Correction of Errors Introduced by Instrument Transformers - Digital Signal Processing in Power System Protection and Control - page 101

between the samples (n) and (n - 1). The simplest way is to assume that the first
order derivatives are equal:

i 2e ð n Þ i 2 ð n 1 Þ
T S

i 2 ð n 1 Þ i 2 ð n 2 Þ
T S

; ð 7 : 7 Þ

which leads to the formula:

i 2e ð n Þ 2i 2 ð n 1 Þ i 2 ð n 2 Þ: ð 7 : 8 Þ

And now one may apply the condition ( 7.4 ) to find out whether there was a
rapid change in the waveshape.
Second and third order derivatives can be calculated with the well known
formulae:

i 00 ð n Þ i 0 ð n Þ i 0 ð n 1 Þ
T S

; ð 7 : 9 Þ

i 000 ð n Þ i 00 ð n Þ i 00 ð n 1 Þ
T S

: ð 7 : 10 Þ

If one assumes that the second order derivative is the same in nth sampling
period, then the value of i 2e ðÞ may be estimated by the formula:

i 2e ð n Þ 3i 2 ð n 1 Þ 3i 2 ð n 2 Þþ i 2 ð n 3 Þ; ð 7 : 11 Þ

which is far more accurate than ( 7.8 ). However, if one wants to increase accuracy
even more, one may assume that the third derivative is to be the same between the
samples, what gives the condition:

i 2e ð n Þ 4i 2 ð n 1 Þ 6i 2 ð n 2 Þþ 4i 2 ð n 3 Þ i 2 ð n 4 Þ; ð 7 : 12 Þ

The same procedure may be repeated to estimate the sample i 2e ðÞ what marks
the end of saturation.
Saturations of CTs caused by the primary currents with large DC components
are much more likely than in case of transformation of the steady state symmet-
rical currents. It is because the DC components, particularly the ones with long
time constants, increase the magnetic flux in the core more intensely than the
sinusoidal currents. Therefore, correction of the errors caused by saturation of CTs
in transient states are more needed than the correction in steady states.
Determination of the moments, which mark the beginning of core saturation
and the end of it, may be done by the same formulae, which were developed for
symmetrical currents (Eqs. 7.4 - 7.12 ). This means that between the samples
(n) and (m) the transformation is corrupted by the saturation of the magnetic core.
The other method of marking the CT saturation ending point can be based on
the fact (for CTs with resistive burden) that the integral of the secondary current
within the time span of saturation must be zero: