# Analysis of Synchronous Generators' Local Mode Eigenvalues in Modern Power Systems
## 4 Local Mode Analysis of Synchronous Generators with AVR
### Synchronous Generators' Voltage Control Systems
#### 4.3.1 Hydro-Type Synchronous Generators
An increase in reactive power results in an increase in local mode frequency,  
The minimal damping has operating points with low values of reactive power and high values of active power. The maximal damping has operating points with high values of reactive power and low values of active power. The analysis was also performed on the dependence of local mode eigenvalues on the operating point for turbo-type synchronous generators with rated powers of 25 MVA to 911 MVA. Figures 16-18 show the eigenvalue loci for synchronous generators with nominal powers 25 MVA, 160 MVA, and 911 MVA. Again, the eigenvalue curves had a similar shape for all turbo-type synchronous generators of different powers equipped with an AVR system. It can be seen that the increase in active power can have a negative effect on damping or causes instability only at very small values of reactive power and at very large values of active power. In the remaining (larger) part of the operating range, changing the produced active and reactive power has a similar effect on local mode eigenvalues as that of turbo-type synchronous generators without AVR. Figure 16: Eigenvalue loci of local mode of 25-MVA turbo-type synchronous generator with AVR. It is interesting to note that the increase in active power for hydro-type synchronous generators with an AVR system reduces damping, as seen in Figures 11-14, while the increase in active power in turbo-type generators in most areas of the operating range reduces damping, as seen in Figures 16-18. We were interested to find out which con  
Figure 17: Eigenvalue loci of local mode of 160-MVA turbo-type synchronous generator with AVR. Figure 11:0 Eigenvalue loci of local mode of 911-MVA turbo-type synchronous generator with AVR. struction parameter was crucial for such different behavior of both types of synchronous generators. We analyzed all the parameters of generator models of different rated powers. The analysis showed that a key impact on the correlation between the real part of eigenvalues and the generated active power represents the direct-axis transient reactance \(x_{d}\). Turbo-type synchronous generators generally have lower \(x_{d}\)' values than hydro-types, which is described in the references and was also confirmed by our data. According to [4], the turbo-type generators have direct-axis transient reactances \(x_{d}\)' in the range 0.15-0.4, and hydro-type in the range 0.2-0.5. According to [23], the turbo-type generators have reactances in the range 0.23-0.35, and hydro-type in the range 0.25-0.45. From the study, it was observed that different relations between d- and q-axis synchronous reactances for hydro- and turbo-type generators do not cause the aforementioned different influence of active power on eigenvalues' real parts. Figure 19 shows six curves of local mode eigenvalues of a hydro-type synchronous generator with nominal power 158 MVA with an AVR system at constant reactive power value \(Q=0.6\) pu. Each curve represents the eigenvalues at a different simulated value of the direct-axis transient reactance \(x_{d}\)'. The real value of d-axis transient reactance is \(x_{d}\)' = 0.30; the curves show the eigenvalue loci at \(x_{d}\)' values in the range from 0.15 to 0.40. It is clearly visible that at higher \(x_{d}\)' values the increase in power results in a decrease in the damping, and at lower values of \(x_{d}\)', the increase in power increases the damping of local oscillations.