Correction of Errors Introduced by Instrument Transformers - Digital Signal Processing in Power System Protection and Control - page 102

Z

t m

i 2 ð t Þ dt ¼ 0 ; ð 7 : 13 Þ

t n

where t n is a beginning of saturation, and t m is an end of saturation.
Applying the rectangle integrating formula (Euler's procedure) the continuous
integral ( 7.13 ) can also be approximated numerically as follows:

S ð m Þ¼ T S X

m

i 2 ð k Þ:

ð 7 : 14 Þ

k ¼ n

Now, the detection of the first sample in the new unsaturated period m ? 1 may
be based on the formula:

Sign ½ S ð m Þ 6¼ Sign ½ S ð m þ 1 Þ: ð 7 : 15 Þ

7.2.3 Correction of the Secondary Current

Despite the transient errors caused by the CT core saturation, operation of the
protective devices may be correct, however, it demands careful processing of the
signals, what may be done in a number of ways.
If the aim of processing is to make proper operation of differential relays, the
best way is to use current signals only in the fraction of periods, when the CTs at
both sides are not saturated. Therefore, the differential current is detected taking
into consideration non-corrupted current samples of the input currents:

i 2 n 1 ð Þ; i 2 m þ ð Þ; etc., until the

beginning of saturation in the next period. In fact, this unsaturated fragment may
be artificially expanded particularly in the cases, when the secondary current
samples i 2e ðÞ; i 2e n þ 1

ð Þ; i 2 n 2 ð Þ; i 2 n 3 ð Þ; etc., and i 2 ðÞ; i 2 m þ 1

ð Þ and i 2e n þ 2 ð Þ are estimated by the formula ( 7.12 ),

which returns very accurate results.
If the aim of the processing is the proper operation of protective devices that are
based on the calculation of the fundamental frequency components (overcurrent,
distance, etc.), the amplitude I 1 of the current ought to be determined on the
ground of the distorted current signal. The following simple secondary current
signal model valid in the fraction of period during which the CT core is not
saturated and the transformation of the current is correct, is represented by the
formula:

i 2 ¼ N i i 1 I a e Ta I 1m cos ð xt a Þ; ð 7 : 16 Þ

where N i is a current transformer ratio, i 1 is a primary current, I a is a DC decaying
component initial value, T a is a time constant of the decay, I 1m is an amplitude of
the AC component, and a is a phase angle of the AC component.