[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

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