# Analysis of Synchronous Generators' Local Mode Eigenvalues in Modern Power Systems
###### Abstract
These were the reasons for about 50% of all outages in the world in 2011-2019. Faulty equipment and human error are in second place as reasons for blackouts. In the same time period, these were the reasons for about 31.8% of all global blackouts. From [3], it is evident that, in 2011, there were about 2050 blackouts, which lasted an average of 4 h. The data collected show that blackouts have an extraordinarily negative impact on modern society and cause significant economic damage. The instability of power systems can take different forms and can be influenced by a wide range of factors. According to [3], local oscillation modes and small-signal stability are inherently connected to rotor angle stability. Rotor angle stability refers to the ability of synchronous machines of an interconnected power system to remain in synchronism after being subjected to a disturbance. The rotor angle stability problem involves the study of the electromechanical oscillations inherent in power systems. For convenience in analysis and for gaining useful insight into the nature of stability problems, it is useful to classify rotor angle stability in two subcategories: small-signal rotor angle stability (or small-signal, steady-state, small-disturbance, long-term, or dynamic (in the USA) stability) and large-signal rotor angle stability (or large-signal, transient, short-term, or dynamic (in Europe) stability). Small-signal stability is concerned with the ability of the power system to maintain synchronism under small disturbances. The disturbances are considered to be sufficiently small that linearization of system equations is permissible for purposes of analysis [3]. The instability that may result can be of two forms: an increase in rotor angle through a non-oscillatory (aperiodic) mode due to lack of synchronizing torque, or rotor oscillations of increasing amplitude due to lack of sufficient damping torque. In today's power systems, a small-signal stability problem is usually associated with insufficient damping of oscillations. The aperiodic instability problem has been largely eliminated by the use of continuously acting automatic voltage regulators (AVR) [3]. Synchronous generator oscillations are the main reason for problems concerning small-signal stability. Oscillations occur between the synchronous generator and some other parts of the power system. According to the elements between which oscillations occur, we arrange these oscillations in five classes: between a single synchronous generator against the rest of the power system (called local oscillation modes, local oscillations, local modes, machine-system modes, or single-machine infinite-bus oscillations), between the rotors of a few generators close to each other (inter-machine or interplant oscillation modes), between synchronous generators against a turbine (torsional oscillation modes), between different parts of the power plant due to the interaction of control systems (control oscillation modes), and between a group of generators in one area against a group of generators in another area (inter-area oscillation modes). Most frequently encountered small-signal stability problems are from the class of local oscillation modes [4]. This is the reason why the detailed results of the research of local modes are presented in the article.