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V. V. S. N. Murty, Junior Research Fellow
Dr. Ashwani Kumar, Professor
Department of Electrical Engg.,
NIT Kurukshetra
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
 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.
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.
Three phase three wire radial distribution circuit.
51 murthy
51 murthy
51 murthy
 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.
51 murthy
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
 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.
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.
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
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
Bus 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
Total (kVAr)

Qa
0
0
0
0
27.66
0
0
0
41.85
23.23
0
32.6
23.26
0
95.41
0
0
0
41.89
0
0
32.4
0
0
41.96
360.26

Qb
0
0
0
0
27.66
0
0
0
41.85
23.23
0
32.6
23.26
0
95.41
0
0
0
41.89
0
0
32.4
0
0
41.96
360.26

Qc
0
0
0
0
27.66
0
0
0
41.85
23.23
0
32.6
23.26
0
95.41
0
0
0
41.89
0
0
32.4
0
0
41.96
360.26
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
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
Bus 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
Total (kVAr)

Qa
0
0
0
0
0
0
0
0
87.502
48.734
0
68.539
48.905
0
199.54
0
0
0
86.595
0
0
67.097
0
0
86.898
693.81

Qb
0
0
0
0
0
0
0
0
87.502
48.734
0
68.539
48.905
0
199.54
0
0
0
86.595
0
0
67.097
0
0
86.898
693.81

Qc
0
0
0
0
0
0
0
0
87.502
48.734
0
68.539
48.905
0
199.54
0
0
0
86.595
0
0
67.097
0
0
86.898
693.81
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
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
Bus 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

Qa
0
0
0
0
0
0
0
0
117.15
65.4
0
92.11
65.72
0
267.2
0
0
0
0
0
0
0
0
0
115.53

Qb
0
0
0
0
0
0
0
0
117.15
65.4
0
92.11
65.72
0
267.2
0
0
0
0
0
0
0
0
0
115.53

Qc
0
0
0
0
0
0
0
0
117.15
65.4
0
92.11
65.72
0
267.2
0
0
0
0
0
0
0
0
0
115.53
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
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%.
 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.
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 (%)
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)
Type A-Un balance (%)
A-ph
0
0
0
0
0
0
0
0
87.48
48.712
0

5
B-ph
0
0
0
0
0
0
0
0
0
0
0

A-ph
0
0
0
0
0
0
0
0
87.458
48.691
0

10
B-ph
0
0
0
0
0
0
57.314
0
0
0
0

A-ph
0
0
0
0
0
0
0
0
87.436
48.668
0

15
B-ph
0
0
0
0
0
0
0
0
0
0
0

C-ph
0
0
46.793
75.387
57.054
0
0
57.054
87.48
48.712
61.829

68.515

68.515

48.886
0

A-ph
0
0
0
0
0
0
0
0
87.412
48.646
0

20
B-ph
0
0
0
0
0
0
0
0
0
0
0

C-ph
0
0
46.79
75.386
57.047
0
0
57.046
87.458
48.691
61.809

C-ph
0
0
46.786
75.383
57.04
0
0
57.037
87.436
48.668
61.787

C-ph
0
0
46.782
75.381
57.032
56.564
0
57.028
87.412
48.646
61.766

68.515

68.491

68.491

68.491

68.466

68.466

68.466

68.44

68.44

68.44

48.886
66.816

48.886
66.816

48.867
0

48.867
66.8

48.867
66.8

48.847
0

48.847
0

48.847
66.784

48.827
0

0
0

48.827
66.767

199.5
0
0
0
86.59
0
0

199.5
0
57.328
0
0
0
0

0
0
57.328
56.83
86.59
0
0

199.44
0
0
0
86.585
0
0

199.44
0
0
0
0
0
0

0
0
57.314
56.829
86.585
0
0

199.39
0
0
0
86.579
0
0

199.39
0
57.3
0
0
0
0

0
0
57.3
56.829
86.579
0
56.307

199.34
0
0
0
86.572
0
0

199.34
0
57.285
0
0
0
0

0
0
57.285
56.827
86.572
0
56.296

67.086
0

67.086
0

0
0

67.076
0

67.076
0

0
0

67.064
0

67.064
0

0
0

67.052
0

0
0

0
0

0

47.165

47.165

0

47.157

47.157

0

47.149

47.149

0

47.14

47.14

86.884

86.884

86.884

86.869

86.869

86.869

86.854

86.854

86.838

86.838

86.838

86.838
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
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
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
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
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
Type B- Un balance (%)
A
0
0
0
0
0
0
0
0

5
B
0
0
0
0
0
0
0
0

C
0
0
46.838
0
57.116
0
0
57.118

A
0
0
0
0
0
0
0
0

10
B
0
0
0
0
0
0
0
0

C
0
0
46.88
0
57.171
0
0
57.175

A
0
0
0
0
0
0
0
0

15
B
0
0
0
0
0
0
0
0

C
0
0
46.922
0
57.226
0
0
57.231

A
0
0
0
0
0
0
0
0

20
B
0
0
0
0
0
0
0
0

C
0
0
0
0
57.28
0
0
57.286

87.612

0

0

87.722

0

0

87.831

0

0

87.939

0

0

48.795
0

0
0

0
61.935

48.856
0

0
0

0
62.019

48.916
0

0
0

0
62.103

48.976
0

0
0

0
0

68.632

68.632

68.632

68.724

68.724

68.724

68.816

68.816

68.816

68.907

68.907

0

48.97
0

48.97
66.918

0
0

49.035
0

49.035
67.005

0
0

49.1
0

0
0

0
0

49.164
0

0
0

0
0

199.8
0
0
0

199.8
0
57.417
0

0
0
0
0

200.05
0
0
0

200.05
0
57.492
0

0
0
0
0

200.3
0
0
0

200.3
0
57.566
0

0
0
0
0

200.55
0
0
0

200.55
0
57.64
0

0
0
0
0

86.687
0
0

0
0
0

199.8
0
0

86.778
0
0

0
0
0

86.778
0
0

86.868
0
0

0
0
0

86.868
0
0

86.959
0
0

0
0
0

86.959
0
0

67.164
0

67.164
0

0
0

67.231
0

67.231
0

0
0

67.298
0

67.298
0

0
0

67.364
0

67.364
0

0
0

0

47.221

47.221

0

47.269

47.269

0

47.317

47.317

0

47.364

0

86.987

86.987

86.987

87.075

87.075

87.075

87.163

87.163

87.163

87.251

87.251

87.251

694.647

643.109

625.647

695.471

643.881

513.091

696.292

528.46

513.646

697.11

529.076

288.776
Type-A

Type-B

25000

Savings ($)

20000

15000

10000

5000

0
0%

5%

10%
Load Unbalance (%)

15%

20%
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
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.
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.
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.
[1] D. Thukaram, H.M. Wijekoon Banda, Jovitha Jerome‖ A robust three phase power fl
ow algorithm for radial distribution systems‖, Electric Power Systems Research 50 (1
999) 227–236.
[2] Rade M. Ciric, Antonio Padilha Feltrin, and Luis F. Ochoa, Student Member, IEEE‖
Power Flow in Four-Wire Distribution Networks—General Approach‖, IEEE transacti
ons on power systems , vol. 18, no. 4, november 2003,pp:1283-1290.
[3] R. Ranjan, B. Venkatesh, A. Chaturvedi, D. Das‖ Power Flow Solution of Three-Phas
e Unbalanced Radial Distribution Network‖, Electric Power Components and System
s, 32:421–433, 2004,pp:421-433.
[4] S. Segura,L.C.P. da Silva, R. Romero,‖ Generalized single-equation load flow method
for unbalanced distribution systems‖, IET Gener. Trans. Distrib., 2011, Vol. 5, no. 3,
pp. 347–355.
[5] Jen-Hao Teng, and Chuo-Yean Chang‖ A Novel and Fast Three-Phase Load Flow for
Unbalanced Radial Distribution Systems‖, IEEE transactions on power systems, vol.
17, no. 4, november 2002,pp:1238-1244.
[6] Belal Mohammadi Kalesar, Ali Reza Seifi ―Fuzzy load flow in balanced and unbalanc
ed radial distribution systems incorporating composite load model‖, Electrical Power
and Energy Systems 32 (2010) 17–23.
[7] T.H. Chen N.C. Yang,‖ Three-phase power-flow by direct ZBR method for unbalance
d radial distribution systems‖, IET Gener. Transm. Distrib., 2009, Vol. 3, Iss. 10, pp.
903–910.
[8] M. Crispino, V. Di Vito, A. Russo, P. Varilone ‖Decision theory criteria for capacitor
placement in unbalanced distribution systems‖ 2005 IEEE/PES Transmission and
Distribution Conference & Exhibition: Asia and Pacific Dalian, China, pp:1-6.
[9] G. Carpinelli , C. Noce, D. Proto, A. Russo, P. Varilone‖ Single-objective probabilis
tic optimal allocation of capacitors in unbalanced distribution systems‖ Electric Po
wer Systems Research 87 (2012) 47– 57.
[10] Abdelsalam A. Eajal, and M. E. El-Hawary‖Optimal Capacitor Placement and Sizi
ng in Unbalanced Distribution Systems With Harmonics Consideration Using Pa
rticle Swarm Optimization‖, IEEE transactions on power delivery, vol. 25, no. 3, J
uly 2010,pp:1734-1741.
[11] G. Carpinelli, P. Varilone, V. Di Vito and A. Abur‖ Capacitor placement in three-p
hase distribution systems with nonlinear and unbalanced loads‖ IEE Proc.-Gener.
Transm. Distrib., Vol. 152, No. 1, January 2005,pp:47-52.
[12] J. B. V. Subrahmanyam,C. Radhakrishna‖ A Simple Method for Optimal Capacit
or Placement in Unbalanced Radial Distribution System‖ Electric Power Compone
nts and Systems, 38:1269–1284, 2010,pp:1269-1284.
[13] H. Mohkami, R. Hooshmand, A. Khodabakhshian‖ Fuzzy optimal placement of c
apacitors in the presence of nonlinear loads in unbalanced distribution networks
using BF-PSO algorithm‖, Applied Soft Computing 11 (2011) 3634–3642.
[14] Seyed Abbas Taher, Reza Bagherpour‖ A new approach for optimal capacitor pla
cement and sizing in unbalanced distorted distribution systems using hybrid hone
y bee colony algorithm‖, Electrical Power and Energy Systems 49 (2013) 430–448.
[15] K.V.S. Ramachandra Murthy, M. Ramalinga Raju, ―Capacitive Compensation on
Three Phase Unbalanced Radial Distribution System Using Index Vector Method‖,
International Journal of Engineering and Technology, vol.2, No. 2, Feb., 2012, pp.
284-291.
[16] Luis F. Ochoa, Rade M. Ciric, A. Padilha-Feltrin, Gareth P. Harrison, ―Evaluation
of distribution system losses due to load unbalance‖, in Proc. of 15th PSCC, Liege,
22-26 August 2005 Session 10, Paper 6, Page 1-4.
[17] D. Das, ―Reactive power compensation for radial distribution network using gene
tic algorithm‖ Electric Power Systems Research, vol. 24, 2002, pp. 573– 581.
51 murthy

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51 murthy

  • 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.
  • 9.  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.
  • 11. Cost of Energy Losses (CL): (Total Real power Loss)*(Ec*8760) $ Ec: energy rate ($/kWh) =0.06 $/kWh Cost of capacitor for reactive power support
  • 12.  The load demand at the distribution substation is fluctuating with respect to time.  Distribution feeders are lightly loaded at the mid night and early in the morning and are heavily loaded during the office hours.  Higher load demand also results into lower voltage magnitudes and higher power losses.  Similarly, light load demand also results into high voltage magnitudes and low power losses.
  • 13. In this paper we have consider three different loading conditions i.e. light, medium and high. The total system load is 50%, 100% and 130% of total load for light load, medium and high load operation. By injecting required amount of shunt reactive power, voltage profile can be improved and thereby the power losses will reduce. It means the reactive power supplied by capacitors is proportional to loading conditions.
  • 14. A-ph B-ph C-ph 14 12 Index vector 10 8 6 4 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Bus Number Index Vector profile for 25 bus system at light load
  • 15. Va without Capacitor Vb without Capacitor Vc without Capacitor Va with Capacitor Vb with Capacitor Vc with Capacitor 1.01 1 Voltage (p.u) 0.99 0.98 0.97 0.96 0.95 0.94 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Bus Number Voltage profile for 25 bus system at light load
  • 17. Without capacitor A-phase TPL (kW) TQL (kVAr) Vmin (p.u) B-phase C-phase Total A-phase B-phase C-phase Total 12.39318 13.06759 9.906581 35.367 8.013701 8.428882 6.392486 22.835 13.69854 39.491 8.824555 8.061579 8.512255 25.398 12.5513 13.24069 0.965432 0.965328 0.969208 0.98073 0.979209 0.983683 (%) 2.513073 2.46686 2.161777 1.401089 1.467985 1.119791 Qc (kVAr) ---- ---- ---- Voltage unbalance 360.26 360.26 Cost of energy loss 18589.08 12002.11 capacitor ($) ---- 4242.34 Total cost ($) 18589.08 16244.45228 Savings ($) ---- 2344.6 ($) Cost of 360.26
  • 18. C-ph 12 Va with Capacitor Vc with Capacitor 1.02 10 1 8 Voltage (p.u) Index Vector Vb without Capacitor Vb with Capacitor B-ph Va without Capacitor Vc without Capacitor A-ph 6 4 0.98 0.96 0.94 0.92 2 0.9 0.88 0 1 3 5 7 9 11 13 15 17 19 21 23 25 Bus Number Index Vector profile for 25 bus system at medium load 1 3 5 7 9 11 13 15 17 19 21 23 25 Bus Number Voltage profile for 25 bus system at medium load
  • 20. Without capacitor With capacitor A-phase B-phase C-phase Total A-phase B-phase C-phase Total 52.81328 55.4431 41.86151 150.12 33.66803 35.31495 26.58381 95.567 TQL (kVAr) 58.29014 53.29408 55.69108 167.28 37.02202 33.85069 35.33719 106.21 Vmin (p.u) 0.928412 0.928396 0.936595 0.96067 0.957692 5.334261 5.215524 4.544444 2.975958 3.097951 693.81 693.81 TPL (kW) 0.966898 Voltage unbalance (%) Qc (kVAr) Cost of 78901.97 energy loss ($) 50229.9 Cost of capacitor ($) Total cost 7244.29 78901.97 57474.19459 ($) Savings ($) 21427.7754 2.366941 693.81
  • 21. A-ph B-ph C-ph Va without Capacitor Vc without Capacitor 12 Vb without Capacitor Va with Capacitor Vb with Capacitor 1.02 10 Vc with Capacitor 8 0.98 Voltage (p.u) Index Vector 1 6 4 0.96 0.94 0.92 0.9 0.88 2 0.86 0 0.84 1 3 5 7 9 11 13 15 17 19 21 23 25 Bus Number Index Vector profile for 25 bus system at high load 1 3 5 7 9 11 13 15 17 19 21 23 25 Bus Number Voltage profile for 25 bus system at high load
  • 24. Type A Unbalance Type b Unbalance where lub is the load unbalance factor which determines unbalance in the loads at all nodes in the study system. lub = 0.0 represents the balanced system base case study. In this paper work lub is taken as 5, 10, 15 and 20%.
  • 25.  The total network load remains constant under type A unbalance scenario.  The total network load reduces under type B unbalance scenario.  The load unbalances in the system directly impacts the total power losses and voltage profile.  The main objective of this study to determine required amount of capacitive reactive power needed in the presence of different unbalance scenarios to improve system performance.
  • 26. Without capacitor considering unbalance of type-A for 25 bus system Phase Unbalance 0% 5% 10 % 15 % 20 % A 52.81328 51.53396 50.25238 48.96833 47.68162 B 55.4431 50.70412 46.20817 41.94849 37.91851 C 41.86151 48.23329 55.07561 62.39956 70.21673 Total 150.11789 150.47136 151.53616 153.31637 155.81686 A 58.29014 58.48702 58.67479 58.85355 59.02338 B 53.29408 46.22705 39.66439 33.59785 28.01959 C 55.69108 63.31257 71.48492 80.22349 89.5443 Total 167.27529 168.02664 169.82410 172.67489 176.58727 A 0.928412 0.929145 0.929886 0.930633 0.931388 B 0.928396 0.932337 0.936244 0.94012 0.943964 C 0.936595 0.931385 0.926135 0.920844 0.91551 A 5.334261 5.271712 5.208695 5.145201 5.081221 B 5.215524 4.9143 4.617142 4.323945 4.034603 C 4.544444 4.953752 5.369119 5.790749 6.218856 Cost of energy loss ($) 78901.97 79087.75 79647.41 80583.09 81897.34 Total cost ($) 78901.97 79087.75 79647.41 80583.09 81897.34 TPL (kW) TQL (kVAr) Min Voltage (p.u) Un balance (%)
  • 27. Phase 0% 5% 10 % 15 % 20 % A 33.66803 33.46699 32.73168 31.84653 30.70615 B 35.31495 34.2367 30.55031 28.20139 27.5183 C 26.58381 29.11303 33.51727 37.30539 41.23329 Total 95.56678 96.8167 96.79925 97.35331 99.45773 A 37.02202 36.11431 36.70106 36.53679 35.97869 B 33.85069 32.42506 27.39659 23.82588 21.91705 C 35.33719 41.14802 45.10282 50.35751 56.63392 Total 106.20989 109.68739 109.20047 110.72017 114.52965 A 0.96067 0.961326 0.962004 0.96303 0.964316 B 0.957692 0.955607 0.959332 0.959304 0.956215 C 0.966898 0.967949 0.963476 0.960642 0.958713 A 2.975958 2.944228 2.88706 2.811096 2.709989 B 3.097951 3.177551 2.916197 2.91857 3.122641 C 2.366941 1.913179 2.279138 2.433346 2.578057 A 693.81 693.653 693.127 693.304 693.127 B 693.81 642.18 641.689 575.07 459.043 C 693.81 953.323 952.743 1009.236 1065.603 Total 2081.43 2289.156 2287.559 2277.61 2217.773 Cost of energy loss ($) 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)
  • 28. Type A-Un balance (%) A-ph 0 0 0 0 0 0 0 0 87.48 48.712 0 5 B-ph 0 0 0 0 0 0 0 0 0 0 0 A-ph 0 0 0 0 0 0 0 0 87.458 48.691 0 10 B-ph 0 0 0 0 0 0 57.314 0 0 0 0 A-ph 0 0 0 0 0 0 0 0 87.436 48.668 0 15 B-ph 0 0 0 0 0 0 0 0 0 0 0 C-ph 0 0 46.793 75.387 57.054 0 0 57.054 87.48 48.712 61.829 68.515 68.515 48.886 0 A-ph 0 0 0 0 0 0 0 0 87.412 48.646 0 20 B-ph 0 0 0 0 0 0 0 0 0 0 0 C-ph 0 0 46.79 75.386 57.047 0 0 57.046 87.458 48.691 61.809 C-ph 0 0 46.786 75.383 57.04 0 0 57.037 87.436 48.668 61.787 C-ph 0 0 46.782 75.381 57.032 56.564 0 57.028 87.412 48.646 61.766 68.515 68.491 68.491 68.491 68.466 68.466 68.466 68.44 68.44 68.44 48.886 66.816 48.886 66.816 48.867 0 48.867 66.8 48.867 66.8 48.847 0 48.847 0 48.847 66.784 48.827 0 0 0 48.827 66.767 199.5 0 0 0 86.59 0 0 199.5 0 57.328 0 0 0 0 0 0 57.328 56.83 86.59 0 0 199.44 0 0 0 86.585 0 0 199.44 0 0 0 0 0 0 0 0 57.314 56.829 86.585 0 0 199.39 0 0 0 86.579 0 0 199.39 0 57.3 0 0 0 0 0 0 57.3 56.829 86.579 0 56.307 199.34 0 0 0 86.572 0 0 199.34 0 57.285 0 0 0 0 0 0 57.285 56.827 86.572 0 56.296 67.086 0 67.086 0 0 0 67.076 0 67.076 0 0 0 67.064 0 67.064 0 0 0 67.052 0 0 0 0 0 0 47.165 47.165 0 47.157 47.157 0 47.149 47.149 0 47.14 47.14 86.884 86.884 86.884 86.869 86.869 86.869 86.854 86.854 86.838 86.838 86.838 86.838
  • 29. 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
  • 30. 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
  • 31. 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
  • 32. 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 ($) 3.449616 4.108359 2.921767 63680.89 57294.38 51686.37 70873.59 63680.89 57294.38 51686.37
  • 33. Unbalance Phase TPL (kW) TQL (kVAr) Min Voltage (p.u) Un balance (%) Qc (kVAr) Total Cost of energy loss ($) 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
  • 34. Type B- Un balance (%) A 0 0 0 0 0 0 0 0 5 B 0 0 0 0 0 0 0 0 C 0 0 46.838 0 57.116 0 0 57.118 A 0 0 0 0 0 0 0 0 10 B 0 0 0 0 0 0 0 0 C 0 0 46.88 0 57.171 0 0 57.175 A 0 0 0 0 0 0 0 0 15 B 0 0 0 0 0 0 0 0 C 0 0 46.922 0 57.226 0 0 57.231 A 0 0 0 0 0 0 0 0 20 B 0 0 0 0 0 0 0 0 C 0 0 0 0 57.28 0 0 57.286 87.612 0 0 87.722 0 0 87.831 0 0 87.939 0 0 48.795 0 0 0 0 61.935 48.856 0 0 0 0 62.019 48.916 0 0 0 0 62.103 48.976 0 0 0 0 0 68.632 68.632 68.632 68.724 68.724 68.724 68.816 68.816 68.816 68.907 68.907 0 48.97 0 48.97 66.918 0 0 49.035 0 49.035 67.005 0 0 49.1 0 0 0 0 0 49.164 0 0 0 0 0 199.8 0 0 0 199.8 0 57.417 0 0 0 0 0 200.05 0 0 0 200.05 0 57.492 0 0 0 0 0 200.3 0 0 0 200.3 0 57.566 0 0 0 0 0 200.55 0 0 0 200.55 0 57.64 0 0 0 0 0 86.687 0 0 0 0 0 199.8 0 0 86.778 0 0 0 0 0 86.778 0 0 86.868 0 0 0 0 0 86.868 0 0 86.959 0 0 0 0 0 86.959 0 0 67.164 0 67.164 0 0 0 67.231 0 67.231 0 0 0 67.298 0 67.298 0 0 0 67.364 0 67.364 0 0 0 0 47.221 47.221 0 47.269 47.269 0 47.317 47.317 0 47.364 0 86.987 86.987 86.987 87.075 87.075 87.075 87.163 87.163 87.163 87.251 87.251 87.251 694.647 643.109 625.647 695.471 643.881 513.091 696.292 528.46 513.646 697.11 529.076 288.776
  • 36. 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
  • 37. 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.
  • 38. 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.
  • 39. 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.
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