10.4.1 Apparent impedance during stability swings
As has been observed earlier, the stability swing is characterized by a movement of the rotor angle
over wide ranges. During a stable swing the rotor angle oscillates around an equilibrium point,
while during an unstable swing the rotor angle progressively increases (or decreases), and acquires
values beyond the ±2πr range. Consider the two-machine system shown in Figure 10.6. We will
assume that the receiving end voltage is the reference phasor, and the angle of the voltage Es
represents the position of its rotor. It is this angle which will vary during a stability swing. In order
to develop protection principles for instability detection, it is necessary to analyze the behavior of
current and voltage phasors in the power system for stable and unstable cases.
The phasor diagram for this case is shown in Figure 10.7. The current in the line is given by