2011 IEEE International Conference on Dielectric Liquids

Cole-Cole diagram as Diagnostic Tool for Dielectric Liquids

*Sirucek Martin, Mentlik Vaclav, Trnka Pavel, Bocek Jiri, Pihera Josef, Mraz Petr Department Technologies and Measurement, Faculty of Electrical Engineering

University of West Bohemia Pilsen, Czech Republic

*e-mail msirucek@ket.zcu.cz

Abstract-Dielectric subsystems have an important influence on

reliability, lifetime and power of electrical equipments. Study of dielectric parameters and their changes due to degradation mechanisms provide important information about the equipments. Paper deals with oil-paper systems and their thermal degradation. These systems are used for example in transformer, capacitors and bushings. Thermal degradation causes increasing of moisture content thus number of polar particles. Therefore the main idea of this paper is diagnostic of oil-paper insulation based on a method of polarization measurement. One of the methods is Cole-Cole diagram [I] or its modification e.g. Davidson [5], Havriliak-Negami [11]. The next aim of the paper is measurement of the system parameters (Complex permittivity, Viscosity, Acid value, Resistivity, Polarization index and Dissipation factor) and their changes due to thermal degradation. In experiments are used a normal and an environmental friendly fluid.

Keywords-Cole-Cole diagram; transformer oils; dissipation factor; polarization index; complex permittivity; oil-paper system

I. INTRODUCTION

Process which causes orientation of electric dipole moments within dielectrics into a direction of an outer field is known as an Electrical polarization. Arrangements of centres of gravity positive and negative charge particles have significant influence on the polarization. The next important influence has an amount of impurities and type of a bond between molecules. The polarization mechanisms can be divided in to the three groups based on force of bonds in a dielectric structure. Deformation polarizations occur in dielectrics with strong bond of charge particles in atoms, molecules or crystals. Relaxation polarizations occur within dielectrics with week forces between molecules especially in gases and liquids. The last type is migration polarizations caused by free charge particles in a dielectric. If dielectric is subjected to the outer electric field, the particles are focused in areas of imperfections or irregularities and space charges are developed. The main differences of the polarization types are physical processes within material structures and a value of relaxation (stabilizing) time. The Debey equation (1) describes a polarization in dielectric liquids stress by an AC field [2].

Complex permittivity E·

depends on relative permittivity En frequency f (ro = 2.n.1) and relaxation time T. The real part E' of the complex permittivity is equal to relative permittivity.

978-1-4244-7354-0/11/$26.00 ©2011 IEEE

The imaginary part E" of the complex permittivity represents losses due to alternating field stress.

' ( ' ) cs-coo

C JOJ = Coo + . l+jOJT (1)

For low values roT is s' "" Ss and sIt = O. For very large values

roT is s' "" s'" and sIt is low. Dissipation factor tgo is calculated as ratio of parts of complex permittivity.

C"

c"

tgJ =-, =­C cr

(2)

Cole-Cole diagram shows dependence of complex permittivity on frequency of testing AC voltage. Therefore the diagram can show individual changes in the material structure and individual polarization mechanisms.

Paper deals with insulating liquids used in insulating systems of power and distribution transformers. Insulating system has important influence on reliability and working life of these machines. During transformer operation its insulating system is degraded by different types of mechanisms (electrical, thermal, chemical and mechanical). Deterioration of the system causes significant changes in electric and non­electric parameters [6]. If the degradation factors are applied on insulating liquid for some time an aging occurs. The main factor is heating due to losses especially in a magnetic circuit and winding [7]. Excited thermal energy together with other factors (e.g. oxidation, chemical degradation) causes decomposition of a solid insulation (cellulose) and a liquid itself.

E"

OJ.T = I

E'

Figure 1. Cole-Cole diagram.

Degradation product of cellulose is mostly represented by water and gas (furan, CH4, CzH6, CO, COz etc.). Changes in water quantity have important influence on the electrical properties and the polarization of a liquid [8].

II. EXPERIMENT

Experiment was focused on electrical, physical and chemical properties of insulating liquids and their measurement. Changes of important parameters during thermal aging were observed. The main aim of experiment was construction of Cole-Cole diagram and individual parts of Complex permittivity in frequency range 20 Hz up to 2 MHz. Differences in diagram shapes were used for oils evaluation. Influence of thermal aging on the shape of Cole-Cole diagram was observed too. In the experiment two insulating liquids were tested. The fIrst was mineral oil Technol Y 3000 consists of hydrocarbon molecules and the second biologically easily degradable oil FR3 with natural esters. The experiment was divided into three parts.

The fIrst part was focused on measurement of the important parameters of transformer insulating liquid. Therefore Viscosity, Resistivity, Dissipation factor and Acid number of new and thermal aged (3000 h, 90 DC) oils were measured.

The second part deals with measurement of the dissipation factor and the polarization index. Samples of the oil-paper insulating system at intervals of 25, 50, 125, 225, 500, 1000, 2000, 3000, 4000 h were measured. The paper isolation was represented by transformerboards with dimension 100 x 100 x I mm. Ten samples were tested in each oil. Dissipation factor describes the losses due to polarization mechanisms within a dielectric. One minute polarization index is calculated as the ratio of currents flow through the sample in 15 and 60 second. The polarization index value may indicate moisture content of a solid part of an insulating system. Water content causes increase of polar particles within a dielectric and its polarization too.

In the last part of the experiment were measured differences between the new and thermal aged oils (4000 h, 90 DC). Basis characteristic of individual parts of the complex permittivity and Cole-Cole diagram was calculated and constructed. Cole-Cole linearized diagram was used for determination of Relaxation time. Equation (3) shows logarithmic correlation between ratio of parameters v* and u*

and relaxation time and frequency. Parameter a is number in range 0 up to 1 and describe a distribution of relaxation times. Parameters v* and u* are calculated from values of permittivities measured for maximum and minImum frequency [3]. Liquids were measured in Tettex Zurich electrode system. Measurement on Agilent HP E4980A RLC Impedance meter was done. Equation (2) was used for calculation of til. Both oils and both stages were measured three times for higher accuracy. Measured data in frequency range 20 -7- 200 Hz were removed because they had high dispersion of values. Dissipation factor of oil-paper samples were measured by three electrode system on automatic bridge

LDIC LDV 5. Polarization index was measured by the same electrode system according to CENELEC HD 429 S 1. Power source Keithley 248 (500 V) and pico amperemetr Keithley 6514 were used for this.

*

log';' = (l-a)logr +(l-a)logm (3) u

III. RESULTS

TABLE I. shows parameters for new and thermal aged oils. New and thermal aged oil in the cell of the table were separated by slashes. Mineral oil compared with FR3 achieved better values of tested parameters except dielectric strength. Thermal aged oils had parameters signifIcantly changed, especially FR3. Breakdown voltages were measured on the end of the experiment after 4000 h thermal aging. Both oils values fell approximately about 40 % due to degradation.

Samples of oil-paper insulating system had decreasing trend of dissipation factor during thermal aging. The value of dissipation factor depended on time when suffIciently impregnation of samples by the oil occurred. The samples in the FR3 oil were impregnated earlier (225 h) than in the mineral oil (500 h). Both oils probably require a certain value of viscosity, for faster impregnation of the sample.

The differences between dissipation factor of oil-paper samples impregnated by both thermal aged oils were not as significant (0.04 and 0.08) as in the case of the liquid itself (0.0018 and 0.0450). Therefore Cole-Cole diagram was used only for the oil samples. Results of dissipation factor measurement are shown in TABLE I.

TABLE I. PARAMETERS OF NEW ITHERMAL AGED TESTED OILS.

Parameters

Breakdown voltage [kV/2,5mm]

Kinematic Viscosity [mm2/s]

Acid number [mgKOH/gl

Dissipation factor tgo for 90°C [%]

Resistivity [n.m.l 010]

::::::: 0,12

I 10 ,Sl

Oil Technol FR3

59,2/37,3 74,2/43,2

8,6817,86 33,9/48,86

0,003/0,009 0,053/0,391

0,122/0,182 1,7614,499

383,9/194,6 0,81310,345

� 0,08 .9 �---------------------I�TechnOI _FR3

u n:I U. 5 0,04 :;:; n:I c-'iii Vl 0 is

o 2000 4000

Time of Thermal Aging [h]

Figure 2. Dissipation factor vs. Thermal aging.

4

::I: 3 5 x ' QJ 3 "C

.!: 2,5 c: 2 0 .. 1,5 ra N .;: ra

0 0,5 c..

0

0 1000 2000 3000 4000

Time of Thermal Aging [h]

Figure 3. Polarization index vs. Thermal aging.

Values of one minute polarization index during thermal aging are shown in Fig. 3. Oil achieved relatively stable slow growth in the interval of 0 -i- 1000 h. After 1000 hours different trends occurred in the both oils. FR3 grew up from 2.5 up to 3.5 and Technol decreased from 2.5 to the value 1. FR3 was decreasing in next measured intervals and Technol were fluctuating around 1. After 4000 h the polarization index reached values 1.5 (FR3) and 1 (Technol).

Real part of complex permittivity s' (Fig. 4) in frequency range 200 Hz -i- 47 kHz have values 2.18 (aged oil) and 2.19 (new oil). For frequency higher than 47 kHz an increase of both values occurred. Maximum values were 2.3 and 2.4 for the new and the thermal aged oil.

Behavior of imaginary part of complex permittivity s"

(Fig. 5) was almost identical with Figure 4. For 47 kHz similar increase occurred and curves copied the same direction. Only one main difference for new and thermal aged oil was observed. This difference is the value of s" (new oil had 0.28 and aged oil had 0.26) for maximum frequency.

2,36 Technol new

2,32

2,28 ...... Technolaged

..... , :-' 2,24 101

2,2

2,16

1 4 7 10

log w [-]

Figure 4. Real part of Complex permittivity vs. frequency.

0,035

0,03 Technol new

0,025 ...... Technolaged

:::!: 0,02

=1010,015

0,01 J 0,005

../ 0

1 4 7 10 log w [-J

Figure 5. Imaginary part of Complex permittivity vs. frequency.

0,03 Technol 0,025 � new

/ ...... Technol

0,02 aqed ..... L ..!.. 0,015

/ ·101 0,01

/ 0,005

( 0

2,1 2,2 2,3 2,4 £' [-]

Figure 6. Cole - Cole diagram Technol oil for frequencies 200 Hz + 2 MHz.

Behavior of parameters in Fig. 4 and Fig. 5 corresponded to a shape of Cole-Cole diagram (Fig. 6). New and thermal aged oil had different rate of rise. For aged oil curve was a little bit steepness, because s' is higher for maximum frequency and s" was smaller (approximately 0.001) than new one.

Results of new and aged FR3 oil are shown in Fig. 7 and Fig. 8. Values s' of new oil was about 0.4 smaller than aged oil. Parameter s' began growth for both curves at frequency of 475 kHz.

The shapes of the s" for new and aged oil were almost same in frequency range 200 -i- 10 kHz. If frequency was higher than 10kHz, s" of aged oil began rapidly increase up to 0.164. In the new oil an increase approximately for 25 kHz occurred. The maximum value in new FR3 oil was 0.084 and aged 0.17.

In Fig. 9 Cole-Cole diagram of new and aged FR3 oil is shown. Maximum values of s' and s" were 3.4 and 0.085. The curve of aged oil was two times higher than new one. Drift of real part of permittivity is 0.36. The maximum values of the parts of the complex permittivity were s'

= 3.76 and s" = 0.16.

3,8 I

I ...... FR3new

I 3,7

1 3,6 ...... FR3aged :::!: 3,5

-·101 3,4

� 3,3 J 3,2

3,1

1 4 7 10 log w [-]

Figure 7. Real part of Complex permittivity vs. frequency.

0,18

0,15 ...... FR3new

..... 0, 12 ...... FR3aged , ;-'0,09

11 101 0,06

I 0,03 .L/ 0

. 1 4 7 10

log w [-J

Figure 8. Imaginary part of Complex permittivity vs. frequency.

0,2 -FR3new

0,15 -FR3aged

:::!: 0,1

-w 0,05

°

3 3,5 4

[' [a] Figure 9. Cole - Cole diagram FR3 oil for frequency range 200 Hz + 2 MHz.

Applying (3) on measured data linearized Cole-Cole diagram (Fig. 10) for both oils and both stages was obtained. Linear regression was applied on results of the oils in frequency range 2 kHz up to 2 MHz. Formula of the linear regression was used for calculation of relaxation time 't and distribution parameter a from (3). Results are shown in TABLE II.

IV. CONCLUSION

Results show that s' don't correspond with theoretical suppositions. The s' values should be constant with lower frequencies and for certain frequencies start decrease. But they are increasing with a frequency of testing voltage. Therefore curves of s' are similar to S". For higher frequency (MHz + GHz) of testing voltage is expected that both curves reached the maximum. After the maximum is reached they start slowly decrease. Amount of water created by insulating systems due to thermal degradation (for 90°C) hadn't important influence on real part s' of complex permittivity of mineral oil in measured frequency range. The values of s' are in interval 2.15 + 2.34 for new oil and 2.17 + 2.33 for aged one. The difference between new and aged oil curve is approximately 0.01 + 0.02. In the case of oil based on natural esters a moisture had higher negative influence on the real part of complex permittivity concretely 0.4 + 0.27.

1,5

1

:::!: 0,5 -

° " ::s

;;- -0 5 > '

- -1 C) .2 -1,5

-2

-2,5

TABLE II.

Technol new

I -Techno I aged I

I.J -FR3new

-' -FR3aged

j ./

log w [a] Figure 10. Linearised Cole-Cole diagram.

RELAXATION TIME AND DISTRIBUTION PARAMETER OF NEW 1 THERMAL AGED OILS.

Parameters Oil Technol FR3

T [s] 4,5.10,12/1,3.10,8 5.7. 10.8/1.2.10.8

a [-I 0,92/0,78 0,39/0,69

Results of transformerboard samples in new and aged oils show that the changes and differences between the parameters are not as significant as in the case of oil samples themselves. Therefore it is preferable to apply frequency dependence only on the liquid itself. Comparison of shapes of Cole-Cole diagram in the measured frequency range provides differences between the tested oils. Evaluation of the results shows that the insulating liquid, especially mineral oil, hadn't after thermal exposition a sufficient quantity of polar components, which could be strongly detectable. Application of Cole - Cole diagram is particularly suitable for more polar liquids with a higher degree of degradation (FR3). Mineral oil has only small changes during the thermal degradation compared to the oil based on natural esters FR3. In both cases, the curves s'

and S" have upward character in a certain frequencies. This frequency is 47 kHz for new and thermal aged Technol oil. FR3 has for s' curve of new and aged oil the same frequency 475 kHz. Values of S" new and aged FR3 oil begin upward in 10kHz and 25 kHz. Calculated times of relaxation in frequency range 2 kHz up to 2 MHz show that time decreased due to thermal aging.

ACKNOWLEDGEMENT

This research was funded by the Ministry of Education, Youth and Sports of the Czech Republic, MSM 4977751310 - Diagnostics of Interactive Processes in Electrical Engineering, Students grant system SGS-2010-037. The authors are grateful for the support of this program.

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