Optimal Network Reconfiguration via Improved Whale
Optimization Approach
E. S. ALI1, S. M. ABD ELAZIM2
1Electric Department, Faculty of Engineering, Jazan University, Jazan, KSA,
2Computer Science Department, Faculty of Computer Science and Information Technology,
Jazan University, KSA.
Abstract:- Latterly, reduction of power loss in the distribution system is the objective of many researches due to
its impact on total costs and voltage profiles. It can be handled by an optimal restructure of the Radial Distribution
System (RDS). This article introduces an innovative approach to restructure of RDS by electing the optimal
switches combination subject to the system operating constraints, which is Improved Whale Optimization
Approach (IWOA). The suggested approach combines exploitation of WOA with exploration of Differential
Evolution (DE), and thus it supplies a promising candidate solution. The suggested approach is tested on IEEE
33 and 69 bus RDS. The superiority of the suggested approach compared with other well-known approaches is
verified through simulation results by examining total losses, cost and saving. Also, the impact of alterable
loading is investigated to prove the effectiveness of the suggested IWOA.
KeyWords: Radial Distribution System; Restructure; IWOA; Ohmic Losses; Mitigation.
Received: August 14, 2022. Revised: July 26, 2023. Accepted: August 29, 2023. Published: October 3, 2023.
1. Introduction
Mitigation of ohmic power losses in RDS is still the
target of many researches. Installation of DG,
capacitors, and restructure of RDS are presented as
the three main scenarios to alleviate these losses.
Restructure of RDS is presented as the most
preferable scenario as the costs of operation and
installation of DG, and capacitors are not included.
The restructure process refers to the alteration of
system switches combination and adjustment of the
structure of network operation by closing or opening
the disconnected sectional and tie switches with
satisfied constraint [1-4]. These switches organize
the status of feeders and have a pivotal impact on
branch power flows and total power losses.
Since the charge of ohmic power loss presents
plentiful value of operating charge in RDS, and
thence considerable papers have objective function of
active power loss. ANNs has been implemented in
[5] to assort the proper network topology to reduce
losses for small RDS. FEP has been considered in [6]
as the solution mechanism to restructure of RDS to
acquire the best voltage profile and least kW losses.
In [7], a method for multi-objective restructure of
RDS in FFW using AGA has been presented. A
method to optimize the unbalanced systems to keep
up the voltage profiles with respect to the
consequence of solving the multi-objective
restructure utilizing the FA in a fuzzy domain has
been addressed in [8]. A two-stage solution technique
based on a modified SA approach for general multi-
objective optimization tasks has been discussed in
[9]. A modified SA approach has been developed in
[10] for network restructure in distribution systems
for loss minimization. A method for optimal planning
of RDS has been introduced in [11] based on a
combination of the steepest descent and the SA
programming. TS approach with some modifications
has been mentioned in [12] for restructure of RDS.
The application of a GA with variable population size
to the restructure problem has been demonstrated in
[13]. A new cycle break algorithm that utilizes
elementary cycles or network adjacency matrix with
GA to develop radial network restructure has been
presented in [14]. AGA has been used in [15] to
minimize real loss without involving any additional
cost for the installation of capacitors, tap changing
transformers, and concerned switching equipment.
EGA has been utilized in [16] to solve the restructure
problem, reduce power loss, and improve system
reliability. In [17], an IGA has been developed to
handle the restructure problem considering total
voltage deviation and active power loss. ACA has
been indicated in [18-19] to deal with the restructure
problem of distribution systems while enforcing the
technical constraints like the voltage limits and
transmission capabilities. PSO has been applied on
[20-21] to deal with the distribution feeder
restructure problem considering the effect of DG
units. In [22], PSO has been presented to find the
solution of the two-stage technique, which solves the
optimal network restructure at the first stage and
phase balancing at second stage. MPSO has been
suggested in [23-24] for system restructure to
enhance voltage profiles and minimize losses. In [25-
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26], HPSO has been proposed for network restructure
with DG installation problems. The problem of
system restructure has been framed in [27] as a
nonlinear optimization problem and has been solved
using MBFA. RRA has been developed in [28] for
network restructure problems to lower real loss and
load balance. HS has been given in [29] to obtain the
perfect switching that leads to lower loss. Restructure
of RDS based on GSO has been addressed in [30-31]
to get the minimum losses and voltage profiles. QFA
has been used in [32] to restructure RDS with
different objective functions to improve the
reliability and power quality. MHBMO has been
managed in [33] for network restructure to minimize
the voltage deviation. Restructure of the distribution
network based on ABC has been utilized to get the
optimal switching sequence in [34]. GSA has been
recommended in [35] for restructure of the RDS to
provide optimal performance with keeping the radial
of the network. ALO has been investigated in [36] to
find optimal restructure of the distribution network
for voltage profile enhancement and power loss
minimization. ICA in a fuzzy frame has been
introduced in [37] to handle the network restructure
problem. Reliability indices and power losses have
been included in the objective function. Various
optimization approaches as Jaya optimization,
TLBO, and integrated PSO have been applied in [38]
to optimize the RDS by optimal restructure and DG
installation. FWA has been implemented in [39] to
determine the optimal network restructure
considering the operating constraints. MPGSA has
been proposed in [40] for restructure and DG
installation for small RDS. CSA has been shown in
[41-42] for handling the restructure problem to
reduce real losses and enrich voltage profile. BBO
has been simulated in [43] to achieve minimum
losses and good voltage deviations by restructure of
the distribution system. In [44], the problem has been
formulated as an optimization process and has been
solved using GWOA. However, these algorithms
may not ensure achieving the optimal solution and
may trap in local minimum. In this article, the IWOA
is suggested to handle the problem of restructure in
RDS with an objective function to lessen the total
losses by optimal electing switches combination to
restructure the RDS. Also, the superiority of the
suggested IWOA is proven through statistical
analysis, and variable loading conditions.
Furthermore, the IWOA is not been wasted.
2. Problem Formulation
Line losses mitigation during operation is the used
objective function for restructure of RDS and it could
be written as:
b
N
1m m
R
2
m
I
Loss
P
(1)
Where
m
: The branch number,
b
N
: The total number of branches,
m
I
: The current at branch
m
,
m
R
: The resistance at branch
m
,
Loss
P
: The total active losses in kW,
The annual cost due to power losses can be given
from equation (2):
Loss
PT**
P
Kcost Annual
(2)
Where
P
K
: The cost per kW-Hours and equals to
0.06 $/kW-Hours,
T
: The time in Hours and equals to
8760,
There are various constraints that should be respected
during operation. These constraints are as:
Load flow constraints
The load flow constraints are calculated by equations
(3, 4):
N
qPd(q)
Loss
P
Swing
P
1
(3)
b
N
m
N
qqQd
m
X
m
I
Swing
Q
1 1 )(
2
(4)
Where
qPd )(
: The demand of active power at bus
q
,
qQd )(
: The demand of reactive power at bus
q
,
Swing
P
: The active power of swing bus,
Swing
Q
: The reactive power of swing bus,
m
X
: The reactance at branch
m
,
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• Radially constraint
It means that no closed loops are incorporated
through the network, and thence the number of
branches can be stated by equation (5):
N
b
N1
(5)
where
N
: The number of total buses,
• Feasibility constraint
It assures that no loads are isolated during restructure
tasks.
• Voltage constraint
At each bus, the magnitude of voltage should be
controlled by equation (6), and is picked as 0.90, and
1.0 p.u respectively.
V
i
VV maxmin
(6)
Where
VV max
,
min
: The lower and upper voltages at
bus
i
,
• Current constraint
Equation (7) sets the magnitude of branch current.
max
I<I jj
(7)
Where
maxj
I
: The maximum allowed current in
each branch,
3. Whale Optimization Algorithm
Humpback whales are brilliant mammals. Their
hunting behaviour has three steps: encircling prey,
spiral bubble-net feeding technique, and search for
prey. These steps are addressed as following [45-48]:
Encircling Prey:
Humpback whales detect the prey location as an
initial position
and encircle them. Since the
optimal site is not realized, the WOA assumes that
the current selected solution is the optimum. After the
best search factor is recognized, the other search
factors will upgrade their positions according to
equations (8, 9) [49-50].
(8)
(9)
Where
should be upgraded in each iteration.
and
are meant as equations (10,11) [51]:
(10)
(11)
Where
: The current generation,
: The best elected solution so far,
: Linearly decreased from 2 to 0,
: Random vector in scale [0, 1],
Spiral Bubble-net feeding technique
There are two techniques:
a) Shrinking encircling technique
It's acquired by lowering the scale of . So the new
position of search factors will be the area between the
original position of the factor and the position of the
current best factor [52-53].
b) Spiral updating position
A spiral equation between the whale position and
prey position simulating the helix-shaped path of
humpback whales as in equation (12):
(12)
where
is the distance between
ith selected solution and the best one in the current
iteration.
The humpback whales swim around the prey with
probability (p) of 50% to select between either the
shrinking encircling technique and spiral model to
modernize their positions which qualified by the
following equation [54-55]:
(13)
Where
p
: Random number between 0 and 1.
: Random number between -1 and 1.
: Parameter define the shape of the
logarithmic spiral.
Search for prey
In searching for prey instead of using
a
randomly candidate solution
is picked
out by forcing search factors to shift from the
reference whale via electing
contrary to
exploitation phase, exploration phase permits WOA
to request a global search using equations (14,15)
[55-56].
(14)
(15)
Where
is a random position vector from the
current population.
4. Differential Evolution
DE was mentioned by Price and Storn in 1995 [57]
where mutation, crossover and selection were treated.
The fittest offspring takes the place of its parents.
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Mutation
A newly mutant solution vector will be created
based on three random solution vectors (Xr1, Xr2
and Xr3) and mutation factor (F [0-1]) according
to the following equation:
(16)
Crossover
A newly produced solution vector Uij from
crossover between Vi and Xi based on crossover
mutation (CR) and a random value (jrand [1,2,…,
problem dimension (dim)] according to the
following equation:
(17)
Where
: Random number between 0 and 1,
Selection
It's a selection of the fittest solution from original
solution Xi and Ui according to the following
equation:
(18)
To perfect the exploration ability of WOA, mutation
of DE is incorporated into WOA and another
parameter called search mode is used to
automatically change between exploration and
exploitation phase which yields Improved WOA
(IWOA).
Improved WOA
IWOA is a hybrid operator that merges encircling
prey, search for prey, spiral updating position and
mutation. The two main parts of IWOA are the
exploration and exploitation part. When
the exploration part changes the individuals. is
controlled by equation (19) to a small value from 1 to
0.
(19)
Where
: The greatest number of generations,
In IWOA exploration part, a hyper mutation of DE
and search for pray of the WOA while the
exploitation part is similar to WOA [58]. For the next
generation, the new position for ith individual is the
fittest one among both parents and offspring :
(
( (20)
Where
: The lower and upper bounds of
respectively,
The flowchart of IWOA is described in Fig. (1).
S
t
Initialize the WOA,
population, max iteration
Obtain initial best search factor by
calculating the fitness of each factor
Update a,A,C,Ɩ and p
Update
whale
position
via eq.(13)
Select Xrand and
update whale
position
via eq.(15)
if p ˂ 5
if│A│˂ 1
Update
whale
position
via eq.(9)
if k ˂ max
iteration
Y
e
N
o
Y
e
N
o
K=k+1
N
o
Y
e
Mutation
Selection
Crossover
Obtain the optimal solution
S
Figure (1) Flowchart of the proposed algorithm.
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5. Results and Discussion
To prove the notability of the suggested IWOA, the
results of two RDS are addressed below.
5.1 33-Bus distribution system
The 33 bus system [59] that contains thirty seven
branches, thirty two normally closed switches and
five normally open switches are given in Fig. 2. The
premier ties are numbered from thirty three to thirty
seven. By closing the premier five ties, five loops are
established.
The effectiveness of the IWOA to recognize the best
opened switches compared with those shown in [6,
15, 16, 17, 29, 31, 33, 42, 60-64] is demonstrated
here. Switches S4, S14, S15, S22, and S33 are elected
as an optimal solution by IWOA. Fig. 3, gives the
system after restructure. The total active losses are
diminished from 202.66 kW to 102.55 kW with
active power saving of 100.11 kW. The percentage of
minimization in ohmic losses is developed to 49.4%.
Also, the total cost is reduced to 53900.2 $ which is
the shortest one as obtained in Table 1. The net saving
is upgraded to 52617.9 $ that is the greatest one
compared with others. Moreover, the smallest
voltage is increased to 0.9191 p.u. The improvement
of voltage profile is seen in Fig. 4 due to the
suggested restructure. Furthermore, the losses, net
saving, and total cost using restructure techniques are
better than those utilizing the installation of DG or
shunt capacitors [65-66] as addressed in Table 2.
Finally, the statistical analysis of the suggested
IWOA is given in Table 3 to ensure its superiority
compared with [23, 67, 68, and 69] in terms of the
minimum, mean, standard deviations, number of
iterations, and computational time.
Table (1) Results for the first system using restructure.
Paper
Opened
Switches
active
losses
(kW)
%
Reduction
Cost ($)
Saving
($)
Base case
33,34,35,36,37
202.66
-
106518.1
------
[60]
7,10,14, 32, 37
141.54
30.16
74393.424
32124.67
[15]AGA
7, 9, 14, 32, 37
139.55
31.15
73347.48
33170.62
[16]EGA
[17]IGA
[61]HA
[62]RGA
[63]ACA
[42]CSA
[64]SPSO, BPSO
7, 9, 14, 32, 37
138.92
31.45
73016.35
33501.75
[31]GSO
7, 9, 14, 28, 32
139.26
31.28
73195.056
33323.04
[6]FEP
7, 9, 14, 28, 32
139.83
31
73494.65
33023.45
[29]ITS
7, 9, 14, 36, 37
145.11
28.4
76269.82
30248.28
[29]HSA
7, 10, 14, 36, 37
146.39
27.77
76942.58
29575.52
[33]MHBMO
7, 9, 14, 28, 32
134.26
33.75
70567
35951.1
Suggested
method
4, 14, 15, 22, 33
102.55
49.4
53900.2
52617.9
Figure (3) 33 bus system after restructure.
Figure (2) 33 bus system before restructure.
Figure (4) Impact of reconfiguration on
voltage profiles for the first system.
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Table (2) Comparison between different methods for
first the system.
Paper
Method
Description
Losses
(kW)
%
Reduction
Cost ($)
Base case
None
33,34,35,36,37
202.66
-
106518.1
[65]FPA
Capacitor
placement
Bus 6 with 250 Kvar
Bus 9 with 400 Kvar
Bus 30 with 950 Kvar
134.47
33.65
70677.43
[66]ALO
DG
One PV system
103.053
49.14
54164.66
Suggested
Restructure
4,14,15,22,33
102.55
49.4
53900.2
Table (3) Statistical analysis for the first system.
Paper
Mean
kW
SD
kW
Min loss
kW
Iteration
number
Computational
time (sec)
[23]
-
-
139.5
-
-
[67]
157.5
68.87
139.55
16
100.225
[68]
170.9
71.94
139.9818
17
106.489
[69]
156
68.52
138.6275
5
31.32
Suggested
112.1
63.13
102.55
5
29.97
5.2 69-Bus distribution system
Fig. 5 gives the 69 bus system [70] that comprises
seventy three branches, sixty eight normally closed
switches. The premier ties are numbered from sixty
nine to seventy three. Five loops are arranged by
closing the premier five ties.
The seniority of the IWOA to adjust the optimal
opened switches compared with those cleared in [16,
17, 24, 25, 36, 39, 41, 60, 63, 64, and 71] is ensured
here. Switches S14, S58, S61, S69, and S70 are
selected by IWOA as the best solution. Fig. 6,
presents the system after restructure. The total ohmic
power losses are diminished from 224.95 kW to
98.5952 kW with active power saving of 126.3548
kW. The percentage of minimization in ohmic losses
is 56.17%. Moreover, the value of total cost is
51821.63 $ that is the youngest one as explained in
Table 4. The net saving with the suggested IWOA is
reduced to 66412.1 $ which is the maximum one
compared with others, and the minimum voltage is
upgraded to 0.9495 p.u. The improvement of voltage
profile is shown in Fig. 7 due to the suggested
restructure. Also, the losses, cost, and net saving
using restructure technique are better than the
installation of shunt capacitors [65, 72-74] as seen in
Table 5. Furthermore, the statistical analysis of the
suggested IWOA is shown in Table 6 to confirm its
effectiveness compared with [67, 68, 69, and 75] in
terms of the minimum, mean, standard deviations,
number of iterations, and computation time. Finally,
Table 7 displays the comparison between the
restructured systems, and compensated one for
various loadings in terms of cost, and saving.
Table (4) Results for second system using restructure.
Paper
Opened
Switches
Power
losses
(kW)
%
reduction
Cost ($)
Saving
Base case
69,70,71,72,73
224.95
-
118233.72
--------
[60]
11,14,21,56,62
106.67
52.58
56065.75
62167.97
[71]HA
14,56,62,70,71
99.71
55.67
52407.57
65826.15
[63]ACA
14,55,61,69,70
99.519
55.76
52307.18
65926.54
[39]FWA
14,56,61,69,70
126.36
43.83
66414.82
51818.9
[64]BPSO
13,20,55,61,69
107.05
52.41
56265.48
61968.24
[64]SPSO
14,56,61,69,70
100.6
55.28
52875.36
65358.36
[41]CSA
14,57,61,69,70
126.38
43.82
66425.33
51808.39
[16]EGA
14,59,62,70,71
99.62
55.71
52360.27
65873.45
[25]
MCPSO
12,18,58,61,69
103.62
53.93
54462.67
63771.05
[36]ALO
19,58,64,69,70
125.1
44.38
65752.56
52481.16
[24]MPSO
14,55,61,69,70
100.6
55.28
52875.36
65358.36
[17]IGA
10,14,58,63,70
104.91
53.36
55140.69
63093.03
Suggested
14,58,61,69,70
98.5952
56.17
51821.63
66412.1
Figure (6) 69 bus system after restructure.
Figure (5) 69 bus system before restructure.
Figure (7) Impact of reconfiguration on
voltage profiles for second system.
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Table (6) Statistical analysis for second system.
Approach
Mean
kW
SD
kW
Min.
loss kW
Iteration
number
Computational
time (sec)
[75]
-
-
99.59
-
-
[67]
158.3
178.2
98.6174
16
79.1242
[68]
231.3
245.9
99.5997
12
59.3442
[69]
171.5
168.1
98.6
11
54.3979
Suggested
169.4
164.2
98.5952
9
47.8473
Table (7) Effect of different loading on second system.
Load
ing
Uncompensated
Compensated
[73]
Restructure
100
%
Min voltage
0.9092
0.937
0.9495
Total losses
224.95
145.3236
98.5952
Cost
118233.72
76382.1
51821.6
Saving
---
41851.6
66412.1
75%
Min voltage
0.9343
0.949
0.9826
Total losses
120.8808
82.57
34.5448
Cost
63534.95
43398.79
18156.75
Saving
--
20136.16
45378.2
50%
Min voltage
0.9569
0.9652
0.9884
Total losses
51.5682
35.9451
15.1985
Cost
27104.25
18892.74
7988.33
Saving
--
8211.5
19115.9
6. Conclusions
In this article, IWOA has been successfully
implemented to handle the restructure problem of
RDS. The problem of optimal reconfiguration of
RDS has been formulated as an objective
optimization task to minimize the active losses. The
major contributions of this article can be defined as:
1. IWOA is developed to select the optimal switches
combination subject to the system operating
constraints.
2. The superiority of IWOA is emphasized through
successfully applying on two systems configuration.
3. The ohmic loss with the suggested IWOA is
reduced by 49.4% in the first system, while, and the
loss is diminished by 56.17% in the second system
compared with the original one. Thus, it provides a
notable and promising performance over other
approaches in terms of active power losses, and net
saving.
4. The effectiveness of IWOA for different load
conditions is proved.
5. The validity of IWOA than other new approaches
is verified through statistical analysis, and
computational time, since the number of iterations,
and the computational time with the suggested
IWOA are smaller, and faster than other reported
approaches.
Applications of the network reconfiguration to large
system with the most recent approaches, and
renewable DG are the future scope of this article.
List of abbreviations
DG
Distributed Generation,
RDS
Radial Distribution System,
IWOA
Improved Whale Optimization Approach,
ANNs
Artificial Neural Networks,
FEP
Fuzzy Evolutionary Programming,
FFW
Fuzzy Frame Work,
SA
Simulated Annealing,
TS
Tabu Search,
GA
Genetic Algorithm,
AGA
Adaptive Genetic Algorithm,
EGA
Enhanced Genetic Algorithm,
IGA
Improved Genetic Algorithm,
ACA
Ant Colony Algorithm,
PSO
Particle Swarm Optimization,
MPSO
Modified Particle Swarm Optimization,
HPSO
Hybrid Particle Swarm Optimization,
MBFA
Modified Bacterial Foraging Algorithm,
RRA
Runner Root Algorithm,
HS
Harmony Search,
GSO
Group Search Optimization,
QFA
Quantum Firefly Algorithm,
MHBMA
Modified Honey Bee Mating Algorithm,
ABC
Artificial Bee Colony,
GSA
Gravitational Search Algorithm,
ALO
Ant Lion Optimizer,
ICA
Imperialist Competitive Algorithm,
HA
Heuristic Algorithm,
FWA
Fireworks Algorithm,
MPGS
Modified Plant Growth Simulation,
CSA
Cuckoo Search Algorithm,
BBO
Biogeography Based Optimization,
GWOA
Grey Wolf Optimization Algorithm,
WOA
Whale Optimization Algorithm,
DE
Differential Evolution,
FPA
Flower Pollination Algorithm,
IHA
Improved Harmony Algorithm,
TLBO
Teaching Learning-Based Optimization Algorithm
Table (5) Comparison between various methods for
second system.
Paper
Method
Power
losses (kW)
%
Reduction
Base case
None
224.94
--
[65]FPA
Capacitor
placement
150.28
33.2
[72]FPA
Capacitor
placement
145.777
35.2
[73]IHA
Capacitor
placement
145.3236
35.38
[74]FPA
Capacitor
placement
145.14
35.46
Suggested
Restructure
98.5952
56.17
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DOI: 10.37394/232016.2023.18.15
E. S. Ali, S. M. Abd Elazim
E-ISSN: 2224-350X
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Volume 18, 2023
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WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.15
E. S. Ali, S. M. Abd Elazim
E-ISSN: 2224-350X
148
Volume 18, 2023
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E. S. Ali, S. M. Abd Elazim
E-ISSN: 2224-350X
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E. S. Ali, S. M. Abd Elazim
E-ISSN: 2224-350X
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WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.15
E. S. Ali, S. M. Abd Elazim
E-ISSN: 2224-350X
151
Volume 18, 2023
