Adaptive LFC incorporating modified virtual rotor to regulate frequency and tie-line power flow in multi-area microgrids

This research investigates a new coordination strategy for both isolated single-area and interconnected multi-area microgrids (MGs) using a modified virtual rotor-based derivative technique supported with Jaya optimizer based on balloon effect modulation (BE). Accordingly, the main concept of BE is to assist the classic Jaya to be more sensitive and trackable in the event of disturbances, as well as to provide optimum integral gain value on the secondary frequency controller adaptively for both suggested MGs. The proposed modified virtual rotor mechanism is consisting of virtual inertia and virtual damping that are added as a tertiary controller within proposed MGs considering full participation of the inverter-based energy storage systems. The proposed virtual rotor mechanism is consisting of virtual inertia and virtual damping that are added as a tertiary controller within proposed MGs to emulate the reduction in system inertia and the enhanced damping properties. Several nonlinearities were proposed in this work such as a dead band of governor, generation rate constraints, and communication time-delay are considered within the dynamic model of the suggested MGs. In addition, the proposed design of multi-area MGs takes the interval time-varying communication delays into account for stability conditions. In this study, A comparative study using unimodal (i.e., Sphere) and multimodal (i.e., Rastrigin) benchmark test functions are conducted to validate the proposed direct adaptive Jaya-based BE. Furthermore, Wilcoxon’s rank-signed non-parametric statistical test using a pairwise comparison was performed at a 5 % risk level to judge whether the proposed algorithm output varies from those of the other algorithms in a statistically significant manner. Thence, the superiority and effectiveness of the proposed method have also been verified against a variety of other metaheuristics optimization techniques, including classic electro-search, particle swarm, multi-objective seagull, and Jaya optimizers. In addition, an operative performance is assessed against the conventional integral controller, coefficient diagram method, and classic Jaya with/without virtual inertia. The final findings emphasize the superiority of the proposed direct adaptive Jaya-based BE supported by a modified virtual rotor and state better performance and stability compared to existing controllers.


I. INTRODUCTION
Generally, microgrids (MGs) have two types of operation: grid-connected and islanded operation modes [1], [2]. For islanded patterns, systems for storage and traditional diesel generators are typically responsible for frequency regulation. While a connected mode for the grid, the bulk power system handles the frequencies [3], [4]. The variability of renewable energy sources (RESs) power generations leads to high perturbations in power flow and frequency in the MG, and this will greatly affect the MG operation. Therefore, the high penetration of RESs makes the situation in MG worse due to low inertia and damping; Thus, it creates some issues in stabilizing system frequency and voltage, resulting in a weakening of the MG stability and flexibility. For this point, integrated resource planning in sustainable energy-based distributed microgrids has been alleviated in [5] to solve the issue of intermittency of RESs and to assess the optimal allocation of these suitable integrated resources planning for eco-friendly sustainable energy-based hybrid microgrids with distributed generation.

1) LITERATURE REVIEW
In recent years, distributed generation has had an increasing impact on distribution grids [6]. As the number of active users is increasing in grid dynamics, but due to the presence of certain technical and standards issues, they don't participate in the grid administration. To strengthen the service cohesion, generators and active users ought to be involved in a grid management coordination procedure [7]- [9]; Given this approach to islanded operation, it could be a major key to shifting from traditional into smart grids. Low system inertia occurs because of the connection of the inverter/converter with RESs to MGs. These devices don't have any damping or inertia properties that may lead to significant frequency deviations and system instability as mentioned in [10]. To mitigate the lack of inertia and weak anti-disturbance capability of frequency in MGs, a lot of inertia control techniques have been used to resolve MG frequency control issues, thereby enhancing the stability of frequency [10]- [18]. An adaptive virtual inertia-damping system has been suggested in [11] using the concept of model predictive control (MPC), which relies on the frequency performance enhancement of islanded MGs taking into account the high RESs penetration level. Recently, modified virtual inertia and damping based on derivative control techniques have been utilized to support the stability of frequency in small and large grids [12], [13]. The concept of virtual inertia has been proposed to support the stability of frequency in AC/DC interconnected grids [14], and the virtual inertia is suggested with phase-locked loop impact on deregulated automatic generation control system integrated with parallel AC/HVDC and a novel methodology for tapping of RES potential using virtual inertia are discussed in [15], [16]. In [17], a virtual inertia control based on fuzzy logic-MPC systems have been applied to regulate the frequency. A hierarchical control scheme based on a distributed controller design for frequency and voltage regulation in multi-area microgrid considering virtual synchronous generators is presented in [18]. Getting a proper match between nominal and robust performance is difficult when using old and conventional approaches. Moreover, uncertainty combinations (i.e., modeling of unstructured uncertainty) for control techniques haven't been considered and designed. So, it is difficult to attain both performance and stability in a wide range of uncertainties and disturbances using the abovementioned methods of controlling. Because of the possibility of formulating uncertainty in the control structure procedure, powerful control approaches can effectively solve this issue, such as the MPC used in [19], [20], to deal with the interrelationship between control loops of frequency and voltage excitation, resulting in poor performance of the system. Several works have been made for measuring and evaluating the performance of AGC different power systems applications considering renewable energy sources such as in [21], [22]. Another powerful controller called the coefficient diagram method (CDM) was depicted in [23], [24]. Basically, the CDM is an algebraic method that is applied to a polynomial loop in the parameter space, this controller is proposed in this work for comparison with the proposed direct adaptive Jaya-based BE supported by a modified virtual rotor. Time delays have appeared frequently in many modern industrial control processes in practice to study their impact in power system applications and are further discussed in [25], [26]. Also, time delay leads to oscillation or instability of the control system in many cases. Therefore, a study on the stability of the dynamical model is attracted by many researchers [27], [28]. The major goal in the study of stability analysis for the control system with time delay is to expand the region of the feasibility for maximizing the upper delay bounds of the discussed control system, which also guarantees the system's stable performance with given constraints. Frequency regulation is a critical issue in MGs to sustain the changes in power and system frequency at their set points. To cope with the instability issue, several attempts made to implement optimization techniques [29]- [40] have been used to adjust the controller parameters in the context of adaptive control issue based on soft computing techniques, to solve the complexity in construction and two-adaptive shape as presented in [41], [42] which applied indirectly, and this takes more time for computation that is considered very important in control interval law. On the other hand, the multi-objective seagull has proposed in [40] built on the concept of the dynamic archive which has the feature to cache the non-dominated Pareto optimal solutions. In addition, another mathematical optimizer called Jaya has been proposed in [43] due to it has many benefits such as parameters tuning is not needed at the computations time and can resolve both unrestricted and constrained issues, and is appropriate for discrete optimization problems. In addition, the controller parameters of the algorithm for every moment can be easily determined in less time. Literature has shown that some algorithms have good/bad performance in the implementation of some widely used benchmark functions. The statistical analysis using best, worst, and mean values is not sufficient to verify the effectiveness of optimizers against others. Therefore, we suggested in this research using a non-parametric statistical analysis as introduced before in [44] to validate the proposed Jaya-based BE against other algorithms considering ANOVA test, and also supported with the speed convergence test using unimodal and multimodal benchmark functions. VOLUME XX, 2017 9

2) MOTIVATIONS AND LIMITATIONS
As mentioned in the literature, the variability of RESs and random loads lead to more oscillations in power flow and frequency in the MGs and to poorer response to the common point of coupling (PCC) and active and reactive powers transfer. this penetration resulting from RESs causes some difficulties in regulating the frequency and voltage, resulting in a weakening of the MG stability and resiliency. As a result, severe deviations in system frequency hurt the control performance parameters, and this will cause energizing of under/over frequency relay and disconnect some loads. The conventional controller such as I, PI, and PID can't resolve the uncertainties situation. Also, there are several robust controllers as mentioned in the literature rely on the controller design such as MPC, H∞, CDM, fuzzy logic, and two-step adaptive concept-based optimizers have some design drawbacks and it takes a long time to define the control parameters, and this is not appropriate for control interval. Based on the above observations, this work investigates a coordination scheme between LFC and modified virtual rotor interaction that aims to modify the stability and performance of MG frequency and power regulation in tie-line, using the direct adaptive concept of Jaya-based balloon effect (BE) considering the virtual rotor and virtual damping. The modulation of BE was added to the classic Jaya to raise the algorithm sensitivity to load perturbations and changes in system parameters. In addition, BE has also used the openloop plant inputs and outputs to determine the actual on-time transfer function including disturbances and variations in parameters for the plant.

3) CONTRIBUTION AND PAPER ORGANIZATION
The main reason to write this manuscript is as follows: i. The concept of direct adaptive Jaya-based balloon effect modulation supported by a modified virtual rotor considering full participation of the inverter-based ESS has been demonstrated. ii. The concept of BE modulation is compiled to the classic Jaya optimizer to increase the algorithm interactivity and sensitivity with the online system issues. iii. A non-parametric statistical analysis and ANOVA test have been carried out to validate the performance superiority of the proposed Jaya-based BE. iv. System nonlinearities such as GDB, GRCs, timevarying communication delay are considered within the dynamic MG model. v. The proposed control strategy is compared with I/CDMbased LFC with/without the participation of virtual inertia under the effect of partial/full injection of wind energy and random load variations for both MGs.
The rest of this manuscript is outlined as follows: Section II describes the proposed islanded single area MG dynamic model. Section III illustrates the main control strategy of the modified virtual rotor mechanism. The coefficient diagram method as a robust controller is presented in section IV. A general overview of the classic Jaya and multi-objective seagull optimizers are presented in section V. The main concept of the balloon effect is introduced in section VI. Jaya-based adaptive frequency control with/without the balloon effect is presented in section VII. The performance analysis of the proposed Jaya-based BE is framed in section VIII. Section IX demonstrates the final findings and provides a discussion on the suggested controlled system. Section X introduces multi-are MGs application supported with timevarying delay. The final findings are concluded and offered in section XI.

A. SINGLE AREA ISLANDED MICROGRID
This paper focuses on an islanded MG (20 MW base), which consists of a non-reheated turbine power plant with a capacity of 20 MW, 17 MW of electrical loads, and 6 MW from wind farm (details in Appendix). The RESs power variance, as wind fluctuation and load variation, were considered signs of turbulence for the suggested MG. Figure 1 describes the block diagram of the studied single area MG dynamic model. The following equations can depict the suggested single-area MG dynamic model. The total load-generator dynamic relationship between the supply error and frequency distortion can be expressed as: The dynamic equations of the studied MG in state variable form can be written and derived as follows: Where ∆ , ∆ , ∆ , ∆ , ∆ ∆ are changes in diesel, load, inertia, governor, wind, and supplementary control power respectively. D is the damping coefficient, R is the governor speed regulation, H is the overall system inertia, and D is the damping coefficient. is the inverter-based energy storage system (ESS) time constant that is used to emulate the ESS dynamic control in the isolated and interconnected MGs. , , and mean the participation ratio coefficient, the virtual inertia, and damping constants. The criteria for choosing the virtual inertia and damping coefficients are concerning the desired dynamic response and MG stability. Here in this study, the virtual parameters are obtained using the Eigenvalue analysis as discussed in [13].

III. MODIFIED VIRTUAL ROTOR CONTROL
In islanded and interconnected MGs, several control issues may occur due to the non-uniform RESs nature such as frequency instability issues, which may boundary their penetration. As a result, MGs are becoming more susceptible to disturbances than traditional ones, and thus encounter disturbances such as abrupt disconnection in loads and shortcircuit faults with long clearance times [45], [46]. Therefore, the concept of the modified virtual rotor (inertia +damping) considering full participation of inverter-based ESS ( = 100%) can be used to compensate for the inertia induced by RESs in the isolated and interconnected MGs and enhance the low-damping properties. In this work, an ESS has been applied as a source of a virtual inertia power used to emulate the kinetic energy as found in a real synchronous generator. The law of the control strategy using ESS based derivative technique is shown in Fig. 2. The strategy is to add sufficient active power to the community by calculating the ROCOF using a derivative technique [10], [13]. Therefore, the suggested modified virtual inertia structure can diminish the desired power system inertia and damping characteristics, resulting in the enhancement of the overall inertia within the MG system, frequency stability, and preventing outage of the power. The power provided by the modified virtual rotor control system to the MG is described in Eq. (5). The dynamic structure of the modified virtual rotor emulation-based ESS connected to the islanded microgrid.

IV. COEFFICIENT DIAGRAM METHOD
CDM can be classified as an algebraic design algorithm in which the bode diagram has been replaced by coefficient one [23]. CDM is considered a method of arranging the closedloop poles to reach the desired system time response [47] Figure 3. illustrates the block diagram of the CDM algorithm for a single-input-single-output (SISO) linear time-invariant system.
The system's output can be described as: where ( ) can be defined as follow: where ( )and ( ) can be calculated as follow: Since and are coefficients of the controller polynomial. The case of p ≥ q should be verified for practical considerations.
The actuating signal for the closed-loop can be defined as: To acquire the characteristic polynomial ( ), the controller polynomial from Eq. (12) are substituted in Eq. (13) to get: , > 0 (15) Parameters such as the equivalent time constant ( ), the stability indices ( ), and the stability limits ( * ) relate to the coefficients of the characteristic polynomial ( ) as follows: The value of τ is an important step in the design operation and chosen as: According to the standard form of Manabe, values have been chosen as {2.5, 2, 2. . .2}. These values can be changed by the designer. Using and , The target characteristic polynomial, can be framed as where ( ) = ( ) Also, the reference numerator polynomials ( ) can be calculated from: VOLUME XX, 2017 9

A. FOR SEAGULL OPTIMIZER
The multi-objective seagull optimization technique was introduced in [40]. It is an extension of the classic SOA algorithm, with multi-objectivity and search space distinction. It has an archival search space while classic SOA has to do the extra task of providing optimal solutions. Moreover, it has many benefits over classic one such as doesn't need weight factors and usually generate combinations of solutions, allowing computation of an approximation of the entire Pareto front. This algorithm essentially simulates the attacking behavior and migration nature of seagulls. Seagulls are globespanning seabirds and are considered very intelligent birds because they have their own strategy (breadcrumbs) to attract prey and make the sound of rain on their feet to attract earthworms hiding underground. The attacking (exploitation) and migration (exploration) strategies of seagulls are their most important behavioral features shown in Fig. 4. Also, they are discussed mathematically and also, and the main steps of the classic and multi-objective SOA are stated in (see [40]). The following three assumptions are made regarding seagulls: ▪ Seagulls conduct their migration behavior in the form of a swarm. The exact location of each seagull varies to prevent them from colliding into each other. ▪ Seagulls can move towards the direction of the best seagull in a group. The best seagull indicates the optimal solution with the best value of the fitness function. ▪ Seagulls always change their location based on their initial position.

B. FOR STANDARD JAYA OPTIMIZER
Jaya was introduced by R. V. Rao in [43]. It does not require adjusting its parameters as compared with other optimizers. The essential precept of the proposed Jaya optimizer is centered around getting the solution by moving towards the best solution and staying away from the worst one. Therefore, its performance is exquisite and powerful, not affected by the wide dimension issue. The procedural steps of the Jaya algorithm are stated in the flowchart shown in Fig. 5. Jaya algorithm has several benefits such as: • The issue of selecting the algorithm controller parameters does not exist in this technique • It can solve unrestricted, restricted issues, and is suitable for discrete optimization problems. • Plain coding, ease to use, less computational time.
• It is considered more powerful against system uncertainties and variations due to its victorious nature.  Figure 6 shows the addition of the standard Jaya optimizer for adaptive tunning the integral control system supported with the modified virtual rotor control loop. In this technique, only the actual output signal is used to feed the optimizer and it is only utilized to stop the determination in case of lying within a small deviation (about 0.001 pu). The BE has been added to increment the interactivity of Jaya with the system issues. Figure 7 illustrates the concept of BE. It is noted that the effect of the system problems on ( ) is like that of air on the balloon volume [32]. The block diagram of the modified virtual rotor and Jayabased BE for the adaptive control system is shown in Fig. 8.
Also ( ), can be driven using its nominal value 0 ( ) as: is the balloon coefficient parameter and

VII. JAYA-BASED ADAPTIVE FREQUENCY REGULATION
The mismatch between seeking real power and generating it at an agreeable frequency causes an issue in load frequency control (LFC). Therefore, BE was introduced based on Jaya optimizer to calculate its effectiveness in resolving these problems within the LFC.

1) CLASSIC JAYA WITHOUT BALLOON EFFECT
In Fig. 9, there are three control loops used in this work: primary that uses the droop characteristics (1/R) for switching the valve of the governor, secondary that represents in LFC, and tertiary (proposed in this study) for modified virtual rotor mechanism. According to the simplified model of the proposed islanded single area MG with Jaya shown in Fig. 9, the closed-loop transfer function can be calculated as: Where , , and are the initial values of , , and , respectively, In this work, the integral square error (ISE) has been chosen as our main objective function ( ) and it could be worded as: Which is subject to limitations of the I-controller gain as: ≤ ≤ (33) From Eqs. (22)(23)(24), at any iteration (i) it can be noted that (j = f(k i )).
From Eqs. (34, 35, and 37): at any iteration (i) it can be observed that ( = ( , )). This supports that the objective function will be affected immediately with or system changes. Finally, the procedural steps of the suggested direct adaptive Jaya optimizer based on the BE modulation are constructed in the flowchart as shown in Fig. 11.

VIII. PERFORMANCE ANALYSIS OF THE PROPOSED JAYA BASED BE ON BENCHMARK FUNCTIONS
The effectiveness of the proposed adaptive Jaya-based BE is validated by comparing its performance with other metaheuristics techniques such as particle swarm (PSO) [29], Electro-search (ESO) [38], multi-objective SOA [40], and classic Jaya algorithms. This validation of the superiority of the Jaya based BE is made into two stages as below:

1) VALIDATION BASED ON A SPEED CONVERGENCE TEST
In this sub-section, a statistical analysis for unimodal (i.e. Sphere) and multimodal (i.e. Rastrigin) benchmark test functions are stated in Table I. In addition, a comparative analysis to measure the performance and speed convergence of the proposed method compared to standard algorithms such as PSO, Jaya, SOA, and ESO was described. was described. The same number of sets and iterations in each test function was used to solve optimization problems using 20 independent runs performed totally for all of the proposed algorithms and taking 50 as the population size. It is noted from Table I that the proposed adaptive Jaya-based BE converges relatively faster and provides superior to the other algorithms in terms of the best, worst and average error values. Each run stops when the error obtained is less than 10 7 . In general, non-parametric statistics have not relied on assumptions, i.e. data can be gathered from a pattern that does not put up with a definite distribution. In this study, pairwise comparisons are used to show the superiority of the proposed adaptive Jaya-based BE compared to standard PSO, ESO, SOA, and Jaya algorithms. In order to apply two algorithms to a common set of problems, these statistical tests are routed for the purpose of comparing them in performance. In this work, the use of the Wilcoxon signed ranks test was introduced [44], as an example of a non-parametric test, due to its simplicity, popularity, safety, and robustness for pairwise comparisons. This section will concentrate on the characterization of Jaya's behavior-based BE, in 1×1 comparisons with the rest of the suggested algorithms mentioned in Table II. The Wilcoxon's test is performed as follows: assume be the difference between the two algorithms' performance scores on i th out of n-problems (if it is known that these scores are represented in different ranges, then they can be applied within the interval [0, 1]. The differences are categorized regarding their entire values (for more details see [44]). suppose + is the ranks summation for the problem where the first algorithm superior the second, and − is the ranks summation to the reverse. Ranks of = 0 are divided equally between the sums assumed using continuous differences ; if there is an odd number, one of them is discarded:

=0
From the statistical point of view, this test does not suppose normal distributions and therefore it is considered a safer experience. The first step is to calculate the + and − related comparisons between Jaya-based BE and the rest of the algorithms. Once obtained, their associated − v l e can be stated. Note that, for each comparison, the property + + − = ×( +1) 2 must be true. Table II outlines the − v l e , + , − / , and − r k level calculated for all the pairwise comparisons concerning Jaya-based BE. It is noted that the adaptive Jayabased BE shows a worthy enhancement against standard PSO, ESO, SOA, and Jaya algorithms, with a significance level (α = 0.05). The score will be '+' if the control algorithm performs statistically better than the counterpart statically, '−' in the case of the vise verses, and if there are no significant differences found, the result will be '~'. Where − v l e is the probability of obtaining a result at least as extreme as the one observed. Moreover, it provides information about whether a statistical hypothesis test is relevant or not and also points out something about how significant the result is: the smaller − v l e, the stronger the evidence over the null hypothesis. As stated in Table II, using the standard ESO algorithm shows non-significant improvement over Jaya (meaning there is no difference found '~′).  The final findings indicate that the positive difference ranks summation was greater than the whole negative difference for all scenarios with Jaya-based BE, otherwise, the computed α is much less than the critical value. Thus, this analysis provides extra proof that the proposed adaptive Jaya-based BE algorithm outperforms the other algorithms.
To be more specific, analysis of the variance (ANOVA) test of control performance = obtained by different algorithms are shown in Fig. 12.

IX. RESULT AND DISCUSSION
The suggested adaptive Jaya-based BE modulation supported by a modified virtual rotor is used to adjust the LFC of an islanded single area MG system. MATLAB/Simulink software environment is used for validation in this work. The proposed MG system with virtual inertia and virtual damping parameters are included in Table III. In addition, the nominal parameters for the suggested Jaya and SOA are stated in Table  IV and V in a row: To assess the efficacy of the suggested control strategy (adaptive Jaya-based BE + modified virtual rotor), the proposed single area MG system has been checked into three case studies. The performance specifications: undershoot (Min.), overshoot (Max.), and settling time of the proposed strategy has been presented as numerical evidence for the superiority in performance and compared with multi-objective SOA algorithm, classic Jaya with/without virtual inertia, Jaya based BE with virtual inertia, CDM, and conventional integral controllers.  Here, the studied single area MG system with the introduced coordination method (adaptive Jaya-based BE + modified virtual rotor) is simulated during a step load demand scenario (∆ changes by 0.015 at the time of 3 sec). Figure 13a demonstrates the frequency response of the MG system with common as well as suggested adaptive controllers in this case, similarly in the absence as well as the presence of the proposed modified virtual inertia. It was clear that the MG provides the best performance as well as a higher decline in frequency deviations for adaptive Jaya-based BE modulation (less oscillation and less settling time) as compared to the conventional integral controller, CDM, SOA, and classic Jaya. Moreover, the existence of a modified virtual rotor clearly impacted the system frequency response in the case that it accomplished lessening the undershoot value. Therefore, the MG system with the introduced control strategy can afford the best response (lowest settling time and under/overshoot value Where the deviation in frequency in the case of fixed Icontroller, CDM, and adaptive controller tuned by SOA and Jaya optimizers was kept between ±0.075 Hz, ±0.044 Hz, ±0.0301 Hz, and ±0.035 Hz respectively. Whereas ∆ with adaptive Jaya-based BE with modified virtual rotor was kept between ±0.0016 Hz at the same step load disturbance as shown in Table VI. Consequently, the studied islanded MG frequency response with the suggested adaptive proposed strategy has a lower steady-state error and is better in damping than other ones.

A)
Frequency deviation. Figure 13b shows the diesel power response in this case of load demand. As shown in Table VI, the proposed system with adaptive Jaya-based BE supported by a modified virtual rotor gives a power change of 0.0149 p.u. It is clear that the system with the proposed strategy can give preference to diesel power (less settling time) as compared to other ones.

B)
Diesel power distortion. Figure 13. System response in case of a step load perturbation.

2) CASE 2: PERFORMANCE ASSESSMENT FOR RANDOM LOAD VARIATIONS.
On the way to authenticate the MG system with the suggested control system, the MG system is simulated underneath arbitrary load variations. Figure 14 illustrates the trend of arbitrary load demand. It is obvious that from Fig. 14, the load is varied by +1% at a certain time (20 sec), +0.5% at 80 sec, afterward reduced by 2% at the time of 150 sec, then -0.5% at the time of 210 sec, while after all stopped at the time of 270 sec. As shown in Fig. 15a, the superior frequency response with fewer over/undershoot is got by means of the introduced control strategy (adaptive Jaya-based BE) intended for online adjusting of the integral controller with the modified virtual rotor as linked to fixed I-controller, CDM, SOA, and classic Jaya with/without virtual inertia controller. Consequently, the planned MG's response with the introduced control scheme is considered to be faster and well-damped than other controllers. To strengthen the result gained from Fig. 15a, the diesel mechanical power demonstrated in Fig. 15b highlights the predominance of the implied integral controller tuned by the adaptive Jaya-based BE supported by improving virtual rotor.

3) LAST CASE: PERFORMANCE EVALUATION UNDER PARTIAL INJECTION OF WIND ENERGY AND RANDOM LOAD VARIATIONS.
In this study, the performance of the studied islanded single area MG with the proposed control scheme has been tested in face of the uncertainties produced by wind turbine generators and random loads penetrations. The injection of the arbitrary load demand, as well as wind energy, are planned as follows: ∆ plugin at the time of 20 sec as well as plug out at 250 sec, ∆ plug in at 80 sec, then plug out at the time of 180 sec for a total simulation of 300 sec. Figure 16 indicates the variant shapes of arbitrary demand as well as wind turbine energy. Figures 17a and 17b illustrate the system response during plug-in/out moments of random loads and wind turbines. A system with an integrated controller adjusted by adaptive Jaya-based BE with the participation of a modified virtual rotor can deal effectively with these variations, whether for frequency or diesel power.   In addition, Fig. 18 demonstrates the interaction between the power change of the virtual rotor and the balloon effect. It is obvious that using adaptive Jaya-based BE in presence of the modified virtual rotor can increase the total amount of inertia power provided to the grid. The positive and negative values indicate the charging/discharging power. Therefore, ESS controlled by the suggested technique is highly charged and discharged in response to any abnormal conditions. Therefore, in the case of high RESs penetration, a fast and stable response can be achieved using the proposed adaptive control strategy.

A. INTERCONNECTED TWO-AREA MICROGRID SYSTEM
The introduced control scheme is expanded to interconnect two areas MGs. It is essential to maintain the power of tieline ∆ at the planned values and to rebuild the MG system frequency to its needed level. Digital analyses were achieved to confirm the effectiveness of the introduced coordination control scheme by using adaptive Jaya-based BE modulation carried by a modified virtual rotor (as a tertiary control loop). The nominal data of the introduced two-area MG are defined in Table VII. The simplified model of the interlinked two-area MG is shown in Fig. 19. The system has been studied and examined under two scenarios through a generation rate constraint (GRC) equal to 10% per minute and 0.05 %. for the highest value of dead band for the governor of every area, along with the communication time delay is supposed to be fixed = 1 second as in [10], [33].

A) SCENARIO 1: PERFORMANCE EVALUATION UNDER THE EFFECT OF A 2.5% STEP LOAD CHANGE.
In this scenario, the system is examined under the effect of a 2.5% change in load ∆ at 1 sec. In Figure 20, the deviation in frequency for both areas, diesel power, and the change in tie-line power ∆ were presented. The system responds with the proposed adaptive Jaya based BE along with modified virtual rotor improved the overall transient MG performance in terms of over/undershoot, settling time, and steady-state error as compared to the fixed (I) controller, CDM, SOA, and classic Jaya with/without virtual inertia in presence of BE. It is noted from Fig. 20d that the change in tie-line power between both areas is effectively enhanced with the proposed control strategy compared to other ones. As a consequence, this offers a robust indication for the strength of the introduced control scheme over the other relative techniques by enhancing the total transient MG performance as expressed in Table VIII.

B) SCENARIO 2: PERFORMANCE EVALUATION UNDER THE EFFECT OF WIND TURBINE AND RANDOM LOADS UNCERTAINTIES.
In this study, the change in tie-line power ∆ and frequency in both areas ∆ 1 ∆ 2 have been tested under the effect of the injection of wind turbine and loads uncertainties using the same capacity as single area MG in this paper. The changes in wind turbine power ∆ and loads are shown in Fig. 21. In Fig. 22, the deviation in the system frequency for SOA, classic Jaya with/without virtual inertia, conventional integral, and CDM controllers reaches an unacceptable value, which leads to system collapse and instability. In contrast, the proposed coordination strategy (adaptive Jaya-based BE + modified virtual rotor) provides superior performance when successfully treating this contingency. In addition, the power change in the tie-line power as indicated in Fig. 22d is effectively improved to support the superiority of the proposed online tuned (adaptive Jaya-based BE) controller supported by a modified virtual rotor as compared to other ones.   In Fig. 23, it is clear that using adaptive Jaya-based BE modulation in presence of the modified virtual rotor can increase the total amount of inertia power supported to the MGs. It is obvious that the ESS controlled by the suggested technique is highly charged and discharged in response to any abnormal conditions. Therefore, in the case of high RESs penetration, larger participation can be achieved using the proposed adaptive control strategy.

B. SPECIAL CASE STUDY: SYSTEM ASSESSMENT CONSIDERING TIME-VARYING DELAY
To demonstrate the stability of the dynamical system, Lyapunov-Krasovskii functional (LKF) is one of the most working techniques, in which terms for stability analysis are derived in terms of linear matrix inequality (LMIs) [27]. Figure 19 shows the linearized model of multi-area MGs with time-varying delays (the i th control area (i = 1, 2, …, N)). The state-space representation is given below: For more details on matrices and state vectors ( ), ( ), A, B, and C (see [27], [28]). As reported in the literature survey, we observed that an increment of ( ) affects a less stable LFC system and may affect a notable mimicking in delay margins. To check the stable delay margins correctness, time-domain simulations were carried out in Fig. 24 using Matlab/Simulink R2021a. In this particular study, we tested the proposed interconnected MG in case of 0 ≤ µ > 1 for the maximum delay of 7.59 in case of ( = 0.3) fixed/tuned by the proposed Jaya-based BE modulation. The main target is to demonstrate maximum upper bound and get less conservation. Moreover, graphical results of deviation variables ∆ 1 , ∆ 2 , ∆ − are shown in Fig. 24 with consideration of fixed/adaptive sets of I-controller. It is observed from Fig 24a that  The final finding regarding this special case study of the suggested MG model becomes stable in the case of the proposed direct adaptive Jaya-based BE modulation within 0 ≤ µ > 1. In addition. It becomes unstable for the other proposed controllers if the delay is exceeding the derived upper bounds for all cases of µ > 1. Therefore, it can be easily seen that the upper bound of the delay is increased beyond the derived upper bound, the system turns into unstable nature as shown in Fig. 24b for CDM controller (which can't handle the delay for all suggested cases) and conventional integral controller and classic optimizers which start to increase until fall into the unstable region due to the incremental in by time.

XI. CONCLUSION
This paper investigates a new coordination strategy for solving LFC issues in islanded single and interconnected areas MGs. The help of using optimization techniques is appeared in this study using multi-objective seagull and Jaya optimizers. The concept of the direct adaptive control has been introduced with Jaya optimizer-based BE modulation for frequency and tieline power flow regulations considering a modified virtual rotor (virtual inertia + virtual damping) considering full participation of inverter-based ESS (100%) as a tertiary controller within both MGs to dampen the oscillations in the system. The entire balloon effect concept is designed to sense a plant's input and output signals to determine the actual transfer function at each iteration (i). Therefore, this aid increases the efficiency of the Jaya algorithm to deal with system difficulties. The main purpose of using a modified mechanism of the virtual rotor is to emulate the reduction in system inertia and the enhanced damping properties by taking into account the participation of inverter-based ESS. A performance comparative study between the proposed coordination strategy (direct adaptive Jaya-based BE modulation with the modified virtual rotor), conventional integral controller, coefficient diagram method, multiobjective seagull optimizer, and classic Jaya with/without virtual inertia controller is performed for islanded single-area and interconnected two-area MGs. It is obvious that the proposed scheme can be effectively applied to the studied MGs for online tuning of the integral secondary controller gain to minimize the deviations in the system frequency and regulate the power in the tie-line. For superiority of the proposed method, a non-parametric statistics analysis was carried out to prove the effectiveness of the proposed method against other standard metaheuristics algorithms (i.e. PSO, ESO, and SOA) and classic Jaya algorithms. This validation was supported with the speed convergence test and analysis in variance ANOVA. The final findings emphasized the effectiveness of the proposed scheme in comparison to other controllers. In addition, it has achieved effective performance and stability during high perturbations of load demands and penetrations of wind generators. In addition, it proved that the direct adaptive Jaya-based balloon effect significantly outperforms other algorithms in terms of solution quality, convergence speed, and robustness, especially for unimodal and multimodal functions. Additionally, the non-parametric statistical test confirmed that the optimality of solutions was enriched significantly.

DRAWBACKS, LIMITATIONS, AND FUTURE WORKS:
i.
The proposed algorithm has still been applied to small-scale optimization problems (<100 design variables). ii.
Additionally, we do not actually know which objective functions we wish to optimize since they rely on the behaviour of the running model. Therefore, we gather information about the objective function from past observations and use that knowledge to optimize it. iii.
Absence of the online tunning for the proposed virtual inertia and virtual damping coefficient parameters. For future works: This coordination concept can be extended in several applications such as Self-adaptive tuning of virtual rotor parameters, and Grid-forming converters applications based on the hierarchical control strategy for large-scale power plants.

DECLARATION OF COMPETING INTEREST
The authors declare no conflicts of interest concerning this work. Varying coefficient for initial time.

A.1 Power Generation of Wind
A simplified white noise-based wind power generation model is shown in Fig. A1 to obtain a precise output power profile in the renewable sources and random speeds that are adjusted by the white mass noise using MATLAB software environment that is duplicated by the initial speed of the wind. The arithmetic equations for the wind energy system can be depicted as follows: = 0.5 3 ( , ) ( . 1) where is the area of rotor sweep (m 2 ), is the density of air (kg/m3), is the wind speed (m/s) (rated), and is the rotor blade's power coefficient. is the pitch angle and it is defined below in terms of turbine coefficient 1 − 7 . where is the rotor radius.

A.2 Random load model
In [10], illustrates more details about the random load simplified model that is suggested in this research. In this model, the load deviation is simulated close to an actual load change by the following function: ∆ = . √∆ ( . )