The sum of the first and the third term of the severity equation is analogous to the operate quantity of a conventional
approach, and the last term is analogous to the restraint quantity of a conventional approach. The second term arises from
the orientation of the ellipse. The equation yields an adaptive elliptical restraint characteristic. The size, shape, and orienta-
tion of the ellipse adapt to power system conditions. The computed severity is zero when the operate phasor is on the ellip-
tical boundary, is negative inside the boundary, and positive outside the boundary. Outside of the restraint boundary, the
computed severity grows as the square of the fault current. The restraint area grows as the square of the error in the mea-
It is interesting to compare the severity equation with conventional approaches that are based on operate and restraint
terms. For example, one typical operating characteristic based on restraint and operating quantities is shown in Figure 8–1.
The restraint current in the conventional approach is derived from the sum of the magnitudes of the terminal currents, and
is analogous to the last term in the elliptical severity equation. The operating current for the conventional scheme is derived
from the sum of the currents, and is analogous to the first and third term of the elliptical severity equation.
Another way of plotting the conventional restraint curve as a region in the complex plane is shown in Figure 8–2. The
restraint region is the area inside the circle. Whenever the sum of the current phasors falls within the circle, the conven-
tional approach is restrained. The diameter of the circle depends on the restraint current.
Figure 8–2: CONVENTIONAL RESTRAINT CHARACTERISTIC IN TERMS OF PHASORS
The adaptive elliptical restraint has several advantages over the conventional approach. Although both the adaptive
approach and the conventional approach have a restraint region that changes size, the adaptive elliptical restraint region
more accurately reflects the sources of measurement error. For example, the conventional approach does not take into
account the effects of traveling waves and switching surges on the accuracy of measurements. The adaptive elliptical
restraint region provides the best statistical confidence and is more sensitive and more secure than the conventional
Figure 8–1: CONVENTIONAL RESTRAINT CHARACTERISTIC
L90 Line Differential Relay
8 THEORY OF OPERATION
GE Power Management