Application of the JAYA Algorithm in Solving the Problem of the Optimal Coordination of Overcurrent Relays in Single-and Multi-Loop Distribution Systems

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Introduction
Power systems are growing day by day, which has created some unwanted security problems and threat issues related to the reliability and stability of the systems under a threat condition.Such issues are highly important for power system engineers [1][2][3].To keep the system in a reliable condition and to ensure that there is continuous power without any interruption to industries, telecommunication networks, and at the consumer level, there is a need for a fast, stable, and reliable system that can handle such a problem in a quick manner without any delay.In a power system, the protection system is one of the counteragents that detects and clears a fault as soon as possible [4,5].
e protection system is a combination of di erent overcurrent relays (OCRs) and circuit breakers.ese protection relays sense the faulty portion in the system and isolate it in order to guarantee that the system excludes the least amount of the strong portion of the system in real time.In a protection system, the applicable strategy of relays is necessary to keep the proper operation of the overall protection system smooth.e key objectives of the coordination problem are to guarantee that the relays do not work out of the circle, to hide the unimportant disconnectivity of the robust portion, and to evade maloperation of the relays.e faulty portion in a power system is promptly disengaged with the help of circuit breakers by these relays once it satis es the necessities of selectivity, sensitivity, and reliability that makes the coordination important for these relays [6].e OCRs are a useful choice in a technical and economic sense for the industrial area in view of the primary protection in a sub-transmission system and backup protection in a transmission system [7,8].e goal of optimal coordination issue is to sort out the minimal relay setting, which is subject to Complexity 2 relay characteristic graphs, constraints, and the restriction of the relay settings [9].e optimization theory dealing with nding the optimal relay coordination performs a vital part in power network [10].Recently, scholars and researchers have used different types of optimization methodologies are not only limited to OCR coordination problem but also have signi cant application in di erent elds [11][12][13].In [14], whale optimization algorithms were introduced to relay coordination problem.In [15], a re y algorithm (FA) was used to analyse directional overcurrent relay (DOCR).In [16], grey wolf optimization was used to interrogate the relay problem.In [17][18][19][20][21][22], various styles of particle swarm optimization were interrogated to deal with the relay coordination issue.In [23][24][25][26], a di erent version of a genetic algorithm to enhance the convergence characteristics of the genetic algorithm was applied.In [27,28], root tree algorithms were introduced to relay coordination problem.In [29], the CFA was proposed to assess the coordination issues.In [30], a hybrid symbiotic organism optimizer was proposed to resolve OCR issue.In [31], comparative study was done using di erent metaheuristic algorithms.In [32], the DOCR is formulated as mixed-integer nonlinear problem and was solved using hybrid whale optimization.
e drawback of the previous optimization techniques, as well as the metaheuristic, and evolutionary optimizations is the possibility of merging to standards that may not be optimal but instead are trapped at a local optimal value.To comprehend this problem, a JAYA algorithm strategy is inspected in this investigation to determine the precise and optimal OCR coordination and is related to other up-to-date algorithms.
is paper proposes the JAYA algorithm for nding the optimal coordination of OCR.To con rm the e ciency of the suggested JAYA algorithm, it is related to other methods of factors identi cation problems for di erent OCR models.e simulation results and analyses validate that JAYA shows a greater performance in terms of its precision and consistency.e e ciency of JAYA is validated through inclusive simulations and evaluations on parameters identi cation problems of various multi-loop distribution systems.us, JAYA can be an actual substitute for other complex optimization issues of higher and more complicated bus systems.

Formulation of OCR Problem
e relay coordination in a single-and multi-loop system is explained as an optimization issue.e objective function related to this problem is as follows: where the parameters and , are the weight and operational time of the relay, respectively.For every relay, = 1 [33, 34].Hence, the characteristic curve for the operational relay can be taken from a section of the selectable pronouncement of IEC rules and can be characterized as follows: where and are stable parameters that illustrate the relay features and are most likely equal to = 0.14 and = 0.02 for a normal inverse-type relay.e terms and are the pickup current and time multiplier setting of the ℎ relay, respectively, while is the fault current moving through relay .
where is the primary or main pickup current and PSM stands for the plug setting multiplier and Condition 4 shows the nonlinear behaviour because of the variable factor of PSM.ese problems can be converted into linear programming by assuming that the PSM is constant and taking the operational time of the relays, which is a linear function of the TMS.In the case of a linear problem, all the parameters are kept constant except for TMS, which is continual, so condition 4 becomes: where erefore, the objective function can be expressed as follows:

Constraints.
e aggregate operational time can be limited under two sorts of requirements, containing the limitations of the relay factor and the constraints coordination.e primary limitations comprise the cuto points of the TMS, while the alternate requirements are pertinent to the coordination of the primary/backup relays.e bounds on the constrained problem can be seen as follows: where the parameters and are the primary (or main) and backup (or secondary) relay operating times, respectively, and CTI is the coordination time interval.

JAYA Algorithm
e JAYA algorithm is a recently developed populace-built merger method for resolving di erent types of optimization problems, including the constrained and unconstrained (5) = , ) − 1 .
, Complexity problems developed by Rao in 2016 [35].e key objective of the JAYA algorithm is that once the solution is achieved for a particular problem, the optimal result must be reached, thereby simultaneously avoiding the worst result.JAYA is a Sanskrit word meaning victory.e JAYA algorithm dependably endeavours victory by achieving accomplishments for discovering an optimal solution and attempts to overlook discontent by moving a long way from the worst solution.e JAYA algorithm attempts extraordinary endeavours to successfully discover the genuine result and solution, so it is named the JAYA algorithm.is optimization technique is very pretentious in an application perspective.Additionally, it contains noalgorithm-speci c parameters and congregates to optimum elucidation in reasonably fewer number of function evaluations.e main advantage of the JAYA algorithm compared to further evolutionary algorithms is that it is unrestricted to algorithm-speci c parameters and utilizes only two common parameters, that is, population size and the number of iterations.In cases of other optimization techniques, which require a scaling factor and crossover prospect, for example, when a particle swarm optimization needs an inertia weight, the learning factor and acceleration coe cient are used for the initial initialization.In this way, an imperative advantage of the JAYA calculation is its expert abilities, as far as ignoring the endeavour of changing constraints and reducing the time required for the optimization process.ere are many applications of the JAYA algorithm in di erent research areas.In [36], JAYA was used for thermal devices.In [37], the JAYA algorithm was used in a linear power system to nd an interconnection.In [38], JAYA was used in the area of modern machining processes.In [39], an optimal power ow solution was resolved by JAYA.In [40], elitist-JAYA was used for design optimization of heat exchanger.In [41], JAYA was used for maintenance consideration of heat exchanger.In [42,43], JAYA was used to solve di erent engineering optimization problems.In [44], JAYA was used for the optimization of an integral controller.In [45,46], an economic load dispatch optimization was validated using di erent version of JAYA.Suppose f(x) is an objective function with D dimensional factors (j = 1,2,...,D), and x i,j is the estimation value of the j th variable for the i th competitor solution.us, xi = (x i,1 , x i,2 ,..., x i,D ) is the position of the i th candidate solution.e best competitor solution x = (x best,1 , x best,2 ,..., x best , D ) has the best estimation of f(x) in the present populace, while the worst candidate solution x worst = (x worst,1 , x worst,2 ..., x worst,D ) is the estimation of f(x) in the present populace.At that point, x i,j , is simpli ed using Eq. ( 10).

Where
, and , are the values of the j th variable for the best and worst solutions, respectively.ὔ , is the updated value of , and ᐈ ᐈ ᐈ ᐈ ᐈ , ᐈ ᐈ ᐈ ᐈ ᐈ is the absolute value of , .rand 1 and rand 2 are two equally disseminated arbitrary numbers within [0, 1].In Eq. ( 10), the term rand 1 .
the a ection of the clari cation that attracts the best solution and improves the worth of the superlative clari cation in each iteration.Exploring the JAYA optimization technique, once the solution is achieved, it moves closer to the nest result and starts moving away from the worst solution.In this entire procedure, the JAYA algorithm seeks to achieve victory by forthcoming to the preeminent result; thus, it is entitled as JAYA.

Structure of JAYA.
In view of the previously mentioned explanations, the pseudocode of the JAYA optimization technique can be condensed in Algorithm 1.In addition, the owchart of JAYA is shown in Figure 1.It can be seen that the con guration of JAYA is straightforward and unique, and no extra parameters are required for the initialization in the JAYA; that is, JAYA is likewise unrestricted from algorithm-speci c parameters.

Results and Discussion
A proper code has been generated in MATLAB so ware to nd the optimal value of the OCR in a single-and multi-loop distribution network using JAYA.e e ciency and performance of JAYA were tested for the di erent single-and multi-loop systems, and it was found that JAYA gave the most satisfactory and even better results in all case studies.ree case studies were used, and the system details of all the case studies can be seen in references [23,29,47,48].In each case study, the following JAYA factors were used.
Populace size = 50.A maximum number of iterations = 200.e far-reaching clari cation of the issue plan and the use of JAYA to locate the optimal resolution are demonstrated for all case studies.

Case 1.
As shown in Figure 2, a multi-loop network with 6 OCRs is taken into account and with negligible line charging admittances.A di erent combination and con guration of primary/backup pairs are modelled depending on the location of fault currents in di erent feeders.  1 shows the line data of the system.Table 2 shows the primary/ backup pair of relays.For this illustration, 4 fault locations considered are depicted in Figure 2. Table 3 shows the CT ratios and plug settings.Table 4 shows constant and the current seen by relays for di erent fault locations.
In this illustration, the entire number of constraints that arise is eleven; six constraints are due to bounds on the relay operating time, and four constraints are by reason of the coordination criteria.e minimum operating time (MOT) of each relay is 0.1 s. e TMSs of all six relays are x 1 -x 6 .
e optimization problem can be formulated as follows: ( Hence, the constraints mentioned in equations ( 13) to (17) oppose the constraints of the minimum value of the TMS.However, these constraints are renovated as follows: e constraints arising as a result of the coordination of relays with CTI taken as 0.3 are as follows:

Application of JAYA.
To implement JAYA into the proposed idea, the objective function had been rst changed to an unconstrained issue by incorporating the limitations of relay into the objective function, as discussed in Section 2.
e lesser and higher limit of the entire TMS of the relay is deliberated as between 0.025 and 1.2, except for x 1 , which (18) 2 ≥ 0.025,   6. e JAYA outperforms the CGA, FA, CFA, and RTO in overall time gain and gives bene t of 4.0072 s, 4.3772 s, 2.8172 s, and 0.0572 s, respectively.However, in the case of CPSO, similar optimal result is obtained by using the JAYA algorithm with more execution time, where the computational and execution time taken by the CPSO to reach the optimum solution is approximately 8.007417 s.While in the case of JAYA, the computational and executive time is 0.041196 s when the CTI is 0.3 s.All in all, the algorithm that requires fewer capacity assessments to obtain a similar best arrangement (result) can be considered to be better when contrasted with an alternate algorithm [35].Moreover, the JAYA algorithm is superior to the further optimization methods cited in the references in terms of using less computational exertion, which is a requisite to achieve the most superlative and nest solution.Be that as it may, the other algorithms speci ed in the literature require legitimate tuning of particular algorithm parameters, notwithstanding tuning of the regular controlling parameters.An adjustment in the tuning of the algorithm particular parameters impacts the viability of the algorithm, while in the case of JAYA, it is free from algorithm-speci c parameters.

Case 2.
A multi-loop system with 8 OCRs is depicted in Figure 5.A di erent combination and con guration of the value obtained over the span of recreation for the best applicant in each generation is depicted in Figure 3, which shows that the convergence is faster and a reasonable value is achieved in fewer iterations.e optimal value of the objective is found to be 11.8728 s by assuming CTI is 0.3 s, which is obtained in less than 25 iterations.e values appearing in Table 5 demonstrate that the JAYA algorithm gives a perfect course of action and a streamlined total working time up to the optimum values.
e optimal values ensure that the relay will enact in the most reduced diminished conceivable time in the system for a fault at any portion.Figure 4 delineates a graphical portrayal of the time multiplier setting contrasted with the literature.e aggregate net pickup in time accomplished by the suggested JAYA is shown in Table 6, exhibiting the predominance and favourable circumstances of JAYA over the strategies said in the literature.

Comparison of JAYA with the CGA, FA, CFA, CPSO, and RTO Algorithms.
To evaluate the performance of the suggested JAYA technique, the outcomes obtained by utilizing the JAYA technique are contrasted with the outcomes acquired by the other metaheuristic optimization methods, such as the continuous genetic algorithm (CGA), re y (FA), chaotic re y (CFA), continuous particle swarm (CPSO), and RTO optimization technique available in the literature as shown TMS CPSO [22] (CTI ≥ 0.3) CGA [23] (CTI ≥ 0.3) RTO [27] (CTI ≥ 0.3) FA [29] (CTI ≥ 0.3) CFA [29] (CTI ≥ 0.    Hence, the constraints stated in equations ( 31), ( 32), (35), and (36) oppose the constraints of the minimum TMS value.Hence, these constraints are renovated as follows: e constraints arising as a result of the coordination of OCRs with the CTI taken as 0.6 s are as follows:  -Indicates the fault is not seen by the relay.all the coordination constraints.Figure 7 depicts the optimized graphical representation of the TMS values of all eight relays with the other techniques mentioned in the literature.JAYA outperforms GA and RTO in this case study as well and obtaining the best result over RTO and GA.

Fault point
e aggregate net time gain accomplished by the proposed JAYA is shown in Table 10, exhibiting the predominance and points of interest of JAYA over the genetic and RTO algorithms speci ed in the literature.

Comparison of JAYA with the Genetic Algorithm and RTO Algorithm.
e outcomes obtained by utilizing the JAYA calculations are contrasted, and the outcomes acquired by the genetic and RTO algorithms are shown in Tables 9 and 10.JAYA outperforms the GA and RTO in attaining optimum values of e outcomes depicted in Table 9 guarantee that the OCRs operate at any proportional conceivable period for a fault at any time in the network and will also maintain coordination.
e objective function obtained over the span of the simulation for the preeminent candidate solution in every iteration is shown in Figure 6, which shows that the convergence is faster and obtains the optimum solution in fewer number of iterations.All the optimal values obtained by JAYA satisfy is overall time gain is su cient given that it is a very small system.In all conditions, the JAYA performed outstandingly in minimizing the overall operational time up to an optimal value and will maintain proper coordination as well during a fault condition.Additionally, less computational and execution time is taken by JAYA to reach the optimum solution.In all the situations, the value obtained by JAYA for all the OCRs will ful l the coordination constraints.Moreover, no desecration has been established regarding the coordination constraints.

Case 3.
A parallel single end feeder distribution system that is nourished from a solitary end is shown in Figure 8 with ve overcurrents.ree various fault locations were deliberated.e load current for the period of the fault was presumed to be negligible.Table 11 shows the primary and backup associations of the OCR CT.Table 12 shows CT ratios and plug settings of the OCRs.To assess the execution of the suggested JAYA technique, the results obtained by utilizing the JAYA technique are di erentiated with the results acquired by the other optimization methods, that is, the two-phase simplex method (TPSM), FA and CFA optimization techniques available in the references, as depicted in Table 15.e JAYA outperforms the FA and CFA in overall time gain, contributing an advantage of 1.01 s and 0.091 s for the optimization problem stated in equation (49).In the second optimization problem stated in equation (50) of Case 3, the JAYA is again contributing an improvement of 0.0769 s over the TPSM algorithm, respectively.e optimum value of the objective function is determined to be 0.7286 s for the objective function depicted in equation (49) and 2.1931s for the objective function depicted in equation (50), which is obtained in less than 25 iterations.Figure 11 portrays the streamlined graphical portrayal of the TMS, which demonstrates that the TMS is minimized up to ideal and optimal values.

Conclusion
In this paper, the JAYA algorithm is suggested to exactly and progressively evaluate the constraints of various OCR models.
e aforementioned JAYA technique does not involve any parameters for tuning and hence is simple to implement.JAYA is analysed over parameter identi cation issues of OCR models.
e simulation results demonstrate that JAYA has a better performance in terms of precision and consistency compared with other methods in the literature.e results obtained by JAYA technique e ectively minimize all the three models of the issue.
e performance of JAYA can be seen from the minimum function estimation acquired by the JAYA to reach the optimal value compared to other algorithms from the literature.
In Case 1, the objective function value is minimized up to optimum value by JAYA and gives an advantage in total net gain in time of 4.0072 s, 0.0572 s, 4.3772 s, and 2.8172 s over CGA, RTO, FA, and CFA.In case 2, the JAYA gives a total net gain in time of 1.728 s and 6.93 s, over RTO algorithm and GA, while in case 3, the JAYA gives a total net gain in time of 1.01 s, 0.91 s, and 0.0769 s over the FA, CFA, and TPSM algorithm.us, JAYA is a hopeful candidate solution for solving the constraint identi cation problem of OCR models.
In the future work, this technique will be used to solve issues of OCR and DOCR of higher and more complex case studies in power systems.e objective function was utilized by the suggested JAYA algorithm with indistinguishable parameters.e optimal values of the TMS and the total operating time attained are given in Table 14, which likewise furnishes the similar a ere ect of JAYA with other numerical and developmental improvement strategies in the literature.In this delineation, no infringement or miscoordination of the relay has been discovered.It has been discovered that the time taken by relay R1 to start its activity is the slightest for a fault at point A and will need additional time for a fault at points B and C. Table 14 guarantees that the relay will e ort at any proportion at any conceivable time for a fault at any time in the system.e objective function value obtained during the course of the simulation for the nest candidate arrangement in every iteration appears in Figures 9 and 10, which validates that the convergence is prompter and acquires the preeminent values in fewer iterations.All the TMS values obtained for OCR values ful lled all the coordination limitations.Figure 11 portrays the streamlined graphical portrayal of the TMS values of all ve relays with the other optimization methods stated in the references.Additionally, the JAYA outperformed the TPSM, FA, and CFA in this case study and obtained the satisfactory and best results, rather than another optimization algorithm.Table 15 shows the overall time gain accomplished by the suggested JAYA, exhibiting the predominance and favourable circumstances of JAYA over the TPSM algorithm, and FA and CFA speci ed in the references.

T 5 :
Optimal TMS values for Case 1.

F 3 :
Convergence characteristics of JAYA for 20-time execution for Case 1. Complexity the primary/backup association of the relay.

T 8 :
Constants and relay currents for Case 2.

F 6 :
Convergence characteristics of JAYA for 20-time execution for Case 2.

F 9 :
Convergence characteristics of JAYA for 20-time execution for Case 3 for the objective function mentioned in equation (49).

F 10 :
Convergence characteristics of JAYA for 20-time execution for case 3 for the objective function mentioned in equation (50).Complexity 4.3.3.Comparison of JAYA with the FA, CFA, and TPSM Algorithm.

F 11 :
Comparison of the graphical representation of optimal TMS with FA, CFA, and TPSM algorithm for Case 3.

T 15 :
Comparison of the total net time gain achieved by the proposed method for Case 3. 49, 50 represent the objective function mentioned in equations (49) and (50).
was con ned by lesser and higher bounds.epopulacewascarried to the tness function, and the corresponding values of the objective function are recognized.By performing 200 iterations, the optimum values of the obtained TMS are given as in Table5.Table5depicts the optimal TMS value acquired by the depicted technique for this illustration and assessment with the aforementioned techniques.e objective function

Table 8
+ 28.975 2 + 37.736 3 + 11.502 4 + 3.297 5 + 3.297 6 + 4.9807 7 + 30.7994 8 .primary/backuppairsaremodelleddepending on the location of the fault currents in the di erent feeders.Six fault locations were deliberated.Table7shows the overall fault current and Comparison of the graphical representation of TMS with the CGA, FA, CFA, and CPSO and RTO algorithms for Case 1. JAYA algorithm with indistinguishable factors from that clari ed in case study 1. e ideal estimations of the acquired TMS are given in Table9, which demonstrates that the TMS and the overall operational time are optimized.
Comparison of the graphical representation of the optimal TMS with the RTO algorithm and GA for Case 2. Mathematical Modelling of the Problem Formulation.In this case study, the total number of constraints is nine; ve constraints are bounded by relay operational time, and four constraints arise as a result of the coordination criteria.0.1 s is the MOT of each OCR.e CTI is considered as 0.2 s. e TMSs of all the relays are x 1 -x 5 .Table13shows constant for various fault areas.In this illustration, two problems are formulated from Table13to compare them properly with the literature.=13.719 1 + 6.265 2 + 13.719 3 + 6.265 4 + 2.004 5 .theTMS and overall time gain, contributing an advantage of 6.93 s and 1.728 s over the GA and RTO algorithm, respectively.