# Analysis of Synchronous Generators' Local Mode Eigenvalues in Modern Power Systems
### Existing Solutions and Literature Review  
Synchronous generator oscillations are an important engineering problem and an interesting scientific challenge. Accordingly, there is great activity and a number of publications in this area.  
An appropriate mathematical model is required to estimate and predict the characteristics of oscillations. A simplified linearized model of a single machine connected to an infinite bus (SMIB) is considered to be the fundamental model for the local oscillation analysis. The model was presented in [5] and named, according to the authors, the Heffron-Phillips model (H-P model). The H-P model was supplemented and changed constantly. This process is still ongoing, e.g., [6; 7], but the fundamental H-P model is still considered the basis for research in this area. Analytical determination of H-P model parameters is described in detail in [4,8], along with the identification of the model's parameters in [9,10].  
The first articles that give a model-based quantitative assessment of the frequency of oscillation of synchronous generators are more than 20 years old. In [11], the author estimates that the control oscillation frequencies are in the range of 1.5-2.5 Hz, and the torsional oscillations are in the range of 10-50 Hz. In [12], it is estimated that the local oscillations are in the range of 0.8-1.8 Hz and the inter-area oscillations in the range of 0.2-0.5 Hz. These findings still apply to the indicative values. A broad overview of the sources, characteristics, and analyses of natural oscillatory behaviors in power systems is provided in [13]. Inter-area electromechanical modes in ambient response are considered explicitly in this report.  
Although the constructions of synchronous generators, control concepts, and network connections have changed significantly over time, we do not find recent publications in the literature in which local oscillation frequencies are estimated based on the analysis of a large number of synchronous generators. An additional research gap is that there are no publications where the expected damping of these oscillations is evaluated in detail. A mode's damping influences how quickly (and if) a related oscillation subsides. Therefore, damping is the parameter tied most closely to system stability [13]. The need for knowledge in this area is confirmed by recent publications that address the damping of oscillations resulting from new solutions and equipment according to synchronous generators. The damping of oscillations produced due to the introduction of a photovoltaics virtual synchronous generator is considered in [14]. Reference [15] studies the oscillations of wind farms' synchronous generators. Reference [16] describes the implementation of an energy storage system for the damping of electromechanical oscillations of synchronous generators. References [17-19] describe the effects of control appliances on the power grid frequency, power system blackouts, and cascading failures. Reference [20] highlights the small-signal oscillations of a synchronous motor-generator pair, which are exposed and treated in more detail. It is just one of the articles that confirms the topicality of the considered matter.