the mixing of BOA with ten chaotic maps is performed to broaden its variability and prevent getting confined to local minima.Four different algorithms are compared with the CBOA.The findings demonstrate that CBOA outperforms the other techniques and can accurately minimize the performance indicators regarding LFC.

Contribution and paper organization
The article's main contributions can be summarized as: 1.For multi-connected areas, a sophisticated cascadedbased controller in the form of PI-PD is proposed with the capacity to handle LFC for RESs alongside aggregated model of EVs. 2. For tunning the gains of the cascaded controller, modified chaotic BOA is implemented to achieve the objective function which is the minimization of ITEA. 3. The effectiveness of the proposed controller is tested on a multi-area power system.In comparison to four other controllers ARA-1 + PD, CGO-1 + PI, DSA-FOPID, and FA-PID.The proposed controller has demonstrated robust results.4. To ensure the proposed controller design is adaptive, several evaluation indicators are analyzed, such as loadchanging, nonlinearities in the test system, and sensitivity analysis.5.The primary innovative concept revolves around the CBOA-tuned cascaded PI-PD controller design and its ability to guarantee the stable operation of the deregulated power system under high penetration of RESs along with EVs.
The rest of the paper is structured as Sect. 2 offers the mathematical modeling of power systems.The newly proposed approach and optimization technique is introduced in Sect.3. Section 4 contains the findings and a discussion of them.In Sect. 5 the paper is concluded.

Model under investigation
The layout of the connected areas is shown in Fig. 1 by employing tie-lines to exchange power between the multiple areas.
The multiarea power system setup that is being proposed in this article is shown in Fig. 2. It consists of two areas,

Photovoltaic system modeling
A photovoltaic (PV)-based energy system is one of the most affordable, durable, and well-known renewable energy sources.Solar energy converts into electricity directly by the converters in PV energy systems.This technique has no moving parts and produces no emissions that could harm the environment.PV systems are developed to utilize photons of light emitted by the sun into electricity.Moreover, PV energy-based system is nonlinear as the alignment of the sun is non-stationary.The two important parameters that mainly affect the power produced by PV modules are irradiance and temperature.It is a challenge to get maximum power from the system.In a power-voltage curve of PV, a point appears in the curve where the maximum power can be achieved using MPPT algorithms from the PV module.In this research, the PV system is operated at MPP with 1000 W/m 2 irradiation at 25 °C temperature, where the penetration level is 45% [40].
A PV array is usually exposed to the number of events to be connected to a thermal unit.Several components make up the PV system architecture, such as a DC-DC boost converter that raises the voltage to an adequate level for the operation of a current inverter input.The current inverter generates AC which must be compatible with an AC grid, where capacitors are utilized to absorb the undesirable harmonics at low frequencies.Finally, modeling and calculation of instantaneous and average power will be fed to the grid.
The approximation of AC voltage is given in Eq. ( 1) where K stands for the system gain between AC and DC voltages, which is often less than 0.86.Its value for a given model is 0.7.Equations ( 2) and ( 3) are used to estimate the transfer function of the boost converter.
where G 1 is converter's gain.Equation (4) shows the transfer function of the inverter which is the ratio of AC to DC. Where, i AC has Laplace transform s 2 s 2 + w 2 to i DC .
To calculate the instantaneous power, the transfer function is given by Eq. ( 5) where at 50 Hz, the w = 314.12rad/sec.The gain for P inst is shown in Eq. ( 6) Average power is calculated by Eq. ( 7) Instantaneous to average power gain is expressed in its simplest form in Eq. ( 8) The derived transfer functions are applied to create a PV model that is appropriate for the thermal unit.

Wind system modeling
The primary consideration is how wind energy would affect the electricity system.Variation in wind energy pushes the power system towards auxiliary power imbalance and results in frequency deviations from its nominal value.Due to this, the LFC issue is driven by the integration of wind into the power grid.The wind system is modeled for 150 kW capacity.The wind turbine generator can be modeled in Eq. ( 9) [40] where P w is the wind power, ρ denotes air density, A is the cross-sectional area and V w is the wind speed.
The mechanical power P m is presented in Eq. ( 10) C p is related to λ which is the tip speed ratio and β denotes the pitch angle of a turbine.Furthermore, C p can be simplified in Eq. ( 11) Tip speed ratio (TSR) can be expressed in Eq. ( 12)

Thermal system modeling
In a thermal system, a governor is a fundamental controller which assists in balancing the demand and generation by regulating the steam of a turbine.The mechanical turbine of a thermal system revolves based on injected steam, recovering energy loss after it has passed through a re-heater.Now, the prime mover speed is maneuvered as part of the droop control process used to operate this tribune system.The governor's valve is in charge of regulating the steam input.A thermal power plant is modeled for a 150 kW at 50 Hz capacity [40].
The speed governor equation is based upon reference power and change in frequency shown in Eq. ( 13) where, P gi (s) is the output power of the governor, P ref (s) is the reference power, 1 R is the droop that controls the flow and f i (s) is the frequency change.
The transfer function H g (s) of the governor with gain G g and time constant T g can be expressed in Eq. ( 14) The turbine has gain G t and time constant T t , Eq. ( 15) gives the transfer function of turbine.
Similarly, the transfer function H R (s) of re-heater for the given gain G R and time constant T R which is represented as Eq. ( 16) The generator has a transfer function H m (s) given in Eq. ( 17) For ith area, the area central error (ACE), and the change in power of the tie-line is expressed in Eq. ( 18) where, B i is the bias factor that is introduced in multi-area modeling to measure the power which flows between two areas via HVDC and HVAC.The generator output f i is dependent upon load disturbance, consisting of inputs P R (s) and P d (s).So, the output can be presented in Eq. ( 19) where, P d (s) denotes load disturbance in the system.

Modeling of hydro-plant
The hydro plant unit is comprised of three main components: governor, droop compensation, and water penstock turbine [27].Equation ( 20) can be used to express the hydro-plant system transfer function.
where, G g (s) is a transfer function of the governor written as: represents the transfer function of droop as: G w (s), the transfer function of water penstock is expressed as: Equation ( 20) can be re-written as Eq. ( 24) where, T 1 , T R , and T 2 stand for the governor's time constants, transient droop time constant, and the hydraulic governor's reset time, respectively.However, T w denotes the water penstock's start time.

Electric vehicle modeling
The The relationship between the V OC and the SOC of EV is implemented using the Nernst Eq. ( 25) as mentioned in [53].Table 1 lists the key characteristics of the power system that was examined in this research [27,40,52,53].

Structure of controller and objective function
Integral-based controllers are typically employed in automatic gain control to reduce Area control errors (ACE).Until now, utilizing an integrated controller alone has the potential to result with a noticeably longer response time in a closed loop system.Proportional Integral (PI) improves the dynamic response of the power system and provides additional benefits including easy design, relatively inexpensive, and effectiveness when created for linear and steady systems.However, when higher order complex, nonlinear and unstable systems are involved, traditional PI controllers are typically ineffective.One strategy used to improve system performance is cascading control [54-57].Cascaded PI-PD controllers for control systems have subsequently been proposed in the literature due to their extensive benefits [58].Figure 4 represents the layout of the cascaded PI-PD controller.
The initial stage is a PI stage and the secondary is PD stage in a cascade PI-PD controller.The cascade PI-PD controller has more advantages over the conventional PID controller because of its lower steady-state error, which results in fewer where K P1 , K I , K P2 , K D stands for gains of the proportionalintegral and proportional-derivative cascaded controllers.

Optimization problem
A performance index or objective function can be generated using ITAE of the frequency deviation of both Area-1, Area-2, and tie-line power.The main purpose of the proposed controller (CBOA: PI-PD) controller is to minimize the objective function (J ).Equation ( 27) defines the objective function or the fitness function ITAE Fitness = min(ITAE) where f 1 represents the frequency variation in Area-1 and f 2 represents the frequency variation in Area-2, respectively.The power exchange between two areas is indicated by P tie .The overall goal is to reduce the ITAE.

Chaotic butterfly optimization algorithm
A newly developed SI method, the butterfly optimization algorithm (BOA), mimics the natural food-seeking behaviors of butterflies [59].The methods used by butterflies to find food are developed as an optimization strategy based on regional and global movements.The BOA exhibits potent characteristics as it is straightforward to use, derivative-free, adaptable, scalable, and easy to adapt to any optimization issue.Likewise, in other meta-heuristic algorithms BOA faces two issues that are trapping in local optima, and experiencing a poor rate of convergence.Consequently, BOA has been modified and used for a variety of optimization challenges.In this work, the mixing of BOA with ten chaotic maps [60] is performed to broaden its variability and prevent getting stuck in local minima.
The butterflies produce an odor while flying.Several senses like hearing, sighting, tasting, smelling, and touching assist them in finding food, and locating mates for mating and migration, thus avoiding predators.Flying butterflies produce a powerful scent.The quantity of other butterflies attracted to the scent depends on its potency.Equation ( 28) represents the fragrance of each butterfly.
where P i represents the odor intensity of butterflies, M s stands for sensor modality, and I s indicates impulsive intensity, and Y stands for the power component.The butterfly motion consists of three stages (i) the Global search stage (ii) the Local search stage, and (iii) Solution assessment.
During the global search stage, butterflies maneuver in such a manner that can be characterized as [59] To regulate the butterfly while traveling to the optimal solution with the least fitness in local search or global search, the n value and D value are compared.The optimal solution vectors for the ith butterflies are m and q * , where n is a random value and D = 0.8.
Butterflies' motion during the local search stage can be presented as Butterflies helped in the search for space are gth and hth represented as m g and m h .
During the third phase of solution assessment, the odor strength serves as the fitness function.Factor n in Eqs. ( 29) and ( 30) demonstrate the process of randomness and entanglement of butterflies as they search for the ideal value.Consequently, BOA's weak merging rate and trapping in local optima are its main flaws.Authors in [60] offer a novel solution to these problems wherein chaotic maps are proposed to play the part of the BOA's random value.BOA's randomized nature is enhanced by chaotic maps, enabling it to approach at global minima and prevent getting trapped in local minima, which accelerates the speed of convergence.The steps of the anticipated CBOA are presented below: Rather than employing on random numbers that were explained earlier where the decision was made on the comparison of n and D, where n was a random number now in this strategy, the butterfly's position is updated using chaotic maps.When n is less than D butterflies move towards best butterfly calculating Eq. ( 31) rather than (29), likewise if its greater than D then they move towards the position calculated by Eq. ( 32) instead of (30).
In order to achieve greater accuracy and minimum objective function than the BOA, which used random values, the C j used where j = [1, 2,…, 10], which are chaotic values [60] generated using 10 chaotic maps, have been substituted with the n.
The binary CBOA represents the search area in binary digits [0, 1].whereas continuous CBOA could dynamically explore the feature space for the best feature pair and predicted to be significantly stronger than binary.Equations ( 33) and (34) below illustrate how binary CBOA is represented where s stands for the transfer function, rand() is used to generate a random value from a homogenous distribution [0, 1], and x t+1 i stands for the newly updated solution.The proposed algorithm CBOA is utilized to find the appropriate controller parameters.Figure 5 illustrates the CBOA algorithm's flowchart.

Results and discussions
The case study of the integrated multi-area power system is shown in Figs. 1 and 2. The overall system's modeling is carried out in MATLAB/Simulink to examine how it performs under various RESs variability and load change scenarios.The power system experiences frequency variations while providing the required power.Efficient control is necessary to handle the power system ever-increasing problems, and for this, a robust controller is proposed that can manage such nonlinearities.CBOA-based PI-PD controller is proposed, whose effectiveness is determined under varied load conditions.
The investigated power system model is interfaced with the CBOA algorithm to carry out the optimization procedure.Testing scenarios for the investigated algorithm include step load, identical multiple loads stepping on both areas and random load stepping situations for both areas.The time resolution is 20 s for the studied system.Multiple heuristic and metaheuristic optimization strategies, such as the Artificial Rabbits algorithm (ARA), Chaos Game algorithm (CGA), Dragonfly Search algorithm (DSA), and Firefly algorithm (FA) are compared to the CBOA convergence trend.For the examined scenarios, it could be observed that the CBOA tuned PI-PD controller approach has a smoother curve and a faster rate of convergence than the other controllers.Several scenarios have been conducted under identical operating conditions to compare the dynamic response of the recommended algorithm with respect to the conventional PID, FOPID, 1 + PI, and 1 + PD controllers in to explore the effectiveness of the proposed controller.Moreover, the convergence curve of the objective function is shown in Fig. 6.

Scenario 1 (CBOA: PI-PD response under 15% load variation)
This section shows the CBOA tuned PI-PD performance during a 15% change in load.The suggested controller's performance is evaluated in correlation with DSA-FOPID, FA-PID, CGO-1 + PI, and ARA-1 + PD controllers.As the load changes, the CBOA tuned PI-PD outperforms other controllers through its ability to tolerate frequency fluctuations.The suggested controller response for the change in frequency for the two areas is presented in Fig. 7.Moreover, scheduled power transfer between two areas is managed outstandingly.Figure 8, which depicts the power balance between the two areas, highlights the CBOA: PI-PD controller's superior response in comparison to the rest of the controllers in terms of key performance indicators.
Table 3 demonstrates how various controllers have responded for Area-1 and Area-2, with each controller's response time in terms of steady-state (SS), overshoot (OS), and undershoot (US) under 15% load-changing scenario.The result shows that the CBOA: PI-PD controller adjusts in about Fig. 7 Frequency response under change a f 1 for Area-1 b f 2 for Area-2 Fig. 8 Two-area interconnected power response under 15% load change 9.4 s for a 15% load variation to reach its steady-state value.Moreover, the other controller's maximum dips of fluctuation that is undershoot are 0.88, 0.48, 0.98, and 1.31, but CBOA: PI-PD indicates approximately only 0.1.The reliability of the recommended controller above existing controllers is demonstrated by an overshoot duration of only 0.5.Similarly for Area-2 controller response and performance are also monitored and the suggested controller exhibits a similar trend, with a faster settling time of 9.4 s, a little undershoot of 0.09, and an overshoot of 0.58 at 15% of load change.Further to that, the suggested controller for the tie-line power is settled in just 11 s, which is faster than the other controllers.

Scenario 2 (CBOA: PI-PD response for the load change in Area-1 and 2)
In this situation, the power system under consideration is subjected to a multiple load stepping profile with four perturbed steps at 10%, 20%, 50%, 30%, and 10%, as illustrated in Fig. 9. Figures 10 and 11 display the simulation outcomes for the dynamic response of system frequency for Area-1, and Area-2.
The findings of Area-1 clearly show that the suggested controller provides system stability with a minimal overshoot of 0.58 and no undershoot as contrasted with other traditional controllers as shown in Fig. 10.Further, analysis is extended to Area-2, and Fig. 11 depicts the proposed controller's response to multiple load circumstances.In this case, the controller maintains its reputation and exhibits a fast steady time of 10, 86, 126 s, with no undershoot and minimum overshoot.Whereas, other controllers have slow response characteristics.The tie-line power variations are shown in Fig. 12.
Table 4 include the calculations for this scenario of maximum OS, US, and SS.

Scenario 3 (CBOA: PI-PD response for the random load change in Area-1 and 2)
Evaluation of the two-area power system performance is evaluated while taking into account distinct load changing patterns for Area-1 and Area-2 as shown in Fig. 13.The automatic gain control (AGC) regulation signal is based on the input signal from the area control error (ACE) and AGC signal is the output response of the controller against ACE.The output signal for both areas has been shown in Fig.      Figure 15 shows the findings for the frequency that was attained from Area-1.The DSA-FOPID, FA-PID, CGO-1 + PI, and ARA-1 + PD controller's performance is degraded in terms of damping down the variations in the system frequency.
The proposed controller in contrast to FOPID, PID, 1 + PI, and 1 + PD controllers, shows much better performance in reducing the overshoot, undershoot, and steady state values of both parameters that are frequency variations and tie-line power variations throughout Area-2 load shift as depicted in Fig. 16.
Moreover, the transfer of power between two areas is investigated.The tie-line power between the two locations is depicted in Fig. 17.Power exchanges should be kept to a minimum for a good response, which justifies the controller's fineness.
The comparison table for distinct load changing pattern is for Area-1, Area-2 and tie-line is shown is Table 5.The performance index ITAE serve as evidence of controller's effectiveness.The performance comparison of CBOA: PI-PD along with other controllers is shown in Fig. 18.
The stability analysis for the proposed control approach has been presented in Fig. 19.The bode plot shows the system stability under the designed controller approach.

Conclusion
This paper discusses an optimized technique to mitigate the LFC issue when a multi-area power system is connected.The PI-PD controller that is presented in this research aims to reduce the LFC issue.Also, a CBOA metaheuristic optimization technique is devised to find the parameters of the controller.The results validate the effectiveness of the proposed controllers in comparison to the normally utilized conventional controllers like (PID, 1 + PD, 1 + PI, and FOPID) especially, with the fluctuating nature of the renewable sources and EVs.It is seen that various areas are connected by transmission lines, with the primary goal of the CBOA: PI-PD being to stable the system's overall response regardless of any load disturbance.Additionally, the designed work is put through several kinds of testing scenarios, including similar-load-fluctuations in multiarea, distinct-load-variations in multiarea, uncertainty in the power system's parameter values, nonlinearities in the power system, and sensitivity analysis, to determine the performance of the proposed controller.In comparison to other controllers, the CBOA: PI-PD settles itself in about 8.5 s for distinctload variation for both area-1 and area-2.Whereas 1 + PD, 1 + PI, FOPID, and PID took 11.5 s, 14 s, 11 s and 25 s, respectively.Moreover, in case of similar-load changes in both areas, the proposed cascaded controller shows superiority in terms of settling time and overshoot, i.e., 9.6 s and 0.58 s with no undershoot.The validation supports the claim that the suggested controller can limit OS, US, and SS values while dampening frequency oscillations and controlling the tie-line power.

Fig. 3
Fig. 3 Layout of EV model

Fig. 5
Fig. 5 Flow chart of chaotic butterfly optimization algorithm

Fig.
Fig. 19 Stability response of the power system model of the electric vehicle is necessary to explore the effect of the PEVs on LFC [50, 51].Most of the research has been studied on the PEV as an aggregated battery storage model.A precise dynamic model of the EV is shown in

Table 1
Examined power system parameters

Table 2
Examined parametric values

Table 4
Overshoot, undershoot and steady state performance for scenario 2

Table 5
Overshoot, undershoot and steady state performance for scenario 3

19 Stability response of
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