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Voltage Distribution Along Surge Arresters Under Influence of Temperature CHRISTOPH HIPPLER KARSTEN LAUE Voltage distribution along surge arresters under influence of temperature Christoph Hippler1 Karsten Laue2 1 Technische Universität Ilmenau, Inter-departmental Center for Energy Technologies, Research Unit HighVoltage Technologies, Germany 2 TRIDELTA Meidensha GmbH, Head of Development, Germany Abstract The design of high voltage surge arresters is a challenging assignment, due to the fact, that, in praxis the voltage and temperature over a metal-oxide varistor block (MO-block) of a surge arrester may be stressed differently from MO-block to MO-block. This voltage and temperature stress depends on the installation place, distribution of MO-blocks inside the arrester or the operation voltage. Therefore, it is favourable to measure both the voltage distribution and the temperature distribution. The selection of an appropriate measurement method is limited, in order to the fact, that the chosen method shall minimal influence the voltage or temperature distribution. Thus, the aim of this contribution is to present one possibility to measure the non-linear voltage distribution by using one sphere spark gap. Simultaneously the temperature distribution is recorded during all measurements. Preliminary measurements as well as simulations are realised in order to show the feasibility of using a spark gaps in the kind of application. After all, the designed spark gap is used to show the various voltage stress over each MO-block at two different surge arrester configurations as well as different temperatures. All FEM simulations and analytical calculations are verified by voltage measurements. 1 Introduction MO-surge arrester are established as an efficient, economical and reliable form for the overvoltage protection against slow- and fast front surges in electrical transmission systems. This objective can only be achieved when the high voltage surge arrester will not be overstressed due to a large non-linear voltage- and temperature distribution. The emergence of such higher voltage or temperature stresses is different and generally upper MO-blocks are more affected. The cause of higher voltage stress are the stray capacitances to ground and to high voltage potential which determine the axial voltage distribution along the surge arrester by applying a continuously rated alternating voltage. Additionally, the particular temperature of each MO-block has also to consider as an important factor for the voltage distribution. In order to ensure a reliable operation of surge arresters, large safety factors are settled by manufactures in order to prevent the risk of overstressing. In recent years an increasing demand and by the wide application range of arresters have shown the need for a combined determination of the voltage- and temperature distribution along the MO-column. There are different possibilities available to measure the voltage distribution, but the chosen measurement method shall minimal interact with the test object. Hence, air sphere spark gaps are precise, easy to implement devices, used to measure reliable the peak voltage 1/15 above 3 kV with frequencies up to 500 Hz and the influence of the potential field distribution is low due to the small size. This work addresses the usage of one spark gap in parallel to one MO-block as a sensitive measurement method for the determination of the voltage distribution. The spark gap spacing set is permanently constant to a specific gap which keeps constant during all measurements. Then the spark is mounted to the MO-block. When the spark gap ignites, the peak voltage at the terminal of the arrester is repetitive detected and reporting. Afterwards, the spheres are cleaned up and the contemporary position of spark gap is chanced to the next MO-block. This procedure is repeated for all MO-blocks. The determination of the percentage portion of each MO-block is calculated and shows the voltage distribution along the surge arrester. The measurement results are used to indicate possible weaknesses during the design of surge arrester and utilised to verify or improve surge arrester models. These models are deployed to calculate the potential- and temperature distribution in advance (before type tests begin). The aim of this paper is to show the voltage and temperature distribution at two different surge arrester configurations under ambient and increased temperature. Both voltage distributions are calculated and measured by an applied alternating 50 Hz voltage. Further, both surge arrester configurations are built without ceramic housing to simplify the measurements. The axial temperature distribution is measured by using fibre optical temperature sensors between each MO-block. 2 Preliminary considerations - Measurement by Spark gap It is expected that the operation and the performance of the spark gap is slightly different by connecting a MO-block in parallel to the spark gap, due to the chanced surrounding and inner electrical field distribution. Hence, several preliminary measurements and calculations with and without MO-block parallel to the spark gap are realised to verify this measurement method. 2.1 Test circuit The used test circuit arrangement is shown in Figure 1. The operating voltage form is configured as a variable voltage by an AC source which it connected to the high voltage transformer and in serial to the test object. Between both, source and test object, a high voltage resistor (330 kOhm) is connected in serial to limit the short circuit current. The voltage measurement is achieved by using a conventional high voltage probe with a voltage ratio of 1000:1 and a sufficient bandwidth of 100 MHz. The current measurement in the spark-gap/MOV branch is achieved by using a current transformer with a sensitivity of 0.1Volt/Ampere and a high 3 dB cut-off frequency of 20 MHz. 2/15 Figure 1: Measurement circuit; VT: variable voltage source; HVT: high voltage transformer; R1: high voltage resistor; CSG: spark-gap; MO-block: Metal-OxideVaristor block; CT: current transformer; VD: voltage probe. 2.2 Comparison of breakdown voltage characteristic of spark gap โ with and without MO-block in parallel The diameter, the gap spacing, the atmospheric conditions, the material and the surface condition of a spark gap are decisive factors for the measurement of the breakdown voltage. Furthermore, the electrical strength of gases is also a function of the duration of voltage stress, the applied voltage form as well as the velocity of voltage rise. After several attempts, it has been found, that the standard deviation is smallest when the velocity voltage rise is constant increased with 1 kV per second in each 50 Hz period, during the tests. In Figure 2 is the preliminary measurement circuit shown. The distance (d) between the spark gap and the parallel MO-block is studied to clarify the influence of this parallel circuit. It is known, that any extraneous objects, such as walls or supporting frameworks influence the breakdown characteristic as well as the homogeneity of the electrical field of the spark gap. Hence, measurements are realised to consider if any deviation of the breakdown voltage characteristic occurs. Tests on various spark gap spacing distances (s), with and without MO-block in parallel, have been carried out to determine the breakdown voltage characteristic. Figure 2A depicts the spark gap with the insulating support (1) which is used to adjust the spacing between the spark gap for the measurements without MO-block. In Figure 2B the MO-block and spark gap are mounted between two rounded brass electrodes (2, 3) and the parameter (d and s) are varied during the test procedure. The diameter of the brass spheres are 12 mm and the surface of the spheres are polished and free from any trace of varnish or grease before every test starts. The breakdown-voltage tests are realised with at least 15 alternating voltage ignitions for each distance (parameter d and s). All measurements are made during a period when the atmospheric conditions (temperature, pressure, and humidity) in the high voltage laboratory are not constant. Hence, the corrections factors for temperature, pressure and humidity are applied. Two quantities are used to characterise the non-uniform electrical field between the spark gap. First, the geometry factor (p) of the spark gap which results from the ratio: ๐ = (๐ + ๐ )/๐, whereby ๐ is radius of the sphere, ๐ the spark gap spacing. It results that p is in the range from 1.06 to 1.16 for a spacing (s) from 0.6 mm to 1.6 mm. The second quantity is the utilisation factor ๐ (Schwaiger factor) which requires the geometry factor to readout ๐ from diagrams. The utilisation factor is in the range from 0.90, for the largest spacing, to 0.95 for the smallest spacing. 3/15 Figure 2: Schematic representation of spark-gap, A: spark gap between insulating support (1), B: spark-gap between two brass electrodes (2, 3) in parallel to MO-block. The results of the breakdown voltage characteristic of the air spark gap for configuration B (shown in Figure 2B) by variation distance parameter d and constant spacing s = 1 mm is shown in Figure 3. For this measurement, the gap (s) between the spark gap is held constant at 1 mm and the parameter (d) between the shell surface of MO-block and the vertical axis of the spark gap is varied between 13 mm to 52 mm. As can be seen form Figure 3, that the breakdown voltage characteristic is approximately constant for all four distances with around 5.3 kV. The standard deviation is further illustrated in Figure 3 - shows that the smallest standard deviation can be reached by 13 mm and increases slightly with the distance (d). Nevertheless, the parameter (d) with a value of 39 mm is laid down for the next measurements due to the small difference between the breakdown voltages and can be easily implemented in a construction. The sphere gap spacing is adjustable but the brass electrodes (2, 3) permanent fixed through the insulating support. The designed and mounted spark gap is shown in Figure 5. Figure 3: Breakdown voltage as function of distance between spark gap axis and MO-block, constant spark gap spacing s = 1 mm, number standard deviation above curve, mean value below curve. 4/15 Figure 4 shows the results of the measured breakdown voltage characteristic of the spark gap as a function of the gap spacing with and without MO-block as well as the calculated curve. For the calculation of the breakdown voltage curve, Ub is given in equation 1 where A, B = experimentally determined gas constant, p = pressure, s = gap spacing and ฮณ = material and gas type coefficient [1]. ๐๐ = ๐ตโ๐โ๐ ๐ดโ๐โ๐ ln ( ) ln(1 + 1/๐พ) (1) In this contribution, the parameters are chosen as follows: A = 1130 [1/(mm*bar)], B = 27.4 [kV/(mm*bar)] and ๐พ for copper with 0.025. Further, the calculated breakdown voltages are converted to the case normal conditions for a better comparability. As expected, the measured breakdown voltage values are proportional to the gap spacing for both configurations (with and without MO-block in parallel). Furthermore, Figure 4 illustrates also, that the breakdown voltages of spark gap in parallel with the MO-block is higher for small gap spacing distances (< 1.2 mm) and the curves get closer for higher gap spacing distances (> 1.4 mm). The standard deviation is also illustrated in Figure 4 and shows that the standard deviation for the spark gap with MO-block is slightly higher than without the MOblock in parallel. Both, the variation between the breakdown curves and the standard deviations can be attributed to the change in the electrical field distribution and by measurement uncertainties. Figure 4: Breakdown voltage characteristic of spark gap (SG) โ with (red curve) and without (blue curve) MO-block in parallel and calculated breakdown voltage curve (black) for d = 39 mm. 2.3 Calculation electrical field distribution of Spark gap with and without in parallel to MO-blocks A column of five MO-blocks with and without mounted spark gap is numerically designed and the electrical field is calculated by using COMSOL finite element package for the time depending analysing. The permittivity is provided as a constant value and the conductivity of the metal-oxide is assumed to be non-linear curve. The material parameters are known from 5/15 measurements. The illustration of the named MO-column with spark gap is illustrated in Figure 5. Moreover, the figure shows the geometry of the MO-block with a height of 45 mm and diameter of 64 mm, also the varied parameter d and s are shown. The spark gap is mounted at MO-block Nr. 3 (middle) and spark gap position is not modified for all calculation. The only variable that is changed during the FEM calculation is the parameter d. The operation high voltage is selected by a peak voltage of 25 kV with a frequency of 50 Hz, which was adopted that the maximum voltage between both spheres is roughly 5 kVpeak before the ignition starts. This is chosen, because to be become assured, that, the electric field stress is under the self-breakdown voltage of the spark gap. Figure 5: Left side: MO-block column with mounted spark gap, HV: high voltage potential, GND: ground potential; right side: selected area show electrical field distribution (normalized to 0.5 kV/mm). The distribution of the electric potential in and surrounding the MO-column can be found from Maxwell´s equations based on the non-linear material parameter โ conductivity and the assumed constant permittivity. In all calculations, the non-linear voltage depending conductivity is stored as a lock-up table in COMSOL. The ambient medium is air with open boundaries, set as Neumann criterion. 6/15 To get an exact description how the potential or rather the electrical field strength is changed through the MO-column by variation of spark gap arrangement, the following distinctions are made: ๏ท ๏ท ๏ท without spark gap (referred as line 1) with spark gap and parameter d set by 13 mm (referred as line 2) with spark gap and parameter d set by 39 mm (referred as line 3) The results are shown in Figure 6 for all three lines which represent the electrical field strength along the vertical axis of the MO-column, see also the yellow line in Figure 5 left side. As expected, it was found that the difference of the electrical field strength through the MO-column is negligible small for all three lines, as it shown in the magnified Figure 6. The figure shows small negligible variations between each line. However, the electrical field distribution is more homogeneous by mounting a spark gap. One of the observations derived from the computational results is that the electrical field distribution inside the MO-column is, overall, not effected by the spark gap as well as distance between the MO-block and the spark gap. The result of the field distribution by using a 2D cut-surface for the case with mounted spark gap is shown in Figure 5, right side. The maximum electrical field strength is normalized to 0.5 kV/mm. Figure 6: Electrical field strength inside the MOcolumn, peak voltage 25 kV. As an intermediate result, the measurements and FEM-calculations show that it is possible to use a sphere spark gap for the measurement of the voltage distribution under consideration of the correction factors. The measurement errors by using a spark gap are very small and the chosen distance between the MO-block and the spark gap has no further impact of the breakdown voltage characteristic or the electrical field distribution inside the MO-block. 7/15 3 3.1 Measurement of the voltage and temperature distribution Experimental arrangement The experimental arrangement of the surge arrester configuration I and II is shown in Figure 7 and Figure 8. Both surge arresters are built up of 22 MO-block, without porcelain insulator, between each block an aluminium sheet is inserted and the arrester is installed on a pedestal of 0.5 m height. The blue arrows indicate the temperature measuring points which are positioned in holes into the aluminium sheet or - spacer. Configuration I Configuration II Figure 7: Surge arrester configuration I, black numbers are MO-block, blue indicates temperature sensor. Figure 8: Surge arrester configuration II, black numbers are MO-block, blue indicates temperature sensor. 3.2 Test procedure The measurement circuit is shown in Figure 9. The single phase alternating voltage source contains of an isolated transformer, a variable voltage and frequency source to set the voltage and frequency at the high voltage transformer. The measurement coil at the high voltage transformer is used to measure the high voltage potential at the surge arrester terminal (VHS). The current measurement in the surge arrester branch for the detection of the 8/15 impulse is achieved by using a current transformer (same CT as above mentioned). The connection of a high voltage resistor in serial to limit the short circuit current is not necessary, due to the high resistance of the remaining MO-blocks. In this test procedure, the spark gap spacing is always set to 1 mm to fulfil the breakdown voltage of around 5 kVpeak which is a bit lower than the continuous operating voltage of the used MO-block. This implies that the measurement is performed in the range of leakage current when the resistive current component is very small compared to the capacitive current (dissipation factor < 0.1). Figure 9: Measurement circuit; VT: variable voltage source; HVT: high voltage transformer; MC: measurement coil; SG: spark-gap; MO-block: Metal-Oxide-Varistor block; A: current transformer; DSO: digital stored oscilloscope. Measurement process, first, the spark gap including the provided isolated support is mounted in the above presented measurement circuit (Figure 1 and Figure 2B) to determine the contemporary voltage breakdown of the spark gap. Then, the spark gap is connected to the surge arrester at the first position, compare with Figure 9 - SG1. Then, the voltage is continuously increased until the spark gap ignites, the voltage is decreased until the sparks extinguish, after 10 seconds the voltage is again increased until the spark ignites between the gaps. This process is repeated with at least 15 ignitions. The voltage at the surge arrester terminal (VHS), the contemporary determined breakdown voltage and the current is reported for all measurements, independently from the polarity of the terminal voltage. These measurements are summarized to a series. Afterwards, the average voltage value is calculated and multiplied with the correction factor (due to different atmospheric conditions). Simultaneously to the measurement of the voltage distribution, the temperature distribution is reported. There are four optical temperature sensors in use to measure the temperature between the MO-blocks with a measurement error of 0.5 K. The ambition is to record all temperatures, thereby one sensor is permanent mounted at the warmest position, the temperature is maintained constant, whereas the other sensors are located near the spark gap. 9/15 3.3 Test results When an air spark gap is connected in parallel with one MO-block from the column of the surge arrester, the voltage distribution can be measured at different temperatures. The results of the test measurements are shown in Figure 10 and Figure 11 for configuration I and II at a temperature of 20°C and 60°C. The number of MO-blocks is specified, by which the y-axis starts referencing the bottom MO-block. The voltage stress is expressed at a ratio of measured voltage drop to mean voltage stress and is hold onto the x-axis. Both figures show that bottom MO-blocks are exposed to a lower voltage than the head MO-blocks and the voltage stress increases almost uniformly. There is a small measureable change in the voltage distribution between 20°C and 60°C for both configurations. However, the biggest variations are shown for the head, from MO-block number 14 of both configurations. For case the surge arrester is warmed, the voltage distribution intends to a uniform distribution which can be explained by an increase of the leakage current whereas the capacitive currents (based on the stray capacitances) remains constant. Figure 10: Measurement results of voltage distribution by 20°C and 60°C for surge arrester configuration I Figure 11: Measurement results of voltage distribution by 20°C and 60°C for surge arrester configuration II Completely in contrast is the temperature distribution of both configurations which is depicted in Figure 12. As expected, it was found that the temperature hot spots are located in the upper third section of both configurations and temperature of the top MO-block is lower due to the cooling of the metal flange contact. The biggest deviation between both temperature curves is, that, configuration II consist of long metal tube in the middle of the surge arrester which leads to active cooling of the adjacent MO-blocks. It is likewise become clear that two smaller metal tubes (as provided in configuration I) lead not to the same effect as a long metal tube. Additionally, the temperature along configuration I is almost evenly distributed only the first six and upper three MO-blocks are cooler. It must be mentioned that the 10/15 porcelain housing of the surge arrester did not exist and thus the head radiation as well as the head conduction are changed. Figure 12: Results of temperature measurement for configuration I (green curve) and configuration II (orange curve) 4 Calculation of the voltage distribution The alternating voltage distribution of high voltage surge arrester at a voltage level under the continuous voltage is not equal because of the capacitive characteristic of the MO-blocks and the stray capacitances effect in the direction to the ground as well as to the high voltage potential. This means, the non-uniform voltage distribution depends on height of the arrester and also on the supply of the grading ring. However, this non-uniform voltage distribution of the arrester can be calculated by using analytical approaches as well as numerical tools like the finite element method (FEM). The analytical approaches are suitable as an easy and initial calculation of the voltage distribution, provided that the arrangement of surge arrester is two dimensional and has a cylindrical symmetry shape. Thereby, to calculate the voltage drop ux analytical equations (2) can be used [3, 4]: ๏ฎ by only taken stray capacitances to ground into account: ๐ข๐ฅ = ๏ฎ ๐ ๐๐โ(๐พ๐ โ๐) ๐ ๐๐โ(๐พ๐ โ๐ง) (2) by taken stray capacitances to ground and to HV potential into account: 1 ๐บ๐๐ท +๐ถ๐ป๐ ๐ข๐ฅ = ๐ถ ๐ ๐๐โ(๐พ โ๐) โ (๐ถ๐บ๐๐ท โ ๐ ๐๐โ(๐พ๐ โ๐ง) + ๐ถ๐ป๐ โ (1 โ ๐ ๐ ๐๐โ(๐พ๐ โ(๐งโ๐)) ๐ ๐๐โ(๐พ๐ โ๐ง) )) (3) 11/15 ๐ = 0โฆ๐ + 1 Nodes ๐ Number of MO-blocks ๐ ๐ข๐ฅ = ๐ ๐ Ratio voltage drop of applied high voltage ๐ป๐ 1 ๐ถ ๐พ๐ = 2 โ ๐๐๐๐ ๐๐โ (2 โ โ๐ถ๐บ๐๐ท ) ๐๐๐ ๐ถ๐บ๐๐ท +๐ถ๐ป๐ ๐ถ๐๐๐ Capacitance ratio of simple linkage calculation ๐พ๐ = โ Capacitance ratio of double linkage calculation ๐ถ๐บ๐๐ท Capacitance to ground ๐ถ๐ป๐ Capacitance to high voltage potential ๐ถ๐๐๐ Capacitance MO-block ๐๐ป๐ Applied high voltage The voltage distribution of surge arresters by using the mentioned equations is deeply depending on the stray capacitances. The first step is the determination of the stray capacitance to ground and the following assumptions are made: Coaxial cylinders (source [5]): (4) Surge arrester configuration I Surge arrester configuration II CGND 1.8 pF 6.4 pF CHV 0.18 pF 0.64 pF Table 1: Calculated stray capacitances. In general, the analytical determination of the stray capacitances assumes that the electrical field between two different potentials is homogenously which can be made, as first approximation, for stray capacitances to ground. But, for the calculation of the stray capacitances in the direction to high voltage potential it is advisable to divide the volume in several smaller parts, due to the numerousness of calculation a numerical calculation is recommended. In real applications, the stray capacitances to ground are generally bigger than stray capacitances to high voltage potential [3]. It is assumed, that the stray capacitances to ground are 10 times larger than the capacitances in direction of high voltage potential. The results of the all non-uniform capacitive calculated voltage distribution are shown in Figure 13. Additionally, the axial voltage distribution of both configurations is numerically solved by using a time depending solver for the 2D model which reflects the non-linear current-voltage 12/15 curve of the MO-block. The curves are illustrated in Figure 13-A and -B as a green trace and compared in Figure 13-C. A) B) C) Figure 13: A) calculated axial voltage distribution for configuration I; B) calculated axial voltage distribution for configuration II; C) FEM capacitive-resistive calculation of axial voltage distribution for configuration I and II; FEM: Finite Element Method; DLC: double linkage capacitance; SLC: single linkage capacitance ; As expected, the voltage drop at higher MO-blocks is greater than the voltage drop for the lower position MO-blocks and consequently higher MO-blocks are more stressed than the other MO-blocks. The configuration of the active part of the surge arrester has a significant influence of the voltage distribution, due to the changed stray capacitances. Both calculations by taking the non-linear resistive effect of the MO-block into account provides a clearly information about the distribution, as can be shown in Figure 13-C. As a result, it is evident that the effect of a long metal tube in the middle of the active part of the surge arrester leads to a significant higher stress for the MO-blocks at the head, compare FEM I and FEM II. 13/15 5 Comparison between measurement and calculation Figure 14 and Figure 15 show the calculated and the measured voltage distribution for surge arrester configuration I and II at a temperature of 20°C. Both calculated curves are the result of the numerical calculation (FEM). The variation between the measurement and calculation is within the inaccuracy of the standard deviation of the spark gap, the adopted boundary conditions in the simulation as well as the small deviation of each voltage current curve of the MO-block. As can be seen, that the non-linear resistive capacitive simulation give a good approximation about the voltage distribution. In Figure 14, U/Umean is smaller than one over a wide range until MO-block 14/15 for the measurements as well as for the calculations. In comparison to configuration I, configuration II leads overall to a higher voltage stress from MO-block number 12/13 upwards. Nevertheless, the highest voltage stress occurs, verified by simulation and measurements, at MO-block 22 for the surge arrester configuration I. Figure 14: Measured and calculated voltage distribution for surge arrester configuration I at 20°C 6 Figure 15: Measured and calculated voltage distribution for surge arrester configuration II at 20°C Conclusion In this contribution, a sphere spark gap is used as one possibility to determine the nonuniform voltage distribution along two surge arrester configurations. Preliminary experimental tests and simulations have shown that the breakdown voltage characteristic of the spark gap that is arranged in parallel with a MO-block is almost identical to an arrangement with only one spark gap. Hence, it can be concluded, that the spark gap is a suitable method for the measurement of the voltage distribution as it has a minimum influence on the electrical field strength between the MO-block and the sphere gaps. The voltage and temperature distribution measurements have shown that the voltage and temperature stress for each MO- 14/15 block is different. For both configurations, the voltage drop over the upper MO-blocks is always higher than the rest of the MO-column, even though, the upper MO-blocks show not the highest temperature. The temperature distribution shows a strong dependence of the position and the size of the metal tubes. The greatest cooling could be achieved with configuration II which also shows a lower average temperature than configuration I. It should be pointed out, that during all measurements the porcelain housing was not assembled. Further, the voltage distribution is numerical calculated with the help of 2D surge arrester models. Several 2D numerical FEM models have been created to simulate the voltage distribution by taking into account the permittivity and the non-linear conductivity. The simulation results show a good agreement with the measurements and verify the assumed parameters of the surge arrester model. The measurements have shown that the voltage distribution depends, next to the stray capacitances, also on the temperature distribution of the surge arrester column. As a future prospect, the realised simulation models will be supplemented by a coupled electrical-thermal calculation in order to calculate the voltage distribution and temperature distribution in advance (before type tests begin). 7 Acknowledgments This work was mainly supported by TRIDELTA Meidensha GmbH. Further, I am grateful for the support of the graduating school PhotoGrad. 8 References [1] A. Küchler, โHochspannungstechnik: Grundlagen - Technologie - Anwendungenโ, 2nd edition, Berlin, 2005. [2] E. Kuffel, W. Zaengl, J.Kuffel, โHigh Voltage Engineering: Fundamentalsโ, 2nd edition, Oxford, Newnes, 2000. [3] M. Beyer, W. Boeck, K. Möller, W. Zaengl, โHochspannungstechnik: Theoretische und praktische Grundlagen für die Anwendungโ, Berlin, Springer, 1992. [4] A. Schwab, โHochspannungsmesstechnik: Messgeräte und Messverfahrenโ, 3rd edition, Berlin, Springer, 2011. [5] L. Baxter, โCapacitive Sensor: Design and Applicationsโ, New York, IEEE Press, 1997. 15/15