A novel strategy for directional overcurrent relays (DOCRs) coordination is proposed. In the proposed method, the objective function is improved during the optimization process and objective function coefficients are changed in optimization problem. The proposed objective function is more flexible than the old objective functions because various coefficients of objective function are set by optimization algorithm. The optimization problem is solved using hybrid genetic algorithm and particle swarm optimization algorithm (HGAPSOA). This method is applied to 6bus and 30bus sample networks.
Protection of distribution networks is one of the most important issues in power systems. Overcurrent relay is one of the most commonly used protective relays in these systems. There are two types of settings for these kinds of relays: current and time settings. A proper relay setting plays a crucial role in reducing undesired effects of faults on the power systems [
So far, some researches have been carried out on coordination of overcurrent relays [
In [
In this paper, a new method for directional overcurrent relay coordination is proposed in which not only the miscoordination is omitted but also operation times of the relays are the smallest. This is because, in this novel algorithm, the coefficients of the previous proposed objective function are considered a part of the optimization problem. So the coefficients of the objective function are not constant and they are not set by try and error. In the proposed method, the coefficients are calculated based on the optimization technique. The optimization problem of this paper is solved using a hybrid genetic and particle swarm optimization algorithm. This method is applied to 6bus and 30bus sample networks. The results of this method are compared with the results of the existing ones. The simulation results and the comparisons demonstrate the effectiveness and the advantage of the proposed algorithm.
By incorporating the GA into the PSO, the novel HGAPSO algorithm is obtained [
Flowchart of the proposed method.
Finally, if any of the following stopping criteria (in this study maximum number of iterations), then go to the following module. This module is used to transfer the optimal relay TMSs calculated from HGAPSOA through the interface system to each relay.
To prevent overcurrent relays miscoordination and to find the optimum results of the objective function of [
The first term of (
If the coefficient
In this paper, the five coefficients of (
To understand the importance of these coefficients the following notes are helpful.
To assure minimizing the main relay operating time, a great value must be assigned to
To assure minimizing the backup relay operation time, a great value must be assigned to
To prevent miscoordination and have faster and more accurate convergence, choose a large value for
According to the above notes, it is obvious that determining these five coefficients as well as the TMS of the relays with an optimization algorithm will result in a better relay coordination. Therefore, the method presented in this paper optimizes the objective function coefficients as well as the TMSs of the relays to have a tradeoff between the fast operating time and preventing miscoordination. The algorithm applied to the relays coordination optimization problem for the proposed technique is provided in Figure
There are many mathematical models for the overcurrent relays. In this study, the mathematical model of overcurrent relays is considered to be the standard inverse type. In this mathematical model, the operating time of the overcurrent relay is expressed as follows [
As described in Section
In (
Case study 1 is 6bus network shown in Figure
Case study 1 network.
All the information about this network including shortcircuit current of backup and main relays and relevant information relative to main/backup relays have been provided in [
Main/backup pair information.
Main relay  Backup relay  Primary relay SC current  Backup relay current 

8  9  4961  410 
8  7  4961  1520 
2  7  5362  1528 
2  1  5362  804 
3  2  3334  3334 
4  3  2234  2234 
5  4  1352  1352 
6  5  4965  411 
6  14  4965  1522 
14  1  4232  794 
14  9  4232  407 
1  6  2682  2682 
9  10  1443  1443 
10  11  2334  2334 
11  12  3480  3480 
12  14  5365  1529 
12  13  5365  805 
13  8  2490  2490 
7  5  4232  407 
7  13  4232  794 
Table
Relay number  Maximum load current  Relay number  Maximum load current 

1  416  8  458 
2  666  9  450 
3  500  10  458 
4  666  11  541 
5  458  12  458 
6  458  13  500 
7  541  14  666 
All control parameters of algorithm are listed in Table
The input parameters of the optimization algorithm.
Mutate range  0.3 
Crossover range  0.7 
Number of variables  19 
Number of population  100 
Maximum iteration  200 
Maximum subiteration GA  10 
Maximum subiteration PSO  10 
The results of the proposed method by GAPSO algorithm and the best results of [
The coordination results.
Coordination output  Reference [ 
GAPSO 


0.15  0.066 

0.35  0.1833 

0.25  0.146 

0.1  0.069 

0.1  0.08 

0.25  0.13 

0.2  0.12 

0.25  0.12 

0.05  0.095 

0.15  0.135 

0.25  0.174 

0.4  0.273 

0.1  0.05 

0.15  0.1 



0.5894  0.27 

1.2173  0.66 

0.9621  0.58 

0.6636  0.46 

0.7660  0.61 

0.7623  0.4 

0.7059  0.43 

0.7625  0.37 

0.3479  0.66 

0.6883  0.64 

0.9835  0.71 

1.1847  0.82 

0.4665  0.24 

0.5944  0.43 



0  0 

0.4673  0.296 

0.0028  0 

0.6290  0 

0.2657  0 

0.2057  0 

0.1885  0 

0  0 

0.4825  0.418 

1.3181  0.258 

0  0 

0.0532  0 

0.3173  0 

0.2195  0 

0.0492  0 

0.0489  0 

0.8135  0.065 

0.2292  0 

0  0 

1.4086  0.511 



6.699  1.55 

2.75  1.741 
With attend to Table
The object function parameters.

25 

0.1 

15.722 

100 

2 
For the other test case, 30bus IEEE network is considered. This network has 86 OC relays. It consists of 30 buses (132 and 33kV buses), 37 lines, 6 generators, 4 transformers, and 86 OC relays [
IEEE 30bus system.
In this paper, four different cases are simulated for a suitable comparison. Three cases are simulated according to the method of [
Algorithm parameters information.
Mutate range  0.3 
Crossover range  0.8 
Number of variables  91 
Number of population  200 
Maximum iteration  500 
Maximum subiteration GA  10 
Maximum subiteration PSO  10 
Firstly, the results of the proposed method by GAPSOA are shown in Tables
Coordination output results.
Relay number 

TMS 

1  0.3092  0.117 
2  0.3092  0.117 
3  0.3467  0.119 
4  0.2095  0.068 
5  0.7561  0.102 
6  0.5671  0.227 
7  0.248  0.091 
8  0.7271  0.189 
9  0.5679  0.107 
10  0.6679  0.245 
11  0.67  0.241 
12  0.423  0.160 
13  0.621  0.195 
14  0.9412  0.25 
15  0.9268  0.170 
16  0.2343  0.074 
17  0.5493  0.139 
18  0.5749  0.190 
19  0.3947  0.105 
20  0.5669  0.163 
21  0.2716  0.059 
22  0.5094  0.090 
23  0.5468  0.139 
24  0.7716  0.142 
25  0.7482  0.217 
26  0.6391  0.239 
27  0.6033  0.203 
28  0.6351  0.184 
29  0.6351  0.184 
30  0.6358  0.183 
31  0.4274  0.088 
32  0.5374  0.118 
33  0.252  0.090 
34  0.2694  0.089 
35  0.3322  0.084 
36  0.8262  0.174 
37  0.4902  0.106 
38  0.1732  0.05 
39  0.1731  0.061 
40  0.1627  0.068 
41  0.6102  0.123 
42  0.2748  0.115 
43  0.656  0.25 
44  0.2103  0.076 
45  0.2249  0.084 
46  0.397  0.081 
47  0.1756  0.056 
48  0.5501  0.179 
49  0.7792  0.155 
50  0.1803  0.061 
51  0.654  0.211 
52  0.6578  0.166 
53  0.6173  0.129 
54  0.5556  0.093 
55  1.0366  0.224 
56  0.5839  0.143 
58  0.6095  0.176 
59  0.2618  0.065 
60  0.4635  0.129 
61  0.2769  0.056 
62  0.3095  0.061 
63  0.3954  0.066 
64  0.5534  0.128 
65  0.3576  0.094 
66  0.5278  0.099 
67  0.5855  0.099 
68  0.7435  0.161 
69  0.5109  0.095 
70  0.6543  0.113 
71  0.2269  0.078 
72  0.477  0.143 
73  0.2072  0.070 
74  0.6521  0.204 
75  0.3362  0.104 
76  0.5226  0.115 
77  0.2853  0.073 
78  0.4494  0.116 
80  0.4341  0.137 
81  0.3934  0.111 
82  0.8588  0.154 
83  0.9303  0.202 
84  0.5091  0.077 
85  0.3488  0.144 
86  0.3566  0.079 
Time difference for each pair of M/B relays.

0.3529 

0.0021 

0 

0 

0.0122 

0 

0.1591 

0.0337 

0 

0.0025 

0.3146 

0 

0 

0.1002 

0 

0.3418 

1.0402 

0 

0 

0 

0.3529 

0 

0 

0 

0 

0 

0.0027 

0 

0.5927 

0 

0.3146 

0 

0.3238 

0.1788 

0 

0.3565 

0.5459 

0.3147 

0 

0 

0 

0.0023 

0.3 

0.1665 

0.0003 

0 

0 

0 

0.0008 

0 

0.56 

0.2384 

0 

0.3069 

0 

0.1792 

0 

0 

0 

0 

0 

0.3009 

0 

0 

0.0081 

0.5385 

0 

0 

0 

0 

0.5848 

0 

0.3518 

0 

0.2501 

0.6558 

0.4949 

0 

0 

0 

0.015 

0.2957 

0.3118 

0.0312 

0.0048 

0 

0 

0.2971 

0.0022 

0.2319 

0.2883 

0 

0.3311 

0.3093 

0 

0.0488 

0 

0.3843 

0 

0.4701 

0.0184 

0 

0 

0.0059 

0 

0.0165 

0 

0 

0.1605 

0 

0.0076 

0 

0 

0.3125 

0 

0 

0 

0.2759 

0 

0 

0.2671 

0.0514 

0.0489 

0 

0 

0.0494 

0.6332 

0.0171 

0.0072 

0.2437 

0.0161 

0 

0.5228 

0.2319 

0 

0.5093 

0.0416 

0.0163 

0 

0.3633 

0 

0.2067 

0 

0 

0 

0.0881 

0 

0 

0 

0 

0.3288 

0 

0 

0.0239 

0 

0.0006 

0.2988 

0 

0 

0 

0 

0.2264 

0 

0 

0 

0.005 

0.2523 

0 

0.0006 

0 

0.027 

0 

0 

0.0331 

0 

0.0001 

0.3152 

0 

0.0202 

0 

0.0001 

0.3684 

0 

0.0155 

0 

0 

0.0055 

0 

0 

0 

0.0262 

0 

0 

0 

0 

0 

0 

0 

0.0003 

0.0116 

0 

0 

0.0082 

0.0368 

0.2807 

0 

0.1969 

0 

0.0215 

0.0363 

0 

0 

0.2863 

0 

0.5105 

0 

0.5089 

0.0169 

0.0031 

0 

0 

0.3278 

0.5088 

0.0142  

0.0001 

0.0333 

0.0146 

0.006 
In Table
Comparison between the proposed method and the method of [
Case 
Case 
Case 
Case 






























29.8211  24.115  26.9  22.19 



15.15  14.55  15.6  11.32 
The advantage of the proposed method is revealed when the results of the proposed method (Case 4) are compared with the best results of the traditional method of [
In this paper, a new flexible technique for overcurrent relays coordination has been proposed. In this new technique, the coefficients of the conventional objective functions have been improved by optimization problem to obtain the minimum values for the TMSs of the relays. In the proposed technique, GAPSOA optimization method is used to solve the optimization problem. This proposed method is tested on 6bus case study and 30bus IEEE case study. The results of the simulation show the flexibility of the technique and the best reliability because of the smallest
The authors declare that there is no conflict of interests regarding the publication of this paper.