Page 230 - Power Quality in Electrical Systems

212 Chapter Fourteen

The magnitude of the sensed voltage is

I R 1
p B
ZV Z a b s0.5V ds0.999648d 0.4998 V
sense N 2
s L v
m
a b 1
Ä R B
Therefore, the magnitude error is only 0.04 percent. We find the
11
angle as follows:
vL m
1
/V 90 tan a b 90 88.5 1.5
sense R B
Therefore, the sensed voltage has a 1.5 phase shift in relation to the
primary current. The power dissipated in the burden resistor is due to
the secondary current of 0.5A, and is

2
P diss 5 I s R 5 0.25 W.
B
Example 14.2: CT error. A CT is utilized in a data acquisition system and
is used in the calculation of real power, reactive power, and the power
factor in a single-phase system with sinusoidal voltages and currents.
CT has an ideal magnitude response, but a positive phase shift of 5
degrees. Using data from this CT and other instrumentation, the data
acquisition system calculates values of:

■ Apparent power S 10 kVA
■ Real power P 9 kW
■ Reactive power Q 4.36 kVAr
■ Power factor PF 0.9 lagging
We shall determine the error in the four measurements due to the
phase shift through the CT.
The calculation of apparent power is correct, since calculation of S does
not depend on the phasing of the measured voltage and current. So, we
find

S 10 kVA

11
The 90 is due to the inductor at low frequencies. For a purely inductive circuit, the
voltage leads the current by 90 degrees.