Ferroresonant Circuit Research Articles

Experimental investigation of impact of remnant flux on the ferroresonance initiation

Objective: The paper presents an experimental and numerical investigation carried out on a ferroresonant circuit in order to determine to what extent the initiation of ferroresonance depends on remnant flux.Methods: In order to gain the full insight of impact of initial conditions on the initiation of ferroresonance in general, the investigation was carried out varying the initial capacitance voltage and the phase shift as well. Ferroresonant circuit under study comprises a linear capacitor, sinusoidal voltage source and a coil designed for 30V nominal primary voltage with the core made of oriented transformer sheets (M5-type). Additionally, the response of the circuit was obtained using a coil with the same core type (M5-type), but designed for higher nominal primary voltage (36V) and a coil designed for 30V nominal primary voltage, but with the core made of Ni–Fe alloy (Trafoperm N3).Results/Conclusions: Based on measurements and simulation results, it is shown that the remnant flux and initial conditions in general, as well as phase shift have significant impact on initiation of ferroresonance for all used coil types. Thereby, the odd-symmetry of responses was observed as a consequence of odd-symmetric characteristics of passive circuit elements. The impact of initial conditions is explained theoretically as well, using a bifurcation diagram and calculation of Floquet multipliers.

Spectral analysis of voltages and currents during different modes of ferroresonance in switchgear

This paper presents a spectral analysis of three different modes of ferroresonance. Voltage and current signals of the fundamental, subharmonic and chaotic ferroresonance modes are processed. The signals are obtained by modeling a ferroresonance circuit in alternative transient program-electro magnetic transient program (ATP-EMTP). The magnitude spectrum and total harmonic distortion are calculated for each case. The results show that voltages and currents of different modes of ferroresonance produce different features, which may be used for ferroresonance identification, classification and mitigation in the future.

Effect of metal oxide arrester on the chaotic oscillations in the voltage transformer with nonlinear core loss model using chaos theory

In this paper, controlling chaos when chaotic ferroresonant oscillations occur in a voltage transformer with nonlinear core loss model is performed. The effect of a parallel metal oxide surge arrester on the ferroresonance oscillations of voltage transformers is studied. The metal oxide arrester (MOA) is found to be effective in reducing ferroresonance chaotic oscillations. Also the multiple scales method is used to analyze the chaotic behavior and different types of fixed points in ferroresonance of voltage transformers considering core loss. This phenomenon has nonlinear chaotic dynamics and includes sub-harmonic, quasi-periodic, and also chaotic oscillations. In this paper, the chaotic behavior and various ferroresonant oscillation modes of the voltage transformer is studied. This phenomenon consists of different types of bifurcations such as period doubling bifurcation (PDB), saddle node bifurcation (SNB), Hopf bifurcation (HB), and chaos. The dynamic analysis of ferroresonant circuit is based on bifurcation theory. The bifurcation and phase plane diagrams are illustrated using a continuous method and linear and nonlinear models of core loss. To analyze ferroresonance phenomenon, the Lyapunov exponents are calculated via the multiple scales method to obtain Feigenbaum numbers. The bifurcation diagrams illustrate the variation of the control parameter. Therefore, the chaos is created and increased in the system.

Voltage transformer ferroresonance analysis using multiple scales method and chaos theory

In this article, the Multiple Scales Method is used to analyze the chaotic behavior and different types of fixed points in ferroresonance of voltage transformers considering core loss. This phenomenon has nonlinear chaotic dynamics and includes subharmonic, quasi‐periodic, and also chaotic oscillations. In this article, the chaotic behavior and various ferroresonant oscillations modes of the voltage transformer is studied. This phenomenon consists of different types of bifurcations such as Period Doubling Bifurcation (PDB), Saddle Node Bifurcation (SNB), Hopf Bifurcation (HB) and chaos. The dynamic analysis of ferroresonant circuit is based on bifurcation theory. The bifurcation and phase plane diagrams are illustrated using a continuous method and linear and nonlinear models of core loss. To analyze ferroresonance phenomenon, the Lyapunov exponents are calculated via Multiple Scales Method obtaining Feigenbaum numbers. The bifurcation diagrams illustrate the variation of the control parameter. Therefore, the chaos is created and increased in the system. © 2013 Wiley Periodicals, Inc. Complexity 18: 34‐45, 2013

RECONSTRUCTION AND IDENTIFICATION AND CONTROL METHOD OF FERRORESONANCE OVERVOLTAGE BASED ON VOLTAGE TIME SERIES

Ferroresonance overvoltage and over-current can be restrained using nonlinear dynamics. However, the ferroresonance simplified model, which cannot reflect the huge ferroresonance circuit in the grid precisely and cannot satisfy real-time analysis, is adopted in the traditional nonlinear control method. Owing to these shortcomings, the strategy of controlling ferroresonance overvoltage based on voltage time series is proposed. Based on the voltage time series analysis methods, the ferroresonance system is identified using the best embedding dimension and the best time delay obtained from the phase space reconstruction. Afterward, the feedback controller is designed based on the platform of the identified model. Results show that fundamental, subharmonic and chaotic ferroresonance overvoltage can all be controlled using the method presented in this paper even without the system parameters and the accurate system model. Therefore, the control strategy is generally more applicable.

Chaotic oscillations control in the voltage transformer including nonlinear core loss model by a nonlinear robust adaptive controller

In this paper, control of chaos is done in presence of ferroresonant oscillations in a voltage transformer with nonlinear model of core losses. In order to control the chaotic oscillations, nonlinear adaptive approach is employed. Moreover, a Time Delay Feedback Controller (TDFC) is implemented to stabilize Unstable Periodic Orbits (UPOs). Also multiple scales method to analyze chaotic behavior and types of fixed points in ferroresonance occurrence at voltage transformers considering different types of core loss models is applied. In the literature ferroresonance phenomenon in voltage transformers is proved to be classified in chaotic dynamics systems. In this contribution, chaos occurs in the system from a sequence of Period Doubling Bifurcation (PDB). This phenomenon consists of different types of bifurcations such as Period Doubling Bifurcation (PDB), Saddle Node Bifurcation (SNB), Hopf Bifurcation (HB) and chaos. Dynamic analysis of ferroresonant circuit is performed using bifurcation theory. bifurcation diagrams and phase plane diagrams are illustrated using a continuation method for linear and nonlinear core loss models. For analyzing ferroresonance phenomenon, Lyapunov exponents are calculated using multiple scales method and feigenbaum numbers are obtained. Bifurcation diagrams illustrate variation of parameter control and as a result chaos is created and increased in the system.

Nonlinear dynamic analysis and chaos control for third order sub-harmonic in a ferroresonant circuit

In this paper, the nonlinear dynamics of a non-autonomous system model for third order sub-harmonic in a basic ferroresonant circuit are analyzed in details, including phase trajectory, Poincare map, bifurcation diagram, dissipativity analysis and Spectrogram map. Furthermore, a sliding mode controller of the system is designed and both theory analysis and numerical simulation are presented, which shows the effectiveness and potentials of the proposed techniques. Key words: Third order sub-harmonic model, dynamics analysis, sliding mode control.

Teaching ferroresonance in power system to undergraduate students by using MATLAB–SIMULINK

AbstractAccurate knowledge characteristics of a power system are very essential to have an idea of its operation conditions. The ferroresonant circuit exhibits oscillations characterized by frequency that is in accordance to the voltage applied on, and the currents circulating through the components of the circuit. The dominant frequency of these periodic oscillations could be the network frequency (fundamental ferroresonance) or a fraction of it (sub‐harmonic ferroresonance). This phenomenon (both fundamental and sub‐harmonic ferroresonance) is characterized by overvoltages or overcurrents, which may provoke the equipment damage and malfunctioning of the protective devices. The article presents an approach to teaching high voltage laboratory using specially designed exercises that can be done using MATLAB 6.5. This article present a MATLAB based technology to simulate ferroresonance in power system. Evaluation of the simulation with more than 30 students is very positive in terms of their developing confidence in and understanding of this simulation. © 2009 Wiley Periodicals, Inc. Comput Appl Eng Educ 19: 347–357, 2011

Identifying ferroresonance initiation for a range of initial conditions and parameters

The paper presents an experimental and numerical investigation carried out on a ferroresonant circuit in order to determine to what extent the initiation of ferroresonance depends on initial conditions and phase shift. The range of voltage source values at which the initiation of ferroresonance depends on initial conditions and phase shift is named as a possible ferroresonant range, and is determined numerically and experimentally.

Analytical Approach for the Systematic Research of the Periodic Ferroresonant Solutions in the Power Networks

Ferroresonance is a complex and little known electrotechnical phenomenon. This lack of knowledge means that it is voluntarily considered responsible for a number of unexplained destructions or malfunctioning of equipment. The mathematical framework most suited to the general study of this phenomenon is the bifurcation theory, the main tool of which is the continuation method. Nevertheless, the use of a continuation process is not devoid of difficulties. In fact, to continue the solutions isolats which are closed curves, it is necessary to know a solution belonging to this isolated curve (isolat) to initialise the continuation method. The principal contribution of this article is to develop an analytical method allowing systematic calculation of this initial solution for various periodic ferroresonant modes (fundamental, harmonic and subharmonic) appearing on nonlinear electric system. The approach proposed uses a problem formulation in the frequency domain. This method enables to directly determine the solution in steady state without computing of the transient state. When we apply this method to the single-phase ferroresonant circuits (series and parallels configurations), we could easily calculate an initial solution for each ferroresonant mode that can be established. Knowing this first solution, we show how to use this analytical approach in a continuation technique to find the other solutions. The totality of the obtained solutions is represented in a plane where the abscissa is the amplitude of the supply voltage and the ordinate the amplitude of the system’s state variable (flux or voltage). The curve thus obtained is called “bifurcation diagram”. We will be able to then obtain a synthetic knowledge of the possible behaviors of the two circuits and particularly the limits of the dangerous zones of the various periodic ferroresonant modes that may appear. General results related to the series ferroresonance and parallel ferroresonance, obtained numerically starting from the theoretical and real cases, are illustrated and discussed.

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

The principal contribution of this article is to determine the existence zones of the various periodic ferroresonant modes (fundamental, harmonic and subharmonic) intervening in the electrical power network. The bifurcation diagrams are used for this purpose. To be able to plot a bifurcation diagram of a particular solution, it is initially necessary to locate this solution and then to follow it according to a bifurcation parameter. The developed computation code, resulting from the implementation of the Galerkin method jointly with the pseudo-arclength continuation method, has proved to be a powerful and reliable tool to construct these bifurcation diagrams. Indeed, it enables the electrical power network operators to better understand the problems of the phenomenon which had been observed in its network and to foresee new ferroresonance cases. Applied to the single-phase ferroresonant circuits, both series and parallel, we have been able to easily calculate the existence zones of these modes, as well as the stability limits of the system on ranges of broad variation of the parameters. Several results obtained numerically by software MATLAB, as from the real cases, are presented and commented upon.

Impact of Core Loss Non-linearity on Stability Domain of Ferroresonance

Iron losses strongly influence ferroresonance behavior of power transformers. While a jump-up is the characteristic of the non-linear magnetizing branch, the jump-down phenomenon can only be described when losses or loads are considered. In this article, the impact of core losses (constant resistance or non-linear resistancce) on the turning points of the bifurcation diagram of a ferroresonance circuit is investigated by a developed 2-D bifurcation diagram. The sensitivity of solutions with respect to the circuit parameters are analyzed and discussed. It is shown that the left-side turning point is more affected by the non-linear core loss model than the right side is. Based on the developed method, an operational guideline for the range of values of the load that avoids the jump between steady-state solutions and ferroresonance overvoltages with different source voltage amplitudes is provided. The results obtained by analytical approach are compared with time domain simulations.

Detection and analysis of isolated subharmonic ferroresonant solutions in power transformers

Ferroresonance is characterised by the existence of multiple periodic and non periodic steady states. Depending upon the initial condition the response of a ferroresonant circuit may settle to any one of the following: fundamental, subharmonic, quasi-periodic or chaotic. This paper is concerned with the isolated subharmonic ferroresonant solutions. The initial conditions are obtained by a class of temporal methods and it is referred to here as ‘temporal bifurcation diagram’ approach. Starting with initial conditions provided by temporal bifurcation diagram, a continuation procedure predicts multiple subharmonic solutions. Analysis of isolated subharmonic solutions reveals that in general they form a closed loop. Further, odd symmetric subharmonic solutions give rise to pitchfork bifurcations. The paper also reports the effect of core loss nonlinearity and transformer saturation on the isolated subharmonic solutions. Copyright © 2010 John Wiley & Sons, Ltd.

Modeling of nonlinear coil in a ferroresonant circuit

An adjustment of the standard method of converting measured RMS characteristics of the nonlinear coil into instantaneous characteristics has been suggested. A model of the nonlinear coil, obtained in this way, is used for predicting the prechaotic bifurcation points of a ferroresonant circuit. Slight improvements over the standard method are verified by the experimental results. The cause of the disagreement between the simulation and the measurement is identified.

Analysis of ferroresonance in a neutral grounding system with nonlinear core loss

The chaotic behaviour exhibited by a typical ferroresonant circuit in a neutral grounding system is investigated in this paper. In most earlier ferroresonance studies the core loss of the power transformer was neglected or represented by a linear resistance. However, this is not always true. In this paper the core loss of the power transformer is modelled by a third order series in voltage and the magnetization characteristics of the transformer are modelled by an 11th order two-term polynomial. Extensive simulations are carried out to analyse the effect of nonlinear core loss on transformer ferroresonance. A detailed analysis of simulation results demonstrates that, with the nonlinear core loss model used, the onset of chaos appears at a larger source voltage and the transient duration is shorter.

Flux Reflection Model of the Ferroresonant Circuit

The paper presents a linear model of ferroresonant circuit with flux reflection. The proposed model—flux reflection model—derives from observations of typical flux waveforms of nonlinear coil during ferroresonant steady states. Simulation results of the flux reflection model are compared with simulation results of the usual nonlinear model as well as with measurements carried out on the physical model of the ferroresonant circuit. The flux reflection model enables a novel comprehension of the ferroresonant circuit behavior and simplifies the modeling of the nonlinear coil in the ferroresonant circuit.

Parallel Ferroresonance Circuit Analysis by Chua-type Magnetization Model

This paper studies the nonlinear response of a parallel ferroresonant circuit. To carry out a transient analysis in parallel ferroresonant circuit, we apply Chua-type magnetization model to an inductance exhibiting saturation and hysteretic nonlinear properties of ferromagnetic materials, deriving a state variable equation and solutions by the backward Euler method with automatic modification. The characteristic values of the state transition matrix are calculated in each calculation step of Euler method in order to extract the chaotic characteristics. As a result, it is clarified that the chaotic behavior in the ferroresonant circuit is greatly concerned with the magnetic aftereffect of ferromagnetic materials.

Measurement system for model verification of nonautonomous second-order nonlinear systems

A measurement system for model verification of nonautonomous second-order nonlinear systems is presented. The measurement system is tested on two characteristic examples of nonlinear electrical systems, a boost dc converter and a ferroresonant circuit. In both cases, the models used in simulation are verified.

Analysis of Ferroresonance in a Power Transformer with Multiple Nonlinearities

This paper investigates the chaotic behavior exhibited by a typical ferroresonant circuit under two-phase open condition. The circuit includes multiple nonlinear elements that accounts for transformer core nonlinearities and arrester. In most of the ferroresonance studies the core loss of the transformer is neglected or modeled as linear resistor [1]. The basic model of the system under investigation and solution of the differential equations describing the model are corroborated against MicroTran [2]. Choice of state variables and formulation of state equations are accomplished through a topological approach [3]. Extensive simulations have been carried out to analyze the sensitivity of the state variables with respect to degree of core saturation, amplitude of the Thevenin voltage source and the presence of arrester. Time response plots, phase plots, Poincaré maps and conventional bifurcation diagrams are used to analyze the chaotic behavior. The results reveal that the nonlinear model of core loss has a significant effect on the onset of chaos. The simultaneous presence of arrester and nonlinear model of core loss effectively eliminates the chaotic region for lower value of transformer saturation exponent.

Novel Analytical Solution to Fundamental Ferroresonance—Part II: Criterion and Elimination

For ferroresonant circuits, the sufficient condition for preventing fundamental ferroresonance (FF) from occuring is that there is no intersection between the voltage-current characteristic of the linear part of the circuit, and the saturated power frequency excitation characteristic of the nonlinear part. Based on this understanding, part II of this paper has presented a criterion for the possibility of FF in the form of an analytical expression which is composed of the essential parameters of the circuit. By giving the critical resistance value for damping FF, the expression clearly indicates not only the possibility of FF but also the methods for eliminating the FF. The possibility of FF is judged by comparing the critical resistance value with the real value. In the meantime, the expression suggests how to adjust the essential parameters to suppress FF. The criterion has been proven by both simulation results and field tests. With this criterion, the possibility and elimination of FF can be studied for the first time by a simple yet effective analytical method.