Alstom SHPM 101 - Quadrilateral Ground Fault Characteristics

SERVICE MANUAL R5888B
QUADRAMHO Chapter 1
Appendix B
Page 2 of 2
Quadrilateral ground fault characteristics
A typical Zone 1/Zone 2 quadrilateral ground fault characteristic is shown in
Figure 19. The reach line has a nominal 3° clockwise angle with respect to the
horizontal axis. The reach line will vary however, for fault conditions where the
neutral current I
N
is not in phase with the particular phase current I
Ph
. The resistive
axis of the impedence diagram is in phase with the particular phase current I
Ph
.
For Zone 1 elements, the reach line is in phase with the neutral current I
N
with the
3° variation. For Zone 2 and Zone 3 elements the reach line is in phase with the
combined current I
PH
+ I
N
.
For Zone 1 and Zone 2 the cross polarized directional line is at right angles to the
relay set characteristic angle and passes through the offset point along the source
impedance vector according to the constant K
1
given in table 1 for mho ground
fault elements times p. For Zone 3 the reverse offset line is offset from the origin
along the set characteristic angle according to the reverse offset setting and it is
parallel to the Zone 3 reach line.
The impedance Z
RE
is the ground loop reach setting of the quadrilateral element
and is determined from the relay phase and neutral coarse impedance settings
acted on by the fine zone multiplier settings. Z
SE
is the Source ground loop
impedance behind the relay.
Comparator K
1
K
2
type
Length of captive point vector to 100% cross-polarised characteristic
Phase fault 0.138 – 1.0
α
= cos
–1
(|Z
S
|– 0.16|Z
R
| sin β)
2
(0.16|Z
S
|+ 0.16|Z
R
| cos β)
2
+ (|Z
S
|0.16|Z
R
| sin β)
2
|Z
C
| = ([|Z
S
| sin α)
2
+ (|Z
R
| cos (α – β))
2
])
Earth fault * –K.(3p) –(3p)
(2 + q) (2 + q)
Determined interactively using:
Z
C
sin Θ = 0.16
(2 +
p )
(2 +
q )
. Z
S
+ Z
C
Y = 0.16x
(Figure 2)
*K is found from 6.25 = (2 + p ) – p – p
3K.| p | | p |
p =
Z
S0
Z
S1
q =
Z
R0
Z
R1
α = Angle between (Z
S
+ Z
R
) or (Z
S
' + Z
R
) and Z
S
or Z
S
'
β = Angle between Z
S
or Z
S
' and Z
R
p=
Z
SC
Z
S
Z
R
= Positive sequence impedance reach setting of mho element
Z
S
= Source impedance behind relaying point
Z
C
= Captive point impedance vector
Note: For sketching characteristic in second quadrant use –β in formula to find
new value of α