# Analysis of Synchronous Generators' Local Mode Eigenvalues in Modern Power Systems
## 3 Local Mode Analysis of Synchronous Generators without AVR
### Influence of Synchronous Generator's Operating Point on Local Mode Eigenvalues
#### 3.2.2 Turbo-Type Synchronous Generators  
Turbo-type synchronous generators of nominal powers were analyzed in the range of 25 MVA to 911 MVA, with data in Appendix A, Tables A5-A7. The same eigenvalue analysis was performed as for hydro-generators. Figures 5-7 show the eigenvalue loci as a function of operating point for synchronous generators with nominal powers 25 MVA, 160 MVA, and 911 MVA.  
Figure 4: Eigenvalue loci of local mode of 615-MVA hydro-type synchronous generator without AVR.  
Figure 5: Eigenvalue loci of local mode of 25-MVA turbo-type synchronous generator without AVR.  
Figure 6: Eigenvalue loci of local mode of 160-MVA turbo-type synchronous generator without AVR.  
Eigenvalue analysis was carried out for 48 turbo-generators. For all generators, similar eigenvalue loci were obtained, as shown in Figures 5-7. The eigenvalue loci of turbo-generators differ from the loci of hydro-generators in that the loci of the constant reactive power of turbo-generators are not so straightforward, especially for the curves of low reactive power, whose convexity is evident in the vicinity of the nominal values of the active power. The primary conclusions that the increase in active power decreases the real part \(\sigma\), and that the increase in reactive power increases the imaginary part \(\omega\), still apply. Additionally, the oscillations are better damped at operating points with high values of active power and low values of reactive power. The damping is smaller at high values of reactive power and low values of active power.  
Influences of the Transmission Line between Synchronous Generator and Infinite Bus and the Size of Synchronous Generators on Local Mode Eigenvalues  
Local mode eigenvalues depend on the synchronous generators' parameters and the parameters of the transmission line between the synchronous generator and infinite bus. In the previous section, simulations were carried out with parameters of a real transmission line. It is to be expected that lower transmission line impedance results in higher frequency. For detailed insight, the eigenvalue analyses were performed for cases with different values of transmission line impedance.  
Figure 8 shows the eigenvalue loci of a 158-MVA hydro-type synchronous generator where transmission line impedance was reduced to 50% of its nominal value. Figure 8 could be compared directly to Figure 3. From this analysis, it is visible that changes in transmission line impedance influence the local mode eigenvalues so that a decrease in impedance results in increased oscillation frequency. Because the transmission line parameters usually stay unchanged during the operation, and because this influence is relatively small, a detailed analysis of the correlation between transmission line parameters and local mode eigenvalues is not presented.  
Figure 7: Eigenvalue loci of local mode of 911-MVA turbo-type synchronous generator without AVR.  
Interestingly, it is not possible to conclude how the size of generators correlates with the frequency and damping of oscillations. From Figures 1 and 2, it is evident that generators of similar size (nominal powers 9 MVA and 12 MVA) have (similar courses, but) completely different values of oscillations' frequency and damping. There are also cases where generators with significantly different nominal powers have very similar eigenvalues loci. The conclusion is that more than the size affects the synchronous generator's construction in terms of its local mode eigenvalues.