and six-phase generator, as shown in Figures 1.11a and 1.12b, respectively. A small linear or no change was noted in eigenvalue I and II for both three- and six-phase generator, as shown in Figures 1.11b and c and Figures 1.12c and d, respectively. But, a larger variation in real eigenvalue III was noted for both three- and six-phase generator, as shown in Figures 1.11d and 1.12e, respectively.
Figure 1.11 Variation in eigenvalue of three-phase synchronous machine with field circuit leakage reactance change (a) stator and rotor eigenvalue, (b) real eigenvalue I, (c) real eigenvalue II, (d) real eigenvalue III.
Figure 1.12 Variation in eigenvalue of six-phase synchronous machine with field circuit leakage reactance change (a) stator eigenvalue I and II, (b) rotor eigenvalue, (c) real eigenvalue I, (d) real eigenvalue II, (e) real eigenvalue III.
1.5.3 Parametric Variation of Damper Winding, Kd
In this section, parameter variation of damper winding along d-axis Kd (i.e., resistance rKd and leakage reactance xlKd) is considered in the evaluation of generator eigenvalues. With the increase in resistance rKd, both the stator and rotor eigenvalues were found to be unchanged for three-phase generator, as shown in Figure 1.13a. However, some change was found in stator eigenvalue I and rotor eigenvalue for six-phase generator, as shown in Figures 1.14a and b, respectively. A pronounced increase in the magnitude of real eigenvalue I was found for both three- and six-phase generator, as shown in Figures 1.13b and 1.14c, respectively. But no change in eigenvalue II and III was found for three-phase generator with small variation for six-phase generator, as shown in Figures 1.13c and d and Figures 1.14d and e, respectively.
With the increased value of leakage reactance xlKd, a major variation was only noted on real eigenvalue I for both three- and six-phase generator as shown in Figures 1.15b and 1.16c, respectively. A slight variation in real eigenvalue III was noted for both three- and six-phase generator as shown in Figures 1.15d and 1.16e, respectively. On stator side, a small variation in real component of eigenvalue was noted (with decrease in real component of stator eigenvalue I for six-phase generator) both three- and six-phase generator as shown in Figures 1.15a and 1.16a, respectively. Real component of rotor eigenvalue was noted to have no/small variation for both three- and six-phase generator as shown in Figures 1.15a and 1.16b, respectively.
Figure 1.13 Variation in eigenvalue of three-phase synchronous machine with damper resistance change along d-axis (a) stator and rotor eigenvalue, (b) real eigenvalue I, (c) real eigenvalue II, (d) real eigenvalue III.
Figure 1.14 Variation in eigenvalue of six-phase synchronous machine with damper resistance change along d-axis (a) stator eigenvalue I and II, (b) rotor eigenvalue, (c) real eigenvalue I, (d) real eigenvalue II (e) real eigenvalue III.
Figure 1.15 Variation in eigenvalue of three-phase synchronous machine with damper leakage reactance change along d-axis (a) stator and rotor eigenvalue, (b) real eigenvalue I, (c) real eigenvalue II, (d) real eigenvalue III.
Figure 1.16 Variation in eigenvalue of six-phase synchronous machine with damper leakage reactance change along d-axis (a) stator eigenvalue I and II, (b) rotor eigenvalue (c) real eigenvalue I, (d) real eigenvalue II, (e) real eigenvalue III.
1.5.4 Parametric Variation of Damper Winding, Kq
With the increase in damper winding resistance rKq, small variation was noted on real component of stator eigenvalue in three-phase generator. But in six-phase generator, it was increased by 50% in stator eigenvalue I (and slight increase in stator eigenvalue II), as shown in
