Measurements of resistivity in transformer insulation liquids

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UPTEC E 20009

Examensarbete 30 hp Juni 2020

Measurements of resistivity

in transformer insulation liquids

Jonathan Hägerbrand

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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 insulation liquids

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.

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Sammanfattning

Denna uppsats fokuserar på teknik och resultat för mätning av resistivitet i fyra kommersiellt tillgängliga isolerings oljor som används i transformatorer för HVDC applikationer: mineral olja, ester olja och två isoparaffin 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 noggrannheten av Triangel metoden är föreslagen. Dielektriska egenskaper för olika blandningar mellan mineral & ester och isoparaffin A & B är undersökt. Det är experimentellt bevisat att oljor med hög resistivitet har låg tangent delta. Vatten och fukts inverkan på resistivitet är undersökt i mineral och ester olja, det visar sig att resistivitet och fukthalt beter sig på ett intressant sätt. En tidigare mätcell är omgjord för att lösa diverse hållbarhets problem. Denna cell byggs i koppar och guld. Det visar sig att valet av material för cellen påverkar resistivitetsmätningarna. Två idéer: elektriskt dubbel lager och kontakt resistans är undersökta som en förklaring till detta. Dessa experiment är begränsade till mineral olja och isoparaffin A, det visar sig att kontakt resistans är en rimlig förklaring. Det elektriska dubbel lagret är för litet jämfört med det totala avståndet mellan mätelektroder medans kontakt resistansen är väldigt hög.

Slutligen är framtiden för oljor som isoleringsmaterial i HVDC applikationer diskuterad. Här lyfts både tekniska och miljöbaserade argument fram baserade på resultat från rapporten. Det visar sig att teknologin går framåt, då den nyaste oljan visar både bra isolerande egenskaper och hög bionedbrytbarhet. Resultaten från denna uppsats kan användas som en bas för framtida uppsatsen inom oljor som används som isolerande material för HVDC applikationer.

Arbetet har utförts på Power Grids (PG) avdelningen för ABB i Västerås. Arbetet har pågått mellan januari och juni 2020.

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1. Introduction

With the increasing demand of electricity, more efficient ways of transporting it is always discussed and researched. 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 with AC, can yield higher efficiency [2] and subsequently less conductor material is required. Because of these two aspects, high DC voltage is the voltage of choice when transporting high power over long distances. One downside of HVDC is the conversion stations required to achieve the high voltage. These stations include a transformer which will be electrically stressed with both DC and AC voltages. The insulating material in the DC/DC converter in said transformers are often pressboard submerged in liquids, mainly oils [3]. Because of the size of the transformers and the high operating voltage, much insulating material is required. By understanding the insulating material properties, the transformer and corresponding converter themselves can be dimensioned more efficiently. Resistivity is an important parameter for the insulating material as it is 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 dependence on 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 positive ions, mobility of negative ions and resistivity at thermodynamic equilibrium [4]. From this it is possible to estimate the behaviour of the transformer oil under high DC stress by using data taken from experiments performed under low DC stress. In this study resistivity of various transformer oils are investigated. Outside influences like temperature and moisture as well as various mixtures of oils are studied. The experiments are done in cooperation with the Power Grid section of ABB. ABB is one of the world’s leading companies when it comes to HVDC and UHVDC technology. In 2016 ABB took on a UHVDC project with unprecedented voltage levels, power capacity and distance. The project involved transporting power over a distance of 3,000 kilometers at a voltage of 1,100 kV. The transformers used will each weigh around 800 tons [6]. Considering the 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 long distances. Compared to AC, capacitance isn’t a limiting factor for the DC cables as pure DC doesn’t produce any reactive power. Because of this, the need for shunt capacitors together with the transmission lines is removed. Since the power is transported as DC, it can be used to connect systems which are unsynchronized without worry about matching frequencies. Further, less material for the conductor is required. As AC is usually 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 is a consequence of current passing through a resistive element. From Ohm’s law together with the definition of power, we see that by doubling the voltage, 4 times as much power can be achieved. Similarly, considering a constant power, doubling the voltage will half the current, resulting in less losses due to heat.

Ploss= U I = 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 capacitive properties of transmission lines operating at AC. Further, the power transported at AC is defined from the root mean-square (RMS) of the AC voltage. For a sine-wave the RMS value comes out to ^√¹

2 of the peak- voltage. Or approximately 71% of the peak voltage. Because of this fact, the power delivered by DC compared 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 transported in a conductor, the electrons tend to push towards the surface of the conductor thus making the current density throughout the conductor inhomogenous. With more current passing through the outer part of the conductor, 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]. The model is very practical as it only requires four, relatively easy to measure, parameters (resistivity, relative permittivity, mobility of positive ions & mobility of negative ions) at low voltage to estimate the behaviour of the oil at voltage levels used in HVDC technology. In the ion drift model the transformer oil is considered a weak electrolyte [4]. At thermodynamic equilibrium the negatively and positively charged ions are equal and significantly less than the neutral molecules c. The density of these ions can be described from their conductivity and resistivity [4]

p0= n0= σ

q(µ_p+ µ_n) (3.1)

Here µpand µn are the mobilities for positive and negative ions respectively. q is the elementary charge and σ 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 recombination of ions.

The rate of recombination and dissociation is described by the rate equation [4]

dp dt =dn

dt = k_Dc − k_Rpn (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 dissociation constant, contrary to the recombination constant, is given as a function of the applied electrical field.

kD= k_D⁰F (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 being considered in the term “b” as follows:

b = s

q³|E|

16π₀_rk_B²T² (3.7)

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respectively. The field independant term k_D⁰ 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 equation3.3the field independant term can be written as k_D⁰ = kRn²₀

c (3.8)

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

−

→wp,n= µp,n

−

→E (3.9)

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

D_p,n=k_BT

q µ_p,n (3.10)

Including the drift3.9and diffusion3.10terms to the rate equation3.3yields the following set of equations.

(_∂p

∂t + ∇(−→wp− Dp∇p) = kRn²₀F (E) − kRpn

∂n

∂t − ∇(−→wn− Dn∇n) = kRn²₀F (E) − kRpn (3.11) The relation between charge density and electric potential is given by Poisson’s equation [4]

∇(0r∇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 parameters that all are expected to be measured at thermodynamic equilibrium, as one of the assumptions to find the equations is that the ions are in steady-state equilibrium. Again, to achieve thermodynamic equilibrium, no current should pass. Something that is not possible for measurements to be taken. Getting as close to this as possible is why low voltages are preferred when performing experiments to determine the mobilities and the resistivity.

The final set of equations becomes:











∂p

∂t + ∇(µ_p−→

E_p− Dp∇p) = kRn²₀F (E) − k_Rpn

∂n

∂t − ∇(µn

−

→En− Dn∇n) = kRn²₀F (E) − kRpn

∇(0r∇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 voltage is applied and start drifting towards the electrode with an opposite charge (negatively charged ions drift towards 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

t_transit= d

µ_tV d

= d²

µtV (3.14)

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

µ_t= µ_p+ µ_n (3.15)

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

trelax= 0rρ (3.16)

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

κ = τtransit

τ_relax = d²

₀_rρµ_tV (3.17)

With κ 1 corresponding to longer transit time and κ 1 longer relaxation time. Since the ions in the transformer oil, described by the ion drift model, are considered at thermodynamic equilibrium. A large value of κ is desired. As this would indicate that dissociated ions will recombine faster than they would drift apart. Due to the permittivity, resistivity and mobility being material parameters. The only adjustable parameters are the distance between the electrodes, with smaller distance yielding shorter transit time and applied 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 the ion drift model equivalent to the positively and negatively charged ions. As concentration of ions is not something 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 density of 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 charge equal to the elementary charge. In an applied electric field, these ions will start drifting with the velocity

v = µ_nE (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 concentration 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 chapter7). There will be a varying concentration of ions closer from the surface [8]. The electrical double layer, EDL for short, relates to the two closest layers to 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 surface directly. They are attached due to the charged surface of the electrode, with a positively charged electrode attracting negatively charged ions and vice versa. The second layer, the diffuse layer, is composed of ions that are loosely bound to the surface layer. The ions in the diffuse layer are attracted to the surface layer by the Coulomb force. It will mainly contain ions of the opposite charge as the surface layer, with the importance 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 length

When 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 the high 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 a commonly used measure of the double layer thickness. It is used to determine the distance where the ion’s net electrostatic effect will persist. The Debye length of a monovalent electrolyte, an electrolyte where all ions contain the same charge, is given by equation3.23[29].

κ⁻¹=r 0rkBT

e²N_A2c (3.23)

where c is the concentration in moles per m³, e is the elementary charge and N_A is the Avogadro number 6.022 E23 [mol⁻¹]. Therefore, to calculate the Debye length. The concentration of ions is required, this parameter is consequently dependent of the resistivity and the mobility as shown by equation3.22. Worth noting is that the concentration of ions calculated in equation3.22is in numeric units [m⁻³].

The conversion between numeric and molar units is given by the Avogadro number cmolar =cnumeric

NA

(3.24)

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

κ⁻¹= 2 ×

r 0rkBT

2e²c_numeric (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 ester oil, 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 the technical 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 period of 28 days. As given by the OECD 301 standard [10]. Of the four oils investigated in this study, only two mention biodegradability on their technical data sheet [11]. Both of these oils have used the same, OECD 301, standard.

Oil Biodegradability Viscosity Flash point

Mineral No 7.7 150

Ester Readily biodegradable 29 260

Isoparaffin A No 4.5 145

Isoparaffin 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 filled transformers for longer than 100 years. The combination of low price, good dielectric properties and good cooling 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 new alternate types of transformer oil are actively researched. Two of which are the ester and isoparaffin oils investigated 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 to mineral oil. Ester oil wins out over mineral oil when it comes to operating at higher temperatures. With the flash point, the minimum temperature required to set of a fire, being higher compared to mineral oil. The ester oil used in this study has a flash point almost twice that of the mineral oil counterpart, shown in table 4.1. A downside of the ester oil is the viscosity being high. High viscosity “thicker liquid” yields reduced cooling, a liquid with high viscosity will have lower circulation speed which equates to less oil having its heat dissipated.

4.4 Isoparaffin oil

Isoparaffin is a chemical term used to describe a branched chain of hydrocarbons. Similarly to mineral oil it is produced from crude oil. Depending on the oil, the refining process varies. The refining process related to isoparaffin oil B is unknown. Isoparaffin A uses the patented HT purity process which, according to Petro-Canada [13][14], causes a biodegradability of 60% using the OECD 301 standard. A percentage which should 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 readily biodegradable. Contrary to the ester oil, the viscosity is extremely low. To the point where both isoparaffin oils 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 are explained.

5.1 Resistivity

In the simplest of terms, a perfect insulator should not allow current to pass when under the influence of an applied electrical field. Higher resistivity means better insulating capability in the material. If the material is 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. When measuring resistivity of a liquid material, the area of the liquid will be equal to the area of the electrodes if using a measuring cell with the design of two parallel plates. Since the electrodes are submerged in the liquid. This equation can be used. By changing the distance between these electrodes, the parameter d will change. The area of the liquid will be equal to that of the electrode. Considering a homogeneous electric field between the electrodes, the resistivity will be constant throughout the liquid. Because of this, especially when working with small voltages, it is important to design the electrodes in a way to achieve as close to a homogeneous electrical field as possible. In practice this means to make the surfaces as smooth as possible and to have a consistent distance throughout the entirety of the electrodes. More about the design of the measuring cell used in this thesis is found in chapter7.

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5.2 Temperature

Contrary to conductors, insulators have negative relationship between resistivity and temperature. An increase in temperature means a decrease in resistivity. This phenomenon has to do with the material band gap. The band gap is an energy gap between the valence band and the conduction band where no electrons can exist. For an electron to jump from the valence to the conduction band (this flow of electrons is the current) it needs energy. Material with a wider band gap needs more energy for an electron to make the jump. In conductors the band gap is very small, sometimes nonexistent as the valence and conduction band overlap [15], thus if extra energy is added to the electron (heat). It becomes easy for the electron to make the jump and as such increase the current. This is why resistivity increases with temperature for conductors. The amount of electrons wanting to pass from the valence band to the conduction band are too many. 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 is not negligible. Therefore the risk of having too many electrons passing simultaneously is small. As stated earlier, 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 in conduction is equivalent to a decrease in resistivity. Therefore, higher temperature will cause the resistivity to decrease in insulators. Some insulators turn to conductors at very high temperatures. But in regards to the 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 thesis focuses on the oil aspect of the insulating material. Understanding how a HVDC transformer is insulated is necessary when discussing water content. Keeping the water content down in transformers is recommended as water rapidly increases the aging process of pressboard [16]. In most technical data sheets the water content is expressed in ppm. However, this can be deceiving as different insulating oils have varying water content. A better way is to measure in terms of water activity or relative humidity. Water activity is the ratio 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 of the sample is equal to the relative humidity of the air surrounding the sample [17]. When measuring water activity 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[%] = W aterActivity × 100 (5.2)

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The relative humidity is then compared to a set saturation value unique to each transformer oil. This value indicates the maximum amount of water possible to dissolve in the transformer oil. Adding excess water will cause the water to split from the oil and as a consequence an inhomogeneous blend will occur. A downside of 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 with lower percentage meaning further away from the saturation limit. By measuring relative humidity, the risk of free water formation is thus easier to predict and prevent. It is also easier for workers without knowledge about 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 free from impurities and defects it resembles a capacitor in the sense that an ideal capacitor functions as an open circuit 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 this will be an indication of the resistive properties in the insulator. When impurities or defects reduce the resistive properties, the resistive current will increase causing the angle between the resistive and capacitive current 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 the capacitive. A higher tangent delta value means a reduced capacitive behaviour of the insulator, thus a worse insulator.

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 the molecules oppose an external electric field. Thus, the relative permittivity is a measure of reduction in electric field compared to if the electric field would propagate in vacuum [18]. Higher relative permittivity means more reduction in electric field. In dielectrics such as insulating transformer oil, the permittivity is often 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 is mainly 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 relatively low 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 parameters are calculated. IDA is useful for many applications and uses different models to do the calculations depending on the circumstance. The different impedance models used in this thesis and corresponding parameters are shown in table6.1.

Impedance model Parameter Resistive , ρ, σ Tangent Delta C, tanδ, P F

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, resistivity, loss factor and permittivity. While IDA 200 has more impedance models available. To measure said parameters the resistive and tangent delta models are enough. Since insulation diagnostics is based on material characterization, the geometry of the measuring cell is relevant when calculating material parameters from the measured current and voltage [20]. In other words, before any measurement is done on the oil the measuring cell has to get its geometric capacitance defined. This is done by doing measurement when only air (or vacuum) is between the electrodes. Since no “material” is between the electrodes, the capacitance of the sample is the geometric capacitance of the electrodes. The material is then inserted between the electrodes and this will influence the current that passes through. This influence is then used in the various models 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 system thus not keeping it in ideal thermodynamic equilibrium. A state which the oil is assumed to be in when extrapolating the measured data to use in simulations via the ion drift model. Further, due to the fact that the ions in the oil will start drifting apart under DC stress, the measurement could be affected. Because of this, it is recommended to apply a low AC voltage with very low frequency as the voltage source. The low peak voltage will not affect the equilibrium of the oil in any significant way and applying an AC voltage will keep the ions in the oil from drifting apart (since the positive and negative electrode switch polarity regularly). For most of the experiments related to this study, measurements are done at 1-2 V (rms) and a frequency sweep from 1 kHz to 1 mHz. The measured parameter to be used in future simulations would be the data point at the lowest frequency, 1 mHz, as it best resembles DC.

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6.1.2 Sine correlation technique

According to Peter Werelius, the inventor of the diagnostic tool [21], IDA uses the sine correlation technique to achieve a complex representation of the current and voltage. Both input voltages (one representing the voltage, another the current) are multiplied by a sine and cosine respectively and then averaged over an integer multiple (N) of the interval of time (T). The sine, cosine and the applied voltage have the same exact frequency.

Consider channel zero to be the voltage measurement. The real and imaginary part of the voltage are calculated according to equations6.1and6.2.

Re(Ch0P eak) = 2 N T

Z N T +α 0+α

= Ch0(t) sin (ωt)dt (6.1)

Im(Ch0P eak) = 2 N T

Z N T +α 0+α

= Ch0(t) cos (ωt)dt (6.2)

Since impedance requires both current and voltage to be calculated. A second channel is used. The layout of 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 the internal sine wave generator. Calculating the impedance by ohm’s law Z=U/I means that the phase of the impedance 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 real part being the resistance and the imaginary part being the reactance.

Z = R + iX_c (6.3)

|Z| =p

R²+ (iXc)² (6.4)

φ(Z) = arctanXc

R (6.5)

Since the measured current can be quite small (nA) as a consequence of the low applied voltage (to measure the equilibrium resistivity) and the high resistivity of the oils. Noise is of course an issue. This issue is greatly 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. The capacitance 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 no material (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 capacitance together with the measured impedance. IDA calculates the resistivity using the following equation:

ρ =C0

0

1

Re(_Z¹) (6.8)

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

R = ρd

A (6.9)

C = ₀_rA

d (6.10)

RC = ₀_rρ → ρ = R C

₀_r (6.11)

Since the geometry of the cell is taken into account when there is no material, or air, in between the electrodes. The relative permittivity equates to one and can be neglected as it is shown in equation6.8

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The resistance is given by the real part of the impedance. The reason as to why IDA uses _Re(¹1

Z) instead of Re(Z) could be to clarify that the impedance model considers the capacitance to be in parallel with the resistance. Thus the resistance is given by Re(_Z¹) and the total resistance is given by _Re(¹1

Z) since in parallel circuits the total impedance is generally given by

Z_tot= ( 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 by checking the SI-units.

[Ωm] = [F ] [^F_m]

[1]

[_Ω¹] → [Ωm] = [mΩ] → ok (6.13)

6.1.4 Relative permittivity

The 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 relative permittivity is interesting as the imaginary part relates to losses due to high frequency. Something not relevant to this study as the transformer oil is to be used in HVDC applications. Instead the dielectric losses are 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 utilizes both low voltage and low frequency. By applying a triangular wave to the test cell the theoretical current response can be calculated and the credibility of an actual measurement can be investigated by use of a parameter that is easily extracted from the current response of the measurement. The general expression for 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 the separation distance d and the electric field between said plates are considered homogeneous.

The theoretical current can be expressed as I(t) = σA

d U (t) +0rA 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 as a 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 ^dU_dt as well as the magnitude term U (t) can be calculated and the result allows for plotting the theoretical current response. Here ∆ is an arbitrary small number >0 and τ is the period of the triangular wave. U₀ is the magnitude of the voltage.

t U

^dU_dt

I

0 0

^4U_τ⁰ ^r_d⁰ ^4AU_τ ⁰

τ

4

− ∆ U

₀ ^4U_τ⁰ ^σAU_d ⁰

+

^r_d⁰ ^4AU_τ ⁰

τ

4

+ ∆ U

₀ ^−4U_τ ⁰ ^σAU_d ⁰

−

^r_d⁰ ^4AU_τ ⁰

τ

2

0

^−4U_τ ⁰

−

^r_d⁰ ^4AU_τ ⁰

3τ

4

− ∆ −U

0 −4U0

τ

−

^σAU_d ⁰

−

^r_d⁰ ^4AU_τ ⁰

Table 6.2: Theoretical equations for the triangular method

Plotting the current response using the expressions above shows how easily the capacitive and resistive currents 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 (frequency) is studied later in the report.

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6.2.1 Implementation in Labview

The 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 starting measurements 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 using the general resistivity formula for two parallel electrodes

ρ = RA d = U

I A

d (6.17)

The ^A_d fraction and the amplitude of the voltage is used as an input on the GUI. The script then measures the current twice for each period. The resistivity at that instance of time is calculated using equation6.17.

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 the voltage is achieved when reading the current. Since the measurement is then taken at an interval of ¹₂τ . The measured current will always correspond to when the voltage is at the peak value. This is seen in figure6.3.

Why the script ignores the first period could be to avoid any eventual disturbances in the measurements due to human error such as touching the cables or the sample. The author’s experience is that these kind of errors usually arises at the early stages of an experiment when everything is getting set up. Since the experiments takes 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 are satisfactory. The triangular method, especially the theoretical current response, is then used to determine if the 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 oils needs to be accurately measured. MM70 is an easy tool which displays the humidity in both terms of ppm and water activity (relative humidity)[24]. It also has a logging function which is useful when performing experiments over long sessions of time. To find the saturation value of a specific oil, the tool is sent to VAISALA^TM along with a sample of oil for calibration. Changing between oils is easy as the user only has to 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 to get 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 ethanol and 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 vacuum degassing 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 glass container. When the machine is turned on, the mixing device will start spinning. The combined mixing from 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 is connected. Lower pressure means better vacuum. A pressure in the magnitude of 10⁻² millibar is considered sufficient.

Figure 6.4: Degassing station, the pressure in the container is 5.6E-1 millibar. The container stands on a device 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 optimal measurement conditions is one where the oil’s various parameters (temperature, water content) are constant during the entirety of the measurement. To get close to this ideal, a climate chamber with the possibility of altering humidity and temperature is used. The cell is connected to the measuring equipment by two BNC cables 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 manufacturing 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 electrodes are screwed together and separated by washers to achieve a 2 mm gap. The two conducting electrodes consists of a insulating material in the center and a copper surface on each respective side. Three cables are connected: 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, the same 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 surface from the surface used to measure the current. To keep things consistent, the etched gap is equal to the gap between 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 the opposite sides of the electrodes. The design of two parallel electrodes makes it easy to estimate the geometric capacitance of the cell.

C0= 0Air

A

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 electrode, the one with the etched gap, has it’s surfaces connected to the current measurement and to ground respectively.

7.2 Prototype flaws

There are mainly two flaws with the prototype: durability and time consuming maintenance. To achieve the smooth surface, one of the cables is soldered by drilling a small hole through the plate, attaching a cable through the hole, soldering and smoothing the area of the opposite, conducting, surface. This process takes a long time and can be very difficult if not used to soldering. Further, since the cell has to be cleaned fairly rigorously 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 the durability issues are handled. The cell is designed in the Solidworks software [25] and outsourced to a PCB manufacturing company for construction. Contrary to the prototype, no manual soldering of wires is 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 the diagnostic instrument easier. Similarly to the prototype, each conducting plate consists of an insulating material 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 of via on the market. A “through via” is used in this design, basically a hole is drilled through the PCB and the 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 connected to the current measurement, shown in figure7.2and 7.3.

Via allows for a smoother surface compared to the prototype since no soldering material is used on the conducting surface. Further, because of the PCB design, attaching connection pins at the top part of the cell (which is possible to have above the oil, seen in figure 7.4) gets rid of the need to clean the wires in between 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 since gold 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 the measurements.

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

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

The electrode used to apply voltage is similarly designed to the current & ground electrode. Vias are used to 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 required since 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 which will fill up the gap between the electrodes and resistivity of the liquid can be measured. The cell is held together 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 using the triangular method. Generally the experiments performed using the triangular method are more focused on the method itself. The setup for the triangular method is simpler compared to IDA, as an electrometer and a function generator are the only hardware required. IDA is a complex, industrially used, diagnostic tool. The goal is to investigate if the triangular method could replace IDA when it comes to resistivity measurements. As of the moment of this report, the power grids (PG) division of ABB Corporate Research Västerås has one IDA diagnostic tool. This can cause quite a bottleneck as the measurements themselves take multiple hours depending on the frequency and number of data points. All experiments performed using the triangular method use the old measuring cells.

The experiments related to the investigation of various transformer oils and their dielectric properties are mainly done using IDA. To remove the uncertainties that can arise using the triangular method. Only the experiments which are explicitly stated to use the new measuring cells do so. If nothing is stated, the old measuring cells are used.

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8.1 Experiments: Triangular method

8.1.1 A general measurement

The purpose of this experiment is to give an idea about how a measurement with suitable settings should look.

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

The capacitive and resistive currents are easily identified. Theoretically the most accurate measurement would occur when these currents are equal. The current response presented in this figure is a good indication that the selected frequency is suitable. Before taking a final measurement, the capacitive and resistive currents 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 resistive current to increase.

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8.1.2 Importance of shielding, choice of frequency & voltage

In this experiment the mineral oil is used. Because of the low currents, shielding to minimize the influence of noise as well as proper grounding of measurements are important. In this experiment measurements are taken at varying frequencies and voltages with and without shielding. This experiment is the first experiment performed 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 to satisfy the criteria of thermodynamic equilibrium. The ideal frequency is the lowest frequency as it best resembles DC. Further, suitable settings will vary depending on the transformer oil. Firstly the frequency is altered 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, figure6.3, 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 frequency increases the resistive current and reduces the capacitive current is apparent from the 0.001 Hz and 0.005 Hz measurements. With the lower frequency yielding higher resistive current. Worth noting is the sensitivity of frequency 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 as possible 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 the 2 V measurement and the end of the 6 V measurement are due to people walking around in the room the experiment 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 having noise affecting the results. After shielding the sample by placing it in a aluminium bucket the following is measured.

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. At voltages above 4 V the noise is negligible.

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8.1.3 Accuracy and precision of measurements

In this experiment the mineral oil is used. According to the theory [22], the ratio of capacitive and resistive current can be used to estimate how accurate a measurement is (this will be investigated experimentally in the upcoming section). However, the precision is still unknown. Therefore a set of three measurements using 4 V and 0.005 Hz are done and their measured resistivity compared. The results are presented in the form of mean value and standard deviation. With the standard deviation being expressed both numerically and in 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 4.8E12

2 4.9E12

3 4.8E12

Mean 4.8E12

Standard deviation 5.8E10 Standard 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 oil

In this experiment the mineral oil is used. As the main purpose of the experiments revolving the triangular method is to find if it is a suitable replacement and or addition to IDA. An experiment where the triangular method is performed at the same frequencies as IDA to clearly illustrate the difference in terms of measured resistivity is done. The resistivity is first measured using IDA and then separate measurements for each corresponding 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 and below the room temperature where the triangular method measurements take place. Ideally, the measured resistivity 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 5 mHz yields results most similar to IDA. However, the measured resistivity from the triangular method never lands in between the different IDA measurements.

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From figure8.7the closest measured resistivity is at 4.50 mHz which is compared to IDA’s measured resistivity at 4.64 mHz.

Measuring sequence Resistivity [Ωm]

IDA 20^◦C 4.2E12

IDA 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 increment of 0.5 mHz from 4.0 mHz to 5.5 mHz it shows that the optimum frequency is found in interval 4.5 ± 0.49 mHz.

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

Theoretically the optimum accuracy is found when the capacitive and resistive currents are equal. A ratio of 1.2 is the closest found when using increment of 0.5 mHz. Tuning the frequency with shorter jumps in frequency is of course possible, but very time demanding. It could be that a better frequency choice is in the suggested interval of 4.5 ± 0.49 mHz. Finding this frequency should yield a resistivity closer to the resistivity measured using IDA. Usually resistivity is talked about in order of magnitude when it comes to transformer oil. 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 oil

In this experiment the ester oil is used. The same approach is done as for the experiment using the mineral oil. 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 small enough 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 issues arises. Firstly, looking back to the ion drift model, the aim is to measure the resistivity at as lose to DC as possible. Increasing the frequency is the direct opposite of this. Secondly, with frequencies higher than 0.5 Hz it is too fast for the triangular method to show any relevant data. With most of the measured resistivity showing “Infinite”. The problem of using the triangular method for the ester oil originates from the oil’s low resistivity.

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8.1.6 Different types of grounding

In 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 reference point. The cables were drawn through the aluminium bucket through a hole and connected to the reference point. 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). The ground 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 between experiments. To confirm that the new setup is functional, it is tested using the triangular method. Contrary to IDA, where only the measured parameters are displayed, the triangular method displays the current response 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 between experiments.

Measurements of resistivity in transformer insulation liquids

Examensarbete 30 hp Juni 2020

Measurements of resistivity

in transformer insulation liquids

Jonathan Hägerbrand

Abstract

Measurements of resistivity in transformer insulation liquids

Jonathan Hägerbrand

Contents

1. Introduction

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

2.1 High vs low voltage

2.2 Direct current vs alternating current

3. Physical model

3.1 Ion Drift Model

3.2 Relaxation time & Transit time

3.3 Concentration of ions

3.4 Electrical double layer

3.4.1 Zeta-potential and Debye length

4. Types of transformer oil

4.1 Biodegradability

4.2 Mineral oil

4.3 Ester oil

4.4 Isoparaffin oil

5. Dielectric properties of transformer oil

5.1 Resistivity

5.2 Temperature

5.3 Water content & humidity

5.4 Tangent delta

5.5 Relative permittivity

6. Experimental setup & hardware

6.1 IDA 200 Insulation Diagnostic System

6.1.1 Equivalent circuit

6.1.2 Sine correlation technique

6.1.3 Calculations of parameters

6.1.4 Relative permittivity

6.2 Triangular Method

t U

I

0 0

− ∆ U

+

+ ∆ U

−

0

−

− ∆ −U

−

−

6.2.1 Implementation in Labview

6.3 VAISALA-MM70 handheld moisture and temperature meter

6.4 Cleaning and assembly process

6.5 Degassing process

6.6 Climate chamber

7. Measurement cell

7.1 Prototype

7.2 Prototype flaws

7.3 New measuring cell

8. Experiments & results

8.1 Experiments: Triangular method

8.1.1 A general measurement

8.1.2 Importance of shielding, choice of frequency & voltage

8.1.3 Accuracy and precision of measurements

8.1.4 Triangular method at IDA frequencies - mineral oil

8.1.5 Triangular method at IDA frequencies - ester oil

8.1.6 Different types of grounding