Coupling capacitor voltage transformer: A model for electromagnetic transient studies

Electric Power Systems Research 77 (2007) 125–134

Coupling capacitor voltage transformer: A model for electromagnetic transient studies D. Fernandes Jr. a,∗ , W.L.A. Neves a , J.C.A. Vasconcelos b a

Department of Electrical Engineering, Federal University of Campina Grande, Av. Aprigio Veloso, 882 Bodocongo, 58.109-970 Campina Grande, PB, Brazil b Companhia Hidro El´ etrica do S˜ao Francisco, Rua Delmiro Gouveia, 333 Bongi, 50.761-901 Recife, PE, Brazil Received 7 December 2005; received in revised form 8 February 2006; accepted 12 February 2006 Available online 27 March 2006

Abstract In this work, an accurate coupling capacitor voltage transformer (CCVT) model for electromagnetic transient studies is presented. The model takes into account linear and nonlinear elements. A support routine was developed to compute the linear 230 kV CCVT parameters (resistances, inductances and capacitances) from frequency response data. The magnetic core and surge arrester nonlinear characteristics were estimated from laboratory measurements as well. The model is used in connection with the electromagnetic transients program (EMTP) to predict the CCVT performance when it is submitted to transient overvoltages, as are the cases of voltages due to the ferroresonance phenomenon and circuit breaker switching. The difference between simulated and measured results is fairly small. Simulations had shown that transient overvoltages produced inside the CCVT, when a short circuit is cleared at the CCVT secondary side, are effectively damped out by the ferroresonance suppression circuit and the protection circuit. © 2006 Elsevier B.V. All rights reserved. Keywords: Coupling capacitor voltage transformer; Ferroresonance; Optimization methods; Overvoltage protection; Power system transients

1. Introduction For many years, electric utilities have used coupling capacitor voltage transformers (CCVT) as input sources to protective relays and measuring instruments. The steady-state performance of the CCVT is well known. However, more investigations are necessary when these equipments are submitted to transient overvoltages [1–3]. Brazilian electric utilities have reported unexpected overvoltage protective device operations during normal switching conditions in several 230 and 500 kV CCVT units, affecting the reliability of the power system and even causing failures in some CCVT units [4]. A thorough investigation of the CCVT transient behavior is needed. Many works including field measurements, laboratory tests and digital simulations, have been conducted to study the performance of the CCVT for electromagnetic transient studies. However, there are many problems to obtain

∗

Corresponding author. Tel.: +55 83 33101326; fax: +55 83 33101015. E-mail address: [email protected] (D. Fernandes Jr.).

0378-7796/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2006.02.007

accurate models, especially due to the need of laboratory tests. Some studies have been concentrated on nonlinear behavior of the potential transformer (PT) magnetic core to accurately simulate the transient response of CCVT [1–3]. Other works have considered the effect of stray capacitances in some CCVT elements to explain the measured frequency responses in the linear region of operation [5,6]. There are some problems in obtaining the CCVT parameters. In ref. [5], the used measurement techniques need disassembling the CCVT and in ref. [6], a method was developed to estimate the CCVT linear parameters from frequency response measurements at the secondary side without the need to access its internal components. Saturation effects of the magnetic core were not taken into account. In this work, an accurate CCVT model is developed. It takes into account linear and nonlinear elements. A support routine was developed to compute the linear 230 kV CCVT parameters (resistances, inductances and capacitances) from the magnitude and phase of the CCVT voltage ratio measured in laboratory. The errors were fairly small in the whole frequency range. The magnetic core and surge arrester nonlinear characteristics were also estimated from laboratory measurements.

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For validation purposes of the CCVT model in time-domain, digital simulations were compared to ferroresonance and switching operation tests carried out for the 230 kV CCVT at our high voltage laboratory with small errors. The obtained CCVT model was used to predict its transient response. It was observed that the ferroresonance suppression circuit and the protection circuit are very effective in damping out transient overvoltages produced inside the CCVT when a short circuit is cleared in its terminals. Some of these results were presented in ref. [7]. Fig. 2. CCVT model for estimation of parameters.

2. Underlying concepts The basic electrical diagram for a typical CCVT is shown in Fig. 1. The primary side consists of two capacitive elements C1 and C2 connected in series. The potential transformer provides a secondary voltage vo for protective relays and measuring instruments. The inductance Lc is chosen to avoid phase shifts between vi and vo at power frequency. However, small errors may occur due to the exciting current and the CCVT burden (Zb ) [1]. Ferroresonance oscillations may take place if the circuit capacitances resonate with the iron core nonlinear inductance. These oscillations cause undesired information transferred to relays and measuring instruments. Ferroresonance suppression circuits (FSC) tuned at power frequency (L in parallel with C) and a resistance to ground have been used to damp out transient oscillations requiring a small amount of energy during steadystate [3,6,8].

Fig. 3. (a) FSC design and (b) FSC digital model.

The FSC design is shown in Fig. 3(a). A nonsaturable iron core inductor Lf is connected in parallel with a capacitor Cf so that the circuit is tuned to the fundamental frequency with a high Q factor [3,8]. The FSC digital model is shown in Fig. 3(b). The damping resistor Rf is used to attenuate ferroresonance oscillations.

3. Developed analytical method The diagram shown in Fig. 1 is valid only near power frequency. A model to be applicable for typical frequencies of ferroresonance and frequencies up to a few kilohertz needs to take into account the PT primary winding and compensating inductor stray capacitances at least [2,3,5,6]. In this work, the circuit shown in Fig. 2 was used to estimate the linear CCVT parameters. It comprises a capacitive column (C1 , C2 ), a compensating inductor (Rc , Lc , Cc ), a potential transformer (Rp , Lp , Cp , Lm , Rm ) and a ferroresonance suppression circuit (Rf , Lf1 , Lf2 , −M, Cf ).

3.1. Linear CCVT parameters estimation The circuit shown in Fig. 2 can be replaced by Fig. 4 with impedances Z1 , Z2 , Z3 , Z4 , Z5 and all elements referred to the PT secondary side. The expressions for the referred impedances in the s domain, with s = jω, are: Z1 = [(Rc + sLc )/r 2 ]//(1/r 2 sCc ); Z2 = (Rp + sLp )/r 2 ; Z3 = (Rm /r 2 )//(sLm /r 2 ); Z4 = (sLf1 + 1/sCf )//(sLf2 ); Z5 = Rf − sM.

Fig. 1. Basic electrical diagram for a typical CCVT.

Fig. 4. CCVT model for development of the analytical expressions.

(1)

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where r is the PT ratio and the symbol // denotes that elements are in parallel. The linear parameters R, L, C were obtained from curve fitting algorithm based on Newton’s method to mach the transfer functions represented by the ratio vo /vi . This fitting technique is an improvement over the one presented in refs. [5,6] because here both magnitude and phase curves are fitted simultaneously. The technique is described below. 3.2. Minimization technique of nonlinear functions Methods for minimizing nonlinear functions are usually iterative, that is, given an approximate solution, an estimate of the solution is obtained. The technique used here is based on Newton’s method which uses a second-order Taylor series expansion to the error function F(x) in the matrix/vector form, as follows: 1 F (x + p) ≈ F (x) + pT ∇F (x) + pT ∇ 2 F (x)p, 2

(2)

where the vector x = [x1 , x2 , . . ., xm ] and p is the increment vector in the direction of the estimate solution; p is obtained by minimizing the function F setting its gradient to zero which results in: ∇ 2 F (x)p = −∇F (x).

(3)

The approximate solution xk+1 is given by: −1

xk+1 = xk + p = xk − [∇ 2 F (xk )]

∇F (xk ).

(4)

Newton’s method will converge if [
2 F(x)]−1 is positive definite in each iterative step, that is, zT [
2 F(x)]−1 z > 0 for all z = 0. This technique is known as the full Newton-type method [9]. It is a modification of Newton’s method for that iteration in which [
2 F(x)]−1 is not positive definite. In the procedure,
2 F(x) is replaced by a “nearby” positive definite matrix ∇¯ 2 F (x) and the increment p is computed by solving Eq. (3). The error function F(x) is given by:  n 
yi − y(ωi ; x) 2 (5) F (x) = σi

(4) If the difference is greater than a user-defined tolerance, go back to step 2. Otherwise, stop the iterative process. 4. Laboratory measurements 4.1. Frequency response In order to obtain the frequency response data to be used as input data to the routine developed to compute the linear CCVT parameters, frequency response measurements, for magnitude and phase, were carried out for the CCVT, from 10 Hz to 10 kHz. A signal generator feeding an amplifier was connected across the primary terminal and the ground, and the secondary voltage was measured, as shown in Fig. 5. At 60 Hz, that is the frequency in which the CCVT operates most of the time, the measured voltage ratio and phase shift were 1120.5 and 0◦ , respectively. The rated values are 1154.7 and 0◦ . There is only an error smaller than 3% in the voltage ratio. The signal was applied to the CCVT primary side because the voltage measurements are made directly, without the need of using external elements in the CCVT terminals. In the methodology proposed by [6], the voltage signal is applied to the CCVT secondary side, and the primary voltage was measured, as shown in Fig. 6. In this methodology, it is necessary to choose adequate values for the external resistors R connected on the CCVT primary side and Rb connected on the secondary side in series with the power amplifier, otherwise distortions may occur in the frequency response curves, as shown in some simulation results (sensitivity analysis) presented in Figs. 7 and 8 for a 138 kV CCVT reported in literature [6].

i=1

where ωi is the ith measured frequency value and yi is the ith measured frequency response value of the n data points. σ i is the standard deviation for each yi . x is the vector which contains the m parameters R, L, C to be calculated and y(ωi ; x) is the analytical model function. A computer routine was developed to minimize the error function F(x) using the method described above. Besides the function y(ωi ; x), it is necessary to know its first and second derivatives with respect to each parameter of the vector x. The algorithm is described as follows: (1) Supply the CCVT frequency response values yi for each frequency ωi and enter with a guess for the parameters R, L, C (vector x). (2) Determine F(x) and evaluate F(x + p). (3) Save the value of F(x + p) and for a user-defined number of iterations t, compare the actual value of the error function to its old value t iterations before.

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Fig. 5. Frequency response measurements.

Fig. 6. Frequency response measurements proposed by Kojovic et al. [6].

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minimize high frequency measurement errors, the connections among measuring devices and the CCVT were made with copper ribbons 2.6 cm wide. 4.2. Potential transformer nonlinear characteristic The PT nonlinear peak flux–current (λ–i) characteristic was obtained from measured rms voltage–current (V–I) data using a routine from [10]. The sinusoidal voltage was applied across one of the low voltage terminals and gradually increased from 0 to 251.3 V rms. The air core inductance was calculated by the expression: N 2 µ0 S Lsat ∼ = l

Fig. 7. Simulation results: sensitivity analysis for the 138 kV CCVT magnitude curve to the value of the resistance R considering the methodology proposed by Kojovic et al. [6].

For the simulation results shown in Figs. 7 and 8, the external elements were assumed to be pure resistances with no phase shift in the whole frequency range. In reality, the magnitude and phase of these “resistive” elements depend on the frequency and the use of external elements may significantly affect the CCVT parameters to be calculated. It should be pointed out that even for the correct circuit topology, the performance of the fitting procedure depends on “how good” the measured data are, due to the term [yi − y(␻i ; x)], which is the random measurement error of each point. Careful measurements with standard devices and low noise due to properly made connections, lead to fairly small errors, good convergence properties and realistic physical parameters. To

(6)

where N = 81 (estimated by winding a wire around the core with known number of turns and measuring the voltage ratio to the PT low voltage winding) is the number of turns of the secondary winding, µ0 = 4π × 10−7 H/m is the magnetic permeability in vacuum, S = 91.5 cm2 is the measured core cross-section area and l = 71.28 m is the average length of the secondary winding. It was considered that saturation occurs with a flux density of 2.1 T, which corresponds to λknee = 1.556415 V s. The value of iknee was calculated from [10] after a logarithmic extrapolation of the previous points in the rms V–I curve. This corresponds to the previous to the last point of the λ–i data points shown in Table 1. The last segment slope is Lsat . 4.3. Surge arrester nonlinear characteristic estimation The 230 kV CCVT protection circuit comprises a silicon carbide (SiC) surge arrester connected in parallel with the capacitance C2 . To estimate its v–i characteristics, its sparkover voltage was measured at power frequency. The voltage supplied by a high voltage transformer, rated 100 kV and 10 kVA, was applied gradually across the surge arrester terminals, as shown in Fig. 9, until gap sparkover was reached. For some measurements, the sparkover voltage average value was 58.5 kV rms. Based on these measurements and according to ANSI/IEEE standards [11,12], the v–i characteristic was obtained for a completely assembled gapped SiC arrester. This characteristic depends on the waveform applied to the arrester. The standard wavefront was assumed to be 2 ms since the measurements were made at low frequency (60 Hz). The estimation was based on a Table 1 Nonlinear characteristic of the potential transformer magnetic core

Fig. 8. Simulation results: sensitivity analysis for the 138 kV CCVT magnitude curve to the value of the resistance Rb considering the methodology proposed by Kojovic et al. [6].

Current (A)

Flux (V s)

0.076368 0.720881 1.429369 2.511675 3.662012 4.587227 5.712037 55.527018 5552.7018

0.025772 0.189066 0.396889 0.748388 0.863553 0.903317 0.942706 1.556415 1.562242

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Table 4 138 kV CCVT initial guess parameters Rc = 174.0  Lc = 17.0 H Cc = 58.0 pF Cp = 5.0 pF Rp = 3.0 k

Lp = 7.0 H Rm = 34.0 M Lm = 10.0 kH Lf1 = 650.0 mH Cf = 7.0 ␮F

Lf2 = 270.0 mH Rf = 40.0  M = 193.0 mH – –

Table 5 138 kV CCVT recalculated parameters Fig. 9. Sparkover voltage measurements for the 230 kV CCVT silicon carbide surge arrester. Table 2 Silicon carbide surge arrester nonlinear characteristic Current (A)

Voltage (kV)

100 200 500 1000 2000

20.8 27.9 39.0 42.9 45.5

typical 6 kV silicon carbide arrester characteristic supplied by the manufacturer [13]. The arrester nonlinear characteristic is shown in Table 2. 5. Model validation The nonlinear fitting routine was used for two CCVT. To check if the code was correct, 138 kV CCVT data reported in literatures [5,6] were used as a benchmark. For the 230 kV CCVT, the parameters were obtained from frequency response data points of magnitude and phase measured in laboratory. Normally, in literature, simulation results for the CCVT models are not compared to laboratory measurements of transient overvoltages [5,6]. In our work, ferroresonance and circuit breaker switching operations tests were carried out for the 230 kV CCVT, in order to validate the CCVT model in time-domain studies. The errors were fairly small for both tests.

Rc = 3.25  Lc = 56.55 H Cc = 126.86 pF Cp = 151.44 pF Rp = 833.55 

Lp = 2.88 H Rm = 1.47 M Lm = 10.98 kH Lf1 = 649.78 mH Cf = 7.53 ␮F

Lf2 = 274.34 mH Rf = 36.80  M = 192.7 mH – –

is shown in Table 4. The recalculated parameters are shown in Table 5. Figs. 10 and 11 show the analytical and fitted curves for magnitude and phase, respectively. The curves are nearly the same. The errors for the initial guess parameters and the recalculated parameters are shown in Table 6. The routine converges even for sets of initial guesses far away from the final values. Although differences may occur for some recalculated circuit parameters, for each set of initial guesses the fitted frequency response curves are nearly the same [14]. From these results, the CCVT magnitude and phase can be reproduced by the fitted curves with very small errors.

5.1. 138 kV CCVT benchmark case From the 138 kV CCVT parameters of Table 3 [6], the frequency response magnitude and phase data were computed and used as an input file to the developed fitting routine and the parameters were recalculated back. One set of the initial guesses Table 3 138 kV CCVT parameters from literature Rc = 228.0  Lc = 56.5 H Cc = 127.0 pF Cp = 154.0 pF Rp = 400.0 

Lp = 2.85 H Rm = 1.0 M Lm = 10.0 kH Lf1 = 481.0 mH Cf = 9.6 ␮F

Lf2 = 247.0 mH Rf = 37.5  M = 163.0 mH – –

Fig. 10. 138 kV CCVT magnitude curves obtained from the original parameters [6] and the developed method. Table 6 Magnitude and phase errors for the 138 kV CCVT

Magnitude error (%) Phase error (◦ )

Initial guesses parameters

Recalculated parameters

139.8 94.8

0.026 0.39

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Fig. 11. 138 kV CCVT phase curves obtained from the original parameters [6] and the developed method. Table 7 230 kV CCVT initial guess parameters Rc = 23 k Lc = 47 H Cc = 47 nF Cp = 43 pF Rp = 70 k

Lp = 70 H Rm = 90  Lm = 300 mH Lf1 = 10 mH Cf = 140 ␮F

Lf2 = 95 mH Rf = 4  M = 10 mH – –

Table 8 230 kV CCVT calculated parameters Rc = 9.1 k Lc = 86.3 H Cc = 493.2 nF Cp = 9.3 pF Rp = 920 

Lp = 114.7 H Rm = 50.6  Lm = 700 mH Lf1 = 10.87 mH Cf = 166.39 ␮F

Lf2 = 47.39 mH Rf = 4.99  M = 9.31 mH – –

Fig. 12. Magnitude curves for the measured and fitted 230 kV CCVT voltage ratios.

adjustment. This procedure imposes limitations for the fitting technique, but it gives more realistic results. 5.3. Ferroresonance test IEC 186 Standard [15] establishes that for the ferroresonance test the CCVT must be energized at 1.2 per unit of rated voltage. One of the CCVT secondary terminals with a nearly zero burden is then short-circuited. The short circuit must be sustained during three cycles, at least. For electromagnetic transient studies, the proposed CCVT model is shown in Fig. 14. The magnetizing inductance Lm was replaced by a nonlinear inductance connected across the CCVT secondary terminals whose λ–i data points are shown in Table 1. The protection circuit composed by a silicon carbide surge

5.2. 230 kV CCVT parameters from measurements The initial guess and fitted parameters for the 230 kV CCVT are shown in Tables 7 and 8, respectively. The magnitude and phase curves for the measured and fitted voltage ratios are shown in Figs. 12 and 13, respectively. The errors for initial guess parameters and the calculated parameters are shown in Table 9. According to Figs. 12 and 13, the errors are fairly small for frequencies up to 2 kHz. Near 60 Hz, the magnitude and phase errors are very small. In the fitting process, some previously reasonably known 60 Hz CCVT parameters, which are the cases of Lc and Rp , were allowed to vary within 20% to perform a fine tuning parameter Table 9 Magnitude and phase errors for the 230 kV CCVT

Magnitude error (%) Phase error (◦ )

Initial guesses parameters

Calculated parameters

102.4 13.9

5.2 8.9

Fig. 13. Phase curves for the measured and fitted 230 kV CCVT voltage ratios.

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Fig. 14. Arrangement to perform the ferroresonance test for the 230 kV CCVT.

arrester was included as well. Its v–i nonlinear characteristic is shown in Table 2. In order to perform the ferroresonance test in laboratory, a 20.8 kV rms voltage was applied to the high voltage capacitor divider and the CCVT capacitors C1 and C2 connected in parallel, according to Fig. 14. The short circuit at the CCVT secondary winding was performed by a 17.5 kV and 630 A circuit breaker. The voltage signals across the two voltage dividers were recorded using a digital oscilloscope and the data saved in a microcomputer. The recorded voltage obtained from the high voltage divider was used as the input voltage source to obtain the digital simulations for the voltage at the CCVT secondary terminals. Fig. 15 shows the measured and simulated CCVT secondary voltage waveforms. The full line represents the results obtained from the laboratory measurements and the dotted line represents the results obtained from the CCVT model. The digital simulations were performed using the Alternative Transients Program (ATP) [16]. The short circuit was initiated at t = 102 ms and sustained during 55 ms, approximately. There is good agreement between lab tests and simulations except for the second positive and negative peaks of voltage waveforms. This may be because the breaker was modeled as an ideal switch, neglecting the effect of the arc in the breaker.

Fig. 15. Measured and simulated CCVT secondary voltage waveforms when the CCVT is submitted to the ferroresonance test.

5.4. Circuit breaker switching at the CCVT primary side In order to perform this test, the breaker was moved to the position shown in Fig. 16 and a sinusoidal voltage waveform of 17.4 kV rms was used. The transient response was measured during the close–open switch operation. Again, the recorded voltage obtained from the high voltage divider was used as the input voltage source to obtain the digital simulations for the

Fig. 16. Arrangement to perform the circuit breaker switching at the 230 kV CCVT primary side.

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Fig. 17. Measured and simulated CCVT secondary voltage waveforms during switching operations at the CCVT primary side.

Fig. 18. Transient secondary voltage: CCVT without FSC.

voltage at the CCVT secondary terminals. The dividers here have different voltage ratios from the ones used in the ferroresonance test because voltages are more severe for the ferroresonance case and might damage the oscilloscope. Fig. 17 shows the CCVT voltage waveform at the CCVT secondary side when the circuit breaker is switched on. The solid line represents the results obtained from laboratory and the dotted line represents the results obtained from digital simulations. The breaker contact closes at t = 24 ms and remains closed during approximately 60 ms. The voltage waveforms obtained from laboratory measurements and from digital simulations show good agreement. 6. Simulation results

Fig. 19. Transient secondary voltage: CCVT with FSC.

With the CCVT model validated in time and frequency domains, some digital simulations were performed to predict the CCVT behavior under transient overvoltages.

produced inside the CCVT, when a short circuit is cleared at the CCVT secondary side.

6.1. Ferroresonance simulations

6.2. Current chopping simulations

The importance of the ferroresonance suppression circuit in damping out transients produced inside the CCVT was analyzed by performing two ferroresonance simulations: the first one with the FSC included in the CCVT model and the second one ignoring the FSC. In both cases, the simulations consist of a close-open operation of the switch connected across the CCVT secondary terminals, as shown in Fig. 14. The switch closes at t = 125 ms and remains closed during six cycles, when the short circuit is cleared. Fig. 18 shows the CCVT secondary voltage waveform when the FSC is removed. The oscillations remain up to 500 ms, when the steady state is reached. Fig. 19 shows the same case with the FSC included in the CCVT model. The oscillations are damped in a time smaller than 100 ms, in conformity with ferroresonance standard tests. Fig. 20 shows the CCVT secondary voltage when the FSC is included in the model, but considering the effect of the surge arrester ignored. Comparing Fig. 20 with Fig. 19, one can see that the protection circuit is very effective in limiting overvoltages

Fig. 21 shows a typical power system configuration in which the CCVT is disconnected from the 230 kV bus by opening the switch SW when the current is different from zero value. All breakers D are closed.

Fig. 20. Transient CCVT secondary voltage: surge arrester effects are ignored.

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Acknowledgements The authors are grateful to Companhia Hidro El´etrica do S˜ao Francisco (CHESF) for providing the 230 kV CCVT unit at our high voltage laboratory. The financial support of Mr. Dam´asio Fernandes Jr. from the Brazilian National Research Council (CNPq) is also acknowledged. Fig. 21. Typical power system configuration for current chopping simulations near the CCVT primary side.

Fig. 22. Transient secondary voltage for current chopping: CCVT with and without FSC.

Fig. 22 shows the CCVT secondary voltage for current chopping when the FSC is included in the model (solid line) and ignored (dotted line). The current chopping produces a severe overvoltage with high frequency at the CCVT secondary side. The high voltage is due to the increase of the voltage across the inductive elements when the current is abruptly cut. The FSC is very important in damping out CCVT transient voltages. 7. Conclusions In this work, a CCVT model for electromagnetic transient studies was presented. The model was validated from frequency response measurements, in the range from 10 Hz to 10 kHz, for both magnitude and phase of the CCVT transfer functions. The magnetic core and surge arrester nonlinear characteristics were taken into account in the model in order to improve the transient response to overvoltages. The validation of model in time-domain was achieved when simulations and measurements were compared against and shown that the CCVT model is fairly accurate. There was a good agreement between lab tests and digital simulations for ferroresonance and circuit breaker switching operations. Because of this, the model was used in connection with the ATP to predict the CCVT performance when it is submitted to transient overvoltages. Simulation results had shown how important are the ferroresonance suppression circuit and the protection circuit in damping out and limiting transient overvoltages produced inside the CCVT, when a short circuit is cleared at the CCVT secondary side.

References [1] J.R. Lucas, P.G. McLaren, W.W.L. Keerthipala, R.P. Jayasinghe, Improved simulation models for current and voltage transformers in relay studies, IEEE Trans. Power Deliv. 7 (January (1)) (1992) 152–159. [2] M.R. Iravani, X. Wang, I. Polishchuk, J. Ribeiro, A. Sarshar, Digital timedomain investigation of transient behaviour of coupling capacitor voltage transformer, IEEE Trans. Power Deliv. 13 (April (2)) (1998) 622–629. [3] D.A. Tziouvaras, P. McLaren, G. Alexander, D. Dawson, J. Ezstergalyos, C. Fromen, M. Glinkowski, I. Hasenwinkle, M. Kezunovic, Lj. Kojovic, B. Kotheimer, R. Kuffel, J. Nordstrom, S. Zocholl, Mathematical models for current, voltage and coupling capacitor voltage transformers, IEEE Trans. Power Deliv. 15 (January (1)) (2000) 62–72. [4] H.M. Moraes, J.C.A. Vasconcelos, Overvoltages in CCVT during switching operations, in: 1999 National Seminar on Production and Transmission of Electrical Energy, Foz do Iguac¸u, Brazil, October 17–22, 1999 (in Portuguese). [5] M. Kezunovic, Lj. Kojovic, V. Skendzic, C.W. Fromen, D.R. Sevcik, S.L. Nilsson, Digital models of coupling capacitor voltage transformers for protective relay transient studies, IEEE Trans. Power Deliv. 7 (October (4)) (1992) 1927–1935. [6] Lj. Kojovic, M. Kezunovic, V. Skendzic, C.W. Fromen, D.R. Sevcik, A new method for the CCVT performance analysis using field measurements, signal processing and EMTP modeling, IEEE Trans. Power Deliv. 9 (October (4)) (1994) 1907–1915. [7] D. Fernandes Jr., W.L.A. Neves, J.C.A. Vasconcelos, M.V. Godoy, Coupling capacitor voltage transformer: laboratory tests and digital simulations, in: 2005 International Conference on Power Systems Transients, IPST’05, Montreal, Canada, June 19–23, 2005. [8] Lj. Kojovic, M. Kezunovic, S.L. Nilsson, Computer simulation of a ferroresonance suppression circuit for digital modeling of coupling capacitor voltage transformers, in: 1992 International Conference on Computer Applications in Design, Simulation and Analysis, Orlando, USA, 1992. [9] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in Fortran—The Art of Scientific Computing, second ed., Cambridge University Press, New York, 1992. [10] W.L.A. Neves, H.W. Dommel, On modeling iron core nonlinearities, IEEE Trans. Power Syst. 8 (May (2)) (1993) 417–423. [11] IEEE Standard for Gapped Silicon-Carbide Surge Arresters for AC Power Circuits, ANSI/IEEE Standard C62.1-1989, 1989. [12] IEEE Guide for the Application of Gapped Silicon-Carbide Surge Arresters for AC Systems, ANSI/IEEE Standard C62.2-1987, 1987. [13] IEEE Surge Protective Devices Committee, Modeling of current-limiting surge arresters, IEEE Trans. Power Apparatus Syst. 100 (August (8)) (1981) 4033–4040. [14] D. Fernandes Jr., Coupling capacitor voltage transformers model for electromagnetic transient studies, Ph.D. Dissertation, Department of Electrical Engineering, Federal University of Campina Grande, Campina Grande, Brazil, 2003 (in Portuguese). [15] Voltage Transformers, IEC 186, First Supplement (1970). Amendment No. 1, 1978. [16] Leuven EMTP Center, ATP—Alternative Transients Program, Rule Book, Heverlee, Belgium, 1987. Dam´asio Fernandes Jr. was born in Brazil in 1973. He received the B.Sc. and M.Sc. degrees in electrical engineering from Federal University of Para´ıba, Brazil, in 1997 and 1999, respectively, and the Ph.D. degree in electrical engineering from Federal University of Campina Grande, Brazil, in 2004. Since

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2003, he is with the Department of Electrical Engineering of Federal University of Campina Grande. His research interests are electromagnetic transients and optimization for power system applications.

2002, he was with the Department of Electrical Engineering of Federal University of Para´ıba. Since 2002, he is with the Department of Electrical Engineering of Federal University of Campina Grande, Campina Grande, Brazil.

Washington L.A. Neves was born in Brazil in 1957. He received the B.Sc. and M.Sc. degrees in electrical engineering from Federal University of Para´ıba, Brazil, in 1979 and 1982, respectively, and the Ph.D. degree from the University of British Columbia, Vancouver, Canada, in 1995. From 1982 to 1985, he was with the Faculty of Electrical Engineering of Joinville, Brazil. From 1985 to

Jos´e Carlos A. Vasconcelos was born in Brazil in 1952. He received the B.Sc. degree in electrical engineering from Federal University of Pernambuco, Brazil, in 1976 and the M.Sc. degree in electrical engineering from Federal University of Para´ıba, Brazil, in 2001. He is with the Companhia Hidro El´etrica do S˜ao Francisco (CHESF), Recife, PE, Brazil.