7.4.7
Operation principle
General
Under balanced and stable conditions, a generator operates with a constant rotor angle
(power angle), delivering active electrical power to the power system, which is
approximately equal to the input mechanical power on the generator axis, minus the small
losses in the generator. The currents and voltages are constant and stable. An out-of-step
condition is characterized by periodic changes in the rotor angle, that is, the synchronizing
power, rotational speed, currents and voltages. When displayed in the complex impedance
plane, these changes are characterized by a cyclic change in the complex load impedance
Z(R, X) as measured at the terminals of the generator, or at the location of the voltage
transformers of a power line connecting two power subsystems. This is shown in
-1.5
-1
-0.5
0
0.5
1
1.5
-1
-0.5
0
0.5
1
1.5
-------
------
------
-----
-----
-----
-----
-----
---
--
---
-
---
--
--
--
--
--
--
--
--
--
---
---
---
---
---
---
---
---
----
----
----
----
------
Real part (R) of Z in Ohms
Im
a
g
in
a
ry
p
a
rt
(
X
)
o
f Z
in
O
h
m
s
^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
--
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
--
-
-
0
1
Zone 1
Zone 2
The 1st
pole slip
occurred
relay
X in Ohms
The 2nd
pole slip
occurred
R in Ohms
RE
SE
2
3
to the 3rd
pole-slip
¬
trajectory
of Z(R, X)
Pre-disturbance
normal load
Z(R, X)
0
®
pre-disturbance Z(R, X)
1
®
Z(R, X) under 3-phase fault
2
®
Z(R, X) when fault cleared
3
®
Z when pole-slip declared
lens determined
®
by the setting
Pickup Angle = 120°
limit of reach
®
ANSI10000109-1-en.vsd
ANSI10000109 V1 EN
Figure 76:
Loci of the complex impedance Z(R, X) for a typical case of generator
losing step after a short circuit that was not cleared fast enough
Under typical, normal load conditions, when the protected generator supplies the active
and the reactive power to the power system, the complex impedance Z(R, X) is in the 1st
quadrant, point 0 in
. One can see that under a three-phase fault conditions, the
centre of oscillation is at the point of fault, point 1, which is logical, as all three voltages
are zero or near zero at that point. Under the fault conditions the generator accelerated and
when the fault has finally been cleared, the complex impedance Z(R, X) jumped to the
point 2. By that time, the generator has already lost its step, Z(R, X) continues it way from
1MRK 502 048-UUS A
Section 7
Impedance protection
177
Technical manual
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