# Analysis of Synchronous Generators' Local Mode Eigenvalues in Modern Power Systems
###### Abstract  
New energy sources, storage facilities, power electronics devices, advanced and complex control concepts, economic operating doctrines, and cost-optimized construction and production of machines and equipment in power systems adversely affect small-signal stability associated with local oscillations. The objective of the article is to analyze local oscillations and the causes that affect them in order to reduce their negative impact. There are no recognized analyses of the oscillations of modern operating synchronous generators exposed to new conditions in power systems. The basic idea is to perform a numerical analysis of local oscillations of a large number of synchronous generators in the power system. The paper represents the local mode data obtained from a systematic analysis of synchronous generators in the Slovenian power system. Analyzed were 74 synchronous generators of the Slovenian power system, plus many additional synchronous generators for which data were accessible in references. The mathematical models convenient for the study of local oscillations are described first in the paper. Next, the influences of transmission lines, size of the synchronous generators, operating conditions, and control systems were investigated. The paper's merit is the applicable rules that have been defined to help power plant operators avoid stability-problematic situations. Consequently, boundaries were estimated of the eigenvalues of local modes. Finally, experiments were performed with a laboratory-size synchronous generator to assess the regularity of the numerically obtained conclusions. The obtained results enable the prediction of local oscillations' frequencies and dampings and will be useful in PSS planning. power system; synchronous generators; oscillations; local modes; eigenvalue analysis +
Footnote †: journal: Applied  
16 October 2021222 December 2  
chronous generators operating in the power system. There are three main reasons for that:  
* Changes in the construction of synchronous generators, which come from cost optimization requirements for production and transport of the generators. Consequently, the damping coefficients of the rotor's damping windings and inertia moments are reduced [2]. * Introduction of additional control systems into power systems or their modification, which is inevitable due to altered modes of operation of the power systems (e.g., operation of facilities at their peak performance); reaching novel, strict requirements of transmission system operators; open transmission access; environmental constraints; and increased competitiveness (e.g., additional voltage control systems which are suggested by transmission system operators (TSO) to control the power plant terminal voltage versus reactive power characteristics, modified primary control systems which will be able to assure the TSOs requirements during parallel operation, island operation of the single generators, and parallel operation of a few power-generating modules within one island). The additional or modified control systems improve operation in a particular operation regime. In some other operation conditions, the additional control systems could reduce damping and lead to instability of the power system [2]. * As the demand for energy grows, modern power systems are operated close to the ultimate transmission capability, which can easily lead to a critical situation [3]. For these reasons, synchronous generators in modern power systems are much more sensitive to disturbances in the power system (damages, faults, errors) that cause natural oscillations to become unstable. Consequences of elevated stability problems are observed clearly in an increasing number of significant power system blackouts in recent years. Due to their importance, there are many reviews in the literature, e.g., [3]. It can be seen that the highest number of blackouts was due to abnormal weather conditions, such as severe winds and heavy storms, and trees falling on transmission lines.