Page 227 - Power Quality in Electrical Systems

Power Quality Measurements 209

I s

+

R V
L m B sense
Figure 14.10 A secondary circuit.
The current I s is the primary cur-
– rent referred to the secondary
through the turns ratio N s .
transformer, and termed it I . The value of I is stepped-down from the
s
s
primary and is
I p
r
I p 5
N s
We see that the sensed voltage V sense depends not only on the value of
the burden resistor R , but also on the value of the “magnetizing induc-
b
8
tance” L as measured on the secondary side. The transfer function
m

relating the reflected primary current I to the sensed voltage V sense in
p
the Laplace domain is
V sense ssd 5 L s
m
r
I p ssd L m
s 1 1
R B
9
The magnitude and phase of this transfer function are
2
V sense sv d L v
m
` r 2 ` 5
I p sv d L m 2
a vb 1 1
Ä R
B
V sense svd p 21 vL m
/ 5 2 tan a b
r
I p svd 2 R B
Note that at very low frequencies (well below R B /L m ), the transfer
function magnitude approaches zero. This is as expected, because a
transformer does not pass currents at DC. At very high frequencies,
the magnetizing inductance L m essentially becomes an open circuit and
all the current passes through the R B burden resistor.

8
The magnetizing inductance is the inductance you would measure if you put the sec-
ondary winding on an impedance analyzer.
9
Note that the phase is expressed in radians. The conversion to degrees is degrees
radians (360/2 ).