[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)
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From statement 1, the primary energy required to magnetize the core is a product of the flux in the<br />
core and the magnetic reluctance of the core. This energy is called the magnetomotive force, mmf, and<br />
is defined as follows:<br />
S S<br />
mmp<br />
S S<br />
mmp<br />
mmf = ¬= È Î Í ˘ È ˘ È ˘<br />
f k<br />
Z I<br />
Z I<br />
1 ˙ k2Í<br />
˙ = kk<br />
1 2Í<br />
˙<br />
NS f ˚ Î ACmC˚<br />
Î NS f AC mC˚<br />
(2.6.4)<br />
FIGURE 2.6.4 Typical composite core.<br />
TABLE 2.6.1 Core Materials<br />
Material<br />
(0.009–0.014 in.)<br />
Saturation<br />
Density, T<br />
Initial<br />
Permeability,<br />
@ 0.004 T<br />
Maximum<br />
Permeability,<br />
@ T<br />
Trade Names<br />
80% Ni/Fe/Mo 0.760 35,000 150 k @ 0.4 T SuperPerm 80 a<br />
Hymu 80 Mu-Metal b<br />
4–79 Permalloy c<br />
49% Ni/Fe/Mo 1.200 5,000 60 k @ 0.4 T Super Perm 49 a<br />
High Perm 49 c<br />
48-Ni<br />
4750 b<br />
3% Si/Fe – M3 1.900 8,000 51 k @ 1.15 T Microsil a<br />
Silectron d<br />
Oriented T-S e<br />
Hipersil a<br />
3% Si/Fe – M4 1.900 7,200 48 k @ 1.15 T<br />
3% Si/Fe – M6 1.900 6,700 40 k @ 1.15 T<br />
a<br />
Magnetic Metals Co.<br />
b<br />
Allegheny Ludlum Steel.<br />
c<br />
Carpenter Steel.<br />
d<br />
Arnold <strong>Engin</strong>eering.<br />
e<br />
Armco (now AK Steel).<br />
where<br />
f = flux in the core<br />
¬ = magnetic reluctance<br />
k 1 = constant of proportionality<br />
k 2 = constant of proportionality<br />
Z S = secondary impedance<br />
mmp = core mean magnetic path<br />
I S = secondary current<br />
A C = core cross-sectional area<br />
N S = number of secondary turns<br />
m C = permeability of core material<br />
f = frequency, Hz<br />
The magnetic reluctance, in terms of Ohm’s law, is analogous to resistance and is a function of the<br />
core type used. An annular or toroidal core, one that is a continuous tape-wound core, has the least<br />
amount of reluctance. A core with a straight cut through all of its laminations, thereby creating a gap,<br />
exhibits high reluctance. Minimizing gaps in core constructions reduces reluctance. Figure 2.6.5 shows<br />
some of the more common core and winding arrangements. Generally — after the steel material is cut,<br />
stamped, or wound — it undergoes a stress-relief anneal to restore the magnetic properties that may<br />
have been altered during fabrication. After the annealing process, the core is constructed and insulated.<br />
From statement 2, the core permeability, m C , changes with flux density, f/A C . Neglecting leakage flux,<br />
we can now see the error-producing elements. From Equation 2.6.4, an increase in any of the elements<br />
in the denominator will decrease errors, while an increase in Z S and mmf will increase errors.<br />
There are also other contributing factors that, based on the construction of the instrument transformer,<br />
can introduce errors. The resistance of the windings, typically of copper wire and/or foil, introduces<br />
voltage drops (see Figure 2.6.6). Moreover, the physical geometry and arrangement of the windings —<br />
with respect to each other and the core — can introduce inductance and, sometimes, capacitance, which<br />
has an effect on magnetic leakage, reducing the flux linkage from the primary circuit and affecting<br />
performance. A winding utilizing all of its magnetic path will have the lowest reactance. Figure 2.6.5<br />
shows some typical winding arrangements and leakage paths.<br />
Figure 2.6.6 illustrates an equivalent transformer circuit, where<br />
V P = primary-terminal voltage<br />
R ex = wattful magnetizing component<br />
V S = secondary-terminal voltage<br />
Z = secondary burden (load<br />
E P = primary-induced voltage<br />
X ex = wattless magnetizing componen<br />
E S = secondary-induced voltage<br />
I ex = magnetizing current<br />
I P = primary current<br />
I S = secondary current<br />
N P = primary turns<br />
N S = secondary turns<br />
R P = primary-winding resistance<br />
R S = secondary-winding resistance<br />
X P = primary-winding reactance<br />
X S = secondary-winding reactance<br />
© 2004 by CRC Press LLC<br />
© 2004 by CRC Press LLC