for three-phase generator, and in Figures 1.6c and d for six-phase generator. But a slight increase in real eigenvalue III of three-phase generator with no change was noted in six-phase generator as shown in Figures 1.5d and 1.6e, respectively.
With the increase in stator leakage reactance, a trend of eigenvalue variation was found to be reversed. On stator side, real component of eigenvalue was increased by 31.5% (shown in Figure 1.7a) for three-phase generator, and by 50% and 19.8% in stator eigenvalue I and II for six-phase generator, as shown in Figure 1.8a. However, a slight increase in real component of rotor eigenvalue for three-phase generator was noted, shifting the operation toward instability. But, in six-phase generator, increased magnitude of real component of rotor eigenvalue (shown in Figure 1.8b), signifying the tendency of stable operation. The remaining three eigenvalues remain negative with small variation as shown in Figures 1.7b–d and Figures 1.8c–e for three- and six-phase generator, respectively. It may be noted that the magnitude (with negative sign) real eigenvalues of six-phase generator remain higher (in magnitude); and hence, is more stable when compared with three-phase generator.
Figure 1.5 Variation in eigenvalue of three-phase synchronous machine with stator resistance change (a) stator and rotor eigenvalue, (b) real eigenvalue I, (c) real eigenvalue II, (d) real eigenvalue III.
Figure 1.6 Variation in eigenvalue of six-phase synchronous machine with stator resistance change (a) stator eigenvalue I and II, (b) rotor eigenvalue, (c) real eigenvalue I, (d) real eigenvalue II, (e) real eigenvalue III.
Figure 1.7 Variation in eigenvalue of three-phase synchronous machine with stator leakage reactance change (a) stator and rotor eigenvalue, (b) real eigenvalue I, (c) real eigenvalue II, (d) real eigenvalue III.
Figure 1.8 Variation in eigenvalue of six-phase synchronous machine with stator leakage reactance change (a) stator eigenvalue I and II, (b) rotor eigenvalue, (c) real eigenvalue I, (d) real eigenvalue II, (e) real eigenvalue III.
1.5.2 Parametric Variation of Field Circuit
In this section, the effect of variation in field circuit parameter (resistance rfr and leakage reactance xlfr) is presented for both three- and six-phase generator. With the increase in field circuit resistance, variation in real component of stator eigenvalue was not observed in case of three-phase generator, as shown in Figure 1.9a. But, stator eigenvalue I was increased by 50%, showing the tendency of instability as shown in Figure 1.10b. But on rotor side, operation tends toward stability as shown in Figure 1.10b. A small increase in the value of real component of rotor eigenvalue was noted in three-phase generator, as shown in Figure 1.9a. Real eigenvalue I and III is decreased for three-phase generator as shown in Figures 1.9b and d, respectively, with no variation in real eigenvalue II as shown Figure 1.9c. On the other hand, trend of variation in real component of eigenvalue was found to be different for six-phase generator. All the real eigenvalue I, II, and III was found to be decreasing (in magnitude with negative sign) as shown in Figures 1.10c, d, and e, respectively. It may be noted here that the larger variation was in the smallest real eigenvalue III with no or smaller change in other real eigenvalues. This is because, on rotor, field circuit has largest time constant giving rise to smallest eigenvalue III [15, 18].
Figure 1.9 Variation in eigenvalue of three-phase synchronous machine with field circuit resistance change (a) stator and rotor eigenvalue, (b) real eigenvalue I, (c) real eigenvalue II, (d) real eigenvalue III.
Figure 1.10 Variation in eigenvalue of six-phase synchronous machine with field circuit resistance change (a) stator eigenvalue I and II, (b) rotor eigenvalue, (c) real eigenvalue I (d) real eigenvalue II, (e) real eigenvalue III.
With the increase in field leakage reactance xlfr, magnitude of real component of stator eigenvalue was decreased for both three- and six-phase generator, as shown in Figures 1.11a and 1.12a, respectively. But, a small variation in real component of rotor eigenvalue was noted for both three-
