UPTEC E 20009

Examensarbete 30 hpJuni 2020

Measurements of resistivity in transformer insulation liquids

Jonathan Hägerbrand

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

Measurements of resistivity in transformer insulationliquids

Jonathan Hägerbrand

This thesis focuses on measuring techniques and results of resistivity in four commercially available insulating transformer oils: mineral oil, ester oil and two isoparaffin oils.Two measuring techniques, the industrially used diagnostic system for electrical insulation IDA and the Labview implemented Triangular Method, are used for resistivity measurements and the techniques are compared, a correction algorithm to the triangular method is suggested.Dielectric properties of mineral & ester and isoparaffin A&B mixtures are investigated, it is experimentally shown that the transformer oils that show high resistivity also show low loss factor.The effect moisture has on resistivity in mineral and ester oil are shown both in terms of relative humidity and actual water content in parts per million.A previous measurement cell is redesigned, the cell is manufactured in copper and gold. It is found that the material choice of the cell significantly affects the resistivity measurements.The electrical double layer and contact resistance between the oil and cell are investigated as a way to explain the difference in measured resistivity.These experiments are limited to the mineral oil and isoparaffin oil A, it is found that contact resistance is a plausible explanation. The electrical double layer is fairly constant for both oils and the Debye length of the double layer is negligible compared to the total distance between the electrodes of the cell.

Lastly, the field of insulating transformer oils and its future is discussed, from data obtained regarding the dielectric properties and environmental aspects of the four transformer oils used in this study. A positive trend which combines the high insulating properties with good biodegradability qualities is found.Suggesting a positive future in the field of insulating transformer oils. The results found in this thesis can be used as a basis for future theses regarding transformer oils used for HVDC applications.

Tryckt av: UppsalaISSN: 1654-7616, UPTEC E20009Examinator: Mikael BergkvistÄmnesgranskare: Shi-Li ZhangHandledare: Joachim Schiessling

Sammanfattning

Denna uppsats fokuserar på teknik och resultat för mätning av resistivitet i fyra kommersiellt tillgängligaisolerings oljor som används i transformatorer för HVDC applikationer: mineral olja, ester olja och tvåisoparaffin oljor. Två olika tekniker för mätning av resistivitet jämförs, IDA, ett regelbundet använt mät-system och den Labview implementerade Triangel metoden. En algoritm för att förbättra noggrannhetenav Triangel metoden är föreslagen. Dielektriska egenskaper för olika blandningar mellan mineral & esteroch isoparaffin A & B är undersökt. Det är experimentellt bevisat att oljor med hög resistivitet har lågtangent delta. Vatten och fukts inverkan på resistivitet är undersökt i mineral och ester olja, det visar sig attresistivitet och fukthalt beter sig på ett intressant sätt. En tidigare mätcell är omgjord för att lösa diversehållbarhets problem. Denna cell byggs i koppar och guld. Det visar sig att valet av material för cellenpåverkar resistivitetsmätningarna. Två idéer: elektriskt dubbel lager och kontakt resistans är undersöktasom en förklaring till detta. Dessa experiment är begränsade till mineral olja och isoparaffin A, det visar sigatt kontakt resistans är en rimlig förklaring. Det elektriska dubbel lagret är för litet jämfört med det totalaavståndet mellan mätelektroder medans kontakt resistansen är väldigt hög.Slutligen är framtiden för oljor som isoleringsmaterial i HVDC applikationer diskuterad. Här lyfts bådetekniska och miljöbaserade argument fram baserade på resultat från rapporten. Det visar sig att teknologingår framåt, då den nyaste oljan visar både bra isolerande egenskaper och hög bionedbrytbarhet. Resultatenfrån denna uppsats kan användas som en bas för framtida uppsatsen inom oljor som används som isolerandematerial för HVDC applikationer.Arbetet har utförts på Power Grids (PG) avdelningen för ABB i Västerås. Arbetet har pågått mellan januarioch juni 2020.

Contents

1 Introduction 1

2 HVDC the technology of choice for transporting power 22.1 High vs low voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Direct current vs alternating current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3 Physical model 33.1 Ion Drift Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.2 Relaxation time & Transit time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.3 Concentration of ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.4 Electrical double layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.4.1 Zeta-potential and Debye length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4 Types of transformer oil 94.1 Biodegradability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.2 Mineral oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.3 Ester oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.4 Isoparaffin oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

5 Dielectric properties of transformer oil 115.1 Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115.2 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125.3 Water content & humidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125.4 Tangent delta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135.5 Relative permittivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6 Experimental setup & hardware 146.1 IDA 200 Insulation Diagnostic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

6.1.1 Equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156.1.2 Sine correlation technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166.1.3 Calculations of parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176.1.4 Relative permittivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

6.2 Triangular Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186.2.1 Implementation in Labview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

6.3 VAISALA-MM70 handheld moisture and temperature meter . . . . . . . . . . . . . . . . . . . 216.4 Cleaning and assembly process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216.5 Degassing process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226.6 Climate chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

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7 Measurement cell 237.1 Prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247.2 Prototype flaws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247.3 New measuring cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

8 Experiments & results 288.1 Experiments: Triangular method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

8.1.1 A general measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298.1.2 Importance of shielding, choice of frequency & voltage . . . . . . . . . . . . . . . . . . 308.1.3 Accuracy and precision of measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 348.1.4 Triangular method at IDA frequencies - mineral oil . . . . . . . . . . . . . . . . . . . . 358.1.5 Triangular method at IDA frequencies - ester oil . . . . . . . . . . . . . . . . . . . . . 378.1.6 Different types of grounding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

8.2 Experiments: IDA diagnostic tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408.2.1 A general measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408.2.2 Accuracy and precision of measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 418.2.3 Humidity & resistivity in ester oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428.2.4 Humidity & resistivity in mineral oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438.2.5 Dielectric properties of mineral and ester oil mixtures . . . . . . . . . . . . . . . . . . 448.2.6 Dielectric properties of Isoparaffin mixtures . . . . . . . . . . . . . . . . . . . . . . . . 468.2.7 Material dependency of measuring cells (Copper & Gold) . . . . . . . . . . . . . . . . 48

9 Discussion 549.1 The Ion Drift Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549.2 Comparing the triangular method to IDA diagnostic system . . . . . . . . . . . . . . . . . . . 56

9.2.1 Correction algorithm for the triangular method . . . . . . . . . . . . . . . . . . . . . . 579.2.2 Accuracy and practical problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

9.3 Moisture dependence in ester and mineral oil . . . . . . . . . . . . . . . . . . . . . . . . . . . 599.4 Dielectric properties of transformer oils mixtures . . . . . . . . . . . . . . . . . . . . . . . . . 599.5 Electrode material dependency on measured resistivity . . . . . . . . . . . . . . . . . . . . . . 61

9.5.1 Electrical double layer and Debye length . . . . . . . . . . . . . . . . . . . . . . . . . . 619.5.2 Contact resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

9.6 Technological advancements in the field of transformer oil . . . . . . . . . . . . . . . . . . . . 67

10 Conclusion 68

11 Future work 70

Bibliography 71

1. Introduction

With the increasing demand of electricity, more efficient ways of transporting it is always discussed andresearched. High voltage direct current (HVDC) and the newer technology ultra high voltage direct current(UHVDC) uses high voltages to transport power as it reduces resistive losses [1]. DC, in comparison withAC, can yield higher efficiency [2] and subsequently less conductor material is required. Because of thesetwo aspects, high DC voltage is the voltage of choice when transporting high power over long distances. Onedownside of HVDC is the conversion stations required to achieve the high voltage. These stations include atransformer which will be electrically stressed with both DC and AC voltages. The insulating material in theDC/DC converter in said transformers are often pressboard submerged in liquids, mainly oils [3]. Becauseof the size of the transformers and the high operating voltage, much insulating material is required. Byunderstanding the insulating material properties, the transformer and corresponding converter themselvescan be dimensioned more efficiently. Resistivity is an important parameter for the insulating material as itis a measure of how well the insulating material limits current.Due to the ionic nature of transformer oils (the insulating material), the resistivity has a nonlinear dependenceon the applied electric field. However, it is possible to simulate the behaviour using the “Ion Drift Model”[5]. From this model only four input parameters are required: relative permittivity, mobility of positiveions, mobility of negative ions and resistivity at thermodynamic equilibrium [4]. From this it is possible toestimate the behaviour of the transformer oil under high DC stress by using data taken from experimentsperformed under low DC stress. In this study resistivity of various transformer oils are investigated. Outsideinfluences like temperature and moisture as well as various mixtures of oils are studied. The experiments aredone in cooperation with the Power Grid section of ABB. ABB is one of the world’s leading companies whenit comes to HVDC and UHVDC technology. In 2016 ABB took on a UHVDC project with unprecedentedvoltage levels, power capacity and distance. The project involved transporting power over a distance of 3,000kilometers at a voltage of 1,100 kV. The transformers used will each weigh around 800 tons [6]. Consideringthe size of these transformers, it is clear that the amount of insulating material needed is extensive.

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2. HVDC the technology of choice for transport-ing power

High voltage direct current or HVDC is the technology of choice when transporting high power over longdistances. Compared to AC, capacitance isn’t a limiting factor for the DC cables as pure DC doesn’t produceany reactive power. Because of this, the need for shunt capacitors together with the transmission lines isremoved. Since the power is transported as DC, it can be used to connect systems which are unsynchronizedwithout worry about matching frequencies. Further, less material for the conductor is required. As AC isusually transported in three phases thus requiring three conductors.

2.1 High vs low voltage

Higher voltage means lower power losses. Most power losses from DC occurs in the form of heat and heat isa consequence of current passing through a resistive element. From Ohm’s law together with the definitionof power, we see that by doubling the voltage, 4 times as much power can be achieved. Similarly, consideringa constant power, doubling the voltage will half the current, resulting in less losses due to heat.

Ploss = UI =U2

R(2.1)

2.2 Direct current vs alternating current

As mentioned earlier, Pure DC only produces active power thus removing the need to deal with the capacitiveproperties of transmission lines operating at AC. Further, the power transported at AC is defined from theroot mean-square (RMS) of the AC voltage. For a sine-wave the RMS value comes out to 1√

2of the peak-

voltage. Or approximately 71% of the peak voltage. Because of this fact, the power delivered by DCcompared to AC is approximately 40% higher(

√2) for any given peak voltage when operating at the same

current (considering the current in the DC system to be equal to the RMS of the current in the AC system).Another advantage DC has in comparison to AC is the absence of the skin effect. If AC is transportedin a conductor, the electrons tend to push towards the surface of the conductor thus making the currentdensity throughout the conductor inhomogenous. With more current passing through the outer part of theconductor, the effective area will decrease thus increasing the resistance and consequently the produced heat.

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3. Physical model

3.1 Ion Drift Model

The ion drift model has been proved as a useful model for describing oil under DC stress [3][4][5]. Themodel is very practical as it only requires four, relatively easy to measure, parameters (resistivity, relativepermittivity, mobility of positive ions & mobility of negative ions) at low voltage to estimate the behaviourof the oil at voltage levels used in HVDC technology. In the ion drift model the transformer oil is considereda weak electrolyte [4]. At thermodynamic equilibrium the negatively and positively charged ions are equaland significantly less than the neutral molecules c. The density of these ions can be described from theirconductivity and resistivity [4]

p0 = n0 =σ

q(µp + µn)(3.1)

Here µp and µn are the mobilities for positive and negative ions respectively. q is the elementary charge andσ is the conductivity. Conductivity and resistivity have an inverse relationship

σ =1

ρ(3.2)

Ions are generated from dissociation of ionic pairs, vice versa, ionic pairs are formed by the recombinationof ions.The rate of recombination and dissociation is described by the rate equation [4]

dp

dt=dn

dt= kDc− kRpn (3.3)

Here kD and kR are the dissociation and recombination constants. The recombination constant is given by

kR =q

�0 + �r(µp + µn) (3.4)

Worth noting is that the recombination constant does not depend on the electrical field. The dissociationconstant, contrary to the recombination constant, is given as a function of the applied electrical field.

kD = k0DF (E) (3.5)

The function F (E) is given by

F (E) =I1(4b)

2b(3.6)

Here I1 is the modified Bessel function of first kind and order one. The electric field strength is beingconsidered in the term “b” as follows:

b =

√q3|E|

16π�0�rk2BT2

(3.7)

Here T is the absolute temperature expressed in kelvin, kB is the Boltzmann constant 1.38E-23 [J/K], �0and �r are the permittivity of vacuum 8.854E-12 [F/M] and of the dielectric material (transformer oil)

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respectively. The field independant term k0D is given by assuming steady-state equilibrium of the ions [4],thus the rate of recombination / dissociation is zero and the amount of negative and positive ions are equal.From the rate equation 3.3 the field independant term can be written as

k0D =kRn

20

c(3.8)

When an external electric field is applied to the system, the charge carriers are separated by electrostaticforces and experience drift and diffusion. The negatively charged ions will start drifting towards the positivelycharged electrode and vice versa for the positively charged ions. Their drift velocities are defined as [4]

−→w p,n = µp,n−→E (3.9)

The diffusive fluxes of the ions are proportional to the gradient of the ions densities. The diffusion constantsare given by Einstein’s relation [4].

Dp,n =kBT

qµp,n (3.10)

Including the drift 3.9 and diffusion 3.10 terms to the rate equation 3.3 yields the following set of equations.{∂p∂t +∇(

−→w p −Dp∇p) = kRn20F (E)− kRpn∂n∂t −∇(

−→w n −Dn∇n) = kRn20F (E)− kRpn(3.11)

The relation between charge density and electric potential is given by Poisson’s equation [4]

∇(�0�r∇φ) = −q(p− n),−→E = −∇φ (3.12)

The final set of equations used to describe the behaviour of transformer oil only requires four input parametersthat all are expected to be measured at thermodynamic equilibrium, as one of the assumptions to find theequations is that the ions are in steady-state equilibrium. Again, to achieve thermodynamic equilibrium, nocurrent should pass. Something that is not possible for measurements to be taken. Getting as close to thisas possible is why low voltages are preferred when performing experiments to determine the mobilities andthe resistivity.The final set of equations becomes:

∂p∂t +∇(µp

−→E p −Dp∇p) = kRn20F (E)− kRpn

∂n∂t −∇(µn

−→E n −Dn∇n) = kRn20F (E)− kRpn

∇(�0�r∇φ) = −q(p− n)−→E = −∇φ

(3.13)

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3.2 Relaxation time & Transit time

Since transformer oil is considered an electrolyte, it contains ions. These ions will get excited when voltageis applied and start drifting towards the electrode with an opposite charge (negatively charged ions drifttowards the positively charged electrode and vice versa). The transit time for an ion given a specific distance,considering a parallel rectangular electrode geometry [7], is given by

ttransit =dµtVd

=d2

µtV(3.14)

With d being the distance between the electrodes and µt the mobility. Since the measurements taken duringthis thesis are performed at very low voltages. The oil is considered to be in thermodynamic equilibriumduring the experiments, thus the mobility here denotes the combined mobility of both the negative andpositive ions. Which are considered to be equal.

µt = µp + µn (3.15)

The parameter ’relaxation time’ is used for transformer oil which is under next to no electrical stress. Becauseof the low applied voltage, ionic pairs that might have dissociated into ions should be relatively close to eachother. The relaxation time is a measure of the time it takes for these ions to recombine. It is given by [7]

trelax = �0�rρ (3.16)

If the relaxation time is longer than the transit time, the ions will travel through the gap before theyrelax. This sweep-out of ions will create an almost uniform electric field. If the transit time is longer thanthe relaxation time, the electrical field will be more concentrated at the surfaces of the electrodes. Thesebehaviours, although not universal, have been shown by [4]. The fraction of relaxation and transit time isusually described using κ

κ =τtransitτrelax

=d2

�0�rρµtV(3.17)

With κ � 1 corresponding to longer transit time and κ � 1 longer relaxation time. Since the ions in thetransformer oil, described by the ion drift model, are considered at thermodynamic equilibrium. A largevalue of κ is desired. As this would indicate that dissociated ions will recombine faster than they woulddrift apart. Due to the permittivity, resistivity and mobility being material parameters. The only adjustableparameters are the distance between the electrodes, with smaller distance yielding shorter transit time andapplied voltage, with higher voltage yielding shorter transit time.

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3.3 Concentration of ions

Similarly to the terminology of holes and electrons used when describing conductivity in semiconductors.The holes, positively charged, and electrons, negatively charged that conduct electricity. Is according to theion drift model equivalent to the positively and negatively charged ions. As concentration of ions is notsomething that is easy to directly measure, the parameter is calculated from the mobilities and resistivity.To find an expression for the concentration, the current density is the first step. The total current densityof the transformer oil is the result of the positively and negatively charged ions.

Jtotal = Jn + Jp (3.18)

Let n be the concentration of negatively charged ions and µn their mobility. Each of the ions has a chargeequal to the elementary charge. In an applied electric field, these ions will start drifting with the velocity

v = µnE (3.19)

The total current as a consequence of the drifting negatively charged ions can be expressed as

In = qnµnE (3.20)

The current generated by the positively charged ions is expressed similarly. The total current is given by

Itotal = qnµnE + qpµpE = qE(nµn + pµp) (3.21)

According to the ion drift model, when the transformer oil is in thermodynamic equilibrium. The concen-tration of the negatively and positively charged ions are equal.The final expression for the concentration of ions, both negatively and positively, is the following

n = p =1

qρ(µp + µn)(3.22)

with ρ being the resistivity.

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3.4 Electrical double layer

With the electrolytic transformer oil and the charged metallic surface of the electrode used for measurements(more about the construction of the measuring cell in chapter 7). There will be a varying concentration ofions closer from the surface [8]. The electrical double layer, EDL for short, relates to the two closest layersto the electrode surface.

Figure 3.1: Illustration of the electrical double layer

The first layer, the surface layer, is the layer made up by the ions that are attached to the electrode surfacedirectly. They are attached due to the charged surface of the electrode, with a positively charged electrodeattracting negatively charged ions and vice versa. The second layer, the diffuse layer, is composed of ionsthat are loosely bound to the surface layer. The ions in the diffuse layer are attracted to the surface layerby the Coulomb force. It will mainly contain ions of the opposite charge as the surface layer, with theimportance difference compared to the surface layer, being that they are not fixed in place.

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3.4.1 Zeta-potential and Debye lengthWhen there is a separation of charge (negative and positive ions) there is always an electrical potential.The electrical potential between the surface and diffuse layer is called the Zeta-potential. Because of thehigh concentration of ions at the surface layer and the part of the diffuse layer closest to the surface layer.The Zeta-potential will decrease with distance from the surface of the electrode. The Debye length [9] is acommonly used measure of the double layer thickness. It is used to determine the distance where the ion’snet electrostatic effect will persist. The Debye length of a monovalent electrolyte, an electrolyte where allions contain the same charge, is given by equation 3.23 [29].

κ−1 =

√�0�rkBT

e2NA2c(3.23)

where c is the concentration in moles per m3, e is the elementary charge and NA is the Avogadro number6.022 E23 [mol−1]. Therefore, to calculate the Debye length. The concentration of ions is required, thisparameter is consequently dependent of the resistivity and the mobility as shown by equation 3.22. Worthnoting is that the concentration of ions calculated in equation 3.22 is in numeric units [m−3].The conversion between numeric and molar units is given by the Avogadro number

cmolar =cnumericNA

(3.24)

The final expression for the Debye thickness, considering numerical concentration, is given by:

κ−1 = 2×√

�0�rkBT

2e2cnumeric(3.25)

Since there are two electrodes, thus two electrical double layers, the calculated Debye length is doubled.

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4. Types of transformer oil

In this study three types of transformer oils are used. In total 4 different brand of oils are studied, one esteroil, one mineral oil and two isoparaffin oils. Some properties that are not actively measured in this report,like biodegradability and viscosity, are mentioned. The statements about these parameters are based of thetechnical data sheets corresponding to each oil.

4.1 Biodegradability

When a material is biodegradable, said material is capable of degrade into CO2, H2O, methane, biomass,and mineral salts. Since most material are capable of degradation if given enough time, the classification of‘Readily Biodegradable’ is given when a material is able to biodegrade between 60-100% over a time periodof 28 days. As given by the OECD 301 standard [10]. Of the four oils investigated in this study, only twomention biodegradability on their technical data sheet [11]. Both of these oils have used the same, OECD301, standard.

Oil Biodegradability Viscosity Flash pointMineral No 7.7 150Ester Readily biodegradable 29 260Isoparaffin A No 4.5 145Isoparaffin B Readily biodegradable 9.35 171

Table 4.1: Transformer oil types used in this study together with some non-investigated parameters

4.2 Mineral oil

The most commonly used insulating oil in transformers is mineral oil. Mineral oil has been used in liquid filledtransformers for longer than 100 years. The combination of low price, good dielectric properties and goodcooling properties makes it popular to the extent of having million of tons purchased each year worldwide[12]. Mineral oil originates from petroleum, as such it is not biodegradable. Because of this aspect newalternate types of transformer oil are actively researched. Two of which are the ester and isoparaffin oilsinvestigated in this study.

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4.3 Ester oil

The ester oil used in this study is fully biodegradable and non-toxic. These fluids are vegetable oil based,thus being manufactured from natural sources. Ignoring the obvious environmental benefit compared tomineral oil. Ester oil wins out over mineral oil when it comes to operating at higher temperatures. With theflash point, the minimum temperature required to set of a fire, being higher compared to mineral oil. Theester oil used in this study has a flash point almost twice that of the mineral oil counterpart, shown in table4.1. A downside of the ester oil is the viscosity being high. High viscosity “thicker liquid” yields reducedcooling, a liquid with high viscosity will have lower circulation speed which equates to less oil having its heatdissipated.

4.4 Isoparaffin oil

Isoparaffin is a chemical term used to describe a branched chain of hydrocarbons. Similarly to mineral oilit is produced from crude oil. Depending on the oil, the refining process varies. The refining process relatedto isoparaffin oil B is unknown. Isoparaffin A uses the patented HT purity process which, according toPetro-Canada [13][14], causes a biodegradability of 60% using the OECD 301 standard. A percentage whichshould classify it as readily biodegradable. However, according to the technical data sheet of isoparaffin A[11]. It is only stated “no data available” when it comes to biodegradability. The next-to-pure liquid (99.9%pure) is also claimed to be virtually non-toxic. Similarly to the ester oil, isoparaffin B is classified as readilybiodegradable. Contrary to the ester oil, the viscosity is extremely low. To the point where both isoparaffinoils have a viscosity similar to the mineral oil.

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5. Dielectric properties of transformer oil

In this section some dielectric properties and properties that might indirectly affect said properties areexplained.

5.1 Resistivity

In the simplest of terms, a perfect insulator should not allow current to pass when under the influence of anapplied electrical field. Higher resistivity means better insulating capability in the material. If the materialis shaped as a cuboid, an easy way to measure the resistivity of a material is by using the following equation

ρ = RA

d=U

I

A

d(5.1)

Here A is the cross section area of the material and d is the distance between the edges of the material. Whenmeasuring resistivity of a liquid material, the area of the liquid will be equal to the area of the electrodesif using a measuring cell with the design of two parallel plates. Since the electrodes are submerged in theliquid. This equation can be used. By changing the distance between these electrodes, the parameter d willchange. The area of the liquid will be equal to that of the electrode. Considering a homogeneous electricfield between the electrodes, the resistivity will be constant throughout the liquid. Because of this, especiallywhen working with small voltages, it is important to design the electrodes in a way to achieve as close to ahomogeneous electrical field as possible. In practice this means to make the surfaces as smooth as possibleand to have a consistent distance throughout the entirety of the electrodes. More about the design of themeasuring cell used in this thesis is found in chapter 7.

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5.2 Temperature

Contrary to conductors, insulators have negative relationship between resistivity and temperature. Anincrease in temperature means a decrease in resistivity. This phenomenon has to do with the material bandgap. The band gap is an energy gap between the valence band and the conduction band where no electronscan exist. For an electron to jump from the valence to the conduction band (this flow of electrons is thecurrent) it needs energy. Material with a wider band gap needs more energy for an electron to make thejump. In conductors the band gap is very small, sometimes nonexistent as the valence and conductionband overlap [15], thus if extra energy is added to the electron (heat). It becomes easy for the electronto make the jump and as such increase the current. This is why resistivity increases with temperature forconductors. The amount of electrons wanting to pass from the valence band to the conduction band are toomany. An analogy can be a very trafficked highway, too many cars causes the flow of traffic to be slower.Insulators, however, have a wide band gap [15]. The energy required for an electron to pass the band gap isnot negligible. Therefore the risk of having too many electrons passing simultaneously is small. As statedearlier, when electrons pass the band gap it is called current. Thus, for insulators, adding energy (heat)will increase the amount of electrons passing the band . I.e. the conduction will increase, an increase inconduction is equivalent to a decrease in resistivity. Therefore, higher temperature will cause the resistivityto decrease in insulators. Some insulators turn to conductors at very high temperatures. But in regards tothe subject of insulating transformer oil for HVDC applications. Those temperatures are irrelevant.

5.3 Water content & humidity

In HVDC transformer the insulating material often consists of pressboard soaked in oil. Although this thesisfocuses on the oil aspect of the insulating material. Understanding how a HVDC transformer is insulated isnecessary when discussing water content. Keeping the water content down in transformers is recommendedas water rapidly increases the aging process of pressboard [16]. In most technical data sheets the watercontent is expressed in ppm. However, this can be deceiving as different insulating oils have varying watercontent. A better way is to measure in terms of water activity or relative humidity. Water activity is theratio of vapor pressure of water in a material to the vapor pressure in pure water, at the same temperature.When pressure equilibrium and thermal equilibrium is achieved (a sealed container), the water activity ofthe sample is equal to the relative humidity of the air surrounding the sample [17]. When measuring wateractivity in transformer oil under next to no outside stress, these equilibrium criteria are fulfilled. As such,to get the relative humidity in percent, the measured water activity can simply be multiplied by 100.

RelativeHumidity[%] = WaterActivity × 100 (5.2)

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The relative humidity is then compared to a set saturation value unique to each transformer oil. This valueindicates the maximum amount of water possible to dissolve in the transformer oil. Adding excess water willcause the water to split from the oil and as a consequence an inhomogeneous blend will occur. A downsideof this, comparatively to measuring in ppm, is that the saturation value of the oil has to be identified.However, when the value is found. The water content will always be expressed in a percentage scale withlower percentage meaning further away from the saturation limit. By measuring relative humidity, the riskof free water formation is thus easier to predict and prevent. It is also easier for workers without knowledgeabout the specific water content of a transformer oil to do maintenance.

5.4 Tangent delta

The loss factor, or tangent delta, is a way to determine the quality of an insulator. If an insulator is freefrom impurities and defects it resembles a capacitor in the sense that an ideal capacitor functions as an opencircuit for DC.

Figure 5.1: The angle between the capacitive and resistive current is denoted δ

Since a perfect capacitor should have a 90◦phase shift between voltage and current, any deviation from thiswill be an indication of the resistive properties in the insulator. When impurities or defects reduce theresistive properties, the resistive current will increase causing the angle between the resistive and capacitivecurrent to increase. The impedance is directly proportional to the current and will consequently be affected,with the real part being affected by the resistive current and the imaginary part being affected by thecapacitive. A higher tangent delta value means a reduced capacitive behaviour of the insulator, thus a worseinsulator.

5.5 Relative permittivity

Relative permittivity is a fundamental material parameter which affects the propagation of electrical fields.The relative permittivity is always greater than or equal to 1. Permittivity is a measure of how much themolecules oppose an external electric field. Thus, the relative permittivity is a measure of reduction inelectric field compared to if the electric field would propagate in vacuum [18]. Higher relative permittivitymeans more reduction in electric field. In dielectrics such as insulating transformer oil, the permittivity isoften considered complex [19]. With the real part being related to the stored energy within the material.The imaginary part relates to the loss of energy in the material. However, in this study the real part ismainly investigated as the loss in the material is indirectly investigated using the tangent delta.

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6. Experimental setup & hardware

6.1 IDA 200 Insulation Diagnostic System

IDA 200 is a system used in measurement and analysis of insulating material [20]. By applying a relativelylow voltage, it is possible to acquire parameters like resistivity and permittivity of the insulating material.The only parameters IDA directly measures are the load voltage and current. From this the various param-eters are calculated. IDA is useful for many applications and uses different models to do the calculationsdepending on the circumstance. The different impedance models used in this thesis and corresponding pa-rameters are shown in table 6.1.

Impedance model ParameterResistive �, ρ, σTangent Delta C, tanδ, PF

Table 6.1: IDA 200: Impedance models and corresponding parameters

In the field of transformer oils, the dielectric and resistive properties are of interest. These include, resis-tivity, loss factor and permittivity. While IDA 200 has more impedance models available. To measure saidparameters the resistive and tangent delta models are enough. Since insulation diagnostics is based on ma-terial characterization, the geometry of the measuring cell is relevant when calculating material parametersfrom the measured current and voltage [20]. In other words, before any measurement is done on the oil themeasuring cell has to get its geometric capacitance defined. This is done by doing measurement when onlyair (or vacuum) is between the electrodes. Since no “material” is between the electrodes, the capacitanceof the sample is the geometric capacitance of the electrodes. The material is then inserted between theelectrodes and this will influence the current that passes through. This influence is then used in the variousmodels to do the calculations.

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6.1.1 Equivalent circuit

Figure 6.1: IDA 200: Simplified circuit

When a voltage is applied to the electrodes the ions in the oil start to drift to their respective counterpart,negatively charged ions drift to the positive electrode and vice versa. This brings up a few issues. Firstly,to do a measurement an applied voltage is required. But applied voltage will cause stress to the systemthus not keeping it in ideal thermodynamic equilibrium. A state which the oil is assumed to be in whenextrapolating the measured data to use in simulations via the ion drift model. Further, due to the fact thatthe ions in the oil will start drifting apart under DC stress, the measurement could be affected. Becauseof this, it is recommended to apply a low AC voltage with very low frequency as the voltage source. Thelow peak voltage will not affect the equilibrium of the oil in any significant way and applying an AC voltagewill keep the ions in the oil from drifting apart (since the positive and negative electrode switch polarityregularly). For most of the experiments related to this study, measurements are done at 1-2 V (rms) and afrequency sweep from 1 kHz to 1 mHz. The measured parameter to be used in future simulations would bethe data point at the lowest frequency, 1 mHz, as it best resembles DC.

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6.1.2 Sine correlation techniqueAccording to Peter Werelius, the inventor of the diagnostic tool [21], IDA uses the sine correlation techniqueto achieve a complex representation of the current and voltage. Both input voltages (one representing thevoltage, another the current) are multiplied by a sine and cosine respectively and then averaged over aninteger multiple (N) of the interval of time (T). The sine, cosine and the applied voltage have the same exactfrequency.Consider channel zero to be the voltage measurement. The real and imaginary part of the voltage arecalculated according to equations 6.1 and 6.2.

Re(Ch0Peak) =2

NT

∫ NT+α0+α

= Ch0(t) sin (ωt)dt (6.1)

Im(Ch0Peak) =2

NT

∫ NT+α0+α

= Ch0(t) cos (ωt)dt (6.2)

Since impedance requires both current and voltage to be calculated. A second channel is used. The layoutof the sine correlation implementation is shown below.

Figure 6.2: IDA 200: Sine correlation layout

The result is a complex voltage (Ch 0) and a complex current (Ch 1) both with a phase referring to theinternal sine wave generator. Calculating the impedance by ohm’s law Z=U/I means that the phase of theimpedance will be [φ(U) + φinternal] - [φ(I) + φinternal]= φ(U)-φ(I).

Thus the impedance is represented as a complex number (or equivalent amplitude and phase) with the realpart being the resistance and the imaginary part being the reactance.

Z = R+ iXc (6.3)

|Z| =√R2 + (iXc)2 (6.4)

φ(Z) = arctanXcR

(6.5)

Since the measured current can be quite small (nA) as a consequence of the low applied voltage (to measurethe equilibrium resistivity) and the high resistivity of the oils. Noise is of course an issue. This issue isgreatly reduced by the integrating and averaging part of the sine correlation technique.

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6.1.3 Calculations of parameters

Capacitance

IDA considers the insulating material to have its capacitance modelled in parallel to the resistance. Thecapacitance is calculated from the impedance as follows

C = Re(1

jωZ)(6.6)

The geometric capacitance, as mentioned above in section 6.1, is calculated using this equation when nomaterial (or air) is between the electrodes. Capacitance is measured in Farad.

Tangent delta

IDA calculates the loss factor using the following equation:

tanδ = −Re(Z)Im(Z)

(6.7)

The parameter is unitless. Higher value means worse insulator.

Resistivity

IDA measures the resistivity in ohm meter [Ωm], the value is calculated from the geometric capacitancetogether with the measured impedance. IDA calculates the resistivity using the following equation:

ρ =C0�0

1

Re( 1Z )(6.8)

with �0 being the permittivity in vacuum at 8.854E-12[F/m]. The equation is derived from the more com-monly seen formulas for resistance and capacitance

R = ρd

A(6.9)

C = �0�rA

d(6.10)

RC = �0�rρ→ ρ = RC

�0�r(6.11)

Since the geometry of the cell is taken into account when there is no material, or air, in between the elec-trodes. The relative permittivity equates to one and can be neglected as it is shown in equation 6.8

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The resistance is given by the real part of the impedance. The reason as to why IDA uses 1Re( 1Z )

insteadof Re(Z) could be to clarify that the impedance model considers the capacitance to be in parallel with theresistance. Thus the resistance is given by Re( 1Z ) and the total resistance is given by

1Re( 1Z )

since in parallelcircuits the total impedance is generally given by

Ztot = (1

Z1+

1

Z2+ . . .

1

ZN)−1 (6.12)

Because the equation is derived from other equations it is good to confirm the validity of the equation bychecking the SI-units.

[Ωm] =[F ]

[ Fm ]

[1]

[ 1Ω ]→ [Ωm] = [mΩ]→ ok (6.13)

6.1.4 Relative permittivityThe relative permittivity is calculated using the impedance and the geometric capacitance.

�r = Re(1

jωC0Z) (6.14)

Worth noting is that IDA considers the relative permittivity to be a complex entity. As mentioned previously,this is not uncommon when talking about dielectrics. In this thesis only the real part of the relativepermittivity is interesting as the imaginary part relates to losses due to high frequency. Something notrelevant to this study as the transformer oil is to be used in HVDC applications. Instead the dielectric lossesare investigated using the tangent delta parameter.

6.2 Triangular Method

The triangular method was developed by Uno et. al [22]. It is a resistivity measurement method that utilizesboth low voltage and low frequency. By applying a triangular wave to the test cell the theoretical currentresponse can be calculated and the credibility of an actual measurement can be investigated by use of aparameter that is easily extracted from the current response of the measurement. The general expressionfor current density j(t) as a result of a time dependant field E(t) is

j(t) = σE(t) +d

dt(�0�rE(t)) (6.15)

If the geometry of the measurement cell is set to two parallel conducting plates with the area A and theseparation distance d and the electric field between said plates are considered homogeneous.The theoretical current can be expressed as

I(t) =σA

dU(t) +

�0�rA

d

dU

dt(6.16)

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This current consists of two parts; the capacitive and resistive current. The ratio of these currents is used asa way to estimate the credibility of a measurement. With them being equal giving the optimum sensitivity[22]. Setting U(t) to a triangular wave and looking at set times of a period. The derivative term dUdt aswell as the magnitude term U(t) can be calculated and the result allows for plotting the theoretical currentresponse. Here ∆ is an arbitrary small number >0 and τ is the period of the triangular wave. U0 is themagnitude of the voltage.

t U dUdt I

0 0 4U0τ�r�0d

4AU0τ

τ4 −∆ U0

4U0τ

σAU0d +

�r�0d

4AU0τ

τ4 + ∆ U0

−4U0τ

σAU0d −

�r�0d

4AU0τ

τ2 0

−4U0τ −

�r�0d

4AU0τ

3τ4 −∆ −U0

−4U0τ −

σAU0d −

�r�0d

4AU0τ

Table 6.2: Theoretical equations for the triangular method

Plotting the current response using the expressions above shows how easily the capacitive and resistive cur-rents are identified.

Figure 6.3: Theoretical current response for the triangular method

This current response is only theoretical. Practical examples about sensibility and choice of period (fre-quency) is studied later in the report.

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6.2.1 Implementation in LabviewThe triangular method is implemented using the Labview software [23]. On the graphical user interface (GUI)the parameters: amplitude, frequency, distance between electrodes and area of electrodes are changeable.Therefore the area of and distance between the electrodes needs to be manually measured before startingmeasurements using a new cell. The current can be in the pA range and is measured using a electrometer.The triangular wave is generated using a function generator. In Labview the resistivity is calculated usingthe general resistivity formula for two parallel electrodes

ρ = RA

d=U

I

A

d(6.17)

The Ad fraction and the amplitude of the voltage is used as an input on the GUI. The script then measuresthe current twice for each period. The resistivity at that instance of time is calculated using equation 6.17.The final resistivity is then estimated as the mean value of each resistivity measurement.

ρestimated = mean(ρi) (6.18)

The first resisivity measurement is always taken at approximately 54τ to ensure that the peak value of thevoltage is achieved when reading the current. Since the measurement is then taken at an interval of 12τ . Themeasured current will always correspond to when the voltage is at the peak value. This is seen in figure 6.3.Why the script ignores the first period could be to avoid any eventual disturbances in the measurements dueto human error such as touching the cables or the sample. The author’s experience is that these kind of errorsusually arises at the early stages of an experiment when everything is getting set up. Since the experimentstakes a relatively long time depending on how many resistivity measurements wanted for the final mean-value estimate. The experimental station is usually left untouched until the number of measurements aresatisfactory. The triangular method, especially the theoretical current response, is then used to determine ifthe measured resistivity is accurate. More about this in the discussion part of the thesis.

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6.3 VAISALA-MM70 handheld moisture and temperature meter

To ensure consistent conditions during the experiments, the temperature and moisture content of the oilsneeds to be accurately measured. MM70 is an easy tool which displays the humidity in both terms of ppmand water activity (relative humidity)[24]. It also has a logging function which is useful when performingexperiments over long sessions of time. To find the saturation value of a specific oil, the tool is sent toVAISALATM along with a sample of oil for calibration. Changing between oils is easy as the user only hasto change 2 parameters “A” and “B” to fit the parameters received by the calibration test.

6.4 Cleaning and assembly process

Before each experiment the cell and container has to be cleaned using a certain procedure.

1. Firstly, the cell is disassembled and all parts are cleaned with detergent and rinsed with hot water toget rid of any visual residue (oil) from previous experiments.

2. The wet parts are dried of using either paper towels or an oven. They are then coated with ethanoland rinsed of with distilled water.

3. Lastly they are put into an oven to completely dry off.

4. When all parts are dry and clean, the cell is assembled while wearing vinyl gloves.

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6.5 Degassing process

Some of the experiments in this study require degassed oil. For this purpose, a vacuum pump is used.The oil is placed in a vacuum proof glass container and attached to a vacuum pump. During vacuumdegassing both the water and gasses that may have been dissolved into the oil gets removed.The glass container is placed on a machine that has two functions: heating and mixing.To speed-up the degassing procedure the oil is heated (∼ 70◦ C) and a mixing device is placed into the glasscontainer. When the machine is turned on, the mixing device will start spinning. The combined mixingfrom the convection caused by the heat together with the spinning device shortens the degassing time.To see when a batch is ready, i.e. sufficiently degassed. A sensor showing the pressure within the bottle isconnected. Lower pressure means better vacuum. A pressure in the magnitude of 10−2 millibar is consideredsufficient.

Figure 6.4: Degassing station, the pressure in the container is 5.6E-1 millibar. The container stands on adevice capable of both heating and making a magnet placed inside the container rotate

6.6 Climate chamber

Since the measurements use very low frequencies (down-to 1 mHz for IDA) they take a long time. The optimalmeasurement conditions is one where the oil’s various parameters (temperature, water content) are constantduring the entirety of the measurement. To get close to this ideal, a climate chamber with the possibility ofaltering humidity and temperature is used. The cell is connected to the measuring equipment by two BNCcables through a sealable gap in the chamber to isolate the test sample from the outside environment.

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7. Measurement cell

During this thesis, an already existing measuring cell at ABB was redesigned, manufactured and acquired.This section covers that process.

Figure 7.1: Solidworks design of the new cell. This design is used when communicating with the manufac-turing company. The cell is manufactured in gold and copper.

Top left: current and ground electrode, connection side.Bottom left: current and ground electrode, measuring side.Top right: voltage electrode, connection side.Bottom right: voltage electrode, measuring side.

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7.1 Prototype

This prototype already existed at ABB. The cell contains two parallel conducting electrodes, the electrodesare screwed together and separated by washers to achieve a 2 mm gap. The two conducting electrodesconsists of a insulating material in the center and a copper surface on each respective side. Three cables areconnected: voltage, current and ground. Because the measured currents are very low (down-to pico ampere),the importance of consistent grounding cannot be ignored (to measure both the voltage and current, thesame reference must be used). Thus the electrodes cannot be completely covered in copper. Therefore,a ground surface is created by etching a gap on one of the electrodes. This separates the ground surfacefrom the surface used to measure the current. To keep things consistent, the etched gap is equal to the gapbetween the electrodes. To get as close to a homogeneous electric field between the electrodes as possible,the surface of the electrodes that face each other should be smooth. The cables are therefore soldered on theopposite sides of the electrodes. The design of two parallel electrodes makes it easy to estimate the geometriccapacitance of the cell.

C0 = �0�AirA

d(7.1)

where A is the area of the electrode and d is the distance between the electrodes.One electrode, which is completely covered in copper, is connected to the voltage source. The other elec-trode, the one with the etched gap, has it’s surfaces connected to the current measurement and to groundrespectively.

7.2 Prototype flaws

There are mainly two flaws with the prototype: durability and time consuming maintenance. To achieve thesmooth surface, one of the cables is soldered by drilling a small hole through the plate, attaching a cablethrough the hole, soldering and smoothing the area of the opposite, conducting, surface. This process takesa long time and can be very difficult if not used to soldering. Further, since the cell has to be cleaned fairlyrigorously in between experiments. The thin cables can quite easily get ripped out during this process.

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7.3 New measuring cell

The new measuring cell is based on the design of the prototype but by use of PCB-design many of thedurability issues are handled. The cell is designed in the Solidworks software [25] and outsourced to aPCB manufacturing company for construction. Contrary to the prototype, no manual soldering of wiresis necessary as the connection points for each cable (voltage, current, GND) are hardwired to the PCB.Connection pins are surface mounted on the PCB making the physical connection between the cell and thediagnostic instrument easier. Similarly to the prototype, each conducting plate consists of an insulatingmaterial in between two conducting surfaces for stability, since the conducting surface is very thin.To connect the back to the front surface, something called “via” is used. There are many different kinds ofvia on the market. A “through via” is used in this design, basically a hole is drilled through the PCB andthe hole is coated with conducting material making the hole itself the connection between the surfaces.The original prototype had soldered a bent sheet of copper over one side of the cell to connect the surfaces.The main advantage of the via is to eliminate the need for the complicated soldering of the wire connectedto the current measurement, shown in figure 7.2 and 7.3.Via allows for a smoother surface compared to the prototype since no soldering material is used on theconducting surface. Further, because of the PCB design, attaching connection pins at the top part of thecell (which is possible to have above the oil, seen in figure 7.4) gets rid of the need to clean the wires inbetween oil changes. Only the cell itself has to be cleaned.In terms of material, the surfaces of the cell is changed from being coated in copper to gold. Mainly sincegold doesn’t oxidize easily. This change in surface material should increase the lifespan of the cell.Both copper and gold coated newly designed cells are acquired to investigate if the material affects themeasurements.

Figure 7.2: Front side of electrode used to measure current & connect to ground. Prototype (left) Newdesign (right). The smoothened area is not perfect and quite hard to achieve (time demanding) if not usedto soldering.

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Figure 7.3: Back side of electrode used to measure current & connect to ground. The connection from thecell to the measuring machine is more durable using the pins (right) than the soldered wires (left). Noticethe cable connected to the current being connected to the front side by use of a drilled hole. If too muchsolder is used, the solder will pour out the hole and short circuit the ground & current surfaces (left). Thisissue is not uncommon and tedious to fix.

The electrode used to apply voltage is similarly designed to the current & ground electrode. Vias are usedto connect both front and back surfaces.A surface mounted pin is used as the connection point. The design is simpler as no etched pattern is requiredsince the entirety of the electrode is used at the same potential.The finished cell is built using washers to get a consistent distance between the electrodes.

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Figure 7.4: The complete cell containing both electrodes. The cell is then submerged in the desired oil whichwill fill up the gap between the electrodes and resistivity of the liquid can be measured. The cell is heldtogether using screws and is separated by washers to get a consistent distance between the electrodes.

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8. Experiments & results

In this section the various experiments performed are explained and the corresponding results are represented.This section is divided into two main parts. Experiments done using IDA 200 and experiments done usingthe triangular method. Generally the experiments performed using the triangular method are more focusedon the method itself. The setup for the triangular method is simpler compared to IDA, as an electrometerand a function generator are the only hardware required. IDA is a complex, industrially used, diagnostictool. The goal is to investigate if the triangular method could replace IDA when it comes to resistivitymeasurements. As of the moment of this report, the power grids (PG) division of ABB Corporate ResearchVästerås has one IDA diagnostic tool. This can cause quite a bottleneck as the measurements themselvestake multiple hours depending on the frequency and number of data points. All experiments performed usingthe triangular method use the old measuring cells.The experiments related to the investigation of various transformer oils and their dielectric properties aremainly done using IDA. To remove the uncertainties that can arise using the triangular method. Only theexperiments which are explicitly stated to use the new measuring cells do so. If nothing is stated, the oldmeasuring cells are used.

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8.1 Experiments: Triangular method

8.1.1 A general measurementThe purpose of this experiment is to give an idea about how a measurement with suitable settings shouldlook.

Figure 8.1: An optimal choice of frequency for the triangular method should yield equal capacitive andresistive currents.

The capacitive and resistive currents are easily identified. Theoretically the most accurate measurementwould occur when these currents are equal. The current response presented in this figure is a good indicationthat the selected frequency is suitable. Before taking a final measurement, the capacitive and resistivecurrents should be extracted from the graph and compared. The frequency should then be altered accordingly,increasing frequency causes the capacitive current to increase. Decreasing the frequency causes the resistivecurrent to increase.

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8.1.2 Importance of shielding, choice of frequency & voltageIn this experiment the mineral oil is used. Because of the low currents, shielding to minimize the influenceof noise as well as proper grounding of measurements are important. In this experiment measurements aretaken at varying frequencies and voltages with and without shielding. This experiment is the first experimentperformed using the triangular method. As such, to get a grasp of suitable values of frequencies and voltages.These parameters are altered. Worth noting is that the ideal voltage is the lowest possible voltage as tosatisfy the criteria of thermodynamic equilibrium. The ideal frequency is the lowest frequency as it bestresembles DC. Further, suitable settings will vary depending on the transformer oil. Firstly the frequency isaltered using a fixed triangular wave with a peak-to-peak voltage of 4V.

Figure 8.2: Unshielded measurements with fixed voltage and varying frequency.

The noise is most apparent at lower frequencies. From the experiment with suitable settings, figure 8.1,and the theoretical current response, figure 6.3, the current response is known. Among these measurements,0.005 Hz best resembles said response.

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After shielding the sample by placing it in an aluminium bucket the following is measured.

Figure 8.3: Shielded measurements with fixed voltage and varying frequency.

The shielding reduces the noise to acceptable levels. The theoretical assumption that lowering frequencyincreases the resistive current and reduces the capacitive current is apparent from the 0.001 Hz and 0.005 Hzmeasurements. With the lower frequency yielding higher resistive current. Worth noting is the sensitivity offrequency choice, just a few millihertz difference causes a big change in the current response.

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With a chosen frequency of 5 mHz, the voltage is investigated. The aim is to find a voltage that is as low aspossible without being too noisy. Before shielding the following is measured.

Figure 8.4: Unshielded measurements with fixed frequency and varying voltage.

The influence of noise is significant in all the measurements. The massive spikes seen at the start of the2 V measurement and the end of the 6 V measurement are due to people walking around in the room theexperiment takes place.

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As stated earlier, lower voltage is better. The aim is to find a voltage as low as possible without havingnoise affecting the results. After shielding the sample by placing it in a aluminium bucket the following ismeasured.

Figure 8.5: Shielded measurements with fixed frequency and varying voltage.

There is still some noise apparent at the 2 V measurement to the extent of choosing 4V seems safer. Atvoltages above 4 V the noise is negligible.

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8.1.3 Accuracy and precision of measurementsIn this experiment the mineral oil is used. According to the theory [22], the ratio of capacitive and resistivecurrent can be used to estimate how accurate a measurement is (this will be investigated experimentally inthe upcoming section). However, the precision is still unknown. Therefore a set of three measurements using4 V and 0.005 Hz are done and their measured resistivity compared. The results are presented in the formof mean value and standard deviation. With the standard deviation being expressed both numerically andin percentage of the mean value. This to more fairly compare the triangular method to IDA.

Figure 8.6: Illustration of accuracy and precision

Measurement Resistivity [Ωm]1 4.8E122 4.9E123 4.8E12

Mean 4.8E12Standard deviation 5.8E10Standard deviation

in percentage of mean value 1.2%

Table 8.1: Accuracy of measurements using the triangular method

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8.1.4 Triangular method at IDA frequencies - mineral oilIn this experiment the mineral oil is used. As the main purpose of the experiments revolving the triangularmethod is to find if it is a suitable replacement and or addition to IDA. An experiment where the triangularmethod is performed at the same frequencies as IDA to clearly illustrate the difference in terms of measuredresistivity is done. The resistivity is first measured using IDA and then separate measurements for eachcorresponding frequency are done using the triangular method. Because of no climate chamber at the work-station for the triangular method. The IDA measurement are performed twice at temperatures above andbelow the room temperature where the triangular method measurements take place. Ideally, the measuredresistivity using the triangular method should land in between the measurements taken from IDA.

Figure 8.7: Resistivity measurements using IDA and the triangular method at equal frequencies

Again, the importance in choice of frequency for the triangular method shows. The frequencies close to 5mHz yields results most similar to IDA. However, the measured resistivity from the triangular method neverlands in between the different IDA measurements.

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From figure 8.7 the closest measured resistivity is at 4.50 mHz which is compared to IDA’s measured resis-tivity at 4.64 mHz.

Measuring sequence Resistivity [Ωm]IDA 20◦C 4.2E12IDA 27◦C 3.6E12

Triangular method ∼ 24◦C 4.5E12

Table 8.2: Measured resistivity for mineral oil using IDA and triangular method at ∼ 4.5 mHz

The capacitive and resistive current for the frequencies close to 4.5 mHz are extracted. With an incrementof 0.5 mHz from 4.0 mHz to 5.5 mHz it shows that the optimum frequency is found in interval 4.5 ± 0.49mHz.

Figure 8.8: Extracted capacitive and resistive current ratio at certain frequencies from previous measurementsequence

Theoretically the optimum accuracy is found when the capacitive and resistive currents are equal. A ratioof 1.2 is the closest found when using increment of 0.5 mHz. Tuning the frequency with shorter jumps infrequency is of course possible, but very time demanding. It could be that a better frequency choice is in thesuggested interval of 4.5±0.49 mHz. Finding this frequency should yield a resistivity closer to the resistivitymeasured using IDA. Usually resistivity is talked about in order of magnitude when it comes to transformeroil. As such the difference between the two measuring techniques could perhaps be accepted.

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8.1.5 Triangular method at IDA frequencies - ester oilIn this experiment the ester oil is used. The same approach is done as for the experiment using the mineraloil. Compared to the mineral oil, the ester oil has a much lower resistivity (two order of magnitude less).This causes an issue when applying the triangular method of never having the resistive current being smallenough compared to the capacitive current regardless of frequency.

Figure 8.9: Resistivity measurements using IDA and the triangular method at equal frequencies

It is apparent that higher frequency (larger capacitive current) yields results closer to IDA, but two issuesarises. Firstly, looking back to the ion drift model, the aim is to measure the resistivity at as lose to DC aspossible. Increasing the frequency is the direct opposite of this. Secondly, with frequencies higher than 0.5Hz it is too fast for the triangular method to show any relevant data. With most of the measured resistivityshowing “Infinite”. The problem of using the triangular method for the ester oil originates from the oil’s lowresistivity.

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8.1.6 Different types of groundingIn this experiment the mineral oil is used. As it has higher resistivity thus more sensitive towards noise.Correct grounding and shielding is essential due to the low currents that arise during the measurements.Originally, the grounding was done by connecting all ground cables together and then to a set referencepoint. The cables were drawn through the aluminium bucket through a hole and connected to the referencepoint. This process is quite time extensive as a lot of cable management is required between measurements.The new grounding is done by using the shell of he aluminium bucket as the ground reference. Further,BNC connectors are connected to the bucket and wires are soldered to each corresponding ground, current& voltage connection point of the BNC connectors.

Figure 8.10: The crocodile clips are connected to Ground (black), Current (red) and Voltage (Blue). Theground cable is soldered such that the entire hull of the bucket has ground potential. The two BNC cables(copper color, right side) are connected to the measuring equipment.

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By doing this, less cable management is required and it is a lot faster to get the setup ready in betweenexperiments. To confirm that the new setup is functional, it is tested using the triangular method. Contraryto IDA, where only the measured parameters are displayed, the triangular method displays the currentresponse which makes it easier to identify eventual noise.

Figure 8.11: Current response using different grounding techniques

The difference between the grounding methods are negligible. Using the new setup will save time in betweenexperiments.

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8.2 Experiments: IDA diagnostic tool

8.2.1 A general measurementIn this experiment a general measurement is taken using IDA. As mentioned earlier IDA takes measurementsat various frequencies with the lowest frequency being the equilibrium resistivity as it best resembles DC.The lowest frequency for all experiments performed in IDA is 1 mHz. With this choice, a measuring seriestakes approximately one hour. Most experiments performed in this study take two or three measuring seriesto ensure the validity of the result.

Figure 8.12: A general measurement using IDA diagnostic tool

The resistivity is lower for higher frequencies because as the frequency increases the imaginary part of theimpedance, the reactance, increases and as a consequence the real part, the resistance, decreases. Theresistivity is calculated from the real part of the impedance as shown in equation 6.8.

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8.2.2 Accuracy and precision of measurementsIn this experiment mineral oil is used. Because IDA is an established product that’s used all over the worldof dielectrics. The measurements are considered accurate. The accuracy experiment using the triangularmethod supports this assumption as increasingly theoretically better measurements in terms of accuracyyielded results closer to the results provided by IDA, figure 8.7 and 8.8. The precision of IDA is testedby measuring the resistivity of mineral oil three times. This measurement takes approximately 3 hours.To prevent fluctuations in temperature and humidity, the sample is placed in the climate chamber. Theresults are presented in the form of mean value and standard deviation. With the standard deviation beingexpressed both numerically and in percentage of the mean value. This to more fairly compare IDA to thetriangular method.

Measurement Resistivity [Ωm]1 3.8E122 3.8E123 3.8E12

Mean 3.8E12Standard deviation 0Standard deviation

in percentage of mean value 0%

Table 8.3: Accuracy of measurements using IDA

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8.2.3 Humidity & resistivity in ester oilIn this experiment ester oil is used. As mentioned in the dielectric properties section, water content causesthe pressboard in the transformers to deteriorate. However, studies regarding the effect humidity (moisture)has on the transformer oil resistivity are not easily found. In this experiment the oil is firstly degassed. Thenit is placed in the climate chamber as to keep the temperature constant. The humidity of the climate chamberis gradually increased to increase the water content of the transformer oil. Each resistivity measurement isgathered by having IDA do two measurement series. After a set of series are finished, the water content ofthe oil is measured in ppm and relative humidity by use of the MM70 handheld moisture meter.

Figure 8.13: Humidity measurements using ester oil

To calculate the concentration of ions the mobility of the oil is needed. Another master thesis that focuseson the mobility of the same transformer oils as this thesis is done in parallel to this study. The mobilityvalues for the various oils are received from that study. From the experiment we see that for ester oil theresistivity decreases with increasing water content. Because of the inverse relationship between concentrationof ions and resistivity as shown in equation 3.22. Increasing the water content of the oil also increases theion concentration.

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8.2.4 Humidity & resistivity in mineral oilIn this experiment mineral oil is used. The experiment is performed the same way as the experiment usingester oil. The mineral oil is degassed using vacuum and the climate chamber is used to adjust the watercontent of the oil. Each measurement is taken from two measurement series. The provided mobility valuefor the mineral oil is higher compared to the ester oil.

Figure 8.14: Humidity measurements using mineral oil

Contrary to ester oil, the resistivity and humidity are not linearly dependent in mineral oil. With theresistivity increasing for low moisture contents (5-10 ppm), stagnating (10-25 ppm) and finally decreasing(25-30+ ppm).

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8.2.5 Dielectric properties of mineral and ester oil mixturesIn this experiment mineral and ester oil are mixed. The ester and mineral oil are mixed in different quantities,the mixing is done by placing the sample overnight on a mechanical stirring machine. After a measurementis done, the cell is disassembled, cleaned and rebuilt. No heat is added to the oil during the mixing process.Due to the climate chamber being occupied, the measurements are taken at room temperature. For eachmeasurement the temperature is read. The maximum deviation of temperature in the oil throughout theexperiment is approximately 2◦C. This small variation in temperature is assumed to be negligible. Thedielectric parameters tangent delta, resistivity and relative permittivity are measured. From the measure-ments, the concentration of ions and relaxation time are calculated. The mobilities of pure ester and mineraloil are known and assumed to behave linearly in the mixture. The relative permittivity and tangent deltaare measured at close to the grid frequency (50Hz). The resistivity and relaxation time are presented on alogarithmic scale.The resistivity is displayed two ways. Firstly, by using the measured values from IDA. Secondly, by assumingan additive behaviour of the resistivity. The calculated resistivity using the linear assumption is calculatedby use of the resistivity at 100% ester and mineral oil respectively.

ρestimated =Mixture%

100ρester +

100−Mixture%100

ρmineral (8.1)

The purpose of this calculation is to illustrate how much the linear increment of mineral oil in ester oil andvice versa deviates from a linear behaviour in resistivity.

Figure 8.15: Measured and estimated resistivity for mineral and ester oil mixtures

The resistivity cannot be assumed to be linearly dependent on the mixture. With small percentages of esteroil relative to mineral oil in the mixture drastically reducing the resistivity. The resistivity increases withhigher percentage of mineral oil in the mixture.

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The calculated concentration of ions and relaxation time uses the measured resistivity.

Figure 8.16: Dielectric parameters for ester and mineral oil mixtures. µmineral = 5E − 10[m2/V s]µester = 2E − 10[m2/V s]

From the results it is observed that with increasing resistivity the loss factor (tangent delta), calculatedconcentration of ions and relative permittivity are decreasing. The relaxation time increases with resistivity.

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8.2.6 Dielectric properties of Isoparaffin mixturesIn this experiment the two isoparaffin oils (A & B) are mixed. Due to not having enough oil of bothisoparaffin A & B, a 0-100% mixture experiment where each batch is mixed individually with new oil couldnot be performed. A measurement at 100% isoparaffin B is done and then isoparaffin A is gradually addedto the mixture. This process continues until around a 50/50 mixture. The equipment is cleaned and ameasurement at 100% isoparaffin A is done with gradually added isoparaffin B.Similarly to the mixture experiment containing ester and mineral oil the mixing is done mechanically.In this experiment the new gold coated measuring cell is used. As for the mineral and ester mixtures, themobility of pure isoparaffin oil A & B are known individually from the other master thesis working in parallelto this one, and assumed to behave linearly when mixed. As for the mixture experiment using ester andmineral oil, the resistivity is displayed two ways. Using additive behaviour and the measured values. Thecalculated resistivity using the linear assumption is calculated by use of the resistivity at 100% isoparaffinoil A and B respectively.

ρestimated =Mixture%

100ρisoparaffinA +

100−Mixture%100

ρisoparaffinB (8.2)

Figure 8.17: Measured and estimated resistivity for isoparaffin oil A and B mixtures

As for the mineral and ester mixture, the resistivity cannot be assumed to be linearly dependent on themixture of isoparaffin A and B.

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The dielectric properties of the isoparaffin oil mixture are shown in figure 8.18.

Figure 8.18: Dielectric parameters for isoparaffin A and isoparaffin B mixtures.µisoparaffinA = 4.8E − 10[m2/V s], µisoparaffinB = 12.5E − 10[m2/V s]

From the results it is observed that with increasing resistivity the loss factor (tan δ) and calculated concen-tration of ions are decreasing. The relaxation time increases with resistivity. All parameters, apart from therelative permittivity, which remains fairly constant, have the same increasing/decreasing behaviour as theresistivity for the ester and mineral oil mixtures.

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8.2.7 Material dependency of measuring cells (Copper & Gold)In this experiment the new measuring cells (Cu & Au) are used. This experiment is meant to study if thematerial choice of the measuring cells can affect the results. Two measuring cells with a distance equal toprevious experiments, 2 mm, using the old measuring cell are simultaneously placed in a container filledwith transformer oil. One measuring cell is made of gold, the other of copper. The geometric capacitanceof both cells are measured and IDA’s settings are adjusted correspondingly for each measuring cell. Thenthe resistivity is measured. Firstly, degassed mineral oil is used. The oil is warmer than room temperatureafter degassing, because of the heating plate, figure 6.4. As such the test is done three times, alternatingbetween gold and copper, while the oil cools down in the climate chamber. This gives three set of resistivitymeasurements that can be compared.

Figure 8.19: Measured resistivity using Cu and Au cells. Distance between plates = 2.0 mm

The results are a significant difference in measured resistivity. This result is unexpected and a cause formore experiments being performed. Before this result the hypothesis was that there would be no differencebetween the materials as IDA calculates the resistivity only using the geometric capacitance and the realpart of the impedance.

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The geometric capacitance of the cell should depend on the distance between electrodes and their area, givenby equation 7.1. As the geometric design measurements are equal for both the gold and copper electrodesthis parameter is thought to be constant. Measurements of the geometric capacitance confirms this as thedifferent cells differ at the top end (when the distance between electrodes is smallest) around ∼ 5pF. Thisdifference is within acceptable limits as the distance between the electrodes vary a bit depending on thequality of the washers and how tightly the electrodes are screwed together.The geometric capacitance value is therefor set as a constant for each corresponding distance. These valuesare shown in table 8.4.

Distance between electrodes [mm] Geometric capacitance [pF]1.3 802.0 503.3 30

Table 8.4: Geometric capacitance increases with shorter distance between electrodes

The impedance parameter depends on the measured voltage and current by the electrodes. Gold and copperare both good conductors, the small difference in conduction relative to the insulating properties of thetransformer oil shouldn’t affect the measured results as significantly as the results show.

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The cell is cleaned and rebuilt using a longer distance (∼ 3.3 mm). Another set of three, alternating,measurements are done using the same batch of oil as the previous measurement of 2 mm distance.

Figure 8.20: Measured resistivity using Cu and Au cells. Distance between plates = 3.3 mm

Less difference in resistivity is shown at the new distance. This information is interesting and needs to beconfirmed. Therefore two tests, one using isoparaffin oil A another using mineral oil, are done with alteringdistance between the electrodes of 1.3 mm and 3.3 mm. The upcoming experiments are performed morecarefully compared to the previous two.A set of electrodes, either 1.3 mm or 3.3 mm, are placed in the same container. The container is placed inthe climate chamber and left for at least 30 minutes. This to consider the temperature as a constant. Theresistivity is measured for a pair (copper and gold with equal distance between electrodes) and then the pairis replaced with the other pair. In between the experiment using isoparaffin A and the mineral oil. Thesetup (cell + container) are cleaned according to the cleaning procedures.

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The new measured resistivity using the isoparaffin oil A with different distances and electrode material areas follows.

Figure 8.21: Measured resistivity using Cu and Au cells. Distance between plates = 1.3 mm (left) and 3.3mm (right)

Isoparaffin A shows the same behaviour as longer distance yields less difference in result. The measuredresistivity is higher for gold than copper for both distances. This corresponds to the results from theprevious measurement at 3.3 mm, figure 8.20, and 2 mm, figure 8.19.

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The new measured resistivity using the mineral oil with different distances and electrode material are asfollows.

Figure 8.22: Measured resistivity using Cu and Au cells. Distance between plates = 1.3 mm (left) and 3.3mm (right)

The measured Au values for the 1.3 mm distance is taken from the mean value of 6 measurements. Generally,there is a noticeable difference when it comes to both distance and choice of material of the electrodes. Withgold showing higher resistivity than copper and larger distance between electrodes yielding greater differencein measured resistivity.

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The percentage difference between Au and Cu for the different measurements throughout this section aredisplayed below. Since the initial measurement of 2 mm, using mineral oil, consists of measurements ofvarying temperature, the result corresponding to the lowest temperature, closest to room temperature thusclosest in temperature to the other measurements, is considered. Regarding the first measurement of 3.3mm, using mineral oil, a mean of the three measured results is considered. As the percentage difference isa relative term between two measurements. Although resistivity cannot be fairly compared for each set ofexperiments as the environment changes. For a relative comparison of results, this should not be an issue.Percentage difference between two numbers is given by

Difference[%] = 100× |x1 − x2|x1+x22

(8.3)

Figure 8.23: Percentage difference in measured resistivity using Cu and Au cells with varying distance andtransformer oil. Green = Isoparaffin oil A, Blue = Mineral oil.

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9. Discussion

In this chapter the results from previous experiments and theory are discussed. It starts with observationsabout the ion drift model, then the triangular method is compared to IDA. A correction algorithm is suggestedto the triangular method and pros/cons for the two measurement techniques are discussed. Afterwards themoisture and dielectric properties of the various transformer oils used in this study are gone into withobservations regarding the moisture of certain oils that the author finds to be especially interesting. Theelectrode material of Cu and Au yielding different resistivity measurements is, as the writing of this report,still an unexpected result. Some ideas on to what may cause this phenomenon are argued for/against.Lastly, general ideas about the technological advancements in the field of transformer oils are brought upwith arguments based of results obtained in this thesis together with information about the environmentalconsequences related to the different transformer oils.

9.1 The Ion Drift Model

One of the advantages of the ion drift model is that it only requires four parameters, which are measuredat low voltages; mobility of positive and negative ions, resistivity and relative permittivity, to simulate thedielectric behaviour of the transformer oil at very high voltages.In this study it is found that the relative permittivity remains fairly constant for each of the four oils. Withester oil showing the highest relative permittivity of ∼ 3 and the remaining three oils spanning from 2.0-2.2,shown in figure 8.16 and 8.18. This constant behaviour of the relative permittivity could allow for a reductionof parameters required in the model from 4 to 3. Giving the relative permittivity a constant value. Thisconstant behaviour of the relative permittivity is especially noticeable for transformer oil which originatesfrom crude oil (isoparaffin & mineral oil). As mentioned earlier, the triangular method can only measureresistivity. By knowing the constant behaviour of the relative permittivity, it would remove the necessityto use the more complex IDA diagnostic tool. As both the mobility and resistivity can be measured usingexisting Labview software at ABB Power Grids Västerås.

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As mentioned in the ion drift model description, the ions are generated from dissociation of ionic pairs. Thisprocess relates to the applied electric field as given by the “b” term related to the field dependent equation3.7. Plugging in the constants and a temperature of 300 Kelvin. It’s clear that the required applied voltageto affect the dissociation of ionic pairs is large.

b ≈√

24.5× 10−6|E| (9.1)

Considering this, the chosen voltage for the experiments, up to 4 V peak to peak for the triangular method,should not affect the ions in the transformer oil in any substantial way.By a quantitative comparison between the relaxation time to the transit time by help of the κ-term.

κ =τtransitτrelax

=d2

�0�rρµtV(9.2)

The chosen, adjustable, parameters such as voltage and distance between the electrodes can be evaluated.Using a voltage of 2 V and a distance of 2 mm (the originally recommended settings, used in most exper-iments), taking the measured resistivity, relative permittivity and mobility