# Analysis of Synchronous Generators' Local Mode Eigenvalues in Modern Power Systems
## 6 Conclusions
* For synchronous generators of all analyzed types and sizes, the increase in generated active power results in the increase in local mode damping, and the increase in lagging reactive power results in the increase in local mode damped frequency; the operating points with the weakest damped local oscillations are at high values of reactive power and low values of active power. * Based on the analysis of all synchronous generators operating within the nominal conditions, we can estimate that the frequencies (\(f\)) of local oscillations of the present power plants' synchronous generators will be in the range of 0.45-1.75 Hz (which is lower than the estimated frequencies in studies from decades ago), and the damping ratio (\(\zeta\)) of local oscillations will be in the range of 0.004-0.17 (comparison of damping ratio is not possible, because no such analyses have been performed in the past). * An important conclusion is that the AVR affects the local oscillations immensely and can lead to instability in endangered operating areas. The AVR gain must be selected carefully so as not to cause undamped oscillations. A practical recommendation was made, which, based on the known time constant of the excitation system \(T_{\text{AVR}}\) and synchronous generator open-circuit time constant of a direct-axis time constants \(T^{\prime}_{\text{d0}}\), provides sufficiently damped local oscillations in the entire operating range (i.e., similar damping as without the AVR system). * The range of frequencies and dampings of local oscillations of the considered generators with AVR systems with gain calculated by the given recommendation was estimated; frequencies were in the range 0.5-1.5 Hz, and damping's range was similar to that of synchronous generators without AVR systems. * The changing of the operating point of the synchronous generator with the AVR system has a large influence on the frequency and damping of oscillations. * The correlation between the operating points and oscillations is, for synchronous generators with AVR systems, less straightforward. While the increase of reactive power follows in all cases in the increase of undamped frequency, the increase of active power by hydro-type synchronous generators always decreases the damping of oscillations, and for turbo-type synchronous generators, it mainly increases the damping except for small values of reactive power and high values of active power. The different dependence of the eigenvalues of the different types of generators with an AVR system on the operating point is mainly due to the different values of direct-axis transient reactance. * It was evident from the numerical results and confirmed with a root locus diagram that for hydro- and turbo-type synchronous generators with AVR systems, the less damped operating points represent a combination of generated small reactive power and large active power. The sizes of frequency and damping of oscillations of the laboratory synchronous generator with nominal power \(S_{\mathrm{n}}=15\) kVA were expected to deviate from the obtained values of generators in the nominal power range of 1 to 1000 MVA, but the experiments confirmed the discovered correlation between operating points and oscillations' dampings and frequencies. The presented findings answered the initial questions. The results of the study enable the estimation of expected oscillations, the evaluation of the adequacy of the AVR parameters, the distinction of local oscillations from other oscillations, the prediction of stability-problematic operation, the design and synthesis of PSS, etc. Our goal is also that engineers and scientists who work with measurements of local oscillations compare the results of their measurements with the paper's conclusions and confirm or correct them. Conceptualization, J.R.; data curation, J.R.; formal analysis, J.R.; funding acquisition, J.R.; investigation, J.R. and B.P. ; methodology, J.R.; project administration, J.R. and B.P. ; resources, J.R. and B.P. ; software, J.R.; supervision, J.R.; validation, J.R. and B.P.