ABB Relion 670 series - Page 196

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 37,
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