40220140504001

International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 5, Issue 4, April (2014), pp. 01-10 © IAEME
1
STATUS OF ALL BRANCHES OF DISTRIBUTION NETWORKS IN
CHRONOLOGICAL ORDER FOR COMPOSITE LOADS USING
DISTRIBUTED GENERATION
D Banerjee, S K Saha, S Banerjee
Electrical Engineering Department, Dr. B. C. Roy Engineering College, Durgapur, India
ABSTRACT
This paper presents status of all branches of radial distribution networks in chronological
order for loads of composite type using distributed generation at optimal position by considering the
concept of reactive loading index technique. Although under different situations for all the branches
the identified weakest branch remains same up to some specified conditions but the corresponding
loading at different branches in chronological order has been categorically identified. The
effectiveness of the proposed idea has been successfully tested on 12.66 kV radial distribution
systems consisting of 33 nodes and the results are found to be in very good agreement.
Keywords: Active Power Loss; Composite Load; Distributed Generation; Reactive Loading Index;
Radial Distribution Networks; Weakest Branch.
I. INTRODUCTION
VOLTAGE stability [1] is one of the important factors that may be explained as the ability of a
power system to maintain voltage at all the nodes of the system so that with the increase of load, load
power will increase and both the power and voltage are controllable. The problem of voltage stability
[1] has been defined as inability of the power system to provide the reactive power [2] or non-
uniform consumption of reactive power by the system itself. Therefore, voltage stability is a major
concern in planning and assessment of security of large power systems in contingency situation,
specially in developing countries because of non-uniform growth of load demand and lacuna in the
reactive power management side [3]. The loads generally play a key role in voltage stability analysis
and therefore the voltage stability is known as load stability. Literature survey shows that a major
work has been done on the voltage stability analysis of transmission systems, but so far the
researchers have paid very little attention on the voltage stability analysis for a radial distribution
network [4-10] in power system.
Radial distribution systems having a low reactance to resistance ratio, which causes a high
power loss whereas the transmission system having a high reactance to resistance ratio. So, the
INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING &
TECHNOLOGY (IJEET)
ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 5, Issue 4, April (2014), pp. 01-10
© IAEME: www.iaeme.com/ijeet.asp
Journal Impact Factor (2014): 6.8310 (Calculated by GISI)
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IJEET
© I A E M E

2
conventional load flow methods like Newton Raphson and fast decoupled method cannot be
effectively used for the load flow analysis of radial distribution systems.
The current article has been developed a novel and simple theory [11-12] to identify the
weakest branch of a radial distribution system for loads of composite type. The effectiveness of the
proposed idea is then tested on 33 node radial distribution system.
II. METHODOLOGY
We consider a simple 2-node system as shown in Fig. 1.
Fig 1: A simple 2-node system
Here a load having an impedance of φ∠= LL ZZ
r
is connected to a source having an
impedance of α∠= SS ZZ
r
. If line shunt admittances are neglected, the current flowing through the
line equals the load current;
From Figure 1,
*
L
LL
S
LS
V
jQP
Z
VV
rr
rr
−
=
−
(1)
Using simple calculation, we can write load reactive power LQ as
( ) αδαδ sinsin
2
S
L
SL
S
LS
L
Z
V
Z
VV
Q −−+= (2)
The load voltage LV can be varied by changing the load reactive power LQ . The load reactive
power LQ becomes maximum when the following condition is satisfied.
0=
L
L
dV
dQ
(3)
Now, from (2) and (3)
( ) 0sinsin2 =−+− SL
S
L
V
V
δαδα (4)
LLL VV δ∠=
α∠= SS ZZ
φ∠= LL ZZ
SI
LI
SSS VV δ∠=

3
Now, at no load, L SV V= and L Sδ δ= . Therefore at no load, the left hand side (LHS) of (4) will
besinα . However, at the maximum reactive power LQ , the equality sign of (4) hold and thus the LHS
of (4) becomes zero.
Hence the LHS of (4) is considered as a reactive loading index, qL of the system that varies
between sinα (at no load) and zero (at maximum reactive power).
Thus,
( )SL
S
L
q
V
V
L δαδα −+−= sinsin2 (5)
Here, 0sin ≥≥ qLα (6)
In radial distribution system the power flow problem can be solved by distflow technique.
The active and reactive power flow through the branch near bus i is ( )iP and ( )iQ respectively
and the active and reactive power flow through the branch near bus (i+1) is ( )1+iP and
( )1+iQ respectively.
Hence we can write
( ) ( )
( ) ( )
( )
( )iR
iV
iQiP
iPiP
1
11
1
2
22
+
+++
++=
(7)
( ) ( )
( ) ( )
( )
( )iX
iV
iQiP
iQiQ
1
11
1
2
22
+
+++
++=
(8)
Here, ( ) ( ))11( +++ ijQiP is the sum of complex load at bus (i+1) and all the complex
power flow through the downstream branches of bus (i+1).
Now, the voltage magnitude at bus (i+1) is given by
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( )iV
iXiRiQiP
iXiQiRiPiViV
2
2222
22
))((
)(21
++
++−=+
(9)
The power flow solution of a radial distribution feeder involves recursive use of (7) to (9) in
reverse and forward direction. Now beginning at the last branch and finishing at the first branch of
the feeder, we determine the complex power flow through each branch of the feeder in the reverse
direction using (7) to (9). Then we determine the voltage magnitude of all the buses in forward
direction using (9).
III. LOAD MODELING
For the purpose of loading status of all branches of radial distribution networks, composite
load modeling is considered. The real and reactive power loads of node ‘i’ is given as:

4
( ) ( ) ( ) ( )( )2
3210 iVciVcciPLiPL ++= (10)
( ) ( ) ( ) ( )( )2
3210 iVdiVddiQLiQL ++= (11)
Here ( ),, 11 dc ( ),, 22 dc and ( )33 , dc are the compositions of constant power (CP), constant
current (CI) and constant impedance (CZ) loads respectively. Now, for constant power load
,111 == dc ,03322 ==== dcdc for constant current load ,122 == dc ,03311 ==== dcdc and
for constant impedance load ,133 == dc 02211 ==== dcdc . Here, for composite load, a
composition of 40% of constant power ( ),4.011 == dc 30% of constant current ( )3.022 == dc and
30% of constant impedance ( )3.033 == dc loads are also considered.
IV. RESULTS AND DISCUSSIONS
With the help of MATLAB programme, the effectiveness of the proposed idea is tested on
12.66 KV radial distribution systems consisting of 33-nodes for composite types of loads. The single
line diagram of the 33-node system is shown in Fig. 2 and its data is given in appendix (Table III).
Fig. 2: Single line diagram of a main feeder
The reactive loading index of all branches of the 33-node system is evaluated using equation
(5). Then the reactive loading index of all branches of the system is shown in Fig.3 (normal loading
condition only) and the investigation reveals that the value of the reactive loading index qL to be
minimum in the branch 5 (connected between buses 5 and 6). Thus branch 5 can be considered as the
weakest branch of the system. In nominal loading condition, the active power loss is 179.8 kW and
reactive loss is 119.3 kVAr. Under this condition, the minimum system voltage is 0.9186 pu at
node 18.
1 3 75 942 6 8 13121110 1514 1716
25
21
20
19
24
23
322827 29 31 3330
26

5
From Fig. 3, a chart has been prepared as depicted below. From the chart we observe that the
values of the reactive loading index of different branches are always in ascending order as listed
below.
B5-B2-B27-B28-B3-B4-B23-B8-B12-B9-B7-B30-B19-B22-B29-B6-B24-B1-B26-B13-B16-B25-
B11-B14-B15-B31-B10-B20-B21-B17-B18-B32.
Now we insert unity power factor DG in the existing 33-node system. DG is considered as an
active power source and hence DG is considered as negative load. The maximum size of the DG is
assumed to be total load demand of the system. For this test case, DG capacity is assumed to be
3.715 MW. With the help of optimization technique it is seen that the power loss will be minimum if
2600.5 kW unity power factor DG is placed at node 6. In this case, the active power loss is 98.0 kW.
With the help of optimization technique it is also seen that that the power loss will be 98.6 kW, if
2229.0 kW unity power factor DG is placed at node 7.
Fig. 3: Reactive loading index of all branches of the 33-node system under nominal loading
conditions for composite load
Now, DG is placed at node 6 and capacity of DG is varied from 10% to 100% in step of 10%
of total DG capacity. Now, the reactive loading index of all branches of the modified 33-node system
is evaluated using equation (5) at every step.
A chart has been prepared as depicted below under head ‘A’, ‘B’, ‘C’, ‘D’, ‘E’, ‘F’, ‘G’, ‘H’, ‘I’, and
‘J’. From the chart we observe that the values of the reactive loading index of different branches are
always in ascending order as listed below. This ascending order pattern is changing for different
capacities of DG at node 6.
The investigation reveals that the value of the reactive loading index )( qL is minimum in
branch 5 and B5 can be considered as the weakest branch of the system up to 30% DG capacity at
node 6. From 40% to 100% DG capacity, B27 can be considered as the weakest branch of the
system.
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Branch number
Reactiveloadingindex

6
A. 10% DG capacity
B11-B14-B15-B31-B10-B20-B21-B17-B18-B32.
B. 20% DG capacity
B11-B14-B15-B31-B10-B20-B21-B17-B18-B32.
C. 30% DG capacity
B11-B14-B15-B31-B10-B20-B21-B17-B18-B32.
D. 40% DG capacity
B11-B14-B15-B31-B10-B20-B21-B17-B18-B32.
E. 50% DG capacity
B11-B14-B15-B31-B10-B20-B21-B17-B18-B32.
F. 60% DG capacity
B11-B14-B15-B31-B10-B20-B21-B17-B18-B32.
G. 70% DG capacity
B15-B3-B31-B10-B4-B20-B21-B17-B18-B32.
H. 80% DG capacity
B27-B28-B23-B8-B12-B9-B7-B2-B30-B19-B22-B29-B24-B6-B26-B13-B16-B5-B25-B11-B14-
B15-B1-B31-B10-B20-B21-B17-B18-B32-B3-B4.
I. 90% DG capacity
B1-B31-B10-B20-B21-B17-B18-B32-B5-B3-B4.
J. 100% Load
B31-B10-B1-B20-B21-B17-B18-B32-B3-B5-B4.

7
Table I: Active power loss, reactive power loss and minimum system voltage after inserting DG at
node 6
DG capacity
(%)
Ploss
kW
Qloss
kVAr
Minimum
Voltage (pu)
Node
number
10 156.7 105.0 0.9237 18
20 137.4 93.2 0.9288 18
30 122.0 83.8 0.9338 18
40 110.3 76.9 0.9388 18
50 102.5 72.3 0.9438 18
60 98.3 70.2 0.9488 18
70 98.0 70.4 0.9537 18
80 101.3 73.0 0.9587 18
90 108.4 78.0 0.9636 18
100 119.2 85.4 0.9685 18
Table I shows the active power loss, reactive power loss and minimum system voltage after
inserting unity power factor DG at node 6 and capacity of DG is varied from 10% to 100% in step of
10% of total DG capacity. From Table I, we observe that the active power loss loss will decrease, up
to 70% DG capacity is inserted at node 6 and after that the active power losses will increase. We also
observe that the reactive power loss loss will decrease, up to 60% DG capacity is inserted at node 6
and after that the reactive power losses will increase. But minimum system voltage will increase up
to maximum size of DG.
Similarly, DG is placed at node 7 and capacity of DG is varied from 10% to 100% in step of
10% of total DG capacity. Now, the reactive loading index of all branches of the modified 33-node
system is evaluated using equation (5) at every step.
A chart has been prepared as depicted below under head ‘K’, ‘L’, ‘M’, ‘N’, ‘O’, ‘P’, ‘Q’, ‘R’, ‘S’,
and ‘T’. From the chart we observe that the values of the reactive loading index of different branches
are always in ascending order as listed below. This ascending order pattern is changing for different
capacities of DG at node 7.
The investigation reveals that the value of the reactive loading index )( qL is minimum in
branch 5 and B5 can be considered as the weakest branch of the system up to 30% DG capacity at
node 7. From 40% to 100% DG capacity, B27 can be considered as the weakest branch of the
system.
K. 10% DG capacity
B11-B14-B15-B31-B10-B20-B21-B17-B18-B32.
L. 20% DG capacity
B11-B14-B15-B31-B10-B20-B21-B17-B18-B32.
M. 30% DG capacity
B11-B14-B15-B31-B10-B20-B21-B17-B18-B32.

8
N. 40% DG capacity
B11-B14-B15-B31-B10-B20-B21-B17-B18-B32.
O. 50% DG capacity
B14-B15-B6-B31-B10-B20-B21-B17-B18-B32.
P. 60% DG capacity
B14-B15-B31-B10-B20-B6-B21-B17-B18-B32.
Q. 70% DG capacity
B15-B3-B31-B10-B4-B20-B21-B17-B18-B32-B6.
R. 80% DG capacity
B1-B31-B10-B20-B21-B17-B18-B3-B32-B4-B6.
S. 90% DG capacity
B31-B10-B20-B21-B17-B18-B32-B5-B3-B6-B4.
T. 100% Load
B10-B1-B20-B21-B17-B18-B32-B6-B3-B5-B4.
Table II: Active power loss, reactive power loss and minimum system voltage after inserting DG at
node 7
DG capacity
(%)
Ploss
kW
Qloss
kVAr
Minimum
Voltage (pu)
Node
number
10 155.8 102.4 0.9242 18
20 136.1 89.1 0.9297 18
30 120.5 79.2 0.9351 18
40 109.1 72.9 0.9405 18
50 101.8 70.2 0.9459 18
60 98.6 70.9 0.9513 18
70 99.6 75.1 0.9567 18
80 104.6 82.7 0.9617 33
90 113.7 93.8 0.9666 33
100 126.8 108.4 0.9714 33

9
Table II shows the active power loss, reactive power loss and minimum system voltage after
inserting unity power factor DG at node 7 and capacity of DG is varied from 10% to 100% in step of
10% of total DG capacity. From Table II, we observe that the active power loss loss will decrease, up
to 60% DG capacity is inserted at node 6 and after that the active power losses will increase. We also
observe that the reactive power loss loss will decrease, up to 50% DG capacity is inserted at node 7
and after that the reactive power losses will increase. But minimum system voltage will increase up
to maximum size of DG.
V. CONCLUSIONS
From the above discussion, it is observed that branch 5 has shown the lowest value which is
the weakest branch (under nominal loading condition as well as up to 30% DG capacity), although
the value of other branches exceeds the value of the weakest branch for different loadings at all node
points. From 40% DG capacity at node 6, it is observed that branch 27 has shown the lowest value
which is the weakest branch. In this paper the loading status of all branches of radial distribution
systems for composite load are arranged in chronological order using reactive loading index. The
effectiveness of the proposed idea has been successfully tested on 12.66 kV radial distribution
systems consisting of 33 nodes and the results are found to be in very good agreement.
REFERENCES
[1] H. K. Clark, “New challenges: Voltage stability” IEEE Power Engg Rev, April 1990, pp. 33-37.
[2] T. Van Cutsem: “A method to compute reactive power margins with respect to voltage collapse”,
IEEE Trans. on Power Systems, No. 1, 1991.
[3] R. Ranjan, B. Venkatesh, D. Das, “Voltage stability analysis of radial distribution networks”,
Electric Power Components and Systems,Vol. 31, pp. 501-511, 2003.
[4] M. Chakravorty, D. Das, “Voltage stability analysis of radial distribution networks”, Electric
Power and Energy Systems,Vol. 23, pp. 129-135, 2001.
[5] Das, D., Nagi, H. S., and Kothari, D. P., “Novel method for solving radial distribution networks”,
IEE Proc. C, 1994, (4), pp. 291-298.
[6] J.F. Chen, W. M. Wang, “Steady state stability criteria and uniqueness of load flow solutions for
radial distribution systems”, Electric Power and Energy Systems,Vol. 28, pp. 81-87, 1993.
[7] D. Das, D.P. Kothari, A. Kalam, “Simple and efficient method for load solution of radial
distribution networks”, Electric Power and Energy Systems,Vol. 17, pp. 335-346, 1995.
[8] Goswami, S. K., and Basu, S. K., “Direct solution of distribution systems”, IEE Proc. C, 1991,
138, (1), pp. 78-88.
[9] F. Gubina and B. Strmcnik, “A simple approach to voltage stability assessment in radial
network”, IEEE Trans. on PS, Vol. 12, No. 3, 1997, pp. 1121-1128.
[10] K. Vu, M.M. Begovic, D. Novosel and M.M. Saha, “Use of local measurements to estimate
voltage-stability margin”, IEEE Trans. on PS, Vol. 14, No. 3,1999, pp. 1029-1035.
[11] Banerjee,Sumit, Chanda,C.K., and Konar, S.C., “Determination of the Weakest Branch in a
Radial Distribution Network using Local Voltage Stability Indicator at the Proximity of the
Voltage Collapse Point”, International Conference on Power System,(Published in IEEE Xplore)
ICPS 2009, IIT Kharagpur, 27-29 December 2009.
[12] Banerjee, Sumit, and Chanda, C.K., “Proposed Procedure for Estimation of Maximum
Permissible Load Bus Voltage of a Power System within Reactive Loading Index Range”, IEEE
Conference TENCON 2009, Singapore, 23-26 November 2009.
[13] Priyanka Das And S Banerjee, “Optimal Allocation of Capacitor in a Radial Distribution System
using Loss Sensitivity Factor and Harmony Search Algorithm”, International Journal of Electrical
Engineering & Technology (IJEET), Volume 5, Issue 3, 2014, pp. 5 - 13, ISSN Print : 0976-6545,
ISSN Online: 0976-6553.

10
APPENDIX
Table III: Line data and nominal load data of 33 node radial distribution system
Line
No.
From
Bus
To Bus Branch
resistance
(ohm)
Branch
reactance
(ohm)
Load at Receiving end node
PL0 (kW) QL0 (kVAr)
1 1 2 0.0922 0.0477 100.0 60.0
2 2 3 0.4930 0.2511 90.0 40.0
3 3 4 0.3660 0.1840 120 80
4 4 5 0.3811 0.1941 60 30
5 5 6 0.8190 0.7000 60 20
6 6 7 0.1872 0.6188 200 100
7 7 8 0.7114 0.2351 200 100
8 8 9 1.0300 0.7400 60 20
9 9 10 1.0400 0.7400 60 20
10 10 11 0.1966 0.0650 45 30
11 11 12 0.3744 0.1238 60 35
12 12 13 1.4680 1.1550 60 35
13 13 14 0.5416 0.7129 120 80
14 14 15 0.5910 0.5260 60 10
15 15 16 0.7463 0.5450 60 20
16 16 17 1.2890 1.7210 60 20
17 17 18 0.7320 0.5740 90 40
18 2 19 0.1640 0.1565 90 40
19 19 20 1.5042 1.3554 90 40
20 20 21 0.4095 0.4784 90 40
21 21 22 0.7089 0.9373 90 40
22 3 23 0.4512 0.3083 90 50
23 23 24 0.8980 0.7091 420 200
24 24 25 0.8960 0.7011 420 200
25 6 26 0.2030 0.1034 60 25
26 26 27 0.2842 0.1447 60 25
27 27 28 1.0590 0.9337 60 20
28 28 29 0.8042 0.7006 120 70
29 29 30 0.5075 0.2585 200 600
30 30 31 0.9744 0.9630 150 70
31 31 32 0.3105 0.3619 210 100
32 32 33 0.3410 0.5302 60 40

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