voltage and nominal current. The impedances from the position of the out-of-step
protection in the direction of the normal load flow can be taken as forward.
The out-of-step relay, as in Figure
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
StartAngle
.The lens is broader for smaller values of the
StartAngle
, and becomes a circle for
StartAngle
= 90 degrees.
When the complex impedance Z(R, X) enters the lens, pole slipping is imminent, and a
start 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.
7.6.7.2
Detecting an out-of-step condition
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
. 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
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
1MRK502052-UEN B
Section 7
Impedance protection
267
Technical manual
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