This paper examines the impact of DC faults on the transient stability of a multi-machine power system using two transmission configurations: HVDC and hybrid HVAC-HVDC. The study indicates that while both configurations experience fluctuations, the hybrid HVAC-HVDC setup offers a smaller adverse impact on transient stability compared to the pure HVDC system. The results reveal differences in rotor angle stabilization times and voltage recovery between the two configurations after a fault is applied at the DC terminal.

1. IEEE AFRICON 2009
23 - 25 September 2009, Nairobi, Kenya
Effect of Converter DC fault on the Transient
Stability of a Multi-Machine Power System with
HVDC Transmission lines
1
D.T. Oyedokun MIEEE, 2K. A. Folly MIEEE, 3S.P. Chowdhury MIEEE
Department of Electrical Engineering
University of Cape Town
Cape Town, South Africa.
1
davoyedokun@ieee.org, 2komla.folly@uct.ac.za, 3sp.chowdhury@uct.ac.za
Abstract—This paper deals with the effect of DC faults on the
transient stability of a Multi-Machine Power System with two
transmission line configurations; HVDC and a hybrid HVACHVDC transmission line. The faults are located at the DC
terminals of the HVDC converter station. In order to carry out
this study, two case studies are presented. In the first case study a
double HVDC transmission line is used to transmit 2000MW to
an area of the power system called Pookland which has a total
load demand of 2440MW. In case two, a parallel hybrid HVACHVDC transmission line is used to transmit the same amount of
power to Pookland. In both cases, the impact of a short term
converter DC fault on the transient stability of the entire system
was investigated. This was done by studying the response of the
rotor angle of G2 in Pookland, G3 in the Bing Coal plant and the
voltage profile at the terminals of the generators to the DC fault
at the HVDC converter station. Amongst other results, it was
established that in case 1 which has a double HVDC transmission
line, the rectifier side (in the Bing coal plant) has less rotor angle
oscillations when compared to the inverter side (in Pookland),
but the rectifier side took longer than the inverter side for the
rotor angle of the generators to stabilize. In case 2, the voltage at
G2 in Pookland took six times the amount of time it took G3 in
the Bing coal plant to stabilize while the voltage in the Bing Coal
plant dipped by 0.35pu (smaller than case 1 which dipped by
0.4pu). In conclusion, the converter DC fault had a smaller
impact on the transient stability of the Multi-Machine power
system when the hybrid HVAC-HVDC transmission line was
adopted.
Keywords-component; HVDC, HVAC, Hybrid HVAC-HVDC
transient stability, transmisison, rotor angle
I.
INTRODUCTION
The ability of a power system to withstand and recover
from system faults in a fast and successfully manner is critical
to the stability of the power system. According to [1], the use
of High Voltage Direct Current (HVDC) transmission for long
distance applications has seen an increase due to the following
reasons:
•
It is a more economical mode of power transfer as
compared to HVAC over long distances exceeding
500km [2].
•
HVDC
transmission
lines
(i.e.
submarine,
underground and overhead transmission lines) do not
make use of the three phase cables used in HVAC
transmission therefore, the power losses incurred in
the DC lines are lower than that of AC lines.
•
HVDC can be used to interconnect asynchronous
systems. Examples of such connections are in North
America, between the South-West Power Pool (SPP)
and also between Quebec and its neighbors (New
England and the Maritimes) [3].
Large HVDC schemes exist worldwide. These include the
pacific intertie which has a total of 3100MW over a distance of
1360km and the Hydro Quebec New England link [4]. Itaipu in
Brazil has an HVDC scheme of 6300MW, the cross channel
UK- France scheme has a capacity of 2000MW, Wybord in
Russia has a capacity of 1050MW. The scheme between North
and south Islands of New Zealand is 1240MW and the CahoraBassa Hydro scheme between Mozambique and South Africa
has a Capacity of 1920MW [5]. As of 2005, the worldwide
installed HVDC capacity was 55GW which is 1.4% of the
worldwide installed generation capacity [6].
HVDC is obtained directly from High Voltage Alternating
Current (HVAC) through the use of HVDC converters and
their associated devices like filters, reactors and capacitor
banks which provide reactive power support for the HVDC
converters. In most HVDC schemes around the world, the 12
pulse thyristor converter configuration has been adopted to
reduce the requirements for smoothing the DC waveform [7].
With regards to power system stability, it has been stated that
the use of HVDC transmission lines in parallel with HVAC
transmission lines increases the strength and the stability of the
system. An example of such an interconnection is the Pacific
Intertie in California and Oregon [8].
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2. IEEE AFRICON 2009
23 - 25 September 2009, Nairobi, Kenya
As faults on HVDC converter stations could lead to instability
in the power system, this paper looks at the effect of converter
DC faults on the rotor angle of the generators for a multimachine power system. This is done by looking at two
transmission line configurations between the Bing Coal plant
and Pookland as indicated in fig.2 while a DC fault is induced
in the converter station.
Firstly, a double HVDC transmission line is considered for
transmission and secondly, parallel transmission using hybrid
HVAC-HVDC is considered. In each of the configurations, a
50msec fault is applied on the rectifier DC terminal. The effect
of this fault on the rotor angle of the generator G1 in Pookland
and generator G3 in the Bing coal plant are investigated.
II.
CONVERTER FAULTS AND EQUATIONS
A. Converter Equations
Fig.1 shows the schematics of the rectifier side of a HVDC
scheme.
Fig.1 Rectifier side of a HVDC scheme
V DC =
3 2
π
VS BT cos α
VDC ( I ) =
I DC =
3 2
π
3 2
π
From (3) and (4), the DC power output from the rectifier is
given as follows:
PDC = V DC ( R ) ⋅ I DC
(5)
QR = PDC ⋅ tan(α )
(6)
Where QR is the reactive power absorbed by the rectifier.
Similarly
QI is the reactive power absorbed by the inverter
B. Converter faults
Natural or line commutation is the process through which
rectifiers convert AC to DC and inverters convert DC to AC.
This process can further be described as the transfer of current
between two converter valves with both valves carrying
current simultaneously. When this process is interrupted by
e.g. faults in the converter station, instability may arise in the
system which can affect the AC side of the HVAC scheme
depending on the duration of the fault and the protection
scheme adopted [9]. Possible location of fault within the
converter station are across a non-conducting valve, across the
bridge DC terminals, ground faults on the Bridge DC
terminals and also ground faults at the DC bus [10].
III.
(1)
SYSTEM MODEL AND RESULTS
V SR BT cos α
(2)
VSI BT cos γ
(3)
DigSILENT power factory was used in the simulations.
From fig.2, the Bing coal plant has two generating stations G3
and G4 which are connected to bus 12 and bus 13 respectively.
Each of the generating stations has a capacity of 1080MW.
Pookland which is on the left side of the network has a total
local generating capacity of 600MW of which 400 is from G2
and the rest if from G1. Furthermore Pookland has two
distribution centers. The first distribution center is at bus 7
which is connected to bus 6 via a 1600MVA 500/11 kV step
down transformer.
(4)
The second distribution center in Pookland is at bus 8 which is
connected to bus 6 via a 1600MVA 500/11 kV step down
transformer. The load at bus 7 is 1064MW while the load at
bus 8 is 1379MW.
Where: B = Number of converter bridges
T = Transformer turns ratio
VDC ( R ) =
RI is the resistance of the Inverter
RL is the resistance of the HVDC Line
IDC is the DC line current
α is the firing angle
VDC ( R ) −V DC ( I )
RR + RL + RI
Where: VDC(R) is the rectifier DC voltage
VSR is the rectifier AC Voltage
VDC(I) is the inverter DC voltage
VSI is the Inverter AC Voltage
γ is the inverter extinction angle
RR is the resistance of the Rectifier
The details of the transmission line data are given in the
appendix. Capacitor banks are connected to Bus 5 and Bus 9
contributing a total reactive power compensation of 1000Mvar.
For the HVDC scheme in fig.3, series rectors each of 0.86H are
connected to each end of the HVDC transmission line. A
combination of two 6-pulse converters is used for the rectifier
end in the Bing coal plant and at the inverter end of the HVDC
transmission line which is in Pookland
978-1-4244-3919-5/09/$25.00 ©2009 IEEE
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3. IEEE AFRICON 2009
23 - 25 September 2009, Nairobi, Kenya
In the simulations, generator G1 in Pookland is a slack bus, G2
in Pookland is a PV bus, G3 and G4 in the Bing coal plant are
both set as PV buses.
The converter transformers in fig.3 are connected via remote to
buses 5 and 9 in fig.2.
Fig.4 Case 1: G3 Rotor Angle
Fig. 2 The Entire power network excluding the HVDC scheme
Fig.5 Case 1: G3 Terminal Voltage
The following fig.6 and fig.7 shows the results obtained from
the generator (G2) in Pookland.
Fig. 3 The remote HVDC scheme between the Bing coal
plant (bus 9) and Pookland (Bus 5)
A. Case 1: HVDC Transmission to Pookland
The HVDC transmission line is scheduled to deliver about
2000MW over 500km to Pookland with current control at the
rectifier and extinction angle control at the inverter. The
current order of the rectifier was set at 3.6kA. A 50ms fault
was applied at the DC terminal of the rectifier. The effect of the
DC fault on the rotor angle stability as well as the recovery of
the voltage level at the generating stations in Pookland and the
Bing coal plant is investigated.
Fig.6 Case 1: G2 Rotor Angle
The simulation results obtained for case 1 are given in fig.4 to
fig.7.
Fig.4 and fig.5 show the results obtained from G3.
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4. IEEE AFRICON 2009
23 - 25 September 2009, Nairobi, Kenya
Fig.8 Case 2: G3 Rotor Angle
Fig.7 Case 1: G2 Voltage
During the 50ms fault applied at the DC side of the terminal,
the two inverters in Pookland went automatically into
blocking mode. This was done to prevent forward current
flowing through the inverter. During this time the rotor angle
of G3 the Bing coal plant increased from -85º to 160º in figure
4 while the terminal voltage dropped to 0.63pu from 1.0 pu in
figure 5. After the fault was cleared, inverter 1 returned to
normal operation and 7ms later, inverter 2 returned to normal
operation while the two rectifiers in the Bing coal plant went
into blocking mode for 5ms and then a commutation failure
lasting for 2msec.
Following this, the rectifier returned to normal operation while
the voltage level at G3 in the Bing coal plant and G2 in
Pookland normalized. It took about 70secs for the rotor angle
of G3 to return to a stable value of -52º with the largest swing
between 170º to
-170º as opposed to G2 in Pookland which
had the largest swing between -86.97º and -86.74º in figure 6
whose oscillations damped out in about 7.5 seconds.
Fig.9 Case 2: G3 Voltage
The following fig.10 and fig.11 shows the results obtained
from the generator in Pookland.
B. Case 2: HVAC/HVDC Transmission to Pookland
The HVDC transmission line is scheduled to deliver about
1000MW over 500km to Pookland with current control at the
rectifier and extinction angle control at the inverter. The
current order of the rectifier was set at 1.8 kA. The HVAC line
transmitted the rest 1000MW.A 50ms fault at the DC terminal
of the rectifier was applied. The effect of the fault on the rotor
angle stability and the recovery of the voltage at the generating
stations are investigated.
The results obtained from the simulation using HVAC/HVDC
transmission to Pookland are given in fig.8 to fig.11.
The following fig.8 and fig.9 show the results obtained from
the generator in the Bing coal Plant.
Fig.10 Case 2: G2 Rotor Angle
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5. IEEE AFRICON 2009
23 - 25 September 2009, Nairobi, Kenya
Furthermore, the effect of the DC fault was more prominent in
the Bing coal plant as the pu voltage at G3 reduced to 0.63 in
fig. 5 but retuned to its prefault value at 0.3sec after the fault.
In Pookland, there was a sharp increase of the voltage level at
G2 from 1.0pu to 1.025pu which took 1.2sec to drop to a post
fault level of 0.995pu.
Fig.11 Case 2: G2 Voltage
During the 50ms fault induced at the DC side of the terminal,
the two inverters at Pookland went into blocking mode.
During this time, the rotor angle of G3 in the Bing coal plant
decreased from -31º to -54º while the terminal voltage dropped
to 0.64 pu from 1.0 pu. After the fault was cleared, inverter 1
returned to normal operation and 7ms later, inverter 2 returned
to normal operation while the two rectifiers went into blocking
mode for 5ms and then a commutation failure lasting for 2ms
based on the control scheme in operation.
Following this, the two rectifiers returned to normal operation
while the voltage level at G3 in the Bing coal plant and G2 in
Pookland normalized. During this time there was a repeated
return to blocking mode by both rectifier 1 and inverter1. This
occurred six times.
From fig.4 and fig. 8 it can be seen that it took 38sec (almost
half when compared to case 1) for the rotor angle of G3 to
return to its pre fault angle of -44º with the largest swing
between -31º to -54º as opposed to G2 in Pookland which had
the largest swing between -86.96º and -86.81º whose
oscillations damped out in about 30 seconds.
IV.
ANALYSIS AND DISCUSIONS
From the simulation of DC faults on the rectifier end of the
HVDC scheme for the HVDC transmission and HVDCHVAC transmission the following analysis are made:
For the HVDC transmission scheme in case 1, the rectifier DC
fault had a large impact on the generator close to the rectifier
end at the Bing coal plant. The rotor angle of G3 had only one
large step change between 160º and -160º and returned to its
pre fault angle of -80º after 70sec. On the contrary, the
rectifier DC fault had a smaller impact on the rotor angle
displacement of generator G2 which is in Pookland (the
inverter end if the HVDC scheme). G2 had smaller
oscillations between -86.97º and -86.74º which is a very small
range.
For the HVAC-HVDC scheme in case 2, the rectifier DC fault
had a different impact on the generator close to the rectifier
end in the Bing coal plant as compared to case 1. The rotor
angle of G3 had more oscillations with the largest between
-31º and -55º returning to its prefault angle of -44º after 45sec.
On the contrary, the rectifier DC fault had a smaller impact on
the rotor angle displacement of generator G2 which is in
Pookland (the inverter end if the HVDC scheme). G2 had
lesser oscillations between -86.83º and -86.99º which is a very
small range and returned to its prefault angle of -86.89º in
32sec.
Regarding the effect of the DC fault on the voltage profile, G3
in the Bing coal plant had a greater voltage dip of 0.4pu with
few oscillations which stabilized after 5.7sec. In Pookland,
there was a slight increase of the voltage level at G2 from
1.0pu to 1.01pu with large oscillations which took 34sec to
drop to a post fault level of 1.0pu.
V.
OBSERVATIONS
In case 1, the rectifier side has less rotor angle oscillations
when compared to the inverter side, but rectifier side takes
longer than the inverter side for the rotor angle of the relevant
generators to stabilize. The peak to peak amplitude of the rotor
angle oscillation in the Bing coal plant is 300º and that of
Pookland has a high of 0.23º The voltage at G2 in Pookland
(the inverter end) took twice the amount of time it took G3 in
the Bing coal plant to stabilize.
In case 2, the rectifier side had more rotor angle oscillations
when compared to the inverter side and the rectifier side also
takes longer (13sec more than the inverter side) to stabilize
The largest peak to peak amplitude of the multiple rotor angle
oscillation in the Bing coal plant is 24º and that of Pookland
has a high of 0.16º which is 9 times damper than case 1.
Hence when these values are compared with case 1, it can be
seen that the oscillations have been damped in case 2.The
voltage at G2 in Pookland (the inverter end) took six times the
amount of time it took G3 in the Bing coal plant (rectifier end)
to stabilize while the voltage in the Bing coal plant dipped by
0.35pu (smaller than case 1 which dipped by 0.4pu).The
voltage rise in Pookland was about 0.01pu but with 14
oscillations. When compared to case 1, the oscillations are
more but the amplitude of the oscillations is smaller.
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6. IEEE AFRICON 2009
VI.
23 - 25 September 2009, Nairobi, Kenya
CONCLUSION
From the simulation result, analysis and observations, the
following conclusions are made:Firstly, the rectifier DC faults when a hybrid HVAC-HVDC
transmission line is used for transmission has a smaller impact
on the generators closer to the inverter end as the rotor angle
of the generator has fewer oscillations with reduced
amplitudes. Secondly, the hybrid HVAC- HVDC transmission
line induces more oscillations with lower amplitudes in the
terminal voltage of the generator at the inverter end in
Pookland.
APPENDIX
Table A1: Transmision line Parameters
Line
HVAC
HVDC
Resistance
(Ω/km)
0.028
0.015
Reactance
(Ω/km)
0.325
0.025
Susceptance
(μS/km)
4.35
0.45
Length
(km)
500
500
ACKNOWLEDGMENTS
Munificent thanks to God for sustained life and wisdom, to
our colleagues at the UCT Power System Research Group, to
family and friends for their support, to Eskom for their
financial support and to the beautiful City of Cape Town for
her pseudo-random weather conditions.
REFERENCES
[1]
D T Oyedokun, K.A Folly, “Power Flow studies in HVAC and HVDC
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2008
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1993).
[3] Brian K. Johnson, The ABCs of HVDC Transmission Technologies,
IEEE power and energy magazine, March/April 2007.
[4] M Hausler, “Multi terminal HVDC for High Power transmission in
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[5] N.G Hingorani, “High- Voltage DC Transmision: A power electronic
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[6] JM Perez de Andres et all, “Prospects for HVDC- Getting more power
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[7] D. T .Oyedokun, “Using DigSILENT and PSCAD for planning and
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