V. V. S. N. Murty, Junior Research Fellow

Dr. Ashwani Kumar, Professor

Department of Electrical Engg.,

NIT Kurukshetra

Capacitor Allocation In Unbalanced Distribution System With Different Unbalances And Loading Conditions

INTRODUCTIONUNBALANCED DISTRIBUTION SYSTEM LOAD FLOW ANALYSISANALYSIS OF UNBALANCED SYSTEM UNDER DIFFERENT LOADING CONDITIONS ANALYSIS OF UNBALANCED DISTRIBUTION SYSTEM UNDER TYPE-A AND TYPE-B UNBALANCESRESULTS AND DISCUSSIONSCONCLUSIONS

PRESENTATION OUTLINE

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 op-eration 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 ac-ceptable voltages at all buses along the distribution feeder under all loading conditions and load unbal-ances 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.

INTRODUCTION

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.

Contd….

UNBALANCED DISTRIBUTION SYSTEM LOAD FLOW ANALYSIS

Three phase three wire radial distribution circuit.

MATHEMATICAL MODEL FOR RADIAL DISTRIBUTION SYSTEMS

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.

Index Vector Based Method

Contd….

Cost of Energy Losses (CL):(Total Real power Loss)*(Ec*8760) $Ec: energy rate ($/kWh) =0.06 $/kWhCost of capacitor for reactive power

support

Cost of energy loss and cost of capacitors

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.

ANALYSIS OF UNBALANCED SYSTEM UNDER DIFFERENT LOADING CONDITIONS

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.

Contd….

At Light Load

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250

2

4

6

8

10

12

14

A-ph B-ph C-ph

Bus Number

Inde

x ve

ctor

Index Vector profile for 25 bus system at light load

At Light Load

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250.94

0.95

0.96

0.97

0.98

0.99

1

1.01

Va without Capacitor Vb without Capacitor Vc without Capacitor

Va with Capacitor Vb with Capacitor Vc with Capacitor

Bus Number

Vol

tage

(p.

u)

Voltage profile for 25 bus system at light load

Capacitor sizes at light load conditionBus No. Qa Qb Qc

1 0 0 02 0 0 03 0 0 04 0 0 05 27.66 27.66 27.666 0 0 07 0 0 08 0 0 09 41.85 41.85 41.8510 23.23 23.23 23.2311 0 0 012 32.6 32.6 32.613 23.26 23.26 23.2614 0 0 015 95.41 95.41 95.4116 0 0 017 0 0 018 0 0 019 41.89 41.89 41.8920 0 0 021 0 0 022 32.4 32.4 32.423 0 0 024 0 0 025 41.96 41.96 41.96

Total (kVAr) 360.26 360.26 360.26

Results for 25 bus system at light load condition

Without capacitor

A-phase B-phase C-phase Total A-phase B-phase C-phase Total

TPL (kW) 12.39318 13.06759 9.906581 35.367 8.013701 8.428882 6.392486 22.835

TQL (kVAr) 13.69854 12.5513 13.24069 39.491 8.824555 8.061579 8.512255 25.398

Vmin (p.u) 0.965432 0.965328 0.969208 0.98073 0.979209 0.983683

Voltage

unbalance

(%) 2.513073 2.46686 2.161777 1.401089 1.467985 1.119791

Qc (kVAr) ---- ---- ---- 360.26 360.26 360.26

Cost of

energy loss

($)

18589.08 12002.11

Cost of

capacitor ($)---- 4242.34

Total cost ($) 18589.08 16244.45228

Savings ($) ---- 2344.6

At Medium Load

1 4 7 10 13 16 19 22 250

2

4

6

8

10

12

A-ph B-ph C-ph

Bus Number

Inde

x V

ecto

r

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

Va without Capacitor Vb without Capacitor

Vc without Capacitor Va with Capacitor

Vb with Capacitor Vc with Capacitor

Bus Number

Vol

tage

(p.

u)

Voltage profile for 25 bus system at medium load

Index Vector profile for 25 bus system at medium load

Capacitor sizes at medium load conditionBus No. Qa Qb Qc

1 0 0 02 0 0 03 0 0 04 0 0 05 0 0 06 0 0 07 0 0 08 0 0 09 87.502 87.502 87.50210 48.734 48.734 48.73411 0 0 012 68.539 68.539 68.53913 48.905 48.905 48.90514 0 0 015 199.54 199.54 199.5416 0 0 017 0 0 018 0 0 019 86.595 86.595 86.59520 0 0 021 0 0 022 67.097 67.097 67.09723 0 0 024 0 0 025 86.898 86.898 86.898

Total (kVAr) 693.81 693.81 693.81

Results for 25 bus system at medium load condition

Without capacitor With capacitor

A-phase B-phase C-phase Total A-phase B-phase C-phase Total

TPL (kW) 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 0.966898

Voltage

unbalance

(%)5.334261 5.215524 4.544444 2.975958 3.097951 2.366941

Qc (kVAr) 693.81 693.81 693.81

Cost of

energy loss

($)

78901.97

50229.9

Cost of

capacitor

($) 7244.29

Total cost

($)

78901.97 57474.19459

Savings ($) 21427.7754

At High Load

1 4 7 10 13 16 19 22 250

2

4

6

8

10

12

A-ph B-ph C-ph

Bus Number

Inde

x V

ecto

r

1 4 7 10 13 16 19 22 250.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

Va without Capacitor Vb without Capacitor

Vc without Capacitor Va with Capacitor

Vb with Capacitor Vc with Capacitor

Bus Number

Vol

tage

(p.

u)

Voltage profile for 25 bus system at high loadIndex Vector profile for 25 bus system at high load

Capacitor sizes at high load conditionBus No. Qa Qb Qc

1 0 0 02 0 0 03 0 0 04 0 0 05 0 0 06 0 0 07 0 0 08 0 0 09 117.15 117.15 117.15

10 65.4 65.4 65.411 0 0 012 92.11 92.11 92.1113 65.72 65.72 65.7214 0 0 015 267.2 267.2 267.216 0 0 017 0 0 018 0 0 019 0 0 020 0 0 021 0 0 022 0 0 023 0 0 024 0 0 025 115.53 115.53 115.53

Total (kVAr) 723.11 723.11 723.11

Results for 25 bus system at medium load condition

Without capacitor With capacitor

A-phase B-phase C-phase Total A-phase B-phase C-phase Total

TPL (kW)

93.0239 97.35278 73.28935263.67

62.20085 65.02331 48.8517176.08

TQL (kVAr)102.5659 93.62979 97.2082

293.468.45781 62.53135 64.90851

195.9

Vmin (p.u)

0.904789 0.904949 0.916012 0.945143 0.941683 0.953737

Voltage unbalance

(%) 7.208388 7.028391 6.099434 4.496543 4.595769 3.624808

Qc (kVAr)755.66 755.66 755.66

Cost of energy loss

($)

138582.9 92545.47

Cost of capacitor ($) 7507.99

Total cost ($) 138582.9 100053.4608

Savings ($) 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%.

Type A and B Unbalances

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.

Contd…

TPL (kW)

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

TQL (kVAr)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

Min Voltage (p.u)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

Un balance (%)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

Type A UnbalanceWithout capacitor considering unbalance of type-A for 25 bus system

TPL (kW)

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

TQL (kVAr)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

Min Voltage (p.u)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

Un balance (%)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

Qc (kVAr)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

With capacitors considering unbalance of type-A for 25 bus system

Type A-Un balance (%)5 10 15 20

A-ph B-ph C-ph A-ph B-ph C-ph A-ph B-ph C-ph A-ph B-ph C-ph0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 46.793 0 0 46.79 0 0 46.786 0 0 46.7820 0 75.387 0 0 75.386 0 0 75.383 0 0 75.3810 0 57.054 0 0 57.047 0 0 57.04 0 0 57.0320 0 0 0 0 0 0 0 0 0 0 56.5640 0 0 0 57.314 0 0 0 0 0 0 00 0 57.054 0 0 57.046 0 0 57.037 0 0 57.028

87.48 0 87.48 87.458 0 87.458 87.436 0 87.436 87.412 0 87.41248.712 0 48.712 48.691 0 48.691 48.668 0 48.668 48.646 0 48.646

0 0 61.829 0 0 61.809 0 0 61.787 0 0 61.766

68.515 68.515 68.515 68.491 68.491 68.491 68.466 68.466 68.466 68.44 68.44 68.44

48.886 48.886 48.886 48.867 48.867 48.867 48.847 48.847 48.847 48.827 0 48.8270 66.816 66.816 0 66.8 66.8 0 0 66.784 0 0 66.767

199.5 199.5 0 199.44 199.44 0 199.39 199.39 0 199.34 199.34 00 0 0 0 0 0 0 0 0 0 0 00 57.328 57.328 0 0 57.314 0 57.3 57.3 0 57.285 57.2850 0 56.83 0 0 56.829 0 0 56.829 0 0 56.827

86.59 0 86.59 86.585 0 86.585 86.579 0 86.579 86.572 0 86.5720 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 56.307 0 0 56.296

67.086 67.086 0 67.076 67.076 0 67.064 67.064 0 67.052 0 00 0 0 0 0 0 0 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

693.653 642.18 953.323 693.477 642.014 953.139 693.304 575.07 1009.236 693.127 459.043 1065.603

Type A Unbalance

1 4 7 10 13 16 19 22 250.88

0.9

0.92

0.94

0.96

0.98

1

1.02

Va without Capacitor Vb without Capacitor

Vc without Capacitor Va with Capacitor

Vb with Capacitor Vc with Capacitor

Bus Number

Vol

tage

(p.

u)

1 4 7 10 13 16 19 22 250.88

0.9

0.92

0.94

0.96

0.98

1

1.02

Va without Capacitor Vb without Capacitor

Vc without Capacitor Va with Capacitor

Vb with Capacitor Vc with Capacitor

Bus Number

Vol

tage

(p.

u)

Voltage profile for 25 bus system with Type-A unbalance case-1 Voltage profile for 25 bus system with Type-A unbalance case-2

Type A Unbalance

1 4 7 10 13 16 19 22 250.88

0.9

0.92

0.94

0.96

0.98

1

1.02

Va without Capacitor Vb without Capacitor

Vc without Capacitor Va with Capacitor

Vb with Capacitor Vc with Capacitor

Bus Number

Vol

tage

(p.

u)

1 4 7 10 13 16 19 22 250.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

Va without Capacitor Vb without Capacitor

Vc without Capacitor Va with Capacitor

Vb with Capacitor Vc with Capacitor

Bus Number

Vol

tage

(p.

u)

Voltage profile for 25 bus system with Type-A unbalance case-4

Voltage profile for 25 bus system with Type-A unbalance case-3

Type A Unbalance

TPL-A w

ithou

t Cap

acito

r

TPL-B w

ithou

t Cap

acito

r

TPL-C w

ithou

t Cap

acito

r

Total T

PL with

out C

apac

itor

TPL-A w

ith C

apac

itor

TPL-B w

ith C

apac

itor

TPL-C w

ith C

apac

itor

Total T

PL with

Cap

acito

r0

20

40

60

80

100

120

140

160

180

Unbalance 0% 5% 10% 15% 20%

Tot

al R

eal P

ower

Los

s (k

W)

Vmin-A w

ithou

t Cap

acito

r

Vmin-B w

ithou

t Cap

acito

r

Vmin-C w

ithou

t Cap

acito

r

Vmin-A w

ith C

apac

itor

Vmin-B w

ith C

apac

itor

Vmin-C w

ith C

apac

itor

0.88

0.89

0.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

Unbalance 0% 5% 10%15% 20%

Vm

in (

p.u)

Minimum Voltage with and without Capacitor considering Unbalances

Total Real Power Loss with and without Capacitor considering Unbalances

TPL (kW)

Phase Unbalance

0 %5 % 10 % 15 % 20 %

A 52.8132853.3283 53.83323 54.32848 54.81446

B 55.4431 48.09286 41.29643 35.03965 29.30897

C 41.86151 33.42204 26.02881 19.63945 14.21441

Total 150.11789 134.84320 121.15846 109.00757 98.33783

TQL (kVAr)A 58.29014 59.29373 60.29409 61.29132 62.28552B 53.29408 48.02609 43.05916 38.38843 34.00912

C 55.69108 43.52779 32.96989 23.95894 16.44025

Total 167.27529 150.84760 136.32313 123.63868 112.73488

Min Voltage (p.u)A 0.928412

0.927592 0.926783 0.925983 0.925192B 0.928396 0.933194 0.937955 0.942679 0.947367

C 0.936595 0.943955 0.951205 0.95835 0.965394

Un balance (%)A 5.334261

5.404609 5.474275.543272

5.611641B 5.215524 4.841294 4.472285

4.1083593.74938

C 4.544444 3.990296 3.449616 2.921767 2.406159

Cost of energy loss ($)

78901.97

70873.59 63680.89 57294.38 51686.37

Total cost ($) 78901.97 70873.59 63680.89 57294.38 51686.37

Type B UnbalanceWithout capacitor considering unbalance of type-B for 25 bus system

TPL (kW)Phase

Unbalance

0 % 5 % 10 % 15 % 20 %A 33.66803 33.87315 34.24613 34.25481 34.25354B 35.31495 30.95504 26.33051 23.79063 18.9619C 26.58381 25.22272 19.54578 13.79437 13.35143

Total 95.56678 90.05091 80.12242 71.83980 66.56687

TQL (kVAr)A 37.02202 37.95326 38.9732 38.45706 40.24009B 33.85069 31.0514 27.54172 25.4146 20.98355C 35.33719 30.65602 22.5021 17.12555 13.34035

Total 106.20989 99.66067 89.01703 80.99721 74.56399

Min Voltage (p.u)

A 0.96067 0.961206 0.960645 0.960886 0.961072B 0.957692 0.959875 0.964899 0.961139 0.967898C 0.966898 0.960363 0.964338 0.97167 0.966326

Un balance (%)A 2.975958 2.981026 3.01902 3.018978 3.024577B 3.097951 2.889593 2.482542 2.611763 2.129901C 2.366941 2.319529 2.177754 1.616577 1.969987

Qc (kVAr)A 693.81 694.647 695.471 696.292 697.11B 693.81 643.109 643.881 528.46 529.076C 693.81 625.647 513.091 513.646 288.776

Total 2081.43 1963.403 1852.443 1738.398 1514.962

Cost of energy loss ($) 50229.9 47330.76 42112.35 37759 34987.55Cost of

capacitor ($) 7244.29 6890.209 6557.329 6215.194 5544.886Total cost ($) 57474.19459 54220.97136 48669.67662 43974.19514 40532.43394Savings ($) 21427.77541 16652.61864 15011.21338 13320.18486 11153.93606

With capacitors considering unbalance of type-B for 25 bus system

Type B- Un balance (%)5 10 15 20

A B C A B C A B C A B C0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 46.838 0 0 46.88 0 0 46.922 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 57.116 0 0 57.171 0 0 57.226 0 0 57.280 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 57.118 0 0 57.175 0 0 57.231 0 0 57.286

87.612 0 0 87.722 0 0 87.831 0 0 87.939 0 0

48.795 0 0 48.856 0 0 48.916 0 0 48.976 0 00 0 61.935 0 0 62.019 0 0 62.103 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 48.97 0 49.035 49.035 0 49.1 0 0 49.164 0 00 66.918 0 0 67.005 0 0 0 0 0 0 0

199.8 199.8 0 200.05 200.05 0 200.3 200.3 0 200.55 200.55 00 0 0 0 0 0 0 0 0 0 0 00 57.417 0 0 57.492 0 0 57.566 0 0 57.64 00 0 0 0 0 0 0 0 0 0 0 0

86.687 0 199.8 86.778 0 86.778 86.868 0 86.868 86.959 0 86.9590 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0

67.164 67.164 0 67.231 67.231 0 67.298 67.298 0 67.364 67.364 00 0 0 0 0 0 0 0 0 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

694.647 643.109 625.647 695.471 643.881 513.091 696.292 528.46 513.646 697.11529.07

6288.77

6

Savings with installation of capacitors in Type-A &B Load Unbalances

0% 5% 10% 15% 20%0

5000

10000

15000

20000

25000

Type-A Type-B

Load Unbalance (%)

Sav

ings

($)

Un balance (%) Type-A

Powers taken from the substation (kVA)Without capacitor With capacitor

0 3390 +2560.3i 3335.5+417.78i5 3390.3+2561i 3336.7+213.48i

10 3391.5+2562.7i 3336.7+214.54i15 3393.3+2565.5i 3337.3+225.96i20 3395.8+2569.3i 3339.4+289.56i

Un-balance (%) Type-B

Power taken from the substation (kVA)

Without capacitor With capacitor

0 3390+2560.3i 3335.5+417.78i5 3212.2+2423.8i 3167.5+409.21i

10 3036.1+2289.2i 2995+389.47i15 2861.4+2156.5i 2824.3+315.45i20 2688.2+2025.5i 2656.5+472.4i

Powers taken from the substation for 25 bus system with type-A/B unbalance

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 C-phase.

5. It is also observed that savings are slightly increasing with increase of load unbalance.

Type A 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.

Type B 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 percentage of type-A unbalance. Voltage unbalance in phase-B decreasing and in phase-C increasing. Shunt capaci-tive reactive power requirement in phase-B is lower than phase-C.Total shunt capacitive reactive power supplied un-der type-A unbalance is more than type-B unbalance.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.

CONCLUSIONS

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