Ferroresonance Phenomena in Unloaded Transformers Applying MOV

Transcription

1 International Journal of oputer and Electrical Engineering, Vol. 4, No. 5, October Ferroresonance Phenoena in Unloaded Transforers Applying MOV Haid Radanesh, Matin Nadei, and Marya Nadei Abstract This Paper studies the effect of a parallel Metal Oxide Varistor (MOV) on the ferroresonance oscillations of the transforer including nonlinear core losses. It is expected that the arresters generally cause ferroresonance dropout'. Tie-doain siulation has been carried out using MATLAB SIMULINK to study this effect. Siulation has been done on a three phase unloaded transforer with one open phase. Effect of varying input voltage has been studied. The siulation results reveal that connecting the arrester to the transforer poles, exhibits a great itigating effect on ferroresonant overvoltages. Phase plan along with bifurcation diagras are also presented. Significant effect on the onset of chaos, the range of paraeter values that ay lead to chaos and agnitude of ferroresonant voltages has been obtained, showed and tabulated. Index Ters Power transforer, nonlinear core losses effect, chaos, ferroresonance, Metal Oxide Varistor (MOV) I. INTRODUTION In siple ters, ferroresonance is a series of resonance involving nonlinear inductance and capacitances. It typically involves the saturable agnetizing inductance of a transforer and a capacitive distribution cable or transission line connected to the transforer. Its occurrence is ore likely to happen in the absence of adequate daping. Research involving ferroresonance in transforers has been conducted over the last 8 years. The word ferroresonance first appeared in the literature in 9 [], although papers on resonance in transforers appeared as early as 97 []. Practical interest was generated in the 93 s when it was shown use of series capacitors for voltage regulation caused ferroresonance in distribution systes [3], resulting in daaging overvoltages. The first analytical work was done by Rudenberg in the 94 s [4]. More precise and detailed work was done later by Hayashi in the 95 s [5]. Subsequent research has been divided into two ain areas: iproving the transforer odels and studying ferroresonance at the syste level. An understanding of the nonlinear paraeters describing a transforer core is prerequisite to dealing with ferroresonance. Swift [6] and Jiles [7] provide insights into transforer core behaviour and the separation of hysteresis and eddy current losses. Frae [8] and others have developed piecewise-linear ethods of odelling the nonlinearities in saturable inductances. Manuscript received Septeber, ; revised October 5,. Haid Radanesh is with Electrical Engineering Departent, Shahab Danesh Institute of Higher Education, gho, Iran(e-ail: Haid.radanesh@aut.ac.ir). Matin Nadei and M. Nadei are with Departent of Electrical Engineering, Islaic Azad University, Takestan Branch, Takestan, Iran(e-ail: hrbscstudent@gail.co; a.nadei@gail.co). Hopkinson [9] perfored syste tests and siulations on the effect of different switching strategies on the initiation of ferroresonance in three-phase systes. Sith [] categorized the odes of ferroresonance in one type of three-phase distribution transforer based on the agnitude and appearance of the voltage wavefors. Abrupt transition or jup fro one state to another is triggered by a disturbance, switching action or a gradual change in values of a paraeter. Typical cases of ferroresonance are reported in [], []. The theory of nonlinear dynaics has been introduced to provide deeper insight into the phenoenon [3]. Fundaental theory of nonlinear dynaics and chaos can be found in [], [4]. The susceptibility of a ferroresonance circuit to a quasi periodic and frequency locked oscillations are presented in [5], [6]. Paper in [7] investigated the effect of transforer odeling on the predicted ferroresonance oscillations. Using a linear odel, [8] have brought the effect of core loss in daping ferroresonance oscillations. In [9] ephasizes treating core loss as a nonlinear function of voltage on transforer. An algorith for calculating core losses based on no-load characteristics of transforer is given in []. The itigating effect of transforer connected in parallel to a MOV is illustrated in []. Analyze chaotic ferroresonance phenoena in power transforers including neutral resistance effect have been given in []. Effect of circuit breaker shunt resistance on chaotic ferroresonance in voltage transforer has been studied in [3]. In all previous studies, the effects of MOV on power transforer including nonlinear core losses are neglected. In previous works, it has been shown that nonlinear core loss can decrease ferroresonance phenoena in power transforer [4]. This paper studies the effect of MOV on the global behaviour of a ferroresonance circuit with nonlinear core loss. i II. SYSTEM MODELING E Rcore Lcore Fig.. Basic ferroresonance circuit i i V imosa MOSA Transforer is assued to be connected to the power syste while one of the three switches are open and only two phases of it are energized, which produces induced voltage in the open phase. This voltage, back feeds the distribution line. Ferroresonance will occur if the distribution line is highly 753

2 International Journal of oputer and Electrical Engineering, Vol. 4, No. 5, October capacitive. Syste involves the nonlinear agnetizing reactance of the transforer's open phase and resulted shunt and series capacitance of the distribution line. Base syste odel is adopted fro []. The MOV connected across the transforer winding which is showed in Fig.. Linear approxiation of the peak current of the agnetization reactance can be presented by (): i L = aλ However, for very high currents, the iron core ight be saturated where the flux-current characteristic becoes highly nonlinear. The λ-i characteristic of the transforer can be deonstrated by the polynoial which is given in () [4]: i L q = aλ + bλ Arrester can be expressed by the so-called alpha equation []: () () / α V = KI (3) where, V represents resistive voltage drop, I represents arrester current and K is constant and α is nonlinearity constant. In this paper, the core loss odel adopted is described by a third order power series which coefficients are fitted to atch the hysteresis and eddy current nonlinear characteristics given in []: R 3 + h V + hv h3v i = h + Per unit value of i R is given in (5) R V.73V.39V i = + The differential equation for the circuit in Fig. can be derived as follows: dvl de = k α.( v ) α l q ( h + h v + h v + h v ) ( aλ + bλ ) 3 l l 3 l dv l d λ = where, ω represents the power frequency and E is the peak value of the voltage source, shown in Fig.. III. SIMULATION RESULTS TABLE I: TYPIAL VALUES FOR VARIOUS SYSTEM PARAMETERS [] Power syste Power syste paraeters value paraeters a.8 q 7, 9 and b.7 L 36μH.47 k 3.5 E -7pu α 6.5, 5, 5 ω pu R 5, Typical values for various syste paraeters considered for siulation are listed in Table I. (4) (5) (6) (7) Initial conditions: dλ λ( ) =.; () = For the cases including arrester, it can be seen that ferroresonant drop out will be occurred. Figs., 3 and 4 show the phase plan diagra of syste states without arrester for E=3 pu. Figs. 4, 5 and 6 show the bifurcation diagra without arrester for E=-6 pu which depicts chaotic behavior. V oltage of Transfor er Phase Plan Diagra with q=7 including nonlinear core losses effect&without MOV Fig.. Phase diagra of syste including nonlinear core losses and without MOV, q=7 Figs. 5, 6 and 7 show the corresponding bifurcation diagras of the syste states without MOV and including nonlinear core losses for q=7, 9, which depicts chaotic behavior. In Fig. input voltage has been plotted against the flux of the power transforer. When the agnitude of the input voltage is 3pu, trajectory of the syste has chaotic behavior and aplitude of the flux and ferroresonance overvoltage reaches up to 7pu. By increasing in the degree of core nonlinearity, q, the behavior of the syste has being ore chaotic as shown in Fig. 3. In this case q=9 and oscillation in the voltage of the transforer goes up. V oltage of Transfor er Phase Plan Diagra with q=9 including nonlinear core losses effect&without MOV Fig. 3. Phase diagra of syste including nonlinear core losses and without MOV, q=9 V oltage of Transfor er 5-5 Phase Plan Diagra with q= including nonlinear core losses effect&without MOV Fig. 4. Phase diagra of syste including nonlinear core losses and without MOV, q= 754

3 International Journal of oputer and Electrical Engineering, Vol. 4, No. 5, October Fig. 4 shows the Phase plan diagra has been siulated by q=. It shows that chaotic resonance is highly dependent on the transforer odeling. Another tool that can show anner of the syste in vast variation of paraeters is bifurcation diagra. In Fig. 5, voltage of the syste has been increased to 6pu and ferroresonance has been begun in 4pu, it is shown that if input voltage goes up due to the abnoral operation or switching action, ferroresonance occurs, because of the nonlinearity in core losses, ferroresonance began in the big value of the input voltage. Voltage of Transfor er Bifurcation Diagra with q=7 Including NonLinear ore Losses&without MOV Fig. 5. Bifurcation diagra with q=7, without MOV Fig. 5 shows the abnoral phenoena in the unloaded transforer with the core odel nonlinearity q=7, it clearly shows when the q degree changes fro 7 to 9; ferroresonance begins in 3.9 pu. By coparing Fig. 6 with Fig. 7, it is clear that argin of the beginning ferroresonance has been decreased Bifurcation Diagra with q=9 Including NonLinear ore Losses&without MOV Fig. 6. Bifurcation diagra with q=9, without MOV Bifurcation Diagra with q= Including NonLinear ore Losses&without MOV Fig. 7. Bifurcation diagra with q=, without MOV Fig. 7 shows the bifurcation diagra of the overvoltage with q=. It shows that with q=, syste behavior reaches to.6 pu. Figs. 8, 9 and show the corresponding phase diagra for the syste in Fig.. Also, Figs., and 3 show the bifurcation diagras for corresponding syste including MOV. It is shown that chaotic region itigates by applying MOV Phase Plan Diagra with q=7 including Nonlinear core losses and MOV effect Fig. 8. Phase plan diagra of syste with q=7, applying MOV The use of geoetric graphical ethods like phase plan projections and bifurcation can be applied to obtain a better understanding of ferroresonance. Figs., and 3 show the bifurcation diagras for corresponding syste including MOV. It is shown that chaotic region itigates by applying MOV. This occurs ore typically for very large values of q Phase Plan Diagra with q=9 including Nonlinear core losses and MOV effect Fig. 9. Phase plan diagra of syste with q=9, applying MOV Phase Plan Diagra with q= including Nonlinear core losses and MOV effect Fig.. Phase plan diagra of syste with q=, including MOV In Fig., the degree of transforer core is q=7, in this figure, one jup has occurred in the trajectory of the syste and voltage of the transforer has period-3 oscillation. 755

4 International Journal of oputer and Electrical Engineering, Vol. 4, No. 5, October Bifurcation Diagra with q=7 Including NonLinear ore Losses and MOV siulated are very close for the period s one, two, and three. Period five is generally correct, with slightly lower than actual peak aplitudes predicted. The chaotic response predicted is slightly higher than the actual one. The odel used a siplistic linear resistance to represent the core losses of each core. The syste has been greatly affected by arrester paraeter. Maintaining sae paraeters, except transforer losses, siulations repeated, which showed that the tendency to fall in chaotic regions increases while, core losses decreases Fig.. Bifurcation diagra with q=7, applying MOV Bifurcation Diagra with q=9 Including NonLinear ore Losses and MOV IV. ONLUSION The dynaic behaviour of a transforer can be characterized by ultiple solutions. Inclusion of nonlinearity in the core loss reveals that bifurcation diagras will be soother when copared with linear odels. It has been shown that syste has been greatly affected by MOV. The presence of the MOV results in claping the Ferroresonance over voltages in studied syste. The MOV successfully, suppresses or eliinates the chaotic behaviour of proposed odel. onsequently, the syste shows less sensitivity to initial conditions in the presence of the MOV Fig.. Bifurcation diagra with q=9, applying MOV In Fig., q=9 and by considering MOV in the syste, there is no nonlinear phenoena and voltage of the transforer has a period-3 oscillation. By increasing the core nonlinearity, behavior reains in periodic oscillation and MOV can cause ferroresonance drop out Bifurcation Diagra with q= Including NonLinear ore Losses and MOV Fig. 3. Bifurcation diagra with q=, applying MOV A bifurcation is essentially a jup fro one ode of ferroresonance to another. A siulation technique was developed to very slowly rap the capacitance and record jups fro one ode to another. Due to nonlinearities, it is iportant to rap the capacitance both upward and downward, to ensure that as any ferroresonance odes are discovered as possible. Period 3 siply eans that the wavefor takes three periods of the forcing function to repeat, it contains /3 haronics. The odel correctly predicts the existence of all odes of ferroresonance at the correct values of capacitance. The actual wavefors AKNOWLEDGMENT orresponding author would like to appriciate Dr. Ali Nasrabadi of the Shahed University, Tehran, Iran, for providing MATLAB data files for the tie doain siulations, and Mrs. Leila Kharazi for her English editing. REFERENES [] B. A. Mork and D. L. Stueh, Application of nonlinear dynaics and chaos to ferroresonance in distribution systes, IEEE Transactions on Power Delivery, vol. 9, 994. [] J. Bethenod, Sur le transforateur et résonance, L Eclairae Electrique, pp , Nov. 3, 97. [3] J. W. Butler and. oncordia, Analysis of series capacitor application probles, AIEE Trans, vol. 56, pp , Aug [4] R. Rudenberg, Transient Perforance of Electric Power Systes. New York, NY: McGraw-Hill Book opany, 95, ch. 48. [5]. Hayashi, Nonlinear Oscillations in Physical Systes. New York, NY: McGraw-Hill Book opany, 964. [6] R. A. Walling, K. D. Barker, T. M. opton, and L. E. Zieran, Ferroresonance over voltages in grounded wye-wye pad ount transforers with low-loss silicon-steel cores, IEEE Trans. Power Delivery, vol. 8, no. 3, pp , July 993. [7] D.. Jiles and D. L. Atherton, Theory of ferroagnetic hysteresis, in Journal of Magnetis and Magnetic Materials: Elsevier Science Publishers B.V, Jan., 986, vol. 6, pp [8] J. G. Frae, N. Mohan, and T. Liu, Hysteresis odeling in an electroagnetic transients progra, IEEE Trans. PAS, vol. PAS-, no. 9, pp , Sept. 98. [9] R. H. Hopkinson, Ferroresonance during single-phase switching of 3-phase distribution transforer banks, IEEE Trans. PAS, vol. PAS-84, no. 4, pp , Apr [] NREA, Underground Distribution Syste Design and Installation Guide: National Rural Electric ooperatives Association, 994, sec. 6. [] H. W. Doel, A. Yan, R. J. O. D. Marcano, and A. B. Miliani, in: H.P. Khincha(Ed.), Tutorial ourse on Digital Siulation of Transients in Power Systes (hapter 4), IISc, Bangalore, 983, pp. 7-/38. []. Kieny, Application of the bifurcation theory in studying and understanding the global behavior of a ferroresonance electric power circuit, IEEE Transactions on Power Delivery, vol. 6, 99, pp [3] A. E. Araujo, A.. Soudack, and J. R. Marti, Ferroresonance in power systes: chaotic behaviour, IEE Proceedings- 4, 993, pp

5 International Journal of oputer and Electrical Engineering, Vol. 4, No. 5, October [4] B. A. Mork and D. L. Stueh, Application of nonlinear dynaics and chaos to ferroresonance in distribution systes, IEEE Transactions on Power Delivery, vol. 9, 994, pp [5] S. K. hkravarthy and. V. Nayar, Frequency-locked and quasi periodic (QP) oscillations in power systes, IEEE Transactions on Power Delivery, vol. 3, 997, pp [6] S. Mozaffari, M. Saeti, and A.. Soudack, Effect of initial conditions on chaotic ferroresonance in power transforers, IEE Proceedings*/Generation, Transission and Distribution, vol. 44, 997, pp [7] B. A. Mork, Five-legged wound*/core transforer odel: derivation, paraeters, ipleentation, and evaluation, IEEE Transactions on Power Delivery, vol.4, 999, pp [8] B. A. T. A. Zahawi, Z. Ein, and Y. K. Tong, haos in ferroresonance wound voltage transforers: effect of core losses and universal circuit behavioral, IEE Proceedings*/Sci. Meas. Technol, vol. 45, 998, pp [9] IEEE Working Group on Modeling and Analysis of Systes Transients, M.R. Iravani, hair, Modeling and analysis guidelines for slow transients*/part III: the study of ferroresonance, IEEE Transactions on Power Delivery, vol. 5,, pp [] W. L. A. Neves and H. Doel, on odeling iron core nonlinearities, IEEE Transactions on Power Systes, vol. 8, 993, pp [] K. A. Anbarri, R. Raanuja, T. Keerthiga, and K. Kuppusay, Analysis of nonlinear phenoena in MOV connected Transforers, IEE Proceedings Generation Transission and Distribution, vol. 48,, pp [] H. Radanesh, A. Abassi, and M. Rostai, "Analysis of ferroresonance phenoena in power transforers including neutral resistance effect," Southeastcon, 9. SOUTHEASTON '9. IEEE, pp.-5, 5-8 March 9. [3] H. Radanesh and M. Rostai, "Effect of ircuit Breaker Shunt Resistance on haotic Ferroresonance in Voltage Transforer," Advances in Electrical and oputer Engineering, vol., no. 3, pp. 7-77,. [4] H. Radanesh, M. Rostai, and A. Abassi, "Effect of circuit breaker shunt resistance on ferroresonance phenoena in voltage transforer," Southeastcon, 9. SOUTHEASTON '9. IEEE, pp.83-88, 5-8 March 9. Haid Radanesh was born in 98. He studied Telecounication engineering at Malek-Ashtar University of Technology, Tehran, Iran, and received the BS degree in 6, also studied electrical engineering at Shahed University Tehran, Iran, and received the MS degree in 9. urrently, He is PhD student in Airkabir University of Technology. His research interests include design and odeling of power electronic converters, drives, transient and chaos in power syste apparatus. 757