The influence of connection and grounding technique on the repeatability of FRA-results

S. Tenbohlen1, R. Wimmer1*, K. Feser1, A. Kraetge2, M. Krüger2 and J. Christian3 1 University of Stuttgart, IEH, Pfaffenwaldring 47, 70569 Stuttgart, Germany

2OMICRON electronics GmbH, Oberes Ried 1, 6833 Klaus, Austria 3Siemens AG, PTD T TI, Katzwangerstr. 150, 90461 Nuremberg, Germany

*Email: rene.wimmer@ieh.uni-stuttgart.de

Abstract: The frequency response analysis (FRA) is a well-established method used for assessment of the mechanical and electrical conditions of power transformer windings. The evaluation of the winding condition is done by comparison between an actual FRA and a reference FRA, which are carried out previously. A deviation between both FRA curves can indicate a change of the winding condition of the tested transformer. According to the standard of knowledge, the connections between measuring device and transformer terminals, as well as the grounding technique are of main importance for a good repeatability. Additionally, a power transformer is a large construction that needs long cables and grounding lines for the signal transmission. Against this background, it is clear, that the geometric arrangement of the measuring setup may not be the same as it was at the reference measurement and this change can have an influence on FRA results. Therefore, an excellent repeatability of the measurements is needed in order to prevent any problematic to distinguish between measurement failures and real damage within the transformer.

1 INTRODUCTION

High currents resulting from short circuits lead to high mechanical forces in transformer windings and can thus cause winding deformations and displacements. Although these winding damages do not necessarily lead to an immediate transformer failure, they will increase the long-term risk of failure due to previous damages. This is why it is important to determine the degree of these previous damages by measurement in order to enable suitable measures. One suitable diagnosis method is the measurement of the transfer function (TF), from that the FRA results. In case of the FRA, the condition of the winding is determined by comparing the actual frequency response of a winding with a reference curve ideally measured at the factory when the transformer is new. However, experiments using an experimental winding have shown that the changes of the frequency curve caused by a winding deformation can be rather small [2]. Therefore, it is very important that the measurement equipment does not influence the frequency response and that the reproducibility of the FRA measurement is high.

2 THE THEORY OF TWO-PORTS

A transformer can be considered as a network of resistances, self-inductances, ground capacitances, coupling inductances and series capacitances. The varying behavior of the magnetic flux within the iron core leads to a subdivision of the frequency range [1], [3], [4]: § Frequency range 1: f < 10 kHz

In case of low frequencies, the magnetic lines of force enter the limb vertically. With increasing frequency, the core permeability and the developing eddy currents cause a displacement of the magnetic field from the centre of the core [5]. In this frequency range, the non-linear effect of magnetic saturation resulting from too high magnetization can occur.

§ Frequency range 2: f > 10 kHz The magnetic lines of force are nearly completely displaced from the inside core and the iron core does no longer lead any magnetic flux. Therefore, the non-linear core effects are no longer of importance for this frequency range.

Due to this behavior, it is possible to consider a transformer for frequencies above 10 kHz as a passive, causal, time-invariant and linear system and to use the theoretic fundamentals of the two-port theory. It is possible to calculate the corresponding FRA from an excitation signal X(jw) and a system response Y(jw) by calculating the quotient (1).

( ) ( )( )ω

ωω

jXjY

jTF = (1)

Due to the multi-pole arrangement of a transformer, a single-phase excitation signal causes several system responses. Generally, all measurable quantities are suitable for the response signal. According to fig. 1, a separate transfer function can be defined for each response signal.

Transform er

comlex RLCM-Netzwerk

Uout,n (jω) Iout,n (jω)

Iout,2 (jω) Iout,1 (jω)

Uout,2 (j ω)

Uout,1 (jω) . . . Uin (jω)

Iin (jω)

Fig. 1: Description of a transformer as a two-port network

XV International Symposium on High Voltage Engineeringth

University of Ljubljana, Elektroinštitut Milan Vidmar, Ljubljana, Slovenia, August 27-31, 2007 T7-522.pdf

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According to the theory, each of the transfer functions according (2) – (4) represents a system transfer function and is independent of the input signal Uin with reference to time. Consequently, the transfer function is exclusively determined by the electric network of the transformer [6].

( ) ( )( )ω

ωω

jUjI

jTFin

in= (2)

( ) ( )( )ω

ωω

jUjI

jTFin

nout ,= (3)

( ) ( )( )ω

ωω

jUjU

jTFin

nout ,= (4)

3 INFLUENCING FACTORS FOR FRA

FRA is a comparing method and therefore always has to be related to a reference curve. Three types of comparisons are available for FRA: § Time based comparison: comparison against a

reference curve (fingerprint) measured earlier. § Construction based comparison: comparing the

limbs against each other. § Type based comparison: comparison against

another transformer of the same type. A precondition for all three methods is that the

measurements are as far as possible independent of the measurement setup. This particularly applies to the time-dependent comparison, since there may be years between the individual measurements. Therefore, the grounding concept, the arrangement of the cables and the connection technique are of particular importance.

Due to the large dimensions of power transformers, it is necessary to bridge long distances between the transformer terminals and the measuring device. This is normally done using up to 30 m long coaxial cables for signal transmission. However, over such long distances, it is impossible to arrange the coaxial cables between the transformer and the measuring device for follow-up measurements exactly in the same way as for the initial measurement. The requirement resulting from this fact is that FRA measurement has to be independent of the arrangement of the cables.

3.1 Connection and cable technique

One requirement to the connection technique is that the user should be able to install the cables as fast and easy as possible. Furthermore, the user should not use any unshielded cables in order to avoid electromagnetic coupling of interferences to the signal lines, since this would make FRA measurement dependent on the arrangement of the cables.

The following signal line connection technique is used to determine the FRA of a 220 MVA autotransformer for different cable arrangements: Starting from a coaxial cable splitter, the inner

conductor and the shield conductor of a coaxial cable are guided as separate unshielded lines. The line connected to the inner conductor of the coaxial cable leads to the transformer terminal and the other line that is connected to the shield of the coaxial cable is connected to the transformer's tank. The electric connections to the transformer terminal and the tank are performed using clips. The influence of the cables arrangement is investigated using two cases: 1) The cables hang below the bushing as shown in

fig. 2. 2) The cables hang below the bushing as shown for

case 1), but the positions of the connection points at the tank and the connection terminal are changed.

unshielded cable to connection clamp

unshielded cable to ground

coaxial cable to measuring device coaxial cable

splitter

Tran

sfor

mer

Fig. 2: Connection technology with unshielded lines starting from the coaxial cable splitter

As shown in Fig. 3, the resonant frequency varies around 470 Hz depending on the cable arrangement. According to that, the use of partly unshielded cables provides freedom that obviously can lead to measurement errors and consequent misinterpretation. This is why shielded signal cables should be used ideally up to the transformer terminal in order to minimize the dependency from the cable arrangement and to increase the reproducibility.

0.0 frequency f

|TF U

2/U

1(f)|

FRA with unshielded lines FRA of a repeated measurement with unshielded lines and a reconnection to tran sformer

dB

0.2

0

0.4

-10

0.6

-20

0.8

-30

1.0 MHz 1.4

-40 -50 -60

20

Fig. 3: Influence of unshielded signal cables to the FRA depending on the cable arrangement

Fig. 4 shows suitable connection adapters for the transformer terminals that allow the connection of

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coaxial cables. However, it is also possible to use other connection methods, e.g. clips.

Fig. 4: Different transformer terminal adapter

3.2 The grounding concept

Former investigations showed that no significant differences of the FRA curves can be detected depending on the cables arrangement, independent of whether the cable shield is grounded on both line ends or only on the line end at the test object [2]. However, due to the existing electromagnetic fields in substations and for protection of the measuring device, you should not do without the additional grounding at the measuring device and thus provide grounding of the coaxial cable shields on both line ends.

To enable the grounding of the coaxial cable shields at the transformer, an additional line from the transformer tank to the transformer terminal adapter is required. This line can be generally of any suitable type as long as it does not influence the reproducibility of the FRA results. However, it has to be observed that in substations external interferences have to be taken into account that can influence FRA measurement.

3.2.1 The dependence of the geometrical signal line arrangement with different ground conductor

A first examination investigates the dependency of FRA results from the arrangement of the signal lines and from the grounding lines. The measurement setup is again as for normal FRA measurements. After a first measurement has been performed with the corresponding types of grounding, the measurement lines are disconnected. Then, the measurement equipment is placed to another location and the measurement lines are arranged again and reconnected. Following, another FRA measurement is performed with the corresponding types of grounding connection and compared with the first FRA measurement.

Fig. 5 shows that grounding with a normal wire is worse than with a ground strap. Starting from approx. 820 kHz, the FRA measurement with cable shield grounding by a normal wire delivers changed attenuation compared to the previous cable arrangement. The attenuation difference increases with rising frequency. At a frequency of approx. 1.6 MHz, there is also a displacement of the resonant frequency.

With the cable shield grounding by a ground strap, these effects do not occur up to a frequency of 2 MHz. Changed attenuation only occurs for higher frequencies (fig. 6). However, this frequency range is not of importance for the assessment of the winding condition, since the resonance points of power transformer windings are in the frequency range below 1 MHz [7].

0.0 frequency f

|TF

U2/

U1(

f)|

Reference FRA FRA of a repeated m easurement with new arranged line position dB

0.5

0

1.0 1.5

-20

2.0

-30

MHz 3.0

-40

-50

Fig. 5: FRA measurements, cable shield grounding by wire

0.0 frequency f

|TF

U2/

U1(

f)|

Reference FRA FRA of a repeated m easurement with n ew arranged line position

dB

0.5

0

1.0 1.5

-20

2.0

-30

MHz 3.0

-40

-50

Fig. 6: FRA measurements, cable shield grounding by ground strap

3.2.2 The interference resistance of ground conductor

Additionally, the effects of the interference sensitivity of a normal wire and a ground strap to the FRA shall be determined by experiment. The test setup is a normal FRA measurement setup with the corresponding grounding lines. A loop of one winding emitting a sinusoidal interference signal of 80 kHz is placed under the bushing of a 333 MVA autotransformer (fig. 7). The 80 kHz signal is generated by a signal generator and amplified accordingly by an audio amplifier. The current measured at the amplifier output is 1.8 A at a total loop length of 12 m and a conductor cross section of 2.5 mm².

Fig. 8 clearly shows the additional resonant frequencies in the FRA curve caused by the interference signal in case of grounding with a normal wire. The maximum fluctuation range is 7 dB. Since the used frequency of 80 kHz is far above the nominal frequency range of the audio amplifier, the signal distortion caused by the amplifier is such high that the measured FRA does not only show the 80 kHz interference but also interference at 78 kHz.

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Grounding of the cable shield with a 2.5 mm² wire

Grounding of the cable shield with ground strap

Fig. 7: Different transformer terminal adapter

0.0 frequency f

|TF U

2/U

1(f)|

Wire as ground connection for the cable shield Ground strap as ground connection for the cable shield

dB

10

0

20 30

-40

40

-50

kHz 100

-60

-70 50 60 70 80

-30

-20

7 dB

1 dB

Fig. 8: Interference sensitivity of FRA for grounding with normal wire and with ground strap

In case of grounding with a ground strap, the interference signal is of course also clearly visible on the FRA curve but with a maximum fluctuation range of only 1 dB. The conclusion from this is that the interference sensitivity of a ground strap is much less than of a normal grounding wire. This effect can be explained with the self-inductance of the grounding line. Ground straps made of thin single wires have a very large surface and, depending on the frequency, provide considerably lower impedance than normal wires of comparable size. The skin effect probably contributes to the higher interference immunity of ground straps, since a frequency of 80 kHz already causes a considerable current displacement from the centre and a resulting skin depth of the interference signal of only 0.24 mm for copper materials to 0.31 mm for aluminum materials. Due to the characteristics mentioned above, ground straps provide better conductivity for signals of higher frequencies than normal cables can do. Interferences drain off to ground with lower resistance.

3.2.3 The dependence of the FRA because of different types and geometrical arrangement of ground straps

The goal of a standardized measurement setup is to give the user as little freedom as possible in order to avoid any deterioration of the reproducibility of FRA measurements. One kind of freedom is the selection of

the ground strap since these bands are available in different versions, with different dimensions and made of different materials. The following investigation compares two types of grounding bands with the following configurations. 1) Aluminum ground strap

22 x 2 mm (width x thickness), pulled tightly. 2) Copper ground strap

35 x 3 mm (width x thickness), pulled tightly. Fig. 9 shows that different types of ground strap

have only a marginally influence on FRA. The resonance frequency at 470 MHz shifts only 8 kHz.

0.0 frequency f

|TF U

2/U

1(f)|

FRA measured with an aluminum ground strap FRA measured with a copper ground strap

dB

0.2

0

0.4

-10

0.6

-20

0.8

-30

1.0 MHz 1.4

-40 -50 -60

20

Fig. 9: Influence of the type of ground straps to the FRA

However no general statement can be made on the basis of this investigation. Inductance and resistance of the ground strap depend also on its geometrical parameters. Therefore the effective cross section is regarded in the following. In comparison to the aluminum ground strap the dimension of the copper ground strap is larger, but it has the smaller skin depth because of the skin effect. That leads to an effective cross section Aeff of 7.19mm² for copper and 5.89mm² for the aluminum ground strap at 500 kHz. Thereby Aeff is computed as fallows:

( )[ ]δδδ ⋅⋅−+⋅⋅= 22 wlAeff (5)

l: length (see fig. 10) w: width (see fig. 10) δ: skin depth according (6)

σµµπδ

⋅⋅⋅⋅=

rf 0

1 (6)

f: frequency µ0: permeability of free space µr: relative permeability σ: specific conductance Fig. 10 shows the ideal representation of a ground

strap with corresponding skin depth and fig. 11 shows the frequency dependent effective cross section of the following ground straps: 1. Aluminum ground strap with 22 x 2 mm 2. Copper ground strap with 35 x 3 mm 3. Aluminum ground strap with 35 x 3 mm 4. Copper ground strap with 22 x 2 mm

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δ

δ

δ δ

length l

wid

th w

0.0 frequency f

effe

ctiv

e cr

oss

sect

ion

Aef

f

mm²

0.2

30

0.4 0.6

20

1.0 MH z

10

0

50δ of a luminum gr ound strap w ith 2 2 x 2 mm δ of copper ground strap with 35 x 3 mm δ of a luminum gr ound strap w ith 3 5 x 3 mm δ of copper ground strap with 22 x 2 mm

Fig. 10: Profile of an ideal representation of a ground strap with adequate skin depth

Fig. 11: frequency dependent effective cross section using different materials and dimension as ground strap

In fig. 11 is to see, that the effective cross section depends particularly in larger dimensions in a non negligible degree also on ground strap material. Additionally it is visible that the difference of the effective cross section of the investigated ground straps is lower than by ground straps consisting of different materials but same dimensions. Different cross sections lead to different resistance and inductance of the ground strap. Especial the inductance depends practically only on the effective geometrical parameters. Therefore the same ground strap which was used for the reference FRA measurements should be used for the FRA follow-up examination to have reproducibility as high as possible.

Another kind of freedom is the geometrical arrangement of the ground strap. The following scenario is conceivable § the ground strap is pulled tightly along the bushing

for the reference FRA measurement (fig. 12) § the ground strap sags along the bushing for the

repeated FRA measurement (fig. 12)

Ground strap pulled tightly along the bushing

Ground strap sags along the bushing

Fig. 12: Different geometrical arrangement of the ground strap

Fig. 13 shows a displacement of the 570 kHz resonant frequency by 20 kHz. The explanation for this is that not only electrical network of the transformer, but also the electrical network of the measurement setup is recorded with the FRA. In comparison to a pulled tightly ground strap a sagged ground strap has a higher longitudinal inductance, a higher resistance and another coupling capacitance which exist between the bushing and the ground strap.

0.0 frequency f

|TF U

2/U

1(f)|

FRA 1 (ground strap pulled tightly) FRA 2 (ground strap sags)

dB

0.2

0

0.4

-10

0.6

-20

0.8

-30

1.0 MHz 1.4

-40 -50 -60

20

Fig. 13: Influence to FRA with different geometrical arrangement of the ground strap

3.3 Further influencing quantities

Apart from the grounding concept and the connection technique there are several other factors that can influence the FRA. For reasons of comfort, for example, additional coaxial cables can be connected to the transformer's open terminals that are not measured at the moment (fig. 14) so that only the relevant measuring line has to be plugged in at the measuring device when investigating the corresponding phase later. Doing later follow-up measurements without these additional cables directly affects the FRA, as shown in fig. 15. This is why we should do without any unnecessary cables in advance.

impulse generator

transient recorder Ch 3

Ch 2

Ch 1 50 Ω 50 Ω

50 Ω

50 Ω

UmK VmK WmK

UK

MpmK

Fig. 14: Measurement setup using additional unused cables

0.0 frequency f

|TF U

2/U

1(f)

|

FRA without the additional 30 m unused cables FRA with additional 30 m unused cables

dB

0.2 0.4 0.6

-70

0.8

-80

1.0 MHz 1.4

-90

-100

-50

Fig. 15: Influence of additional cables to the FRA measurement

In case of high-impedance voltage measurements, the FRA can also be influenced by the cable lengths due to the reflections on the line. For SFRA measurement, these influences cannot be eliminated by a 0 dB calibration.

Fig. 16 shows that the FRA depends strongly on the used line length if the voltage is high impedance measured. The position of the main resonance frequency

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from the 7 m long line at 850 kHz shifts with the factor 2.15 if the line is extended by 23 m. In case of impedance matching no resonant frequency shift is visible. However slightly different damping can be recognized in a range from 0.6 MHz and 1.8 MHz (fig. 17). In comparison to high impedance measurements it can be said that the influence on the FRA due to different line lengths is substantially smaller, if impedance matching is performed at the measuring device.

0.0 frequency f

|TF U

2/U

1(f)

|

FRA measured with 30 m cables and high input impedance FRA measured with 7 m cables and high input impedance

dB

0.2 0.4 0.6

-10

0.8

-20

1.0 MHz 1.4

-30

-60

10

1.2 1.6 2.0

-40 -50

Fig. 16: Influence of the cable length to the FRA in case of high-impedance termination

0.0 frequency f

|TF U

2/U

1(f)

|

FRA measured with 30 m cables and 50 Ω input impedance FRA measured with 7 m cables and 50 Ω input impedance

dB

0.2 0.4 0.6

-30

0.8

-32

1.0 MHz 1.4

-34

-40

-26

1.2 1.6 2.0

-36 -38

Fig. 17: Influence of the cable length to the FRA in case of impedance matching

4 CONCLUSION

In case of non-isolated signal transmission, shielded

cables must be used in order to prevent electromagnetic coupling of interferences. Even the connection of sensors should, as far as possible, be done without the use of unshielded cables. The best solution is to attach a corresponding sensor fixture to the transformer terminal adapter for the coaxial cables.

Apart from the connection technique and the aspects regarding the cables, the grounding concept is of particular importance. A poor grounding concept can lead to unreproducible and therefore unusable FRA results. In order to achieve as good as possible FRA measurements, the grounding connections should provide an as large as possible surface. This is why ground straps should be preferred to normal wire-like conductors. Ground straps are less sensitive to interferences and make the FRA independent from the

cable arrangement. In order to achieve a high grade of reproducibility, the connection of the cable shield to the transformer tank should exclusively be done with ground straps that are pulled tightly along the bushing. Furthermore, the dimensions of ground straps and their material should be recorded in a test report.

For FRA follow-up measurements it is in general of particular importance to use the same measurement setup as for the reference measurement. Particularly in case of existing freedom for test setup, cable lengths and types, tap changer setting, sensor types and location of current measurement, the used configuration should be recorded exactly in a test report. The use of unnecessary cable connections can lead to errors in later follow-up measurements. This is why FRA measurement should be performed according to the minimum principle and only those cables and sensors should be connected that are absolutely necessary for the measurement.

5 REFERENCES

Papers from Conference Proceedings (Published): [1] J. Bak-Jensen, B.Bak-Jensen, S.D. Mikkelsen: ”Detection of

Faults and Aging Phenomena in Transformers by Transfer Functions”, IEEE Transactions on Power Delivery, Vol. 10, No. 1, Jan. 1995, pp. 308-314

Dissertations:

[2] J. Christian: “Erkennung mechanischer Wicklungsschäden in Transformatoren mit der Übertragungsfunktion“, Dissertation, Universität Stuttgart, 2002

[3] M. Nothaft: “Untersuchung der Resonanzvorgänge in Wicklungen von Hochspannungsleistungstransformatorenmittels eines detaillierte n Modells“, Dissertation, Technische Hochschule Karlsruhe

[4] G. B. Gharehpetian: “Modellierung von Transformatorwicklungen zur Untersuchung schnellveränderlicher transienter Vorgänge”, Dissertation, RWTH Aachen und Universität Teheran, 1996

[5] E. Rahimpour: “Hochfrequente Modellierung von Transformatoren zur Berechnung der Übertragungsfunktion“, Dissertation, Universität Stuttgart und Univeristät Teheran, 2001

[6] T. Leibfried: “Die Analyse der Übertragungsfunktion als Methode zur Überwachung des Isolationszustandes von Großtransformatoren“, Dissertation, Universität Stuttgart, 1996

[7] M. Lenz: “Anwendung der Wavelet-Transformation bei der Blitzstoßspannungsprüfung von Leistungstransformatoren“, Dissertation, Universität Stuttgart, 2003

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