1.
V. V. S. N. Murty, Junior Research Fellow
Dr. Ashwani Kumar, Professor
Department of Electrical Engg.,
NIT Kurukshetra
2.
INTRODUCTION
UNBALANCED DISTRIBUTION SYSTEM LOAD FLOW
ANALYSIS
ANALYSIS
OF
UNBALANCED
SYSTEM
UNDER
DIFFERENT LOADING CONDITIONS
ANALYSIS OF UNBALANCED DISTRIBUTION SYSTEM
UNDER TYPE-A AND TYPE-B UNBALANCES
RESULTS AND DISCUSSIONS
CONCLUSIONS
3.
It is well known fact that distribution systems
can
operate under unbalanced loading conditions.
So, the distribution system planner have to consider
these load unbalances for better planning and oper
ation of the system.
It is observed from the literature survey that, many
authors have done optimal placement of capacitors
without consideration of load unbalances.
The prime purpose of this paper is to maintain accep
table voltages at all buses along the distribution feed
er under all loading conditions and load unbalances
by optimal placement of capacitors.
In this paper we consider the impact of two types of
load unbalances and different loading conditions on
optimal capacitor sizes and locations.
4.
The main objective of this paper:
Finding optimal sizes and locations of capacitors in
Unbalanced Distribution Systems (ubds) using
Index Vector Approach.
Impact of different loading conditions (low, medium
and high loading) on optimal placement of
capacitors in ubds is analyzed.
Impact of type-A and type-B unbalances on voltage
profile, voltage unbalance, total power losses and
cost of energy losses in ubds is evaluated.
Impact of type-A and type-B unbalances on optimal
capacitor allocation problem is addressed.
The results are obtained on 25-bus unbalanced
radial distribution system.
5.
Three phase three wire radial distribution circuit.
6.
In this article Index Vector is used to find
out optimal locations and sizes of capacitors
in unbalanced distribution systems.
Index Vector is formulated by running the
base case load flow on a given distribution
network.
Index Vector directly gives the optimal
locations and estimated capacitor sizes.
Index Vector, identifies the sequence of
nodes to be compensated. The buses with
high Index Vector value are the potential
locations for capacitor placement.
7.
Cost of Energy Losses (CL):
(Total Real power Loss)*(Ec*8760) $
Ec: energy rate ($/kWh) =0.06 $/kWh
Cost of capacitor for reactive power support
8.
The
load demand at the distribution
substation is fluctuating with respect to
time.
Distribution feeders are lightly loaded at the
mid night and early in the morning and are
heavily loaded during the office hours.
Higher load demand also results into lower
voltage magnitudes and higher power
losses.
Similarly, light load demand also results
into high voltage magnitudes and low power
losses.
9.
In
this paper we have consider three
different
loading
conditions
i.e.
light, medium and high.
The total system load is 50%, 100% and
130% of total load for light load, medium
and high load operation.
By injecting required amount of shunt
reactive power, voltage profile can be
improved and thereby the power losses will
reduce.
It means the reactive power supplied by
capacitors is proportional to loading
conditions.
10.
A-ph
B-ph
C-ph
14
12
Index vector
10
8
6
4
2
0
1
2
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Bus Number
Index Vector profile for 25 bus system at light load
11.
Va without Capacitor
Vb without Capacitor
Vc without Capacitor
Va with Capacitor
Vb with Capacitor
Vc with Capacitor
1.01
1
Voltage (p.u)
0.99
0.98
0.97
0.96
0.95
0.94
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Bus Number
Voltage profile for 25 bus system at light load
13.
Without capacitor
A-phase
TPL (kW)
TQL (kVAr)
Vmin (p.u)
B-phase
C-phase
Total
A-phase
B-phase
C-phase
Total
12.39318 13.06759 9.906581
35.367
8.013701 8.428882 6.392486 22.835
13.69854
39.491
8.824555 8.061579 8.512255 25.398
12.5513
13.24069
0.965432 0.965328
0.969208
0.98073
0.979209
0.983683
(%)
2.513073
2.46686
2.161777
1.401089 1.467985
1.119791
Qc (kVAr)
----
----
----
Voltage
unbalance
360.26
360.26
Cost of
energy loss
18589.08
12002.11
capacitor ($)
----
4242.34
Total cost ($)
18589.08
16244.45228
Savings ($)
----
2344.6
($)
Cost of
360.26
14.
C-ph
12
Va with Capacitor
Vc with Capacitor
1.02
10
1
8
Voltage (p.u)
Index Vector
Vb without Capacitor
Vb with Capacitor
B-ph
Va without Capacitor
Vc without Capacitor
A-ph
6
4
0.98
0.96
0.94
0.92
2
0.9
0.88
0
1
3
5
7
9 11 13 15 17 19 21 23 25
Bus Number
Index Vector profile for 25 bus system at
medium load
1 3 5 7 9 11 13 15 17 19 21 23 25
Bus Number
Voltage profile for 25 bus system at
medium load
16.
Without capacitor
With capacitor
A-phase
B-phase
C-phase
Total
A-phase
B-phase
C-phase
Total
52.81328
55.4431
41.86151
150.12
33.66803
35.31495
26.58381
95.567
TQL (kVAr) 58.29014
53.29408
55.69108
167.28
37.02202
33.85069
35.33719
106.21
Vmin (p.u)
0.928412
0.928396
0.936595
0.96067
0.957692
5.334261
5.215524
4.544444
2.975958
3.097951
693.81
693.81
TPL (kW)
0.966898
Voltage
unbalance
(%)
Qc (kVAr)
Cost of
78901.97
energy loss
($)
50229.9
Cost of
capacitor ($)
Total cost
7244.29
78901.97
57474.19459
($)
Savings ($)
21427.7754
2.366941
693.81
17.
A-ph
B-ph
C-ph
Va without Capacitor
Vc without Capacitor
12
Vb without Capacitor
Va with Capacitor
Vb with Capacitor
1.02
10
Vc with Capacitor
8
0.98
Voltage (p.u)
Index Vector
1
6
4
0.96
0.94
0.92
0.9
0.88
2
0.86
0
0.84
1
3
5
7
9 11 13 15 17 19 21 23 25
Bus Number
Index Vector profile for 25 bus system at high load
1
3 5 7 9 11 13 15 17 19 21 23 25
Bus Number
Voltage profile for 25 bus system at high load
19.
Without capacitor
With capacitor
A-phase
B-phase
C-phase
Total
A-phase
B-phase
C-phase
Total
93.0239
97.35278
73.28935
263.67
62.20085
65.02331
48.8517
176.08
102.5659
93.62979
97.2082
293.4
68.45781
62.53135
64.90851
195.9
0.904789
0.904949
0.916012
0.945143
0.941683
0.953737
7.208388
7.028391
6.099434
4.496543
4.595769
3.624808
755.66
755.66
755.66
TPL (kW)
TQL (kVAr)
Vmin (p.u)
Voltage unbalance
(%)
Qc (kVAr)
Cost of energy loss
138582.9
92545.47
($)
Cost of capacitor ($)
Total cost ($)
Savings ($)
7507.99
138582.9
100053.4608
38529
20.
Type A Unbalance
Type b Unbalance
where lub is the load unbalance factor which
determines unbalance in the loads at all nodes
in the study system.
lub = 0.0 represents the balanced system base
case study.
In this paper work lub is taken as 5, 10, 15 and
20%.
21.
The total network load remains constant under type
A unbalance scenario.
The total network load reduces under type B
unbalance scenario.
The load unbalances in the system directly impacts
the total power losses and voltage profile.
The main objective of this study to determine
required amount of capacitive reactive power
needed in the presence of different unbalance
scenarios to improve system performance.
22.
Without capacitor considering unbalance of type-A for 25 bus system
Phase
Unbalance
0%
5%
10 %
15 %
20 %
A
52.81328
51.53396
50.25238
48.96833
47.68162
B
55.4431
50.70412
46.20817
41.94849
37.91851
C
41.86151
48.23329
55.07561
62.39956
70.21673
Total
150.11789
150.47136
151.53616
153.31637
155.81686
A
58.29014
58.48702
58.67479
58.85355
59.02338
B
53.29408
46.22705
39.66439
33.59785
28.01959
C
55.69108
63.31257
71.48492
80.22349
89.5443
Total
167.27529
168.02664
169.82410
172.67489
176.58727
A
0.928412
0.929145
0.929886
0.930633
0.931388
B
0.928396
0.932337
0.936244
0.94012
0.943964
C
0.936595
0.931385
0.926135
0.920844
0.91551
A
5.334261
5.271712
5.208695
5.145201
5.081221
B
5.215524
4.9143
4.617142
4.323945
4.034603
C
4.544444
4.953752
5.369119
5.790749
6.218856
Cost of energy loss ($)
78901.97
79087.75
79647.41
80583.09
81897.34
Total cost ($)
78901.97
79087.75
79647.41
80583.09
81897.34
TPL (kW)
TQL (kVAr)
Min Voltage (p.u)
Un balance (%)
23.
Phase
0%
5%
10 %
15 %
20 %
A
33.66803
33.46699
32.73168
31.84653
30.70615
B
35.31495
34.2367
30.55031
28.20139
27.5183
C
26.58381
29.11303
33.51727
37.30539
41.23329
Total
95.56678
96.8167
96.79925
97.35331
99.45773
A
37.02202
36.11431
36.70106
36.53679
35.97869
B
33.85069
32.42506
27.39659
23.82588
21.91705
C
35.33719
41.14802
45.10282
50.35751
56.63392
Total
106.20989
109.68739
109.20047
110.72017
114.52965
A
0.96067
0.961326
0.962004
0.96303
0.964316
B
0.957692
0.955607
0.959332
0.959304
0.956215
C
0.966898
0.967949
0.963476
0.960642
0.958713
A
2.975958
2.944228
2.88706
2.811096
2.709989
B
3.097951
3.177551
2.916197
2.91857
3.122641
C
2.366941
1.913179
2.279138
2.433346
2.578057
A
693.81
693.653
693.127
693.304
693.127
B
693.81
642.18
641.689
575.07
459.043
C
693.81
953.323
952.743
1009.236
1065.603
Total
2081.43
2289.156
2287.559
2277.61
2217.773
Cost of energy loss ($)
50229.9
50886.86
50877.69
51168.9
52274.99
Cost of capacitor ($)
7244.29
7867.468
7865.89
7832.83
7653.319
Total cost ($)
57474.19459
58754.33008
58743.57928
59001.73113
59928.30411
Savings ($)
21427.77541
20333.41992
20903.83072
21581.35887
21969.03589
TPL (kW)
TQL (kVAr)
Min Voltage (p.u)
Un balance (%)
Qc (kVAr)
25.
Va without Capacitor
Vb without Capacitor
Vc without Capacitor
Va with Capacitor
Va without Capacitor
Vc without Capacitor
Va with Capacitor
Vb with Capacitor
Vb with Capacitor
Vb without Capacitor
Vc with Capacitor
Vc with Capacitor
1.02
1.02
1
0.98
Voltage (p.u)
Voltage (p.u)
1
0.96
0.94
0.98
0.96
0.94
0.92
0.92
0.9
0.9
0.88
1
3
5
7
9
11 13 15 17 19 21 23 25
Bus Number
Voltage profile for 25 bus system with Type-A unbalance case-1
0.88
1
3
5
7
9
11 13 15 17 19 21 23 25
Bus Number
Voltage profile for 25 bus system with Type-A unbalance
case-2
26.
Va without Capacitor
Vb without Capacitor
Va without Capacitor
Vb without Capacitor
Vc without Capacitor
Va with Capacitor
Vc without Capacitor
Va with Capacitor
Vb with Capacitor
Vc with Capacitor
Vb with Capacitor
Vc with Capacitor
1.02
1.02
1
0.98
0.98
Voltage (p.u)
Voltage (p.u)
1
0.96
0.94
0.96
0.94
0.92
0.92
0.9
0.9
0.88
0.88
0.86
1
3
5
7
9
11 13 15 17 19 21 23 25
Bus Number
1
3
5
7
9
11 13 15 17 19 21 23 25
Bus Number
Voltage profile for 25 bus system with Type-A unbalance case-3 Voltage profile for 25 bus system with Type-A unbalance
case-4
27.
Unbalance 0%
5%
10%
15%
20%
Unbalance 0%
160
10%
15%
20%
0.98
0.97
140
0.96
120
0.95
100
0.94
80
60
40
20
0
Vmin (p.u)
Total Real Power Loss (kW)
180
5%
0.93
0.92
0.91
0.9
0.89
0.88
Total Real Power Loss with and without Capacitor
considering Unbalances
Minimum Voltage with and without Capacitor
considering Unbalances
28.
Without capacitor considering unbalance of type-B for 25 bus system
Phase
Unbalance
0%
A
52.81328
55.4431
53.3283
48.09286
53.83323
41.29643
54.32848
35.03965
54.81446
29.30897
41.86151
33.42204
26.02881
19.63945
14.21441
150.11789
134.84320
121.15846
109.00757
98.33783
A
B
58.29014
53.29408
59.29373
48.02609
60.29409
43.05916
61.29132
38.38843
62.28552
34.00912
C
55.69108
43.52779
32.96989
23.95894
16.44025
Total
A
167.27529
0.928412
150.84760
136.32313
123.63868
112.73488
B
0.928396
0.927592
0.933194
0.926783
0.937955
0.925983
0.942679
0.925192
0.947367
C
0.936595
0.943955
0.951205
0.95835
0.965394
A
5.334261
5.215524
5.47427
4.472285
5.543272
B
5.404609
4.841294
5.611641
3.74938
C
Un balance (%)
20 %
Total
Min Voltage (p.u)
15 %
C
TQL (kVAr)
10 %
B
TPL (kW)
5%
4.544444
3.990296
Total cost ($)
78901.97
78901.97
2.406159
70873.59
Cost of energy loss ($)
3.449616
4.108359
2.921767
63680.89
57294.38
51686.37
70873.59
63680.89
57294.38
51686.37
29.
Unbalance
Phase
TPL (kW)
TQL (kVAr)
Min Voltage
(p.u)
Un balance (%)
Qc (kVAr)
Total
Cost of energy
loss ($)
Cost of
capacitor ($)
Total cost ($)
Savings ($)
A
B
C
Total
A
B
C
Total
A
B
C
A
B
C
A
B
C
0%
33.66803
35.31495
26.58381
95.56678
37.02202
33.85069
35.33719
106.20989
0.96067
0.957692
0.966898
2.975958
3.097951
2.366941
693.81
693.81
693.81
2081.43
5%
33.87315
30.95504
25.22272
90.05091
37.95326
31.0514
30.65602
99.66067
0.961206
0.959875
0.960363
2.981026
2.889593
2.319529
694.647
643.109
625.647
1963.403
10 %
34.24613
26.33051
19.54578
80.12242
38.9732
27.54172
22.5021
89.01703
0.960645
0.964899
0.964338
3.01902
2.482542
2.177754
695.471
643.881
513.091
1852.443
15 %
34.25481
23.79063
13.79437
71.83980
38.45706
25.4146
17.12555
80.99721
0.960886
0.961139
0.97167
3.018978
2.611763
1.616577
696.292
528.46
513.646
1738.398
20 %
34.25354
18.9619
13.35143
66.56687
40.24009
20.98355
13.34035
74.56399
0.961072
0.967898
0.966326
3.024577
2.129901
1.969987
697.11
529.076
288.776
1514.962
50229.9
47330.76
42112.35
37759
34987.55
7244.29
57474.19459
21427.77541
6890.209
54220.97136
16652.61864
6557.329
48669.67662
15011.21338
6215.194
43974.19514
13320.18486
5544.886
40532.43394
11153.93606
32.
Un balance (%)
Type-A
0
5
10
15
20
Un-balance (%)
Type-B
0
5
10
15
20
Powers taken from the substation (kVA)
Without capacitor
With capacitor
3390 +2560.3i
3335.5+417.78i
3390.3+2561i
3336.7+213.48i
3391.5+2562.7i
3336.7+214.54i
3393.3+2565.5i
3337.3+225.96i
3395.8+2569.3i
3339.4+289.56i
Power taken from the substation (kVA)
Without capacitor
3390+2560.3i
3212.2+2423.8i
3036.1+2289.2i
2861.4+2156.5i
2688.2+2025.5i
With capacitor
3335.5+417.78i
3167.5+409.21i
2995+389.47i
2824.3+315.45i
2656.5+472.4i
33.
It is observed that
1. The real and reactive power losses are
decreasing in phase-B and increasing in phase-C
with percentage of type-A unbalance.
2. Voltage magnitudes are decreases with
increasing of percentage of type-A unbalance.
3. Voltage unbalance and cost of energy losses are
also increasing with increasing of type-A
unbalance.
4. Increase in percentage of type-A unbalance
results into decrement of required
capacitive
reactive power in B-phase and increment in Cphase.
5. It is also observed that savings are slightly
increasing with increase of load unbalance.
34.
It is observed that
1. The real and
reactive power losses are
decreasing in phase-B and phase-C with
percentage of
type-B unbalance.
2. Voltage magnitudes are increases with
increase of percentage of type-B unbalance.
3. Voltage unbalance and cost of energy losses
are also decreasing with increasing of type-B
unbalance.
4. Increase in percentage of type-B unbalance
results into decrement of capacitive reactive
power in B-phase and C-phase.
5. It is also observed that savings are decreasing
with increasing of unbalance.
35.
The total power losses, voltage unbalance, shunt
capacitive requirement and cost of energy losses are
varying with loading.
The total power losses are increasing with percenta
ge of type-A unbalance. Voltage unbalance in phase
-B decreasing and in phase-C increasing. Shunt cap
acitive reactive power requirement in phase-B is low
er than phase-C.
Total shunt capacitive reactive power supplied
under type-A unbalance is more than type-B unbala
nce.
Total power losses under type-A unbalance are
more than type-B unbalance.
Voltage unbalance under type-A unbalance are
more than type-B unbalance.
Annual cost savings obtained in Type-A unbalance
are higher than Type-B unbalance.
36.
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