Summary - In this work, a coupling capacitor voltage transformer (CCVT) model from lab measurements is presented. The model takes into account linear and nonlinear elements. A software was developed to compute the linear 230 kV CCVT parameters (resistances, inductances and capacitances) from frequency response data. These frequency response measurements were made directly, without the need of using external resistors in the CCVT terminals. It is shown that the use of external resistors, as proposed in some works in literature, may cause distortions in the frequency response curves. The model may be used in connection with the EMTP (Electromagnetic Transients Program) to predict the CCVT performance when it is submitted to transient overvoltages, as are the cases of voltages due to the ferroresonance and circuit breaker switching operations tests.

A Coupling Capacitor Voltage Transformer Model from Laboratory Measurements

Authors’ names: Affiliation:

Damasio Fernandes Jr. (*) Federal University of Campina Grande Washington L. A. Neves Federal University of Campina Grande Celio A. Silva Federal University of Campina Grande Eubis P. Machado Federal University of Campina Grande Methodio V. Godoy Companhia Hidro Elétrica do São Francisco

Keywords: Coupling capacitor voltage transformer, ferroresonance, overvoltage protection, power system transients, EMTP.

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, specially due to the need of laboratory measurements [1]-[3]. Brazilian electric utilities have reported unexpected overvoltage protective device operations during normal switching conditions in several 230 kV 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. 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. (*) Department of Electrical Engineering – Av. Aprigio Veloso, 882 – Bodocongo, 58.109-970, Campina Grande – PB, Brazil

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. 2. UNDERLYING CONCEPTS

The basic electrical diagram for a typical CCVT is shown in Figure 1. The primary side consists of two capacitive elements C1 and C2 connected in series. The potential transformer (PT) 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. Ferroresonance oscillations may take place if the circuit capacitances resonate with the iron core nonlinear inductance. The oscillations cause incorrect input 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 oscillations requiring a small amount of energy during steady-state [3], [5]-[6].

v o

L I N E

v i

C 1

C 2

PT

FSC

L c

Z b

Figure 1 - Basic electrical diagram for a typical CCVT. 3. CCVT MODELING

The diagram shown in Figure 1 is valid only near power frequency (60 Hz). A model to be applicable for frequencies in the ferroresonance range and up to a few kilohertz needs to take at least the PT primary winding and compensating inductor stray capacitances effects into account [2]-[3], [5]-[6]. In this work, the circuit shown in Figure 2 was used to model the CCVT. It comprises the following linear parameters: a capacitor stack (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). The damping resistor Rf is used to attenuate ferroresonance oscillations.

C2

C1 Cc

Lc Rc Lp Rp

Zb Lm Rm Cp

LINE

Cf

Lf1

Lf2

−M Rf

Figure 2 - CCVT model for identification of parameters. 3.1 Linear CCVT Parameters Estimation

The circuit shown in Figure 2 can be replaced by Figure 3 with impedances Z1, Z2, Z3, Z4, Z5 and all elements referred to the PT secondary side.

2

r2C2

r2C1

Z1 Z2

Zb r2Cp vi/r

vo Z3

Z4

Z5

3

4

LINE

1 2

Figure 3 - CCVT model with blocks of impedances. The expressions for the referred impedances in the s domain, with s = jω, are:

( )[ ] ( )( )( ) ( )( ) (

.

;//1;//

;

;1//

5

214

223

22

221

sMRZ

sLsCsLZrsLrRZ

rsLRZ

sCrrsLRZ

f

fff

mm

pp

ccc

−=

+==

+=

+=

) (1)

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. The fitting 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 follow:

pxpxpxpx )(21)()()( 2 FFFF TT ∇+∇+≈+ . (2)

where the vector and p is the increment vector in the direction of the estimate solution. p is obtained minimizing the function F setting its gradient to zero which results in

],,,[ 21 mxxx L=x

)()(2 xpx FF −∇=∇ . (3) The approximate solution xk+1 is given by:

[ ] ).()(12

1 kkkkk FF xxxpxx ∇∇−=+=−

+ (4)

Newton’s method will converge if [∇2F(x)]-1 is positive definite in each iterative step, that is, zT[∇2F(x)]-1z > 0 for all z ≠ 0. This technique is known as the full Newton-type method [7]. It is a modification of Newton’s method for that iteration in which [∇2F(x)]-1 is not positive definite. In the procedure, ∇2F(x) is replaced by a “nearby” positive definite matrix )(2 xF∇ and the increment p is computed solving Equation (3). The error function F(x) is given by:

∑=

⎥⎦

⎤⎢⎣

⎡σω−

=n

i i

ii yyF

1

2);(

)(x

x . (5)

Where ωi is the i-th measured frequency value and yi is the i-th measured frequency response value of the n data points. σi 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. The algorithm is described as follow:

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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. 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 Figure 4. 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 0o, respectively. The rated values are 1154.7 and 0o. There is only an error smaller than 3 % in the voltage ratio.

vo

Signal generator

Power amplifier

∼

CCVT vi

+

−

+ −

Primary terminal

Secondaryterminal Rb

R

Signal generator 10 Hz – 10 kHz

Power amplifier

vi

∼

CCVT

vo

+

−

+

−

Primary terminal

Secondaryterminal

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 Figure 5. In this methodology 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 Figure 6(a) and Figure 6(b) for a 138 kV CCVT reported in literature [6].

Figure 5 - Frequency response measurements proposed by Kojovic et al [6].

Figure 4 - Frequency response measurements.

R = 60 Ω R = 6 kΩ

R = 60 kΩ

1.0E+1 1.0E+2 1.0E+3 1.0E+4Frequency (Hz)

-100-90-80-70-60-50-40-30-20-10

010

Gai

n (d

B)

1.0E+1 1.0E+2 1.0E+3 1.0E+4

Frequency (Hz)

-100-90-80-70-60-50-40-30-20-10

01020

Gai

n (d

B)

Rb = 1 OhmRb = 100 OhmRb = 1 kOhm

(a) (b) Figure 6 - Simulation results considering the methodology proposed by Kojovic et al [6]: sensitivity analysis for the 138 kV CCVT magnitude curve to the: (a) value of the resistance R. (b) value of the resistance Rb.

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For the simulation results shown in Figure 6(a) and Figure 6(b) 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. 4.2 230 kV CCVT Nonlinear Characteristics The surge arrester and the magnetic core nonlinear characteristics were included in the model to give more realistic results for the simulated CCVT transient response to overvoltages. The point by point silicon carbide (SiC) surge arrester (v − i) curve and the PT nonlinear peak flux − current (λ − i) characteristic were estimated from laboratory measurements according to the procedures presented in [8]. The results are shown in Tables I and II, respectively.

Table I - Silicon carbide surge arrester nonlinear characteristic.

Current (A) Voltage (kV) 100 20.8 200 27.9 500 39.0

1000 42.9 2000 45.5

Table II - Nonlinear characteristic of the PT magnetic core.

Current (A) Flux (V.s) 0.076368 0.025772 0.720881 0.189066 1.429369 0.396889 2.511675 0.748388 3.662012 0.863553 5.712037 0.942706

55.527018 1.556415 5552.7018 1.562242

5. ANALYSIS OF THE RESULTS 5.1 230 kV CCVT Parameters from Measurements The 230 kV CCVT constant parameters were obtained from frequency response data points of magnitude and phase measured at our high voltage laboratory. The fitted parameters are shown in Table III. The magnitude and phase curves for the measured and fitted voltage ratios are shown in Figures 7 and 8, respectively. After the fitting, the average errors of magnitude and phase are, respectively, 5.2% and 8.9o. According to Figures 7 and 8, the errors are fairly small for frequencies up to 2 kHz. Near 60 Hz the magnitude and phase errors are very small. This is the region in which the CCVT operates most of the time.

Table III - 230 kV CCVT calculated parameters.

Rc = 9.1 kΩ Lp = 114.7 H Lf2 = 47.39 mH Lc = 86.3 H Rm = 50.6 Ω Rf = 4.99 Ω

Cc = 493.2 nF Lm = 700 mH M = 9.31 mH Cp = 9.3 pF Lf1 = 10.87 mH − Rp = 920 Ω Cf = 166.39 μF −

5

1.0E+1 1.0E+2 1.0E+3 1.0E+4Frequency (Hz)

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0G

ain

(dB

)Fitted curveLaboratory measurements

1.0E+1 1.0E+2 1.0E+3 1.0E+4Frequency (Hz)

-180.0-150.0-120.0-90.0-60.0-30.0

0.030.060.090.0

Phas

e (d

egre

es)

Laboratory measurementsFitted curve

Figure 8 - Phase curves for the measured and fitted 230 kV CCVT voltage ratios.

Figure 7 - Magnitude curves for the measured and fitted 230 kV CCVT voltage ratios. 5.2 Ferroresonance Test The ferroresonance test was carried out based on IEC 186 Standard [9]. The first test establishes that 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. The silicon carbide surge arrester (original arrester which is part of the CCVT unit) was included in the model. Its v − i nonlinear characteristic is shown in Table I. The PT magnetizing branch is represented by a nonlinear inductance connected across the CCVT secondary terminals whose λ − i data points are shown in Table II. In order to perform the ferroresonance test in laboratory, a 20.8 kV rms voltage source was used and the CCVT capacitors C1 and C2 were connected in parallel, according to the Figure 9. The short-circuit at the CCVT secondary winding was performed using a 17.5 kV, 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. Figure 10 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 ATP (Alternative Transients Program) [10]. 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.

OscilloscopeMicrocomputer

Rc Cc

Lc

Cp

Lp Rp

C1

v − i

~

Rmλ − iLf2

Cf Lf1 −M

Rf

C2

20.8 kVrms

2 MΩ

400 kΩ

1563 nF

0.2 nF

High voltagedivider Low voltage

divider

Circuit breaker

Gap

Figure 9 - Arrangement to perform the ferroresonance test for the 230 kV CCVT.

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Figure 10 - Ferroresonance test: measured and simulated CCVT secondary voltage. 5.3 Circuit Breaker Switching at the CCVT Primary Side In order to perform this test, the breaker was moved to the position shown in Figure 11 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 simulations for the 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.

Oscilloscope Microcomputer

R cC c

L c

Cp

Lp Rp

C 1

v − i ~

Rm λ − i L f 2

Cf

L f 1 − M R f

C 2

17.4 kV rms

1 M Ω 1 MΩ

1 M Ω

288 MΩ

High voltage divider Low voltage divider

Gap

Circuit breaker

Figure 12 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.

Figure 11 - Arrangement to perform the breaker switching at the 230 kV CCVT primary side.

Figure 12 - Measured and simulated CCVT secondary voltage waveforms during switching operations at the CCVT primary side.

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6. 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. Based on these results, it is possible to use the model in connection with the ATP to predict the CCVT performance when it is submitted to transient overvoltages. 7. BIBLIOGRAPHY [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 Transactions on Power Delivery, vol. 7, no. 1, pp. 152-159, January 1992.

[2] M. R. Iravani, X. Wang, I. Polishchuk, J. Ribeiro, A. Sarshar, "Digital Time-Domain Investigation of Transient Behaviour of Coupling Capacitor Voltage Transformer", IEEE Transactions on Power Delivery, vol. 13, no. 2, pp. 622-629, April 1998.

[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 Transactions on Power Delivery, vol. 15, no. 1, pp. 62-72, January 2000.

[4] H. M. Moraes, J. C. A. Vasconcelos, "Overvoltages in CCVT During Switching Operations", (In Portuguese), in Proc. National Seminar on Production and Transmission of Electrical Energy, Foz do Iguaçu, Paraná, October 17th to 22th 1999.

[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 Transactions on Power Delivery, vol. 7, no. 4, pp. 1927-1935, October 1992.

[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 Transactions on Power Delivery, vol. 9, no. 4, pp. 1907-1915, October 1994.

[7] W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran – The Art of Scientific Computing, second edition, Cambridge University Press, New York, 1992.

[8] D. Fernandes Jr., W. L. A. Neves, J. C. A. Vasconcelos, "A Coupling Capacitor Voltage Transformer Representation for Electromagnetic Transient Studies", in Proc. International Conference on Power Systems Transients, New Orleans, September 28th to 2nd October 2003.

[9] Voltage Transformers, IEC 186, First Supplement (1970), Amendment no. 1, 1978. [10] Leuven EMTP Center, ATP - Alternative Transients Program − Rule Book, Heverlee,

Belgium, July 1987.

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