TRANSMISSION AND DISTRIBUTION
Development of standing waves on
long distance HVDC transmission lines
by B R Duncan and J M Van Coller, University of the Witwatersrand
The Cahora Bassa HVDC scheme in Southern Africa can transmit 1920 MW from Mozambique to South Africa. The DC line is experiencing
numerous insulator flashovers. This paper describes an investigation into the possible existence of standing waves on the DC line. The simulation
study used the Cigré benchmark model for HVDC studies, adapted to model the Cahora Bassa HVDC scheme.
Steady state and transient studies were
performed investigating the development
of standing waves on the DC line. The
results show that under certain operating
conditions it is possible to have a standing
wave present on the DC line, which
could increase the number of insulator
flashovers, thereby reducing the overall
performance of the DC line.
HVDC, composite resonance, standing
waves Cahora Bassa
The continued growth of economies
has led to an increased demand for
reliable electrical power [1]. Dwindling
resources near load centres increases
the need to access remote resources
and transmit electrical power over longer
distances. This has led to the use of
high voltage direct current (HVDC) for
bulk power transmission [2]. There are
currently two operational HVDC schemes
in Africa, namely the Cahora Bassa
scheme between Mozambique and South
Africa, and the Inga-Shaba scheme in the
Democratic Republic of Congo (DRC) [3].
The reliability of an HVDC scheme will be
reduced if there are factors that increase
the number of DC line insulator flashovers.
One such factor is where the voltage along
the line is increased by the presence of
standing waves, and this paper describes
a simulation study to investigate this
possible problem.
Standing waves on transmission lines
For a transmission line, a standing wave is
formed by the superposition of two waves
travelling in opposite directions [8]. This is
a result of reflections at the transmission
line ends due to impedance mismatches.
The wave appears to be standing still
and is characterised by a series of nodes
and anti-nodes (maxima and minima) at
fixed positions along the transmission line.
Designing long AC overhead transmission
lines is not as simple as designing shorter
lines [7] and under certain conditions,
reflections can cause standing waves
to develop. This problem is solved by
breaking lines up into shorter segments
with large loads or generation at nodes,
to ensure that the length of segments is
kept well below /4 [5]. This is not always
possible with DC lines since most HVDC
Fig. 1: Impedance at the inverter AC bus. a) Cahora-Bassa model. b) Cigré benchmark model.
Fig. 2: Impedance at the rectifier AC bus. a) Cahora Bassa model. b) Cigré benchmark model.
schemes are point-to-point transmission
systems and generally do not have
tapping points along the line.
Standing waves should not generally be
a problem on DC lines. This is true for
pure DC conditions, but since conversion
between DC and AC takes place at both
ends of the line, characteristic and noncharacteristic ripple frequencies can lead
to the development of standing waves [5].
These are normally small in magnitude and
do not create serious problems, unless the
length of the line corresponds to a multiple
of the half wavelength.
Resonances associated with HVDC
schemes
In HVDC schemes, resonances are present
on both the AC sides and DC sides of the
converters. Parallel resonances are seen as
high impedances and series resonances
are seen as low impedances. These AC
and DC resonances are interconnected
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via the converters. This has led to the
concept of the composite resonance
[6], a resonance that arises when a
parallel resonance on the AC side is
coupled with a series resonance on the
DC side. Instabilities occur when the
overall resistance of the resonant circuit
is negative at the composite resonant
frequency.
The capacitive nature of the reactive
compensation required in HVDC schemes
together with the inductive nature of the
connected AC system produces a parallel
resonance. The impedance measurement
tool in PSCAD can perform an impedance
scan of a system over a specified
frequency range, providing insight into
the actual resonant frequencies. The
impedance is determined assuming that
all transformers are unsaturated and that
all power electronic devices are in their
“off ” state [9]. This means that there is no
access to impedances of HVDC systems
under actual operating conditions and
TRANSMISSION AND DISTRIBUTION
hence time domain simulations are
required.
Modifications to the Cigré benchmark
model
The Cahora Bassa model was based on the
Cigré benchmark model [10] implemented
using PSCAD. The AC filters at the Songo
end were modelled in the same manner
as at the Apollo end, changed only to
accommodate the different voltages
and reactive power compensation. The
DC filters and smoothing reactors were
also modified to match the equipment
installed on the Cahora Bassa DC lines. The
Songo end converter rating was changed
from 1000 MVA, 345 kV to 2000 MVA,
220 kV. The Apollo end converter rating
was changed from 1000 MVA, 345 kV to
2000 MVA, 275 kV.
Fig. 3: Impedances of the 1400 km and 3000 km DC lines
and the Cigré DC line.
The scheme topology was changed from
12-pulse monopole to 24-pulse bipole.
The controllers used for each pole were
those of the Cigré benchmark model. The
converter transformers were modified to
the appropriate voltage and MVA ratings
and the transformer impedances were
dropped from 0,18 to 0,14 pu to more
accurately represent the transformers used
in the Cahora Bassa HVDC scheme [11].
The DC line model was changed from a
single nominal-pi model to nine identical
distributed parameter model sections
with the same line geometry as for the
Cahora Bassa DC line. This allowed for the
monitoring of the voltage at multiple points
along the line – thus making it possible
to derive a voltage profile along the
transmission line. Fourier analysis was used
to determine the amplitudes of the ripple
frequency components along the DC line.
Simulation results – resonances
Steady state simulations were performed
for various line lengths and with various
rectifier constant current-control (CCC)
gains. The rectifier CCC gain has a
significant effect on composite resonances
since the rectifier controller can present
a negative resistance to the resonant
circuit [6]. Varying the length of the DC
line altered the series resonance on
the DC side, thereby also affecting the
composite resonance. The AC and DC
side impedances were measured, using
PSCAD, to verify the composite resonance
condition. Figs. 1, 2 and 3 are impedance
plots of the Cahora Bassa model for
comparison with the Cigré benchmark
model.
Fig. 1a shows the AC bus impedance, as
a function of frequency, at the inverter
end of the Cahora Bassa model (Apollo),
and is compared with the inverter end of
the Cigré benchmark model in Fig. 1b. It
is clear that both systems have a parallel
resonance near the second harmonic
(100 Hz).
Fig. 2a shows the AC bus impedance, as
Fig. 4 (a+b) : Voltage profile along the 1400 km transmission line – low rectifier CCC gain
a) Harmonic components. b) Voltage profile along the line.
a function of frequency, at the rectifier
end of the Cahora Bassa model (Songo),
and is compared with the rectifier end of
the Cigré benchmark model in Fig. 2b.
Again it is clear that both systems have
a parallel resonance near the second
harmonic (100 Hz).
Fig. 3 is an impedance plot of the DC
lines that were modeled – the 1400 km
line based on the Cahora Bassa DC
line geometry, and an extended-length
version of the same line geometr y for
easy comparison. The extended-length
line was chosen to be 3000 km since this
is approximately the length for the Westcor
project, which would transmit power from
Inga in the Democratic Republic of Congo,
to Cape Town in South Africa [4].
graphs. The bottom left plot displays the
harmonic content close to the rectifier
end (Songo). The bottom right plot shows
the harmonic content at the inverter end
(Apollo). The base frequency was 5 Hz and
31 harmonic amplitudes were calculated.
Fig. 4 shows the voltage profile along the
1400 km line operated at a low rectifier
CCC gain of 0,5. As can be seen in
Fig. 4a, the harmonic content, although
small, is greater near the centre of the DC line.
Fig. 4b shows the voltage profile along
the DC line with the measured ripple
magnitude superimposed.
Simulation results – standing waves
Fig. 5 is the voltage ripple amplitude
profile of the same system operated at
a higher rectifier CCC gain of 0,9. It is
clear that the composite resonance level
is greater at higher rectifier CCC gains.
The composite frequency harmonic
magnitude also increases with time as
seen when comparing Fig. 5a to Fig. 5b.
It is important to note that the center of
the DC line appears to have significantly
higher ripple amplitude than the ends of
the DC line. The voltage profile along the
line, in Fig. 5c, verifies that near the ends of
the line, the peak-to-peak standing wave
voltage is less than at the centre of the line.
The harmonic content of the voltage
waveform at various positions along the
DC line is shown using a set of ten bar
This is ver y similar to a half-wavelength
standing wave at the composite resonance
frequency of approximately 65 Hz, with a
Similar to the Cigré benchmark model
[10], both the 1400 km line and the
3000 km line have a series resonance near
the fundamental frequency (50 Hz). Since
these resonant frequencies are both similar
to that of the Cigré benchmark model, we
would expect that under certain conditions
a composite resonance at approximately
70 Hz could be excited [6].
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TRANSMISSION AND DISTRIBUTION
rectifier, rather than at the standing wave
maxima. The peak voltage on the line was
measured to be 0,072 pu greater than the
DC voltage at the rectifier.
Conclusions
Fig. 5 (a+b): Voltage profile along the 1400 km line (rectifier CCC gain of 0,9).
a) Harmonic components, T = 1,5 s. b) Harmonic components, T = 5 s.
For the levels of composite resonance
m o d e l l e d, t h e p e a k-t o - p e a k r i p p l e
voltages along the 1400 and 3000 km
transmission lines were shown to reach
0,14 and 0,2 pu at the maxima, while the
peak-to-peak ripple voltage magnitude
was less than 0,07 and 0,1 pu at the line
ends. Understanding wave conditions the
insulators along the transmission line will
experience a greater stress than under
ideal operating conditions – 0,035 pu for
the 1400 km DC line and 0,072 pu for the
3000 km DC line.
For a polluted insulator suffering high
leakage currents, this could make the
difference between withstand and
flashover. The presence of standing
waves could therefore worsen the DC line
performance.
Acknowledgement
Fig. 5 (c): Voltage profile along the 1400 km line (rectifier
CCC gain of 0,9). c) Voltage peak-to-peak amplitude profile
along the line T = 4,9 to 5 s.
peak-to-peak standing wave voltage
magnitude of 0,14 pu near the center of
the DC line. It important to note that the
voltages at the ends of the DC line show a
peak-to-peak ripple magnitude of less than
0,07 pu under these conditions. We can
also see that although the standing wave
maximum amplitude is measured to be
near the centre of the DC line, that when
superimposed on the DC voltage profile
of the transmission line, the highest peak
voltage is found closer to the rectifier end.
The peak voltage along the transmission
line was measured to be 0,035 pu greater
than the DC voltage at the rectifier end.
This could cause an insulator to flash over
where it would otherwise have withstood
the voltage stress.
The DC line length was then extended
to 3000 km, approximately twice that
of the previous simulations. This also
corresponded to the approximate length
of the proposed DC line for the Westcor
project [4]. The line geometry was assumed
to be the same for easier comparison. The
simulation was conducted in the same
manner as the previous two, but with a
significantly higher rectifier CCC gain of
1,6. The results showed a harmonic voltage
profile along the line with an additional
node near the centre of the DC line as
seen in Fig. 6a. The voltage amplitude
profile along the line shown in Fig. 6b shows
a 70 Hz standing wave. The peak-to-peak
standing wave amplitudes were 0,2 pu at
the maxima and 0,1 pu at the line ends.
Similar to the 1400 km line, the maximum
peak voltages are found close to the
Fig. 6: Voltage profile along the 3000 km line.
a) Harmonic components, T = 5 s,
b) Voltage peak-to-peak amplitude profile along the line T = 4,9 to 5 s.
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This paper was presented at the Cigré
6th Southern Africa regional conference:
Somerset West 2009 and is reprinted with
permission.
References
[1] C D Barker, N M MacLeod, R A Mukhedkar and
R L Sellick. “Extra High Voltage DC Bulk Power
Transmission – Opportunities and Challenges.”
HVDC 2006 Congress, Durban, South Africa,
July 2006.
[2] A Williamson, U Åström, V F Lescale, D Wu and B
Westman, “Latest development in transmission
with 800 kVDC.” HVDC 2006 Congress, Durban,
South Africa, July 2006.
[3] N M Ijumba, A C Britten, L Rajpal, and L Pillay.
“Development of Research Capacity in HVDC
Technology in Southern Africa.” IEEE Africon,
2004.
[4] L Pillay, A C Britten, P Naidoo, D Muftic, F F
Bologna and N M Ijuba “Eskom's Proposed
Strategic Research in Long-Distance HVDC
Transmission.” HVDC 2006 Congress, Durban,
South Africa, July 2006.
[5] J P Reynders. “Elen 437 - Power Transmission
and Protection Course Notes.” Department
of Electrical and Information Engineering,
University of the Witwatersrand, JHB.
[6] J Arrillaga “High Voltage Direct Current
Transmission – 2nd Edition”. , London, United
Kingdom, 1998.
[7] HVDC Transmission Course – Trans Africa Projects,
Midrand, South Africa. 21-23 November 2007.
[8] Definition – Standing Wave www.its.bldrdoc.gov/
fs-1037/dir-034/_5083.htm.
[9] PSCAD Help files.
[10] M Szechtman, T Wess, C V Thio, “First Benchmark
Model for HVDC Control Studies,” Electra, No.
135, April 1991.
[11] Personal communication with Eric Greyling. Line
Manager, Apollo Substation.
Contact B Duncan,
University Witwatersrand,
Tel 011 717-7211,
b.duncan@ee.wits.ac.za or
John Van Coller,
Tel 011 717-7211,
j.vancoller@ee.wits.ac.za 