Contact resistance

Both the triangular method and IDA uses the measured current and voltage to calculate the resistivity. The total resistance of the setup consists not only of the oil’s resistance. Both electrodes has an, albeit small, resistance. There is also a contact resistance which refers to the resistance of the physical contact between the electrodes and the oil.

Figure 9.1: The total resistance of the measurement is a combination of multiple resistances As the equation related to how IDA calculates the resistivity is known, equation6.8.

Together with knowledge about the geometric capacitance for each cell, table8.4, with varying distance and corresponding resistivity, section8.2.7.

The total resistance can be calculated

Rtot= ρmeasured

0

C0

(9.10) with the total resistance being a combination of multiple resistances

Rtot= RElectrode,1+ RContact,1+ ROil+ RContact,2+ RElectrode,2 (9.11) The electrode resistance is negligible. A digital multi meter with an accuracy of ±0.1 Ω could not measure any resistance. Thus the resistance has to be lower than 0.1 Ω, which is negligible.

Assuming equal contact resistances yields the final expression

Rtot= 2RContact+ Roil (9.12)

Calculating the total resistance for each oil and distance gives the following results

Figure 9.2: Total resistance vs distance between electrodes for Mineral and Isoparaffin A oils

A linear approximation is done to find the resistance value at close to no distance. At this distance, the total resistance would be equal twice the contact resistance as given by equation 9.12. Since there is only a negligible amount of oil between the electrodes, the Roil term is close to zero. Worth noting is that the measurements regarding isoparaffin A only has two data points. Thus a linear approximation will always work. However, the fact that the two approximations has a similar inclination indicates that more data points would correspond to the approximation well.

The inclination of the graphs is a measurement of resistance per length of oil. A parameter which should be constant for each respective oil, independent of the electrode material, respectively. The interesting find is that the contact resistance is higher for Au than Cu. Something that would correspond to the resistivity measurements found in section 8.2.7. In said section Au always shows higher measured resistivity at equal distances between electrodes (with high contact resistance, the total resistance (and indirect resistivity) should also be higher). The measurements using the mineral oil contains one extra distance at 2.0 mm.

Because of this, it is seen that a linear behaviour exists for the Cu cell but not the Au cell. An explanation to why the mineral oil interacts with the Au cell this way is, as of the writing of this report, unknown. It is clear that the contact resistance has a big impact on the results, as the resistance is in the 10¹¹Ω range for isoparaffin A and 10¹²Ω for mineral oil using the Cu cell. Any relevant contact resistance for the mineral oil using the Au cell can not be estimated from these measurements. With the exception of the resistivity measurement in mineral oil using the Au cell. Contact resistance could be an explanation towards why different electrode material yields different resistivity measurements.

Calculated resistivity considering contact resistance

The contact resistances found in figure9.2are subtracted from the total resistance at each data point. These new resistance should be equal to the resistance of the oil as given by equation9.12. From this the resistivity is calculated using IDA’s resistivity equation6.8. Important notice is that the geometric capacitance, C0, alternates with distance as given by table8.4. The new resistivity measurements that are taking the contact resistance into account are found in figure9.3.

Figure 9.3: Resistivity measurements adjusted with contact resistance

The new resistivity is lower for both mineral oil and isoparaffin oil A. Further, the constant resistivity behaviour of each respective oil indicates that this is indeed the true resistivity of the oil. The original measuring cells that existed at ABB before this master thesis used 2.0 mm gap as a standard to do mea-surements. That cell was also built of copper, and since the new design is based of the previous. It is fair to assume that the effect of contact resistance should be similar. Taking this into account, the results show a difference in measured resistivity at 2.0 mm for mineral oil of almost a factor 2 or 3 × 10¹²Ωm. Because of this difference, the author finds it necessary to always consider the contact resistance before making any statements regarding an oil’s resistivity. Another, not recommended, approach to get a fairly accurate mea-surement is to significantly increase the distance between the electrodes. As with increasing distance, the resistance of the oil will be relatively larger compared to the contact resistance. Short distances between electrodes and no information about the contact resistance of the setup is something that must be avoided.

As the measured results would not be the true value of the transformer oil.

A mean value of the adjusted resistivity measurements are shown in table9.3. These measurements should be considered the true resistivity of the oil. The resistivity of isoparaffin oil A is taken from previous experi-ment, shown in table9.2, as that experiment was done using 2.0 mm gap. A gap of 2.0 mm was the original distance of choice when working with the previous measuring cell available at ABB. Further, the choice of 2.0 mm is relevant in the next section about the impact contact resistance has on the concentration of ions.

Oil Resistivity (2.0 mm gap) [Ωm] Resistivity (Contact resistance considered) [Ωm]

Mineral 7.5E12 4.3E12

Isoparaffin A 1.2E12 8.3E11

Table 9.3: Resistivity decreases when contact resistance is considered

Calculated concentration of ions considering contact resistance

The concentration of ions is an interesting factor used in the ion drift model, the parameter is indirectly calculated using the measured resistivity and mobility as given by equation3.22. The experiments done to measure the mobility of each of the four oils discussed in this thesis are all done at a distance of 2.0 mm between the electrodes. Mobility should be independent of distance between electrodes, however this has not been confirmed. Because of this, the resistivity of isoparaffin oil A is found from the mixture of isoparaffin A

& B experiment, the values are available in table9.3. Since the mixing experiment was done using a distance of 2.0 mm between the electrodes. The resistivity values used for the mineral oil are taken from table 9.3.

Since the concentration of ions is proportional to the inverse of the resistivity. The calculated concentration will be larger after taking the contact resistance into consideration. Table 9.4 shows the concentration of ions before and after considering the contact resistance.

Oil Concentration of ions (2.0 mm gap) [m⁻³] Concentration of ions (Contact resistance considered) [m⁻³]

Mineral 2.1E15 3.6E15

Isoparaffin A 5.5E15 7.9E15

Table 9.4: Concentration of ions increases when contact resistance is considered

The aim of this section was to find a reason as to why the electrode material and distance between them yielded different resistivity measurements. With the exception of mineral oil using the Au cell showing inconsistent behaviour. Contact resistance is a plausible explanation. The contact resistance does not affect the actual resistivity of the oil, it affects the measured resistance which in turn affects the calculated resistivity. This goes to show the importance of understanding both the measurement cell and measuring equipment of a setup.