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

Fathi Ben Amar, Rachid Dhifaoui

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DOI: 10.4236/epe.2011.34056                

Abstract

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.

Keywords

Transformer, Ferroresonance, Fundamental Mode, Harmonic Mode, Subharmonic Mode, Fractional Mode, Isolat, Limit Point, Bifurcation, Dangerous Zone

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	K. Pattanapakdee and C. Banmongkol, “Failure of Riser Pole Arrester due to Station Service Transformer,” International Conference on Power Systems Transients (IPST’07), Lyon, 4-7 June 2007.
[2]	S. Santoso, R. C. Dugan and H. Peter, “Modeling Ferroresonance Phenomena in an Underground Distribution System,” International Conference on Power Systems Transients (IPST’07) Lyon, 4-7 June 2007.
[3]	R. C. Dugan, “Examples of Ferroresonance in Distribution Systems,” IEEE Power Engineering Society General Meeting, Knoxville, 13-17 July 2003.
[4]	Ph. Ferracci, “Ferroresonance,” Cahier Technique, Group Schneider, 1998.
[5]	C. Kieny, “Application of the Bifurcation Theory in Studying and Understanding the Global Behaviour of a Ferroresonant Electric Power Circuit,” IEEE Transactions on Power Delivery, Vol. 6, No. 2, 1991, pp. 866- 872. doi:10.1109/61.131146
[6]	F. Ben Amar and R. Dhifaoui, “Bifurcation Diagrams and Lines of Period-1 Ferroresonance,” WSEAS Transactions on Power Systems, Vol. 1, No. 7, 2006, pp. 1154-1162.
[7]	F. Ben Amar and R. Dhifaoui, “Study of the Periodic Ferroresonance in the Electrical Power Networks by Bifurcation Diagrams,” International Journal of Electrical Power and Energy Systems, Vol. 33, No. 1, 2011, pp. 61-85. doi:10.1016/j.ijepes.2010.08.003
[8]	B. S. A. Kumar and S. Ertem, “Capacitor Voltage Transformer Induced Ferroresonance: Causes, Effects and Design Considerations,” Electric Power Systems Research, Vol. 21, 1991, pp. 23-31.
[9]	S. K. Chakravarthy and C. V. Nayar, “Series Ferroresonance in Power Systems,” International Journal of Electrical Power & Energy Systems, Vol. 17, No. 4, 1995, pp. 267-274. doi:10.1016/0142-0615(95)00045-R
[10]	M. Rioual and C. Sicre, “Energization of a No-Load Transformer for Power Restoration Purposes: Impact of the Sensitivity to Parameters,” International Conference on Power Systems Transients (IPST’01), Seattle, Vol. 2, 16 July 2001, pp. 892-895.
[11]	N. Janssens, V. Vanderstockt, H. Denoel and P. A. Monfils, “Elimination of Temporary Overvoltages Due to Ferroresonance of Voltage Transformers: Design and Testing of Damping System,” International Council on Large Electric Systems, 1990, pp. 33-204.
[12]	R. G. Kavasseri, “Analysis of Subharmonic Oscillations in a Ferroresonant Circuit,” International Journal of Electrical Power and Energy Systems, Vol. 28, No. 3, 2005, pp. 207-214. doi:10.1016/j.ijepes.2005.11.010
[13]	K. S. Preetham, R. Saravanaselvan and R. Ramanujam, “Investigation of Subharmonic Ferroresonant Oscillations in Power Systems,” Electric Power Systems Research, Vol. 76, No. 9-10, 2006, pp. 873-879. doi:10.1016/j.epsr.2005.11.005
[14]	R. G. Kavasseri, “Analysis of Subharmonic Oscillations in a Ferroresonant Circuit,” International Journal of Electrical Power and Energy Systems, Vol. 28, No. 3, 2005, pp. 207-214. doi:10.1016/j.ijepes.2005.11.010
[15]	M. Val Escudero, I. Dudurych and M. A. Redfern, “Characterization of Ferroresonant Modes in HV Substation with CB Grading Capacitors,” Electric Power Systems Research, Vol. 77, No. 11, 2007, pp. 1506-1513. doi:10.1016/j.epsr.2006.08.033
[16]	S. Mitrea and A. Adascalitei, “On the Prediction of Ferroresonance in Distribution Networks,” Electric Power Systems Research, Vol. 23, No. 2, 1992, pp. 155-160. doi:10.1016/0378-7796(92)90063-7
[17]	M. M. Saied, H. M. Abdallah and A. S. Abdallah, “Damping Effect of Load on the Ferroresonance Phenomenon in Power Networks,” Electric Power Systems Research, Vol. 7, 1984, pp. 271-277. doi:10.1016/0378-7796(84)90011-7