OptiCoord: Advancing directional overcurrent and distance relay coordination with an enhanced equilibrium optimizer

Abstract

In this article, an improved optimization technique is used to get a solution to the problem of coordination between directional overcurrent relays (DOCR) and distance relays. An enhanced version of an equilibrium optimization algorithm (EO), referred to as EEO is proposed to solve this problem. The suggested approach optimises the parameter that regulates the balance between exploration and exploitation to identify the potential optimum solution while enhancing the EO algorithm's exploration properties. The main task for the EEO is to get the best settings. Also, the proposed algorithm shall maintain operation in sequence between the main and backup relays. The capability of the suggested EEO algorithm is assessed in 8-bus, IEEE thirty-bus, and IEEE 39-bus systems. The obtained results prove the effectiveness of the EEO technique in solving the coordination problem of the combined directional overcurrent relays and distance relays. Also, the results show the ability of the suggested algorithm to overcome the drawbacks of the traditional EO algorithm and achieve faster protection (the reduction ratio reaches about 12 % compared to the traditional EO.

1. Introduction

The electric networks are expanding rapidly and the operation complexity of the power system also increased continuously. The protection system shall keep the stability of the power system as the electric network becomes a hazard without protection relays [1]. Where the primary function of the protective devices is to maintain the continuity of the power system and save reliability by detecting any abnormal conditions and isolating the faulted elements rapidly also leaving the non-faulted elements in service [2]. The main role of the design of their protection schemes is rapidly detect and isolate faulty elements quickly. Many protective devices with various principles of operations are used to identify and isolate faults [[3], [4], [5]]. To protect transmission and sub-transmission lines, distance relays and directional overcurrent relays (DOCRs) are frequently utilised. Distance relays and DOCRs shall be well and simultaneously coordinated with each other to keep the reliability and continuity of the power system [[4], [5], [6]]. The coordination between these relays shall be guaranteed [7]. By choosing the appropriate zone-2 settings for distance relays and DOCRs (time dial setting (TDS) and pickup current setting (Ip)), this objective is accomplished. The coordination of distance relays and DOCRs is thought to be a nonlinear optimization issue with numerous constraints. The mathematical complexity of this problem depends on the power system size. Dependable protective relay coordination is the act of determining the proper settings where the major relays must immediately clear the fault in their zone to reduce system outages [7,8]. If the primary protection relays are unable to function, backup protection relays must clear the defective components after a delay period known as the coordination time interval (CTI) [3]. For DOCRs optimal coordination, different methods have been conducted to get solutions for the DOCRs' coordination challenge. Firstly, relay settings were performed manually and using a trial-and-error approach [9,10]. These algorithms have converged at a slow rate [11]. Deterministic methods, and linear and nonlinear programming algorithms, such as dual simplex, simplex, and Big-M techniques have been suggested to find the best DOCRs settings and maintain the coordination between relay pairs [[12], [13], [14], [15], [16]]. Many population-based methods have been suggested to deal with DOCRs coordination problem such as genetic algorithm (GA) [17], particle swarm optimization (PSO) [18], teaching learning-based optimization (TLBO) [19], BBO-Differential Evaluation (DE) [20], Modified Water Cycle Technique (MWCA) [3], Differential Evaluation (DE) [21], Firefly technique (FFA) [22], Evaporation Rate Water Cycle Technique [23], biogeography-based optimization (BBO) [10], Electromagnetic Field Optimization (EFO) [24], Gravitational Search Algorithm (GSA) [25], FA-LP [26], and Improved PSO-LP [27], Gorilla troops optimizer [28], Improved PSO-LP [29], hybrid particle swarm optimization (HPSO) [30], Elite marine predators algorithm (EMPA) [31], Firefly Algorithm and Linear Programming (FFA-LP) [32], and Hybrid Firefly–Genetic Algorithm [33].

Few studies have addressed the coordination issue between DOCRs and distance relays, as the majority of previous publications proposed solutions that exclusively addressed DOCRs' coordination issues. While both relays are used to protect transmission lines [34]. A modified heap-based optimizer (MHBO) was employed to address the coordination issue [35]. In Ref. [36] coordination problems have been solved using the LP technique. Using the multiple embedded cross-over PSO technique, the coordination problem was successfully overcome [8]. The ant colony optimization approach (ACO) was used in Ref. [7] to overcome the coordination problem. The coordination problem has been proposed to be solved using human behaviour-based optimization (HBBO) [6]. Additionally in Ref. [37], the coordination problem was resolved using the improved seagull optimization algorithm (ISOA). Also, particle swarm optimization (PSO) and grey wolf optimization (GWO) [38], genetic algorithm (GA) [39], Hybrid gravitational search algorithm-sequential quadratic programming optimization algorithm (GSA-SQP) [40] have been addressed to deal with coordination problem between DICRs and distance relays.

This work proposes a modified version of EO to identify the best solution for limited nonlinear coordination issues. By modifying the control parameter, which balances the exploitation and exploration stages, the EEO improves the capability of the EO algorithm to find global solutions. For reducing zone-2 operation times and DOCR operating times, the EEO algorithm is suggested. The proposed algorithm will also decide how to coordinate distance relays and DOCRs in the best way possible. In this study, DOCRs and distance relays are coordinated as a single protection strategy to achieve thorough coordination and preserve a time gap between the backup and primary relays. Numerous fault locations are taken into consideration in order to guarantee the time difference between primary and backup DOCRs as well as the primary distance to backup DOCRs over the entire protected line. The proposed method is assessed and compared to earlier optimization methods on the 8-bus, IEEE 30-bus, and IEEE 39-bus networks. The results show that the suggested algorithm's capacity to overcome the limitations of the conventional EO algorithm and offer faster protection (reduction ratio exceeds 12% in comparison to conventional EO). The obtained findings show the effectiveness and superiority of the suggested EEO over traditional EEO algorithms and other optimization strategies in solving the coordination problem.

The remainder of the article is structured as: Section 2 presents the coordination issue between DOCRs and distance relays. Section 3 presents the conventional EO and the suggested EEO algorithm. In section 4, the most important findings are presented. Last but not least, Section 5 presents the main conclusions.

2. Problem formulation

To protect the electrical network, protective relays are placed at both ends of transmission lines. These relays have distance relay and DOCR functionalities. To maintain the stability of the electrical system, it is important to find a solution to the coordination issue between combination DOCRs and distance relays. The optimization algorithm shall maintain the order of operation between the backup and primary relays by obtaining the optimal relay settings [[5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34]]. Coordination issues for DOCRs and distance relays are regarded as constraint problems [7]. It is possible to express the fitness function for this problem as in Eq. (1).

$$Minimize\left(Fitness\right)={\sum }_{j=1}^{Y}T{p}_j+{{\sum }_{j=1}^H{T}_{Z2}}_j$$ (1)

where TZ2 is the operating time for zone-2 and Tp is the primary DOCRs operating time [7]. The DOCR's working time is determined by a non-linear mathematical Eq. and can be described as in Eq. (2) and Eq. (3).

$$T_{i,n}=\frac{ALPA\times TD{S}^j}{{\left(\frac{I_{fault}^j}{I_p^j}\right)}^{BETA}-1}$$ (2)

$$I_p^j=C{R}^j\times P{S}^j$$ (3)

Ifault denotes the fault current (A), while CR denotes the current transformer ratio [1,2]. BETA are the DOCR constant values and they are based on relay characteristics. The standard inverse characteristic has been selected in this paper where constant values ALPHA and BETA are 0.14, 0.02.

2.1. Constraint in DOCRs characteristics

The constraint on DOCRs settings can be expressed as Eq. (4), Eq. (5), and Eq. (6) [[1], [2], [3]].

$$I{p}_{\min }^j\le Ip\le I{p}_{\max }^j$$ (4)

$$P{S}_{\min }^i\le P{S}^i\le P{S}_{\max }^i$$ (5)

$$TD{S}_{\min }^i\le TD{S}^i\le TD{S}_{\max }^i$$ (6)

where, $I{p}_{\max }$ and $I{p}_{\min }$ are the boundaries for pickup current, The highest and lowest values of PS are $P{S}_{\max }$ and $P{S}_{\min }$, respectively [2]. $TD{S}_{\max }$ and $TD{S}_{\min }$ are the lower and highest range for TDS settings, respectively [2,3].

2.2. Limits on Zone-2's operating time

In zone 1, distance relays are set up to find faults on 80–90% of the protected line without delay [34]. The protection of the remaining portion of the line and maintaining adequate margin are the second zone-2's principal responsibilities. There are two borders that affect the operating time of zone-2 distance relays. Following is an explanation of the limitation on the zone-2 distance relays' operating time as described in Eq. (7).

$$T{z_2}_{\min }^j\le T{z_2}^j\le T{z_2}_{\max }^j$$ (7)

Where the upper and lower limits for Tz2 are Tz2_max and Tz2_min, respectively [7].

2.3. Coordination constraints

2.3.1. Coordination constraints at fault1

Both relay pairs sense the fault simultaneously. The margin must be kept as small as feasible in the area isolated by primary relays. Whereas the corresponding backup relays must operate following CTI in order to stop the annoyance of protection relays tripping [1].

In case of failure of main relays, backup protection shall be initiated to satisfy the selectivity requirements. The distance relays and DOCRs can work as the backup and primary relays. In this paper, four fault locations are considered as shown in Fig. 1 for combined distance relays to DOCRs coordination. Faut1 and fault4 are applied on the transmission line at the far and near end. In the middle of the transmission line, respectively, and close to its near end, faults 2 and 3 are applied. If a fault occurs on fault 1, the primary DOCRs must isolate the fault. If the primary DOCR fails to remove the fault as illustrated in Fig. 1 after CTI, the backup DOCR shall isolate fault 1. This restriction can be stated as follows:

$$T_B\left(F1\right)-T_P\left(F1\right)\ge CTI1$$ (8)

Fig. 1.

Coordination between relay pairs.

For fault at fault1, T_B is the operating time of the backup DOCR. Similarly, the order of operation between the main DOCR and the backup distance relay must also be maintained. This constraint will be described as follows:

$$T_{Z2}\left(F1\right)-T_P\left(F1\right)\ge CTI2$$ (9)

As depicted in Fig. 1, the CTI2 is the interval of time between the backup distance relay and the primary DOCRs.

2.3.2. Coordination constraints at fault2

A problem occurring in fault 2 must be immediately isolated by the distance relay zone 1. Backup DOCRs must isolate the problem following time delay if the distance relay is unable to function. The restriction may be stated as described in Eq. (10).

$$T_B\left(F2\right)-T_{Z1}\left(F2\right)\ge CTI3$$ (10)

The main distance relay zone-1 operation time is referred to as TZ1.

2.3.3. Coordination constraints at fault3

When fault 3 occurs, the primary DOCRs must isolate the problem, and the backup relay DOCR must clear the fault after the desired CTI 3. The formulation of this constraint is described in Eq. (11).

$$T_B\left(F3\right)-T_P\left(F3\right)\ge CTI1$$ (11)

2.3.4. Coordination constraints at fault4

As shown in Fig. 1, If the primary DOCRs failed to initiate when a fault occurred in fault4, the backup distance relay zone-2 had to clear the fault after CTI. This limitation may be expressed as in Eq. (12).

$$T_{Z2}\left(F4\right)-T_P\left(F4\right)\ge CTI2$$ (12)

The range for CTI value can be between 0.2 and 0.5 s [3].

3. Suggested optimization technique

3.1. Equilibrium optimizer

The mass balance models that drive the EO forecast dynamic and equilibrium states and are based on physical principles. The position of a solution is thought of as a concentration, and every solution is thought of as a particle. Based on prospective candidates for equilibrium, the agents adjust their positions [41].

3.1.1. Initialization and function evaluation

The optimization process starts with the initial population, which can be described as in Eq. (13) [41]:

$${\mathrm{C}}_{\text{iinit}}={\mathrm{C}}_{\min }+\text{randm}\left({\mathrm{C}}_{\max }-{\mathrm{C}}_{\min }\right)\mathrm{i}=1,2,......\mathrm{k}$$ (13)

where Cmax is the upper value for the decision variables, Cmin is the lower limit of decision variables, Ciinit is the starting location for a solution, R1 is a random number between 0 and 1, and k is the number of particles. To assess the candidates for equilibrium, each solution is computed in accordance with the goal function and ranked [41].

3.1.2. Equilibrium pool

The last convergence state of the EO represents the equilibrium state required for the best solution. The average of the four best candidate solutions is calculated throughout the whole optimization process. The average aids the algorithm in exploitation while the four candidate solutions improve its capability in the exploration stage. Five candidate particles are used to get a vector known as the equilibrium pool, which the equilibrium pool can express as in Eq. (14) [41]:

$${\overrightarrow{\mathrm{C}}}_{\text{equ},\text{pool}}=\left\{{\overrightarrow{\mathrm{C}}}_{\text{equ}\left(1\right)},{\overrightarrow{\mathrm{C}}}_{\text{equ}\left(2\right)},{\overrightarrow{\mathrm{C}}}_{\text{equ}\left(3\right)},{\overrightarrow{\mathrm{C}}}_{\text{equ}\left(4\right)},{\overrightarrow{\mathrm{C}}}_{\text{equ}\left(\text{average}\right)}\right\}$$ (14)

3.1.3. Exponential term (F)

The parameter F will help the algorithm have a balance between the exploitation and exploration phases [41], this parameter can be describe as in Eq. (15).

$$\overrightarrow{\mathrm{F}}={\mathrm{e}}^{-\overrightarrow{\lambda }\left(\mathrm{t}-{\mathrm{t}}_0\right)}$$ (15)

Where λ is a number between 0 and 1. Time, t, is known as an iteration function, and the following formula can be used to express this function as in Eq. (16).

$$\mathrm{t}={\left(1-\frac{\text{It}}{\text{Maxi}-\text{It}}\right)}^{\left({\mathrm{a}}_2\frac{\text{It}}{\text{Maxi}-\text{It}}\right)}$$ (16)

Where I and Maxi_It are the current and the maximum iterations, respectively. The a2 is used to manage exploitation capability, where the value for a2 is set to equal 1. The t0 is the initial start time and its use to guarantee convergence by slowing down and enhancing the exploitation and exploration capability of the EO, which can be formulated as shown in Eq. (17).

$${\overrightarrow{\mathrm{t}}}_0=\frac{1}{\overrightarrow{\lambda }}\ln \left(-{\mathrm{a}}_1\text{sign}\left({\overrightarrow{\mathrm{r}}}_1-0.5\right)\left[1-{\mathrm{e}}^{-\lambda \mathrm{t}}\right]\right)+\mathrm{t}$$ (17)

where the exploration phase is controlled by the constant value a1, which has the value 2. r₁ is a random number between 0 and 1 [41]. The exponential term (F) can be redefined by inserting Eq. (10) into Eq. (8) as describe in Eq. (18).

$$\overrightarrow{\mathrm{F}}={\mathrm{a}}_1\text{sign}\left({\overrightarrow{\mathrm{r}}}_1-0.5\right)\left[{\mathrm{e}}^{-\lambda \mathrm{t}}-1\right]$$ (18)

3.1.4. Generation rate (G)

The exploitation phase is improved by using the generation rate in the EO method, which then provides the precise solution. The generation rate can be stated as in Eq. (19), Eq. (20), and Eq. (21) [41]:

$$\overrightarrow{\mathrm{G}}={\overrightarrow{\mathrm{G}}}_0{\mathrm{e}}^{-\overrightarrow{\lambda }\left(\mathrm{t}-{\mathrm{t}}_0\right)}={\overrightarrow{\mathrm{G}}}_0\overrightarrow{\mathrm{F}}$$ (19)

Where

$$\overrightarrow{\mathrm{G}0}=\overrightarrow{\text{GCP}}\left(\overrightarrow{{\mathrm{C}}_{\text{equ}}}-\overrightarrow{\lambda }\overrightarrow{\mathrm{C}}\right)$$ (20)

$$\overrightarrow{\text{GCP}}=\left\{\begin{array}{l}0.5{\mathrm{r}}_2{\mathrm{r}}_3\ge \text{GP}\\ 0{\mathrm{r}}_3<\text{GP}\end{array}\right\}$$ (21)

Where r1 and r2 are random values between 0 and 1, and GCP is the control parameter for the generation rate that is expressed on the likelihood of the generation term to the updating process. GP is the Generation Probability and the GP is set as a constant value and equal to 0.5. The updating for the EO algorithm can be described as in Eq. (22) [41]:

$$\overrightarrow{\mathrm{C}}=\overrightarrow{{\mathrm{C}}_{\text{equ}}}+\left(\overrightarrow{\mathrm{C}}-\overrightarrow{{\mathrm{C}}_{\text{equ}}}\right).\overrightarrow{\mathrm{F}}+\frac{\overrightarrow{\mathrm{G}}}{\overrightarrow{\lambda }\mathrm{V}}\left(1-\overrightarrow{\mathrm{F}}\right)$$ (22)

3.2. Enhanced equilibrium optimizer

Exploitation and exploration are two important features in population-based algorithms and they are two conflicting phases. A right balance between these features can guarantee to reach the global minimum. All metaheuristic techniques utilize exploration and exploitation features but use different mechanisms and operators. Where the exploration has the capability to escape from local optima. While exploitation capability to locally search around optimum solutions [41,42]. The proposed improved algorithm improves the harmony between exploitation and exploration. In the EO algorithm, the GP control the balance between the exploitation phase and the exploration phase [41]. According to the EO algorithm, the GP manage the probability of participation that is updated by the generation term. When GP is equal to one the exploration ability will increase [41]. In the case of, GP equal to zero, the exploitation capability will increase. The GP value is set as a constant value and equal to 0.5. While in the proposed enhancement the GP will start with a value equal to one and decrease across over iteration to be equal to zero at the end of the iteration, similar to a parameter that regulates the balance between exploration and exploitation in Ref. [43]. The proposed enhancement of the GP value can be expressed as in Eq. (23).

$$\text{GP}={\mathrm{e}}^{{(-\left(\frac{4\text{It}}{\text{Maxi}-\text{It}}\right)}^2)}$$ (23)

The exploration phase is improved in the suggested modified algorithm. Where the parameter a1 in the EO algorithm controls the exploration. The exploration ability increases when the value of parameter a₁ increases. The parameter a₁ in the conventional EO algorithm is set as a constant value and equal to 2. The parameter a₁ in the enhanced algorithm is set to decrease linearly from 2 throughout iteration [42]. The proposed improvement in parameter a₁ can be expressed as in Eq. (24).

$${\mathrm{a}}_1=2-2\left(\frac{\text{It}}{\text{Maxi}-\text{It}}\right)$$ (24)

4. Results

The effectiveness of the suggested EEO in solving the coordination issue using the IEEE 8-bus, 30-bus, and IEEE 39 networks has been assessed to demonstrate the performance of the proposed EEO competitiveness against traditional EO. The EEO algorithm is contrasted with current and well-established methods (GA, DE, African vultures optimization algorithm (AVOA) [44], MAPSO, ACO, ACO-LP, ISOA, and MBHO), Gorilla troops optimizer (GTO) [45]. The TDS thresholds are 0.05 and 1.1. The time margin between really pairs, CT1, CTI2, and CTI3 are set to equal 0.2s as in Refs. [7,35,37]. The operating limits for distance relays in zone 2 are 0.2 and 1.5 s, respectively. The EEO algorithm was run in the MATLAB environment using a PC with 8 GB of RAM and the Windows 10 operating system.

4.1. The 8-bus system

The EEO algorithm is evaluated on the 8-bus network. This network, shown in Fig. 2, consists of seven lines, 42 variables, 14 DOCRs, and 14 distance relays. The data of this system, including the relay pairs' main and backup relationships and their Ip ranges, are provided in Ref. [46]. The optimal values relay settings using EEO and EO methods are given in Table 1. From this table, it can be seen that the optimal settings achieved by the EEO algorithm are superior to those of the settings obtained by the EO algorithm. The operational times of the primary relay, backup relay, and CTI that make utilisation of EEO are listed in Table 2. This table shows that, in the event that the primary relays are unable to function, the backup relays will activate in order to solve this issue. It is possible to state that the suggested algorithm maintains coordination between the main and secondary relays even when there is an adequate margin between the relay pairs.

Fig. 2.

The 8-bus network single-line diagram.

Table 1.

Relay settings for the 8-BUS.

Relay No.	EEO			EO
	Ip (A)	TDS	Z2 (s)	Ip (A)	TDS	Z2 (s)
1	430.991	0.063	0.899	294.481	0.120	0.780
2	265.143	0.238	0.898	479.614	0.201	0.896
3	285.309	0.157	0.688	107.344	0.256	0.766
4	479.934	0.072	0.602	254.578	0.115	0.623
5	189.964	0.076	0.641	242.993	0.057	0.898
6	367.081	0.128	0.602	247.056	0.200	0.843
7	319.226	0.165	0.786	278.135	0.193	0.889
8	328.773	0.133	0.609	302.362	0.176	0.767
9	229.759	0.053	0.663	230.966	0.059	0.831
10	480.000	0.064	0.547	478.517	0.068	0.579
11	123.183	0.215	0.687	121.262	0.224	0.691
12	174.495	0.281	0.814	389.702	0.209	0.849
13	479.983	0.059	0.758	472.437	0.071	0.748
14	318.973	0.175	0.808	85.743	0.320	0.858
OF (s)	15.08			16.77

Table 2.

The 8-bus system's Operating time for DOCRs.

Relay pairs		EEO			EO
		Tp(s)	Tb (s)	CTI	Tp(s)	Tb (s)	CTI
1	6	0.238	0.441	0.203	0.372	0.572	0.200
2	1	0.541	0.741	0.201	0.573	0.854	0.281
2	7	0.541	0.741	0.200	0.573	0.796	0.223
3	2	0.433	0.637	0.204	0.501	0.705	0.204
4	3	0.317	0.517	0.200	0.359	0.567	0.209
5	4	0.261	0.470	0.208	0.225	0.468	0.243
6	5	0.338	0.656	0.317	0.456	0.714	0.258
6	14	0.338	0.758	0.420	0.456	0.748	0.292
7	5	0.441	0.656	0.216	0.489	0.715	0.225
7	13	0.441	0.764	0.324	0.489	0.883	0.393
8	7	0.335	0.741	0.406	0.429	0.796	0.367
8	9	0.335	0.666	0.331	0.429	0.751	0.322
9	10	0.197	0.399	0.202	0.221	0.421	0.200
10	11	0.277	0.495	0.217	0.292	0.512	0.219
11	12	0.435	0.635	0.200	0.450	0.650	0.200
12	13	0.558	0.763	0.205	0.548	0.881	0.333
12	14	0.558	0.758	0.200	0.548	0.748	0.200
13	8	0.246	0.446	0.201	0.290	0.567	0.277
14	1	0.463	0.743	0.280	0.552	0.855	0.303
14	9	0.463	0.667	0.204	0.552	0.752	0.200

The total operating time of primary DOCRs utilising the EEO algorithm (5.07 s) is 12% lower than the total operating time of primary DOCRs utilising the EO algorithm (5.77 s). Additionally, the total operating times for zone-2 of the distance relays employing EEO are drastically reduced from 11.01 s using the suggested EO to 10.01 s, a decrease ratio of almost 9% in comparison to the traditional EO. As shown in Table 1, Table 2, Table 3 the proposed EEO algorithm maintains the coordination gap between relay pairs at various fault sites while satisfying all relay setting limitations.

Table 3.

CTIS using EEO at different fault locations.

Relay pairs		Fault1		Fault 2	Fault 3
		CTI1	CTI2	CTI3	CTI1
1	6	0.203	0.364	0.379483	0.239955
2	1	0.201	0.359	0.91305	1.087639
2	7	0.200	0.245	0.727413	0.369098
3	2	0.204	0.465	0.537037	0.216759
4	3	0.200	0.371	0.439598	0.208083
5	4	0.208	0.341	0.440593	0.349964
6	5	0.317	0.303	0.824598	1.443924
6	14	0.420	0.470	0.789654	0.75079
7	5	0.216	0.200	1.705031	20.4942
7	13	0.324	0.318	12.37927	20.4942
8	7	0.406	0.451	0.806147	0.889429
8	9	0.331	0.328	1.228458	20.63024
9	10	0.202	0.350	0.358978	0.321113
10	11	0.217	0.410	0.409331	0.215008
11	12	0.200	0.379	0.55236	0.213806
12	13	0.205	0.200	0.921222	0.997536
12	14	0.200	0.250	0.730516	0.335511
13	8	0.201	0.363	0.381565	0.225103
14	1	0.280	0.437	9.985233	20.47051
14	9	0.204	0.200	10.74	20.47051

Fig. 3, Fig. 4 present the operating times for DOCRs when using the proposed EEO and traditional EO algorithms, respectively. It can be observed from these figures that the main DOCR will initiate first to clear the fault. The backup DOCRs will activate after a certain time interval to clear fault in the event that the main DOCRs fail to work. Additionally, it can be observed that both techniques succeed in maintaining the sequential operation between relay pairs without any violation as shown in these figures.

Fig. 3.

Operating times for Main and backup DOCRs using EEO (8-bus system).

Fig. 4.

Operating times for Main and backup DOCRs using EEO (8-bus system).

The values for CTIs at various fault positions are presented in Table 3, Table 4. These tables indicate that the proposed EEO is successful in preserving sequential operation between the backup and main relays without any interference between the main and backup relays.

Table 4.

CTIs at fault4.

Primary (DOCR)	Backup Zone-2	Fault 4
		CTI 3
1	1	0.518
2	2	0.292
3	3	0.201
4	4	0.200
5	5	0.255
6	6	0.200
7	7	0.202
8	8	0.206
9	9	0.352
10	10	0.200
11	11	0.212
12	12	0.203
13	13	0.359
14	14	0.200

The fitness function of the suggested algorithm EEO and the conventional EO are presented in Fig. 5. As shown in this figure, the EEO algorithm finds the optimal relay settings and provides better fitness compared with the traditional EO algorithm. The objective function value using EEO reached 15.08 s compared to the EO 16.77 s, where the objective function found by the EEO is reduced to 10 % less than that obtained by the traditional EO. The EEO reaches the objective function (15.08 s) after a computation time of about 192 s. While the EO algorithm reaches the minimum objective function (16.77 s) after a computation time of about 283 s.

Fig. 5.

The EEO and EO (8-bus network) conversion curve.

The DOCRs operating time determined by the EEO, recent, and other well-known algorithms are displayed graphically in Fig. 6 and shown in Table 5 as well. This table shows that the total operating times for DOCRs and zone-2 distance relays provided by the proposed EEO are less than those acquired using alternative approaches. This highlights the potency of the proposed approach to address the complex coordination problem involving distance relays and DOCRs simultaneously.

Fig. 6.

Comparison of several optimization techniques using eight bus network.

Table 5.

Comparison of several algorithms (8-BUS).

Techniques	Fitness function (s)
EEO	15.08
EO	16.77
GA	17.39
DE	16.93
GTO	16.71
AVOA	17.65
MAPSO	16.33
ACO	23.51
ACO-LP	23.3
SOA	25.11
ISOA	17.84
MHBO	17.23

4.2. IEEE 30-bus network

The proposed EEO approach is evaluated on the IEEE 30-bus network. This system has 38 DOCRs, 38 distance relays, and there are 114 decision variables as shown in Fig. 7, the detailed data for this network can be found in Ref. [3].

Fig. 7.

IEEE 30-bus system.

The PS limits are 1.5 and 6. Table 6 lists the optimum DOCR settings and operation times for distance relays in zone-2 that use EEO and EO algorithms. The zone-2 operation period and the optimal DOCR parameters using EEO and EO algorithms are shown in Table 6.

Table 6.

The relay settings (IEEE 30-BUS).

Relay No.	EEO			EO
	Ip (A)	TDS	Z2 (s)	Ip (A)	TDS	Z2 (s)
1	5.848	0.139	0.858	5.223	0.159	0.896
2	4.213	0.100	0.708	2.380	0.163	0.867
3	5.957	0.093	0.904	6.000	0.106	0.890
4	5.919	0.087	0.775	5.376	0.117	0.869
5	5.926	0.068	0.775	5.199	0.087	1.485
6	5.384	0.050	1.364	4.786	0.050	1.499
7	1.781	0.087	0.706	3.522	0.060	1.497
8	4.398	0.050	1.500	2.334	0.054	0.868
9	5.361	0.145	0.794	5.014	0.193	1.470
10	1.798	0.284	1.053	5.323	0.165	1.096
11	3.255	0.150	0.932	5.999	0.104	1.310
12	1.537	0.178	1.500	3.230	0.181	1.419
13	1.512	0.202	0.815	2.158	0.211	1.389
14	3.038	0.077	0.715	1.500	0.193	0.897
15	5.529	0.051	0.746	2.012	0.159	0.861
16	5.632	0.051	0.673	4.569	0.076	0.743
17	1.504	0.055	0.732	1.500	0.052	0.712
18	2.618	0.124	0.783	1.500	0.213	0.947
19	2.981	0.115	0.720	5.946	0.093	0.984
20	1.838	0.119	0.852	3.104	0.079	1.178
21	2.131	0.068	0.916	2.392	0.057	1.499
22	3.643	0.123	0.756	5.993	0.077	1.110
23	2.528	0.128	0.833	5.158	0.051	0.728
24	2.167	0.087	1.030	1.532	0.132	0.916
25	1.510	0.160	1.213	1.512	0.188	0.861
26	1.559	0.050	0.200	1.500	0.050	0.202
27	1.553	0.050	0.559	1.504	0.060	1.229
28	1.559	0.147	1.493	3.212	0.058	0.884
29	4.817	0.050	0.759	2.768	0.170	1.495
30	2.555	0.134	0.739	3.085	0.202	1.094
31	3.886	0.078	0.891	5.069	0.050	0.950
32	2.317	0.130	1.019	5.895	0.054	1.032
33	5.984	0.080	1.326	4.930	0.092	1.498
34	5.773	0.084	1.015	5.700	0.080	1.500
35	2.784	0.134	0.846	2.398	0.144	1.290
36	2.171	0.050	0.620	1.529	0.061	0.619
37	5.737	0.064	0.858	1.710	0.160	1.439
38	4.211	0.089	0.856	1.723	0.189	1.264
OF (s)	49.35			59.06

This table shows that the relay settings provided by the EEO algorithm are superior to those provided by the EO algorithm. Table 7 displays the CTI value and the operating times for the primary and backup relays while using EEO. The backup relays will begin to clear the fault, as shown in the table if the primary relays are unable to do so. When there is a margin between relay pairs that is bigger than the set time margin value, it is possible to claim that the provided methods maintain coordination between the primary and secondary relays. The total operating time of primary DOCRs using the EEO algorithm (15.52 s) is 11.7% less than that of primary DOCRs using the EO method (17.58 s). The entire operating times for zone-2 of the distance relays are also significantly reduced by the recommended EEO, going from 41.48 s to 33.83 s, a reduction of around 18.4% from the conventional EO. Table 6, Table 7 make it clear that the suggested EEO algorithm satisfies all requirements for relay settings and coordination at various fault locations associated with the relay pairs.

Table 7.

IEEE 30-BUS: EO and EEO algorithms relay operating time for main and backup relays.

Relay pairs		EEO			EO
		Tp(s)	Tb (s)	CTI	Tp(s)	Tb (s)	CTI
1	21	0.504	1.891	1.387	0.542	2.940	2.398
1	28	0.504	0.859	0.356	0.542	0.878	0.336
1	29	0.504	0.762	0.258	0.542	1.162	0.620
2	20	0.303	1.007	0.704	0.391	1.882	1.490
2	28	0.303	0.860	0.556	0.391	0.879	0.488
2	29	0.303	0.763	0.460	0.391	1.163	0.771
3	1	0.508	0.753	0.245	0.586	0.789	0.204
4	2	0.384	0.715	0.331	0.487	0.727	0.240
4	3	0.384	0.613	0.228	0.487	0.707	0.220
5	4	0.320	0.630	0.310	0.375	0.770	0.395
5	37	0.320	0.756	0.436	0.375	0.611	0.236
6	5	0.430	0.659	0.229	0.375	0.710	0.336
7	6	0.261	0.674	0.413	0.257	0.549	0.292
8	6	0.251	0.673	0.422	0.184	0.548	0.365
9	20	0.507	1.000	0.493	0.655	1.845	1.190
9	21	0.507	1.862	1.355	0.655	2.858	2.203
9	29	0.507	0.762	0.255	0.655	1.162	0.507
10	20	0.648	1.001	0.353	0.598	1.851	1.253
10	21	0.648	1.869	1.221	0.598	2.876	2.279
10	28	0.648	0.860	0.212	0.598	0.881	0.283
11	10	0.642	0.884	0.243	0.725	1.023	0.298
12	9	0.425	0.626	0.201	0.592	0.803	0.212
13	11	0.518	0.730	0.212	0.627	0.899	0.273
14	12	0.336	0.539	0.203	0.580	0.826	0.246
15	13	0.351	0.599	0.248	0.540	0.742	0.203
16	14	0.282	0.494	0.212	0.360	0.746	0.386
16	36	0.282	1.082	0.800	0.360	0.634	0.274
17	14	0.126	0.494	0.368	0.121	0.746	0.625
17	35	0.126	0.648	0.522	0.121	0.626	0.505
18	4	0.418	0.630	0.212	0.562	0.770	0.207
18	24	0.418	0.713	0.295	0.562	0.768	0.206
19	15	0.404	0.722	0.319	0.512	0.729	0.217
19	16	0.404	0.663	0.259	0.512	0.712	0.200
19	17	0.404	0.754	0.350	0.512	0.718	0.206
20	22	0.379	0.583	0.204	0.337	0.554	0.218
21	3	0.187	0.613	0.426	0.164	0.707	0.543
21	23	0.187	0.718	0.531	0.164	0.679	0.515
22	2	0.505	0.715	0.210	0.449	0.727	0.278
22	23	0.505	0.718	0.213	0.449	0.679	0.229
23	24	0.497	0.713	0.216	0.332	0.768	0.436
23	37	0.497	0.756	0.259	0.332	0.611	0.279
24	25	0.517	0.725	0.208	0.604	0.851	0.247
26	8	0.285	2.511	2.225	0.277	0.484	0.207
27	7	0.211	0.411	0.200	0.247	0.532	0.285
28	31	0.655	0.863	0.208	0.488	0.960	0.472
29	30	0.328	0.544	0.216	0.725	0.925	0.200
30	32	0.491	0.693	0.203	0.825	1.027	0.202
31	33	0.470	0.772	0.302	0.394	0.697	0.303
32	34	0.550	0.815	0.265	0.536	0.759	0.224
33	35	0.419	0.648	0.228	0.418	0.626	0.207
33	36	0.419	1.078	0.658	0.418	0.633	0.215
34	16	0.424	0.663	0.240	0.398	0.712	0.314
34	17	0.424	0.754	0.330	0.398	0.718	0.320
34	38	0.424	0.658	0.234	0.398	0.710	0.312
35	15	0.444	0.722	0.278	0.442	0.729	0.286
35	17	0.444	0.756	0.312	0.442	0.720	0.278
35	38	0.444	0.657	0.213	0.442	0.710	0.268
36	15	0.131	0.723	0.592	0.141	0.729	0.588
36	16	0.131	0.665	0.534	0.141	0.713	0.572
36	38	0.131	0.658	0.527	0.141	0.710	0.569
37	19	0.360	0.580	0.220	0.447	0.961	0.514
38	18	0.430	0.659	0.229	0.558	0.790	0.233

Fig. 8, Fig. 9 present the operating times for DOCRs when using the proposed EEO and traditional EO algorithms, respectively. It can be observed from these figures that the main DOCR will initiate first to clear the fault. The backup DOCRs will activate after a certain time interval to clear fault in the event that the main DOCRs fail to work. Additionally, it can be observed that both techniques succeed in maintaining the sequential operation between relay pairs without any violation as shown in these figures.

Fig. 8.

Operating times for main and backup DOCRs using EEO of (IEEE 30-bus system).

Fig. 9.

Operating times for main and backup DOCRs using EO of (IEEE 30-bus network).

As the obtained CTIs at various fault locations are higher than the CTI without any violation between the primary and secondary relays, Table 8, Table 9 show how the suggested solution maintains the main and backup relays' consecutive operation.

Table 8.

CTIS using the EEO algorithm for the IEEE 30-BUS system at different fault locations.

Relay pairs		Fault1		Fault 2	Fault 3
		CTI1	CTI2	CTI3	CTI1
1	21	1.387	0.412	1.871	0.702
1	28	0.356	0.989	0.839	0.485
1	29	0.258	0.255	0.742	0.586
2	20	0.704	0.549	0.987	0.209
2	28	0.556	1.190	0.840	0.886
2	29	0.460	0.456	0.743	1.343
3	1	0.245	0.350	0.733	0.264
4	2	0.331	0.323	0.695	0.571
4	3	0.228	0.520	0.593	0.423
5	4	0.310	0.454	0.610	0.693
5	37	0.436	0.537	0.736	1.928
6	5	0.229	0.346	0.639	0.302
7	6	0.413	1.103	0.654	2.943
8	6	0.422	1.113	0.653	1.431
9	20	0.493	0.345	0.980	1.154
9	21	1.355	0.409	1.842	20.435
9	29	0.255	0.252	0.742	1.104
10	20	0.353	0.204	0.981	25.647
10	21	1.221	0.268	1.849	99.234
10	28	0.212	0.845	0.840	4.720
11	10	0.243	0.411	0.864	0.242
12	9	0.201	0.368	0.606	0.301
13	11	0.212	0.414	0.710	0.316
14	12	0.203	1.164	0.519	0.206
15	13	0.248	0.464	0.579	0.204
16	14	0.212	0.433	0.474	0.238
16	36	0.800	0.338	1.062	99.612
17	14	0.368	0.589	0.474	0.583
17	35	0.522	0.720	0.628	1.242
18	4	0.212	0.356	0.610	0.525
18	24	0.295	0.612	0.693	0.614
19	15	0.319	0.343	0.702	1.144
19	16	0.259	0.269	0.643	1.208
19	17	0.350	0.328	0.734	1.309
20	22	0.204	0.377	0.563	0.357
21	3	0.426	0.717	0.593	6.071
21	23	0.531	0.645	0.698	0.620
22	2	0.210	0.203	0.695	0.315
22	23	0.213	0.328	0.698	0.205
23	24	0.216	0.533	0.693	0.308
23	37	0.259	0.361	0.736	0.805
24	25	0.208	0.696	0.705	0.206
26	8	2.225	1.215	2.491	20.329
27	7	0.200	0.495	0.391	0.253
28	31	0.208	0.236	0.843	0.406
29	30	0.216	0.412	0.524	0.208
30	32	0.203	0.528	0.673	0.256
31	33	0.302	0.856	0.752	0.568
32	34	0.265	0.465	0.795	0.442
33	35	0.228	0.427	0.628	0.284
33	36	0.658	0.200	1.058	30.650
34	16	0.240	0.249	0.643	1.904
34	17	0.330	0.308	0.734	1.934
34	38	0.234	0.433	0.638	0.390
35	15	0.278	0.302	0.702	0.636
35	17	0.312	0.288	0.736	20.475
35	38	0.213	0.412	0.637	0.276
36	15	0.592	0.615	0.703	1.898
36	16	0.534	0.542	0.645	20.834
36	38	0.527	0.725	0.638	0.819
37	19	0.220	0.360	0.560	0.386
38	18	0.229	0.353	0.639	0.393

Table 9.

CTI3 at fault 4.

Primary (DOCR)	Backup Zone-2	Fault 4
		CTI 3
1	1	0.201
2	2	0.219
3	3	0.328
4	4	0.234
5	5	0.245
6	6	0.781
7	7	0.318
8	8	1.012
9	9	0.204
10	10	0.241
11	11	0.231
12	12	0.996
13	13	0.241
14	14	0.284
15	15	0.203
16	16	0.214
17	17	0.564
18	18	0.213
19	19	0.201
20	20	0.283
21	21	0.597
22	22	0.200
23	23	0.202
24	24	0.383
26	26	3.745
27	27	0.200
28	28	0.722
29	29	0.244
30	30	0.212
31	31	0.215
32	32	0.377
33	33	0.694
34	34	0.358
35	35	0.280
36	36	0.438
37	37	0.278
38	38	0.287

Fig. 10 graphically displays the fitness curve of the suggested EEO algorithm versus the traditional EO method. The EEO method, as demonstrated by this figure, identifies the ideal relay settings and offers better convergence when compared to the conventional EO algorithm. The EEO method, as demonstrated by this picture, identifies the ideal relay settings and gives better convergence when compared to the conventional EO method. The objective function value using EEO reached 49.35 s compared to the EO (59.06 s), where the objective function found by the EEO is reduced to 16.43 % less than that obtained by the traditional EO. Also, the EEO reaches the objective function (49.35 s) after a computation time of about 371 s, while the EO algorithm reaches the minimum objective function (59.06 s) after a computation time of about 542 s.

Fig. 10.

The EEO and EO's fitness function (IEEE 30-bus).

The DOCRs operating time obtained by the EEO, recent, and other well-known algorithms are shown in Table 10 and shown in Fig. 11. It is clear from the table and figure that the fitness function estimated using the suggested EEO is less than those computed using other approaches. This shows the suggested algorithm's ability to handle the challenging simultaneous coordination of DOCRs and distance relays.

Table 10.

The Fitness function for different optimization techniques (IEEE 30-bus).

Methods	Fitness function (s)
EEO	49.36
EO	59.07
GA	82.58
GTO	63.04
AVOA	69.59
ACO	141.15
ACO-LP	113.20

Fig. 11.

Comparison of several optimization algorithms (IEEE 30-Bus).

4.3. IEEE 39-bus network

The proposed approach has been assessed using the IEEE-39 bus network. Fig. 12 displays the single-line diagram for this system. There are 12 transformers, 34 lines, 10 generators, 68 DOCRs, 68 distance relays, and 204 variables. The detailed parameters of this system can be found in Ref. [47].

Fig. 12.

IEEE 39-bus network single-line diagram.

The best values for DOCR settings utilising EEO and EO algorithms are shown in Table 11, in addition to the best values for zone-2 distance relay operating time.

Table 11.

The IEEE 39-BUS network relay settings.

Relay No.	EO			EEO
	Ip (A)	TDS	Z2 (s)	Ip (A)	TDS	Z2 (s)
1	293.527	0.273	1.012	257.477	0.440	1.499
2	597.067	0.142	1.204	230.218	0.415	1.498
3	724.691	0.081	0.685	258.820	0.298	1.489
4	1218.994	0.202	1.039	349.684	0.564	1.500
5	420.131	0.240	1.089	101.233	0.690	1.500
6	227.531	0.199	0.840	138.882	0.374	1.495
7	1527.224	0.095	1.097	622.808	0.309	1.486
8	517.328	0.300	1.025	697.049	0.387	1.493
9	1124.259	0.181	1.044	635.775	0.398	1.500
10	2216.873	0.071	0.895	742.823	0.293	1.493
11	1079.098	0.139	0.944	496.342	0.377	1.498
12	840.643	0.130	0.842	302.803	0.390	1.487
13	467.533	0.220	0.877	203.097	0.560	1.499
14	546.551	0.177	1.071	226.410	0.514	1.498
15	2110.171	0.066	1.091	678.589	0.329	1.498
16	1174.633	0.150	0.989	674.496	0.394	1.485
17	3298.567	0.054	1.375	887.044	0.294	1.499
18	919.998	0.053	0.874	730.389	0.159	1.500
19	554.377	0.221	1.059	516.036	0.324	1.499
20	1184.958	0.084	0.633	415.084	0.315	1.499
21	521.946	0.181	0.990	207.646	0.495	1.479
22	271.428	0.188	1.073	285.176	0.399	1.500
23	1687.058	0.090	1.255	677.613	0.326	1.493
24	666.807	0.101	1.051	532.989	0.318	1.500
25	573.238	0.181	0.860	312.874	0.401	1.500
26	484.672	0.261	1.072	294.769	0.507	1.500
27	1735.664	0.082	0.958	370.652	0.394	1.493
28	1149.803	0.176	0.932	498.092	0.408	1.497
29	259.284	0.320	1.423	56.617	0.776	1.498
30	18.129	0.604	1.012	79.064	0.612	1.499
31	1569.211	0.109	1.100	489.755	0.364	1.499
32	1020.867	0.216	1.060	479.093	0.455	1.495
33	2936.210	0.104	1.082	962.310	0.353	1.500
34	1636.283	0.052	1.094	642.006	0.239	1.453
35	162.606	0.344	1.142	105.352	0.636	1.497
36	96.504	0.424	1.143	76.193	0.690	1.500
37	1999.149	0.088	0.884	979.271	0.282	1.488
38	2004.513	0.070	0.994	404.130	0.383	1.500
39	737.670	0.162	0.896	470.494	0.374	1.500
40	1961.047	0.100	0.943	577.942	0.383	1.497
41	2461.176	0.058	1.402	666.759	0.335	1.488
42	2445.428	0.066	0.849	1242.770	0.248	1.499
43	1747.901	0.075	0.883	668.371	0.319	1.500
44	2388.344	0.085	1.315	672.829	0.383	1.500
45	1908.999	0.084	1.133	577.344	0.341	1.483
46	2202.567	0.054	0.803	540.492	0.338	1.496
47	98.395	0.408	1.152	69.638	0.718	1.497
48	468.753	0.180	1.348	128.025	0.529	1.379
49	2345.375	0.059	1.332	535.712	0.355	1.499
50	1163.787	0.105	0.855	567.388	0.290	1.489
51	727.122	0.082	1.209	329.045	0.348	1.500
52	474.268	0.078	1.162	346.138	0.241	1.500
53	676.795	0.143	1.273	259.448	0.396	1.500
54	282.411	0.165	1.014	274.201	0.264	1.500
55	898.789	0.058	0.898	541.335	0.174	1.496
56	639.337	0.150	0.918	604.511	0.253	1.499
57	822.596	0.140	0.962	721.764	0.217	1.499
58	1423.004	0.069	1.179	627.067	0.245	1.499
59	508.169	0.173	0.863	141.389	0.523	1.500
60	118.399	0.356	1.033	218.761	0.439	1.498
61	2288.734	0.052	0.730	987.279	0.251	1.497
62	1255.257	0.131	1.105	1130.670	0.189	1.485
63	2053.678	0.120	1.246	540.339	0.358	1.493
64	1420.412	0.063	0.922	605.180	0.244	1.483
65	454.969	0.226	0.776	252.984	0.445	1.499
66	672.958	0.113	1.028	170.573	0.416	1.499
67	2577.465	0.143	1.390	1289.072	0.177	1.496
68	969.603	0.053	1.330	879.510	0.056	1.499
OF (s)	104.419			163.441

From this table, it can be seen that the EEO algorithm's optimum settings are superior to those produced by the EO algorithm. Table 12 displays the CTI values utilising EEO together with the relay's operation times for the primary and backup relays. The backup relays will operate to solve the issue if the primary relays are unable to commence, as can be seen from the table. It is obvious to highlight that the recommended approaches maintain coordination between the primary and secondary relays when the distance between relay pairs is higher than the CTI value. Comparing the overall operating time of primary DOCRs utilising EEO (33.66 s) to those using the EO algorithm (61.86 s), there is a reduction of approximately 45.5%. Furthermore, compared to the conventional EO, the proposed EEO significantly decreases the total operating times for zone-2 of the distance relays from 101.573 s to 70.756 s, a reduction ratio of 30.3%. The suggested EEO algorithm satisfies all requirements for relay settings and coordination at various fault locations connected to the main and backup relay, as shown by Table 11, Table 12.

Table 12.

IEEE 39-BUS: OPERATING time for main and backup relays using EO and EEO algorithms.

Relay pairs		EEO			EO
		Tp(s)	Tb (s)	CTI	Tp(s)	Tb (s)	CTI
1	4	0.617	0.886	0.269	0.950	1.359	0.409
2	7	0.327	0.775	0.448	0.716	1.215	0.500
2	10	0.327	0.886	0.559	0.716	1.221	0.505
3	2	0.387	0.601	0.214	0.821	1.097	0.276
4	6	0.379	0.654	0.275	0.774	0.988	0.214
5	3	0.342	0.545	0.203	0.745	0.990	0.245
6	21	0.541	0.760	0.219	0.845	1.317	0.472
7	48	0.568	0.777	0.209	1.031	1.242	0.211
8	1	0.679	0.889	0.211	0.973	1.345	0.372
8	10	0.679	0.883	0.204	0.973	1.219	0.246
9	1	0.568	0.889	0.321	0.985	1.345	0.359
9	7	0.568	0.773	0.205	0.985	1.214	0.229
10	12	0.432	0.659	0.227	0.898	1.120	0.222
10	25	0.432	0.676	0.244	0.898	1.119	0.221
11	9	0.457	0.826	0.369	0.894	1.311	0.418
11	25	0.457	0.676	0.219	0.894	1.119	0.225
12	14	0.416	0.632	0.217	0.838	1.249	0.411
12	46	0.416	0.864	0.448	0.838	1.259	0.421
13	11	0.546	0.753	0.207	1.057	1.257	0.200
13	46	0.546	0.863	0.318	1.057	1.259	0.202
14	16	0.466	0.673	0.207	1.002	1.292	0.290
14	24	0.466	0.698	0.232	1.002	1.788	0.787
15	13	0.472	0.727	0.255	1.073	1.309	0.236
15	24	0.472	0.698	0.226	1.073	1.788	0.715
16	18	0.570	0.810	0.240	1.140	1.617	0.477
16	43	0.570	0.782	0.212	1.140	1.346	0.206
17	15	0.347	0.702	0.356	0.838	1.266	0.428
17	43	0.347	0.783	0.436	0.838	1.346	0.508
18	20	0.230	0.439	0.208	0.605	0.909	0.303
19	17	0.706	1.048	0.342	1.001	1.210	0.209
20	22	0.344	0.565	0.221	0.787	1.227	0.440
20	23	0.344	0.786	0.442	0.787	1.317	0.531
21	19	0.479	0.867	0.388	0.954	1.220	0.266
21	23	0.479	0.787	0.308	0.954	1.318	0.364
22	5	0.411	0.620	0.209	0.888	1.143	0.255
23	13	0.364	0.727	0.364	0.853	1.309	0.456
23	16	0.364	0.673	0.310	0.853	1.292	0.439
24	19	0.319	0.867	0.547	0.908	1.220	0.312
24	22	0.319	0.565	0.245	0.908	1.227	0.319
25	28	0.526	0.743	0.217	0.921	1.127	0.206
26	9	0.623	0.826	0.203	1.025	1.311	0.286
27	26	0.556	0.791	0.235	1.052	1.254	0.202
28	30	0.595	0.826	0.230	0.967	1.217	0.250
28	32	0.595	0.811	0.216	0.967	1.200	0.233
29	27	0.593	0.806	0.214	0.999	1.202	0.202
29	32	0.593	0.812	0.219	0.999	1.200	0.201
30	49	0.758	0.969	0.212	1.080	1.280	0.200
31	27	0.569	0.806	0.237	1.001	1.201	0.200
31	30	0.569	0.826	0.257	1.001	1.217	0.216
32	34	0.647	0.877	0.230	1.016	1.218	0.202
32	64	0.647	0.857	0.210	1.016	1.232	0.216
32	66	0.647	0.886	0.239	1.016	1.263	0.247
32	67	0.647	3.210	2.563	1.016	1.221	0.205
33	31	0.518	0.768	0.250	0.963	1.163	0.200
33	64	0.518	0.857	0.339	0.963	1.232	0.269
33	66	0.518	0.886	0.368	0.963	1.263	0.299
33	67	0.518	3.211	2.693	0.963	1.221	0.257
34	36	0.503	0.806	0.303	0.989	1.228	0.239
35	33	0.616	0.828	0.212	1.017	1.219	0.202
36	38	0.660	0.915	0.255	1.018	1.229	0.211
36	45	0.660	0.881	0.220	1.018	1.260	0.242
37	35	0.482	0.771	0.288	0.976	1.241	0.265
37	45	0.482	0.880	0.398	0.976	1.259	0.283
38	40	0.483	0.720	0.237	1.000	1.201	0.201
39	37	0.603	0.808	0.205	1.115	1.319	0.204
40	41	0.564	0.812	0.248	1.069	1.274	0.205
41	44	0.522	0.800	0.278	1.102	1.309	0.207
42	39	0.498	0.712	0.213	1.069	1.271	0.202
43	42	0.489	0.696	0.208	1.078	1.281	0.203
44	15	0.496	0.702	0.205	1.066	1.266	0.200
44	18	0.496	0.810	0.313	1.066	1.617	0.551
45	11	0.420	0.753	0.333	0.902	1.257	0.355
45	14	0.420	0.632	0.212	0.902	1.249	0.347
46	35	0.334	0.771	0.437	0.910	1.241	0.331
46	38	0.334	0.915	0.581	0.910	1.228	0.318
47	8	0.606	0.817	0.211	0.988	1.197	0.210
48	50	0.507	0.720	0.214	0.957	1.159	0.202
48	52	0.507	0.726	0.220	0.957	1.568	0.612
48	54	0.507	0.870	0.364	0.957	1.360	0.404
49	47	0.497	0.797	0.300	1.053	1.272	0.219
49	52	0.497	0.726	0.229	1.053	1.568	0.515
49	54	0.497	0.870	0.373	1.053	1.360	0.307
50	29	0.513	0.748	0.235	0.936	1.173	0.237
51	47	0.241	0.798	0.556	0.756	1.273	0.517
51	50	0.241	0.722	0.480	0.756	1.160	0.405
51	54	0.241	0.873	0.632	0.756	1.365	0.609
52	55	0.239	0.684	0.446	0.642	1.097	0.455
53	47	0.408	0.797	0.390	0.798	1.273	0.475
53	50	0.408	0.721	0.313	0.798	1.160	0.362
53	52	0.408	0.729	0.321	0.798	1.573	0.775
54	56	0.466	0.674	0.208	0.736	1.095	0.359
55	53	0.444	0.913	0.469	0.848	1.327	0.479
56	51	0.538	0.819	0.281	0.881	1.610	0.729
57	60	0.443	0.660	0.217	0.648	0.984	0.337
58	65	0.267	0.527	0.260	0.643	0.858	0.214
59	58	0.520	0.938	0.418	0.994	1.270	0.277
60	62	0.594	0.944	0.349	0.869	1.223	0.354
61	59	0.324	0.617	0.293	0.881	1.106	0.225
62	63	0.603	0.830	0.226	0.810	1.047	0.237
63	31	0.472	0.769	0.296	0.788	1.164	0.376
63	34	0.472	0.877	0.405	0.788	1.218	0.431
63	66	0.472	0.887	0.415	0.788	1.263	0.476
63	67	0.472	3.214	2.742	0.788	1.221	0.433
64	61	0.413	0.626	0.213	0.876	1.218	0.343
65	31	0.462	0.768	0.306	0.767	1.163	0.397
65	34	0.462	0.876	0.414	0.767	1.218	0.451
65	64	0.462	0.857	0.395	0.767	1.232	0.466
65	67	0.462	3.209	2.747	0.767	1.221	0.454
66	57	0.656	0.986	0.330	1.108	1.349	0.240
68	31	0.150	0.769	0.619	0.152	1.164	1.011
68	34	0.150	0.878	0.728	0.152	1.219	1.066
68	64	0.150	0.858	0.708	0.152	1.233	1.080
68	66	0.150	0.887	0.737	0.152	1.263	1.111

Fig. 13, Fig. 14 present the operating times for DOCRs when using the proposed EEO and traditional EO algorithms, respectively. It can be observed from these figures that the main DOCR will initiate first to clear the fault. The backup DOCRs will activate after a certain time interval to clear fault in the event that the main DOCRs fail to work. Additionally, it can be observed that both techniques succeed in maintaining the sequential operation between relay pairs without any violation as shown in these figures.

Fig. 13.

Operating times for primary and backup DOCRs using EEO (IEEE 39-bus network).

Fig. 14.

Operating times for primary and backup DOCRs using EO (IEEE 39-bus network).

Table 13, Table 14 show the effectiveness of the suggested method in preserving the sequential operation of the main and backup relays when the obtained CTIs at various fault locations exceed the designated coordination margin without any violation between the relay pairs.

Table 13.

CTIS using the EEO algorithm for the IEEE 39-BUS system at different fault locations.

Relay pairs		Fault1		Fault 2	Fault 3
		CTI1	CTI2	CTI3	CTI1
1	4	0.269	0.421	1.050	0.531
2	7	0.448	0.770	1.557	4.847
2	10	0.559	0.568	4.662	99.562
3	2	0.214	0.817	0.625	0.235
4	6	0.275	0.461	1.294	3.479
5	3	0.203	0.343	3.045	99.521
6	21	0.219	0.449	0.793	0.268
7	48	0.209	0.780	0.809	0.229
8	1	0.211	0.333	0.930	0.260
8	10	0.204	0.216	1.175	1.035
9	1	0.321	0.443	0.954	0.373
9	7	0.205	0.529	0.990	0.698
10	12	0.227	0.410	0.716	0.243
10	25	0.244	0.429	0.721	0.236
11	9	0.369	0.587	0.935	0.510
11	25	0.219	0.404	0.767	0.336
12	14	0.217	0.655	0.685	0.257
12	46	0.448	0.387	1.524	4.490
13	11	0.207	0.398	0.808	0.271
13	46	0.318	0.257	1.492	5.527
14	16	0.207	0.523	0.736	0.309
14	24	0.232	0.585	0.782	0.373
15	13	0.255	0.405	0.729	0.212
15	24	0.226	0.579	0.779	0.384
16	18	0.240	0.304	1.201	2.154
16	43	0.212	0.313	0.818	0.271
17	15	0.356	0.744	1.170	0.356
17	43	0.436	0.536	0.904	0.436
18	20	0.208	0.402	0.486	0.289
19	17	0.342	0.669	1.293	0.982
20	22	0.221	0.729	0.563	0.204
20	23	0.442	0.911	0.886	0.673
21	19	0.388	0.581	1.007	0.587
21	23	0.308	0.776	1.142	1.208
22	5	0.209	0.679	0.671	0.267
23	13	0.364	0.513	0.760	0.340
23	16	0.310	0.625	0.793	0.535
24	19	0.547	0.740	1.017	0.945
24	22	0.245	0.754	0.572	0.210
25	28	0.217	0.406	0.787	0.276
26	9	0.203	0.421	0.894	0.298
27	26	0.235	0.515	0.804	0.203
28	30	0.230	0.417	0.834	0.209
28	32	0.216	0.465	0.843	0.243
29	27	0.214	0.365	1.139	1.165
29	32	0.219	0.467	0.891	0.334
30	49	0.212	0.575	1.185	0.764
31	27	0.237	0.389	0.897	0.400
31	30	0.257	0.443	0.827	0.210
32	34	0.230	0.447	1.332	2.059
32	64	0.210	0.275	1.039	0.600
32	66	0.239	0.381	0.971	0.373
32	67	2.563	0.743	4.540	6.536
33	31	0.250	0.581	0.890	0.442
33	64	0.339	0.404	1.095	0.856
33	66	0.368	0.510	0.997	0.517
33	67	2.693	0.871	5.013	9.332
34	36	0.303	0.640	0.809	0.234
35	33	0.212	0.466	1.025	0.641
36	38	0.255	0.333	1.326	1.442
36	45	0.220	0.473	1.254	1.345
37	35	0.288	0.660	0.783	0.231
37	45	0.398	0.651	1.105	0.932
38	40	0.237	0.460	0.788	0.299
39	37	0.205	0.281	0.844	0.263
40	41	0.248	0.838	0.934	0.511
41	44	0.278	0.793	0.839	0.295
42	39	0.213	0.398	0.737	0.224
43	42	0.208	0.361	0.777	0.331
44	15	0.205	0.594	0.852	0.517
44	18	0.313	0.377	1.002	0.716
45	11	0.333	0.524	0.821	0.373
45	14	0.212	0.651	0.692	0.249
46	35	0.437	0.809	0.791	0.387
46	38	0.581	0.660	1.347	2.212
47	8	0.211	0.419	0.920	0.354
48	50	0.214	0.348	0.910	0.621
48	52	0.220	0.656	0.937	0.641
48	54	0.364	0.507	0.996	0.547
49	47	0.300	0.654	0.811	0.215
49	52	0.229	0.665	0.812	0.302
49	54	0.373	0.517	0.922	0.366
50	29	0.235	0.910	0.762	0.210
51	47	0.556	0.910	0.895	0.603
51	50	0.480	0.614	1.227	1.767
51	54	0.632	0.773	3.281	5.065
52	55	0.446	0.660	2.265	99.673
53	47	0.390	0.744	0.871	0.376
53	50	0.313	0.447	1.074	1.057
53	52	0.321	0.754	26.682	99.429
54	56	0.208	0.452	0.770	0.353
55	53	0.469	0.829	0.961	0.523
56	51	0.281	0.671	0.970	0.622
57	60	0.217	0.590	0.716	0.207
58	65	0.260	0.509	0.589	0.265
59	58	0.418	0.659	1.137	0.928
60	62	0.349	0.511	1.051	0.586
61	59	0.293	0.539	0.661	0.323
62	63	0.226	0.642	0.926	0.352
63	31	0.296	0.628	0.913	0.509
63	34	0.405	0.622	1.530	3.474
63	66	0.415	0.556	1.455	4.351
63	67	2.742	0.918	6.356	28.344
64	61	0.213	0.317	0.734	0.416
65	31	0.306	0.638	0.826	0.421
65	34	0.414	0.632	1.098	0.970
65	64	0.395	0.460	1.150	1.275
65	67	2.747	0.928	4.240	5.517
66	57	0.330	0.306	1.027	0.384
68	31	0.619	0.950	0.974	1.098
68	34	0.728	0.944	2.018	99.819
68	64	0.708	0.772	1.415	2.799
68	66	0.737	0.878	1.121	1.272

Table 14.

CTI3 at fault 4.

Primary (DOCR)	Backup Zone-2	Fault 4
		CTI 3
1	1	0.203
2	2	0.686
3	3	0.205
4	4	0.300
5	5	0.537
6	6	0.230
7	7	0.398
8	8	0.250
9	9	0.302
10	10	0.209
11	11	0.295
12	12	0.271
13	13	0.214
14	14	0.498
15	15	0.484
16	16	0.352
17	17	0.710
18	18	0.487
19	19	0.253
20	20	0.228
21	21	0.316
22	22	0.553
23	23	0.675
24	24	0.581
25	25	0.236
26	26	0.333
27	27	0.249
28	28	0.235
29	29	0.719
30	30	0.209
31	31	0.403
32	32	0.299
33	33	0.363
34	34	0.389
35	35	0.419
36	36	0.380
37	37	0.205
38	38	0.276
39	39	0.223
40	40	0.277
41	41	0.708
42	42	0.227
43	43	0.225
44	44	0.631
45	45	0.466
46	46	0.223
47	47	0.407
48	48	0.670
49	49	0.562
50	50	0.207
51	51	0.687
52	52	0.738
53	53	0.558
54	54	0.360
55	55	0.314
56	56	0.288
57	57	0.232
58	58	0.609
59	59	0.278
60	60	0.393
61	61	0.231
62	62	0.294
63	63	0.544
64	64	0.306
65	65	0.268
66	66	0.245
68	68	1.126

The objective function of the suggested EEO algorithm and the traditional EO algorithm is graphically presented in Fig. 15.

Fig. 15.

The fitness function of the EEO and EO (IEEE 39-bus).

In comparison to the traditional EO method, the EEO algorithm determines the ideal relay settings and provides better convergence, as illustrated in this figure. Where the objective function value using EEO reached 104.419 s compared to the EO 163.441 s, where the objective function found by the EEO is reduced by about 36% less than that obtained by the traditional EO. Also, the EEO reaches the objective function (104.419 s) after a computation time of about 586 s, while the EO algorithm reaches the minimum objective function (163.441 s) after a computation time of about 725 s.

5. Conclusion

In order to address the difficult nonlinear coordination problem, an improved optimization algorithm (EEO) has been suggested in this study as a combined scheme DOCRs with distance relays. Using the EEO, the performance of the traditional EO has been improved. This enhancement was made possible by upgrading the parameter that controls the exploration feature as well as the parameter that balances the exploitation and exploration phases. The performance of EEO has been assessed based on different systems (8-bus, IEEE 30-bus, IEEE 39-bus). The proposed algorithm has also been contrasted against well-known competitive optimization strategies. The findings obtained demonstrate that the EEO is able to simultaneously obtain a globally promising solution for all DOCR settings and second zone distance relay timing. At the same time, the EEO successfully maintain the desired selectivity margin between main and secondary relays. Additionally, compared to the conventional EO technique, the suggested algorithm finds the global optimum solution more quickly. In comparison to major DOCRs utilising the EO algorithm, the overall operating duration of main DOCRs employing EEO is higher by more than 12%. Additionally, compared to the EO algorithm, adopting EEO significantly reduces the total operating times for zone 2 with a reduction ratio of more than 9%. Also, the objective function succeeded in decreasing by about 10 % compared to the traditional EO algorithm for all test systems. Furthermore, the results using EEO are superior to those from the other methods.

Additional information

No additional information is available for this paper.

Data availability statement

All required data are involved in the text.

CRediT authorship contribution statement

Ahmed Korashy: Writing – original draft, Conceptualization. Salah Kamel: Writing – review & editing, Methodology. Francisco Jurado: Visualization, Supervision, Formal analysis, Data curation. Wulfran Fendzi Mbasso: Writing – original draft, Software, Resources, Methodology.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.