This paper investigates the stability domain of ferroresonance in asymmetric three-phase three-leg transformers considering magnetic couplings and hysteresis effects of the core. A newly developed and accurate time-domain transformer model capable of simulating dynamic and transient operating conditions is implemented in this study. The model is based on electromagnetic circuit theory and considers dynamic hysteresis effects (major and minor loops) as well as core topology, asymmetry, and magnetic flux cross-coupling interactions of the core legs. Unbalanced switching with series and shunt capacitances, which is known to increase the risk of ferroresonance, is studied with the developed model. The validity of the model under ferroresonant conditions is confirmed by comparisons with extensive experimental data. The main contribution is a new analysis of (a)symmetric three-phase transformer ferroresonance behavior with an accurate core model capable of predicting ferroresonance modes.

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Impacts of Hysteresis and Magnetic Couplings on the Stability Domain of Ferroresonance in Asymmetric Three-Phase Three-Leg Transformers

In this contribution, the analysis of the dynamics of a ferroresonant circuit are presented using continuation techniques and bifurcation theory. Despite its great simplicity, this circuit can assume a diverse range of steady-state regimes including fundamental and subharmonic ferroresonance, quasiperiodic oscillations, and chaos. The system dynamics are explored through the continuation of periodic solutions of the associated circuit equations. A detailed picture is drawn of various transitions between the individual periodic steady-state regimes of the circuit. Bifurcation points are computed, revealing a clearly defined succession of periodic steady-state regimes, including the Feigenbaum route to chaos through a cascade of period doublings. The analysis presented is performed using the freely available software package XPPAUT. The contribution of this paper is to provide a detailed description of how to define the circuit equations in XPPAUT and how to conduct the interactive bifurcation analysis. The proposed approach is shown to be both computationally efficient and robust, as it eliminates the need for numerically critical and long lasting transient simulations.

/pdf/analysis-of-a-ferroresonant-circuit-using-bifurcation-theory-57smunfsd1.pdf

Analysis of a ferroresonant circuit using bifurcation theory and continuation techniques

Study of the periodic ferroresonance in the electrical power networks by bifurcation diagrams

This paper focuses on one aspect of ferroresonance in power systems, i.e., the appearance of a strange attractor with a band-like structure. This attractor was called a "pseudoperiodic" attractor in a previous paper where the phenomenon was first reported. It was found in this study that banded chaos arises from a sequence of period doubling bifurcations. Odd-subharmonics undergo a symmetry-breaking bifurcation before the period doubling cascade takes place. A theoretical discussion of symmetry-breaking and period doubling is given and a route to banded chaos in an actual power system is demonstrated. The Lyapunov exponents for the strange attractor were calculated.

Banded chaos in power systems

Ferroresonance is one of the most destructive transient phenomena in power systems. This complex phenomenon involves the association of nonlinear magnetizing inductances and capacitances, and may be initiated in many different ways, which makes its characterization very difficult. This work links EMTP and MATLAB and presents some computer tools that have been developed for assessing ferroresonance behavior. These tools allow users to visualize 2-D and 3-D bifurcation diagrams which can be used for performing sensitivity analysis, predicting the phenomenon at different stages, and finding safety zones for power system parameter design.

Tools for characterization and assessment of ferroresonance using 3-D bifurcation diagrams

Studying ferroresonance in actual power systems by bifurcation diagram

The article is devoted to in-depth and comprehensive coverage of the formation of a conceptual attitude to the organization, development, compliance and formalization of animal protection based on traditional methods of comparative studies through extra polar comparison of the domestic state of development of the legal plane and principles in the above field. Member States of the European Union (hereinafter — the EU). 
The issue of the position of animal rights and their protection in terms of legal systems is consistently reflected in numerous studies. Issues that affect the aporia of humane treatment of animals, their welfare at the state level, prevention of all possible forms of discrimination and objectively cruel treatment are intended to establish or rethink previously underestimated socio-legal and organizational-legal aspects of regulation and enforcement. Animal welfare and comprehensive prevention of ethically abnormal behavior. 
The main attention and research interest was primarily focused on the specifics of the legal regulation of animal protection in general and the content of current legal mechanisms on this issue in the EU. An equally important segment of the work is focused on detailing and analyzing the current regulation of organizational and legal principles of animal protection within the EU and a comprehensive demonstration of the cluster of Ukrainian legislation containing legal guarantees and key elements of animal protection in Ukraine. The presence of doctrinal and practical diversity in the environment of the chosen topic leads to the emergence of obvious contradictions or gaps, and foreign experience (which in this case should be understood as the interpretation and implementation of provisions and postulates applicable in EU countries) is an effective tool for overcoming miscalculations and reconciling in the ways that will be most rational and acceptable in today's conditions.

D. Shein

Papers

Studying ferroresonance in actual power systems by bifurcation diagram

Comparative aspect of organizational and legal principles of animal protection in Ukraine and the states of the EU