Page 935 - Industrial Power Engineering and Applications Handbook

Carrying power through metal-enclosed bus systems 281885
A = area of cross-section of core in square metres
k = total length of the magnetic circuit in metres

or

where

tarnpings of and ,u is a design parameter for the silicon steel and
0.2-0.5 rnrn thick = BIH.
C.R.G.0 silicon steel
Reactor magnetic laminations where
circuit (length = k) B = flux density in wb/m'
iy - Variable air gap, say, 1.5 rnm to 5.0 rnrn and H = magnetic field strength in Ah
It may be observed that the value of permeability is a
Figure 28.26 A typical reactor core
function of the flux density being attained to energize
the magnetic circuit. It is therefore not a constant parameter
where and is measured at a particular flux density.
L = self-inductance of the choke in henry (H)
@ = flux produced in Weber (wb)
I, = rated current in Amps Example 28.10
Z, = number of turns in the choke = 1 Consider a bus duct having a rated current of 4000 A and an
unbalanced current in the middle phase of 4400A. Determine
(since it will be used like a bar primary. as shown the size of the reactor to achieve a balanced voltage system.
in Figure 28.26)
Solution
Total reluctance R, of the magnetic circuit of the choke If the line voltage = 440 V
- MMF - 2, '1,
($ 4 then Vph = 440/& = 254 V
L ' I,
z, (4dOO 4400
since I$ = ~ :. X, = 254 x - L]
~
- 254x400
4000 x 4400
The total reluctance of an iron choke (Figure 28.26) can
also be expressed by R, = R,,, + R,,,, = 0.00577 = 2 x K x 50 x L (for a 50 Hz system)
whcrc R,,, = reluctance of the air gap or L= 0.00577
21, 2 x 3.14 x 50
-__ = 18.38 x H
-
Po A
Lx l
and R,,,,, = reluctance of the iron path :. Total flux @ = 2
k-21, zc
-
-
PC .Pu, A i.e. 4 = 18.38 x lo4 x 4000 wb
1
(28.9) = 73.52 x wb
Therefore area of cross-section of the core
where
I, = length of the air gap in metres (Figure 28.26)
pel = permeability* of air (free space) = 47r. lo-' H/m
p, = relative permeability of the silicon steel used for
the laminations in H/m - 7352 (assuming B = 1.1 wb/m')
1.1
= 66.84 x square metres.
*Permeability defines the magnetic property of a material, and is a
measure of how easily it can be magnetized. The greater the If we assume the stacking factor of the core laminates to
permeability of a material. the easier it is to magnetize. be 0.9, the gross cross-sectional area of the core