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International Electrical Engineering Journal (IEEJ)
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No. 4, pp. 1841-1849
ISSN 2078-2365
http://www.ieejournal.com/
Optimal Coordination of Directional
Overcurrent Relays using Hybrid
PSO-DE Algorithm
Mohamed Zellagui 1, Almoataz Youssef Abdelaziz 2
1
Department of Electrical Engineering, Faulty of Technology, University of Batna, Algeria
2
Electrical Power & Machines Department, Faculty of Engineering, Ain Shams University, Egypt
E-mail: [email protected], [email protected]

Abstract — This paper presents a new approach for the
optimal coordination of IDMT directional overcurrent relays in
meshed power systems using a hybrid particle swarm
optimization based differential evolution algorithm (PSO-DE).
In protection coordination problem the total operating time of
all main relays is minimized. Constraints of the problem are;
backup relay should operate if primary relay fails to respond
the fault near to it, Time Dial Setting (TDS) and Plug Setting
(PS) and minimum operating time of relay. The operating time
of IDMT directional overcurrent relays holds non-linear
relationship with TDS and PS. The proposed hybrid
optimization algorithm is to minimize total operation time for
each protection relay. Two case studies are modeled and
simulated to check the efficiency of the optimization algorithms
such as IEEE 4-bus and IEEE 6-bus. The results are compared
with the results obtained through other optimization
algorithms. From the comparative results, it is found that the
PSO-DE approach provides the most globally optimum solution
at a faster convergence speed.
Index Terms — Meshed Power Systems, Directional
Overcurrent Protection, Optimal Coordination, Particle Swarm
Optimization, Differential Evolution Algorithm, Hybrid
Optimization Algorithms.
NOMENCLATURE
T
IF
TDS
PS
CT
CTpr-rating
Irelay
OF
TDSmin
TDSmax
Tmin
Tmax
CTI
Operation time
Fault current
Time Dial Setting
Plug Setting
Current transformer
Primary rating of CT
Current seen by the relay
Objective function
Minimum value for TDS
Maximum value for TDS
Minimum value for operation time
Maximum value for operation time
Coordination time interval
Tpri-cl-in
Tpri-far-bus
Tprimary
Tbackup
Operation time for relay to clear near end fault
Operation time for relay to far end fault
Operation time for primary relay
Operation time for backup relay
I. INTRODUCTION
With the development of industrial power systems, the
stability and security are getting more prominent. The main
function of a protective system is to detect and remove the
faulted parts as fast and selectively as possible. Various relays
with different operating principles in the protective system
can be used to detect system abnormalities and execute
appropriate commands to isolate swiftly only the faulty
components from the healthy system. Each protection relay
needs to be coordinated with the relays protecting the adjacent
equipment. One task of the power system protection is to keep
relays operating in the right way and coordinating well with
each other.
So the problem of coordinating protective relays is finding
suitable relay settings such that their fundamental protective
functions are met under the requirements of sensitivity,
selectivity, reliability, and speed. Directional overcurrent
relay is a good technical and economic choice for protection
of transmission and distribution power systems [1]. Such a
relay with inverse time characteristics consists of an
instantaneous unit and a time overcurrent unit. The
overcurrent unit has two parameters to be defined, the PS and
the TDS. The use of computer in power system relay
coordination application has relieved protection engineers
from huge mathematical calculation. Conventionally classical
protection philosophy and parameter optimization techniques
are reported in literature for application of relay coordination
studies. In conventional classical protection approach the
looped transmission and distribution system are treated as
radial for relay coordination studies.
1841
M. Zellagui & A.Y. Abdelaziz,
Optimal Coordination of Directional Overcurrent Relays using Hybrid PSO-DE Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No. 4, pp. 1841-1849
ISSN 2078-2365
http://www.ieejournal.com/
Relays at remote end are set first and thereafter
corresponding backup relays are set from coordination
protection point view. In this way all possible paths are taken
into account for optimal setting of relay parameters. The
coordination of overcurrent relays requires the selection of
optimal settings values. Out of both, only the values of TDS
can be optimized while solving the coordination problem with
the help of optimization algorithms. In protection
coordination problem the total operating time of all main
relays is minimized. Constraints of the problem are;
secondary relay should operate if main relay fails to respond
the fault near to it, TDS and PS and minimum operating time
of relay. The operating time of overcurrent relays hold
non-linear relationship with TDS and PS.
In recent years, many research efforts have been made to
achieve optimum protection coordination (optimum solution
for relay settings and coordination) using different
optimization algorithms including, Evolutionary Algorithms
(EA) is presented in [2] while Differential Evolution
Algorithm (DEA) in [3], Modified Differential Evolution
Algorithm (MDEA) in [4], and Self-Adaptive Differential
Evolutionary (SADE) algorithm in [5]. Application of
Particle Swarm Optimization (PSO) is introduced in [6],
Modified Particle Swarm Optimizer in [7, 8], Evolutionary
Particle Swarm Optimization (EPSO) Algorithm in [9],
Box-Muller Harmony Search (BMHS) in [10], Zero-one
Integer Programming (ZOIP) Approach in [11], Covariance
Matrix Adaptation Evolution Strategy (CMA-ES) in [12],
Seeker Algorithm (SA) in [13],Teaching Learning-Based
Optimization (TLBO) in [14], Chaotic Differential Evolution
Algorithm (CDEA) in [15], Artificial Bee Colony algorithm
(ABC) in [16], Firefly Optimization Algorithm (FOA) in [17,
18], Modified Swarm Firefly Algorithm (MSFA) in [19], and
Biogeography Based Optimization (BBO) is presented in
[20]. Applying hybrid optimization algorithms for this
problem: Evolutionary Algorithm based on Tabu Search
(EA-TS) is presented in [21], Evolutionary Algorithm based
on Linear Programming (DE-LP) in [22], Nelder-Mead and
Particle Swarm Optimization (NM-PSO) in [23], Linear
Programming and Genetic Algorithms (LP-GA) in [24],
Particle Swarm Optimization and Linear Programming
(PSO-LP) in [25], and Genetic Algorithm and Particle Swarm
Optimization algorithm (GA-PSO) is presented in [26].
This research paper studies optimal values for relay setting
and presents the solution of the coordination problem
between primary and backup relay. Hybrid optimization
algorithm namely PSO-DE has been developed in this
research. Moreover, the improvement in minimizing total
operation time (T) for each protection relays for two case
studies are modeled and simulated to check the efficiency of
the algorithm such as IEEE 4-bus and IEEE 6-bus.
II. OPTIMAL RELAY COORDINATION RELAY
Operating time of the IDMT relay is conversely
proportional with current. Hence, overcurrent relay will
operate fast after sensing the high current. However, this kind
of relay is categorized such as standard inverse, very inverse
and extremely inverse types. The relay operation time is
inversely proportional to the fault current. The characteristics
of relay depend on the type of standard selected for the relay
operation; these standards can be ANSI, IEEE, IEC or user
defined.
Typically there are overcurrent relays for protection against
inter phase faults and phase to earth faults on the line. The
tripping time of the relay follows a time over current delayed
curve, in which the time delay depends upon current. Two
decision variables of the relay are TDS and PS. The operating
time of the relay is closely related to TDS, PS and the fault
current (IF). The total operating time is given by a non-linear
mathematic equation [3], [11]-[26] with respect to the
coordination time constraint between the backup and primary
relays:
T
  TDS

(1)


IF

  
 PS  CTpr ration 
Where, α, β and γ are the constants values. The constant
values are given as 0.14, 0.02 and 1.0 respectively according
to IEEE standard [27]. In equation (1), IF is the fault current at
CT primary terminal where fault occurs. CTpr-rating is the
primary rating of CT. The ratio of IF and CTpr-rating gives the
current seen by the relay i.e. Irelay.
I relay 
IF
(2)
CTpr rating
However, the ratio of Irelay and PS indicates the level of
nonlinearity in the equation.
2.1. Objective Function
A close-in fault (or near end fault) is known for a fault that
occurring close to the relay and a far-bus fault (or far end
fault) is known for a fault that occurring at the other end of the
line. These definitions are demonstrated in Figure 1.
Fig. 1. Diagram showing close-in and far-bus faults
for relay RPri-Near.
1842
M. Zellagui & A.Y. Abdelaziz,
Optimal Coordination of Directional Overcurrent Relays using Hybrid PSO-DE Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No. 4, pp. 1841-1849
ISSN 2078-2365
http://www.ieejournal.com/
In coordination studies, the operating time summation of
all the primary relays to clear near end fault or far end fault
can be considered as an objective function [14], [15]. It can be
clearly claimed that the objective function in coordination
studies should be minimized. Therefore, the objective
function (OF) can be express as given by [4], [14], [15]:
Ncl
N far
i 1
j 1
i
j
Minimize OF   Tpri
 cl in   Tpri  far bus
(3)
Where,
T
i
pri  cl in

Tprij  far bus 
For the electromechanical relays, the CTI is varied
between 0.30 to 0.40 sec, while for the numerical relays it’s
varied between 0.10 to 0.20 sec [13, 14]. In this research, the
value of CTI is chosen as 0.30 sec for all case studies. The
value of Tbackup and Tprimary can be determined by equations
(10) and (11) respectively.
i
Tbackup

0.14  TDS i


I Fi
 i

i
 PS  CTpr ration 
Where, Tbackup and Tprimary are the operating time of the
backup relay and the primary relay respectively; CTI is the
minimum coordination time interval.
(4)
0.02
0.14  TDS
1
j


I Fj
 j

j
 PS  CTpr ration 
(5)
i
Tprimary

0.02
1
TDS
 TDS  TDS
(10)
0.02
1
0.14  TDS y


I
 y

i
 PS  CTpr ration 
i
F
(11)
0.02
1
III. HYBRID PSO-DE ALGORITHM
Three constraints need to be considered for the
coordination problem as follow: TDS of the relay is the time
delay before relay operation whenever the fault current
becomes equal to, or greater than PS setting [12-14].
i


I Fi
 x

i
 PS  CTpr ration 
And,
2.2. Constraints
i
min
0.14  TDS x
i
max
(6)
Where, i is varying from 1 to Ncl; TDSimin and TDSimax are
minimum and maximum values for TDS that are 0.05 and 1.10
respectively.
i
i
PSmin
 PS i  PSmax
(7)
Where, i is varying from 1 to Nfar; PSimin and PSimax are
minimum and maximum values of PS which are 1.25 and 1.50
respectively. Relay operating time is related to the fault
current which can be seen by the relay and the pickup current
setting. Relay operating time is based on the type of the relay
and it can be determined by standard characteristic curves of
the relay or analytic formula. Operating time is defined by:
Ti min  Ti  Ti max
(8)
Where, Tmin and Tmax are minimum and maximum values for
operation time that are 0.05 and 1.00 respectively. The
coordination time interval between the primary and the
backup relays must be verified during optimization
procedure. In this paper, the chronometric coordination
between the primary and the backup relays is used as in
equation (9):
Tbackup  Tprimary  CTI
(9)
This section presents a brief description of the three
stochastic algorithms: the PSO, the DE and the hybrid
PSO-DE, together with some relevant implementation details.
3.1. Overview of Particle Swarm Optimization (PSO)
PSO is a population based stochastic optimization
technique inspired on social behavior of bird flocking or fish
schooling. The algorithm searches for the optimum using a
group or swarm formed by possible solutions of the problem,
which are called particles.
The algorithm implemented in this work is inspired on [28,
29]. Each particle is updated as indicated by equation (12) and
the group of particles moves through the search space as
indicated by equation (13).
 wV
. i ,kj1  c1.rand1.  Pbesti , j  Pi ,kj1  

 .FC
V 
 c2 .rand 2 .  Gbesti  Pi ,kj1 



(12)
Pi ,kj  Pi ,kj1  Vi ,kj
(13)
k
i, j
In equations (12) and (13), for component i of particle j.
Pi,jk represents its position and Vi,jk is called speed; c1 and c2
are the acceleration coefficients; FC is the contraction
coefficient calculated as in equation (14) [28]; rand1 and
rand2 are uniformly distributed random numbers in [0, 1],
sampled at each iteration k. The particles of the swarm are
individually analyzed and the one that generates the best
solution along the iterations, i.e. best local solution, is called
Pbest (particle best).
1843
M. Zellagui & A.Y. Abdelaziz,
Optimal Coordination of Directional Overcurrent Relays using Hybrid PSO-DE Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No. 4, pp. 1841-1849
ISSN 2078-2365
http://www.ieejournal.com/
The best solution in the swarm is tracked in Gbest (group
best). Parameter w, called inertia, indicates the contribution of
the previous velocity to the new one. It is updated at each
iteration k by equation (15) [29].
FC 
2
2      4
2
w  wmax 
, with   c1  c2  4
wmax  wmin
.k
Gmax
(14)
(15)
Where, Gmax is the maximum number of iterations; wmax and
wmin are, respectively, maximum and minimum inertia values.
Higher values of w favor global exploration of the search
space, while smaller values tend to facilitate local search [30].
3.2. Overview of Differential Evolution (DE)
The differential evolution algorithm, proposed by Storn
and Price [30], is also a population based algorithm that uses
the mutation, selection and crossing over processes. The DE
implemented in this work is based on [31-34]. The mutation
process initiates with the creation of a mutant vector: an
individual is combined with its difference with the best
individual and with a random term, as described in equations
(16) and (17). The crossing over process is presented in
equation (18):
1
k 1
Vi ,kj  F .  Gbestik 1  Pi ,kj1   F .  Pi ,kran
1  Pi ,ran 2 
(16)
Zik, j  Pi ,kj1  Vi ,kj
(17)
k 1
i, j
P
 Zik, j if (rand (i )  CR) or (i  rnbr (i ))
  k 1
 Pi , j if (rand (i )  CR) and (i  rnbr (i ))
(18)
Where, Gbestk-1 is the best individual in iteration (k - 1) and
is the individual being updated; for component i of
particle j, ran1 and ran2 are random numbers uniformly
distributed in [1, nI] and represent two individuals randomly
selected; nI is the number of individuals; F is the
amplification factor, usually defined in interval [0, 2]; Vjk is
the (nI × 1) obtained mutant vector; rand(i) and rnbr(i) are
also random numbers uniformly distributed on [0, 1] and on
[1, nv], respectively; nv is the individual dimension; the
crossing over parameter CR defines the crossing over
probability.
Pjk-1
3.3. Hybrid PSO-DE Algorithm
The hybrid algorithm implemented is inspired in the
strategy suggested in [35-38] of exploring the search space
first globally and then locally, using two different
evolutionary algorithms. Notice that the crossing over process
of the DE algorithm promotes information exchange among
individuals and favors search in new areas of the search space.
The mutation process aims at increasing population
diversity and the algorithm ability to escape from local
minima [36].
In this work, due to the fact that in high dimension
problems the PSO is easily trapped into local optima,
resulting in a low optimizing precision or even failure [35],
the proposal is to use the PSO algorithm during the first 30%
of the iterations.
In the sequel, during the remaining 70% of the iterations,
the mutation and crossing over operators shown in equations
(16), (17) and (18) are used. The algorithm is structured in the
steps shown bellow [39]:
Step 1 (Initialization of the particles): At the first iteration,
component i of particle j is generated randomly, as indicated
in equation (19), where rd is a uniformly distributed random
number in [0, 1].
Pi ,( kj 1)  Pi ,min  rd .  Pi ,max  Pi ,min 
(19)
Step 2 (Treatment of equality constraints and Pbest
evaluation): In the first iteration, Pbest for each particle
assumes the value of the corresponding particle.
Step 3 (Fitness evaluation): The objective function value is
determined for each particle.
Step 4 (Gbest evaluation): The best particle, i.e. the one that
gives lower generation costs among all the Pbest particle
values, is identified as Gbest.
Step 5 (Velocity update): The velocity is updated using
equation (12) or (17), depending on the current iteration
number.
Step 6 (Position update): The particle’s position is updated
using equation (13) or (18), depending on the current iteration
number.
Step 7 (Treatment of equality and inequality constraints):
The constraints are solved in two stages as explained in Step
2. The inequality constraints are evaluated as indicated in
equation (20):

 Pi if Pi ,kj  Pi

P 
k
 Pi if Pi , j  Pi
k
i, j



(20)
Step 8 (Pbest evaluation): For each particle, the objective
function value is evaluated and compared with that of Pbest.
Step 9 (Check stopping criterion): The stopping criterion
involves a tolerance for the difference among the objective
function associated to all particles values and for the
feasibility condition of the optimization problem. If
convergence is not attained, continue from Step 4.
1844
M. Zellagui & A.Y. Abdelaziz,
Optimal Coordination of Directional Overcurrent Relays using Hybrid PSO-DE Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No. 4, pp. 1841-1849
ISSN 2078-2365
http://www.ieejournal.com/
IV. CASE STUDY, SIMULATION RESULTS
AND COMPARISON
Table 1. Values of IF and CTpr-rating for cases sudy
with T ipri_cl_in and Tjpri_far_bus
The proposed hybrid optimization algorithm PSO-DE is
validated and tested on two case studies namely IEEE 4-bus,
and 6-bus, shown in Figures 2.a, and 2.b respectively. The
first case study consists of a two power generators, fourth
lines and 8 protection relays. For the optimization problem of
this model, we have to coordinate the settings of all the 8
protection relays.
a) IEEE 4-bus, b) IEEE 6-bus
Accordingly, there are 16 decision variables i.e. TDS1 to
TDS8 and PS1 to PS8. The second case study consists of three
power generators, seventh lines and 14 protection relays. For
the optimization problem of this cases study, we have to
coordinate the settings of all the 14 overcurrent relays.
Accordingly, there are 28 decision variables i.e. TDS1 to
TDS14 and PS1 to PS14 [40].
(a)
T ipri_cl_in
TDSi
TDS1
TDS2
TDS3
TDS4
TDS5
TDS6
TDS7
TDS8
Ii F
20.32
88.85
13.60
116.81
116.70
16.67
71.70
19.27
T jpri_far_bus
CTipr-rating
0.4800
0.4800
1.1789
1.1789
1.5259
1.5259
1.2018
1.2018
TDSj
TDS2
TDS1
TDS4
TDS3
TDS6
TDS5
TDS8
TDS7
CTjpr-rating
0.4800
0.4800
1.1789
1.1789
1.5259
1.5259
1.2018
1.2018
(b)
T ipri_cl_in
TDSi
TDS1
TDS2
TDS3
TDS4
TDS5
TDS6
TDS7
TDS8
TDS9
TDS10
TDS11
TDS12
TDS13
TDS14
(a)
Ij F
23.75
12.48
31.92
10.38
12.07
31.92
11.00
18.91
Ii F
2.5311
2.7376
2.9723
4.1477
1.9545
2.7678
3.8423
5.6180
4.6538
3.5261
2.5840
3.8006
2.4143
5.3541
T jpri_far_bus
CTipr-rating
0.2585
0.2585
0.4863
0.4863
0.7138
0.7138
1.7460
1.7460
1.0424
1.0424
0.7729
0.7729
0.5879
0.5879
TDSj
TDS2
TDS1
TDS4
TDS3
TDS6
TDS5
TDS1
TDS2
TDS3
TDS4
TDS5
TDS6
TDS1
TDS2
Ij F
5.9495
5.3752
6.6641
4.5897
6.2345
4.2573
6.3694
4.1783
3.8700
5.2696
6.1144
3.9005
2.9011
4.3350
CTjpr-rating
0.2585
0.2585
0.4863
0.4863
0.7138
0.7138
1.7460
1.7460
1.0424
1.0424
0.7729
0.7729
0.5879
0.5879
Table 2. Values of IF and CTpr-rating for cases sudy
with Txbackup and T yprimary
a) IEEE 4-bus, b) IEEE 6-bus
(a)
T xbackup
(b)
Fig. 2. Power system for cases study:
a) IEEE 4-bus, b) IEEE 6-bus.
For all case studies in this paper the CTI is fixed to 0.30 sec.
The values of constants IF and CTpr_rating for the two case
studies are given in Tables 1 and 2 [15, 40]. For each model
there are two tables, one is with respect to the TiPri-far-bus and
TjPri-far-bus, the other is with respect to the, Txbackup and T yprimary.
Relay
No.
5
5
7
7
1
2
2
4
4
T ypimary
IFi
CTipr-rating
20.32
12.48
13.61
10.38
116.81
12.07
16.67
11.00
19.27
1.5259
1.5259
1.2018
1.2018
0.4800
0.4800
0.4800
1.1789
1.1789
Relay
No.
1
1
3
3
4
6
6
8
8
IFj
CTjpr-rating
20.32
12.48
13.61
10.38
116.81
12.07
16.67
11.00
19.27
0.4800
0.4800
1.1789
1.1789
1.1789
1.5259
1.5259
1.2018
1.2018
1845
M. Zellagui & A.Y. Abdelaziz,
Optimal Coordination of Directional Overcurrent Relays using Hybrid PSO-DE Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No. 4, pp. 1841-1849
ISSN 2078-2365
http://www.ieejournal.com/
(b)
T xbackup
Relay
No.
8
11
8
3
3
10
10
13
1
1
12
12
14
3
3
11
2
11
2
13
4
13
4
14
6
14
6
8
2
8
2
12
6
12
10
4
10
4
Typrimary
IFi
CTipr-rating
4.0909
1.2886
2.9323
0.6213
1.6658
0.0923
2.5610
1.4995
0.8869
1.5243
2.5444
1.4549
1.7142
1.4658
1.1231
2.1436
2.0355
1.9712
1.8718
1.8321
3.4386
1.6180
3.0368
2.0871
1.8138
1.4744
1.1099
3.3286
0.4734
4.5736
1.5432
2.7269
1.6085
1.8360
2.0260
0.8757
2.7784
2.5823
1.7460
0.7729
1.7460
0.4863
0.4863
1.0424
1.0424
0.5879
0.2585
0.2585
0.7729
0.7729
0.5879
0.4863
0.4863
0.7729
0.2585
0.7729
0.2585
0.5879
0.4863
0.5879
0.4863
0.5879
0.7138
0.5879
0.7138
1.7460
0.2585
1.7460
0.2585
0.7729
0.7138
0.7729
1.0424
0.4863
1.0424
0.4863
Relay
No.
1
1
1
2
2
3
3
3
4
4
5
5
5
6
6
7
7
7
7
9
9
9
9
11
11
11
11
12
12
12
12
13
13
13
14
14
14
14
IFj
CTjpr-rating
5.3752
5.3752
2.5311
2.7376
5.9495
4.5897
2.9723
4.5897
4.1477
6.6641
4.2573
1.9545
4.2573
6.2345
6.2345
4.1783
4.1783
3.8423
3.8423
5.2696
5.2696
4.6538
4.6538
3.9005
3.9005
2.5840
2.5840
3.8006
3.8006
6.1144
6.1144
4.3350
4.3350
2.4143
2.9011
2.9011
5.3541
5.3541
0.2585
0.2585
0.2585
0.2585
0.2585
0.4863
0.4863
0.4863
0.4863
0.4863
0.7138
0.7138
0.7138
0.7138
0.7138
1.7460
1.7460
1.7460
1.7460
1.0424
1.0424
1.0424
1.0424
0.7729
0.7729
0.7729
0.7729
0.7729
0.7729
0.7729
0.7729
0.5879
0.5879
0.5879
0.5879
0.5879
0.5879
0.5879
The convergence characteristics for the hybrid
optimization algorithms proposed (PSO-DE) of the two case
studies IEEE 4-bus and 6-bus are presented in figures 3.a and
3.b respectively.
(a)
(b)
Fig. 3. Convergence characteristics of PSO-DE for all cases study:
IEEE 4-bus, b) IEEE 6-bus.
4.1. Optimal Settings Relays
The new optimal relays settings (TDS and PS) using the
hybrid optimization algorithm PSO-DE for the two case
studies are presented in Tables 3.a and 3.b respectively.
Table 3. Optimal setting of relays: a) IEEE 4-bus, b) IEEE 6-bus.
(a)
Relay
No.
1
2
3
4
5
6
7
8
TDS
PS
0.0560
0.2415
0.0561
0.1732
0.1441
0.0563
0.1543
0.0566
1.4583
1.7156
1.4309
1.6174
1.6172
1.4309
1.7178
1.4305
1846
M. Zellagui & A.Y. Abdelaziz,
Optimal Coordination of Directional Overcurrent Relays using Hybrid PSO-DE Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No. 4, pp. 1841-1849
ISSN 2078-2365
http://www.ieejournal.com/
(b)
Relay
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
TDS
PS
0.4064
0.7506
0.3872
0.4031
0.2005
0.2011
0.2003
0.2133
0.2006
0.2265
0.2610
0.2039
0.2002
0.2837
0.4722
0.4709
0.4119
0.4726
0.4118
0.4437
0.4109
0.4108
0.4124
0.4724
0.4618
0.4739
0.4642
0.3731
1
1
12
12
14
3
3
11
2
11
2
Table 4. Optimal CTI value:
a) IEEE 4-bus, b) IEEE 6-bus.
(a)
TLPO
[14]
0.539
0.649
0.600
0.510
0.432
0.300
0.356
0.355
0.382
PSO-DE
0.304
0.312
0.318
0.313
0.324
0.329
0.322
0.309
0.317
(b)
Relay
No.
8
1
11 1
8
1
3
2
3
2
10 3
10 3
13 3
MDE
[4]
0.288107
4.029328
0.80684
1669.695
0.199929
-0.18123
0.378005
0.300372
TLPO
[14]
2.18859
1.534819
3.249765
2.201281
0.438233
0.418234
1.236218
0.30791
0.843753
0.517069
0.937599
1.525362
1.180526
0.551088
0.30015
1.373804
0.982896
1.472532
1.019525
0.3009
0.3129
0.3455
0.3324
0.3753
0.3435
0.3325
0.3212
0.3564
0.3247
0.3038
4.3. Comparison Study
The CTI between backup and primary overcurrent relay is
calculated from the optimized value of TDS and PS for the
two case studies. The CTI is improved using the proposed
new hybrid optimization algorithm (PSO-DE) as compared to
optimization algorithms MDE and TLBO as represented in
Table 4.
MDE
[4]
0.300
0.348
0.299
0.397
0.299
0.299
0.400
0.299
0.349
0.458382
0.199845
0.225775
0.839275
0.519282
0.578187
0.347919
0.200146
0.238046
0.237149
0.200045
From the results of Table 4, it can be seen that the
proposed hybrid optimization algorithm give best value of
minimized CTI compared to other algorithms.
4.2. Optimal CTI Value
Relay
No.
1
4
2
6
2
6
4
8
4
8
5
1
5
1
7
3
7
3
4
4
5
5
5
6
6
7
7
7
7
PSO-DE
0.3439
0.2362
0.3002
0.3531
0.3004
0.3057
0.3054
0.3003
Table 5 presents the best obtained values of the objective
function using the new proposed hybrid optimization
algorithm (PSO-DE) compared with other published results
obtained with TLBO, DE, and MDE.
Table 5. Comparison with other published results:
a). IEEE 4-bus, b). IEEE 6-bus
(a)
Algorithm
OF (sec)
TLBO [14]
MDE [4]
DE [15]
Hybrid PSO-DE
5.5890
3.6674
3.6774
3.4293
(b)
Algorithm
OF (sec)
TLBO [14]
DE [15]
MDE [4]
Hybrid PSO-DE
23.7878
10.6272
10.3514
9.2671
From the results of Table 5, it can be seen that the proposed
hybrid algorithm (PSO-DE) give better performances and
provide the best solutions compared to other published
results.
V. CONCLUSIONS
The optimization model of overcurrent relays coordination
turns out to be highly constrained and nonlinear in nature.
Efficient optimization algorithm PSO-DE is needed to deal
with these problems. The proposed hybrid optimization
algorithms are validated and tested on two different case
studies.
1847
M. Zellagui & A.Y. Abdelaziz,
Optimal Coordination of Directional Overcurrent Relays using Hybrid PSO-DE Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No. 4, pp. 1841-1849
ISSN 2078-2365
http://www.ieejournal.com/
The results showed that the proposed algorithm is able to
find superior TDS and PS and thus minimum operating time of
the relays and minimum CTI.
[8]
The effectiveness of the hybrid optimization algorithm can
be observed from the results in terms of objective function
values, which are better in comparison to other optimization
algorithms used in the literature.
[9]
The continuity of this work will be the coordination of the
overcurrent relays considering several conflicting objective
functions and various power system topologies and in the
presence of FACTS devices and DG using new hybrid
optimization algorithms.
[10]
[11]
[12]
APPENDIX
The parameters of three optimisation algorithms study is:
A)- PSO : c1 = c2 = 2.0, ωmin = 0.4, ωmax = 0.9, Gmax = 200.
B)- DE : F = 1.7, nI = 80, nv = 80, CR = 0.15, Gmax = 200.
[13]
[14]
C)- PSO-DE : c1 = c2 = 2.2, ωmin = 0.5, ωmax = 0.8, F = 1.8,
nI = 85, nv = 85, CR = 0.17, Gmax = 200.
[15]
ACKNOWLEDGMENT
Authors acknowledge help and support of Pr. Hazli
Mokhlis and Dr. Mazaher Karimi at department of electrical
engineering, university of Malaya in Malaysia.
[16]
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
D. Birla, R.P. Maheshwari, and H.O. Gupta, “An Approach to Tackle
the Threat of Sympathy Trips in Directional Overcurrent Relay
Coordination”, IEEE Transactions on Power Delivery, Vol. 22, No. 2,
pp. 851-858, 2007.
J.A. Sueiro, E. Diaz-Dorado, E. Míguez, and J. Cidrás, “Coordination
of Directional Overcurrent Relay using Evolutionary Algorithm and
Linear Programming”, International Journal of Electrical Power and
Energy Systems, Vol. 42, pp. 299-305, 2012.
R. Thangaraj, T.R. Chelliah, and M. Pant, “Overcurrent Relay
Coordination by Differential Evolution Algorithm”, IEEE
International Conference on Power Electronics, Drives and Energy
Systems (PEDES), Bengaluru, India, December 16-19, 2012.
R. Thangaraj, M. Pant, and K. Deep, “Optimal Coordination of
Overcurrent Relays using Modified Differential Evolution
Algorithms”, Engineering Applications of Artificial Intelligence,
Vol. 23, No. 5, pp. 820-829, 2010.
M. Mohseni, A. Afroomand, and F. Mohsenipour, “Optimum
Coordination of Overcurrent Relays Using SADE Algorithm”, 16th
IEEE Conference on Electrical Power Distribution Networks
(EPDC), Bandar Abbas, Iran, 19-20 April, 2011.
M. Zellagui, R. Benabid, M. Boudour, and A. Chaghi, “Mixed Integer
Optimization of IDMT Overcurrent Relays in the Presence of Wind
Energy Farms using PSO Algorithm”, Periodica Polytechnica Electrical Engineering and Computer Science, Vol. 59, No. 1,
pp. 7-19, March 2015.
H. Zeineldin, E. El-Saadany, and M. Salama, “Optimal Coordination
of Overcurrent Relays using a Modified Particle Swarm
Optimization”, Electrical Power Systems Research, Vol. 76, No. 11,
pp. 988-995, 2006.
[17]
[18]
[19]
[20]
[21]
[22]
[23]
M.M. Mansour, S.F. Mekhamer, and N.E.S. El-Kharbawe, “A
Modified Particle Swarm Optimizer for the Coordination of
Directional Overcurrent Relays”, IEEE Transactions on Power
Delivery, Vol. 22, No. 3, pp. 1400-1410, 2007.
H. Leite, J. Barros, and V. Miranda, “The Evolutionary Algorithm
EPSO to Coordinate Directional Overcurrent Relays”, 10th IET
International Conference on Developments in Power System
Protection (DPSP), Manchester, UK, March 29 - April 1, 2010.
A. Fetanat, G. Shafipour, and F. Ghanatir, “Box-Muller Harmony
Search Algorithm for Optimal Coordination of Directional Overcurrent
Relays in Power System”, Scientific Research and Essays, Vol. 6,
No.19, pp. 4079-4090, 2011.
J. Moirangthem, S.S. Dash, and R. Ramaswami, “Zero-one Integer
Programming Approach to Determine the Minimum Break Point Set in
Multi-loop and Parallel Networks”, Journal of Electrical Engineering
& Technology (IJET), Vol. 7, No. 2, pp. 151-156, 2012.
M. Singh, B.K. Panigrahi, and R. Mukherjee, “Optimum Coordination
of Overcurrent Relays using CMA-ES Algorithm”, IEEE International
Conference on Power Electronics, Drives and Energy Systems,
Bengaluru, India, 16-19 December, 2012.
T. Amraee, “Coordination of Directional Overcurrent Relays Using
Seeker Algorithm”, IEEE Transactions on Power Delivery, Vol. 27,
No. 3, pp. 1415-1422, 2012.
M. Singh, B.K. Panigrahi, and A.R. Abhyankar, “Optimal
Coordination of Directional Overcurrent Relays using Teaching
Learning-Based Optimization (TLBO) Algorithm”, International
Journal of Electrical Power and Energy Systems, Vol. 50, pp. 33-41,
2013.
T.R. Chelliah, R. Thangaraj, S. Allamsetty, and M. Pant,
“Coordination of Directional Overcurrent Relays using Opposition
based Chaotic Differential Evolution Algorithm”, International
Journal of Electrical Power and Energy Systems, Vol. 55, pp.341-350,
2014.
M. Singh, B.K. Panigrahi, and A.R Abhyankar, “Optimal
Coordination of Electro-Mechanical based Overcurrent Relays using
Artificial Bee Colony Algorithm”, International Journal of
Bio-Inspired Computation, Vol. 5, No. 5, pp. 267-280, 2013.
R. Benabid, M. Zellagui, A. Chaghi, and M. Boudour, “Application of
Firefly Algorithm for Optimal Directional Overcurrent Relays
Coordination in the Presence of IFCL”, International Journal of
Intelligent Systems and Applications (IJISA), Vol. 6, No. 2, pp. 44-53,
2014.
S.S. Gokhale, and V.S. Kale, “Application of the Firefly Algorithm to
Optimal Over-Current Relay Coordination”, International Conference
on Optimization of Electrical and Electronic Equipment (OPTIM),
Bran - Romania, 22-24 May 2014.
M.H. Hussain, I. Musirin, A.F. Abidin, and S.R.A. Rahim, “Modified
Swarm Firefly Algorithm Method for Directional Overcurrent Relay
Coordination Problem”, Journal of Theoretical and Applied
Information Technology, Vol. 66, No. 3, pp.741-755, 2014.
M. Zellagui, R. Benabid, M. Boudour, and A. Chaghi, “Optimal
Overcurrent Relays Coordination in the Presence Multi TCSC on
Power Systems Using BBO Algorithm”, International Journal
Intelligent Systems and Applications (IJISA), Vol. 7, No. 2, pp. 13-20,
2015.
C. Xu, X.Zou, R. Yuan, and C. Wu, “Optimal Coordination of
Protection Relays using New Hybrid Evolutionary Algorithm”, IEEE
Congress on Evolutionary Computation (CEC), Hong Kong, 1-6 June
2008.
J.A. Sueiro, E. Diaz-Dorado, E. Míguez, and J. Cidrás, “Coordination
of Directional Overcurrent Relay using Evolutionary Algorithm and
Linear Programming”, International Journal of Electrical Power and
Energy Systems, Vol. 42, pp. 299-305, 2012.
M.T. Yang, and A. Liu, “Applying Hybrid PSO to Optimize
Directional Overcurrent Relay Coordination in Variable Network
Topologies”, Journal of Applied Mathematics, Vol. 2013, 2013.
1848
M. Zellagui & A.Y. Abdelaziz,
Optimal Coordination of Directional Overcurrent Relays using Hybrid PSO-DE Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No. 4, pp. 1841-1849
ISSN 2078-2365
http://www.ieejournal.com/
[24] F.B. Bottura, M. Oleskovicz, D.V. Coury, and S.A. De Souza, “Hybrid
Optimization Algorithm for Directional Overcurrent Relay
Coordination”, IEEE PES General Meeting - Conference &
Exposition, National Harbor, USA, 27-31 July 2014.
[25] A.V.A. Papaspiliotopoulos, T.S. Kurashvili, and G.N. Korres,
“Optimal Coordination of Directional Overcurrent Relays for
Distribution Systems with Distributed Generation based on a Hybrid
PSO-LP Algorithm”, 9th Mediterranean Conference on Power
Generation, Transmission Distribution and Energy Conversion
(MedPower), Athens - Greece, 3-7 November, 2014.
[26] S.H. Mousavi Motlagh, and K. Mazlumi, “Optimal Overcurrent Relay
Coordination using Optimized Objective Function”, SRN Power
Engineering, Volume 2014, Article ID 869617, 2014.
[27] Standard, “IEEE Standard Inverse-Time Characteristic Equations for
Overcurrent Relays”, Number C37.112, published by IEEE, 1996.
[28] S.Y. Lim, M. Montakhad, and H. Nouri, “Economic Dispatch of Power
System using Particle Swarm Optimization with Constriction Factor”,
International Journal of Innovations in Energy Systems and Power,
Vol. 4, No. 2, pp. 29-34, 2009.
[29] A. Nickabadi, M.M. Ebadzadeh, and R. Safabakhsh, “A Novel Particle
Swarm Optimization Algorithm with Adaptive Inertia Weight”,
Applied Soft Computing Journal, Vol. 11, No. 4, 3658-3670, 2011.
[30] J. Praveen, and Srinivasa Rao, “Single objective optimization using
PSO with Interline Power Flow Controller”, International Electrical
Engineering Journal (IEEJ), Vol. 5, No. 12, pp. 1659-1664 2014.
[31] R. Storn, and K. Price, “Differential Evolution - A Simple and Efficient
Heuristic for Global Optimization Over Continuous Spaces”, Journal
of Global Optimization, Vol. 11, pp. 341-359, 1997.
[32] N. Noman, and H. Iba, “Differential Evolution for Economic Dispatch
Problems”, Electrical Power Systems Research, Vol. 78, No. 8,
pp.1322-1331, 2008.
[33] A.A. Abou El Ela, M.A. Abido, and S.R. Spea, “Optimal Power Flow
using Differential Evolution Algorithm”, Electrical Power Systems
Research , Vol. 80, No. 7, pp. 878-885, 2010.
[34] A.A. Abou El Ela, M.A. Abido, and S.R. Spea, “Differential Evolution
Algorithm for Emission Constrained Economic Power Dispatch
Problem”, Electrical Power Systems Research, Vol. 80, No. 10,
pp.1286-1292, 2010.
[35] H. Lu, S. Pichet, Y.H. Song, and T. Dillon, “Experimental Study of a
New Hybrid PSO with Mutation for Economic Dispatch with
Non-Smooth Cost Function”, Electrical Power Systems Research,
Vol. 32, No. 9, pp. 921-935, 2010.
[36] D.L. Jia, G.X. Zheng, B.Y. Qu, and M.K. Khan, “A Hybrid Particle
Swarm Optimization Algorithm for High-Dimensional Problems”,
Computers & Industrial Engineering, Vol. 61, No. 4, pp. 1117-1122,
2011.
[37] R. Thangaraj, M. Pant, A. Abraham, and P. Bouvry, “Particle Swarm
Optimization: Hybridization Perspectives and Experimental
Illustrations”, Applied Mathematics and Computation, Vol. 217,
No. 12, pp. 5208-5226, 2011.
[38] H. Gao, and W. Xu, “Particle Swarm Algorithm with Hybrid Mutation
Strategy”, Applied Soft Computing Journal, Vol. 11, No. 8,
pp. 5129-5142, 2011.
[39] T.D.F. Araújo, and W. Uturbey, “Performance Assessment of PSO, DE
and Hybrid PSO-DE Algorithms when Applied to the Dispatch of
Generation and Demand”, International Journal of Electrical Power
and Energy Systems, Vol. 47, pp. 205-217, 2013.
[40] M. Zellagui, and H.A. Hassan, “A Hybrid Optimization Algorithm
(IA-PSO) for Optimal Coordination of Directional Overcurrent Relays
in Meshed Power Systems”, WSEAS Transactions on Power Systems,
Vol. 10, 2015.
1849
M. Zellagui & A.Y. Abdelaziz,
Optimal Coordination of Directional Overcurrent Relays using Hybrid PSO-DE Algorithm
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