Investigation of ion mobility in insulation liquids for transformers.

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Examensarbete 15 hp Oktober 2020

Investigation of ion mobility

in insulation liquids for transformers.

Bruce Dondogori

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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

Investigation of ion mobility in insulation liquids for transformer.

Bruce Dondogori

This thesis studies a method of measuring ion mobility in insulation liquids for transformers (transformer oil). This method works by using a square wave voltage to make the charged particles (space charge) inside the oil move between two electrodes. By measuring and analysing the resulting current, the ion mobility of the oil can be calculated with an equation derived from the ion drift diffusion model.

In order to study this method, different aspects of the technique were tried. Four different oils were involved, their measured ion mobility is presented at the end. Two different electrode materials were tried and the effects of measuring with different voltages and different frequencies were documented.

At the end it was concluded that in order to get a good measurement using this method, it requires the right combination of voltage and frequency. These parameters are dictated mainly by the oils resistivity and the distance between the electrodes.

Examinator: Mats Ekberg Ämnesgranskare: Shi-Li Zhang Handledare: Joachim Schiessling

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Sammanfattning

Denna avhandling studerar en metod för att mäta jonmobilitet i isoleringsvätskor för transformatorer (transformatorolja). Denna metod fungerar genom att använda en fyrkantig vågspänning för att få de laddade partiklarna (space charge) inuti oljan att röra sig mellan två elektroder.

Genom att mäta och analysera den resulterande strömmen kan jonmobiliteten hos oljan beräknas med en ekvation härledd från "ion drift diffusion model".

För att studera denna metod har olika aspekter av tekniken testats. Fyra olika oljor var inblandade, deras uppmätta jonmobilitet presenteras i slutet. Två olika elektrod- material testades och effekterna av att mäta med olika spänningar och olika frekvenser dokumenterades.

I slutet drogs slutsatsen att för att få en bra mätning med den här metoden krävs det rätt kombination av spännings amplitud och frekvens. Dessa parametrar dikteras främst av oljans resistivitet och avståndet mellan elektroderna.

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1 Introduction

As the worlds energy consumption grows, it is necessary to have an efficient way to transport power between the production and the consumption centers. HVDC stands for High Voltage Direct Current, it is a technology for energy transport that uses high voltage DC instead of the more common AC. HVDC has many advantages compared to AC- transmission when it comes to transporting large amounts of power over long distances.

A few of them being that HVDC is both cheaper and more efficient(less losses) when used over longer distances. In some instances HVDC is better than AC-transmission for shorter distances, for example when sending power through underwater cables HVDC avoids the large capacitive currents required. Another example where HVDC is moti- vated despite the higher cost of DC conversion equipment is when connecting two places with different grid frequency/voltage.

HVDC transformers are a key component in the use of HVDC-technology. These transformers make it possible to convert large amounts of power between high voltage AC and high voltage DC. Two key components in the insulation system of HVDC transformers are pressboard and oil.

The oil in the transformer is subjected to stresses during operation or during switching on (or off) of the transformer. And so when designing the transformer, it is important to know how the oil will react in order to ensure that the insulation system can stand up to the stresses. The ion drift diffusion model is a physical model that describes the behaviour of charges in the oil when affected by electric fields. Simulations can be made in COMSOL using the ion drift model to understand and model the electrical properties of the insulation liquids. The ion mobility of the oil is a key parameter in this model.

This thesis looks closer into a method of measuring the ion mobility so called the square wave method. It experiments with different ways to measure by varying the measuring voltage, frequency and by mixing 2 different oils and observing the effect on the measured ion mobility.

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1.1 List of variables and their SI-units

Below is a list of the varibles used in this report and their coresponding SI-units.

• p = positive ion density [1/m³].

• n = negative ion density [1/m³].

• c = initial ion pair density, depending on p₀, n₀, k_D and k_R [1/m³].

• p₀ = initial positive ion density [1/m³].

• n₀ =initial negative ion density [1/m³].

• k₁ and k₂ = kinetic rate constants.

• k_D = Dissociation constant.

• k_D⁰ = Dissociation constant at equilibrium.

• k_R = Recombination constant.

• Σ = Conductivity [S/m].

• ρ = Resistivity [Ωm].

• q = Elementary charge (1.602e-19 C).

• µ = ion mobility [m²/V s].

• µ_p = positive ion mobility [m²/V s].

• µ_n = negative ion mobility [m²/V s].

• s = ion drift velocity [m/s].

• ₀ = vacuum permitivity (8.854e-12 F/m).

• _r = relative permitivity.

• T = Absolute temperature [K].

• K = Boltzmann constant (1.38e-23J/K).

• E = Electric field [V /m].

• U = The applied voltage on the electrodes [V ].

• F_{f ield} = The force exerted by the electric field [N ].

• Fretardation = The drag force between the liquid and the moving ions [N ].

• z = number of ions.

• r = ion radius [m].

• η = Viscosity [Kg/ms].

• t_transit = Transit time [s].

• t_relaxation = Relaxation time [s].

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• t_peak = Time of current peak(maximi point in I-t curve) [s].

• T OF = Time of flight [s].

• j_p = displacement current density [A/m²].

• j_p = positive ion current density [A/m²].

• j_n = negative ion current density [A/m²].

• j_total = Total ion current density [A/m²].

• Dp = Positive ion diffusion constant.

• D_n = Negative ion diffusion constant.

• d = The gap distance between the electrodes [m].

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2 Theory

A good understanding of the behaviour of transformer oil under DC and AC stresses need to be gained in order to achieve a good HVDC transformer design. The AC field can be modeled using standard numerical methods. Because of space charge, the DC field is more complicated to calculate. There are a few models that can be used in order to understand and model the behavior of ions in dielectric fluids. One of them is the "ion drift diffusion model", it explains the behavior of ions in dielectric liquids.

In this model the "ion" is not an individual charged molecule, it is a "quasi ion/particle"

which is one charged molecule with a sphere of polarised molecules around it. In this case "ion movement" means that this quasi particle travels through the oil.

In reality there are many different types of molecules in the oil and those molecules have different ion mobilities. So the calculated ion mobility value does not represent only one type of ions.

2.1 Ion drift diffusion model

Oil is a weak electrolyte and when an electric field is applied, conduction occurs mainly because of the ions in the liquid and the ion injected in the liquid from electrodes. Charge carriers are generated by dissociation or by ion injection on the liquid-metal interface according to Bjerrums theory. The theory of conduction in liquids is based on the Thomson model which describes ionic conduction in gases. As described in equation 2.1, the conduction is controlled by 2 main processes: The dissociation of neutral ion-pairs to form free ions and the recombination of free ions into neutral ion pairs.

B₁B₂ ^k¹

k2

B₁⁺B⁻₂

kD

kR

B₁⁺+ B₂⁻ (2.1)

B₁⁺B₂⁻ represents a neutral ion pair and B₁⁺+ B₂⁻represents 2 free ions. An ion pair con- sists of a positive ion and a negative ion temporarily bonded together by the electrostatic force of attraction between them, these occur in concentrated electrolyte solutions(oil in this case)[2]. k₁ and k₂ are kinetic rate constants, k_D is the dissociation constant and k_R is the recombination constant.

∂p

∂t = ∂n

∂t = k_Dc − k_R (2.2)

Equation 2.2 is called the rate equation and dictates the dynamics of the ions in the oil.

p and n are the positive and negative ion concentration respectively and c is the ion pair concentration which is much higher than the positive/negative ion concentration. Equa- tion 2.2 tells that the change in the positive and negative ion concentration is dictated by the dissociation and the recombination constant.

At thermodynamic equilibrium the positive and negative ions concentrations are described by equation 2.3 where σ is the conductivity, µ_n and µ_p are the negative and positive ion mobility respectively and q is the elementary charge.

p = n = σ

q(µn+ µp) (2.3)

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The recombination constant is given by equation 2.4, the Langevin formula for the recombination of ions in gases.[3] It shows that the recombination constant is not dependent of the electric field, it is only a function of the dielectric properties of the liquid.

k_R= q (µ_p+ µ_n)

0r

(2.4) The dissociation constant(K_D) is given by equation 2.5 where K_D⁰ is the dissociation constant when the elecrtic field is zero (E −→ 0), I1 is a bessels function of first order and is calculated with equation 2.6.

k_D = K_D⁰ I₁(4b)

2b (2.5)

b =

q² 8π₀_rKT

q

4π₀_r|E|

0.5 (2.6)

In equation 2.6 K is the boltzman constant, T is the absolute temperature and q is the elementary charge. Equations 2.5 and 2.6 shows that the dissociation constant is dependant on the electric field. When the electric field increases, more ions will be dissociated increasing the ion concentration which will lead to a higher conductivity.

2.2 Ion mobility in viscous liquids

Transformer oil is a viscous liquid with a resisivity of around 1e13 Ωm. When a viscous liquid is exposed to an electric field the large ions within the liquid will move inside the liquid causing a current. An ion is atom with an unequal number och protons and electrons, this makes the atom charged. Different atoms have different electron affinity and different ion radius which means that the different ions in the liquids have different ion mobilities. In the case of ion drift the 2 main contributing forces are: The force from the electric field and an opposite force from the drag between the ions and the liquid.

When a balance is reached between these two forces, the ions have reached their drift velocity.

F_{f ield} = zqE (2.7)

Fretardation = 6πηrs (2.8)

s = µE (2.9)

In equation 2.7, F_{f ield} is the force exerted by the electric field on the ions, z is the number of the ion charges and q is the elementary charge. Equation 2.8 describes Stokes law, Fretardation is the drag force exerted by the liquid on the ions η is the viscosity, r is the ion radius, s is the ion drift velocity and µ is the ion mobility.

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When these two forces are equal, the ions have reached their drift velocity and equation 2.10 is valid.

qzE = 6πηrs (2.10)

s = qzE

6πηr (2.11)

From equations 2.9 and 2.11 we see that the ion mobility µ [^m_sV²] becomes:

µ = qz

6πηr (2.12)

Transit time is the time that it takes the ions to cross the gap between the electrodes.It is a function of the applied voltage at the electrodes, the geometry of the electrodes and the mobility of the ions. In this case rectangular parallel electrodes were used and so the transit time is obtained with equation 2.13.

t_transit = d²

µ_p,n| U | (2.13)

d is the distance between the electrodes, U is the applied voltage and µ_p,n is the ion mobility.

µ_p,n= s

E = d²

U t_transit (2.14)

U is the voltage between the electrodes and t is the time that it takes the ions to cross the gap between the electrodes.

2.3 Relaxation time

Relaxation time is the mean time that it takes for dissociated ions to return to the thermo- equilibrium state(to recombine) after a weak disturbance, in this case after the small applied voltage is removed. It is dependant on the dielectric properties and resistivity of the oil as seen in equation 2.15.

t_relaxation = ₀_rρ (2.15)

In equation 2.15 _r is the dielectric constant and ρ is the resistivity of the oil.

2.4 Electrical double layer

When an object comes in contact with a liquid a structure of ion layer is formed on the object, this structure is called the electrical double layer (EDL). In this case the object is the electrodes and the liquid is a light electrolyte(oil). The first layer bonds to the material because of chemical reactions and the second one is in the bulk liquid and is attached to the material because of an external electrical field, in this case because of the electrical potential applied to the electrodes. The first layer is called the surface layer, it can be positive or negative depending on the properties of the solid material and the second one is called the diffuse layer, its size can vary depending on the magnitude of the electrical potential between the electrodes.

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Figure 1: Electrical double layer

2.5 Ion mobility measurement based on I-t curve

The equations below describe the current that is observed as the ions move across the gap between the electrodes. This current gives rise to a "peak" that is visible on the I-t curve. Equation 2.16 shows the positive ionic current density and equation 2.17 shows the negative ionic current density. Both equation show how the ionic current is dependent on the electric field(E), the free ion concentration(p/n) and the ion mobility(µ). Dn and D_p are diffusion constants and D_p∇p accounts for ion movement driven by different ion concentrations. Equation 2.18 shows that the total ionic current is equal to the sum of the negative and positive ionic currents.

−

→j_p = q(µ_p−→

E p − D_p∇p) (2.16)

−

→j_n = −q(µ_n−→

E n + D_n∇n) (2.17)

−−→j_total =−→ j_p +−→

j_n (2.18)

The resulting I-t curve after a measurement is a sum of the total ionic current(equation 2.18) and the displacement current. The displacement current is the current that is generated by the change in the electric field as described in equation 2.19.

−→

JD = r0

∂−→ E

∂t (2.19)

Figure 2 shows a simulated I-t curve using the ion drift diffusion model. The duration of the "peak" is called TOF and it stands for Time Of Flight, it is the time difference from when the voltage is applied to the time the current reaches a local maximum value. It is the equivalent of the transit time(TOF = ttransit) from equation 2.13. In this thesis, TOF was approximated to be two times bigger than t_peak(Figure 9). And so the ion mobility is calculated by equation 2.20

µ_p,n= s

E = d²

2t_peakU (2.20)

Figure 2 is taken from a report in a report titled "Measurement of ion mobility in dielectric liquids" done by Mohsen Zadeh in 2011. My work in this thesis is based on the simulated

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Figure 2: Total current at cathode physical model from Mohsens report[5].

In a report done at ABB a simulation using the ion drift model was compared side by side to an experimental measurement[6]. The results show a similar trend in the curve form between the simulation and the experimental measurement. However the simulations curves are not identical to the curve measured during the experiment. This can be seen in Figure 3.

Figure 3 shows a comparison between a simulation of the ion drift model and an experimental measurement. The red curve shows the measured data, the green curves show the the simulated model.

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Figure 3: Comparison of simulated (blue and green lines) and measured (red line) I-t curves, The inset shows simulation 1 in a different scale to emphasize the peak position.[6]

2.6 The oils used in this thesis

Electrical power equipment generate a lot of heat during operation and due to the high voltages, they need a good insulation system to prevent inside arcing and corona effects inside and around them. A good example for this is large power oil-filled transformers, the main purpose of the oil is to insulate and act as a coolant. The oils is usually circulated though the transformer by natural convection but in some large applications the oil is circulated by a pump though a radiator.[7]

Transformer oil has to have good dielectric properties as well as high heat conduction capacity. In order for the transformers to have a longer service life, the oil used in the insulation system has to be chemically stable[7]. Before putting the oil in a transformer, it has to go through a process called degassing. This is where undesirable gasses and moisture is removed from the oil, it is done by pulling a vacuum in the oil container.

In Figure 4 the oil container is standing on a magnetic stirrer and a vacuum is pulled inside the container. The main reason why this process is done is because the water moisture in the oil can reduce the service life of the pressboard(made of cellulose cells) in the insulation system and the water moisture also reduces the resistivity of the oil and the moister leads to a degradation of the cellulose.

In this thesis, 3 types of oil were used: mineral, ester and isoparafinnic oils.

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Figure 4: Vacuum being pulled from oil bottle standing on a heating plate with a magnetic stirrer.

2.6.1 Mineral oil in transformers

Mineral oil is obtained by refining hydrocarbons and is the most widely used oil in transformers. The reason for this is its relatively high availability, good heat conduction and good insulation properties.

The drawbacks with mineral oil are its relatively low flash point(150^oC), and it is a environmental contaminant.[8]

Figure 5: Schematic structure of classes of molecules in mineral oil

There are 5 types of mineral oil: Paraffin, isoparaffin, naphthenes,aromatic and polyaro- matic. Their chemical structures are shown in Figure 5. The mineral oil that was used in this thesis is a naphthenic oil which means that the main contribution is naphthenic and the aromatic contribution is rather small.

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2.6.2 Ester oil

Ester oil is the most popular of synthetic oils, this means that it is made of chemical compounds that are artificially made, usually based on vegetable oil. As a result, it has more environmental benefits compared to mineral oil as it is biodegradable and non- toxic. The ester oil also has a much higher flash point compared to the mineral oil(ester oil flashpoint: 260^oC) which means it is safer to use at higher temperature compared to mineral oil[9].

2.6.3 Isoparaffinic oils

Isoparaffinc oil is a type of mineral oil, it is refined from crude oil. Its main benefits compared to other mineral oils are higher heat capacity, higher thermal conductivity and higher resistance to oxidation. In practice it means that isoparaffinic oils are a better coolant because of their higher heat capacity and higher thermal conductivity.

Isoparaffinic oil also last longer thanks to their higher resistance to oxidation [11].

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3 Experiments

In this section, we get an overview of the experiments that were done during this thesis.

The main goal was to investigate the "square wave method" of measuring ion mobility.

The ion mobility is measured by using a measuring cell. The cell is two parallel rectangular copper(or gold-plated) electrodes. The gap distance between the electrodes is 2mm. After the electrodes are cleaned with ethanol and deionized water, they are sunk into the oil.A voltage is applied and a current is measured by an electroscope. The applied voltage is a zero-centered square wave with a certain voltage and frequency. For the first half of the first period the ions are pulled towards one side of the cell and for the second half the ions are "repelled" towards the opposite side of the cell. The current going between the electrodes is measured and the ion mobility is determined by the time that it took the ions to move from one side to the other(t_transit).

3.1 Equipment

The first step was to design the cell in solidworks and specify all the dimensions and the materials. The design was based on an existing design that was improved. Then a pcb-maker was contacted in order to specify the finer details(the conductive material, the thickness of layers, etc) and an order was placed. The new cards were ordered in 2 varieties, one with copper as the conductive layer and another with gold as the conductive layer. This was done in order to see if the material of the electrodes had an effect on the measured currents in the oil.

Figure 6: electrode design

In Figure 6, the 2 cards that make up the measuring cell can be seen. The 2 cards are sandwiched together with their front-side facing each other with a 2mm gap between them. The conductive surfaces on the back of both card are grounded, the front-side

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of Card2 is connected to the voltage source(electrometer) and the front-side of Card1 is connected to a the electrometer for current measurement. The electrometer that was used is a Keithley6517A.

Figure 7: Measurement equipment setup

Figure 7 shows the equipment setup for the measurements. Item-1 is a stationary computer with LabView, item-2 is an electrometer(Keithle 6517A), item-3 is a vacuum oven, item-4 is a aluminium container with 2 BNC-connections, item-5 is the measuring electrode and item-6 is a glass container filled with oil. The computer to electrometer com- munication is done through a GPIB interface, the applied voltage is controlled by the computer and the current measurement is read by the electrometer and then sent to the computer.

Before each measurement, the measuring card and the oil container are carefully cleaned in order to minimize contamination in the oil. The cleaning process starts with tap- water and soap, then the cards are cleaned with ethanol and at last rinsed off with distilled water. The oil is then filled into a 1liter glass container and a measuring cell (the electrodes) is sank into the oil. The distance between the cells electrodes is always 2mm for all the measurements. Because the measured signal was low, the oil container was placed inside a grounded closed aluminium container in order to minimize noise/electromagnetic interference.

Figure 8 shows the raw data from a measurement on the ester oil with 60V at 0.0005Hz.

From the same figure, notice that the positive half of the first period(from t=0s to t=1000s) the current curve-form is different compared to the other periods. It is clearly seen that the I-t signal from the first period is different due to preconditioning of the electrodes with ionic layers. To evaluate the ion mobility data from higher periods are used.

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Figure 8: Typical measurement shows the applied voltage (blue) and current measured (red) for a number of periods.

3.2 Analysis

During a measurement the current is being measured every 250ms.The resulting data is: time and current. After the measurement, a plot is made with time[s] on the x-axis and current[A] on the y-axis. From this plot an analysis can be done, for example: ion mobility, the amount of displaced ions, FWHM.

3.2.1 Ion mobility

In Figure 9 is an example of what a typical current curve looks like(zoomed in on half of a period on x-axis) for the mineral oil. The voltage in the curve is 35V and this particular curve is the positive half of the second period.

The peak current of the curve corresponds to the movement of the ion in the oil. The time that it takes the ions to cross from one electrode to the other is called transit time(t_transit) and the time at the current peak (tpeak) is approximately half of ttransit.

3.2.2 Amount of displaced ions and FWHM

The current curve can be approximated by adding up 3 parts: a capacitive current, a steady state current and a current generated by the migration of ions(ionic current).

The capacitive current is the spike in the beginning of the curve, it fades very fast. This current can be approximated by the capacitive current equation.

I_cap = U Re⁻

t

RC (3.1)

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Figure 9: Measurement example, Mineral-oil

U is the applied voltage, R is the resistance between the electrodes, t is the time after the voltage is applied and C is the capacitance between the electrodes. Icap is not used in the analysis because it goes to zero too quickly to affects the results in a noticeable way.

Figure 10: Different parts of the total current

The steady state current is the current marked in region 2 in Figure 10, that is the current level without the capacitive current and the ionic current. This current does not vary as much as the 2 others. It is the result of the applied voltage and the resistivity of the oil between the electrodes.

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The region 1 in Figure 10 show the ionic current, that is the current generated by the migration of the ion between the 2 electrodes. The goal is to isolate this region in order to calculate the area under this curve and calculate its width.

The area under region1 is obtained by integrating the current over time and so it is equal to the amount of displaced charges(in Coulomb).

To compare the width of the curve between the different measurements, FWHM can be used. FWHM stands for Full Width at Half Maxima. In this application, it is used to give an idea of how wide the top of the curve is.

If the top value of the curve is f_max, FWHM is the difference between the two x-values at f_max

2 as seen in Figure 11 [12].

Figure 11: Full Width at Half Maxima

By approximating the steady state current and the capacitive current, they can be removed from the curve so that only the top part(ionic current) is left. This way, its width(in [s]) and the amount of ionic charge(in [C]) can be calculated for later comparisons.

Figure 12: Base and total

In Figure 12, the blue curve is the total current as measured, the red curve is a sum of the approximated capacitive current and the approximated steady state current.

Figure 13 shows the ionic current curve, that is the resulting curve after subtracting the

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Figure 13: Top only

capacitive and steady state current.

3.2.3 Margin of error in ion mobility

The ion mobility is calculated using tpeak which is manually selected from the curve. At times the curve top is very wide and this makes it less clear as to what is t_peak. A solution to this is to introduce a term that expresses how precise a measurement is which makes it easier to make comparisons and to interpret the results.

In Figure 14, the part of the curve between the blue crosses represent what could be considered as tpeak. Those blue crosses are placed at 99.5% of the peak current and the margin of error is the difference between the ion mobility represented by those two times.

Various ways to measure were tried in order to compare the results and find the optimal way to measure with this method. Different variable were tried, for example:

• The effect of changing the voltage and/or frequency.

• Mixing the mineral and ester oil.

• The effect och different electrode material.

• A measurement on 2 isoparaffinic oils.

3.3 Voltage/frequency dependency analysis.

In this section an analysis was done in order to compare and observe the effects of the voltage and frequency on the measurement of ion mobility using the voltage reversal method. This was divided into two parts, in the first part the frequency was varied but the voltage was kept the same and in the second part the voltage varied but the frequency stayed the same. This was done on 2oils: the mineral oil and the ester oil.

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Figure 14: Margin of error example 3.3.1 Same voltage; different frequencies

The aim of this experiment was to do measurements with the same voltage but vary the frequency in order compare and determine the best frequency for measuring.

Measurement Voltage [V] Frequency [Hz]

1 20 0.005

2 20 0.0025

3 20 0.001

4 20 0.0002

5 20 0.0001

Table 3.1: Ester oil

The table 3.1 show what measurements were done with the ester oil. The length of each measurement is longer than 2 periods of the applied square wave voltage on the electrodes.

3.3.2 Same frequency; different voltages

The objective of this experiment was to do measurements with the same frequency but vary the voltage in order to compare and determine the most optimal voltage for future measurements. Oil-A and oil-B were used in this experiment.

Table 3.2 shows the different voltages that were used in the measurements on the mineral oil.

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1 20 0.0005

2 50 0.0005

3 100 0.0005

4 150 0.0005

Table 3.2: Mineral oil

1 20 0.0005

2 50 0.0005

3 60 0.0005

4 150 0.0005

Table 3.3: Ester oil

Table 3.3 shows the different voltages that were used in the measurements on the ester oil.

3.4 Mixing of the 2 oils

After determining the optimal frequency and voltage for measurements in the mineral and ester oil. The 2 oils were mixed to see how much this affected the ion mobility. This was performed in 20% increments, the percentage refers to the amount of ester-oil in the mix compared to the total mix. 0% is only the mineral-oil and 100% is the ester-oil only.

Before every measurement the mixture was put onto a magnetic stirrer overnight in order to insure that the oil-mixture was as homogeneous as possible.

Measurement Voltage [V] Frequency [Hz] % ester oil in the mixture

1 150 0.0002 0

2 150 0.0002 20

3 150 0.0002 40

4 150 0.0002 60

5 150 0.0002 80

6 150 0.0002 100

Table 3.4: Mix of mineral and ester oil

Table 3.4 shows the measurements that were done on the mixed oils and how the mixing was done.

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3.5 Electrode material comparison

After drawing new cards to order, an option was available to order the cards with the electrodes coated in different materials. A choice was made to try a set of cards with copper electrodes and another set with gold plating on the electrodes. This was done in order to measure and compare the difference that these different materials would make in the measurement.

Measurement Voltage [V] Frequency [Hz] Electrode material

1 150 0.0002 Gold

2 150 0.0002 Copper

Table 3.5: gold vs copper

Table 3.5 shows what measurements were done with the different electrode materials.

Both measurement were performed with the mineral oil.

3.6 Ion mobility in the isoparaffinic oils

In this section measurements were performed for the 2 newer isoparaffinic oils in order to measure the ion mobility, the curve form and the area under the curve. These 2 oils are going to be referred to as isoparafinic-1 and isoparafinic-2.

Measurement Voltage [V] Frequency [Hz] Oil type

1 150 0.0002 isoparaf in1

2 150 0.0002 isoparaf in2

Table 3.6: new isoparaffins

These measurements were both performed with the copper electrodes.

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4 Results

In this chapter, the results from the experiments will be presented with figures and tables with shorter descriptions in order to lead to the discussion which is in the next chapter of the report.

4.1 Frequency dependency analysis

Figure 15: different frequencies ester(y-axis is adjusted for a better view of the curve form)

Figure 15 shows 2 measurements that were done on the mineral-oil. Both were done with the same voltage(20V) but at different frequencies. The blue shorter one has 0.0002Hz and the red longer one was done at a lower 0.0001Hz.

According to the model, both curves should be identical and the only difference should be the length. Meaning that the blue curve should look like the red one but with half the period. The experiment result shows that for a lower frequency, there is a change in the peak magnitude and peak position(t_peak).

The other measurements for frequency dependency are not shown here because they were too noisy to be of use in this study.

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4.2 Voltage dependency analysis

Figure 16: I-t curves for a range of voltages for ester oil.

Figure 16 shows measurements on the mineral-oil. The 4 measurements in the figure have the same frequency(0.0005Hz). Observe that the curves are not flat, they appear so because of the large range on the y-axis.

Figure 17: Normalized currents from figure 16

Normalizing(in this case) was made by putting all the data to be in a range of 0-1. Each curve was divided by its maximum value and so the highest point of that curve is 1.

z_i = x_i

max(x); z_i is the normalized point, x_i is a data point at the curve and max(x) is the maximum value of the curve.This means that each curve is divided by its highest value, this makes it easier to compare the curve-forms between different voltages. Figure 17 has the same measurements as Figure 16, the difference is that the curves in Figure 17 are normalized.

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Figure 18: I-t curves for a range of voltages for mineral oil.

Figure 18 shows 6 measurements that were made on the mineral oil. All the measurements in the figure have the same frequency(0.0002Hz). The "area" refers to the area under the curve which is equal to the amount of displaced ions.

Due to the relatively high resistivity of the mineral oil, the measurement is very noisy.

The curves in Figure 18 (except the 100V-curve) are averaged over a number of periods to reduce the noise.

Figure 19: Calculated ion mobility and estimated charges from the peak in the I-t curves for the applied voltages measured with ester oil.

In Figure 19, the ion mobility and amount of charge are plotted against the applied voltage.

The plot in Figure 20 shows on the applied voltage on the x-axis, the ion mobility on the left y-axis and the amount of charge on the right y-axis. Observe that the right y-axis(amount of charge) is in logarithmic scale.

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Figure 20: Calculated ion mobility and FWHM of the peak in the I-t curves for the applied voltages measured with ester oil.

4.3 Mixing of the 2 oils

The first result(Figure 21) for this section is an overview of the mixtures measurements.

The 0%ester means that it is 100%mineral-oil; observe that it is not 0A, it is in the pA range which makes it look like 0A when plotted against the 100%ester-oil which is in the nA range.

Figure 21: Various percentage of ester oil in the mixture of ester and mineral oil.

Figure 22 shows the mixtures measurements but here they are normalized for better comparison of the curve-forms.

Figure 23 shows the percentage of ester-oil in the mixture on the x-axis. On the left y-axis

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Figure 22: The mixtures from figure 21 normalized

Figure 23: Amount of charges and FWHM vs degree of oil mixture.

is the amount of charge (on a logarithmic scale) and on the right there is the FWHM on a linear scale.

Figure 24 shows the ion mobility on the left y-axis and FWHM on the right y-axis. This can be used to see how the width of the curve affects the ion mobility for the different mixtures.

In Figure 25 on the left y-axis is the ion mobility and on the right there is the amount of charge. This is later used to compare and observe how the amount of charge and the ion mobility changes for the different mixtures.

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Figure 24: Ion mobility and FWHM vs degree of oil mixture.

Figure 25: Ion mobility and amount of charge vs degree of oil mixture".

In Figure 26 the ion mobility is plotted against the percentage of ester-oil in the mixtures.The error-bars show how the accuracy of the ion mobility readings varies with the percentage of ester-oil in the mixtures. Figure 27 shows the steady state current values of every mixture. The current ranges from 4.132 pA for the 0% mixture to 7.134 nA for the 100% mixture.

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Figure 26: Error marginal in estimation of ion mobility

Figure 27: Steady state current

4.4 Electrode material comparison

Here Figure 28 shows the 2 measurements that were done using the same card design but with different materials for the electrodes. The blue curve is for the gold-platted electrodes(Au) and the red curve is for the copper(Cu) electrodes. Both measurements were done on the mineral oil. The data-tip in the figure are located at t_peak. The current obtained with Au electrodes is significantly higher.

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Figure 28: Electrode comparison

4.5 Ion mobility for the 2 new isoparaffinic oils

Figure 29: I-t curves of two Isopraffinic oils

Figure 3.6 shows measurements on the 2 isoparaffinic oils. The blue curve is the isoparaf- fin2 and the red curve is the isoparaffin1. The area is equal to the amount of displaced ions. Observe that in order to calculate the area, the background/offset current is removed first. The background current here is defined as everything below the steady state current which in this case is the current at t=2500s.

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5 Discussion

5.1 The voltage and frequency analysis.

From section 4.1, Figure 15 shows a side by side comparison of measurements with the same voltage(20V) but with different frequencies. The red curve has the lower frequency(0.0001Hz) and hence the longer period. This means that the voltage is applied for 5000 seconds before the voltage polarity reverses. From the ion drift model no frequency dependency in the measurement is expected, thus should show the same current magnitude and development with time. Our observation is that the current is decreasing for a long time, thus the frequency of the measurement should be as low as possible in order to get close to steady state condition. In Figure 15, the measurement with the lower frequency reaches a lower current level and shows that the curve is still descending.

As for the comparison between the different voltages, in section 4.2 at Figure 16 and 17 we can see side to side how different voltages affect the I-t curve. A couple of observations can be made, the first one is that the higher the voltage is, the higher the signal to noise ratio is thus making it easier to handle the data, this can be seen in Figure 17, this is due to Ohms law. For the same resistance, a higher voltage will yield a higher current thus giving the signal better readability.

A suitable measurement voltage is determined mostly by the oils resistivity, the voltage should be high enough to produce a current that is much higher than the noise. A higher signal to noise ratio is always desired but a potential drawback of high voltage is that the fast movement of ions can introduce electro hydrodynamic movement of the oil, which in turn will lead to a lower "apparent" mobility of the ions[13]. If the voltage is too low and the oils resistivity is relatively high, the resulting measurement will have too much noise, for example in Figure 15 the 20V ester-oil measurement.

The second observation is that as the voltage increases, the top gets narrower, the FWHM decreases(Figure 17). In the same Figure, it can be seen that as the voltage increases the peak-time (t_peak) decreases.

According to equation 2.20, the peak-time (t_peak) should decrease with the increasing voltage and the ion mobility should stay the same. But looking in Figure 20, the ion mobility does not stay the same. As the applied voltage increases, the ion mobility increases almost linearly. Given that results obtained from the experiments are reliable (with some uncertainties), they do not agree with the model. The measurement results are reproducible however they do not always agree with the simple model used to describe the ion mobility. A conclusion can be drawn that there might be factors the model does not account for, for example: electrohydro effects, the distribution of ions(ion shell/quasi ion), field dependent charge acculation effects at the electrode oil interface, etc.

Third observation: Figure 19 shows on the x-axis the applied voltage, the left y-axis(blue line) shows the ion mobility and the right y-axis(orange line) shows the amount of charge.

As the voltage increases, the amount of displaced charges increases as well which can be explained by equation 2.5 and 2.6. The increasing voltage puts a higher electric field in the oil which will increase the dissociation constant and give more charges. However the dissociation of molecules is a complex process and it is not completely certain that the increase in the electrical potential between the electrodes fully explains the increase in

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the amount of charges.

As for the ion mobility, it should theoretically be the same for all the voltages due to the fact that a higher voltage yields a smaller t_peak and the ratio between the applied voltage and tpeak stays the same. The cause for the variation in the ion mobility for the different voltages could be due to the uncertainties on the lower voltages. At lower voltages the top is wider, this can be seen in Figure 20. The FWHM-value becomes higher as the voltage decreases and this makes it harder to mark tpeak accurately thus making the uncertainty higher. Though the uncertainty is higher at lower voltages, it does not fully explain the big difference in the measured ion mobility at the lower voltages versus the higher voltages.

The best voltage and frequency combination that worked for all the oils involved is 100V at 0.0002Hz. For the oils (like the mineral oil) with a higher resistivity, an effective way to considerably reduce the noise without noticeably affecting the curve, is to take an average over many periods(<11periods) of a measurement. When averaging, if too many periods are used, it can affect/alter the measurement in a noticeable way.

5.2 Mixing the ester and mineral oil.

The primary goal of this experiment was to observe how mixing the 2 oils would affect the ion mobility. The results were as expected, the mixtures ion mobility were in the middle of the ester and mineral oils mobility. In Figure 21, we can see that the unmixed mineral oil is at the bottom and that the ester oil is on the top. This is because the ester oils resistivity is much lower compared to the mineral oil and so the ester oil lets through more current. As the amount of ester oil in the mixture increases, the mixtures resistivity is lowered.

Figure 22 shows the same data as Figure 21 but the curves are normalized here for better comparison of the curve forms. It is apparent that the ester oil has a wider top compared to the mineral oil(0%ester).

Figure 23, 24 and 24 show the three means of comparison(FWHM, ion mobility and amount of charge) against each other. In Figure 23, the increase of ester oil in the mixture leads to an increased FWHM, this indicates that the curve get wider. The black curve in Figure 23 shows an increased amount of charge as the amount of ester oil in the mixture increases. This can be explained by the fact that the ester oil has lower resistivity which leads to a higher current an thus more charges moving between the electrodes.

As for the ion mobility when the amount ester oil in mixture increases, the ion mobility decreases as seen in Figure 24 and 25. This is an expected result as the mineral oil has the higher ion mobility(4.9e-10 [m²/V s]) and so as more ester oil is added to the mixture the ion mobility decreases.

5.3 Comparison between gold platted and the copper electrodes.

For this experiment, the results show that the gold platted electrodes give more current compared to the copper ones. This leads to a clearer signal from the gold electrodes compared to the copper. As of now I do not have a good explanation to why the gold electrodes give significantly more current but from these result it is clear that the material

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choice on the electrode does affect the results.

5.4 The 2 isoparaffinic oils.

Compared to the mineral and ester-oil, the two isoparaffinic oils were much easier to measure because the peak current is higher and the top is very small and sharp. As seen in Figure 29, the curve-form is clearly different from that of the mineral and ester oil.

This is just an observation of the experimental result as there is no clear explanation now of why the isoparaffinic oils I-t curves look so different from the other measured oils.

6 Conclusions

The main goal of this study was experiment with the square wave method of measuring ion mobility in transformer oils. To summarize, the biggest takeaway is that in order for this method to give good results it requires a good combination of voltage and frequency.

The optimal voltage and frequency can vary from oil to oil and this is mostly dictated by the oils I-t curve form and its resistivity. For the 4 oils that were tested here 100V at 0.0002Hz seems to work for all of them.

The ester and mineral oil can be mixed in order to alter the resistivity or the ion mobility of the mixture. For the other properties such as the oils flash point, solubility and viscosity, it is unclear what happens there when the 2 oils are mixed.

As the measured ion mobility seems to strongly depend on the applied voltage, one recommendation for future work is to investigate the model on a deeper level. This could be by investigating why measuring with different voltages yields different ion mobilities while the model dictates that the ion mobility should stay constant when measuring at different voltages.

Given the observed width in the I-t curves, it is hard to give one ion mobility value but for practical simulation purposes in Table 6.1 is the needed input parameter. Table 6.1 shows the measured ion mobility for the 4 oils that were mentioned in this thesis.

Oil ion mobility[m²/V s]

Ester 1.6e-10

Mineral 4.9e-10

isoparaffin1 4.88e-10 isoparaffin2 12.5e-10

Table 6.1: Measured ion mobility for the 4 oils

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