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Electrical Machines

LSEGG216A9080V

TransformerTransformerLosses & EfficiencyLosses & Efficiency

Week 3Week 3

ObjectiveObjectivess1. Describe the power losses which occur in a transformer

2. Describe the tests which allow the power losses of a transformer to be calculated

3. Calculate transformer losses and efficiency using test results

4. Define the all day efficiency of a transformer5. Calculate the all day efficiency of a transformer

6. Describe the relationship between transformer cooling and rating

5. Calculate the all day efficiency of a transformer

6. Describe the relationship between transformer cooling and rating

7. Describe the methods of cooling

8. List the properties of transformer oil

9. Describe the tests conducted on transformer oil

Objectives

Transformer RatingsTransformer RatingsTransformers are rated to supply a given output in

Volt Ampsor

VAat a specified frequency and terminal voltage.

Transformer RatingsTransformer RatingsThey are NOT rated in Watts

The load power factor is unknown

IVS PFSPower

PFPowerS

Transformer RatingsTransformer RatingsThey are NOT rated in Watts

The load power factor is unknown

ProblemV1 = 6,351

VV2 = 230 V

S = 2 kVA

Power output at unity PF ?

P = 2 kVA x 1

P = 2 kW

Power = S x PF

Problem

PFVSI

V1 = 6,351 V

V2 = 230 V

S = 2 kVA

Full load secondary current at 0.8 PF ?

I = 10.87 A0.8230

2000I

Student Exercise 1

PFSPower

V2 = 200 VV1 = 1270 V

S = 20 kVA

0.1000,20 P

P = 20 kW

(a) Power output at unity power factor

PFSPower

V2 = 200 VV1 = 1270 V

S = 20 kVA

8.0000,20 P

P = 16 kW

(b) Power output at 0.8 power factor

VxPFSI

V2 = 200 VV1 = 1270 V

S = 20 kVA

I = 100 A

(c) Full-load secondary current at unity power factor

200x1.020,000I

VxPFSI

V2 = 200 VV1 = 1270 V

S = 20 kVA

I = 62.5 A

(d) Secondary current when transformer supplies 10 kW at 0.8 power factor

200x0.810,000I

EfficiencyPowerInputPowerOutputη

LossesOutputInput

LossesPowerOutputPowerOutputη

Ratio between Input power and Output Power

PowerInputLossesPowerInputη

Efficiency

100PowerInputPowerOutputη%

Efficiency is normally expressed as a percentage

Transformer Efficiency

PowerIn

PowerOut

OvercomeIron

Losses

Overcome Copper Losses

Some Poweris used to:

η = 100%η = 95%η = 90%

Student Exercise 2

PFSPower

V1 = 230 V V2 = 32 V

S = 20 kVA

η = 90% PF = 0.85

(a) Power output of transformer

0.85100P

P = 85 W

InOutη

V1 = 230 V V2 = 32 V

S = 20 kVA

η = 90% PF = 0.85

(b) Power input

P = 94.4 Wη

OutIn

0.9W 85In

LossesOutIn

V1 = 230 V V2 = 32 V

S = 20 kVA

η = 90% PF = 0.85

(c) Losses

P = 9.4W

Losses8594.4

Transformer Losses

Copper Losses (Cu)

•Varies with load current

•Produces HEAT •Created by resistance of windings•Short circuit test supplies copper losses

Short Circuit TestCopper Losses

(Cu)

SecondaryShort Circuited

Limited

Supply Voltage ≈ 5-10 %

Wattmeter indicates Copper Losses (Cu)

Short Circuit Test

1000.5lossCopper 2

Copper Losses (Cu)•Finds Cooper losses at full load

•Copper losses vary with the square of the load Full load Cu loss = 100

WTransformer loaded at 50%

PCu = 25 W1000.25lossCopper

0102030405060708090

100110120130140150

0 10 20 30 40 50 60 70 80 90 100 110

Copper Losses (Cu)

% Load

Cu L

osse

s (W

)

Transformer LossesIron Losses

(Fe)•Fixed•Always present•Related to transformers construction

Eddy CurrentsReduced by laminationsProduces HEAT

HysteresisReduced by using special steels in laminations

Open Circuit TestFinds Iron Losses

(Fe)

Full Supply Voltage

SecondaryOpen Circuit

Wattmeter indicates Iron Losses (Fe)

Transformer EfficiencyStudent Exercise 3

100PowerInputPowerOutputη%

LossesCuLoadFullload 2%Cu Losses

100PowerInputPowerOutputη%

Sout = 30 kVA Fe = 220 WCu FL= 840 W

Calculate η%at Full Load

100Losses OutputPowerOutputη%

100k 0.22k 84k 30k 30η%

.0

η% = 96.6%

100Losses OutputPowerOutputη%

Sout = 30 kVA Fe = 220 WCu FL= 840 W

Calculate η%at 75%Load

1000.220.75 22.522.5η% 2

84.0

η% = 97%

1000.220.4725 22.522.5η%

5.223075.0 outS 5.47284075.0 2 75%Cu

100Losses OutputPowerOutputη%

Sout = 30 kVA Fe = 220 WCu FL= 840 W

Calculate η%at 50%Load

1000.220.5 1515η% 2

84.0

η% = 97.21%

1000.220.21 1515η%

15305.0 outS

100Losses OutputPowerOutputη%

Sout = 30 kVA Fe = 220 WCu FL= 840 W

Calculate η%at 25%Load

1000.220.25 7.57.5η% 2

84.0

η% = 96.49%

1000.220.0525 7.57.5η%

5.73025.0 outS

100% η = 96.6%75% η = 97%50% η = 97.21%25% η = 96.49%

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 30 40 50 60 70 80 90 100 11096.00

97.00

% Load

Loss

es (

W)

η%

Cu Losses

Fe Losses

η%

Fe = Cu =Max η

Maximum Efficiency

Fe = Cu =Max η CuLoadFe 2

2LoadCuFe

LoadCuFe

Load840220

Fe = 220

Cu = 840

Load %= 51.18%

1000.220.5118 300.5118300.5118η% 2

84.0

1000.2215.35η%

22.035.15

η%= 97.21%

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 30 40 50 60 70 80 90 100 11096.00

97.00

All Day Efficiency

• Most Transformers are connected permanently

• The time that the transformer has to be calculated when determining efficiency

• Able to determine the best transformer for the application

by its efficiency

All Day EfficiencyTransformer A

Sout = 300 kVA Fe = 1.25 kVA Cu = 3.75 kVAHours Load kW kWh % Load Cu Loss Cu kWh Fe kWh Losses kWh Input kWh

1.00 6.00 5 100 500.0 33.33 0.42 2.08 6.25 8.33 508.336.00 7.00 1 200 200.0 66.67 1.67 1.67 1.25 2.92 202.927.00 8.00 1 300 300.0 100.00 3.75 3.75 1.25 5.00 305.008.00 9.00 1 360 360.0 120.00 5.40 5.40 1.25 6.65 366.659.00 12.00 3 300 900.0 100.00 3.75 11.25 3.75 15.00 915.0012.00 14.00 2 280 560.0 93.33 3.27 6.53 2.50 9.03 569.0314.00 18.00 4 300 1200.0 100.00 3.75 15.00 5.00 20.00 1220.0018.00 20.00 2 360 720.0 120.00 5.40 10.80 2.50 13.30 733.3020.00 22.00 2 280 560.0 93.33 3.27 6.53 2.50 9.03 569.0322.00 1.00 3 200 600.0 66.67 1.67 5.00 3.75 8.75 608.75

5900.0 5998.02

98.37

Time Period

P out kWh = P in kWh =

% Eff =

All Day EfficiencyTransformer B

Sout = 300 kVA Fe = 2.5 kVA Cu = 2.5 kVAHours Load kW kWh % Load Cu Loss Cu kWh Fe kWh Losses kWh Input kWh

1.00 6.00 5 100 500.0 33.33 0.28 1.39 12.50 13.89 513.896.00 7.00 1 200 200.0 66.67 1.11 1.11 2.50 3.61 203.617.00 8.00 1 300 300.0 100.00 2.50 2.50 2.50 5.00 305.008.00 9.00 1 360 360.0 120.00 3.60 3.60 2.50 6.10 366.109.00 12.00 3 300 900.0 100.00 2.50 7.50 7.50 15.00 915.0012.00 14.00 2 280 560.0 93.33 2.18 4.36 5.00 9.36 569.3614.00 18.00 4 300 1200.0 100.00 2.50 10.00 10.00 20.00 1220.0018.00 20.00 2 360 720.0 120.00 3.60 7.20 5.00 12.20 732.2020.00 22.00 2 280 560.0 93.33 2.18 4.36 5.00 9.36 569.3622.00 1.00 3 200 600.0 66.67 1.11 3.33 7.50 10.83 610.83

5900.0 6005.34

98.25% Eff =

Time Period

P out kWh = P in kWh =

Transformer Cooling• Transformer ratings can be increased if their windings are cooled

by some external means

• The most common cooling mediums are in direct with transformer windings;

and/orAir Oil• The most common methods of circulation are

Forced

and/or Natural

Transformer Classification• Transformers are allocated symbols which indicate the type of

cooling used• Can consist of up to 4 letters indicating the cooling system

1st Letter 2nd Letter 3rd Letter 4th Letter

The cooling medium in contact with the windings

The cooling medium in contact with the external cooling

system

Kind of Medium

Circulation type

Kind of Medium

Circulation type

Transformer ClassificationType AN

Dry Transformer withNatural Air Flow

Air Natural

Transformer ClassificationType AF

Dry Transformer withForced Air Flow

Air Forced

Transformer ClassificationType ONAN

Oil Tank Cooling Natural Oil Flow - Natural Air Flow

Oil Natural Air Natural

Transformer ClassificationType ONAF

Oil Tank Cooling Natural Oil Flow - Forced Air Flow

Oil Natural Air Forced

Transformer ClassificationType OFAF

Oil Tank Cooling Forced Oil Flow – Forced Air Flow

Oil Forced Air Forced

Transformer Oil

• Low Viscosity• High Flash point• Chemically inert• Good insulator

Acts as Coolant & Insulator

Transformer Oil Tests• Dielectric Strength• Acidity • Power factor • Interfacial tension • Dissolved Gas

THE END