Optimal Coordination of Standard and Non-Standard Direction Overcurrent Relays Using an Improved Moth-Flame Optimization

In this paper, an efficient optimization technique, called improved moth-flame optimization (IMFO) is proposed to improve the performance of conventional Moth-flame optimization (MFO). Then, both of MFO and IMFO are applied to solve the coordination problem of standard and non-standard directional overcurrent relays (DOCRs). In the proposed IMFO, the leadership hierarchy of grey wolf optimizer is used to improve the performance of conventional MFO with the aim of finding the best optimum solution. The major goal for optimal coordination of DOCRs is to minimize the total operation time for all primary relays as well as satisfy the selectivity criteria between relay pairs without any violation in the operating constraints. The performance and feasibility of proposed IMFO are investigated using three different networks (8-bus network, 9-bus network, and 15-bus). The proposed IMFO is compared with conventional MFO and other well-known optimization techniques. The results show the effectiveness of the proposed IMFO in solving both standard and non-standard DOCRs coordination problems without any violation between primary and backup relays. In addition, the results show the power of proposed IMFO in finding the best optimal relay settings and minimizing the total operating time of relays which its reduction ratio reaches more than 28% with respect to the conventional MFO. Furthermore, the reduction in the total operating time of primary relays reaches more than 50 % with the usage of the non-standard relay curve.


I. INTRODUCTION
Protective relays play an important role in saving continuity of the electric power network. The main goals of a protective relay are to isolate only fault part quickly, keep healthy parts in service, and maintain the reliability of the electric network. DOCRs are generally applied in the protection of distribution networks and sub-transmission networks [1]. DOCRs initiate when the current magnitude exceeds a predetermined value (pickup current) and flows in front of the relay [2]. The coordination problem of DOCRs is considered as a non-linear optimization problem with many operating The associate editor coordinating the review of this manuscript and approving it for publication was Mohammad Ayoub Khan .
constraints [3]. The operating time of DOCRs depends on pickup current (Ip) and time dial setting (TDS). In optimal coordination of DOCRs, the right chosen of these settings is very important [4]. The primary relay shall isolate faults quickly in its own area to minimize the system outage to the smallest area. After a specified delay time, backup relays shall be initiated to clear the fault in case of primary relays failed to work [5]. Hence, the main goal of optimal coordination of DOCRs aims to minimize the summation operating time for all relays and keep a time margin between backup and primary relays [6]. Different methods have been reported to find the optimal solution for relays coordination problem. Many heuristic methods were suggested to solve the coordination problem. The trial-and-error method was initiated to find the optimal setting of DOCRs [7]. However, the obtained TDS values of the relays using this method are relatively high, that may lead to damage electrical equipment or reduce their life span [4]. Linear programming (LP) algorithm and Non-Linear Programming (NLP) have been suggested to solve DOCRs coordination problems. In LP, methods such as simplex methods [8] and Big-M methods [9] has been suggested. In this method, the nonlinear coordination problem is converted to the linear problem by a fixed value of pickup current (Ip) [1]. Despite LP is a fast and simple method, it only helps in optimizing the TDS. Also, it may not yield an optimal solution [10]. In NLP, a method is used to solve the coordination problem by in order to optimize both relay settings such as sequential quadratic programming (SQP) which has been proposed in [11]. NLP may get stuck in local minima due to their dependency on the initial values of relay settings [12]. Nowadays, solving the DOCR coordination problem using metaheuristic algorithms has received great consideration [13]. Different techniques have been proposed to deal with the optimal coordination problem such as teaching learning-based optimization (TLBO) [13], genetic algorithm (GA) [14], particle swarm optimization (PSO) [15], Modified water cycle algorithm (MWCA) [1], and biogeography-based optimization (BBO) [7], have been proposed to find the optimal solution for the DOCRs coordination problem. User-defined characteristics using non-standard curve has been suggested in [16]. However, in [16], large operating times are obtained.
In this paper, an efficient optimization technique, called IMFO is proposed and applied for solving the optimal coordination problem of DOCRs. The proposed technique enhances the convergence performance of the conventional MFO technique with the aim of finding the best optimum solution. The proposed technique is applied for two cases, standard and non-standard DOCRs characteristic curves, using three test systems for each case. Digital relays can be operated according to the conventional relay characteristics, as well as other large range of characteristics. Hence, two variables are added to conventional relay settings in case of non-standard DOCR characteristics curve. In this case, the DOCRs have four variables (TDS, Ip, α, and β). The proposed technique will find their optimal values and maintain the coordination margin between relay pairs. However, the main contributions of this paper could be summarized as follows: -An effective optimization technique, called improved moth-flame optimization (IMFO) has been proposed to improve the performance of conventional Moth-flame optimization (MFO). -Both conventional and proposed MFO techniques have been adapted to solve the optimal coordination problem of DOCRs. -Both standard and non-standard DOCR characteristics have been considered in solving the optimal coordination problem of DOCRs using conventional and proposed MFO techniques.
-The performance and feasibility of the proposed IMFO technique has been assessed and investigated using three different networks (8-bus network, 9-bus network, and 15-bus) in each case of standard and non-standard DOCR characteristics. -Using the proposed IMFO technique, remarkable minimization in total operating time of all primary relays subject to the sequential operation between relay pairs has been achieved. -The results obtained by the proposed IMFO technique has been compared with those obtained by the conventional MFO. From these results, the effectiveness and superiority of proposed IMFO to solve the DOCRs coordination problem and converge to the global minimum solution faster than the conventional MFO technique has been proved. -The results show the power of the proposed technique to find the best optimal relay settings and minimize the total operating time of relays which its reduction ratio reaches more than 28% with respect to the conventional MFO in case of standard relay curve. The obtained results prove the effectiveness and superiority of the proposed technique compared with well-known and recent optimization algorithms. The rest of this paper is organized as follows. Section II describes the objective functions, coordination problem formulation of DOCRs. Section III illustrates MFO and proposed IMFO techniques. Section IV presents the results obtained by MFO and proposed IMFO techniques for three different test networks. The conclusions are given in Section V.

II. PROBLEM FORMULATION
The main goal of solving the DOCRs coordination problem is to maintain the reliability of the electric networks. The main objectives of this paper are to minimize the total operating VOLUME 8, 2020 time of all primary and keep selectivity between relay pairs without any violation [1], [17]. The proposed objective functions can be written as follows: Tpr k (1) where, Tpr is the operating time of primary relay and E is the number of primary relays in the system. According to IEC 60255, the operating time for DOCR can be expressed as follows [1], [18]: where, CT is the current transformer ratio, I f is the fault current (A). The relay values, α and β, are presented in TABLE 1 [19].

A. CONSTRAINTS
The goal functions should be met under two categories of constraints. These categories include relay characteristics and coordination constraints.

1) CONSTRAINTS OF RELAY CHARACTERISTICS
Boundaries of relay settings can be expressed as follows: where, Ip min and Ip max are the lower and upper boundaries of pickup current, respectively, Ps min and Ps max are the lower and upper of PS, respectively. TDS max and TDS min are the upper and lower boundaries of TDS, respectively. Tp max and Tp min are the limits range of operating time for primary relays [19]. The β min and β max are the upper and lower constant values of overcurrent relay characteristics, respectively, α min and α max and are the limits range for constant of DOCR relay characteristics, respectively [16].

2) COORDINATION CONSTRAINTS
The selectivity criteria and avoiding mal-operation are the main purposes of the coordination constraints. These criteria can be guaranteed through the right sequential operation between relay pairs [20]. All relays (backup and primary and relays) sense fault simultaneously. After a certain time, backup relays shall initiate in order to maintain the selectivity criteria and create a discrimination margin between relays pair in case of primary relay failed to work [7]. This time is known as the coordination time interval (CTI), which can be expressed as follows: where, Tb is the operating times of backup relays. The CTI value varies from 0.20 to 0.50 s [1].

III. MFO AND IMFO TECHNIQUES A. MOTH-FLAME OPTIMIZATION
MFO algorithm is one of the metaheuristic optimization technique, that is motivated by movement methods of moth's respect to the moonlight. The moth exploits a mechanism called transverse orientation for movement. The candidate solutions in the MFO algorithm is moths. The variables of the optimization problem are the position of moths in the space. The MFO is a population-based algorithm, the set of moths is represented as follows [ 21]: where, h is the variables numbers and m is the moth numbers. A matrix for storing moths corresponding to goal function values can be expressed as follows: where, m is the moths' number. In MFO algorithm, there are other components called Flames. The set of flames is represented as follows: Based on the goal function values, the flames are sorted, which can be express as follows: Flames and moths are both solutions in the MFO algorithm. The main difference between flames and moths is the way of updating them in each iteration [21]. The moths move around the search space. Flames can be regarded as flags and each moth searches around a flag and updates it in case of finding a better solution. The mathematical model of updating location of moth regarding to a flame can be expressed as follows: 87380 VOLUME 8, 2020 where Y w indicates the w th flame, K r indicates the r th moth, and D r indicates the distance of the r th moth for the w th flame. The parameter q is a constant and g is a random number in [-1, 1], which can be calculated as follows: where, Max.Iter is a maximum number of iterations, Iter is a current iteration, and rand is a random number (0,1). In general, the MFO algorithm is performed using three functions that can be described as follows: The function I initializes a random population between limits of the variables of moths and calculates the fitness function values. The function P is the main function, which it is executed iteratively run until the function T becomes true. The function T becomes false if the conversions criteria are not met else it will be true and the search agents are returned as the best obtained.

B. PROPOSED IMFO ALGORITHM
In this paper, a novel improvement is proposed to enhance the performance of conventional MFO algorithm. The MFO performs in three phases (function I, which initialize a random population, function P which is the main function, and function T which become true or false depending on the convergence criteria is met or not). The suggested enhancement to improve performance of MFO is performed on function P. The suggested enhancement utilizes the leadership hierarchy of grey wolf optimizer [22]. As mentioned before, the moths are search agents and flames are the best locations of moths.
Also, the moths update their locations with respect to the corresponding flames. Flames can be considered as flags which are dropped by moths when searching in the search space. In the proposed technique, there are three best flames (the first level alpha (AL), and the second and third levels in the group are beta (BE) and delta (DE)) and moths update their location regarding the location of these three best flames. The proposed mathematical model for updating the locations of three moths respect to flames can be mathematically expressed as follows: The three phases of the proposed IMFO can be summarized in Fig.1.

A. CASE 1: SOLVING THE DOCRs COORDINATION PROBLEM WITH STANDARD CHARACTERISTIC CURVE
In this case, three test networks are used to prove the robustness of the proposed technique. The constant relay characteristic, α and β, for each test systems, in this case, are taken as follows; α = 0.14, and β = 0.02. The upper and lower operating time of primary relay is considered as 0.1 s and 2 s, respectively.

1) TEST NETWORK 1: 8-BUS TEST NETWORK
Firstly, the proposed IMFO technique is evaluated on the 8-bus network. In this network, there are seven lines with two relays at both ends of these lines, two transformers, and two generators as shown in Fig. 2.
The lower and upper limits for TDS are 0.05 and 1.1, respectively. The CTI is 0.3 s as in [19]. More information about this network like the fault currents are given in [35]. The optimal values of the two design variables (DOCR settings) are presented in Table 2. From Table 2, it can be observed  that the IMFO satisfied the constraint of relay characteristics and succeed to find the optimal relays settings within Ip and TDS boundaries ranges. The operating time of the relay pairs (backup and primary relays) and time margin (CTI) values using the proposed IMFO is given in Table 3 and shown in Fig. 3.
It is worth to mention that the backup relays initiate after time margin in case of primary relays failed to operate as shown in Fig. 3. Also, it can be noticed that the proposed technique maintains discrimination time between relays pairs without any miscoordination.
The fitness function converges of IMFO and MFO algorithms are shown in Fig. 4. From this figure, it can be observed that the IMFO technique succeed to reach the global optimum solution. It is worth to mention that the IMFO technique gives the better convergence than MFO technique, where the fitness  function value for the IMFO is reduced to 28.4% less than that given by the conventional MFO. The objective function values obtained by the proposed technique and other optimization algorithms are given in Table 4 and shown in Fig. 5. It can be noticed that the proposed technique gives the least objective function (5.444 s) which confirms the robustness of the proposed technique for solving the coordination problem of DOCRs.

2) TEST NETWORK 2: 9-BUS TEST NETWORK
The proposed IMFO technique is evaluated on the 9-bus network. In this network, there are twelve lines with two relays at both ends of these line as shown in Fig. 6 [1]. The upper and lower limits for TDS are 1.2 and 0.025, respectively. The CTI is set to 0.2 s as in [1]. The upper and lower limits of the Ip are given in [19]. More information about this network such as the fault currents and relationship between relay pairs, are given in [25].
The optimal values of the two design variables (DOCR settings) are given in Table 5. From Table 5, it can be observed that the IMFO satisfied the constraint of relay characteristics  . Test network 2: 9-bus test network [25]. and succeed to find optimal relays settings within Ip and TDS limits ranges. The operating time of the relay pairs (backup and primary relays) and time margin (CTI) values obtained by the IMFO are given in Table 6 and shown in Fig.7.
It is worth to mention that the backup relays initiate after time margin in case of primary relays failed to operate as shown in Fig. 7. Also, it can be noticed that the IMFO maintains the discrimination time between relays pairs without any violations.
The convergence characteristics of the fitness function for IMFO and MFO are shown in Fig. 8. From this figure, it can VOLUME 8, 2020  be observed that the IMFO technique succeed to reach the global optimum solution. Also, the IMFO technique gives the better convergence than MFO technique, where the fitness function value for the IMFO is reduced to 67.02% less than that obtained by the conventional MFO.
The objective function values obtained by the IMFO and other optimization techniques are given in Table 7 and shown in Fig. 9. The IMFO technique gives the least total operating time compared with the conventional MFO, GWO, EFO, MEFO, DE, BH, PSO, WCA, MWCA, and HS. It can be realized that the IMFO is an effective tool for solving the coordination problem of DOCRs.

3) TEST NWTEORK 3: 15-BUS TEST NETWORK
The proposed IMFO technique is evaluated on the 15-bus network shown in Fig. 10 [5]. In this network, there are  twenty-one lines with two relays at both ends of these lines. The lower and upper limits for TDS are 0.1 and 1.1, respectively. The CTI is set to 0.2 s as in [1], [19]. More information about this network such as the fault currents and relationship between relay pairs are given in [5].
The optimal values of the two design variables (DOCR settings) are given in Table 8. From this table, it can be observed that the IMFO satisfied the constraint of relay characteristics and succeed to find optimal relays settings within Ip and TDS boundaries ranges. The operating time of the relay pairs (backup and primary relays) and time margin (CTI) values obtained by the IMFO are given in Table 9. It is worth to mention that the backup relays initiate after time margin in case of primary relays failed to operate as shown in Fig. 11. Also, it can be noticed that the proposed technique maintains discrimination time between relays pairs without any miscoordination.  The convergence characteristics of the fitness function for IMFO and MFO are shown in Fig. 12. From this figure, it can be observed that the IMFO succeed to reach the global optimum solution. It is worth to mention that the IMFO gives the better convergence than MFO, where the fitness function value obtained by the IMFO is reduced to 52.94 % less than that given by the conventional MFO. VOLUME 8, 2020 The objective function values obtained by the IMFO and other optimization techniques are given in Table 10  In this case, three test networks are used to evaluate the proposed IMFO technique using non-standard   DOCR characteristics. The constant relay characteristic (α and β) are considered as continuous decision variable settings. For each test networks, the upper and lower limits for these variables are taken as follows: α min and α max are 0.14, 120, respectively, and β min and β max are 1 and 2, respectively.

1) TEST NETWORK 1: 8-BUS TEST NETWORK
The optimal relay settings are revealed in Table 11. From this table, it can be observed that the IMFO satisfied the constraint of relay characteristics and succeed to find the four optimal relays settings within Ip, TDS, α, and β limits ranges. The operating time of the relay pairs (backup and primary relays) and time margin (CTI) values obtained by the IMFO are given Table 12. Table 12 illustrates that the backup relays initiate after time margin in case of primary relays failed to operate.  Also, it can be noticed that the proposed technique maintains discrimination time between relays pairs without any violation.
The comparison between Case #1 and Case #1 using IMFO and MFO is depicted in Fig. 14. It can be observed that the objective function in Case #2 tends to give more reduction in total operating time of DOCRs using both techniques (IMFO and MFO) compared with Case #1. As shown in Fig. 14, the fitness function using MFO reduced more than 63% in Case #2 less than that given by Case #1. Also, it can be observed that the fitness function using IMFO reduced more than 47% in Case #2 less than that given by Case #1. This indicates the power of using the non-standard curve in reduction operating time of DOCRS. VOLUME 8, 2020

2) TEST NETWORK 2: 9-BUS TEST NETWORK
The optimal relay settings for this test network are revealed in Table 13. From Table 13, it can be observed that the IMFO satisfied the constraint of relay characteristics and succeed to find the four optimal relays settings within Ip, TDS, α, and β limits ranges. The operating time of the relay pairs (backup and primary relays) and time margin (CTI) values obtained by the IMFO are given in Table 14. Table 14 illustrates that the backup relays initiate after time margin in case of primary relays failed to operate. Also, it can be noticed that the proposed IMFO maintains discrimination time between relays pairs without any violation.
The comparison between Case #1 and Case #2 using IMFO and MFO is depicted in Fig. 15. It can be observed that the objective function in Case #2 tends to give more reduction in the total operating time of DOCRs compared with Case #1. As shown in Fig. 15, the fitness function using MFO reduced more than 60% in Case #2 compared with Case #1. Also, it can be observed that the fitness function using IMFO reduced more than 17% in Case #2 less than that given by  Case #1. This indicates the power of using the non-standard DOCR characteristic in reduction operating time of relays, that led to maintain the reliability, stability, and continuity of the power network.

3) TEST NETWORK 3: 15-BUS TEST NETWORK
The optimal relay settings of this test network are revealed in Table 15  satisfied the constraint of relay characteristics and succeed to find the four optimal relays settings within Ip, TDS, α, and β limits ranges. The operating time of the relay pairs (backup and primary relays) and time margin (CTI) values using the IMFO are given in Table 12.  Table 16 illustrates that the backup relays initiate after time margin in case of primary relays failed to operate. Also, it can be noticed that the proposed technique maintains the discrimination time between relays pairs without any violation.
The comparison between Case #1 and Case #2 using IMFO and MFO is shown in Fig. 16. From this figure, it can be observed that the objective function in Case #2 tends to give more reduction in the total operating time of DOCRs compared with Case #1. As shown in Fig. 16, the fitness function using MFO reduced more than 64% in Case #2 less than that given by Case #1. Also, it can be observed that the fitness function using IMFO reduced more than 59% in Case #2 less than that given by Case #1. This indicates the power of using the non-standard curve in reduction operating time of DOCRs, that led to maintain the reliability, stability, and continuity of the power network.

V. CONCLUSION
This paper has proposed an efficient optimization technique called IMFO, with the aim of improving the performance of conventional MFO. In addition, both of MFO and IMFO have been applied for solving the optimal coordination problem of DOCRs. The proposed IMFO improves the performance of conventional MFO using a social hierarchy of the grey wolf optimizer. In addition to Ip and TDS, the variables α and β of DOCR which control the form of relay characteristics have been considered as continuous decision variables. These four variables have been optimally determined. The effectiveness of IMFO has been evaluated using three test networks (8-bus, 9-bus, and 15-bus) in case of standard and non-standard DOCRs characteristic curves. The reported results show that the proposed IMFO is able to converge to the best optimum solution and minimize the total operating time of relays. In addition, the proposed IMFO successfully maintains the selectivity between relay pairs in case of standard and non-standard DOCR characteristics. The results obtained by the proposed IMFO for three different networks are better than those obtained by the conventional MFO, where the reduction in objective function reached more than 28% relative to the conventional MFO. The obtained results also showed that the proposed IMFO is better than the other well-known optimization algorithms. It can be concluded that the proposed IMFO appears to be a robust and flexible optimization technique for solving the DOCR coordination problem. In addition, the reduction in the total operating time of DOCR reached more than 50 % in the case of the non-standard relay curve.