ABB RELION 670 Series Technical Manual page 196

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