Electrical Stress Distribution in Cable Accessories when Testing at Different Frequencies

JJ (Jerry) Walker

Walmet Technologies (Pty) Ltd

Vereeniging, Republic of South Africa

jerrywalker@walmet.co.za

ADW (Dries) Wolmarans

Xamax Electrical SA (Pty) Ltd

Johannesburg, Republic of South Africa

dwol@mweb.co.za

Abstract—This paper report on an theoretical investigation

using FEA simulations on the stress distribution in medium

voltage cable joints. Three different supplies namely 50 Hz

sinusoidal, VLF 0.1 Hz sinusoidal and VLF 0.1 Hz cosine square

were evaluated. The simulation results show that phase shifts

occur in the stresses under 0.1 Hz sinusoidal voltages and that

only above 10 Hz sinusoidal no phase shifts occur. With the

application VLF 0.1 Hz cosine square the stresses are totally

different to normal operating stresses. The reason for these

differences is the influence of the volume resistivity and the

interfacial polarization during low frequencies. The

mechanisms involved to determine the stress distribution in the

joint which as a multi layer insulation system is totally different

to a cable which is a single layer insulation system. This should

be taken into account when the most appropriate test voltage

and frequency are selected for commissioning tests.

I. INTRODUCTION

High voltage testing of cables are done to verify the integrity of the accessories after installation on a new cable system and as a control measure of the jointing process on a service aged cable and its accessories following a failure. Application of a high DC voltage is the most attractive option due to the simplicity and light weight of the test equipment. It has however been widely reported that the application of a DC voltage will cause premature failures in XLPE (Cross-linked Polyethylene) insulated cables due to the formation of space charges [1]. This led to the development of VLF (very low frequency) test equipment to test the cable at a frequency of 0.1 Hz. The 0.1Hz sinusoidal technology applies a sinusoidal wave with a frequency of 0.1 Hz or a period of 10 seconds to the cable system under test. The 0.1 Hz cosine square technology generates a square wave with positive and negative DC voltages of approximately 5 seconds duration respectively. The transition between the positive and negative peaks follows a sinusoidal wave with a half period time equal to the power frequency (50 or 60 Hz). The effects of the different frequencies and wave shapes (cosine square) on XLPE insulation has been reported in a number of papers and are normally cited when motivation for a specific test condition are done. These motivations ignore the effect of the frequencies and wave shape on the accessories which is a complex multi layer insulation system. This paper investigates the stress distribution in the accessories of cables

when the different test frequencies and wave shapes are applied to the accessory. This is a theoretical (simulation) investigation making use of the Transient Electrical simulation process of a FEA (finite element analysis) software program.

II. QUICKFIELDTM

FEA PROGRAM

For this investigation the electrical stress in a typical MV (medium voltage) joint on an XLPE insulated cable was simulated using Quickfield

TM simulation software. The same

model with the same number of nodes and the same grid size was used in all the simulations. The model of the joint used was not drawn to exact scale but the dimensions used are only an approximation of the material thicknesses in a typical joint on a 95mm

2, 11 kV cable. The problem was defined as an

axis-symmetrical type and therefore only the top half of the joint in the length was drawn. The values for the electrical properties of the insulation materials used for the simulation are given in Table 1.

Table 1 Material Properties

Material Permittivity (εr) Conductivity (σ)

XLPE 2.5 1 x 10-14

Heat Shrink Insulation 2.5 1 x 10-10

Stress Control 22 1 x 10-11

The permittivity and conductivity of the materials was taken as being constant under all frequencies and electrical fields.

It is desirable that the applied test voltage shall simulate the stresses that will occur during the normal operation of the cable and to be able to make a decision on failing or passing the test, the test voltage is usually higher than the normal operating voltage [2]. The magnitude of the recommended test voltages applied during after laying tests on a new installation are normally given in the appropriate national standards for the specific country. For this investigation the recommended test voltages in South Africa was used [3]. No distinction is made between VLF sinusoidal and VLF cosine square test voltages and the peak value of the VLF sinusoidal voltage was used as the DC part of the VLF cosine square

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voltage. The voltage in all three the transient simulations (50 Hz sinusoidal, 0.1 Hz sinusoidal and 0.1 Hz cosine square) was defined as a function of time in the Quickfield

TM problem

file in order to present the stress in the stress plots as a function of time as well. The recommended test voltages are given in Table 2 with the highlight values used for this investigation.

Table 2 Test Voltage

Test waveform

Duration

(min)

6.6 kV 11 kV 22 kV 33 kV

VLF

(0.1 Hz)

60 11 19 38 57

50 Hz 60 8 13 25 38

III. SIMULATION RESULTS

From the results three points in the joint were identified to be used as the evaluation points to display the results of all the simulations. In the XLPE the measurements were done at the semi-conductive core screen cut back point. The stress in the high permittivity stress tube was measured at the XLPE / stress tube interface at the connector (ferrule). The stress in the heat shrink insulation was measured in line with the connector (ferrule) in the middle of the joint.

The simulation for the 50 Hz power frequency case was done over one complete cycle (20 milli seconds) with the voltage and stress values calculated and stored at 0.5 milli second intervals. The stress values as a function of time and the applied voltage obtained from the simulation is shown in Fig 1. The values of the stresses are displayed as absolute values (kV/mm) in relation to the applied voltage.

Power Frequency (50Hz)

-25

-20

-15

-10

-5

0

5

10

15

20

25

0 0.005 0.01 0.015 0.02

Time

kV

(Su

pp

ly)

/ k

V/m

m(S

tre

ss

)

XLPE

Stress Tube

Insulation

Supply

Figure 1 Stress plots for 50 Hz simulation

For the VLF 0.1 Hz sinusoidal case the simulation was done over one cycle of 10 seconds with the results calculated and stored in 250 milli second intervals. The simulation results are shown in Fig 2.

VLF - Sinusoidal (0.1Hz)

-30

-20

-10

0

10

20

30

0 2 4 6 8 10

Time

kV

(Su

pp

ly)

/ k

V/m

m(S

tre

ss

)

XLPE

Stress Tube

Insulation

Supply

Figure 2 Stress plots for VLF 0.1 Hz sinusoidal simulation

The VLF simulation was done over one full cycle of ten seconds with the results calculated and stored every two milli seconds. The very short calculation and storage time of the results allowed for the stress plots and the applied voltage to be displayed over the transition period of ten milli seconds from maximum positive to maximum negative values. The simulation results for the complete cycle are shown in Fig 3 and the results for only the transition period are shown in Fig 4.

VLF - Cosine Square (0.1 Hz)

-30

-20

-10

0

10

20

30

0 2 4 6 8 10

Time (Seconds)

kV

(Su

pp

ly)

- k

V/m

m(S

tre

ss

)

XLPE

Supply

Insulation

Stress Tube

Figure 3 Stress plots for VLF 0.1 Hz cosine square simulation

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VLF - Cosine Square (0.1 Hz) Transition

-30

-20

-10

0

10

20

30

4.994 4.996 4.998 5 5.002 5.004 5.006

Time

kV

(Su

pp

ly)

/ k

V/m

m(S

tre

ss

)

XLPE

Supply

Insulation

Stress Tube

Figure 4 Stress plots for VLF 0.1 Hz cosine square simulation over transition period

IV. DISCUSSION OF THE RESULTS

A joint in a cable system is a complex multi layer insulation system where the number of insulation layers varies between three (from the core screen cut back to the connector) and two layers (in the middle of the joint at the connector or ferrule). The differences of the permittivity and volume resistivity of the materials have the effect that the combination of materials (three layers and two layers) will respond differently to different frequencies.

Consider a two layer insulation model.

When a direct voltage is applied across the combination the voltage distribution (at t=0+) will be:

VCC

CV ×

+

=

21

21 (1)

and,

VCC

CV ×

+

=

21

12 (2)

When the steady state is reached at t = ∞ the voltage distribution will be:

VRR

RV ×

+

=

21

11 (3)

and,

VRR

RV ×

+

=

21

22 (4)

The charge stored in each dielectric will change during the transition period with the redistribution rate of the charges depending on a number of factors.

With the application of high frequency voltages the voltage (and consequently the stress) distribution will be a function of the permittivity of the materials and at steady state DC the voltage (and consequently the stress) distribution will

be a function of the volume resistivity of the materials. One of the processes that take place in multi layer dielectrics and that may form part of the explanation for the results is interfacial polarization, also known as space charge polarization. During the transition period from high frequency to steady state DC the relaxation time for interfacial polarization can be as large as a few seconds in heterogeneous and semi-crystalline polymers [4].

It can be seen from the stress plots for the 50 Hz simulation that no phase shifts is present between the stresses in the different materials. With the application of 50 Hz voltages the effect of the conductivity of the material in the interfacial polarization process is very small if not negligible and the stress distribution is purely a function of permittivity of the materials as in (1) and (2).

As the frequency of the supply voltage is reduced and at a certain frequency the influence of the conductivity of the materials will become more dominant and other processes like interfacial relaxation plays bigger role in the charge distribution. The results of the simulation at 0.1 Hz sinusoidal voltage shows that even with these low frequencies the charge distribution is dependant on both the permittivity and the conductivity of the materials.

The frequency for sinusoidal test voltages where no phase shift will occur is a function of the conductivity and permittivity of the materials and will not be a constant for all joints.

Fig 5 shows the stress distribution in this model for a frequency of 10 Hz.

Sinusoidal (10Hz)

-30

-20

-10

0

10

20

30

0 0.02 0.04 0.06 0.08 0.1 0.12

Time

kV

(Su

pp

ly)

/ k

V/m

m(S

tre

ss

)

XLPE

Stress Tube

Insulation

Supply

Figure 5 Stress plots for 10 Hz sinusoidal simulation

At frequencies below 10 Hz it is noticeable that phase shifts do occur whereas above 10 Hz no phase shifts occur.

With the application of the cosine square wave, at the time instant before the transition from peak positive to peak negative, the stress distribution in the materials has reached steady state values and is according to the conductivities of the materials as given in (3) and (4). With the higher frequency (50 Hz) nature of the transition it seems that the steady state

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voltage is superimposed on the applied voltage resulting in a high peak stress of very short time duration after which during the DC part of the wave the complex redistribution of charges takes place.

V. CONCLUSIONS

When high voltage commissioning tests and control tests after a repair is done on cables, it will always be done with the cables connected to the accessories and the accessories will therefore also be tested. Evaluation of the most appropriate test voltage, frequency and wave shape must not be done on the effect on the XLPE insulation only but must also consider the effect on the joints and terminations.

The ideal test frequency and wave shape should stress the cable and terminations the same as under normal operating conditions and based on the model used for the simulations only sinusoidal voltages at frequencies above 10 Hz will actually stress the cable similar to operating conditions.

The effect of the phase shifts of the stresses on the suitability of sinusoidal voltages below 10 Hz and especially at 0.1 Hz were not studied and should form part of further studies.

Claims that the application of cosine square wave voltages with a power frequency transition time, stress the cable under the same conditions as power frequency sinusoidal voltage, could not be verified with this simulation exercise. This simulation exercise actually shows that the complex charge redistribution processes distort the stresses in the joint to such an extent that it does not resemble power frequency conditions at all.

The stresses were only taken at three pre-defined areas of the joint and if the joint is modeled exactly to scale with the exact dielectric constants for the materials used different results can be obtained.

No particular attention was paid to the peak stresses during the simulations but it can be concluded that the interpretation of the voltages recommended in the standards can lead to very high stresses in the materials during VLF testing (sinusoidal and cosine square).

REFERENCES

[1] Oetjen, H, “Principles and Field Experience with 0.1 Hz VLF Method regarding the Test of Medium Voltage Distribution cables,” Conference Record of the 2004 IEEE International Symposium on Electrical Insulation, Indianapolis, In USA, 19-22 September 2004.

[2] SANS 10198-13, “The Selection, Handling and Installation of Electric Power Cables of Rating not Exceeding 33 kV. Part 13: Testing, Commissioning and Fault Location,” Edition 1, 1988

[3] Hauschield, W, “Frequency-tuned Resonant test Systems for HV On-site Testing of XLPE Cables and SF6 Insulated Apparatus,” Proceedings of the 5th International Conference on Properties and Applications of Dielectric Materials, May 25-30, 1997, Seoul, Korea.

[4] Raju, G, “Dielectrics in Electric Fields”, Marcel Dekker, 2003, ISBN: 0-8247-0864-4.

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