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Improvement in the Radial Distribution Primary System Design to Overcome Feeder Outage

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Improvement in the Radial Distribution Primary System Design to Overcome Feeder Outage
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.4, pp. 1869-1876
ISSN 2078-2365
http://www.ieejournal.com/
Improvement in the Radial Distribution
Primary System Design to Overcome Feeder
Outage
A. El-zein and E. Safie El-din
Elec. Power & Machines Dept. Zagazig University- Egypt
[email protected]
Abstract— This paper studies the outage of the feeders
branching from the distribution substation in a redial
distribution system and introduces the required
improvement in the system design to overcome the outage of
any feeder and to achieve the continuity of supply to the
consumers. Also, this paper calculates the increase in the
cost to overcome the outage of a specified feeder and the
increase in the cost to overcome the outage of any feeder
branching from the substation. Finally, the paper discusses
the probability of occurring each outage case and the
corresponding number of consumers who get benefit from
this design. The proposed algorithm is applied on two cases:
The first case is 25 load points with a 20kv substation and
the second case is 104 load points with a 11kv substation.
Index Terms— distribution planning , radial system, rural
system, feeder outage, feeder reconfiguration.
I
INTRODUCTION
The part of the electric utility system that is between
the distribution substation and the distribution
transformers is called the primary system [1]. There are
three fundamentally different ways to lay out a power
distribution system used by electric utilities, each of
which has variations in its own design, radial , loop and
network systems differ in how the substation feeders are
arranged and interconnected about the substation. Most
power distribution systems are designed to be radial, to
have only one path between each consumer and the
substation. The power flows exclusively away from the
substation and out to the consumer along a single path, if
interrupted, results in complete loss of power to the
consumer [2]. So, there must be an improvement that
increases the grid resiliency i.e., the ability of a system to
absorb external stresses [3]. To make this improvement,
the first step is to study the feeder outage as in [4], [5]
and [6] and to search for a method of feeder
reconfiguration, i.e., altering the topological structures of
distribution feeders by changing the open/closed states of
the sectionalizing and tie switches [7] as in [8] and [9].
In this paper, the radial distribution primary system is
modified to overcome the outage of any one (or more
than one) of the source feeders branching from the
distribution substation and calculate the increase in the
cost in each case. Also, the paper discusses the
probability of occurring each outage case and the
corresponding number of consumer that get benefit from
this design.
II
PRINCIPLES OF THE METHOD
In the original design (i.e., without improvement), a
number of source feeders branch from the distribution
substation. Each source feeder reach the middle of a
bridge feeder as shown in Fig. 1. Each bridge feeder
branches into two main feeders. Each main feeder feeds a
number of load points by lateral feeders.
Fig. 1 Original design
This paper introduce an improvement in
this design to overcome the outage of any source
feeder and to achieve the continuity of supply for all
load points (i.e., villages). This technique will be
1869
El-zein and Safie El-din
Improvement in the Radial Distribution Primary System Design to Overcome Feeder Outage
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.4, pp. 1869-1876
ISSN 2078-2365
http://www.ieejournal.com/
done in steps. Each step discuss the outage of one
source feeder and determine the change required in
feeder reconfiguration and feeder CSA to overcome
this outage and calculate the increase of cost due to
this change. After that, it determines the change in
CSA to overcome the outage of any source feeder
and the corresponding cost. The last step is to
calculate the probability of occurring each case of
feeder (or feeders ) outage and the number of
consumers that get benefit from the design
improvement. This paper mentions the cases of
feeder outage that are affected by this improvement
in the design. In this research, we focus on the fixed
cost because the fixed cost is affected by the design.
However, the variable cost is affected by the change
in loads. the fixed cost includes the cost of the
feeders and the cost of the land occupied.
Steps of calculation:
1.1
Remove the first source feeder which feeds the
first and second main feeders.
1.2
The second main feeder will be fed from the
source feeder after the removed one (i.e., second source
feeder) while the first main feeder will be fed from the
source feeder before the removed one (i.e., last source
feeder) as shown in Fig. 2.
Fig. 2 Outage of first source feeder
1.3
Determine the best CSA for the second source
feeder by calculating the voltage drop at the end of source
feeder using equation (1) . This voltage drop must be
within the limit (1%).
vd s  ds  I 2s  k s
(1)
I2s:summation for all currents of villages 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 (2). It depends on the
resistance, the reactance of the conductor and the load
power factor.
k s  rs cosφ  x s sinφ
(2)
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.
ϕ: Power factor angle of load. It is assumed constant and
equal to 0.8 lag.
First, select the smallest CSA for the source feeder and
calculate the voltage drop at the end of the source feeder.
If the voltage drop exceeds 1% the next CSA is selected
and so on until the voltage drop is within the limit.
1.4
Determine the best CSA of the middle bridge
feeder by calculating the voltage drop at the end of this
bridge feeder (points bf1 and bf2) using equations (3) and
(4). This voltage drop must be within the limit (2%).
vd
 k d I  vd
(3)
bf1
b1 b1 b1
S1
vdbf2  k b2db2Ib2  vdS2
(4)
Where:
vdbf1 and vdbf2 are the voltage drop at point bf1 and bf2
kb1 and kb2 are the voltage drop constants corresponding
to the CSA of the first and the second bridge feeders.
db1 and db2 are the lengths of the first and second bridge
feeders.(first bridge feeder is the feeder between points
S1 and bf1 while second bridge feeder is the feeder
between points S2 and bf2).
1.5
Determine the CSA of each main feeder and the
associated bridge feeder by calculating the voltage drop at
the end of the main feeder. This voltage drop must be
within the limit (4%).
When the first source feeder is out of service, the source
feeder after it (and before it) will feed three main feeders
The voltage drop at the end of the main feeder (between
point m2 and m22) 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 ( 5) : (10)
ns
vd m  vd s   I j Ld j k m  I1 (dis  d)k m
j2
(5)
ds: the length of the source feeder.
1870
El-zein and Safie El-din
Improvement in the Radial Distribution Primary System Design to Overcome Feeder Outage
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.4, pp. 1869-1876
ISSN 2078-2365
http://www.ieejournal.com/
d  (x b1  x mid ) 2  (y b1  y mid ) 2
(6)
Ld j  L j  L j-1
Lj 
(7)
2
2
x j  y j cos(θ jp  θ mp )
(8)
ns
I1   It j
j1
I j  I j1  It j-1
(9)
,j=2,…..ns
(10)
Where:
vdm: The voltage drop at the end of the main feeder.
d: Half the length of bridge feeder (i.e., the distance
between point s1 and m2 )
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.
km : Voltage drop constant corresponding to the CSA of
main feeder.
While the voltage drop at the end of the middle main
feeder, i.e., voltage at point bf11, is the summation of the
voltage drop at the end of the middle bridge feeder, i.e.,
point bf1, and the voltage drop in each segment of the
main feeder. The voltage drop at the end of the third main
feeder, i.e., at point m11, is the summation of the voltage
drop at point bf1 , the voltage drop in the bridge feeder
(between points m1 and bf1) and the voltage drop in each
segment of the main feeder.
1.6
Determine the CSA of each lateral feeder by
calculating the voltage drop at the village. This voltage
drop must be within the limit (8%).
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
(11) and (12).
k
vdvk  vds   (k mLd jI j )  k m (d  dis)I1  k k Ltk It k
j2
(11)
2
Lt k  x 2
k  y k sin(θ kp  θ mp )
(12)
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.
1.7
Calculate the fixed cost corresponding to the
new feeder CSA.
The fixed cost may be divided into two main items: AIC
and APL. AIC is the annual cost of installed feeder and
attachments, this includes the cost of three phase source,
main, bridge and lateral feeders. APL is the annual cost of
pole land occupation, 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 (13)
TAC  AIC  APL
(13)
b
s
m
t
AIC  3I F (  IC s ds j   IC m L main   IC L   IC k Lt j )
b
b
j
j
j
j
j1
j1
j j j1
j1
(14)
Where:
IF: Annual fixed charge rate for feeders. The number three
presents the three phase conductor.
ICs, ICm, ICk and ICb Cost of feeder and attachments per
km corresponding to CSA of source, main, lateral and
bridge feeders respectively.
Lmain and Lb are Lengths of the main and the bridge
feeders
APL can be calculated using equation (15)
m
s
APL  C Ln  25  (  L main   ds j 
j
j1
j 1
b

j 1
L )  1000
b
j
(15)
Where:
The number 25 represent twice the 1.25 length of pole
over ground (10m).
CLn: Annual cost of feeder land occupation per m2.
1.8
Repeat the above steps by removing one
different source feeder in each time.
1.9
Choose the best values of CSA for each feeder
that overcome the outage of any source feeder and then
calculate the corresponding fixed cost.
1.10
Study all the possible states of the source feeders
i.e, 1 for on state and 0 for off state.
1.11
Identify the accepted state i.e, this design will be
useful only for the accepted state.
1871
El-zein and Safie El-din
Improvement in the Radial Distribution Primary System Design to Overcome Feeder Outage
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.4, pp. 1869-1876
ISSN 2078-2365
http://www.ieejournal.com/
1.12
Calculate the probability of occurring each one
of the accepted states.
1.13
Calculate the number of consumers that will get
benefit from this design when occurring each state of the
accepted states and also calculate the sum of the kVA
used by theses consumers.
8
13
14
6
17
15
20
16
CASE STUDY
The mentioned technique is applied to two cases used in
[10]. In the first case, when the first source feeder is out
of service the feeder routing and feeder CSA are shown in
Fig. 3 and table 1 and to overcome this outage there must
be a change in some feeder cross section area. This
change will increase the fixed cost by 11.8709% .
23
18
2
22
19
4
Y axis (km)
III
10
21
11
0
10
12
-2
8
25
-4
1
9
4
-6
2
3
6
5
-8
7
-10
-5
0
X axis (km)
5
10
Fig. 3 Outage of the first source feeder
s
csa_s
vd_s
csa_b
Table 1 Outage of the first source feeder-case(1)
m
vd_b
csa_m
vd_m
11
35/6
0.0217
12
35/6
0.0211
35/6
1
35/6
0.038
35/6
2
35/6
0.0207
3
35/6
0.0162
4
35/6
0.0113
35/6
6
2
150/25
95/15
0.0139
0.0088
70/12
35/6
0.0185
0.0148
35/6
Where the first column represents the order of the
source feeders, the second and third columns are the
cross section area of the source feeders and the
voltage drop at the end of the source feeders. The
fourth column is the cross section area of the bridge
feeders branching from the source feeders having the
order indicated in first column and arranged
anticlockwise. The two numbers ( 0.0185 and
0.0148) in the fifth column are the voltage drop at
points (bf1 and bf2) indicated in Fig. 2. The sixth
column is the order of the main feeder. The seventh
and eighth columns are the cross section area of the
main feeder and the voltage drop at the end of the
main feeder. The ninth column is the order of the
village. The tenth column is the cross section area of
t
4
5
7
6
8
9
10
21
23
24
20
22
18
19
17
csa_t
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
0.0174
0.0195
0.022
0.022
0.0226
0.0241
0.0306
0.0381
0.0381
0.0385
0.0197
0.0212
0.0187
0.0197
0.0113
the lateral feeder and the last column represents the
voltage drop at each village. The cross section area of
the other feeders remain unchanged. Now another
source feeder will be out and the above steps are
repeated and so on until finishing the study of all
source feeder outage. After that, all the results are
gathered to obtain the emergency design. i.e., the
design which overcome the outage of any one source
feeder. This improvement is also beneficial in case of
two source feeder outage if there are two healthy
source feeders between them. Almost all the changes
required in feeder cross section area are in source
feeders except for one bridge feeder shown in table 1
and the additional bridge feeder that link two source
feeder (not found in the original design). There is no
1872
El-zein and Safie El-din
24
Improvement in the Radial Distribution Primary System Design to Overcome Feeder Outage
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.4, pp. 1869-1876
ISSN 2078-2365
http://www.ieejournal.com/
change in main feeder CSA or in lateral CSA
between emergency and normal cases. This
emergency design increases the fixed cost by
54.32%. Table 2 shows a comparison between
normal and emergency CSA of source feeders
S
1
2
3
4
5
6
Table2 Comparison between normal and emergency-case(1)
Normal
Emergency
csa
Csa
150/25
150/25
70/12
120/21
95/15
150/25
35/6
70/12
35/6
70/12
120/21
150/25
There are 26 states of the source feeders. One of
them is 111111 . it represents the ideal states when all the
feeders are in the service the other states can be divided
into acceptable and unacceptable states. In the acceptable
states, there must be at least two feeders (sate 1) between
any two feeders (state 0). Table 3 shows the acceptable
states for source feeders.
Table 3 Acceptable states – case(1)
s1
s2
s3
s4
s5
s6
prob
no of cons
kVA
1
1
0
1
1
0
0.0004
11
2200
1
1
1
1
1
0
0.0181
6
1100
1
0
1
1
0
1
0.0004
6
1100
1
1
1
1
0
1
0.0181
3
400
0
1
1
0
1
1
0.0004
8
1700
1
1
1
0
1
1
0.0181
2
500
1
1
0
1
1
1
0.0181
5
1100
1
0
1
1
1
1
0.0181
3
700
0
1
1
1
1
1
0.0181
6
1200
The first six column are the state of the six
source feeders. The seventh column is the probability of
occurring this state (the failure rate of the transmission
line is taken as 0.02 [11]. The eighth column represents
the number of consumers that get benefit from this design
and enjoy continuity of supply. In case of feeder outage
The last column is the summation of kVA consumed by
these consumers.
This technique is applied to the second case.
When the first source feeder is out of service, the rout and
cross section area of the feeders are as shown in Fig. 4
and table 4. The fixed cost will be increased by 1.1366 %.
1873
El-zein and Safie El-din
Improvement in the Radial Distribution Primary System Design to Overcome Feeder Outage
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.4, pp. 1869-1876
ISSN 2078-2365
http://www.ieejournal.com/
4
4
52
3
52
3
94
94
51
51
2
1
42
Y axis (km)
Y axis (km)
2
93
0
1
42
93
0
102
41
102
41
-1
-1
92
92
-2
-2
0
1
2
3
4
X axis (km)
5
6
7
0
1
2
3
4
X axis (km)
5
6
7
Fig. 4 Outage of source feeder no:1- case (2)
Table 4 Outage of source feeder no:1 – case (2)
s
csa_s
vd_s
csa_b
vd_b
35/6
20
150/25
0.0179
150/25
0.0205
35/6
35/6
70/12
2
150/25
0.0185
m
csa_m
vd_m
t
csa_lat
vd_vill
39
35/6
0.019
92
35/6
0.019
40
35/6
0.0215
41
35/6
0.0235
102
35/6
0.0245
1
35/6
0.0291
93
35/6
0.0291
2
35/6
0.0228
42
35/6
0.0228
3
35/6
0.0186
94
35/6
0.0224
51
35/6
0.0177
4
35/6
0.0192
52
35/6
0.0193
0.0151
35/6
At the left side of Fig. 4, the first source feeder is
between the second source feeder an the last source
feeder. The first source feeder feeds the first and the
second main feeders. While the right side is after the
outage of the first feeder. The first main feeder is fed by
the last source feeder and the second main feeder is fed
by the second source feeder.
After studying the outage of each one of source
feeders, the emergency design will be as follows: The
change required in source feeder CSA is limited because
most of the original CSA are 150/25 (the greatest CSA).
The change required in main feeder CSA is more than of
the source feeder. The almost all bridge feeder CSA s
have to be changed. The CSA of all the lateral feeders are
35/6 (the smallest CSA) for original and emergency
design except for those of the emergency design shown in
table 5
Table 5 CSA of lateral feeder for emergency-case(2)
S
m
6
4
7
11
6
13
t
csa_t
vd_vill
75
120/21
0.08
96
150/25
0.0804
101
150/25
0.0803
83
150/25
0.088
97
150/25
0.0889
98
150/25
0.0891
99
150/25
0.0898
100
150/25
0.0899
81
150/25
0.0815
85
150/25
0.0839
87
150/25
0.085
88
150/25
0.0853
64
150/25
0.0918
80
150/25
0.1058
1874
El-zein and Safie El-din
Improvement in the Radial Distribution Primary System Design to Overcome Feeder Outage
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.4, pp. 1869-1876
ISSN 2078-2365
http://www.ieejournal.com/
The CSA of lateral feeder that has to feed village
75 must be 120/21 to satisfy the voltage drop constraints.
The voltage drop of the other thirteen village in table 5 is
out of limit (i.e., more than 8%) but it is acceptable
because we are studying the worst case and the worst
voltage drop is 10.58% at village 80. The villages that
have voltage drop out of limit is only 13 villages of 104
villages i.e., 12.5% .This emergency design increases the
fixed cost by 48.78%. Fig. 5 shows the number of
consumers who get benefit from the new design in each
case. The average of the number of consumer = 19.4%
with respect to the total number of consumers (104
consumers)
40
35
No of consumers
30
25
20
15
10
5
0
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Case number
Fig. 5 the number of consumer who benefit from the new design
Table 6 shows a comparison between case(1)
and case(2) according to the increase in fixed cost due to
emergency design.
Table 6: Comparison between case(1) and case(2)
Norma
Emergency
Increase
Increase
l×106LE
×106LE
×106LE
%
Case
(1)
Case
(2)
11.6
17.9
6.3
54.32
32
47.6
15.6
48.78
case
(1)
case
(2)
Aic
×106LE
Table 7: Comparisonc mal case
Land
Fixed
Total
×106LE
×106LE
×106LE
8
3.6
11.6
16.505
70.2817
21.9
10.1
32
97.2
32.9218
IV
The percentage of increased cost in case (1) is
more than that of case (2) and also the percentage fixed
cost ,with respect to the total cost, in case (1) is twice that
of case (2) as shown in the last column of table 7 that is
because case (1) represents a small number of villages
dispersed in large area while, case (2) is a crowded area
fixed %
Conclusion
Improvement in the radial distribution system
design to overcome feeder outage is presented in this
paper . this technique aiming at achieving continuity of
supply to the consumer and with an acceptable limit of
voltage drop by a slight change in CSA of existing
feeders and also by the addition of sum feeders. Finally,
this paper calculate the number of consumers who get
1875
El-zein and Safie El-din
Improvement in the Radial Distribution Primary System Design to Overcome Feeder Outage
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.4, pp. 1869-1876
ISSN 2078-2365
http://www.ieejournal.com/
benefit from this design in each case of source feeder
outage and the kVA that are consumed by them.
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