# Transfer functions for UHF partial discharge signals in GIS

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11th International Symposium on High Voltage Engineering, London, August 1999

TRANSFER FUNCTIONS FOR UHF PARTIAL DISCHARGE SIGNALS IN GIS

M D Judd and O Farish

University of Strathclyde, UK

Abstract
∅0.1 m                     5.0 m
•
The principles of electromagnetic radiation by partial            ∅0.5 m
discharges (PD) in gas insulated substations (GIS) are                                              GIS
described. Calculated transfer functions are presented,
showing that transverse electric modes are predominant
for radial PD currents in the coaxial geometry. By using                     plane containing             plane of the
the PD source                UHF coupler
actual PD current pulses from a free moving particle
together with the measured sensitivity of a UHF coupler,     Fig. 1 Relative position of PD source and coupler
the entire transfer function for the PD detection problem           used in the transfer function calculations.
is modelled. The relationship between UHF signal energy
at the coupler output and the electronic component of the   To gain a qualitative understanding of how the modes
PD pulse is investigated using the model, revealing a       are excited, consider the PD source as a short burst of
significant degree of correlation.                          current flowing in a radial direction from r = r1 to
r = r2. Let the distance l over which this current flows
1. Introduction                                             be small, l = ∆r = r2 - r1. In simple terms, the current
The theory of UHF signals excited by partial                will excite a particular mode in proportion to the
discharges (PD) in gas insulated substations (GIS) has      potential difference V which that mode would impress
been described in detail previously [1]. In this paper,     across l. Thus if a mode satisfies the condition of
we present examples of calculated GIS transfer              equation (1) it will not be excited at all by the radial
functions and explore the implications for UHF PD           component of PD current.
detection. The transfer of energy from PD to distant                               r2
coupler is undoubtedly a complex process. However, a                           V = ∫ E ⋅dr = 0                  (1)
proper understanding of the transfer functions will                                    r1
assist with the interpretation of UHF signals when          Conversely, the PD will excite maximum signal
used in conjunction with improved measurements of           amplitude in that mode if it occurs at a radius where
typical PD current pulses in SF6 and information about      the integral in (1) is a maximum. If l is small, the
the defect that can be gained from phase resolved           integral in (1) can be approximated by
measurements.                                                                   l Er                            (2)

2. Theory                                                   where Er is the radial component of E. Now it is clear
that a small radial PD will excite a mode in proportion
Essentially, the PD is a current pulse that occurs          to the magnitude of its radial electric field at the PD
somewhere in the insulating region between the high         position. The TEM mode can be used to illustrate this
voltage (HV) conductor and the metal cladding. The          principle. In a GIS with conductor radii a = 0.05 m
conductors form a coaxial "waveguide" in which, at          and b = 0.25 m (see Fig. 1), the electric field of the
sufficiently high frequencies, many higher-order            TEM mode is 5 times greater at the inner conductor
modes can be excited in addition to the familiar TEM        than at the outer conductor. A PD occurring at the
mode. These modes are designated transverse electric        inner conductor would therefore excite a TEM mode
(TE) or transverse magnetic (TM) and each one has a         signal with an amplitude 5 times that generated by an
unique three-dimensional electromagnetic field pattern      identical PD at the outer conductor.
inside the GIS. For the TEM mode, the electric field
has only a radial component whose magnitude varies          The excitation of higher-order modes by PD in GIS is
with 1/r, where r is the distance from the axis of the      primarily due to the combination of two factors:
HV conductor (cylindrical co-ordinate system). While        1.    The PD is small and cannot excite fields that are
the TEM mode electric field is independent of the                 independent of φ over the GIS cross-section
angular co-ordinate φ, the fields of higher-order modes           because of the propagation delay at velocity c.
have amplitudes that are modulated over the GIS             2.    The PD current i exhibits a very high rate of
cross-section by cos(nφ), where n is the integer in the           change (di dt ) .
designation of a mode as TEnm or TMnm. In addition,
radial variations of the field patterns in higher-order     Higher-order modes are only a mathematical
modes involve Bessel functions and their derivatives.       approximation to reality, representing three-

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dimensional fields by summing repetitive field patterns                                                       Fig. 2 shows two examples of the GIS transfer function
in the spatial domain. This is analogous to the way in                                                        |G(ω)| calculated using the theoretical approach
which a periodic signal in the time-domain can be                                                             described in [1]. The PD source is identical in both
represented by a Fourier series. If one considers the                                                         cases, but in Fig. 2(a) it is located at the outer
early stages of radiation from a PD, the time taken for                                                       conductor while in Fig. 2(b) it is located at the inner
the transient field to spread out from the defect to the                                                      conductor. G(ω) relates the electric field at the coupler
surface of a sphere of radius r0 is t = r0/c. When t is                                                       to the PD current flowing at the site of a defect and has
small, this field clearly cannot be represented by the                                                        units of Vm-1/A. Signal reflections and ohmic losses
TEM mode alone, which is non-zero over the whole                                                              have not been included. At frequencies below TE11 cut-
cross-section of the GIS. Thus any TEM mode                                                                   off only the TEM mode propagates. In this region the
contribution must be offset by higher-order modes in                                                          transfer function is independent of ω, and if the graphs
the exact proportions required to ensure that the fields                                                      are compared the magnitude ratio is seen to be 5,
cancel everywhere except inside the volume defined by                                                         corresponding to the ratio of the conductor radii. At
r0. The overall transfer function G(ω) between a PD                                                           higher frequencies, as each new mode begins to
source and the UHF electric field at a distant coupler is                                                     propagate, there is a step in the transfer function
the sum of the transfer functions of the individual                                                           followed by a series of ripples. In practice, these steps
modes. This leads to a complex relationship that is                                                           will not be so abrupt because, although signal
best investigated using mathematical simulation                                                               attenuation is generally quite low, it does increase
software.                                                                                                     sharply for each mode at frequencies close to cut-off.
The ripples are introduced because the phase of each
3. GIS transfer function                                                                                      mode changes rapidly at frequencies just above cut-off.
Consider the section of GIS shown in Fig. 1, in which
a PD source and UHF coupler (both at φ =0) are                                                                G(ω) is dominated by the TEn1 modes, particularly
separated by a distance z = 5.0 m. The cut-off                                                                when the PD source is at the outer conductor. In Fig.
frequencies fc of the higher-order modes can be                                                               2(a), their contribution increases with n, while the
calculated from the conductor diameters. All those for                                                        TEn2 and TEn3 modes are visible only as minor ripples
which fc < 2000 MHz are listed in Table 1.                                                                    just above their cut-off frequencies. When the PD

Table 1 - List of modes used in the simulation and their cut-off frequencies (MHz) in the 400 kV GIS.
TE11                                      325.4          TE61     1431.6          TE32     1519.9       TM01     728.3       TM51     1674.1     TM32      1884.5
TE21                                      579.2          TE71     1637.1          TE42     1769.9       TM11     808.4       TM61     1896.3
TE31                                      801.4          TE81     1841.2          TE13     1609.5       TM21     996.6       TM01     1485.9      TEM      n/a
TE41                                     1014.8          TE12      946.8          TE23     1822.6       TM31    1220.4       TM12     1537.4
TE51                                     1224.4          TE22     1239.6                                TM41    1448.7       TM22     1680.3

1000
(a) PD at outer conductor
TE31
100
TE21
GIS transfer function |G(ω)| (Vm /A)
-1

TE11

10

1
Legend:              all modes                TE only              TM only           TEM
1000
(b) PD at inner conductor

100

10

1
0                         500                        1000                    1500                 2000
frequency ( MHz )
Fig. 2 Transfer function |G(ω)| for a GIS, relating the electric field at the coupler to the PD current.
In these examples the PD source is a 10 mm protrusion. In (a) the protrusion is on the outer
conductor, while in (b) it is on the inner conductor. Contributions from the TEM, TE and TM
type modes to the overall transfer function are also shown.

page 2 of 4
10

sensitivity |H| (mV/Vm )
source is at the inner conductor, the TE mode

-1
contribution does not increase so markedly with n. The
explanation lies in the fact that for a given value of n,
the cos(nφ) variation of the fields results in a greater                                                                      1
rate of change with distance at the surface of the inner
conductor so that fewer modes are required to
represent the same source field.                                                                                             0.1
0   500          1000       1500     2000
frequency ( MHz )
How should the complex information presented in Fig.
2 be interpreted? To evaluate variations in the                                                         Fig. 5 Frequency response of the UHF coupler.
transfer function, consider the frequency band 500 -
1500 MHz, which is typical of broadband UHF PD                                                    4. A study using the transfer function
detection systems. Taking the average the value of |G|
over this range, we obtain a value of 65 Vm-1/A for PD                                            Until now we have only been concerned with signal
at the outer conductor and 45 Vm-1/A for PD at the                                                transfer from PD current to electric field at the
inner conductor. More generally, if the transfer                                                  coupler. To complete the transfer function for UHF PD
function is calculated at 10 mm intervals as the PD                                               detection we need to know the sensitivity H(ω) of the
source is moved between the conductors, we find that                                              UHF coupler, which relates the coupler output voltage
its average value varies as shown in Fig. 3. This                                                 to the incident electric field. Calibration results for
variation does not imply that the energy radiated by                                              actual couplers [2] can be used. In this case we will use
the PD source varies with its position. Remember that                                             real data from an internal disk-type coupler. The
the coupler only extracts a small portion of the energy                                           magnitude response |H(ω)| for the coupler is shown in
travelling along the GIS. In this example, the PD                                                 Fig. 5.
source will generate a maximum electric field at the
As input data to the simulation, broadband
coupler if it is located at r = 0.225 m.
measurements of real PD pulses can be used. To
The effect of the size of the PD source can be seen in                                            illustrate the use of the transfer function to simulate
Fig. 4. If all other parameters remain constant, the                                              PD detection, a randomly selected set of 64 current
amplitude of the UHF electric field passing over the                                              pulses generated by a free moving particle was
coupler is proportional to the length l over which the                                            analysed. These pulses were recorded for an
PD current flows. This relationship holds provided                                                aluminium sphere of diameter 2 mm in SF6 at a
l << λ, where λ is the wavelength at the maximum                                                  pressure of 380 kPa [3]. For each PD, the total
frequency of interest.                                                                            electronic charge qe in the fast component of the pulse
was determined by numerical integration of the
current. In simulating the UHF signals that would be
80
generated in a GIS, the particle was taken to be at the
average |G| (Vm /A)

outer conductor
-1

outer conductor, with the current flowing over a total
HV conductor

60
length l = 2.5 mm. The energy Uc of the UHF signal at
40                                                                          the coupler output was determined by integrating the
20                                                                          instantaneous simulated coupler output power V2/RL,
where RL = 50 Ω. The integration was limited to the
0                                                                           first 500 ns of the UHF signal, as most of the signal
0        0.05        0.1        0.15      0.2     0.25
radial position r of the PD source ( m )                      energy arrives within this time. A typical PD current
pulse and two stages of the simulation process are
Fig. 3 Effect of radial position of the PD source on the
illustrated in Fig. 6.
average transfer function (500 - 1500 MHz).
Typical signal energy Uc at the coupler output
150
outer conductor                                        predicted for this particle is 5×10-15 J (corresponding
average |G| (Vm /A)

HV conductor                                           to qe ≈ 100 pC). This energy is accumulated in 500 ns,
-1

100                                                                         giving an average UHF signal power of 10 nW or
-50 dBm, which is comparable with the expected
50                                                                         signal levels for small particles [4].

0
As calculating Uc involves squaring the coupler output
0                  5   10         15            20                 voltage, we have plotted √Uc when looking for
length l of the PD source ( mm )                               correlation with qe. The data is presented in Fig. 7,
Fig. 4 Effect of PD source size on the average transfer                                 which shows results for PD pulses of both polarities.
function (500 - 1500 MHz), showing results for                                   Note that the polarity of qe relates to the charge
the PD occurring at the inner and outer                                          acquired by the particle from the measurement
conductors of the GIS.                                                           electrode.

page 3 of 4
2                                                                                  0.25
(a) PD pulse
PD current

area = 123pC

PD current
1                                                                                    0
(A)

(A)
0
area = -111pC
-1                                                                                 -0.5
0          0.5           1.0                  1.5          2.0                       0   0.5        1.0       1.5         2.0
time ( ns )                                                                 time ( ns )
coupled signal

10                                                                       Fig. 8 Example of a negative PD pulse with precursor.
(b) coupler output
( mV )

0
conventional method, PD current is essentially
-10                                                                    integrated to obtain the apparent charge. The UHF
10                                                                     method is primarily sensitive to charge acceleration at
(×10 J)

the defect site and therefore requires a different
energy

Uc
-15

5                                                                     approach to the issue of calibration.
(c) integral of signal power
0
0        100         200       300              400    500       6. Conclusions
time ( ns )
Fig. 6               (a) Measured PD current pulse, (b) calculated                   Calculated transfer functions for UHF PD detection in
coupler output voltage into 50Ω and                              GIS show that transverse electric modes are the
(c) integrating signal power to determine the                    dominant modes excited by a radial PD current. The
energy received at 500 ns.                                       amplitude of the UHF signals is primarily dependent
on the acceleration and deceleration of charge in the
4                                            PD. The shape of the PD current pulse therefore plays
a critical role in determining UHF signals. However,
Uc (fJ)1/2

3
the physics of SF6 ionisation can lead to quite
consistent pulse shapes, in which case a linear
relationship between the electronic component of the
2
PD charge and the square root of the coupled UHF
signal energy can be demonstrated.
1
double
pulses                                                                 Further experimental work is required to address
issues of risk assessment using UHF PD detection. An
-150               -100      -50           0               50      100    150
appreciation of the underlying theoretical principles is
charge qe transferred to the particle ( pC )
important if the potential of the technique is to be fully
Fig. 7 Correlation between qe and √Uc.                                               realised.

5. Discussion                                                                           7. Acknowledgement
This work is funded by an EPSRC research grant.
On the whole, correlation between qe and √Uc is quite
good. An analogous result has been derived for VHF                                      8. References
signals in GIS [5]. Previous experiments [1] have
shown that the UHF signal is very sensitive to the rate                                 [1] M D Judd, O Farish and B F Hampton, "Excitation of
of change of PD current (di/dt), so this correlation is                                     UHF signals by partial discharges in GIS", IEEE Trans.
DEI, Vol. 3, No. 2, pp. 213-228, April 1996
an indication of the similarity of PD pulses with
different amplitudes. A significant deviation occurs for                                [2] M D Judd and O Farish, "A pulsed GTEM system for
some of the larger negative pulses shown in Fig. 7. An                                      UHF sensor calibration", IEEE Trans. Instrumentation
examination of the time-domain records revealed that                                        and Measurement, June 1998
these were all double pulses, in which a larger PD                                      [3] M D Judd and O Farish, "High bandwidth measurement
pulse followed a smaller precursor. The contribution                                        of partial discharge current pulses", Conf. Record IEEE
from both pulses was included in the calculations for                                       Int. Symp. on Electrical Insulation (Washington),
qe. The reason for the lower Uc in these cases is the                                       Vol. 2, pp. 436-439, 1998
reduced di/dt associated with these pulses, one of                                      [4] R Kurrer and K Feser, "Attenuation measurements of
which is shown in Fig. 8. This observation is a natural                                     UHF partial discharge signals in GIS", Proc. 10th ISH
consequence of electromagnetic radiation arising from                                       (Montreal), Vol. 2, pp. 161-164, 1997
the acceleration and deceleration of charges [6],
[5] H-D Schlemper, A Vogel and K Feser, "Calibration and
remembering that                                                                            sensitivity of VHF partial discharge detection in GIS",
di   d 2 qe                                                                 Proc. 9th ISH (Graz), Vol. 5, paper 5619, 1995
=                  (3)
dt    d t2                                                              [6] G S Smith, "On the interpretation for radiation from
Herein lies the fundamental difference between                                              simple current distributions", IEEE Antennas and
Propagation Magazine, Vol. 40, No. 3, pp. 9-14,
conventional and UHF PD measurements. In the
June 1998

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