Voltage Distribution Along Surge Arresters Under Influence of

Temperature

CHRISTOPH HIPPLERKARSTEN LAUE

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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 High-Voltage 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

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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.

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Figure 1: Measurement circuit; VT: variable voltage source; HVT: high voltage

transformer; R1: high voltage resistor; CSG: spark-gap; MO-block: Metal-Oxide-Varistor block; CT: current transformer; VD: voltage probe.

2.2 Comparison of breakdown voltage characteristic of spark gap – 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: 𝑝 = (𝑟 + 𝑠)/𝑟, whereby 𝑟 is

radius of the sphere, 𝑠 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 𝜂

(Schwaiger factor) which requires the geometry factor to readout 𝜂 from diagrams. The

utilisation factor is in the range from 0.90, for the largest spacing, to 0.95 for the smallest

spacing.

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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.

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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 γ = material

and gas type coefficient [1].

𝑈𝑏 = 𝐵 ∙ 𝑝 ∙ 𝑠

ln (𝐴 ∙ 𝑝 ∙ 𝑠

ln(1 + 1/𝛾))

(1)

In this contribution, the parameters are chosen as follows: A = 1130 [1/(mm*bar)],

B = 27.4 [kV/(mm*bar)] and 𝛾 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 MO-

block 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) – 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

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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 – 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.

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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:

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 MO-

column, 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.

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3 Measurement of the voltage and temperature distribution

3.1 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

Figure 7: Surge arrester configuration I, black

numbers are MO-block, blue indicates temperature sensor.

Configuration II

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

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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.

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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

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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]:

by only taken stray capacitances to ground into account:

𝑢𝑥 =𝑠𝑖𝑛ℎ(𝛾𝑒∙𝑛)

𝑠𝑖𝑛ℎ(𝛾𝑒∙𝑧) (2)

by taken stray capacitances to ground and to HV potential into account:

𝑢𝑥 =1

𝐶𝐺𝑁𝐷+𝐶𝐻𝑉∙ (𝐶𝐺𝑁𝐷 ∙

𝑠𝑖𝑛ℎ(𝛾𝑑∙𝑛)

𝑠𝑖𝑛ℎ(𝛾𝑑∙𝑧)+ 𝐶𝐻𝑉 ∙ (1 −

𝑠𝑖𝑛ℎ(𝛾𝑑∙(𝑧−𝑛))

𝑠𝑖𝑛ℎ(𝛾𝑑∙𝑧))) (3)

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𝑘 = 0 … 𝑛 + 1 Nodes 𝑛 Number of MO-blocks

𝑢𝑥 =𝑈𝑛

𝑈𝐻𝑉 Ratio voltage drop of applied high voltage

𝛾𝑒 = 2 ∙ 𝑎𝑟𝑐𝑠𝑖𝑛ℎ (1

2∙ √

𝐶𝐺𝑁𝐷

𝐶𝑀𝑂𝑉) Capacitance ratio of simple linkage calculation

𝛾𝑑 = √𝐶𝐺𝑁𝐷+𝐶𝐻𝑉

𝐶𝑀𝑂𝑉 Capacitance ratio of double linkage calculation

𝐶𝐺𝑁𝐷 Capacitance to ground

𝐶𝐻𝑉 Capacitance to high voltage potential 𝐶𝑀𝑂𝑉 Capacitance MO-block 𝑈𝐻𝑉 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

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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.

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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

Figure 15: Measured and calculated voltage

distribution for surge arrester configuration II at 20°C

6 Conclusion

In this contribution, a sphere spark gap is used as one possibility to determine the non-

uniform 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-

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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, “Hochspannungstechnik: Grundlagen - Technologie - Anwendungen”,

2nd edition, Berlin, 2005.

[2] E. Kuffel, W. Zaengl, J.Kuffel, “High Voltage Engineering: Fundamentals”, 2nd edition,

Oxford, Newnes, 2000.

[3] M. Beyer, W. Boeck, K. Möller, W. Zaengl, “Hochspannungstechnik: Theoretische und

praktische Grundlagen für die Anwendung”, Berlin, Springer, 1992.

[4] A. Schwab, “Hochspannungsmesstechnik: Messgeräte und Messverfahren”, 3rd edition,

Berlin, Springer, 2011.

[5] L. Baxter, “Capacitive Sensor: Design and Applications”, New York, IEEE Press, 1997.