Effect of Temperature on Frequency Dependent ... - IEEE Xplore

IEEE Transactions on Dielectrics and Electrical Insulation

Vol. 21, No. 2; April 2014

653

Effect of Temperature on Frequency Dependent Dielectric Parameters of Oil-paper Insulation Under Non-sinusoidal Excitation A. K. Pradhan, B. Chatterjee and S. Chakravorti Department of Electrical Engineering Jadavpur University Kolkata, West Bengal, India, 700032

ABSTRACT Frequency domain spectroscopy is a potential tool for non-invasive condition assessment of oil-paper insulation in power equipment. On the other hand, it is well known that the results of frequency domain spectroscopy are affected predominantly by temperature. Moreover, the voltage used for frequency domain spectroscopy is sinusoidal is nature. But the actual insulation system at site is stressed by voltage that may deviate significantly from sinusoid during operation. Considering these two aforesaid facts, in this paper, the response of oil-paper insulation has been studied at different temperatures using both sinusoidal as well as non-sinusoidal excitation. An experimental sample has been prepared in the laboratory that emulates the composite insulation of oil immersed type power transformer at site. The results of frequency response using sinusoidal voltage waveform at different temperature show good agreement with the conventional results that validates the scheme of the experimental setup. Some more information is obtained from the response of non-sinusoidal excitation that could help to get a better interpretation of the actual physical condition of oil-paper composite insulation. Index Terms - Sinusoidal excitation, non-sinusoidal excitation, complex capacitance, dissipation factor, harmonics component, cross-over point, oil-paper insulation, condition monitoring.

1 INTRODUCTION IN electric utilities around the world, significant numbers of power transformers are operating beyond their design life. Sudden failures of such transformers operating at a pivotal position may cause major power disruption resulting in substantial loss of money and time. Thus all over the globe, there has been an urge to give priority attention to research into improved diagnostic techniques for determining the condition of the insulation in aged transformers. Aging of a transformer is primarily due to the aging of its insulation. So, condition assessment of the insulation in a transformer is required to interpret its aging status. At present, emphasis is given on non-invasive method for condition assessment of oil-paper insulation of power transformers among which, dielectric spectroscopy is in use for the last decade. Dielectric spectroscopy is divided into three major categories. Of these, two are in time domain and the other one is in frequency domain. Time domain spectroscopy methods are Polarization and Manuscript received on 23 December 2012, in final form 8 August 2013, accepted 30 October 2013.

Depolarization Current (PDC) [1] and Recovery Voltage (RV) [2] measurement and frequency domain method is commonly known as Frequency Domain Spectroscopy (FDS) [3]. FDS is a potential tool that can be used to get an idea about the actual physical condition of oil-paper insulation system by obtaining reliable information about different dielectric parameters such as dissipation factor (tan-delta), real and imaginary parts of the complex capacitance at different frequencies. But the results of FDS are influenced by different environmental factors among which temperature is predominant [3]. The effect of temperature can adversely affect the results of FDS in outdoor where the environmental condition is unpredictable. So, the results of FDS at different temperatures must be studied for a comprehensive database for proper evaluation of the actual condition of insulation, irrespective of environmental conditions. Another important factor in FDS is the excitation voltage. The voltage waveform that is used for conventional FDS measurement is sinusoidal in nature [35]. But the actual insulation system at site is often stressed by voltages that may deviate significantly from sinusoid

DOI 10.1109/TDEI.2013.003602

A. K. Pradhan et al.: Effect of Temperature on Frequency Dependent Dielectric Parameters of Oil-paper Insulation

2 BACKGROUND ON FREQUENCY DOMAIN SPECTROSCOPY 2.1 CONVENTIONAL FDS When a sinusoidal voltage is applied across an insulation system, polarization processes start inside the insulation material resulting in a flow of current through it [1]. By using Laplace or Fourier transform of the polarization current, an analytical transition from time domain to frequency domain is possible [1]. For an excitation voltage U ( ) , the resultant current that flows through the insulation system at a particular frequency () can be written as

I ( )  j C ( )U ( )

Since C ( ) is complex, it can be further split into real and imaginary parts as shown below

C ( )  C ( )  jC ( ) ''

 C ( )  C0  r' ( )  

(2)

    j  r'' ( )  0    0   

(3)

Here, C0 and  0 represents geometric capacitance and dc conductivity respectively.  0 is the absolute permittivity. The dissipation factor (tan-delta) can be written as the ratio of imaginary part to the real part of the complex capacitance. tan  ( ) 

C '' ( ) C ' ( )

(4)

From eqn. 3 and 4, it can be inferred that C ( ) and tan are dependent on frequency of the applied voltage [7]. Thus, in conventional FDS, the sample under test is subjected to sinusoidal voltage over a wide frequency range and the amplitude and phase of the response current flowing through the insulation are recorded from which, dissipation factor and complex capacitance are determined [1, 8]. 2.2

FREQUENCY RESPONSE MEASUREMENT FROM NON-SINUSOIDAL EXCITATION As highlighted in this paper, non-sinusoidal excitation over a wide frequency range (1 mHz-1 kHz) is applied across the sample under test and corresponding responses are measured. As non-sinusoidal excitation, in the form of triangular voltage waveform is chosen that is applied to the sample and the response current is measured. The time period and magnitude of the applied nonsinusoidal excitation is kept same as that of the time period and magnitude of the applied pure sinusoidal excitation. Figure 1a shows the sinusoidal excitation and Figure 1b shows the triangular excitation of having same time period (T) and same magnitude of 100 V. From the applied triangular voltage and corresponding measured current waveforms, harmonic components (fundamental, 3rd, 5th, 7th, etc) of voltage and current are extracted using FFT [5-8]. Dielectric parameters (dissipation factor, complex capacitance, etc) are calculated from the corresponding harmonic components of the voltage and current waveform using the equations (1) - (4) as discussed in section 2.1. 100

100

T

T

(1)

Where C ( ) is the complex capacitance which is related to dielectric permittivity of the insulation material [6].

'

Since the real and imaginary parts of the capacitance is related to the permittivity of the dielectric material, so eqn. (2) can be further expressed as

Voltage(V)

during operation. Thus, as an extension to the conventional FDS, use of non-sinusoidal voltage waveform for the condition assessment of oil-paper insulation system is desirable to get some added information about the actual condition of the insulation. Considering the aforesaid facts, in this paper, FDS is performed at different temperatures using both sinusoidal as well as non-sinusoidal excitation in an oil-paper insulation sample that has been prepared in the laboratory. The sample is prepared carefully to emulate the oil-paper insulation system of a real life transformer. In the next step, different parameters like dielectric dissipation factor (tan-delta) and complex capacitance of the test sample have been determined by conventional FDS by applying sinusoidal excitation at different frequencies. The nature of variation of these parameters with the variation of temperature has been studied. For non-sinusoidal voltage excitation, the harmonic components (Fundamental, 3rd, 5th, 7th, etc.) are extracted from the applied voltage and corresponding response current waveforms at different frequencies are obtained using Fast Fourier Transform (FFT). Next, tan-delta and complex capacitances are calculated for each of these harmonic components. The nature of the variation of the obtained parameters with respect to the temperature has also been studied. The variation of different dielectric parameter with the variation of temperature for sinusoidal and non-sinusoidal excitation has been compared at different frequencies. It has been observed that the physical condition of the oilpaper insulation system can be interpreted closely from the results of sinusoidal excitation whereas this can be interpreted more elaborately from the results of nonsinusoidal excitation.

Voltage(V)

654

0

-100 0

100 Time(s)

200

0

-100 0

100 Time(s)

200

(a) (b) Figure 1. Voltage waveform of same time period (T) and same magnitude of 100 V. (a) Sinusoidal, (b) Triangular.


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3 PREPARATION OF TEST SAMPLE A test sample that emulates the oil-paper insulation of real transformer is prepared in the laboratory for experimental purpose. A GI sheet A having dimensions of 50 × 50 mm square cross section and height of 100 mm forms the core of the test sample over which a press board cylinder B having diameter of 70 mm and height of 100 mm is fitted. Over the press board cylinder B, an unimpregnated kraft paper C is wrapped. A copper foil D is placed over C that emulates the low voltage windings of the transformer. Another layer of unimpregnated kraft paper E is wrapped over the copper foil D. After that, pressboard strips F having a thickness of 1mm is placed over E with a separation of 10 mm, over which another layer of unimpregnated kraft paper G is wrapped. The pressboard strips between E and G act as oil-ducts. Another layer of copper foil H is placed over G which emulates the high voltage terminal. Finally, another layer of unimpregnated kraft paper I is wrapped over H to complete the process. The kraft paper is used to prepare the sample is relatively new. The whole specimen is placed into another GI tank J having crosssection area of 130 × 130 mm square and height of 110 mm. The GI tank J is filled with the transformer oil to impregnate the paper and pressboard material. The whole specimen is placed inside a sealed chamber for some days for proper impregnation. Figure 2a shows the cross sectional view of the test sample and Figure 2b shows the actual photograph of the test specimen.

655

Voltage waveforms are generated using an arbitrary waveform generator DAC from National Instruments™. The output of DAC is 10Vp, hence a voltage amplifier is used to step up the voltage up to the desired level. Analog Data

Analog Voltage Data Attenuator

Voltage Generating Module

Two-Channel ADC Sample under Test

Voltage Amplifier

DAC

Analog Data

Arbitrary Waveform Voltage Data File

Digital Data

Digital Data Stored in Computer

Analog Measured Current data

Digital Data

Computer

Figure 3. Block diagram of overall scheme used in laboratory for experiment.

The voltage across the sample and the corresponding current data that are obtained are analog in nature. Since the computer accepts digital data, an 8-bit high speed digitizer is used for analog to digital conversion purpose that is controlled by the computer. The digitizer is a two channel, 100 MS/s, model NI USB-5133 from National Instruments™. The sampling frequency for data acquisition is kept at 1kfundamental frequency of the applied waveform for reliable reproduction of the current waveform and is well above the Nyquist frequency to prevent any aliasing. 4.2 EXPERIMENTAL PROCEDURE

(a) (b) Figure 2. Prepared test sample in the laboratory. (a) Sectional drawing and (b) actual photograph.

4 EXPERIMENTAL SETUP AND PROCEDURE 4.1 EXPERIMENTAL SETUP In the experimental setup, both sinusoidal as well as nonsinusoidal voltage waveform is applied separately across the test specimen and the corresponding response from the dielectric material is recorded as current waveform to investigate the condition of the insulation material under test. Figure 3 shows the block diagram of overall scheme that is used in laboratory for experimental purpose. An arrangement is made to generate sinusoidal as well as non-sinusoidal voltage waveform of different frequencies in a span of 1 mHz to 1 kHz. A file in the computer containing the information of required waveshape, including amplitude and phase, is parsed and sent to DAC (Digital to Analog Converter) module.

Though relatively new kraft paper has been used for the sample construction nevertheless the completed sample is heated at 90 DegC in a low-pressure chamber for sufficient time to remove any residual moisture that might have ingressed during sample preparation. After the heating process, the weight (Wb) of the sample is measured with a precision balance. The sample is then heated to the required temperature in an oven under normal atmospheric pressure. After allowing sufficient time to achieve moisture ingress, the weight (Wa) of the sample is measured. From Wb and Wa , the moisture ingress in the sample is calculated from the eqn 5. Moisture content in the sample (m.c.) at a particular temperature =

w w w a

b

× 100 %

(5)

b

A specific sample has been prepared for which that the variation of weight is about 5.5% at 50 DegC. This variation is solely due to moisture absorption by the sample. The sample is then immersed in oil to stop further ingress of moisture. Thereafter the sample is heated for several days continuously at 30, 40, 50, 60, 70 and 80 DegC. After heating at each predefined temperature (starting from 80 DegC and decreasing to 30 DegC) following dipping in oil, the dielectric responses at different frequencies (1 mHz- 1 kHz) for sinusoidal and

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A. K. Pradhan et al.: Effect of Temperature on Frequency Dependent Dielectric Parameters of Oil-paper Insulation

non-sinusoidal excitation are measured. The photograph of the whole experimental set up used in laboratory is shown in Figure 4. At the preliminary stage of experiment and data acquisition, there was problem with too low amplitude for 3rd, 5th and 7th harmonics where the response signal becomes too small to be analyzed correctly. To overcome this situation, in the later stage of experiment, amplitude of the excitation for the triangular waveform was increased to 1000 V especially at low frequency ranges. This improved the voltage level of harmonics (3rd, 5th and 7th) and their corresponding responses approximately in the range of 20 V facilitating analysis of signal with better accuracy.

Figure 4. Photograph of the experimental setup used in the laboratory.

5 RESULTS AND DISCUSSION Different dielectric parameters (Dissipation factor, real and imaginary parts of complex capacitance) are calculated at each frequency from the corresponding voltage and current waveforms for sinusoidal as well as triangular excitation using the mathematical formulae as discussed in section 2 at different temperatures mentioned in the experimental procedure. For a comparative study, the fundamental, 3rd, 5th and 7th harmonic components of the triangular voltage waveform are extracted using FFT as discussed in section 2.2. Pure sinusoidal voltage waveforms having same magnitude and same frequency corresponding to the aforesaid fundamental, 3rd, 5th and 7th harmonic components of the triangular voltage waveform are applied to the sample and corresponding current data are acquired at the stated temperatures. From these voltage and current data, dielectric parameters such as dissipation factor (tan-delta) and complex capacitance at each frequency are calculated at 30, 40, 50, 60, 70 and 80 DegC. The parameters are then plotted against the frequency at each temperature and the nature of variation of the plotted curves with change in temperature for both sinusoidal as well as triangular excitation have been studied and compared. 5.1 DISSIPATION FACTOR (TAN-DELTA) Dissipation factor for sinusoidal excitation is calculated from the voltage and corresponding current waveforms for each frequency at the aforesaid temperatures. The tan-delta values that have been calculated from the extracted

fundamental, 3rd, 5th and 7th harmonic components of voltage and corresponding current waveforms for triangular excitation have been plotted along with tan-delta values for pure sinusoidal excitation of same frequency and same amplitude. The plotted values for fundamental, 3rd, 5th and 7th harmonic components at each of above-mentioned temperatures are shown in Figure 5, 6, 7, 8. It may be observed that the nature of variation of tan-delta with frequency for pure sinusoidal excitation shows a good agreement with the results as reported in [6, 13-16]. Along with sinusoidal excitation, dielectric responses for non-sinusoidal excitation at different temperatures are studied in which case multiple frequencies superimposed on each other are applied to the sample at different temperatures. Hence, the results show the effect of such superimposed excitation at varying temperatures. It may be observed from Figure 5, 6, 7, 8 that at lower frequency range (upto frequency of 10 Hz), tan-delta increases as frequency decreases but at higher frequency range (after 10 Hz), tan-delta value increases when the frequency increases at each temperature for both sinusoidal as well as triangular excitation. It may also be observed from Figures 5- 8 that there is a horizontal logarithmic shift of amplitude and frequency of the tan-delta curves for both sinusoidal and triangular excitation. This may happen due to the change of absolute temperature and corresponding increase in activation energy at higher temperature [3, 17-18]. The shift is independent of frequency. The vertical shift in y-direction of tan-delta for both sinusoidal and triangular excitation may be due to the change in oil-conductivity, as temperature increases [3, 17]. As the temperature increases, the mobility of the ions present in oil increases which in turn increases the conductivity of the oil [5]. So it may be stated that oil conductivity varies with change in temperature. If the tan-delta curves for each frequency component of triangular excitation and the corresponding sinusoidal input at the same frequency are compared as shown in Figures 5 - 8 it may be observed that at 1 mHz, the tan-delta value for triangular excitation is higher than the tan-delta value for sinusoidal input at each of aforesaid temperatures. But as the frequency increases up to 10 Hz, a cross-over occurs between the two tan-delta curves. This cross-over may be due to the non-linear behavior of the insulation system of the test sample. When triangular voltage is applied to the sample, the excitation contains different harmonic components superimposed with the fundamental. So, the response extracted from the current waveform using FFT for a particular component in triangular excitation is not the same as that obtained when the excitation is pure sinusoidal in nature having the same frequency. This implies that the superposition theorem is not applicable for oilpaper insulation. This discrepancy could be explained with the presence of non-linearity in the oil-paper insulation sample. The non-linear behavior of the insulation system of test sample may be caused by the field dependent ionic oscillations [19]. Since the triangular excitation contains the different harmonic components superimposed with the fundamental, so the influence of electric field on the ions present in oil-paper insulation under triangular excitation is quite different from that under sinusoidal excitation. This is expected to play a role in the change in dielectric response. The tan-delta value at


Vol. 21, No. 2; April 2014

1

657

1

10

10

0

tan-delta

10

Sinusoid Sinusoid Sinusoid Sinusoid Sinusoid Sinusoid Triangular Triangular Triangular Triangular Triangular Triangular

30 DegC,Sinusoid 40 DegC,Sinusoid 50 DegC,Sinusoid 60 DegC,Sinusoid 70 DegC,Sinusoid 80 DegC,Sinusoid 30 DegC,Triangular 40 DegC,Triangular 50 DegC,Triangular 60 DegC,Triangular 70 DegC,Triangular 80 DegC,Triangular

0

10

tan-delta

30 DegC, 40 DegC, 50 DegC, 60 DegC, 70 DegC, 80 DegC, 30 DegC, 40 DegC, 50 DegC, 60 DegC, 70 DegC, 80 DegC,

-1

10

-1

10

-2

10

-3

10

-2

10

-2

-1

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0

1

10 Frequency(Hz)

2

10

10

0

tan-delta

0

1

10 10 Frequency(Hz)

2

3

10

10

4

10

Figure 8. Dissipation factor (tan-delta) for sinusoidal and 7th harmonic component of triangular input of same frequency.

cross-over point and the value of frequency at which the cross-over between the two tan-delta curves occur at each of the above-mentioned temperatures have been presented in Table 1 and the variation of tan-delta value at cross-over point with the variation of temperature for fundamental, 3rd, 5th and 7th harmonic components has been shown in Figure 9.

1

10

10

-1

10

10

Figure 5. Dissipation factor (tan-delta) for sinusoidal and fundamental component of triangular input of same frequency.


-2

10

3


0

10

-1

-2

10

-3

-2

10

-1

10

0

10

1

2

10 10 Frequency(Hz)

10

3

4

10

10

tan-delta

10

-1

10

Figure 6. Dissipation factor (tan-delta) for sinusoidal and 3rd harmonic component of triangular input of same frequency.

Fundamental Third harmonics Fifth harmonics Seventh harmonics

1

10

-2

10

0

10

30

35

40

45

50 55 60 Temperature (DegC)

65

70

75

80

tan-delta

Figure 9. tan-delta value at cross-over point at different temperature. -1

10


-2

10


-3

10

-3

10

-2

10

-1

10

0

1

10 10 Frequency(Hz)

2

10

3

10

4

10

Figure 7. Dissipation factor (tan-delta) for sinusoidal and 5th harmonic component of triangular input of same frequency.

From Figure 9, it may be observed that tan-delta value at cross-over point increases for each component (Fundamental, 3rd, 5th and 7th harmonics) when the temperature increases. This may happen due to the change in oil- conductivity at increased temperature [3, 17]. At a given temperature, tandelta value at cross-over point decreases as the order of harmonic increases. It was observed in Figure 5, 6, 7 and 8 that tan-delta values for both sinusoidal, as well as triangular excitation decreases as frequency increases (upto 10 Hz). Therefore, increase of harmonics order implies decrease of tan-delta value. So, the tan-delta value at cross-over point decreases when harmonic order increases.

658

A. K. Pradhan et al.: Effect of Temperature on Frequency Dependent Dielectric Parameters of Oil-paper Insulation Table 1. tan-delta and Frequency Value at Cross-Over point at Different Temperatures. 5th harmonic Fundamental 3rd harmonic tan-delta Frequency(Hz) tan-delta Frequency(Hz) tan-delta Frequency(Hz) 0.079 0.017 0.012 0.150 0.011 0.200 0.110 0.100 0.080 0.160 0.040 0.220 0.120 0.020 0.110 0.040 0.090 0.150 0.130 0.045 0.120 0.085 0.110 0.200 0.330 0.055 0.250 0.090 0.210 0.230 0.340 0.090 0.320 0.100 0.250 0.250

Temperature(DegC) 30 40 50 60 70 80

7th harmonic tan-delta Frequency(Hz) 0.010 1.100 0.020 1.200 0.085 0.160 0.092 0.310 0.200 0.320 0.210 0.600

1

10

The variation of frequency at cross-over point has been plotted in Figure 10.


1

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tan-delta

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Frequency (Hz)

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Figure 11. Dissipation factor (tan-delta) for sinusoidal input having frequency equals to fundamental, 3rd, 5th and 7th harmonic components of triangular excitation at 50 DegC. -2

10

30

1

35

40

45

50 55 60 Temperature (DegC)

65

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80


Figure 10. Frequency value at cross-over point at different temperature.

0

10 tan-delta

It may be observed from Figure 10 that the value of frequency at cross-over point increases with the increase of temperature when the temperature goes above 50 DegC. This may be caused by the increase of activation energy as the temperature increases [3, 17-18]. It may also be observed from Figure 10 that the frequency value at cross-over point increases when order of harmonic increases. Increase of harmonics order implies increase of frequency, so the value of frequency at cross-over point increases when order of harmonics increases at each temperature. Figure 5, 6, 7 and 8 shows that at cross-over point the values of tan-delta for both sinusoidal and triangular excitation have the same magnitude. This implies that if test can be performed at the frequency of cross-over point, crossvalidation of results could be performed. Therefore, for data analysis using non-sinusoidal excitation, this cross-over point could be an important feature. The dielectric parameters (e.g. dielectric dissipation factor) have been compared for fundamental and harmonics. For sinusoidal excitation, the comparison as shown in Figure 11 shows a simple shift of the curves along the frequency axis. Hence this case is not emphasized. However, the comparative study in the case of triangular excitation as shown in Figure 12 shows that these values don’t simply shift along frequency axis. Figure 11 and Figure 12 together shows this difference in the nature of variation for sinusoidal and triangular excitation. These Figures also bring out the fact that more details could be had from the results of triangular excitation.

-1

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Figure 12. Dissipation factor (tan-delta) for fundamental, 3rd, 5th and 7th harmonic components of triangular excitation at 50 DegC.

It may also be observed from Figures 5 - 8 that the minimum tan-delta value for sinusoidal excitation is higher than the minimum tan-delta value for triangular excitation. The difference between the two minimum tan-delta is higher when the temperature increases. The difference of minimum tandelta may be caused by the non-linear behavior of the insulation system of test sample [19]. As the temperature increases the field dependent ionic oscillation increases and non-linear behavior of the insulation system becomes more prominent. As a result, the differences between the two minima of tan-delta increases with increase in temperature. The minimum tan-delta is an important parameter in FDS that determines the moisture content in paper [20] in the composite insulation. The minimum tan-delta values for sinusoidal and triangular excitation have been tabulated in Table 2 and 3.


Vol. 21, No. 2; April 2014

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Table 2. Minimum tan-delta value for triangular and sinusoidal input (Fundamental and 3 harmonic ). Temperature (DegC)

Using only the fundamental component of triangular excitation (f1)

30

0.0114

0.0118

0.0004

0.0085

0.0107

0.0022

40

0.0129

0.0135

0.0006

0.0126

0.0179

0.0053

50

0.0222

0.0229

0.0007

0.0170

0.0223

0.0053

60

0.0331

0.0352

0.0021

0.0255

0.0346

0.0091

70

0.0509

0.0532

0.0023

0.0365

0.0553

0.0188

80

0.0693

0.0819

0.0126

0.0612

0.0783

0.0171

Using sinusoidal Using sinusoidal Using only the 3rd harmonic excitation of same Difference excitation of same Difference of triangular excitation (f3) frequency as that of f1 frequency as that of f3

Table 3. Minimum tan-delta value for triangular and sinusoidal input (5th and 7th harmonic) Temperature Using only the 5th harmonic (DegC) of triangular excitation (f5)

Using sinusoidal Using sinusoidal Using only the 7th harmonic Difference excitation of same excitation of same Difference of triangular excitation (f7) frequency as that of f5 frequency as that of f7

30

0.0064

0.0126

0.0062

0.0101

0.0107

0.0006

40

0.0129

0.0136

0.0007

0.0141

0.0160

0.0019

50

0.0159

0.0217

0.0058

0.0220

0.0233

0.0013

60

0.0199

0.0366

0.0167

0.0330

0.0372

0.0042

70

0.0444

0.0535

0.0091

0.0504

0.0566

0.0062

80

0.0602

0.0752

0.0150

0.0617

0.0723

0.0106

% pm= 15.297 + 2.53267× ln(tanδmin)

0.09 Triangular Sinusoid

0.08 0.07 M inim um value of tan-delta

In order to compare the value of paper moisture obtained using sinusoidal and triangular excitation, a typical case is tabulated in Table 4 at 50 DegC. Furthermore, it was reported by Zaengl [20] that moisture present in paper, (pm) maintains a direct relation with the minimum value of tan-delta. In the present work, sample with known moisture content is prepared as discussed in section 4.2. In this sample, paper moisture content is calculated using eqn. 6 [6, 20] for both sinusoidal and triangular excitation. It is observed that for any given temperature, the value of paper moisture predicted using triangular excitation is closer of the actual value than that obtained using sinusoidal waveform.

0.06 0.05 0.04 0.03

(6) 0.02

Figure 13 shows that the minimum value of tan-delta for sinusoidal input is higher than that obtained for triangular excitation at each temperature. In addition, existing literature shows that the minimum value of tan-delta maintains a direct relationship with aging [6, 20]. As in the present work, the sample is prepared using a relatively new kraft paper and oil combination, it can be observed that sinusoidal excitation overestimates the paper moisture content in the insulation. In the case of real-life transformer insulation, over estimation of paper moisture by the use of sinusoidal excitation gives a pessimistic view of the insulation condition, while triangular excitation provides a more realistic view. So FDS using triangular excitation is economically beneficial to power utilities from asset management point of view.

0.01 30

35

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65

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80

Figure 13. Variation of minimum value of tan-delta with temperature for sinusoidal and triangular excitation.

5.2 REAL PART OF CAPACITANCE The variation of real part of capacitance for fundamental component of triangular excitation and sinusoidal excitation of same frequencies at the experimental temperatures has been plotted in Figure 14. The variation of real part of capacitance for harmonic component of triangular excitation and sinusoidal excitation is similar as shown in Figure 14.

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A. K. Pradhan et al.: Effect of Temperature on Frequency Dependent Dielectric Parameters of Oil-paper Insulation Table 4. Comparison of paper moisture for triangular and sinusoidal excitation at 50 DegC. % paper moisture (using Minimum value of tan-delta Actual paper moisture (%) column 2) 0.0222 5.65 5.5 0.0229 5.73

Triangular Sinusoidal

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10 Imaginary Capacitance(nF)

Real Capacitance(nF)

2.72 4.18

3

3

10

30 DegC, Sinusoid 40 DegC, Sinusoid 50 DegC, Sinusoid 60 DegC, Sinusoid 70 DegC, Sinusoid 80 DegC, Sinusoid 30 DegC, Triangular 40 DegC, Triangular 50 DegC, Triangular 60 DegC, Triangular 70 DegC, Triangular 80 DegC, Triangular

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% Error

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Figure 14. Real capacitance for sinusoidal and fundamental component of triangular input at same frequency.

It may be observed from Figure 14 that the value of real capacitance is almost constant at low frequency ranges whereas for triangular excitation, this real value decreases when frequency increases from 1 mHz to 4 mHz. After 4 mHz, the value again increases upto frequency of 0.1 Hz and becomes constant thereafter. A probable cause for the variation of real part of capacitance for triangular excitation in the range of 1 mHz to 4 mHz can be the by-products produced in the composite insulation as a result of thermal aging and deterioration of the pressboard material with age. It may also be observed from Figure 14 that at higher frequency (above 100 Hz) the value of real capacitance for triangular excitation is higher than the value of real capacitance for sinusoidal voltage input at same frequency at each of above mentioned temperature. The difference of values of real part of capacitance may be due to non-linear behavior of the oil-paper insulation [19] as discussed in section 5.1. 5.3 IMAGINARY PART OF CAPACITANCE The values of imaginary part of capacitance for fundamental component of triangular input voltage and sinusoidal input voltage at same frequencies at each of aforesaid temperatures have been plotted in Figure 15. It may be observed that the imaginary part of capacitance increases as the temperature increases for both sinusoidal as well as triangular excitation. This may be caused by the increase of activation energy in the material as temperature increases [3]. It may also be observed from Figure 15 that the imaginary part of the capacitance for triangular input is higher than the corresponding imaginary part of capacitance for sinusoidal input. This may be caused by the nonlinearity of the composite insulation [19] of the test specimen as discussed in section 5.1.

10

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Figure 15. Imaginary capacitance for sinusoidal and fundamental component of triangular input of same frequency.

6 CONCLUSIONS For conventional FDS, pure sinusoidal excitation is used for condition assessment of oil-paper insulation of power equipment. A scheme is proposed here that can be used for condition monitoring purposes of oil-paper insulation of power equipment using sinusoidal as well as non-sinusoidal excitation. Pure sinusoidal excitations of different frequencies were applied to the test sample and the results obtained were compared with the results of conventional FDS reported in literature. A good agreement has been obtained between the results of the developed scheme and the conventional FDS results. Different dielectric parameters were calculated from the corresponding responses that were obtained for both sinusoidal as well as non-sinusoidal excitations at different temperature. The results obtained for sinusoidal and non-sinusoidal excitations were compared. It was observed that the dielectric parameter values that were obtained for sinusoidal and non-sinusoidal excitation differ from each other at each temperature. It is known that the physical condition of the oil-paper insulation can be interpreted closely using sinusoidal excitation. The results of the present work show that more realistic estimation of paper moisture content can be obtained by the use of triangular excitation.

ACKNOWLEDGMENT Financial support for conducting this research work was provided by DST, Govt. of India (Grant No. SR/S3/EECE/0097/2010).

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Arpan Kumar Pradhan (M’12) was born in West Bengal, India in 1985. He received his Bachelor degree in electrical engineering from Jadavpur University in 2007. He obtained his Master of Engineering degree with specialization in high voltage engineering from Jadavpur University in 2011. Currently, he is working as a research scholar in High Tension Laboratory, Electrical Engineering Department, Jadavpur University. His area of interest is condition monitoring of insulation system in large electrical equipments. Biswendu Chatterjee (M’12) received the M.E.E. and Ph.D. degrees in engineering from Jadavpur University, Kolkata, India, in 2004 and 2009, respectively. He is currently working as an Assistant Professor in the Electrical Engineering Department of Jadavpur University. His current research interests include data acquisition and condition monitoring related to high voltage systems. Sivaji Chakravorti (M'92-SM'00) did his BEE, MEE and Ph.D. degrees from Jadavpur University, Kolkata, India, in 1983, 1985 and 1993, respectively. Since 1985 he has been a full-time faculty member of Electrical Engineering Department of Jadavpur University, where he is currently Professor in Electrical Engineering. He worked at the Technical University of Munich as Humboldt Research Fellow in 1995-96, 1999 and 2007, respectively. He served as Development Engineer in Siemens AG in Berlin in 1998. He has also worked as Humboldt Research Fellow in ABB Corporate Research at Ladenburg, Germany, in 2002. He worked as US-NSF guest scientist at the Virginia Tech, USA, in 2003. He is the recipient of AICTE Technology Day Award for best R&D project for the year 2003. He is Fellow of the Indian National Academy of Engineering, Fellow of the National Academy of Sciences India, and distinguished lecturer of IEEE Power and Energy Society. He has published about 140 research papers, has authored a book, edited three books and developed three online courses. His current fields of interest are numerical field computation, computer aided design and optimization of insulation system and condition monitoring of transformers.