# Minimum Cost Analysis in Radial Distribution System Planning Using Genetic Algorithm

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Minimum Cost Analysis in Radial Distribution System Planning Using Genetic Algorithm
```International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.3, pp. 1792-1802
ISSN 2078-2365
http://www.ieejournal.com/
Distribution System Planning Using Genetic
Algorithm
A. El-zein and E. Safie El-din
Elec. Power & Machines Dept. Zagazig University- Egypt
[email protected]
Abstract— This paper introduces a new feeder branching
technique using Genetic Algorithm (GA) to obtain the best
location of distribution substation and the optimal feeder
routing. This technique aims at achieving minimum cost and
voltage drop constraint. To confirm the ability of this
technique to find the optimal solution of the general planning
problem, the proposed algorithm is applied on two cases: The
first case is 25 load points dispersed in a region of 30×20 km2
have to be fed by a 20kv substation and the second case is 104
load points dispersed in a region of 18×15 km2 have to be fed
by a 11kv substation. the location and the apparent power of
Index Terms— radial system, distribution planning,
geographic information systems (GIS), feeder routing,
substation location, Genetic Algorithm.
I INTRODUCTION
be over 200 MVA [7]. However, in agriculture project it is
a planning for single type of consumers who has a
consistent developing policy with less uncertain data[8].
In this paper, GA is used to solve a type of general
planning problem to obtain the best location of distribution
substation, the optimal routing of radial feeders and the
best cross section area CSA of these feeders while
satisfying minimum cost and voltage drop limit.
II PRINCIPLES OF THE METHOD
Steps of feeder branching technique are:
If a load point is placed at (x 0 ,y0) and the location of the
distribution substation is chosen at (xs,ys) .So, the new
coordination of the loads (xn,yn) is:
x
Electric power distribution system is the portion of the
power delivery infrastructure that takes the electricity from
the highly meshed, high voltage transmission circuits and
delivers it to customers. At a distribution substation, a
substation transformer takes the incoming transmission
level voltage and steps it down to several distribution
primary circuits, which spread out from the substation.
Different mathematical techniques have been developed
over the past decades to solve the distribution planning
optimization problem such as a Simulated Annealing
technique [1] genetic algorithm [2]. or incorporating the
genetic algorithm and least squares support vector
machine [3], Component Geographical Information
Systems (ComGIS) network analysis and Multi-objective
Genetic Algorithm (MOGA) as presented in [4], Highly
Distributed Power Systems (HDPS) as illustrated in [5].
Geospatial Technique as used in [6] which depends on
Geographic Information System and Also, the distribution
planning design is different according to the type of
interested area. A small rural substation may have a
nominal rating of 5 MVA while an urban substation may
n
x
0
x
s
y n  y 0  ys
(1)
(2)
2- Selection of the scanning angle:
The spatial load region area is divided into a number of
equal sectors with angle θ, each sector has one main
feeder. The number of main feeders in each quadrant is
(nf)
θ 
90
(3)
nf
3- main and lateral feeders routing
Each sector contains a number of villages and has one
main feeder and a number of lateral feeders equal the
number of villages. To determine villages belong to each
sector, the angle of each village (θ k) are first calculated by
Equation (4)
θ k  tan
1 y k
(4)
xk
The angle θk may be in the first, second, third or fourth
quadrant according to the sign of the coordinates xk and yk.
1792
El-zein and
El-din
Minimum Cost Analysis In Radial Distribution System Planning Using Genetic Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.3, pp. 1792-1802
ISSN 2078-2365
http://www.ieejournal.com/
The angles of villages in sector no: j with angle θ must
satisfy equation (5)
(j - 1)  θ  θ k  j  θ
(5)
The equation of the straight line representing the main
feeder is:
y  mx
(6)
The slope of the main feeder is determined by least square
error method to minimize the length of the lateral feeders
n
 x k yk
k 1
m
n 2
 xk
k 1
(7)
Where:
n: No of villages in this sector.
All lateral feeders are perpendicular to the main one and
each one reaches one village.
4- source and bridge feeders routing
The number of source feeders are half the number of main
feeders. Each two main feeders are fed by one source
feeder which is fed directly from the substation and ends
at the middle of the bridge feeder. So, the number of
bridge feeders equals the number of source feeder as
shown in figure 1. This figure is a sample of feeders
routing design which contains one source feeder, one
bridge feeder, two main feeders and numbers of lateral
feeders.bo1 is the point of intersection between the first
main feeder and the lateral feeder of the nearest village to
the substation
figure 1:design sample
bo2 is the point of intersection between the second main
feeder and the lateral feeder of the nearest village to the
substation
In order to know which village is the nearest one to the
substation, the planner has to calculate the distance (L) for
each village k using equation (8):(10)
Lk 
2
2
x k  y k cos(θ kp  θ mp )
θ kp  θ k
θ mp  tan
(8)
(9)
1
m
(10)
Where:
Lk :The distance between the substation and the
orthogonal projection of village k.
So, the nearest village to the substation is the village that
has the shortest length (L).
Points b1 & b2 are located after a distance (dis) as shown
in figure 1. The bridge feeder extends from point b1 to
point b2 and the source feeder extends from the substation
to the center of the bridge feeder.
5- Determination of feeder cross section area (CSA)
First, the CSA of source feeder is chosen to make the
voltage drop at the end of the source feeder within the
limit (1%). Then, the CSA of the main feeder is selected to
make the voltage drop at the end of it within the limit
(4%). The half of the bridge feeder which is near the first
main feeder has the same CSA as the first main feeder.
Similarly, The half of the bridge feeder which is near the
second main feeder has the same CSA as the second main
feeder. Finally, the CSA of the lateral feeder is chosen to
make the voltage drop at village within the limit (8%).
Practically, there is a list of feeder CSA's considered for
overhead transmission lines in distribution system; in this
thesis the following feeders of Aluminum Conductor Steel
Reinforced (ACSR) has been used: 35/6, 70/12, 95/15,
120/2 and 150/25mm2.The smallest CSA (35/6) has been
chosen to calculate the voltage drop corresponding to this
CSA. If the voltage drop is out of limit, the next CSA
(70/12) has been taken and so on until the voltage drop is
within the limit. This CSA is to be selected. The voltage
drop at the end of the source feeder is calculated using
equation (11)
(11)
vd s  ds  I 2s  k s
Where:
ds: the length of the source feeder. i.e., the distance
between the midpoint of the bridge feeder and the origin.
This distance can be calculated using equations(12)
I2s:summation for all currents of villages in the two sectors
that are fed by this source feeder
ks: Voltage drop constant. It is a constant value for each
cross section area at specified power factor and can be
calculated using equation (17).
ds 
2
2
x mid  y mid
(12)
Where:
xmid & ymid : The Coordinates of the midpoint of the
bridge feeder and are obtained by solving the equation
(13) and equation (14).
1793
El-zein and
El-din
Minimum Cost Analysis In Radial Distribution System Planning Using Genetic Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.3, pp. 1792-1802
ISSN 2078-2365
http://www.ieejournal.com/
(x b1  x mid )
2
 (y b1  y mid )
2

(x b2  x mid )
2
 (y b2  y mid )
(13)
(14)
y mid  m b x mid  c b
Where :
xb1 and yb1 : The Coordinates of point b1
xb2 and yb2, :The Coordinates of point b2.
mb and cb are constants of straight line equation that
represent the bridge feeder. They can be calculated using
equation (15) and equation (16).
mb 
y b2  y b1
(15)
x b2  x b1
c b  y b1  x b1m b
(16)
The voltage drop constants ks depends on the resistance,
the reactance of the conductor and the load power factor.
Ks can be calculated using equation (17).
k s  rs cosφ  x s sinφ
(17)
Where:
rs: Resistance per unit length of the conductor
corresponding to the selected CSA of source feeder.
xs: Reactance per unit length of the conductor
corresponding to the selected CSA of source feeder.
factor is usually lag and varies from 0.7 to 0.9. So, the
load power factor is assumed constant and equal to 0.8 lag.
The voltage drop at the end of the main feeder is the
summation of the voltage drop at the end of the source
feeder and the voltage drop in each segment of the main
feeder. It is calculated using equation ( 18) : (23)
ns
vd m  vd s   I j Ld j k m  I1 (dis  d)k m
j2
d
(x b1  x mid )
2
 (y b1  y mid )
Ld j  L j  L j-1
Lj 
2
(18)
(19)
(20)
2
2
x j  y j cos(θ jp  θ mp )
ns
I1   It j
j1
I j  I j1  It j-1 ,j=2,…..ns
(21)
2
km : Voltage drop constant corresponding to the CSA
of main feeder.
The voltage drop at each village vdvk is the
summation of the voltage drop at the end of the source
feeder, the voltage drop for all segments of the main
feeder before reaching this village and the voltage drop for
the lateral feeder of this village. Vdvk is calculated using
equation (24) and (25).
k
vdv k  vd s   (k m Ld j I j )  k m (d  dis)I1  k k Lt k It k
j2
Lt k 
2
2
x k  y k sin(θ kp  θ mp )
(24)
(25)
Where:
vdvk: Voltage drop at village no k.
Ltk: Length of lateral feeder which reaches village no k.
kk: Voltage drop constant corresponding to the CSA of
lateral feeder of village k.
6- Power loss calculation
It is very important to calculate the power loss since
the cost of the power loss is considered in the cost
equation. The total power loss may be divided according
to feeder CSA into:
 Power loss in source feeder.(pls)
 Power loss in main feeder. With half of the bridge
feeder.(plm)
 Power loss in lateral feeder.(plt)
Total power loss pl is calculated using equation (26).
s
m
t
pl   pl s   pl m   pl t
j
jj
j 1
j1
j 1 j
(26)
Where:
s: Number of source feeders.
m: Number of main feeders.
t: Number of lateral feeders.
The power loss of each source feeder pls is calculated
using equation (27), The power loss of each main feeder
plm is calculated using equation (28). While, The power
loss of each lateral feeder plt is calculated using equation
(29).
(22)
2
pl s  3  I 2s  ds  rs
(27)
(23)
ns 2
2
pl m  3[  I j Ld j  I1 (dis  d)]rm
j2
(28)
Where:
vdm: The voltage drop at the end of the main feeder.
d: Halh the length of bridge feeder.
Ij: Current in segment no j on the main feeder.
I1: Current in first segment. i.e., in half the bridge
feeder and segment with length (dis).
Ldj: Length of segment no j on the main feeder.
ns: No of villages in the sector.
tj: Current in lateral feeder which reaches village no j.
pl t
k
 3It k Lt k rt
k
(29)
Where:
rm: Resistance per unit length of the conductor
corresponding to the selected CSA of main feeder.
rt: Resistance per unit length of the conductor
corresponding to the selected CSA of lateral feeder.
7- Cost calculation:
1794
El-zein and
El-din
Minimum Cost Analysis In Radial Distribution System Planning Using Genetic Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.3, pp. 1792-1802
ISSN 2078-2365
http://www.ieejournal.com/
The total annual cost of the project can be divided into
four terms:
 Annual cost of installed feeder and attachments (AIC),
this includes the cost of three phase source, main and
lateral feeders.
 Annual demand cost incurred to maintain adequate
system capacity to supply losses in feeders (ADC),
this term presents the cost of the system (that includes
generation, transmission and distribution) that feeds
only the power losses of the system.
 Annual cost of energy losses in conductors (AEC), this
is the cost of kWh loss per year.
 Annual cost of pole land occupation (APL), when an
overhead transmission line is passed over a certain
land, the area under and around the feeder line
conductors is useless as any pole (that carries the
conductors) may fall down, with its conductors, in
both sides of the route. So, this area can be considered
as a rectangular shape with length equal the length of
the feeder and width equal twice 1.25 the apparent
length of pole over the ground. ( as the rules used by
Ministry of Electricity and Energy.)
The total annual cost (TAC) can be calculated as in
Equation (30)
(30)
TAC  AIC  ADC  AEC  APL
Where:
AIC: Annual cost of installed feeders and attachments.
system capacity to supply losses in feeders.
AEC: Annual cost of energy losses in conductors.
APL: Annual cost of feeder land occupation.
AIC is may be calculated using equation (31).
s
m
t
AIC  3I F (  ICs ds j   ICm L main   ICk Lt j )
j
j j1
j
j1
j1
j
(31)
Where:
IF: Annual fixed charge rate for feeders. The number three
presents the three phase conductor.
ICs: Cost of feeder and attachments per km corresponding
to CSA of source feeder.
ICm: Cost of feeder and attachments per km corresponding
to CSA of main feeder.
ICk: Cost of feeder and attachments per km corresponding
to CSA of lateral feeder.
Lmain: Length of the main feeder and the half of bridge
feeder. It is calculated using equation (32).
L main  L max  L min  dis  d
(32)
Where:
Lmax: The length (L) for the Furthest village from the
substation.
Lmin: The length (L) for the nearest village to the
substation. ADC is calculated using equation (33).
ADC  Pl  FLS  FPR  FR [CG i G  C T i T  CSi S ]
(33)
Where:
Pl: Total power loss illustrated in Equation (26).
FLS: Loss factor presented in Equation (34) after [9].
FPR:Peak responsibility factor.
FR: Reverse factor. CG: Cost of generation system.
CT: Cost of transmission system.
CS: Cost of distribution substation.
iG: Annual charge applicable to generation system.
iT: Annual charge applicable to transmission system.
iS: Annual charge applicable to distribution substation.
2
FLS  0.16 FLD  0.84 FLD
(34)
Where:
AEC is calculated using equation (35)
AEC  Pl  Ec  FLS  8760
(35)
Where: Ec: Cost of energy.
APL can be calculated using equation (36)
m
s
APL  C Ln  25  (  L main   ds j )  1000
j
j1
j 1
(36)
Where:
The number 25 represent twice the 1.25 length of pole
over ground (10m).
CLn: Annual cost of feeder land occupation per m2.
In this technique, genetic algorithm GA are used to
select the optimal value of :
No of feeder in each quadrant (nf).
X coordinate of substation location (xs).
Y coordinate of substation location (ys).
The distance (dis).
In each generation, GA assigns values for nf, xs,ys and
dis and calculates the corresponding cost. There are 100
individuals in each generation GA. i.e., there are 100 costs
in each generation. GA keeps individuals with lower costs
and discards those corresponding to higher cost. Mating
and mutation take place and after many generations, GA
selects the optimum values for these individuals
corresponding to least cost.
III
CASE STUDY
The proposed technique is applied to two cases: the first
one is a realistic study case used in [10]. The coordinates
of the loads are illustrated in Table 1 with the apparent
power of each load, while the second case data are shown
in table 2 The available conductor cross section area
(CSA) and corresponding parameters are illustrated in
Table 3. And Table 4 represents values of factors used in
calculation.
1795
El-zein and
El-din
Minimum Cost Analysis In Radial Distribution System Planning Using Genetic Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.3, pp. 1792-1802
ISSN 2078-2365
http://www.ieejournal.com/
Table 1: Load data for case (1)
Village no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
X (km)
8
12
16
20
22
24
26
24
28
28
12
14
2
4
6
10
12
16
18
20
22
24
26
28
16
Y (km)
-4
-6
-6
-4
-6
-4
-8
0
-2
2
2
0
10
8
6
6
8
4
6
8
4
8
6
6
-2
Table 2: Load data for case (2) (cont.)
S (kVA)
300
200
100
300
100
100
200
200
200
100
300
200
200
200
100
300
300
200
200
100
300
200
300
200
100
Table 2: Load data for case (2)
Vill. No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
X (km)
1.33
4.5
4.25
6.68
7.1
10.8
12.43
10.1
8.2
5.75
1.17
2.5
2.65
3.4
4.4
6.6
7.5
9.3
11.73
11.9
12.7
11.75
9.45
5.72
0.4
1.75
3.9
4.5
7
Y (km)
0
0
0.4
0.55
0.8
0.9
1.42
1.6
2
2
1.15
0
2.55
2.38
2
2.45
2.4
2.65
2.55
3
2.75
3.65
3.83
3.47
3.35
4.9
4.45
4.72
4.75
S (MVA)
0.205
0.137
0.137
0.137
0.137
0.137
0.5448
0.5448
1.0882
0.96
0.137
0.2731
0.137
0.137
0.137
0.137
0.2731
0.6803
0.2731
0.2731
0.448
0.8166
0.137
0.2731
0.2731
0.4086
0.137
0.137
0.205
Vill. No.
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
X (km)
7.5
10.6
11.1
11.7
10.65
7
6.4
3.4
0.75
6.5
8.25
12.6
12.13
6.8
5.72
4.35
3.1
2.5
1.7
5.25
11
11.75
12.75
10.9
9.6
8.75
8.7
7.8
6.05
6.4
6.6
4.45
2.95
1.5
5.95
11.6
10.5
9.55
8.4
2.1
4.07
6
7.38
8.4
10.2
12.75
12.05
11.2
9.1
6.05
4.55
Y (km)
4.63
5
4.45
4.2
5.85
5.13
5.45
5.9
5.9
6.25
6.55
6.13
7.68
7.57
7.35
7.57
7.75
7.4
8.6
8.95
8.98
9.01
9.95
9.85
9.6
10.2
9.13
8.9
8.35
8.77
9.45
9.18
10.35
9.5
11
10.35
12.1
12.07
12.5
11.35
13.5
13.65
13.45
13.82
13.6
13.25
15
14.27
14.1
15.2
14.6
S (MVA)
1.7671
0.5448
0.137
0.137
0.7484
0.205
0.137
0.137
0.205
0.205
0.1642
0.137
0.205
0.137
0.2731
0.205
0.137
0.6803
0.2731
0.2731
0.6803
0.137
0.137
0.137
0.137
0.137
0.137
0.137
0.137
0.137
0.137
0.6122
0.205
0.1642
0.96
0.2731
0.1778
0.137
0.2731
0.5448
0.137
0.137
0.1642
0.137
0.137
0.4928
0.6803
0.137
0.137
0.137
1.1556
1796
El-zein and
El-din
Minimum Cost Analysis In Radial Distribution System Planning Using Genetic Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.3, pp. 1792-1802
ISSN 2078-2365
http://www.ieejournal.com/
Table 2: Load data for case (2) (cont.)
X (km)
7
9.5
12.65
9.25
7
5.7
7.5
7.5
12.2
14.1
14.07
14.2
13.77
13.6
14
13.1
13.5
13.9
13.75
14.1
14.37
13.1
14.7
14.05
Y (km)
15.25
15
15.75
16.25
16.75
16.1
17.63
17.5
1
1.65
4.05
5.28
7.55
9.5
11.15
13.65
14.55
15.28
16.52
15.88
13.5
6.2
3.08
1.55
S (MVA)
0.2731
0.137
0.137
0.137
0.137
0.137
0.2731
0.137
0.137
0.2731
0.137
0.137
0.5448
0.4359
0.1642
0.3456
0.4086
0.137
0.137
0.2186
0.137
0.2186
0.137
0.137
Table 4: Values of factors
Pf
IF
Fpr
Fr
CG
CT
Cs
iG
iT
Is
Ec
Fld
CLn
Ir
power factor
Annual fixed charge rate for feeders
peak responsibility factor
reverse factor
cost of generation system (L.E/kW)
cost of transmission system (L.E/kW)
cost of distribution substation (L.E/kW)
annual charge applicable to generation system
annual charge applicable to transmission system
annual charge applicable to distribution substation
cost of energy (L.E)
Annual cost of feeder land occupation (L.E/ m2)
interest rate
IV
0.8
0.25
0.82
1.15
600
195
60
0.21
0.18
0.18
0.1
0.3
2
0.11
RESULTS
When applying this techniques on the first case, the
overall cost is 1.6503×107 LE as shown in figure 2, the
total power loss is 3.8198×104 kw and the values of best
individuals are shown in table 5.
1.9
x 10
7
1.85
1.8
cost
Vill. No.
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
1.75
1.7
1.65
1.6
1.55
Table 3: Transmission line parameters
Order
CSA
1
2
3
4
5
35/6
70/12
95/15
120/21
150/25
R
(Ω/km)
0.97
0.485
0.357
0.283
0.226
x
(Ω/km)
0.49
0.44
0.41
0.349
0.336
Where:
r: resistance of unit length of conductor.
x: reactance of unit length of conductor.
IC: cost of feeder and attachments per km.
0
10
20
30
40
50
generation
60
70
80
90
100
Figure 2: Cost of each generation for case (1)
IC
L.E/km
108000
121500
132000
141000
150000
Table 5: Best individuals for case (1)
Variable
xs
ys
Dis
nf
Best value
15.4 km
0.55 km
10 m
3
The results in details are shown in figure 4 and table 6.
1797
El-zein and
El-din
Minimum Cost Analysis In Radial Distribution System Planning Using Genetic Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.3, pp. 1792-1802
ISSN 2078-2365
http://www.ieejournal.com/
Table 6: Results for case 1
vd_s
slop_s
m
1
1
150/25
0.0089
3
70/12
0.0061
5
4
5
95/15
35/6
35/6
0.0082
0.0068
0.0051
120/21
0.0087
0.0218
t
vd_vill
10
0.0143
21
0.0219
23
0.0218
24
0.0223
20
0.0109
22
0.0124
18
0.01
19
0.0111
17
0.0087
13
0.0136
14
0.0171
15
0.02
0.3538
35/6
0.0119
35/6
1.0339
0.011
2.2809
35/6
0.0087
35/6
-2.1912
0.0213
-0.6843
-0.5932
16
0.0214
6
35/6
0.0098
-0.4265
11
0.0098
7
35/6
0.0087
0.3929
12
0.0087
8
35/6
0.0097
0.6149
1
0.0097
9
35/6
0.0066
1.9265
2
0.0066
3
0.0067
10
35/6
0.0077
-7.5833
25
0.0077
4
0.0123
5
0.0144
7
0.0168
6
0.0122
8
0.0128
9
0.0143
0.5797
2.9829
11
6
35/6
slop_m
-5.1838
4
3
vd_m
0.6674
2
2
csa_m
35/6
0.0165
-0.8741
-0.4803
12
Where:
s: Order of source feeder.
m: Order of main feeder.
t:order of village.
csa_s: CSA of the source feeder.
csa_m: CSA of the main feeder.
CSA of all lateral feeders are 35/6.
vd_s: Voltage drop at the end of source feeder.
vd_m: Voltage drop at the end of main feeder.
slop_s: slope of source feeder.
slop_m: slope of main feeder.
vd_vill: Voltage drop at village.
35/6
0.014
-0.2478
When applying this techniques on case (2), the overall
cost is 9.71822 ×107 LE as shown in figure 3, the total
power loss is 5.0814 ×105 kw and the values of best
individuals are shown in table 7. The results in details are
shown in figure 5 and table 8
1.08
x 10
8
1.06
1.04
cost
s
csa_s
1.02
1
0.98
0.96
0
10
20
30
40
50
generation
60
70
80
90
100
Figure 3: Cost of each generation for case (2)
1798
El-zein and
El-din
Minimum Cost Analysis In Radial Distribution System Planning Using Genetic Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.3, pp. 1792-1802
ISSN 2078-2365
http://www.ieejournal.com/
Table 7: Best individuals for case (2)
Variable
xs
ys
Dis
nf
10
Best value
8.04 km
6.78 km
10 m
10
13
8
14
17
6
15
20
16
19
4
23
18
2
24
21
11
10
0
12
8
-2
25
-4
9
1
4
-6
2
6
3
5
-8
7
-10
-5
0
X axis (km)
5
10
Figure 4: Feeder branching technique design for case 1
87
88
10
85
82
80
71
70
77
61
48
49
58
47
38
46
45
36
14
15
10
3
12
-6
-4
41
34
30
92
32
23
16
11
4
93
17
102
31
24
13
94
51
42
35
29
28
25
50
40
39
27
56
57
52
43
44
37
26
-4
65
53
54
60
59
0
-8
101
66
67
55
63
1
96
95
62
-6
75
64
4
-2
97
74
68
2
76
78
73
72
6
69
100
98
83
81
79
8
99
84
86
Y axis (km)
Y axis (km)
22
18
9
33
22
20
19
91
8
89
6
5
103
21
7
90
104
2
-2
0
X axis (km)
2
4
6
Figure 5 Feeder branching technique design for case 2
1799
El-zein and
El-din
Minimum Cost Analysis In Radial Distribution System Planning Using Genetic Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.3, pp. 1792-1802
ISSN 2078-2365
http://www.ieejournal.com/
- Table 8 Results for case (2)
s
csa_s
vd_s %
slop_s
1
150/25
0.0118
0.17
2
150/25
0.0118
0.551
3
4
5
6
7
8
150/25
150/25
150/25
150/25
150/25
120/21
0.0275
0.01
vd_m %
0.0158
0.0133
0.0156
slop_m
0.1344
0.22
0.4892
4
35/6
0.0158
0.6455
5
35/6
0.0369
0.7352
6
150/25
0.0434
1.1891
7
150/25
0.059
1.5827
8
150/25
0.0433
2.1707
9
70/12
0.0346
3.8634
10
35/6
0.0359
8.364
11
150/25
0.054
-11.0311
12
35/6
0.0364
-3.8669
13
150/25
0.049
-2.1822
14
35/6
0.037
-1.7115
15
35/6
0.0103
-1.2134
16
35/6
0.0388
-0.7724
1.9287
0.0176
0.0291
csa_m
35/6
35/6
35/6
0.9512
0.031
0.0224
m
1
2
3
6.2345
-4.5596
-1.9761
-0.9708
t
93
42
94
51
52
50
95
53
65
75
96
101
54
83
97
98
99
100
66
76
77
55
56
67
74
82
68
73
78
84
57
72
81
85
87
88
71
79
86
64
80
60
70
59
49
58
69
csa_lat
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
vd_vill %
0.0158
0.0133
0.0156
0.0143
0.0159
0.0316
0.0369
0.0301
0.0342
0.0447
0.0448
0.044
0.0363
0.0583
0.0588
0.0587
0.0594
0.0595
0.0353
0.0415
0.0445
0.0238
0.027
0.0315
0.0342
0.0354
0.0285
0.033
0.0335
0.036
0.0315
0.0457
0.051
0.0531
0.0544
0.055
0.032
0.0355
0.0365
0.0361
0.0499
0.0313
0.037
0.0103
0.0125
0.0197
0.0388
1800
El-zein and
El-din
Minimum Cost Analysis In Radial Distribution System Planning Using Genetic Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.3, pp. 1792-1802
ISSN 2078-2365
http://www.ieejournal.com/
Table 8 Results for case (2) (cont.)
s
csa_s
vd_s %
slop_s
9
150/25
0.015
-0.4583
10
150/25
0.0197
-0.1514
11
150/25
0.0142
0.1744
12
95/15
0.0094
0.5339
13
14
15
150/25
150/25
150/25
0.0148
0.021
vd_m %
slop_m
17
95/15
0.0389
-0.6884
18
35/6
0.0192
-0.4159
19
70/12
0.0371
-0.246
20
21
35/6
35/6
0.0294
0.0168
-0.1119
0.1207
22
35/6
0.0276
0.2604
23
35/6
0.031
0.4449
24
35/6
0.0132
0.5709
25
70/12
0.0323
0.8368
26
35/6
0.0386
1.1291
27
70/12
0.0395
1.733
28
70/12
0.0327
2.3479
29
70/12
0.0386
4.4993
30
35/6
0.0302
6.7958
31
32
35/6
35/6
0.0314
0.0291
-29.875
-3.2778
33
70/12
0.0335
-2.2426
34
35/6
0.018
-1.3894
35
150/25
0.0415
-1.1899
36
150/25
0.0443
-0.8646
2.131
0.0241
5.8139
150/25
0.0252
-6.2752
17
150/25
0.0156
-1.596
150/25
csa_m
1.0447
16
18
m
0.02
-0.885
t
43
61
62
63
44
45
46
48
47
38
26
37
25
39
27
28
11
13
14
36
1
12
15
2
3
24
29
35
10
16
4
30
5
17
9
18
6
8
23
89
7
19
40
20
21
22
32
90
104
csa_lat
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
vd_vill %
0.027
0.0375
0.039
0.0192
0.0274
0.0322
0.0351
0.0377
0.0294
0.0168
0.0213
0.0284
0.015
0.0311
0.0125
0.0133
0.0207
0.0306
0.031
0.0324
0.0261
0.038
0.0395
0.0279
0.0293
0.0352
0.0394
0.0399
0.0293
0.0347
0.0365
0.0387
0.0284
0.0302
0.0314
0.0291
0.0245
0.034
0.0337
0.018
0.0255
0.0395
0.0419
0.032
0.0384
0.0407
0.042
0.0445
0.0443
1801
El-zein and
El-din
Minimum Cost Analysis In Radial Distribution System Planning Using Genetic Algorithm
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.3, pp. 1792-1802
ISSN 2078-2365
http://www.ieejournal.com/
Table 8 Results for case (2) (cont.)
s
csa_s
vd_s %
slop_s
19
150/25
0.0157
-0.5213
20
120/21
0.0097
-0.194
m
csa_m
vd_m %
slop_m
37
35/6
0.0248
-0.6009
38
35/6
0.0225
-0.4375
39
35/6
0.0108
-0.2435
40
35/6
0.0135
-0.1271
t
31
33
103
34
91
92
41
102
csa_lat
35/6
35/6
35/6
35/6
35/6
35/6
35/6
35/6
vd_vill %
0.0187
0.0213
0.0251
0.0191
0.0226
0.0108
0.0127
0.0137
V CONCLUSION
New feeder branching technique using GA is addressed
in this paper. This design can be applied on any system
The main goal is to achieve minimum cost of the
system while satisfying voltage drop constraint. GA is
number of feeders outgoing from it and the best length of
source feeder before branching into two main feeders. The
routing of the main feeder is chosen according to least
square error method to minimize the length of lateral
feeders and CSA of all the feeders are selected as the
smallest CSA that satisfy the voltage drop constraint.
[1]
[2]
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1802
El-zein and
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Minimum Cost Analysis In Radial Distribution System Planning Using Genetic Algorithm
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