The out-of-step relay, as in Figure 204 looks into the system and the impedances in that direction
are forward impedances:
•
ForwardX
= Xtr + Xline + Xeq (All values referred to generator voltage)
•
ForwardR
= Rtr + Rline + Req (All values referred to generator voltage)
The impedances that can be measured in the reverse direction are:
•
ReverseX
= Xd' (Generator transient reactance suitable for this protection)
•
ReverseR
= Rg (Relatively very small, can often be neglected)
Resistances are much smaller than reactances, but in general can not be neglected. The ratio
(
ForwardX
+
ReverseX
) / (
ForwardR
+
ReverseR
) determines the inclination of the Z-line,
connecting the point SE (Sending End) and RE (Receiving End), and is typically approximately 85
degrees. While the length of the Z-line depends on the values of
ForwardX
,
ReverseX
,
ForwardR
,
and
ReverseR
, the width of the lens is a function of the setting
PickupAngle
.The lens is broader for
smaller values of the
PickupAngle
, and becomes a circle for
PickupAngle
= 90 degrees.
When the complex impedance Z(R, X) enters the lens, pole slipping is imminent, and a pickup
signal is issued. The angle recommended to form the lens is 110 or 120 degrees, because it is this
rotor (power) angle where problems with dynamic stability usually begin. Rotor (power) angle 120
degrees is sometimes called “the angle of no return” because if this angle is reached under
generator power swings, the generator is most likely to lose step.
7.11.7.2 Detecting an out-of-step condition
GUID-5BBAE253-3D01-4C97-A7CF-A12084FD1810 v4
An out-of-step condition is characterized by periodic changes of the rotor angle, that leads to a
wild flow of the synchronizing power; so there are also periodic changes of 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 instrument transformers of a power line
connecting two power sub-systems. This was shown in
Figure 200. When a synchronous machine
is out-of-step, pole-slips occur. To recognize a pole-slip, the complex impedance Z(R,X) must
traverse the lens from right to left in case of a generator and in the opposite direction in case of a
motor. Another requirement is that the travel across the lens takes no less than a specific
minimum traverse time, typically 40...60 milliseconds. The above timing is used to discriminate a
fault from an out-of-step condition. In
Figure 200, some important points on the trajectory of Z(R,
X) are designated. Point 0: the pre-fault, normal load Z(R, X). Point 1: impedance Z under a three-
phase fault with low fault resistance: Z lies practically on, or very near, the Z-line. Transition of the
measured Z from point 0 to point 1 takes app. 20 ms, due to Fourier filters. Point 2: Z immediately
after the fault has been cleared. Transition of the measured Z from point 1 to point 2 takes
approximately 20 ms, due to Fourier filters. The complex impedance then travels in the direction
from the right to the left, and exits the lens on the opposite side. When the complex impedance
exits the lens on the side opposite to its entrance, the 1st pole-slip has already occurred and more
pole-slips can be expected if the generator is not disconnected.
Figure 200 shows two pole-slips.
Figures like Figure 200 and Figure 202 are always possible to draw by means of the analog output
data from the pole-slip function, and are of great help with eventual investigations of the
performance of the out-of-step function.
7.11.7.3 Maximum slip frequency
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A pole-slip may be detected if it has a slip frequency lower than a maximum value
fsMax
. The
specific value of
fsMax
depends on the setting (parameter)
PickupAngle
(which determines the
1MRK 502 066-UUS B Section 7
Impedance protection
383
Technical manual
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