Busbar design

David Chapman
Copper Development Association
david.chapman@copperdev.co.uk
Busbar Design Basics

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 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

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Busbar System Current Ratings
Busbar ratings are determined only by the
maximum desired working temperature
At working temperature:
heat generated = heat lost

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Busbar ratings depend on:
• Working and ambient temperatures
• Heat lost from the busbar
– by convection
– by radiation
• Heat generated in the busbar

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25.0
25.1
66.7
v
Pcv
θ
=
Power dissipated by convection is given by:
where
θ is the temperature rise above ambient
v is the vertical height of the surface
Pcv1Pcv2
v

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Power dissipation per metre length v Vertical height
0
40
80
120
160
0 50 100 150 200
Vertical height (mm)
Powerdissipationpermetrelength(W)Convection (for 80 C temperature rise)

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Power dissipated by radiation is given by:
( ) 84
1
4
2 107.5 −
×−= TTPr ε
where
Pr is the power dissipated per square metre
T2 is the working temperature, K
T1 is the ambient temperature, K
ε is the emissivity
Pr
Pr

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The emissivity, ε, 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

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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!

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Pr
Pr
Pr
Pr
Pr Pr
No radiation heat loss
from internal surfaces

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Radiation power dissipation v Working temperature
0
20
40
60
80
100
273 323 373
Absolute Working Temperature (K)
Powerdissipation(Wpersqm)
Radiation (for 30 C ambient)

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for 100 mm vertical height, 30 C ambient
Total 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)
Powerdissipation(Wpersqm)
Convection
Radiation
Total

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RIP 2
=
a
l
IP
ρ2
=
The power generated by current in the busbar is:
where
ρ is the resistivity of the material
a is the cross sectional area
l is the length

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At some temperature, the heat generated in the
busbar is equal to the total heat lost by convection
and radiation.
[ ] [ ]rci PPP +=

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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

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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

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Cost of bar
0
5
10
15
0 100 200 300 400 500 600
Cross sectional area (sqmm)
Costofbarpermetre($)

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Cost of losses - 5 years
0
10
20
30
0 100 200 300 400 500 600
Costoflossesover5years($)

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Economic Sizing of Busbars
Total cost - 5 years
0
10
20
30
0 100 200 300 400 500 600
Lifetimecostpermetre($)
Cost of bar
Cost of loss
Total

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Busbar calculation software

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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

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Summary of Busbar Material Characteristics
High 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
david.chapman@copperdev.co.uk

Busbar design

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