[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

Current carrying
conductor
Flux in core
Steel core
Flux lines
Exciting winding
Second winding
FIGURE 1.1 Magnetic field around conductor.
Flux lines
FIGURE 1.3 Two coils applied on a steel core.
B = 0 H (1.7)
FIGURE 1.2 Magnetic field around conductor induces voltage in second conductor.
and
E = N d/dt (1.5)
= (2E)/(2 f N) (1.6)
Since the amount of flux linking the second coil is a small percentage of the flux from the first coil,
the voltage induced into the second coil is small. The number of turns can be increased to increase the voltage
output, but this will increase costs. The need then is to increase the amount of flux from the first coil
that links the second coil.
1.2 Iron or Steel Core Transformer
Second conductor
in flux lines
The ability of iron or steel to carry magnetic flux is much greater than air. This ability to carry flux is
called permeability. Modern electrical steels have permeabilities in the order of 1500 compared with 1.0 for
air. This means that the ability of a steel core to carry magnetic flux is 1500 times that of air. Steel cores
were used in power transformers when alternating current circuits for distribution of electrical energy
were first introduced. When two coils are applied on a steel core, as illustrated in Figure 1.3, almost
100% of the flux from coil 1 circulates in the iron core so that the voltage induced into coil 2 is equal
to the coil 1 voltage if the number of turns in the two coils are equal.
Continuing in the MKS system, the fundamental relationship between magnetic flux density (B) and
magnetic field intensity (H) is:
where 0 is the permeability of free space 410 –7 Wb A –1 m –1 .
Replacing B by /A and H by (I N)/d, where
= core flux in lines
N = number of turns in the coil
I = maximum current in amperes
A = core cross-section area
the relationship can be rewritten as:
where
d = mean length of the coil in meters
A = area of the core in square meters
Then, the equation for the flux in the steel core is:
= ( N A I)/d (1.8)
= ( 0 r N A I)/d (1.9)
where r = relative permeability of steel 1500.
Since the permeability of the steel is very high compared with air, all of the flux can be considered as
flowing in the steel and is essentially of equal magnitude in all parts of the core. The equation for the
flux in the core can be written as follows:
= 0.225 E/fN (1.10)
where
E = applied alternating voltage
f = frequency in hertz
N = number of turns in the winding
In transformer design, it is useful to use flux density, and Equation 1.10 can be rewritten as:
where B = flux density in tesla (webers/square meter).
B = /A = 0.225 E/(f A N) (1.11)
© 2004 by CRC Press LLC
© 2004 by CRC Press LLC