Digital Signal Processing Reference
In-Depth Information
Fig. 7.1 Equivalent circuit
of a capacitive voltage
transformer
C
L
L
T1
R
R
T1
L
L
T
2
R
R
T2
L
R
v
1
R
R
f
0
C
C
L
v
2
v
i
T1
m
C
L
L
f
0
R
FFe
where N
u
is a transformation ratio of the CVT, F(s) is a Laplace transfer function
of the circuit, and v
1
;
v
2
are primary and secondary CVT voltages.
The correction ought to process the secondary voltage by a transfer function
which is equal to inverse of the CVT transfer function. Therefore, the corrected
secondary voltage v
2c
becomes:
v
2c
¼
v
2
F
1
ð
s
Þ
v
1
N
u
;
ð
7
:
2
Þ
where F
1
ð
s
Þ¼
1
=ð
F
ð
s
ÞÞ:
Digital representation of the transfer function F
1
ðÞ
may be obtained by
introducing discrete operators of integration, e.g. the Euler's operator:
s
1
)
T
S
z
1
1
z
1
;
ð
7
:
3
Þ
remembering, that multiplication by z
-1
in the Z-transform domain represents
delay by one sampling period T
S
in time domain.
7.2 Correction of Current Transformer Errors
7.2.1 Formulation of the Problem
The problems with errors of current transformers are much greater than the ones of
voltage transformers. It is so because:
• errors of the CTs are much more damaging for proper operation of digital
devices,
• current transformers are strongly non-linear, because of the non-linear magne-
tizing characteristic of the cores, therefore their errors are much more difficult to
calculate and correct,
• due to the hysteresis loop of the magnetization characteristic of the core it is
hardly possible to establish the starting value of the core flux,
• range of levels of primary currents and the time constants of their DC com-
ponents are great.
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