Zeq(Req, Xeq), and the setting PickupAngle, for example 120 degrees. All impedancesmust be referred to the voltage level where the out-of-step protection relay is placed; inthis case shown in Figure 72 this is the generator nominal voltage level. Theimpedances from the position of the out-of-step protection in the direction of thenormal load flow can be taken as forward.The out-of-step relay, as in Figure 72 looks into the system and the impedances in thatdirection 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 can in general not be neglected. Theratio (ForwardX + ReverseX) / (ForwardR + ReverseR) determines the inclination ofthe Z-line, connecting the point SE (Sending End) and RE (Receiving End), and istypically approximately 85 degrees. While the length of the Z-line depends on thevalues of ForwardX, ReverseX, ForwardR, and ReverseR, the width of the lens is afunction of the setting PickupAngle.The lens is broader for smaller values of thePickupAngle, and becomes a circle for PickupAngle = 90 degrees.When the complex impedance Z(R, X) enters the lens, trouble is imminent, and apickup signal is issued. The angle recommended to form the lens is 110 or 120 degrees,because it is this rotor (power) angle where real trouble with dynamic stability usuallybegins. Rotor (power) angle 120 degrees is sometimes called “the angle of no return”because if this angle is reached under generator swings, the generator is most likely tolose step.7.3.7.2 Detecting an out-of-step conditionAn out-of-step condition is characterized by periodic changes of the rotor angle,synchronizing power, rotational speed, currents and voltages. When displayed in thecomplex impedance plane, these changes are characterized by a cyclic change in thecomplex load impedance Z(R, X) as measured at the terminals of the generator, or atthe terminals of a power line connecting two power sub-systems. This was shown inFigure 68. When a synchronous machine is out-of-step, pole-slips occur. To recognizea pole-slip, the complex impedance Z(R,X) must traverse the lens from right to left incase of a generator and in the opposite direction in case of a motor. Anotherrequirement is that the travel across the lens takes not less than a specific minimumtraverse time, typically 40 – 60 milliseconds. (To require that the impedance Z(R, X)travels through each of the two halves of the lens for, for example 25 milliseconds,Section 7 1MRK 502 043-UUS BImpedance protection156Technical Manual
