current between samples (
D
I) are brought from the input memory and fed to a recursive Fourier
filter.
The filter provides two orthogonal values for each input. These values are related to the loop
impedance according to equation
D
= × +
×
w
D
0
X
i
V
R i
t
EQUATION1547 V1 EN-US
(Equation 37)
in complex notation, or:
0
Re ( )
Re ( )
Re ( )
X
I
V
R
I
t
D
=
×
+
×
w
D
EQUATION1548 V1 EN-US
(Equation 38)
0
Im ( )
Im ( )
Im ( )
X
I
V
R
I
t
D
=
×
+
×
w
D
EQUATION1549 V1 EN-US
(Equation 39)
with
w
0
2
p
f
0
× ×
=
EQUATION356 V1 EN-US
(Equation 40)
where:
Re
designates the real component of current and voltage,
Im
designates the imaginary component of current and voltage and
f
0
designates the rated system frequency
The algorithm calculates
R
m
measured resistance from the equation for the real value of the
voltage and substitutes it in the equation for the imaginary part. The equation for the X
m
measured reactance can then be solved. The final result is equal to:
× D
-
× D
=
D
×
- D
×
m
Im (V)
Re (I) Re (V)
lm(I)
R
Re (I) lm(I)
lm(I) Re (I)
EQUATION1550 V1 EN-US
(Equation 41)
×
-
×
= w
D
×
- D
×
× D ×
m
0
Re (V) lm(I) lm(V) Re (I)
X
Re (I) lm(I)
lm(I) Re (I)
t
EQUATION1551 V1 EN-US
(Equation 42)
Section 7
1MRK 502 066-UUS B
Impedance protection
190
Technical manual
Содержание Relion 670 series
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