IDA is an industrially used diagnostic tool for dielectric measurements. Using IDA compared to the triangular method is easier as there is no need to find a suitable frequency for each oil. Compared to the triangular method which only measured resistivity, IDA can be used to measure various other dielectric parameters.
The downsides of IDA compared to the triangular method are the measuring time and the complexity of the equipment itself. In this study two oils are used to compare the two techniques, mineral and ester oil.
The mineral oil has a higher resistivity compared to the ester oil by two orders of magnitude. With higher resistivity less current is measured and as a consequence noise affects the measurement more. Shielding the equipment is therefore crucial as shown in the shielding experiments related to the triangular method, figure 8.4 and 8.3. Using mineral oil the triangular method yielded resistivity measurements that corresponded well to the IDA measurements when using a frequency of around 4.5 mHz. To estimate the precision of the triangular method the fraction of resistive and capacitive current is a good indicator if the measurement is accurate or not. With IIC
R = 1 yielding optimal accuracy [22]. Experiments with the mineral oil using a frequency of 4.5 mHz resulted in IIC
R = 1.2 as shown in figure8.8. While it is probably possible to find a better frequency, it would require fine tuning with increments of lesser than 0.5 mHz. As stated earlier in the report, the Labview script used to implement the triangular method calculates the resistivity using the formula for parallel electrodes, equation6.17.
Changing the script to take the IIC
R fraction into consideration when calculating the resistivity would only require the user to find a frequency that yielded a current response “close enough” to the theoretical current response and then the Labview script would adjust the calculations according to the IIC
R fraction.
9.2.1 Correction algorithm for the triangular method
Derivation
Consider the theoretical current response shown in figure6.3.
The capacitive current can be expressed as the current jump between t1=τ4− ∆ and t2=τ4+ ∆.
The theoretical expression for the current at these times are expressed in table6.2.
The capacitive current is thus calculated:
R should be equal to one and can be calculated by dividing equation9.3with9.4.
IC thus giving an expression for the theoretical resistivity as
ρ = τ 40r
IC IR
(9.7) Applying the same derivation to a real measurement assuming the error from the real measurement is included in the IIC
R term.
The measured resistivity can be expressed as
ρ0= τ 40r
(IC IR
)0 (9.8)
The period and permittivity are related to the dielectric properties of the oil and the measuring frequency, as such they should remain constant independant of the accuracy of the measurement. Thus the theoretical resistivity, ρ, the resistivity at optimum sensibility. Can be estimated from the measured resistivity, ρ0 and corresponding measured (IIC
R)0 fraction.
ρ = ρ0 1 (IIC
R)0 (9.9)
Implementation of algorithm
As the extraction of the capacitive and resistive current is only available for one oil, the mineral oil, the small sample size can not be overlooked. However, for this measurement. The algorithm yields a resistivity measurement that agrees with the measurement provided by IDA.
Applying this correction-equation to the results from "Triangular method at IDA frequencies", table 8.2, where IDA measured 4.2E12 Ωm and 3.6E12 Ωm at 20◦C and 27◦C respectively. The measured resistivity from the triangular method at 4.5E12 Ωm and 24◦C with an (IIC
R)0 fraction of 1.2 (shown in figure 8.8).
Comes out to 3.8E12 Ωm. This resistivity value is within the desired resistivity interval provided by the IDA measurements [3.6E12,4.2E12] Ωm.
9.2.2 Accuracy and practical problems
Accuracy comparison between the triangular method and IDA diagnostic tool
In terms of accuracy, both the triangular method and IDA show similar accuracy results in terms of standard deviation as a percentage of the measured result. With the triangular method having a deviation of 1.2%, table (8.1), and IDA 0%, table (8.3). These values are calculated when limiting the amount of significant numbers to 2. This because the error lays in the measured current more so than the corresponding calculated resistivity. This measured current depends on the area and distance between electrodes of the measurement cell, these parameters are in turn measured in the 10th of a millimeter (i.e. 1.3 mm etc).
Practical problems with the triangular method for low resistivity measurements and suggested solutions
The most significant and apparent issue of the triangular method is the frequency choice, for the mineral oil this issue is manageable but in regards to the, less resistive, ester oil. Just altering the frequency isn’t enough to get any relevant measurements, as shown in figure8.9. It is clear that by increasing the frequency, thus increasing the capacitive current and decreasing the resistive current, the measured resistivity converges to the result given by IDA. However, at frequencies above 0.5 Hz, no measurements can be made due to the program not being able to calculate any realistic data. The issue probably arises from the inherently low resistivity of the ester oil. This low resistivity gives rise to a high resistive current which would explain why reducing the resistive current by increasing the frequency causes the result to converge towards IDA’s result.
Although not tested, increasing the distance between the electrodes will increase the resistance of the oil, since there is more oil between the electrodes, and reduce the magnitude of the measured current. Which should in turn decrease the resistive current. However, this needs to be investigated. This gives rise to another issue solely for the triangular method. If an experiment is done where the resistivity is prone to have drastic changes, it could require manual changes to the distance between the electrodes of the measuring cell. Something one doesn’t have to worry about when working with the IDA diagnostic tool.