40220140505002

International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 08-18 © IAEME
8
GENETIC ALGORITHM APPROACH FOR THE OPTIMAL
COORDINATION OF OVER CURRENT RELAYS
ABSTRACT
Operating times of over current relays can be greatly reduced and proper coordination can be
obtained if a proper choice of Plug Setting (PS) and Time Setting Multiplier (TMS) is made. Over
Current Relay (OCR) characteristic is inherently non-linear in nature. Classical Optimization
methods such as steepest decant method, non-linear programming have limitations in searching for
an absolutely optimal settings and sometimes get trapped in local optimal settings. This paper
systematically exploits the Genetic Algorithms (GA) tool to solve this complex and non-convex
optimization problem.
Key Words: Genetic algorithm, optimal over current relay coordination, power system protection.
I. INTRODUCTION
Shunt fault is characterized by the sudden increase in current which is sensed by the
overcurrent relays [1, 2]. Directional overcurrent relays have become the economic alternative to
protect sub-transmission and distribution systems [3-5]. In a protection environment, each relay
should get sufficient opportunity to protect the equipment which it is supposed to protect. In case the
primary protection fails to clear the fault, the backup protection should be made to clear the fault.
Both primary and backup protection must be properly coordinated for minimum disruption of power
supply to the system. The basic objective of relay coordination is to avoid mal operation of relays
which happens to be the major concern for power system protection [5, 6]. The problem of optimum
coordination of OCRs is generally modelled as an LPP in which pick up value of currents (PS) of
relays are assumed to be known and operating time of each relay is considered as a linear function of
its TMS [5].
A. Sudha
Dept of Electrical Engg.,
K. D. K. College of Engg.,
Nagpur, India
Dr. R. M. Moharil
Dept. of Electrical Engg.,
Yashwantrao Chavan
College of Engg., Nagpur,
India
Dr. P. Devnani
Dept of Electrical Engg.,
S. R. M. College of Engg.,
for Women, Nagpur, India
INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING &
TECHNOLOGY (IJEET)
ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 5, Issue 5, May (2014), pp. 08-18
© IAEME: www.iaeme.com/ijeet.asp
Journal Impact Factor (2014): 6.8310 (Calculated by GISI)
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IJEET
© I A E M E

9
In this paper, a comparative study has been made after carrying out optimal relay
coordination using GA to two typical cases: PS fixed as a discrete integer and finding TMS, finding
both PS and TMS with suitable modification in the mathematical model of the problem.
II. PROBLEM FORMULATION
The coordination problem of directional OCRs in a ring fed distribution system, can be seen
as an optimization problem, where the sum of operating times of relays of the system is to be
minimized [8-10]
)1(min ,.
1
kii
m
i
tWz ∑=
=
Where
m is the number of relays,
t i, k is the operating time of relay Ri, for a fault at k and
Wi is the weight assigned for operating time of the relay Ri
In distribution systems where the lines are short and are of equal length, equal weight (=1) is
assigned for operating times of all relays [5, 6, 9, 11]. The objective function defined in (1) has to be
minimized under the below mentioned five constraint sets.
A. Constraint set I – Coordination Criteria
Fault is sensed by primary as well as back up relay simultaneously. In order that the back-up
relay does not mal-operate, primary relay has to be given sufficient time to act and clear the fault.
And back up relay has to act in case the primary relay fails to operate. If Rj is the primary relay for
fault at k, and Ri is the backup relay for the same fault, then the coordination constraint can be stated
as
)2(,, ttt kjki ∆≥−
Where,
t j, k is the operating time of primary relay Rj for a fault at k,
t i,k is the operating time for backup relay Ri for the same fault and ∆t is the coordination time
interval.
B. Constraint set II – Relay characteristics
Over current relays are named on the type of characteristic they tend to exhibit. However,
OCRs are governed by the general characteristic given in equation (3) and the details of the
nomenclature is as per the details mentioned in Table I [1,6,9,12,13,14].
Where,
opt indicates the operating time of the relay,
TMS indicates the time multiplier setting
PS is the plug setting.
I relay is the current seen by the relay.
)3(
1)(
)(
−
= γ
λ
PSI
TMS
t
relay
op

10
TABLE I
VALUES OF λ AND γ FOR DIFFERENT TYPES OF OCR
C. Constraint set III – Limits on the Relay Operating Time
Constraint imposed due to the restriction on the operating time of relays can be
mathematically stated as
)4(max,,min, ikii ttt ≤≤
Where,
t i, min is the minimum operating time of relay at location i, for fault at any point in the zone of
operation
t i, max is the maximum operating time of relay at location i, for fault at any point in the zone of
operation
D. Constraint set IV – Limits on the TMS of the Relays
The limits on the TMS of relays can be stated as
)5(max,min, iii TMSTMSTMS ≤≤
Where,
TMS i, min is the minimum value of TMS of relay Ri
TMS i, max is the maximum value of TMS of relay Ri
TMS i, min and TMS i, max are 0.025, 1.2 respectively [12]
E. Constraint set V – Limits on the PS of the Relays
The limits on the PS of relays can be stated as
)6(max,min, iii PSPSPS ≤≤
Where,
PS i, min is the minimum value of PS of the relay Ri;
PS i, max is the maximum value of PS of the relay Ri
PS i, min and PS i, max are selected as the rule of thumb [12];
PS ≥ 1.25 times maximum load current and PS ≤ 0.67 times minimum fault current
OCR type Λ Γ
Instantaneous Operating time is fixed. No Intentional time delay can be introduced.
Definite time Operating time is predefined but time delay can be introduced.
Inverse definite
minimum time
0.14 0.02
Very inverse 13.5 1
Extremely Inverse 80 2

11
III. GENETIC ALGORITHM
Genetic algorithm begins and ends like any other optimization technique. It starts with the
definition of design variables and objective function. And it ends after testing for convergence.
However, in between the algorithm is different [17].
In GA, the design variables are represented as strings of binary numbers. If each design
variable x i, i = 1, 2,…, n is coded in string of length q, a design vector is represented using a string
of total length of nq. This is achieved by placing the strings of all the variables side by side. Thus a
chromosome is formed. GA essentially starts with a group of chromosomes called population.
In numerical optimization using GA, basic operations of natural genetics like reproduction,
crossover and mutation are applied. Reproduction is a process in which the individuals are selected
based on their fitness values relative to that of the population. Individuals with higher fitness values
are selected for mating and subsequent genetic action. After reproduction, crossover operation takes
place. Crossover is a process of generating new set of chromosomes called offsprings from the parent
chromosomes. The parents and the offsprings form a new population. Mutation is applied after
crossover. Mutation is an occasional, random alteration of a binary digit in a string, The chromosome
obtained after mutation is performed replaces original chromosome in the population.
GA basically finds the optimum of an unconstrained problem [16], [19]. To solve a
constrained optimization problem, we need to transform the original constrained problem into an
unconstrained problem. Transformation methods are the simplest and the most popular optimization
methods of handling constraints. The constraints can be included in the objective function with the
help of penalty method [18].
IV. APPLICATION OF GA
The flow chart of GA is given in Appendix A. From (3), it is clear that the objective function
is of minimization type, a large number is taken as penalty. It is described by the following algorithm
1. Set penalty =10000 (a large number).
2. Set k = 1 (start with the first chromosome of the population.
3. Take kth
chromosome.
4. Calculate the objective function for the kth
chromosome.
5. n=1
6. If nth constraint is violated for the kth chromosome
z(k) = z(k) + penalty
7. Set penalty =10000 (a large number).
8. Set k = 1 (start with the first chromosome of the population.
9. Take kth
chromosome.
10. Calculate the objective function for the kth
chromosome.

12
11. n=1
12. If nth constraint is violated for the kth
chromosome, z(k) = z(k) + penalty
13. n=n+1
14. If n > number of constraints then go to step 9 or else go to step 6.
15. k=k+1
16. If k > population size then go to step 11 or else go to step 6.
17. Return objective function value for the chromosome.
With this when the population is sorted according to the objective function, values of the
chromosomes in the population, the chromosomes with higher value of objective function (for which
one or more constraints are violated) go the bottom and are automatically discarded in the next
iteration.
V. IMPLEMENTATION OF THE ABOVE METHOD
The problem is first converted into unconstrained optimization problem. As the objective
function, coordination constraints and operating time constraints are written using relay
characteristics (3), the relay characteristic constraint gets automatically incorporated in the objective
function, coordination constraints and operating time constraints.
The constraints due to bounds on TMS and PS, are taken care of by defining the lower and
upper limit of variables representing TMS and PS of relays, respectively, in the GA program. The
constraints due to operating time of relays, and the constraints due to coordination criteria, are
included in the objective function using penalty method, thus the problem gets converted into a
unconstrained optimization problem.
Number of bits to represent each parameter is decided and then a population of suitable
number of chromosomes is generated randomly. The value of variables in each chromosome is
bounded by lower and upper limits as described above.
After this, the generations (iterations) of GA are sorted. The population is passed through the
fitness function (objective function). Then the population is sorted according to the fitness. As the
objective function is of minimization type the chromosome giving minimum value is most fit
chromosome. This chromosome has been treated as elite chromosome in the paper.
The proposed method was tested for several systems and one illustration is presented here in
this paper. The chromosomes with higher fitness value survive and are called parent chromosomes.
These are used for mating.
Pairs of parent chromosomes are made for mating. Using the pairs of parent chromosome,
crossover is performed. For each pair the crossover site is selected randomly. One pair (two parent
chromosomes) generates two offsprings after crossover. All the parent chromosomes and all
offsprings are placed together to form the population for the next generations. The population for all
generations is maintained the same.
Mutation is applied after crossover. The number of mutations to be performed is decided by
mutation rate which is one of the GA parameters to be supplied at the beginning of the program. For
each mutation the chromosome is selected randomly. The bit to be mutated is again selected
randomly.

International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976
ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp.
At this point, an iteration of GA is complete.
criteria in this paper and hence the chromosome that results at the end of stopping gives the result.
VI. ILLUSTRATIONS
Fig. 1: Single line diagram of a 6 bus, 7 line system
Fig. 1 shows a test system having 6
transformers. It is a 150 kv, 100 MVA system.
sec. The CTI is assumed to be 0.4 sec
analysis. The constraints due to bounds on TMS were taken care by defining the lower and the upper
limits of the variables x 1 to x 14. The constraints due to bounds on PS were taken care by defining the
lower and the upper limits of the variables
TMS of OCRs 1 to 14 and x 15 to x 28
The objective function formed by (1) and (3
1)/(
14.0
min 02.0
24
24
1 −
=
+=
∑ irelay
i
i xI
x
z
I relay is the current seen by the relay under consideration.
Coordination constraints were formed by (2) and (3), and relay operating time constraints
were formed by (2) and (4). The constraints due to bounds on TMS and PS of relays were formed
using (5) and (6), respectively.
Line between
Buses
B1 – B2
B1 – B3
B3 – B4
B4 – B5
B5 – B6
B6 – B2
B6 – B1
Electrical Engineering and Technology (IJEET), ISSN 0976
6553(Online) Volume 5, Issue 5, May (2014), pp. 08-18 © IAEME
13
At this point, an iteration of GA is complete. Number of iterations is used as the stopping
in this paper and hence the chromosome that results at the end of stopping gives the result.
Single line diagram of a 6 bus, 7 line system
a test system having 6 buses, 7 lines with 14 OCRs, two generators and two
. It is a 150 kv, 100 MVA system. The minimum operating time of relay is taken as 0.2
CTI is assumed to be 0.4 sec. The currents seen by the relays were obtained by short circuit
onstraints due to bounds on TMS were taken care by defining the lower and the upper
. The constraints due to bounds on PS were taken care by defining the
lower and the upper limits of the variables x 15 to x 28. i.e. x 1 to x 14 were taken to represent the
28 were taken to represent the PS of the OCRs 1 to 14.
ve function formed by (1) and (3) is:
)7(
1
is the current seen by the relay under consideration.
TABLE II
LINE DATA
Line between
Buses
R (pu) X (pu) V (kV)
B2 0.0018 0.0222 150
B3 0.0018 0.0222 150
B4 0.0018 0.02 150
B5 0.0022 0.02 150
B6 0.0022 0.02 150
B2 0.0018 0.02 150
B1 0.0022 0.0222 150
B4
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
used as the stopping
in this paper and hence the chromosome that results at the end of stopping gives the result.
, two generators and two
The minimum operating time of relay is taken as 0.2
obtained by short circuit
onstraints due to bounds on TMS were taken care by defining the lower and the upper
. The constraints due to bounds on PS were taken care by defining the
were taken to represent the
were taken to represent the PS of the OCRs 1 to 14.

14
TABLE III
LOAD CURRENT AND CT DATA
Relay
Number
Load
Current (A)
CT ratio
(A/A)
Relay
Number
Load Current
(A)
CT ratio
(A/A)
1 104 150:1 8 109 150:1
2 166 200:1 9 118 150:1
3 125 150:1 10 110 150:1
4 180 250:1 11 135 200:1
5 129 150:1 12 122 150:1
6 114 150:1 13 125 150:1
7 141 200:1 14 166 200:1
TABLE IV
PRIMARY AND BACKUP RELAY PAIRS AND FAULT CURRENTS
P/B relays Fault currents (A)
Primary Relay Backup Relay Primary Relay Backup Relay
1 6 2682 2682
2 1 5428 828
2 7 5428 1571
3 2 3505 3505
4 3 1769 1769
5 4 1103 1103
6 5 4936 340
6 14 4936 1565
7 5 4184 337
7 13 4184 816
8 7 4933 1563
8 9 4939 640
9 10 1174 1174
10 11 2589 2589
11 12 3655 3655
12 13 5431 828
12 14 5431 1573
13 8 2492 2492
14 1 4184 816
14 9 4184 337
Table II, Table III and Table IV give the line data, load current data and the fault currents as
obtained from the short circuit analysis respectively.

15
VII. RESULTS AND DISCUSSIONS
TABLE V
RESULTS OBTAINED BY NLP AND GA METHODS
Relay No Conventional method Modified GA
PS TMS PS TMS
1 0.5 0.29 0.512 0.3043
2 1.25 0.31 1.228 0.2917
3 1.25 0.26 1.324 0.2543
4 1.25 0.19 1.243 0.1851
5 0.75 0.18 0.612 0.1700
6 1.25 0.26 1.122 0.2711
7 0.75 0.54 0.325 0.5316
8 0.75 0.24 1.149 0.2387
9 1.0 0.17 0.436 0.1865
10 1.25 0.19 1.015 0.1895
11 1.25 0.21 1.345 0.2014
12 1.25 0.3 0.989 0.2890
13 0.75 0.23 0.302 0.2207
14 0.25 0.51 0.233 0.5278
O.F 17.38 15.69
The problem of relay coordination was solved in a conventional manner as a constrained non
linear programming problem using the function available in MATLAB and the results are tabulated
in Table V. Later the same problem is solved using a modified objective function developed as in (7)
for GA. GA parameters used are as follows:
Population size is 256, No. of bits per parameter is 8, Crossover rate is 0.5 (50%), Mutation is
0.1(10%)

16
The results obtained are also tabulated in Table V. The objective function obtained in
modified GA is less compared to the conventional NLP approach. Table VI gives the operating time
of back up and primary relays for a typical near end fault and it is seen that the coordination
constraint is met in all the cases. No constraint is violated and the objective function which is the
total operating time is less than in the modified method.
TABLE VI
OPERATING TIME OF BACKUP AND PRIMARY RELAYS FOR NEAR END FAULTS
Back Up relay Primary Relay
Relay No. Operation Time (Sec) Relay No. Operation Time (Sec)
6 1.121 1 0.817
1 1.017 2 0.718
7 0.948 2 0.659
2 1.033 3 0.768
3 1.033 4 0.923
4 1.069 5 0.89
5 1.036 6 0.914
14 0.956 6 0.664
5 1.031 7 0.664
13 1.088 7 0.784
7 1.057 8 0.768
9 1.057 8 0.884
VIII. CONCLUSION
In this paper, a novel method of applying GA to relay coordination problem has been
developed. A systematic procedure for formulation of the problem as an optimization problem has
been proposed. Firstly the problem is solved as a constrained NLPP in this paper. The constraints
were included in the objective function and then solved using GA. The algorithm is tested on several
systems and one illustration is presented. The results obtained were found satisfactory. The proposed
method can be applied to any system easily.

17
APPENDIX A
Yes
Yes
Select bit position for mutation, complement the bit,
m = m + 1
No
Fig. 2: Flowchart of genetic algorithm
No
Define test function
Enter the number of Parameters
Enter the Number of iterations “n”
Define GA Parameters Create initial population
Iter = 1
Evaluate the cost for each chromosome
Sort the cost & associated parameters
Is iter > n
Form pairs for mating & Set k= 1
Pick up kth
pair for mating
Select crossover site
Perform crossover, k =k + 1
Is
k > n pair
Select chromosome for mutation
Is selected
chromosome elite
Is m > nmut
iter = iter + 1
m = 1
Display
Output
Stop
Yes
No
Yes
Start

18
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