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Journal of Engineering Science and Technology Vol. 14, No. 1 (2019) 087 - 107 © School of Engineering, Taylor’s University

87

OPTIMAL CONDUCTOR SELECTION IN RADIAL DISTRIBUTION SYSTEMS USING WHALE OPTIMIZATION ALGORITHM

SHERIF M. ISMAEL1, SHADY H. E. ABDEL ALEEM2,*, ALMOATAZ Y. ABDELAZIZ3

1Engineering for the Petroleum and Process Industries (Enppi), Cairo, Egypt 215th of May Higher Institute of Engineering, Mathematical and Physical Sciences,

Helwan, Cairo, Egypt 3Faculty of Engineering and Technology, Future University in Egypt, Cairo, Egypt

*Corresponding Author: [email protected]

Abstract

Nowadays, electrical power system networks are driven harder, and they are

required to deliver more energy. Electrical losses reduction is one of the most

important ways to conserve the generated energy, especially in the distribution

systems. In this regard, the optimal conductor selection can reduce the electrical

power losses, while enhancing the voltage profile in a cost-effective manner. In

this paper, a novel approach based on a recent meta-heuristic algorithm, known

as whale optimization (WO) algorithm is proposed to solve the optimal conductor

selection problem of radial distribution networks. An updated practical

conductor’s library is introduced. Further, practical techno-economic aspects are

considered such as load growth considerations and payback period calculations.

The objective function is to minimize the combined cost of energy loss and

conductors’ investment cost. The considered constraints are the bus voltage limits

and the conductors’ current carrying capacities. The proposed approach is applied

to two different systems; the first one is a 16-bus small-scale system and the

second is a large-scale 85-bus system. The obtained results are compared with

other results available in the literature, and showed the effectiveness of the

proposed algorithm in reducing the network losses, maximizing the overall

saving, while maintaining the specified constraints over almost a five-year period

while taking into account high annual load growth rate.

Keywords: Optimal conductor selection; Whale optimization algorithm; Radial

distribution networks.

88 S. M. Ismael et al.

Journal of Engineering Science and Technology February 2019, Vol. 14(1)

1. Introduction

Due to the gap between the increasing electrical demand and the limited power

generation resources, researchers focused on conserving the electric energy in line with

increasing the generated power to cater for this continuous growth in electrical

demands. Power loss reduction is considered as one of the most important ways of

conserving the generated energy. The significant power losses in the overall power

system networks are concentrated in the distribution systems because they are usually

characterized by their reduced voltage levels, high lines’ currents, and low lines’

resistances [1, 2]. Researchers have explored many methodologies for power losses

reduction in distribution networks such as shunt capacitors placement, network

reconfiguration, distributed generation (DG) allocation, and optimal conductor

selection. Optimal selection of the conductor sizes of a distribution network is a

complicated problem as it should take into account many constraints such as the

specified voltage limits for the different buses, current carrying capacity of the feeders,

loading profile alteration, and load growth, as well as other economic considerations

that concern with cost of losses and conductors, and interest and depreciation rates.

In the literature, the idea of selecting the optimal conductor sizes had been

tackled years ago [1-4]. Funkhouser and Huber [1], in 1955, introduced the idea of

the selection of the Aluminium Conductor Steel Reinforced (ACSR) sizes based on

economic considerations. Ponnavaikko and Rao [2] presented a mathematical

method for the selection of the optimal set of conductors considering a non-uniform

distribution of loads, the maximum permissible voltage drop, and load growth in

future years. Tram and Wall [3] completed the work of [2] by introducing a

computerized methodology for the selection of optimal conductor sizes. Ranjan et

al. [4] proposed an optimization algorithm for the optimal conductor sizes selection

using evolutionary programming (EP).

One can see that the methodologies presented in the literature for solving the

optimal conductor selection problem can be categorized into two main approaches;

the first one is based on conventional analytical algorithms [5-14] and the second

is based on new intelligent meta-heuristic algorithms [15-20].

The analytical approaches have been utilized effectively in the optimal

conductor selection. Islam and Ghani [5] proposed an analytical algorithm for

optimal selection of conductors in radial distribution networks. Wang et al. [6]

introduced a practical procedure for optimal conductor selection considering the

non-uniform loading. Sivanagaraju et al. [7] proposed an analytical algorithm based

on radial network load flow to select the optimal conductor size in order to

maximize saving in energy loss and conductor investment costs. Mandal and Pahwa

[8] presented a method for selection of the optimal set of conductors considering

both technical and economic constraints. Falaghi et al. [9] introduced an analytical

algorithm for optimal selection of conductors in radial distribution networks

considering many factors such as the capital cost of conductors, cost of energy

losses, bus voltage profile, current carrying capacity of conductors, and load growth

within a specific period. Satyanarayana et al. [10] presented a model for improving

the maximum allowable loading of radial distribution feeders for different types of

load models based on the optimal selection of the conductors and incorporating

load growth profile. Kaur and Sharma [11] developed a generalized model for

optimal conductor size selection considering the non-uniform loading pattern, load

growth, load factor and diversity in load peaks. Raju et al. [12] proposed an

Optimal Conductor Selection in Radial Distribution Systems using Whale . . . . 89


analytical method for conductor selection based on the cost of energy losses and

the interest and depreciation rates on the investment. Abul’Wafa [13] presented a

generalized model for optimal conductor size selection based on branch wise

minimization (BWM) technique. Franco et al. [14] developed an optimization

algorithm based on a mixed-integer linear programming (MILP) model for optimal

conductor selection in radial distribution systems.

Mendoza et al. [15], on the other side, the intelligent optimization techniques

have inspired many researchers to employ it for solving the optimal conductor

selection problem, such as evolutionary strategy (ES), discrete particle swarm

optimization (DPSO) [16], genetic (GA) [17], harmony search (HS) with a

differential operator [18], analytic and GA [19], Grasshopper Optimization

algorithm (GOA) [20], Crow search algorithm (CSA) [21] and sine-cosine

optimization algorithm (SCA) [22]. The practical selection of the optimal

conductors set should consider present loads in addition to the expected load growth

for a certain time span [23-25].

Optimal conductor selection can allow additional penetration of DGs into

distribution networks. Nowadays, the maximum amount of DG units that can be

integrated into the distribution system, without violating the system operational

performance limits, is called the hosting capacity (HC). One of the approaches used

by network operators to face the challenges of continuous load growth and high

DG penetrations is to reinforce the network. It is believed that network

reinforcement and optimal conductor selection are considered as effective

techniques for HC enhancement that will play a significant role in future power

systems and smart grids [26, 27].

The WO algorithm is proposed in this work due to the intelligent behaviour of

crows in storing their excess food, hiding their food place from others, and bringing

their food back when they need [28]. The WO algorithm has multiple advantages

such as having few parameters to be set, faster convergence capability and higher

sensitivity when compared to the widely known meta-heuristic algorithms. Due to

these advantages, it has been recently employed to solve many engineering

problems in the literature [29, 30].

In this paper, a novel approach based on a recent meta-heuristic algorithm, whale

optimization (WO) algorithm [28] is proposed to solve the optimal conductor selection

problem of radial distribution networks. From the literature survey, it is clear that

application of WO has not been discussed so far to solve the optimal conductor selection

problem in radial distribution systems. This encourages utilizing this algorithm for the

problem. A practical conductor’s library containing twenty conductor types is

introduced based on actual manufacturer data that comply with the BS 50182 [31]. This

rich library explores a wider search space and ensures finding the most optimal set of

conductors that satisfy the economic objective functions while complying with the pre-

set constraints. A constrained objective function is employed to minimize overall cost,

and comply with the system voltage limits and the conductors’ current carrying

capacities. Practical aspects are considered such as available market conductors

utilization, load growth considerations, and payback period calculations. The proposed

WO algorithm is applied on two different test systems, 16-bus system, and 85-bus

system. The achieved results are compared with other methods available in the literature

and showed the effectiveness of the proposed algorithm in reducing the network losses,



maximizing the overall saving, while maintaining the specified constraints over a five-

year period taking into account high annual load growth rate.

2. Problem formulation

2.1. Objective function

In optimal conductor selection problem, the goal is to select conductor size and type

from a set of available inventory such that the total cost is minimized while

satisfying nonlinear constraints on voltage limits of the buses and maximum

ampacities of the conductors. The cost consists of the annual cost of energy losses

and the capital investment cost of the conductor which is formulated as follows:

(1) , , , Cost j c CL j c CC j c

(2), , loss p eCL j c P j c k k LSF T

The loss factor which is defined as the ratio of energy loss in the system during

a given time period to the energy loss that could result if the system peak loss had

persisted throughout that period. LSF is expressed in terms of the load factor, the

average load to the peak demand in a given time period, as follows [16, 18]:

2

0.2 0 (3).8 LSF LF LF

Thus, the total annual cost of the energy loss can be expressed as follows:

( , 4)

b ntotal

loss p e

j c

CL P j c k k LSF T

The capital investment cost of the conductor is defined in the terms of the annual

depreciation of the capital cost of the jth branch with the cth conductor, thus:

, ( ) 5CC j c IDF l j A c IC c

so that,

( 1)

( (6)

1) 1

F

F

i iIDF

i

The objective function (OF) for the optimal selection of types and sizes of the

conductors can be expressed as:

OF min (7)total totalCL CC

2.2. Constraints

The considered constraints can be expressed, as follows:

Bus voltage constraint

, ) 8, ( min maxU m U m c U m m k c n

where Umin(m) and Umax(m) are considered as 0.9 p.u. and 1.1 p.u., respectively.

Conductor current carrying capacity constraint

, , 9 ( )maxI j c I c j b c n



2.3. Additional techno-economic considerations

Load growth

Practically, optimal conductor sizes selection should consider the existing loads in

addition to possible load growth for a certain planning period [10]. This period is

usually determined by the feeder ability to accept load growth without violating the

node voltage or the branch's current constraints. During the ‘pre-determined’

planning period, the load growth can be considered as an annual growth rate in

proportion to the connected loads in the base year (1st year). Mathematically, the

active and reactive power loads at the Nth year is given by:

1 for = 1, 2, 3,... (10)

1 for = 1,...

1 for = 1, 2, 3,...

1

1

(11) 1 1 for =

1

1,...

N

L

M

L

N

L

M

L

L

L

P g N M

P g N M F

Q g

P N

Q NN M

Q g N M F

Equations (8) and (9) of the proposed constraints shall be checked initially in

the base year, and then the load growth shall be calculated according to Eqs. (10)

and (11). Further, the loading pattern shall increase gradually till violation of any

of the constraints occurs. In this condition, the breaking year ‘M’ is reached and the

maximum duration that the feeder can handle the load growth without violating the

preset constraints is determined. Beyond the breaking year, the optimally selected

conductors can accept additional load growth until the end of their lifetime, but

with the support of external compensators such as the shunt capacitors, DGs, and

energy storage schemes. Additionally, Fig. 1 shows the load growth pattern during

the conductor’s lifetime. Table 1 gives the numerical values of the parameters used

in the formulation of the objective function and the constraints.

Fig. 1. Load growth pattern during conductor lifetime.

Table 1. Numerical values of the used parameters.

Parameter Value Parameter Value

kp (Rs/kW) 2500 i (%) 8

ke (Rs/ kWh) 0.5 F (years) 25

IC(c) (Rs/mm2/km) 500 IDF 0.1

LF 0.4 g (%) 10

LSF 0.2

Load

PL(N)

PL(1)

N ……

Load growth is possible with alternative solutions

Feeder cannot accept load growth due to

Constraint

violation

breaking

year

M1 year

base

year

planned

lifetime

F

Feeder can accept load growth



Payback period

The optimal selection of distribution system conductors may result in purchasing of larger

conductor sizes which means additional conductors’ cost. This additional cost should be

justified to the planners of the distribution system (decision makers), as follows:

Optimally selected conductors will result in reduced overall network losses,

therefore allows for more rigid load growth plans.

Reducing the network losses will result in enhanced system performance and

will save annual energy consumption

The cumulative annual energy saving will equalize with the additional initial

conductors cost in a certain period known as the payback period. After this

period, the annual energy saving is purely gained by the network operators.

Considering that optimal conductors’ selection led to increasing the original

system conductor size from the base case area say Ax (j,c) to the optimized area Ay

(j,c). Accordingly, the procedure for calculating the payback period can be

presented as follows:

The total cost of the original system conductors can be formulated as follows:

, ( 2) 1

bor g

x

j

iC A j c l j IC c

The total cost of the optimized system conductors can be formulated as follows:

, (13)

j

bOpt

yC A j c l j IC c

The total additional cost due to optimal conductor selection is:

(14)total Opt origC C C

The cost of annual energy saving due to optimal conductor selection for all

network branches is:

(15)( )x x Optbase

as loss elossC P P T K

(16 )

total

as

CPP

C

3. Whale Optimization Algorithm (WO)

Nature-inspired meta-heuristic algorithms have shown surprisingly efficient results to

tackle difficult problems. Mirjalili and Lewis [28] developed n this domain, the WO,

which is a nature-inspired meta-heuristic optimization algorithm based on mimicking

the hunting behaviour of humpback whales. Whales are considered as highly intelligent

animals with emotions. Whales have common cells in their brains similar to those of

human called spindle cells. These cells are responsible for judgment, emotions, and

social behaviours in humans. The hunting technique of the humpback whales is called

bubble-net feeding technique. Humpback whales prefer to hunt small fiishes (preys)

close to the surface. When the humpback whale detects its prey, it dives around 12 m

down and then starts to create bubbles in a spiral shape around the prey. The prey fears

to cross these bubbles that appear as a trap. At that moment, the whale swims up to the

surface and collects his trapped prey as shown in Fig. 2.



(a) Illustrative scheme

for the technique

(b) Real scene of the

hunting process

Fig. 2. Bubble-net hunting technique of the humpback whales.

3.1. Mathematical model

The bubble-net feeding technique of the humpback whales is mathematically

modelled in three stages [28], as briefed below.

i. Encircling the prey

ii. Bubble-net hunting method (exploitation phase)

a. Shrink mechanism

b. Spiral update of the position

iii. Globalization of the search (exploration phase)

3.1.1. Encircling the prey

Humpback whales can recognize the location of prey and encircle them. Since the

position of the optimal design in the search space is not known in advance, the WO

algorithm assumes that the current search agent is the target prey or is close to the

optimum one. After the best search agent is defined, the other search agents will try

to update their positions towards the best search agent which is represented by the

following equations:

. ( ) ( 7)( 1)C X t X tD

( ) . ( 1) (18)X t X t A D

The vectors A and C are calculated as follows:

2 . (19)a r aA

2 . (20)rC

3.1.2. Bubble-net hunting technique

a. Shrink mechanism

This behaviour is achieved by decreasing the value of a in Eq. (19) from 2 to 0.

Accordingly, the value of A is also decreased by a random value in the interval [-



a, a]. Figure 3 shows the possible positions from the random whale's position at (X,

Y) toward the prey position at (X*,Y*) that is applied to (0 ≤ A ≤ 1).

b. Spiral update of the position

In this stage, the attacking mechanism is executed and the distance between the

whale located at (X, Y) and the prey located at (X*,Y*) is calculated. Then, a spiral

equation is created between the position of the whale and prey to mimic the helix-

shaped movement of the whales as shown in Fig. 4 and Eq. (21).

*' . . cos (( 1) (21)2 ) ( )szD e z tX Xt

*' ( ( 2) )( 2)i X t X tD

It is worth mentioning that humpback whales swim around the prey within a

shrinking circle and along a spiral-shaped path simultaneously. To model these

simultaneous movements; a 50% probability is assumed to choose between either

the shrinking or updating the spiral movements to the whales’ position, as follows:

*

' *

. if < 0.5 (23)

. . cos (2 ) ( ) ( 1)

( 1) if 0.5sz

X A D p

D e z

t

X pX tX t

t

Fig. 3. Bubble-net search technique.

Fig. 4. Spiral updating of the position.



3.1.3. Globalization of the search

The position of the search agent is updated according to a randomly chosen search

agent instead of the best search agent found so far. To consider this randomness;

Eqs. (17) and (18) are updated after replacing X* with Xrand, as follows:

. ( ) (2( 4) )randC X t X tD

( )( 1) ( . 25)rand t DX X At

The WO algorithm includes two internal parameters to be adjusted (A and C) depending

on the selection of the vector a . To sum up, the WO procedure is shown in Fig. 5.

Fig. 5. Flowchart for the WO algorithm.



4. Results and Discussion

In this work, twenty conductor types are used. The numerical values of the used

parameters are summarized in Table 1. Ismael et al. [22] and Leppert and Allen

[23] described, that the load flow analysis is based on a forward-sweep algorithm

is performed and the corresponding fitness function is calculated using the WO. In

order to verify the effectiveness of the proposed WO algorithm; two radial

distribution networks are examined in MATLAB platform, the first one is a small-

scale network of 16-bus system, the second one is a large-scale network of 85-bus

system.

4.1. 16-bus system

The 16-bus system configuration is shown in Fig. 6, the base voltage and apparent

power of this system is 11 kV and 100 MVA respectively. The substation bus

voltage (bus 1) is 1 p.u. and the line and load data for this system are obtained from

[4]. Practical conductor’s library is introduced based on actual manufacturer data

[33]. The available conductor types and their electrical specifications are presented

in Table 2. According to Thenepalle [19], the conductors’ library is presented in

Table 3 to be compared with the results obtained using the proposed algorithm.

Other published results for the 16 bus are excluded from the comparison because

of noncompliance with the considered constraints.

Fig. 6. Configuration of 16-bus radial distribution network.

Table 2. Electrical specifications of the used ACSR conductors.

Conductor

type A (mm2) R (Ω/km) X (Ω /km) Imax (A)

1 6.5 2.718 0.374 70

2 13 1.374 0.355 120

3 16 1.098 0.349 130 4 20 0.9116 0.345 150

5 25 0.6795 0.339 175

6 30 0.5449 0.335 200 7 40 0.4565 0.353 250

8 42 0.3977 0.327 270

9 45 0.3841 0.327 257 10 48 0.3656 0.329 260

11 50 0.3434 0.328 270

12 55 0.302 0.327 290 13 65 0.2745 0.315 305

14 80 0.2193 0.282 395

15 80 0.2214 0.268 380 16 80 0.2221 0.271 385

17 95 0.1844 0.266 425

18 110 0.1589 0.261 470 19 130 0.1375 0.256 510

20 140 0.1223 0.252 560



Table 3. Electrical specifications of the used ACSR conductors in [19].

Conductor

type A (mm2) R (Ω/km) X (Ω /km) Imax (A)

A 12.90 1.3760 0.3896 115

B 15.91 1.098 0.3100 138

C 19.55 0.9108 0.3797 150

D 25.87 0.6795 0.2980 180

E 32.26 0.5441 0.3673 208

F 37.32 0.4565 0.2850 226

G 42.07 0.3841 0.2795 250

H 48.39 0.3657 0.3579 270

The used parameters of the proposed WO algorithm are presented in Table 4.

The obtained WO results are compared to those obtained using EP [4] and HSDE

[18] and the comparison is presented in Tables 5 and 6. It is noticed that the

network active power loss optimized by the proposed algorithm is reduced to

26.0841 kW, which is less than other published results; this means the power loss

is reduced by 51.275% compared to the original network loss. The optimal annual

cost obtained by the proposed algorithm is 180,167.364 Rs./year, which will save

about 22.34% of the original network cost with a payback period of 6.76 years.

The bus voltage values of the original network and that optimized using the

proposed algorithm are presented in Fig. 7. Figure 8 shows the current flow in

branches compared to their maximum limits. The response of the WO algorithm

is presented in Fig. 9. The load growth results are presented in Table 7. Voltage

profile and branch current flows of the 16-bus system over a five-year span are

presented in Figs. 10 and 11, respectively. From the presented figures, one can

notice that the proposed optimal conductor selection algorithm succeeded in

minimizing the overall system costs and keeping the bus voltages and branch

currents within the prescribed limits not only for the current load profile but also

for a five-year span with high annual load growth factor of 10%. As shown in

Table 7, the voltage of bus 16 begins to exceed its allowable limit (0.9 p.u.).

Therefore, other compensation techniques should be adopted to allow for more

load growth without violating the system limits.

A sensitivity analysis has been performed for selecting the optimum WO

algorithm parameters, mainly vector ā and n. A case study was examined to

calculate the losses’ cost of the 16-bus system considering various WO parameters

as presented in Table 8. Three independent values were assumed for each of ā and

n. It is assumed that all other parameters are kept constant. It was concluded that

the linear decrement of vector ā from 2 to 0 leads to improved results while other

values give worse results because they de-emphasize exploitation and exploitation

process. In addition, it was noticed that large number of search agents allow for

better reach to the global optimum.

Table 4. Numerical values of the used parameters of the proposed WO algorithm.

Parameter Value

Number of search agents (n) 100

a Linearly decreases from 2 to 0

Maximum number of iterations 500



Table 5. Comparison of conductor selection results for the 16-bus system.

Branch

no.

From

bus

To

bus

EP

[4]

HSDE

[18]

The proposed

WO

1 1 2 Raccoon H 17

2 2 3 Raccoon H 17

3 3 4 Raccoon H 14

4 4 5 Raccoon H 14

5 5 6 Raccoon H 12

6 6 7 Raccoon H 12

7 7 8 Raccoon H 12

8 8 9 Raccoon H 12

9 9 10 Raccoon G 12

10 10 11 Raccoon G 8

11 11 12 Rabbit H 6

12 12 13 Rabbit G 6

13 13 14 Rabbit F 5

14 14 15 Weasel E 3

15 15 16 Squirrel E 1

Table 6. Comparison of final results for the 16-bus system.

Variables Original

system

After optimal conductor selection

EP [4] HSDE [18] The proposed WO

Umin at node 16 0.8867 0.9153 0.9288 0.9300

Power Loss (kW) 53.47 37.36 36.17 26.0841

Loss reduction (%) - 30.14 32.36 51.275

Optimal cost (Rs) 231,990 208,796 200,783 180,167.36

Net saving (%) - 10 13.45 22.34

Payback period (years) - - - 6.76

Fig. 7. Bus voltages of the original and optimized 16-bus network.

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Vo

ltag

e (

pu

)

Bus number

Original network Optimized netwok by WO



Fig. 8. Branch currents compared to their maximum limits.

Fig. 9. The variation of fitness function for the16-bus network.

Table 7. The load growth results obtained for 16-bus system.

Year Total active

power (kW)

Total power

losses (kW)

Umin at bus

16 (p.u.)

1 675.75 26.08 0.9300

2 743.33 31.95 0.9225

3 817.66 39.63 0.9141

4 899.42 48.15 0.9048

5 989.37 59.28 0.8943

Fig. 10. Voltage profile over a five-year span for the 16-bus system.

0

50

100

150

200

250

300

350

400

450

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Cu

rren

t (A

)

Branch no.

Branch current flow Branch current capacity

0.88

0.9

0.92

0.94

0.96

0.98

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Vo

ltag

e (p

u)

Bus number

1st Year 2nd Year 3rd Year 4th Year 5th Year



Fig. 11. Branch currents over a five-year span with 10% load growth factor.

Table 8. Sensitivity analysis for the WO algorithm parameters.

n= 10 n= 40 n= 100

ā = from 1 to 0 208,972.04 195,963.53 188,010.24

ā = from 2 to 0 193,021.91 185,919.58 180,167.36

ā = from 4 to 0 197,029.68 186,964.29 181,332.88

4.2. 85-bus system

The 85-bus system configuration is shown in Fig. 12, the base voltage and apparent

power of this system is 11 kV and 100 MVA respectively. The substation bus voltage

(bus 1) is 1 p.u. and the line and load data for this system are initiated [32] and

developed [18]. The obtained WO results are compared to those obtained using BWM

[13], HSDE [18], and CSA [21] and the comparison is presented in Tables 9 and 10.

It is noticed that the network active power losses optimized by the proposed algorithm

are reduced to 83.55 kW, which is less than other published results; this means the

power loss is reduced by 73.55% compared to the original network loss. The optimal

annual cost obtained by the proposed algorithm is 372,243.95 Rs./year, which will

save about 66.36 % of the original network cost with a payback period of 0.53 years.

The bus voltage values of the original network and that optimized using the proposed

algorithm are presented in Fig. 13. Figure 14 shows the current flow in branches

compared to their maximum limits.

Fig. 12. Configuration of 85-bus radial distribution network.

0

50

100

150

200

250

300

350

400

450

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Cu

rren

t (A

)

Branch no.

1st Year 2nd Year 3rd Year

4th Year 5th Year Branch current capacity

43

40 41 42 44 45 46 47

37 38 39

23

25 26 27 28 29 30 31 32 33 34 35 36

22 21 20 19 18

24

78 85 48

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 49

50 56

51

55 54 53 52

57

16 17 58

24 23

59 55

77 80 81 82

60 61 62

83 84

63 64 65 66 76

67 68 69 70 71

72

79 75 73 74

SS



Fig. 13. Bus voltages of the original and optimized 85-bus network.

Fig. 14. Branch currents compared to their capacities for the 85-bus system.

Voltage profile and branch current flows of the 85-bus system over a five-year

span are presented in Figs. 15 and 16, respectively. From the presented figures, one

can notice that the proposed optimal conductor selection algorithm succeeded in

minimizing the overall system costs and keeping the bus voltages and branch

currents within the prescribed limits not only for the current load profile but also

for a five-year span with high annual load growth factor of 10%. After the 5th year,

the voltage of bus 54 begins to reach its minimum allowable limit (0.9 p.u.).

Therefore, other compensation techniques should be adopted to allow for more load

growth without violating the system limits.

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85

Vo

lta

ge (

pu

)

Bus number

Original network Optimized network via WO

0

100

200

300

400

500

600

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82

Cu

rren

t (A

)

Branch no.

Branch current flow Branch current capacity



Table 9. Comparison of conductor selection results for the 85-bus system.

Bra

nch

no

.

From

bu

s

To b

us

BW

M

[13

]

HS

DE

[18

]

CS

A [

21

]

Pro

po

sed

WO

Bra

nch

no

.

From

bu

s

To b

us

BW

M

[13

]

HS

DE

[18

]

CS

A [

21

]

Pro

po

sed

WO

1 1 2 F H F 20 43 34 44 B H C 3

2 2 3 F H D 20 44 44 45 B D B 2

3 3 4 F H A 20 45 45 46 B G A 1 4 4 5 F H F 20 46 46 47 B D C 1

5 5 6 F H B 20 47 35 48 B E G 8

6 6 7 E H A 20 48 48 49 B A E 3 7 7 8 E H A 20 49 49 50 B D C 2

8 8 9 E H D 20 50 50 51 B D C 1

9 9 10 E G D 12 51 48 52 B D H 5 10 10 11 B H G 8 52 52 53 B B C 3

11 11 12 B E B 8 53 53 54 B A A 2

12 12 13 B C H 3 54 52 55 B G A 1 13 13 14 B A H 2 55 49 56 B D C 1

14 14 15 B A F 1 56 9 57 B H B 18

15 2 16 B H C 1 57 57 58 B H F 17 16 3 17 B G B 3 58 58 59 B A B 1

17 5 18 B E E 8 59 58 60 B E B 17

18 18 19 B F H 6 60 60 61 B D A 3 19 19 20 B A H 3 61 61 62 B E A 1

20 20 21 B B B 2 62 60 63 B H D 12

21 21 22 B A G 1 63 63 64 B G H 12 22 19 23 B C H 1 64 64 65 B H G 1

23 7 24 B C A 1 65 65 66 B A H 1

24 8 25 B G G 20 66 64 67 B G A 12 25 25 26 B H C 20 67 67 68 B D D 6

26 26 27 B G D 18 68 68 69 B E C 5

27 27 28 B H C 18 69 69 70 B E D 2 28 28 29 B H A 17 70 70 71 B A F 1

29 29 30 B G G 17 71 67 72 B H B 1

30 30 31 B H A 14 72 68 73 B B E 2 31 31 32 B H C 14 73 73 74 B H H 1

32 32 33 B E B 12 74 73 75 B A E 1

33 33 34 B H A 12 75 70 76 B C F 2 34 34 35 B F E 8 76 65 77 B A C 1

35 35 36 B H E 1 77 10 78 B C H 1

36 26 37 B A A 1 78 67 79 B A G 1 37 27 38 B C A 1 79 12 80 B D E 5

38 29 39 B G E 1 80 80 81 B B E 3 39 32 40 B B A 3 81 81 82 B G G 1

40 40 41 B B B 2 82 81 83 B C H 1

41 41 42 B F B 1 83 83 84 B F A 1 42 41 43 B B D 1 84 13 85 B A C 1

Table 10. Comparison of final results for the 85-bus system.

Variables Original

system

After optimal conductor selection

BWM [13] HSDE [18] CSA [21] Proposed

WO

Umin at node 54 0.8713 0.9458 0.9296 0.8900 0.9436

Power Loss (kW) 315.84 134.26 256.96 254.152 83.55

Loss reduction (%) - 57.51 18.64 19.53 73.55

Optimal cost (Rs) 1,106,732 485,040 929,035 927,786 372,243

Net saving (%) - 56.17 16.06 16.17 66.36

Payback period (years) - - - - 0.53



Fig. 15. Voltage profile over a five-year span for the 85-bus system.

Fig. 16. Branch currents over a five-year span for the 85-bus system.

5. Conclusions

In this work, the WO algorithm is proposed to solve the problem of optimal selection

of conductors of radial distribution networks. The WO algorithm is applied on two

different test systems, 16-bus system, and 85-bus system. The achieved results are

compared with other methods available in the literature and showed the superiority

of the proposed algorithm over the other published methods. One can notice that the

proposed set of conductors explored a wider search space that succeeded in finding

the most optimal set of conductors that satisfy the objective functions while

complying with the pre-set constraints. Finally, the proposed WO algorithm

succeeded reducing the network losses, maximizing the overall saving while

maintaining compliance with the specified constraints over five years with a

reasonable payback period, while taking into account high annual load growth rate.

Following highlights are observed through simulation case studies:

0.88

0.9

0.92

0.94

0.96

0.98

1

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85

Volt

age (

Pu

)

Bus number

1st year 2nd year 3rd year 4th year 5th year 6th year

0

100

200

300

400

500

600

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83

Cu

rre

nt

(A)

Branch number

1st Year 2nd Year 3rd Year 4th Year 5th Year Branch capacity



The introduction of the proposed actual conductors library provided optimal

techno-economic results for the problem of conductors selection in radial

distribution networks.

The optimal conductor selection is considered as one of the important tools for

reducing the network losses in a cost effective manner.

The WO algorithm proved its efficiency and suitability for solving small scale

and large scale system applications.

Load growth considerations and payback period calculations are important

techno-economic aspects for the distribution system planners.

Finally, our study was limited to the constant loading profile in balanced and

sinusoidal electrical systems. Another factor that was beyond the framework of this

study, but will be included in future studies, is the consideration of a real-time

loading profile in unbalanced and non-sinusoidal distribution networks.

Nomenclatures

CA

, Coefficient vectors

A(c) Cross section area of the cth type conductor

a

Linearly decreasing factor to represent the shrinking bubbles

b Total number of branches in the system

Cas Cost of annual energy saving due to optimal conductor selection

CC Capital investment cost of the conductor

CCtotal Total capital investment cost of all branches

CL Annual cost of energy losses

CLtotal Annual cost of the energy loss OptC Total cost of the optimized system conductors origC Total cost of the original system conductors

c Branch type

iD distance between the ith whale to the prey

F Planned lifetime of the feeder

g Annual load growth rate

IC(c) Investment cost of the cth type conductor per unit area per unit

length

IDF Interest and depreciation factor

I(j,c) Current flowing in conductor j of type c

Imax(c) Maximum current carrying capacity of the cth type conductor

i Interest rate value

j Branch number

k Total number of buses in the system

kp Cost of peak demand power loss

ke Cost of energy losses

LSF Loss factor

LF Load factor

l(j) Length of branch j

M Breaking year

m Bus number



n Number of the available conductors’ types

OF Objective function

PL(1) Active load power in the 1st year

PL(N) Active load power in the Nth year

Ploss (j,c) Active power loss of the jth branch with a cth conductor under

peak load base

lossP Network losses of the original network

OptlossP Network losses of the optimized network

PP Payback period

p Random number in [0, 1]

QL(1) Reactive load power in the 1st year

QL(N) Reactive load power in the Nth year

r

Random vector in [0, 1].

s Constant for defining the shape of the logarithmic spiral

T Number of hours per year (8760 hour)

t Index for the current iteration

Umax (m) Maximum voltage at bus m

Umin(m) Minimum voltage at bus m

X Random position vector

X* Position vector of the best solution obtained so far

randX

Random position vector (a random whale)

z Random number in [−1, 1]

totalC Total additional cost due to optimal conductor selection

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