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During the analysis, it was assumed that the two sets of stator winding, say, abc and xyz, are identical. Hence, value of resistance and winding leakage inductance will be same (i.e., It may be noted that in figures of the following sections, dark and dash line indicate the real and imaginary component of eigenvalue, respectively.

With increase in stator resistance, generator operation tends toward stability from both stator and rotor side due to higher magnitude of negative real component of eigenvalue, as shown in Figure 1.5a for three-phase generator and Figures 1.6a and b for six-phase generator. Real eigenvalue I and II was found to be decreased as shown in Figures 1.5b and c 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.