A Novel Protection Scheme for Solar Photovoltaic Generator Connected Networks Using Hybrid Harmony Search Algorithm-Bollinger Bands Approach

: This paper introduces a new protection system for solar photovoltaic generator (SPVG)-connected networks. The system is a combination of voltage-restrained overcurrent relays (VROCRs) and directional overcurrent relays (DOCRs). The DOCRs are implemented to sense high fault current on the grid side, and VROCRs are deployed to sense low fault current supplied by the SPVG. Furthermore, a novel challenge for the optimal coordination of DOCRs-DOCRs and DOCRs-VROCRs is formulated. Due to the inclusion of additional constraints of VROCR, the relay coordination problem becomes more complicated. To solve this complex problem, a hybrid Harmony Search Algorithm-Bollinger Bands (HSA-BB) method is proposed. Also, the lower and upper bands in BB are dynamically adjusted with the generation number to assist the HSA in the exploration and exploitation stages. The proposed method is implemented on three di ﬀ erent SPVG-connected networks. To exhibit the e ﬀ ectiveness of the proposed method, the obtained results are compared with the genetic algorithm (GA), particle swarm optimization (PSO), cuckoo search algorithm (CSA), HSA and hybrid GA-nonlinear programming (GA-NLP) method. Also, the superiority of the proposed method is evaluated using descriptive and nonparametric statistical tests.


Introduction
As fossil fuel reserves are depleting, the price and related environmental concerns strongly encourage the use of renewable energies [1][2][3]. The solar photovoltaic generator (SPVG) is one of the premier alternatives to fossil fuels that generates AC from DC power by using inverters. However, the response of SPVG to grid faults is more or less controllable by the power electronics used in an inverter system [1]. Thus, this difference has to be considered when designing a protective system for SPVG-connected networks [4].
In a network without distributed generators (DGs), directional overcurrent relays (DOCRs) are a suitable choice for the protection systems because of their ease in functionality and cost-effectiveness. In the last decade, a range of evolutionary algorithms and their hybrid approaches have become recognized as a means for solving the coordination problem of DOCRs [5][6][7][8][9][10][11]. connect a SPVG system to the grid, a set of devices of protection are provided at PCC. This protection system performs the appropriate functions to prevent the SPVG feeds the network in case of abnormal values of current, voltage and frequency. This paper: • demonstrates that to develop a reliable protection scheme for SPVG-connected networks, voltage-restrained overcurrent relays (VROCRs) are deployed to sense a low fault current on the SPVG side, whereas DOCRs are used to operate with a high fault current on the grid side. VROCRs can sense a low fault current by providing the set overcurrent operating value in proportion to the applied input voltage. Also, VROCRs helps to maintain grid stability because they can avoid unnecessary isolations of SPVG networks against short-term disturbances such as voltage dips due to the fault cleared by DOCRs. • formulates a new problem of optimum coordination of DOCRs-DOCRs and DOCRs-VROCRs in SPVG-connected networks. • hybridizes the Harmony Search Algorithm (HSA) with the Bollinger Bands (BB) approach for accelerating a local search and improving the convergence and accuracy of the results. The BB method is also modified to support HSA in exploration and exploitation. • estimates the performance of the proposed hybrid approach by applying over three case studies.
The outcomes in terms of the total operating time, violations in constraints, and convergence behaviour are compared with the genetic algorithm (GA), particle swarm optimization (PSO), cuckoo search algorithm (CSA), HSA and hybrid GA-nonlinear programming (GA-NLP) methods. • performs a statistical analysis using descriptive and nonparametric tests to demonstrate the more excellent value of HSA-BB.

Problem Formulation of Optimum Relay Coordination
In the optimum coordination of relays, the foremost objective is to obtain relay settings that minimize the total operating time of relays under the coordination and boundary constraints. The objective function and the constraints formulation for optimum relay coordination are shown in the following sub-sections.

Objective Function (OF)
The OF, which needs to be minimized, is the sum of the operation times of relays when they act as primary relays [6].
where TOP i indicates the time of the primary relay R i , and k shows the number of primary relays.

Constraints
The desired constraints in the relay coordination problem should be satisfied while minimizing the OF. These constraints are formulated as follows.

Coordination Time Interval (CTI)
The time interval between the operating time of primary and backup (P/B) protection is essential for preserving selectivity. Its time interval is known as CTI, and it may be stated as: where t b and t p are the operation of times in the order of backup and primary relays.

Bounds on Relay Settings
The DOCR has only two settings of the current pickup setting (I pi ) and time multiplier setting (TMS), whereas VROCR has an additional third setting of voltage pickup setting (V pi ).
The bounds on TMS of the relay may be defined as: TMS range can be represented as a continuous value from 0.1 to 1.1 for DOCRs [5] and 0.05 to 1.1 for VROCRs [36].
The boundaries of I pi of a relay can be presented as: To ensure the security and reliability of protection schemes [6,7], I pi is determined based on two parameters, the maximum full-load current and lowest fault current.
The boundaries of V pi of the relay may be defined as: The fault in the power network is attended by a related voltage dip, while the overload causes an only modest drop in voltage. Therefore, a voltage and current measurement-based fault detection relay-such as VROCR-can discriminate between overload and fault. VROCR becomes increasingly responsive to overcurrent as the voltage of the systems drops [37]. The V pi range can be taken as a continuous value from 0% to 85% of the system nominal voltage.

Bounds on Time of Operation (TOP) of Relay
A certain minimum amount of operating time is needed for a relay. It should not take a long operating time. This constraint is defined as: where TOP min and TOP max are the minimum and maximum operating times of the relay.
where I f is the fault current. Based on the IEC 60255-3 standard, a VROCR characteristic is expressed as [36]: where V and I are the measured values of voltage and current by VROCR. I pi and V pi are the pickup settings of the current and voltage of VROCR, respectively.

Hybrid HSA-BB Method
The proposed hybrid HSA-BB approach is illustrated in this section. In the following sub-sections, a brief introduction of the HSA and BB is shown before explaining the hybridization of HSA-BB.

Harmony Search Algorithm
The HSA is a successful metaheuristic algorithm introduced by Geem et al. [38]. It is stimulated by the ideologies of the musicians' improvisation process for finding the best harmony. The flowchart for HSA is represented in Figure 1. The proposed hybrid HSA-BB approach is illustrated in this section. In the following subsections, a brief introduction of the HSA and BB is shown before explaining the hybridization of HSA-BB.

Harmony Search Algorithm
The HSA is a successful metaheuristic algorithm introduced by Geem et al. [38]. It is stimulated by the ideologies of the musicians' improvisation process for finding the best harmony. The flowchart for HSA is represented in Figure 1. The HSA can be executed in the following stages [8,[38][39][40][41].
Step 1: Initialize the optimization problem and parameters of the algorithm: For the HSA application, the OF with constraints and decision variables should be initialized as: where ( ⃗) is the objective function, P and M represent the numbers of constraints, P (equality), and M (inequality). xi shows the decision variables set, and N is the number of variables. The upper and lower boundaries for decision variables are represented in the order of xi,U, and xi,L. In this step, the algorithm parameters (i.e., harmony memory size (HMS), harmony memory consideration rate (HMCR), pitch adjustment rate (PAR)), and a maximum number of iterations are also provided. All solution vectors are stored in the harmony memory (HM). Solution vectors are improvised using HMCR and PAR, as demonstrated in step 3.
Step 1: Initialize the optimization problem and parameters of the algorithm: For the HSA application, the OF with constraints and decision variables should be initialized as: where f → x is the objective function, P and M represent the numbers of constraints, P (equality), and M (inequality). x i shows the decision variables set, and N is the number of variables. The upper and lower boundaries for decision variables are represented in the order of x i,U , and x i,L . In this step, the algorithm parameters (i.e., harmony memory size (HMS), harmony memory consideration rate (HMCR), pitch adjustment rate (PAR)), and a maximum number of iterations are also provided. All solution vectors are stored in the harmony memory (HM). Solution vectors are improvised using HMCR and PAR, as demonstrated in step 3.
Step 2: Initialize the HM: In this step, the randomly generated solution vectors (x 1 , . . . , x HMS ) are stored in the HM, according to HMS. It is defined by the following equation.
It is possible that infeasible solutions with violated constraints arise. When this occurs, the algorithm forces the search towards a feasible solution area using the static penalty function.
Step 3: Generate a new harmony by improvising the stored harmony in the HM: A new vector of harmony . , x N is formed according to the HMCR, PAR, and a random selection, which is called improvisation. According to the HMCR, ith variable of HMS can be improvised using Equation (11). HMCR is the probability of selecting a value from the stored value in the HM, whereas (1-HMCR) is the probability of randomly generating a new value. The range of HMCR is defined between 0 and 1.
If x i ' is selected from the HM, it is further tuned using PAR. PAR represents the probability of a component from the HM mutating, while (1-PAR) shows the probability of no mutation. It is expressed using the following equation.
where rand [0, 1] represents the randomly generated value in the range of 0 and 1. b w is the bandwidth of arbitrary distance for the design variable.
Step 4: Update the HM: If, according to the OF value, a newly generated vector is better than the worst one that existed in the HM, the worst should be replaced by a new one.
Step 5: Check the criterion for stopping the algorithm: Step 3 and step 4 are repeated until a stopping criterion (e.g., maximum numbers of iteration) has been met.

Bollinger Bands Approach
The Bollinger Bands method is widely used to forecast the upcoming prices of the stocks. It was developed by J. Bollinger [42]. Based on historical data, it computes the mean and standard deviation of the prices for estimating the interval. The BB for each decision variable can be premeditated using the following terms.
The mean is considered as a middle band and can be calculated for decision variable x i as: where n is the number of available samples of each variable. The standard deviation for decision variable xi is calculated as: For decision variable x i , the upper and lower bands are calculated using the following expression.
where UB i and LB i are the upper and lower bands. a is the constant value and selected in the range of 1 to 2. Further, the x i is updated by the following equation.
where x i ' is a newly generated value for variable x, and r is a randomly generated value between 0 and 1.

Hybrid HSA-BB Method
Exploration and exploitation are important parameters for metaheuristic methods. Exploration parameters ensure that algorithms will not be biased in local optima. Exploitation parameters exploit previous solutions for reducing the randomization, which ultimately helps the algorithm in faster convergence. Very strong exploitation can cause the slowing down of the exploration, which ultimately leads to premature convergence and an insignificant solution. To deal with this issue and to develop a more efficient algorithm, different search strategies are hybridized in the literature [6,7,9,39,43]. Similarly, the HSA is useful for exploring to find nearby global regions, but it has a problem of searching the local optima [39]. On the other hand, BB has good exploiting history, since it utilizes all previous components while generating new ones. Therefore, in this study, the HSA is hybridized with BB to enhance the performance of HSA in terms of a local search, accuracy of results, and convergence. Also, BB is modified to help the HSA in exploration during the initial generation and in exploitation during the final generation. The HSA and BB are hybridized as follows.
1. Adaptive Bollinger band: The value of a when calculating the upper and lower bands in BB is illustrated by Equations (15) and (16), and fixed between 1 and 2. However, a higher value of a can cause a larger gap between the upper and lower bands, and a lower value of a makes this gap smaller. From Equation (17), it is clear that during the early generations, smaller gaps will provide smaller values when updating the current value of the component (x i ), which ultimately affects exploration. However, any algorithm should be good at exploring during early generations, so that it may not be trapped in local optima. On the other hand, during final generations, a larger gap will provide a larger value while updating the current component (x i ), which ultimately affects the exploitation. As discussed earlier, weak exploitation slows down the convergence performance of algorithms. To deal with this problem, the parameter a in Equations (15) and (16) is modified such a way that it dynamically changes with each generation. It is shown by the following equation.
where NI represents the maximum number of iterations, whereas gn shows the generation number. 2. Using Equation (12), HSA performs a local search. This equation is modified using Equation (17) of BB. Initially, the HSA completes the course search by using randomization and HMCR and fills the HM. Using the solution vectors stored in the HM, BB calculates the mean and standard deviation as well as the lower and upper bands for each decision variable as given by Equations (13)- (16). It is also noted that the number of samples n is equal to the HMS. Suppose that HMS is considered as 30, then the available number of sample values of each decision variable is 30. Afterward, a new value for each decision variable is computed by Equation (17) of BB in the local search step of HSA (Equation (12) in step 3). This is illustrated as follows.
If the new solution vector of decision variables is better than the worst one stored in the HM, then the worst vector is replaced with new one. The remaining steps of the proposed hybrid approach are the same as the HSA, which is already discussed in Section 3.1.

Simulation Results and Discussion
The performance of a proposed hybrid HSA-BB approach for the optimal coordination of DOCRs-DOCRs and DOCRs-VROCRs is verified on SPVGs connected-three different power networks. The first test case has 14 DOCRs and 1 VROCR, the second has 24 DOCRs and 4 VROCRs, and the third has 78 DOCRs and 3 VROCRs. The SPVG is designed based on the data given in [1,35,[44][45][46]. ETAP software is used for modeling and fault calculation of SPVG-connected networks. Ranges of TMS are considered in all cases, from 0.1 to 1.1 for DOCRs and 0.05 to 1.1 for VROCRs, respectively. The minimum time of operation of each relay and CTI are assumed in order of 0.2 and 0.3 s for test cases 1 and 2. Both are considered to be 0.2 s in test case 3. Simulation outcomes are compared with GA, PSO, CSA, HSA, and GA-NLP for demonstrating the effectiveness of the HSA-BB. The comparative study is conducted in terms of convergence behavior and statistical analysis for an IEEE 30-bus system. The parameter values for all algorithms are given in Table 1. Pitch adjustment rate (PAR) 0.5 0.5 0.5

Case 1: 8-Bus Network
The proposed hybrid approach is implemented on a 40 MW SPVG-connected eight-bus network with a voltage rating of 150 kV. A minimum rating of 40 MW is required for SPVG if it is connected to the high voltage grid of 132 kV or above [1]. Accordingly, the 40 MW SPVG is designed, and it supplies 150 A current to the eight-bus network through bus 5, as shown in Figure 2. The data for the eight-bus network were provided in [47].  Table 2 lists the results of the current magnitude for close-in 3-Φ fault current and P/B DOCRs pairs. Table 3 contains the voltage and current sensed by VROCR for a close-in fault to each DOCR. It is learned from Table 3 that VROCR senses the maximum fault current (1.45 times the rated current supplied by SPVG) for the close-in fault to relays 5 and 11. The voltage drop (0% of system nominal voltage) is also maximum in this case. Similarly, the minimum fault current (1.15 times the rated current supplied by SPVG) and voltage drop (20.42 % of system nominal voltage) are sensed by VROCR for the close-in fault to relays 1 and 13. As shown in Figure 3, the VROCR trips for the current above 110% of the full load current supplied by SPVG, and voltage drops below 85% of the system nominal voltage. The voltage sensed by VROCR is 0 kV for the close-in fault to relays 5 and 11. The characteristic of VROCR presented by Equation (8) becomes undefined. Hence, the maximum value of 20 is assumed for in Equation (8) for the close-in fault to relay 5 and 11 in this case.    Table 2 lists the results of the current magnitude for close-in 3-Φ fault current and P/B DOCRs pairs. Table 3 contains the voltage and current sensed by VROCR for a close-in fault to each DOCR. It is learned from Table 3 that VROCR senses the maximum fault current (1.45 times the rated current supplied by SPVG) for the close-in fault to relays 5 and 11. The voltage drop (0% of system nominal voltage) is also maximum in this case. Similarly, the minimum fault current (1.15 times the rated current supplied by SPVG) and voltage drop (20.42 % of system nominal voltage) are sensed by VROCR for the close-in fault to relays 1 and 13. As shown in Figure 3, the VROCR trips for the current above 110% of the full load current supplied by SPVG, and voltage drops below 85% of the system nominal voltage. The voltage sensed by VROCR is 0 kV for the close-in fault to relays 5 and 11. The characteristic of VROCR presented by Equation (8) becomes undefined. Hence, the maximum value of 20 is assumed (8) for the close-in fault to relay 5 and 11 in this case.  8  6278  7  2068  2  6098  1  1000  8  6278  9  1180  2  6098  7  2068  9  2635  10  2635  3  3560  2  3560  10  4060  11  2520  4  3790  3  2250  11  3917  12  3700  5  2617  4  2400  12  5899  13  989  6  6293  5  1383  12  5899  14  1880  6  6293  14  1880  13  3075  8  3075  7  5402  5  1383  14  5220  1  1000  7  5402  13  989  14  5220  9 1180 .  By implementing all methods, the obtained results of relay settings, TOP of primary relays, and OF value formed by using Equation (1) are displayed in Table 4. HSA-BB provides the best minimized OF (9.636 s) compared to hybrid GA-NLP (9.795 s), HSA (12.325 s), CSA (12.533 s), PSO (14.417 s) and GA (16.916 s). The CTI between P/B DOCRs-DOCRs and DOCRs-VROCR is tabulated in Table 5. As seen from this result, the CTI is maintained at a minimum level (0.3 s) for almost all P/B DOCRs-DOCRs pairs in HSA-BB as compared to other stated methods. The CTI of P/B DOCRs-VROCR pairs is also minimal in HSA-BB as compared to other methods. As the HSA-BB gives better results than other employed methods, further analysis of VROCR operation is discussed only for the results obtained by HSA-BB.  For the close-in fault to relay 5 and 11, the CTI of relay pairs 5-VROCR and 11-VROCR is 0.745 and 0.583 s, respectively. For the close-in fault to relay 6 and 7, relay 5 operates as the first backup and VROCR as a second backup. The CTI of relay pairs 6-5 and 7-5 are 0.4340 and 0.3 s, respectively. Thus, VROCR should operate after a minimum CTI of 0.7340 s (0.4340 + 0.3) and 0.6 s (0.3 + 0.3) for the close-in fault to relays 6 and 7. As shown in Table 5, VROCR operates after 0.8711 and 0.7371 s for the close-in fault to relays 6 and 7, respectively. In the case of close-in fault to relay 10, relay 11 as the first backup operates after 0.3 s time interval. Therefore, VROCR as the second backup should trip after 0.6 s. However, VROCR operates over a long time of 1.2720 s because VROCR senses less voltage reduction and fault current for the close-in fault to relay 10 than a close-in fault to relay 6 and 7, as shown in Table 3. For the close-in fault to relay 1, 2, and 8, VROCR works as a third backup. The CTI of relay pair 1-VROCR (2.2964 s) is more extensive than relay pairs 2-VROCR (1.0884 s) and 8-VROCR (1.3533 s), since VROCR experiences minimum voltage reduction and fault current for the close-in fault to relay 1 as shown in Table 3. The CTI of relay pair 2-7 (0.3 s) is less than the CTI of relay pair 8-7 (0.5649 s). Thus, VROCR trips over a long time to the close-in fault to relay 8 than the close-in fault to relay 2. For the close-in fault to relay 9, VROCR also works as a third backup and operates over 2.0340 s. This is because it experiences a moderate voltage reduction and fault current compared to relays 1, 2, and 8. With the final results of CTI of DCORs-VROCR, it can be deduced that the operation of VROCR depends on sensing the voltage reduction and fault current supplied by the SPVG as well as its action as backup protection.

Case 2: 9-Bus Network
In this case, four SPVG-connected systems with nine buses (b 1 to b 9 ) are considered ( Figure 4). An SPVG of 8-10 MW is required for connecting to a 30-34.5 kV grid [1]. Therefore, each SPVG is designed with ratings of 8 MW and 33 kV. These are connected as SPVG 1 at b 7 , SPVG 2 at b 5 , SPVG 3 at b 9 , and SPVG 4 at b 3 . Each SPVG supplies the current of 138 A to the network. The external grid (EG) with 400-MVA short circuit capacity is connected to b 1 . The impedance of each line segment is (0.0057 + j0.071) Ω/km. The current magnitude for close-in 3-Φ fault sensed by P/B pairs of DOCRs is provided in Table 6. Table 7 shows the voltage and current sensed by VROCRs for the close-in fault to each DOCR. It can be seen that maximum fault current and voltage drop are sensed by VROCR1 for the close-in fault to relay 1, 16 and 18, by VROCR2 for the close-in fault to relay 12, 13 and 22, by VROCR3 for the close-in fault to relay 4 and 5, and by VROCR4 for the close-in fault to relay 8 and 9. Similarly, the minimum fault current and voltage drop are experienced by VROCR1 and VROCR3 for the close-in fault to relay 10 and 11, and VROCR2 and VROCR4 for the close-in fault to relay 2 and 3, respectively. Table 8 shows the use of all the approaches, and the results of relay settings, the TOP of primary relays and the OF value. It is seen from Table 8 that the OF value acquired by using HSA-BB is less as compared to GA, PSO, CSA, HSA, and GA-NLP. The CTI value derived for P/B DOCRs-DOCRs and DOCRs-VROCRs pairs for the close-in fault to each DOCR is presented in Tables 9 and 10, respectively. It is seen in Tables 9 and 10 that all the coordination constraints have been satisfied when determining the results of these methods. Also, the larger value of CTI shows the larger operating time of backup relays, which is not desirable for a protection system. In Table 9, the obtained value of CTI for P/B DOCRs-DOCRs pairs is almost maintained to the minimum prescribed level in the results of HSA-BB. Also, the fast operating time of VROCR may raise unnecessary isolation of SPVG if it is used as a backup of DOCRs, thus putting grid network stability at risk [1]. As shown in Table 10, the purpose of the larger CTI value for DOCRs-VROCRs pairs (i.e., 10-VROCR1 and 11-VROCR1, 2-VROCR2 and 3-VROCR2, 10-VROCR3 and 11-VROCR3, 2-VROCR4 and 3-VROCR4) is to ride through disturbances for avoiding the undesirable removal of SPVG. Therefore, a less sensitive setting is preferred for the VROCR when it needs to operate as a backup of DOCRs, especially for the far fault to the VROCR. SPVG of 8-10 MW is required for connecting to a 30-34.5 kV grid [1]. Therefore, each SPVG is designed with ratings of 8 MW and 33 kV. These are connected as SPVG1 at b7, SPVG2 at b5, SPVG3 at b9, and SPVG4 at b3. Each SPVG supplies the current of 138 A to the network. The external grid (EG) with 400-MVA short circuit capacity is connected to b1. The impedance of each line segment is (0.0057 + j0.071) Ω/km. The current magnitude for close-in 3-Φ fault sensed by P/B pairs of DOCRs is provided in Table   6.     1  5817  17  2980  16  3940  17  2980  2  2338  4  2338  17  8091  20  168  3  3145  1  3145  17  8091  22  122  4  4206  6  4005  17  8091  24  301  5  1731  3  1530  18  3596  2  759  6  5666  8  976  18  3596  15  2636  6  5666  23  4690  19  8091  18  122  7  5666  5  976  19  8091  22  122  7  5666  23  4690  19  8091  24  301  8  1731  10  1530  20  3508  13  1754  9  4206  7  4206  20  3508  16  1754  10  3145  12  3145  21  8091  18  122  11  2338  9  2338  21  8091  20  168  12  5811  14  2630  21  8091  24  301  12  5811  21  2980  22  3596  11  759  13  3940  11  759  22  3596  14  2636  13  3940  21  2980  23  7912  18  122  14  5244  16  1754  23  7912  20  122  14  5244  19  3490  23  7912  22  168  15  5244  13  1754  24  1952  5  976  15  5244  19  3490  24  1952 8 976

Case 3: IEEE 30-Bus Network
To confirm the success of the proposed hybrid approach, its performance needs to be demonstrated using a larger and more complex system. For this task, the IEEE 30-bus network is selected, as shown in Figure 5. It can be considered as a meshed sub-transmission and distribution system [10]. This complex power network has 30 buses (132 kV and 33 kV buses), 37 lines, 78 DOCRs and 3 VROCRs. In addition, three SPVGs with the rating of 8 MW are connected to the distribution network (33 kV) as SPVG 1 at b 19 , SPVG 2 at b 22 and SPVG 3 at b 23 . As it includes VROCRs, the total number of constraints increased to 666 as compared to 426 when considering only DOCRs in the test system. Thus, optimization methods have to consider highly constrained optimization problems in this test case.      Table 11 shows the results obtained by implementing all the methods for the IEEE 30-bus system. It comprises the OF values, numbers of violated coordination constraints, required numbers of iteration, and convergence time. The given OF value by HSA-BB, shown in Table 11, is the minimum compared to all other methods. It is also experienced that during the simulations of this complex system, sometimes hybrid GA-NLP does not converge even at a feasible solution and stops prematurely. Also, a violation of coordination constraints has been observed in GA, PSO, CSA, HSA, and GA-NLP, whereas there is no violation observed in the results of the proposed methods. The convergence of all algorithms is graphically illustrated in Figure 6. As seen in Table 11 and Figure 6, the numbers of iteration and convergence time are also lowest in the HSA-BB method as compared to GA, PSO, CSA, HSA, and GA-NLP methods. The simulation results confirm that HSA-BB gives better results compared to the remaining methods. However, the proposed HSA-BB algorithm has more parameters to be tuned as compared to the other methods. The tuning of the parameters is indeed a time consuming and tedious task. Also, the harmony memory size is bigger than the initially generated nest of the cuckoo search method. Therefore, it requires more memory to store the solutions.   Table 11 shows the results obtained by implementing all the methods for the IEEE 30-bus system. It comprises the OF values, numbers of violated coordination constraints, required numbers of iteration, and convergence time. The given OF value by HSA-BB, shown in Table 11, is the minimum compared to all other methods. It is also experienced that during the simulations of this complex system, sometimes hybrid GA-NLP does not converge even at a feasible solution and stops prematurely. Also, a violation of coordination constraints has been observed in GA, PSO, CSA, HSA, and GA-NLP, whereas there is no violation observed in the results of the proposed methods. The convergence of all algorithms is graphically illustrated in Figure 6. As seen in Table 11 and Figure 6, the numbers of iteration and convergence time are also lowest in the HSA-BB method as compared to GA, PSO, CSA, HSA, and GA-NLP methods. The simulation results confirm that HSA-BB gives better results compared to the remaining methods. However, the proposed HSA-BB algorithm has more parameters to be tuned as compared to the other methods. The tuning of the parameters is indeed a time consuming and tedious task. Also, the harmony memory size is bigger than the initially generated nest of the cuckoo search method. Therefore, it requires more memory to store the solutions. Furthermore, a comparative study of all the methods is performed, using descriptive and nonparametric statistical tests. Table 12 shows the results of a descriptive statistical study based on 50 runs. The lower value of standard deviation in the results of HSA-BB indicates that it gives the most predictable results in all 50 runs, compared to other methods. Additionally, because the mean and worst values are very near to the best value, quality results are obtained by HSA-BB. Moreover, paired t-test and Wilcoxon signed-rank tests are widely used to determine the significant difference in the behavior and superiority of algorithms. However, the paired t-test is a parametric test and needs to be certain that the essential conditions are satisfied, i.e., independence, normality [48,49]. The condition of independence is fulfilled because 50 samples of the OF are obtained by 50 simulations of all algorithms with randomly produced initial seeds. Furthermore, samples from different runs were normal when their behavior assisted a normal or Gauss distribution. Furthermore, a comparative study of all the methods is performed, using descriptive and nonparametric statistical tests. Table 12 shows the results of a descriptive statistical study based on 50 runs. The lower value of standard deviation in the results of HSA-BB indicates that it gives the most predictable results in all 50 runs, compared to other methods. Additionally, because the mean and worst values are very near to the best value, quality results are obtained by HSA-BB. Moreover, paired t-test and Wilcoxon signed-rank tests are widely used to determine the significant difference in the behavior and superiority of algorithms. However, the paired t-test is a parametric test and needs to be certain that the essential conditions are satisfied, i.e., independence, normality [48,49]. The condition of independence is fulfilled because 50 samples of the OF are obtained by 50 simulations of all algorithms with randomly produced initial seeds. Furthermore, samples from different runs were normal when their behavior assisted a normal or Gauss distribution. better fault detection for low fault current contributed by SPVG, and high fault current contributed by the grid. It also avoids unwanted isolation of SPVG in the case of short-term disturbances.
A hybrid HSA-BB method is employed to resolve the unique challenge of optimal coordination of DOCRs-DOCRs and DOCRs-VROCRs on three different SPVG-connected networks. The BB methodology is used in the improvisation stage of HSA. The BB method is also modified to dynamically adjust the gap between upper and lower bands with generation numbers so that it helps HSA in both exploration and exploitation.
For evaluating the capability of the proposed method in solving the relay coordination problem, the obtained results are compared with other well-established methods (GA, PSO, CSA, HSA, and GA-NLP). Outcomes of the comparative analysis validate that a significant reduction in the total operating time of relays is obtained using hybrid HSA-BB without violating the constraints compared to the other methods. In addition, the hybrid HSA-BB method takes minimum iteration to reach the best optimum solution, which reveals that the proposed method is also better in convergence performance. From the descriptive statistical test, it is found that the proposed method gives consistent solutions for different runs, which shows the capability of the proposed method in providing a better-quality solution. Furthermore, the results of nonparametric tests verify the significant difference in behavior as well as the superiority of the hybrid HSA-BB method compared to the other employed methods.