Question

A 1000/1 A, 5 VA, UPF bar-primary measuring current transformer has 1000 secondary turns. The current transformer exhibits a ratio error of 0.1 % and a phase error of 3.438 minutes when the primary current is 1000 A. At this operating condition, the rms value of the magnetization current of the current transformer (in amperes, rounded off to two decimal places) is 

Answer 1

Concept:

Phase Angle error, \(\beta = \frac{{180}}{\pi } \times \frac{{{I_\mu }\cos \delta - {I_w}\sin \delta }}{{n{I_s}}}\)

n is the number of secondary turns

I_s is the secondary current

I­μ is the magnetizing current

I_w is the core loss current

Calculation:

Phase angle error, β = 3.438 mins

\(= \frac{{3.438}}{{60}} = 0.0573^\circ\)

Secondary turns (n) = 1000

Secondary current (I_s) = 1 A

Load is UPF, so δ = 0

Hence, \(\beta = \frac{{180}}{\pi } \times \frac{{I\mu }}{{n{I_s}}}\)

\( \Rightarrow {I_\mu } = \frac{{\beta\; \times \;\pi\; \times \;n\; \times \;{I_s}}}{{180}} = \frac{{0.573\; \times \;\pi\; \times \;1000\; \times \;1}}{{180}} = 1\;A\)

Hence, the rms value of the magnetising current of CT is 1 Amp.