Figure 1.17 Variation in eigenvalue of three-phase synchronous machine with damper resistance change along q-axis (a) stator and rotor eigenvalue, (b) real eigenvalue I, (c) real eigenvalue II, (d) real eigenvalue III.
Figure 1.18 Variation in eigenvalue of six-phase synchronous machine with damper resistance change along q-axis (a) stator eigenvalue I and II, (b) rotor eigenvalue, (c) real eigenvalue I, (d) real eigenvalue II, (e) real eigenvalue III.
1.5.5 Magnetizing Reactance Variation Along q-axis
With the increase in magnetizing reactance xmq along q-axis, real part of stator eigenvalue of three- and six-phase generator was decreased by 34.4% and 68.8% (with no variation in stator eigenvalue I), as shown in Figures 1.20a and 1.21a, respectively. A major effect was noted from rotor side. Value of real part of rotor eigenvalue is increasing linearly for both three-phase and six-phase generator. It may be noted that the generator operation becomes unstable at higher value of xmq due to positive value of real part of rotor eigenvalue, as shown in Figure 1.21b. Hence, six-phase generator is more sensitive toward the variation of magnetizing reactance xmq. Also, a linear increase in the value of real eigenvalue II was noted for both three- and six-phase generator as shown in Figures 1.20c and 1.21d, respectively. But in three-phase generator, a higher decrease in real eigenvalue III was found in comparison with six-phase generator as shown in Figures 1.20d and 1.21e, respectively. No variation in real eigenvalue I was found for both three- and six-phase generator, as shown in Figures 1.20b and 1.21c, respectively.
Figure 1.19 Variation in eigenvalue II with damper leakage reactance change along q-axis in (a) three-phase and (b) six-phase generator.
Figure 1.20 Variation in eigenvalue of three-phase synchronous machine with magnetizing reactance change along q-axis (a) stator and rotor eigenvalue, (b) real eigenvalue I, (c) real eigenvalue II, (d) real eigenvalue III.
Figure 1.21 Variation in eigenvalue of six-phase synchronous machine with magnetizing reactance change along q-axis (a) stator eigenvalue I and II, (b) rotor eigenvalue, (c) real eigenvalue I, (d) real eigenvalue II, (e) real eigenvalue III.
Both three- and six-phase generator evaluated eigenvalues were found to unchanged with the variation in magnetizing reactance xmd along d-axis. Hence, it is not presented.
1.5.6 Variation in Load
Considering the constant grid voltage at 240 V (rms value per phase), eigenvalue of both three- and six-phase generator is plotted in Figure 1.18 for increase in load from 0.25 to 1.0 pu. From stator side, real component of stator eigenvalue decreases (increase in magnitude with negative sign) for both three- and six-phase generator, as shown in Figure 1.22a. (No variation was noted in stator eigenvalue I, hence not shown). Decrease in the value of real part of stator eigenvalue was higher (70.8%) than its three-phase counterpart (47.9%). Hence, tendency toward stability of six-phase generator is higher than three-phase generator. On rotor side, increase (i.e., decrease in magnitude with negative sign) in real component was noted to be same (20.7%) for both three- and six-phase generator as shown in Figure 1.22b. Hence, under load variation, rotor behavior will be the same for both three- and six-phase generator. On real eigenvalue II, a slight increase in the value for three-phase (by 4.5%) and six-phase generator (by 1.5%) was noted, as shown in Figure 1.22c. Also, a very small decrease in real eigenvalue III for six-phase (by 3.2%) was noted with 17.1% variation in three-phase generator as shown in