Electrical Power and Energy Systems 61 (2014) 318–325

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Electrical Power and Energy Systems

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Ferroresonance in subharmonic 3rd mode in an inductive voltagetransformer, a real case analysis

http://dx.doi.org/10.1016/j.ijepes.2014.03.0570142-0615/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +52 55 56233600x8810; fax: +52 55 56233600.E-mail addresses: molguinb@iingen.unam.mx (M.A. Olguín-Becerril), cangelesc@

iingen.unam.mx (C. Angeles-Camacho), cfuerte@umich.mx (C.R. Fuerte-Esquivel).1 Tel.: +52 55 56233600x8810.2 Tel.: +52 4433279 728.

Miguel A. Olguín-Becerril a,1, Cesar Angeles-Camacho a,⇑, Claudio R. Fuerte-Esquivel b,2

a Universidad Nacional Autónoma de México (UNAM), Instituto de Ingeniería, Edificio 12, Circuito Escolar s/n, Ciudad Universitaria, Delegación Coyoacán, C.P. 04510 MéxicoD.F., Mexicob Universidad Michoacana de San Nicolás de Hidalgo, Facultad de Ingeniería Eléctrica, División de Estudios de Posgrado, Cuidad Universitaria, 58030 Morelia, Michoacán, Mexico

a r t i c l e i n f o

Article history:Received 9 May 2013Received in revised form 21 March 2014Accepted 24 March 2014

Keywords:FerroresonanceInductive voltage transformerSubharmonic 3rd modeDamping reactor

a b s t r a c t

This paper focuses on a ferroresonance incident in subharmonic 3rd mode captured in the electrical sub-station Rio Escondido (REC), in the northeast of Mexico. Bearing in mind that this kind of ferroresonancephenomenon is a sporadic event and difficult to record, the contribution of this paper consists of the anal-ysis of this real-life ferroresonance phenomenon and to propose a practical solution that prevents thesekinds of incidents. An analytical calculation to obtain the electrical parameters of a damping reactor usedto damp out the ferroresonance phenomenon registered in the REC substation is reported.

� 2014 Elsevier Ltd. All rights reserved.

Introduction

Ferroresonance occurs because of an interaction between a non-linear inductance with series and parallel capacitances and lowvoltage [1]. In the event analyzed in this paper, ferroresonanceoccurred in the interaction between the nonlinearity of an induc-tive voltage transformer (IVT) with grading capacitors and conduc-tor capacitance. Potential danger comes from a combination of thetransformer and circuit breakers, which are equipped with gradingcapacitors. When the circuit breakers are opened, their capacitorscan equalize the transient voltage at both ends of the breakerand possibly push the voltage transformer into saturation. In thiscase, the inductive reactance of the voltage transformer might beequal to the system’s capacitive reactance providing a circuit forferroresonance in which the nonlinear inductance acts as a‘‘switch’’ allowing the energy trapped by the capacitance to bequickly transferred to other parts of the circuit during saturation.Therefore, this nonlinear phenomenon can induce discontinuousjump, amplitude responses, subharmonic responses or ampli-tude-modulated almost-periodic oscillations. This phenomenoncan be suppressed by several methods, such as the use of

resistance loading in voltage transformers, the use of disconnectorsto remove grading capacitors trapped charge or the use of a damp-ing reactor [1,2].

Recently, the problem of ferroresonance in the Mexican elec-tric power system has assumed great importance due torepeated failures in the IVTs which cause their destruction andin some cases the loss of electrical power. Therefore real-timedetection and the elimination of ferroresonance in IVTs are ofextreme interest. The aim of this paper is to report the studyof a ferroresonance case in subharmonic 3rd mode documentedfrom a relay recorder, which to the best of the authors’ knowl-edge has not been reported in the open literature, and demon-strate how the ferroresonance is damped out by installingdamping reactors.

The event described in this paper occurred on January 8, 2011at 4:34 a.m. in the 400 kV substation Rio Escondido (REC) locatedin the northeast control area of the Mexican interconnectedpower system and caused total damage in an IVT. The cause ofthe problem was a ferroresonant condition in a subharmonic3rd mode characterized by present overvoltages at a 20 Hz fre-quency [3]. Since the recording of this phenomenon is unusual,its study through these ferroresonance’s data captured in thefield allows its reproduction through the appropriate representa-tion of the substation in the Electromagnetic Transient Program(EMTP/ATPDRAW) in order to assess how the failure in the IVToccurred.

Fig. 1. The inductive voltage transformer with damping reactor.

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Ferroresonance features and the computation of the IVTdamping reactor

Ferroresonance is a type of nonlinear resonance characterizedby sustained overvoltages and overcurrents, with highly distortedwaveforms; it can damage the electrical equipment (thermally orfrom insulation breakdown) [4]. The main components that initiateferroresonance are a voltage source, a closed-path involving capac-itance, saturable inductors and low energy. The total capacitance ofa substation is composed of grading capacitors, cable capacitance,bus bar capacitance, coupling between lines, capacitor banks, isola-tion capacitance and capacitive transformers. On the other hand,the saturable or nonlinear inductance is provided by reactors,power transformers and IVTs; additionally, systems with low resis-tance increase the risk of ferroresonance conditions. In the contextof this paper, the magnetization reactance in an IVT is nonlineardue to the core saturation which is made of ferromagnetic mate-rial, so the overvoltages produced by the ferroresonance phenom-enon cause severe dielectric damage in the IVT [5]. The formationof hysteresis is an independent factor which significantly impactsthe ferroresonance modes. For an adequate hysteresis loops model,it must measure properly hysteresis loops at the power frequencyconsidering the dynamic behavior of the core loss resistance [6]. Inthis work, a constant resistance was used to represent the totalcore loss.

Fig. 2. Ferroresonant circuit.

Ferroresonance modes

The classification of ferroresonant modes corresponds tosteady-state conditions. In general, there are four modes of ferrore-sonance [7–9]:

(i) Fundamental. The voltages and currents are periodic with aperiod T equal to the electrical network period and can con-tain a variety of harmonics.

(ii) Subharmonic. The signals are periodic with a nT periodwhich is a multiple of the period of the power supply fromthe electrical network. This mode is called subharmonic nor harmonic 1/n. Subharmonic ferroresonant states are usu-ally an odd number [10].

(iii) Quasi-periodic. This is a non-periodic mode spectrum withdiscontinuity.

(iv) Chaotic. Its spectrum is continuous, i.e. it is not cancelled forany frequency.

One of the fundamental properties of ferroresonance is the factthat multiple stable solutions can exist under steady-state solu-tions. Therefore, small variations in the parameter value of theelectrical system or a transient event could cause a sudden jumpbetween two different stable states and produce two of the mostcommon ferroresonance modes: fundamental and subharmonic[11]. The parameters which determine the ferroresonance modeare the following: (i) the coupling capacitance which determinesthe natural frequency of oscillation; (ii) the amplitude of the volt-age source; and (iii) the resistive losses of the core.

Procedure to compute the IVT damping reactor

The ferroresonance phenomenon can be suppressed by usingeither a damping resistor or a damping reactor. In several recentworks a damping reactor has been used [1,2,12] instead of damp-ing resistors [13–15], as a magnetic switch connecting a resistancein series to the IVT secondary winding. Under normal operationconditions, the damping reactor is seen from the system as a highimpedance device in order to prevent power consumption. On the

other hand, when a disturbance occurs in the system, the dampingreactor reaches its saturate state earlier than the IVT; thus the ser-ies resistor is inserted to damp the ferroresonance [2,13,14]. Fig. 1shows the damping reactor location. Note that this device is notinstalled in the primary side; otherwise it would have the samesaturation characteristics of the IVT.

An analytical calculation to obtain the damping reactor param-eters which permit the damped out of the ferroresonancephenomenon registered in the REC substation, is reported inAppendix A based on the theory described in [16]. All possibletopological configurations in the substation that could producea ferroresonance phenomenon related to fundamental andsubharmonic 3rd mode have been considered. The proposedferroresonant circuit is shown in Fig. 2; it consists of a SeriesCapacitance (SC), a Parallel Capacitance (PC) and a saturable induc-tance provided by the IVT.

Based on this analysis, a damping reactor has been calculatedwith electrical parameters defined by a resistor Rdr with a linearresistance within the range of 0.11–0.15 ohms and a saturationvoltage operating in the range of 76–162 V (see Fig. 1).

Event in electrical substation Rio Escondido

Substation Rio Escondido description

The Mexican electric power system is divided into nine regionaltransmission control areas; one of them, the Baja California PowerSystem (BC-PS), is electrically isolated due to geographical reasons,and eight are electrically interconnected for improving reliability,

320 M.A. Olguín-Becerril et al. / Electrical Power and Energy Systems 61 (2014) 318–325

diversifying generation and supplying security. The electrical sub-station Rio Escondido (REC) is located in the northeast control areaas indicated in Fig. 3.

Among the different electric components of this substation,there are four generators of 300 MW each (two are connected in400 kV and two in 230 kV) as indicated in Fig. 4, two 400/230 kVautotransformers of 350 MVA each and three transmission linesat 400 kV referred to as REC-Carbon Dos (CBD), REC-Hércules Poten-cia (HCP) and REC-Frontera (FRO). The substation diagram at 400and 230 kV is shown in Fig 4.

The substation has three IVTs (one per phase), which areembedded in the 400 kV bus bars 1 (B1-400 kV) and 2 (B2-400 kV) as indicated in Fig. 5. Note that these IVTs did not includean anti-ferroresonant circuit. Finally, each circuit breaker has agrading capacitor and disconnectors.

Fig. 3. Electrical Me

Fig. 4. Electrical substation Rio Esc

Event with ferroresonance

On January 8, 2011 at 0:57 a.m. there was a failure in the ash-compressor motor at generator 4; however, the motor protectiondid not operate because the trip coils of its circuit breaker weredamaged. Under this condition, the scheme of breaker failure oper-ated by tripping all breakers connected to the bus bar 1 at 400 kV(but not the disconnectors), i.e. generators 3 and 4 as well as thetransmission line REC-CBD shown in Fig. 5. In that moment, a fer-roresonance occurred because a ferroresonant circuit was formedwith the gradient capacitors of the circuit breakers; cable capaci-tance, bus bar capacitance and the saturable inductance of theIVT’s phase a, which become damaged.

At 4:34 a.m. bus bar 1 was energized by closing the transmis-sion line REC-CBD, but because the IVT’s phase a was damaged, it

xican network.

ondido in 400 kV and 230 kV.

Fig. 5. REC diagram with damage IVT detail.

M.A. Olguín-Becerril et al. / Electrical Power and Energy Systems 61 (2014) 318–325 321

exploded and the differential protection scheme operated, trippingthe REC-CBD line. In that moment, a ferroresonance appearedagain, this time in b and c phases. Note that in both ferroresonanceevents, the circuit breakers opened but the disconnectors were stillclosed providing access to the voltage across the grading capaci-tors. The event was captured by a relay recorder, which has low-frequency filters for proper operation, installed in a current trans-former (CT) at the circuit breaker A1030 (Fig. 5) of the generatorU3. The recorder provided the three-phase voltages waveformsshown in Fig. 6. The following observations are derived from theanalysis of these waveforms.

At the beginning of the plot, the pre-fault signal (before the busbar 1 energization) is the voltage across the grading capacitors ofcircuit breakers because the disconnectors remained closed andcorresponds to an operation condition before the transmission lineREC-CBD was reconnected. The transmission line REC-CBD wasthen closed at 0 s to energize bus bar 1. In that instant, the IVTphase a exploded because the ferroresonance damage occurred.The failure was cleared in 0.06 s because the differential protection

scheme operated by tripping the REC-CBD line, producing a wave-form distortion in phases b and c voltages as a result of ferroreso-nance. At 0.46 s, the IVT phase a starts to catch fire after itsexplosion.

A detail of voltages signals are shown in Fig. 7 where themoment of the IVT phase a explosion is observed.

Subharmonic 3rd mode

Based on the recording of voltage waveforms, a Fourier analysisof the post-fault voltage measured at phase b was performed, asshown in Fig. 8. The result of this analysis permits the establish-ment of the presence of a subharmonic 3rd or a harmonic 1/3 inthe distorted waveform. This analysis also confirms the assump-tion that a ferroresonance containing a subharmonic 3rd modeprovokes an overvoltage that caused the IVT damage. It is unusualto capture an event where ferroresonance is present, and this is theonly one obtained so far in the REC substation by the relay recor-der. Hence the importance of this analysis.

Fig. 6. Disturbance captured on January 8, 2011 at 4:34 a.m. at REC showing voltages in phases a, b and c.

Fig. 7. Detail of voltage signals.

Fig. 8. Fourier analysis of the distorted waveform to post-fault voltage.

322 M.A. Olguín-Becerril et al. / Electrical Power and Energy Systems 61 (2014) 318–325

Ferroresonance in subharmonic 3rd mode, simulation andsuppression

Simulation and analysis were required to determine the charac-teristics of a damping reactor that avoids the ferroresonance phe-nomenon described above. In order to carry out this study, thetransmission network was represented by equivalent power injec-tions at the 400 kV substation bus bars; the 400 kV transmissionnetwork was represented by the power injections through trans-mission lines REC-CBD, REC-HCP and REC-FRO. Furthermore, the

230 kV transmission network was also represented by the powerinjections through the two autotransformers 230/400 kV depictedin Fig. 4. These power flows were computed by a power flow anal-ysis performed by using the Power System Simulator for Engineer-ing (PSS/E) software. Based on those equivalents, the EMTP/ATPDRAW program to reproduce this ferroresonance event basedon the data file reported in Appendix B. In this case, the graphicalpreprocessor ATPDRAW was used to construct the electrical circuitassociated with the data file using the components provided fromthe program’s menus. The resulting waveforms of the numericalstudy are reported in Fig. 9. Despite that these results have a sim-ilar pattern of behavior to those measured at the substation (Fig. 6),there exists some differences between both sets of results becausethe lack of manufacturer data, such as the inductance value on theIVT secondary side and its magnetization resistance, as well assome substation parameters which could not be measured toachieve a more accurate simulation.

Damping reactors simulation

A damping reactor is connected in the IVT secondary side (oneper phase) as indicated in Fig. 1 in order to damp out the ferrore-sonance phenomenon.

An EMTP/ATPDRAW simulation was performed by using the400 kV circuit shown in Fig. 5 with the following parameters as cal-culated in Appendix A: (i) damping reactor resistance of0.12 ohms; and (ii) damping reactor saturation voltage of 90 V.

Fig. 9. Ferroresonance event reproduction through the EMTP/ATPDRAW program.

Fig. 10. Magnetization curves used for; (a) IVTs and (b) damping reactors.

Fig. 11. Voltage at phase b without (a) and with (b) damping reactor.

M.A. Olguín-Becerril et al. / Electrical Power and Energy Systems 61 (2014) 318–325 323

The magnetization curves for both the IVTs and the damping reac-tors are shown in Fig. 10.

The results obtained from this analysis are reported in Fig. 11(aand b) for the cases in which the damping reactor is not connectedand when it is connected to the IVT, respectively. The results

reported in Fig. 11(a) correspond to the ferroresonancephenomenon recorded in the January 8, 2011 reproduction. Onthe other hand, the possibility of damping out this phenomenonis demonstrated with the results reported in Fig. 11(b), wherethe ferroresonance condition does not appear after the fault is

Fig. 12. Effect of applying the damping reactor on the harmonic content associatedwith the ferroresonance condition.

324 M.A. Olguín-Becerril et al. / Electrical Power and Energy Systems 61 (2014) 318–325

cleared if the damping reactor is used. This is shown in Fig. 12,where the harmonic content associated with the ferroresonancecondition was significantly reduced.

Conclusions

By using a real-life ferroresonance event recorded in the Mexi-can electrical system, it was possible to reproduce a ferroresonancephenomenon by using the program EMTP/ATPDRAW in order tocalculate and to analyze the damping reactor behavior to avoidthe occurrence of the ferroresonance condition. The guidelinesreported in this paper to perform the calculation of this dampingreactor can be applied for both electric transmission and distribu-tion substations considering their corresponding ferroresonantcircuit.

For ferroresonance reproduction adequacy, one must toconsider all the series and parallel capacitance involved in theferroresonant circuit as well as the IVT magnetization curve.

Ferroresonance in subharmonic 3rd mode (20 Hz) andfundamental mode are the most frequent modes presented in anelectrical power substation.

Appendix A:. Calculations of damping reactor parameters

The analytical calculation to obtain the damping reactor param-eters was performed considering the REC substation configurationsin which ferroresonance could be set up and fundamental and sub-harmonic 3rd modes could be avoided [16].

A ferroresonant circuit is integrated by Series Capacitance(SC) + Parallel Capacitance (PC) and saturable inductance providedby IVT.

A critical substation operating configuration when the ferrore-sonance was provided is chosen when the following conditionsare met:

(a) Minimum voltage, to keep ferroresonance in the fundamen-tal mode. It is calculated by using the following equation:

Vmin ¼R1Vsat

2Xcmð1�mÞ ð1Þ

where R1 is the resistance in the primary side, in this case29818.315 ohms. Vsat is the saturation voltage of IVT, in this case568,000 V. XC is the capacitor impedance equivalent i.e.

Xc ¼1

2� p� 60� TCð2Þ

In this case Tc = Sc + Pc = 5500 pF + 4939.3 pF = 10439.3 pFFrom (2); Xc = 254095.8 ohmsSince m = 0.8, therefore, the minimum voltage to maintain fer-

roresonance in the fundamental mode is

Vmin ¼ 208297:45 V

(a) The applied voltage in the IVT as capacitive divisor is calcu-lated by using:

AV ¼ Vnom � Sc=ðSc þ PcÞ ð3Þ

whereVnom = 241,500 V, so AV = 127235.54 VSince the applied voltage is lower than the minimum voltage,

the IVT does not present a ferroresonance in fundamental mode.The minimum voltage in which subharmonic 3rd ferroreso-

nance is maintained is

Vmin ¼R1Vsat

2Xcmðn�mÞ þVsatnXc

ðn�mÞR2ð4Þ

where R2 is the attached resistance to the secondary side andreflected to the primary side in the IVT and is expressed byR2 = (R20)(RT2), RT is the ratio (3500), R20 is the resistance before itis reflected, n is 3 (subharmonic 3rd, 20 Hz).

The first term of (4) considers IVT saturation voltage with theresistance connected in the primary side, whereas the second termconsiders IVT saturation voltage with the resistance connected inthe secondary side and is reflected at the primary side in the IVT.The addition of both terms gives the minimum voltage when sub-harmonic 3rd ferroresonance is maintained.

Several R20 values were proven until 0.15 ohms was obtainedand so

Vmin ¼ 126042:93 V

This value is reached by the applied voltage calculated in (b) if thereis a load resistance in the secondary side of the IVT of 0.15 ohms orless, the applied voltage is lower than the voltage needed for main-taining subharmonic 3rd ferroresonance.

In this way, the resistance of the damping reactor maximumvalue (0.15 ohms) is analytically calculated.

To avoid reaching in a new ferroresonance regimen, it is neces-sary to calculate the resistance of the damping reactor minimumvalue. Using,

ðR1 þ R2ÞVsat2

2XCnðn�mÞUeff2

>R1Vsat1

2XCðn�mÞ þVsat1XC

R2

Ueff1

ð5Þ

where Vsat1 is the saturation voltage of IVT, Vsat2 is the saturationvoltage of damping reactor reflected in the primary side, Xc is thecapacitor impedance equivalent, i.e., m = 0.8 and n = 3 (subharmon-ic 3rd, 20 Hz).

The first expression considers the primary and secondary resis-tance with damping reactor saturation voltage which should behigher than the second expression to avoid reaching a new ferrore-sonance regime.

The second expression indicates the voltage in which subhar-monic 3rd ferroresonance is maintained.

Therefore, when the first expression is bigger than the secondone in (5), the damping reactor minimum is obtained.

The operation voltage of the damping reactor is 38 V, soVsat2 = 38 � 2.35 = 89.3 � 90 V, reflected in the primary side is:90 � 3500, so, Vsat2 = 315,000 V.

Several R20 values were proven to get the one with 0.11 ohms,which satisfy the condition.

Ueff2 ¼ 129352:09 > Ueff1 ¼ 122255:71

Table 1Bus bar data.

Phase Rin (cm) Rout (cm) Rdc (ohm/km) Horiz (m) Vtower (m) Vmid (m) Separ (cm) Alpha (deg) NB

a 0.4 1.5889 0.05848 0 13 13 45 180 2b 0.4 1.5889 0.05848 7 13 13 45 180 2c 0.4 1.5989 0.05848 14 13 13 45 180 2

Table 2Circuit breakers gradient capacitors in REC.

Transmission line pF

REC-CBD 500REC-HCP 1000REC-FRO 500

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In this way, the resistance of the damping reactor minimumvalue (0.11 ohms) is analytically calculated.

The damping reactor is saturated before the IVT. Because thedamping reactor is installed in the secondary side at 69 V, it shouldbe saturated with a higher voltage than 69 � 1.1 = 75.9 V.

The IVT saturated voltage is above 235% of the nominal voltage,i.e. 69 � 2.35 = 162.15 V.

The saturation voltage operating range is between 76 and162 V.

Appendix B:. Dataset for ferroresonance analysis with EMTP/ATPDRAW

See Tables 1 and 2.

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