voltage and nominal current. The impedances from the position of the out-of-stepprotection in the direction of the normal load flow can be taken as forward.The out-of-step relay, as in Figure 115 looks into the system and the impedances inthat 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. 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 StartAngle .The lens is broader for smaller values of theStartAngle , and becomes a circle for StartAngle = 90 degrees.When the complex impedance Z(R, X) enters the lens, pole slipping is imminent, and astart 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 usuallybegin. 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 mostlikely to lose step.7.6.7.2 Detecting an out-of-step conditionAn out-of-step condition is characterized by periodic changes of the rotor angle, thatleads to a wild flow of the synchronizing power; so there are also periodic changes ofrotational speed, currents and voltages. When displayed in the complex impedanceplane, these changes are characterized by a cyclic change in the complex loadimpedance Z(R, X) as measured at the terminals of the generator, or at the location ofthe instrument transformers of a power line connecting two power sub-systems. Thiswas shown in Figure 111. When a synchronous machine is out-of-step, pole-slipsoccur. To recognize a pole-slip, the complex impedance Z(R,X) must traverse the lensfrom 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 specificminimum traverse time, typically 40...60 milliseconds. The above timing is used todiscriminate a fault from an out-of-step condition. In Figure 111, some importantpoints on the trajectory of Z(R, X) are designated. Point 0: the pre-fault, normal loadZ(R, X). Point 1: impedance Z under a three-phase fault with low fault resistance: Zlies practically on, or very near, the Z-line. Transition of the measured Z from point 0to point 1 takes app. 20 ms, due to Fourier filters. Point 2: Z immediately after the faulthas been cleared. Transition of the measured Z from point 1 to point 2 takesapproximately 20 ms, due to Fourier filters. The complex impedance then travels in1MRK502052-UEN B Section 7Impedance protection267Technical manual
