busbar design

David Chapman

Copper Development Association

[email protected]


Busbar Design Basics

www.leonardo-energy.org

Copper Development Associationwww.cda.org.uk

High electrical conductivity

• only silver is better than copper

Good thermal conductor

• heat reaches surface quickly

Strong (at working temperature)

• to withstand short circuit stresses

• low creep

Easy to joint

• resistant to corrosion

Materials for Busbar Systems



Busbar System Current Ratings

Busbar ratings are determined only by the

maximum desired working temperature

At working temperature:

heat generated = heat lost




Busbar ratings depend on:

• Working and ambient temperatures

• Heat lost from the busbar

– by convection

– by radiation

• Heat generated in the busbar



25.0

25.166.7

vPcv

Power dissipated by convection is given by:

where is the temperature rise above ambientv is the vertical height of the surface


Pcv1Pcv2v



Power dissipation per metre length v Vertical height

0

40

80

120

160

0 50 100 150 200

Vertical height (mm)

Po

we

r d

iss

ipa

tio

n p

er

me

tre

len

gth

(W

)Convection (for 80 C temperature rise)




Power dissipated by radiation is given by:

841

42 107.5 TTPr

wherePr is the power dissipated per square metreT2 is the working temperature, KT1 is the ambient temperature, K is the emissivity


Pr

Pr



The emissivity, , describes how effectively the surface radiates heat

For a perfectly polished surface, the value is close to zero - a very poor radiator

For a matt black surface, the value is close to 1 - a very good radiator




Bright copper has an emissivity of about 0.1

During use, the emissivity of the copper surface increases - and the current rating increases - as the copper darkens to reach an emissivity value of about 0.7

Tin plated copper has an emissivity of about 0.3 to 0.5

But painting bars reduces the current rating!





Pr

Pr

Pr

Pr

Pr Pr

No radiation heat loss from internal surfaces



Radiation power dissipation v Working temperature

0

20

40

60

80

100

273 323 373

Absolute Working Temperature (K)

Po

we

r d

iss

ipa

tio

n (

W p

er

sq

m)

Radiation (for 30 C ambient)




for 100 mm vertical height, 30 C ambientTotal power dissipation v Working temperature

0

100

200

300

400

500

600

700

800

900

1000

40 60 80 100 120 140

Working temperature (C)

Po

wer

dis

sip

ati

on

(W

per

sq

m)

Convection

Radiation

Total




RIP 2a

lIP

2

The power generated by current in the busbar is:

where

is the resistivity of the material

a is the cross sectional area

l is the length




At some temperature, the heat generated in the

busbar is equal to the total heat lost by convection

and radiation.

rci PPP




Calculation method:

1 Select working and ambient temperatures

2 Assume initial current density of 8 amps/mm2

3 Find appropriate size in standard range

4 Calculate heat generated due to current

5 Calculate heat loss at working temperature

6 If 4>5, increase size and return to 4

When 4=<5, this is smallest possible size

Minimum size calculation



The most economic size gives the lowest

lifetime cost. It is the minimum total cost of

•material

•installation and

•energy costs

over the circuit lifetime.

Higher purchase cost - lower running costs

Best economic sizing



Best economic sizingCost of bar

0

5

10

15

0 100 200 300 400 500 600

Cross sectional area (sqmm)

Co

st o

f b

ar p

er

me

tre

($)



Best economic sizingCost of losses - 5 years

0

10

20

30

0 100 200 300 400 500 600


Co

st

of

los

se

s o

ve

r 5

ye

ars

($

)



Economic Sizing of BusbarsTotal cost - 5 years

0

10

20

30

0 100 200 300 400 500 600


Lif

etim

e co

st p

er m

etre

($)

Cost of bar

Cost of loss

Total



Busbar calculation software



Further considerations

Having calculated the size of the bar, there are three further considerations:

• voltage drop

• skin effect

– increases apparent resistance by reducing effective area - important for:

thick busbars

high frequencies

harmonics generated by non-linear loads

• short circuit current



Summary of Busbar Material CharacteristicsHigh Conductivity

• low loss, low voltage drop

• >101.5 % IACS

Easy Formability• due to small grain size and advanced production

technology

• easy to bend without surface deformation

Good Flatness• simple reliable jointing

Good Straightness• easy installation, lower joint stress

David Chapman


[email protected]


busbar design

Business

busbar systems

busbar design basics

current rating increases

initial current density

ambient temperatures

c temperature

total heat

radiation heat loss