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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].