John Vincent
March 2012
Bus Bar Design
This document describes rule-of-thumb design laws for unconfined bus bars
operating at or near dc conditions in open space. At higher frequencies the “skin
effect” must be considered. In multiconductor systems (such as magnet coils) the
“proximity effect” must be accounted for and the thermodynamics gets tougher. In
modern power electronics based equipment switching at high frequency, all of these
effects occurring simultaneously contribute to the conductor heating.
Theoretically it is possible to go into this subject in great depth and consider the surface
emissivity, air properties and movement, radiation, convection, and conduction for
different geometry’s in differing orientations; this is not the approach taken here.
This note describes a practical rule-of-thumb for the conductor surface heat transfer limit
and from it derives some useful design relationships. Experimentally, it is found that bus
bars run near room temperature when the heat transfer is limited to 0.1 (Watts/in2). The
bus bars run hot when the heat transfer approaches 0.25 (Watts/in2). (note: since the bus
bar temperature is principally a function of the surface area, the best shape is a very thin
ribbon whereas the worst shape is cylindrical as are all wires!). Using this empirical
knowledge, rule-of-thumb design relationships can be established.
1. (Power Lost)/(Unit Length) in (Watts/cm)
𝑰𝟐𝒐 𝝆
𝑷𝒍 =
𝑨𝒄
where;
𝝆 : resistivity in (Ohms*cm), Ac : Conductor crossectional area in cm2, Io : Amperes
2. (Heat Transfer)/(Unit Area) in (Watts/cm2)
QA =
Pl
I 2ρ
= o
As Ac As
where;
As: conductor surface area in (cm2/unit length)
3. Rules-of-Thumb boundary conditions for heat transfer limits
3. Rules-of-Thumb boundary conditions for heat transfer limits
2
in Watts/in2
0.1 ≤ QA 0.1
≤ 0.25
≤ Qexpressed
A ≤ 0.25 expressed in Watts/in
≤ Qexpressed
expressed
in2Watts/cm2
Watts/cm
0.015 ≤ Q0.015
A ≤ 0.04 in
A ≤ 0.04
cool → hot
cool → hot
2
I o2A
ρ A = I 0 ρ with Q expressed in2 Watts/cm2
A in Watts/cm
QA expressed
Ac As =
c with
s
QA
QA
4. Rectangular
Bus Bar
4. Rectangular
Bus Bar
h
w
(w) + h )(wh )
Ac As = 2 ( wA+c Ahs) (=wh
∴
hence:
2
2
" h−%h +Ac Ahs  + Ac As with h constant
h w=
w = − + $ '2+  2 with hhconstant
#4&
4
2h
or
or
2
2
%w + AcAws  + Ac As with w constant
w h =" w
−
h = − + $ '2 +  2 with wwconstant
#4&
4
2h
if w >>h as is typical then:
if w >>h as is typical then:
w=
Ac As
2hw =
Ac As
h
5. Cylindrical Bus (like wire)
5. Cylindrical Bus (like wire)
5. Cylindrical Bus (like wire)
r
r
Ac As = πr 2 * 2πr = 2π 2 r 3
Ac As = π r 2 * 2π r = 2π 2 r 3
∴
Ac As = πr 2 * 2πhence:
r = 2π 2 r 3
1
6. Test against known values
6. Test against known values
 A A 3 1
r =  ∴!c A2sc As $ 3
r=2#π 2 &
" 2π 1%
 A A 3
r =  c 2s 
 2π 
The following table illustrates the use of this formulation versus NEC data for
The
following unconfined
table illustrates the use of this formulation versus NEC data for
6. Testconfined
againstand
known values cables rated at 90 degrees Celcius.
confined and unconfined cables rated at 90 degrees Celcius.
The following table illustrates the use of this formulation versus NEC data for
confined and unconfined
cablesConductor
rated at 90Current
degreesRating
Celcius.
Circular
1800
Amperes Amperes
1600
Circular Conductor Current Rating
1400
1800
1200
1600
1000
1400
800
1200
600
1000
400
800
200
600
0
400 0
500000
1000000
1500000
2000000
Circular Mils
200
0
0
NEC 90 DEG C Rating
Q=0.04
500000
1000000NEC 901500000
2000000
Q=0.015
DEG C Confined
Circular Mils
NEC 90 DEG C Rating
Q=0.015
Q=0.04
NEC 90 DEG C Confined