IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 1, JANUARY 2005
427
VSC Transmission Operating Under Unbalanced AC
Conditions—Analysis and Control Design
Lie Xu, Member, IEEE, Bjarne R. Andersen, Senior Member, IEEE, and Phillip Cartwright
Abstract—This paper presents an analysis and a new control
design of a voltage-source converter (VSC) transmission system
operating under unbalanced network conditions. The system
is analyzed in the positive and negative synchronous reference
frames. The proposed control strategy contains a main controller
and an auxiliary controller. The main controller is implemented in
the positive d–q frame using decoupling control without involving
positive/negative-sequence decomposition. The auxiliary controller is implemented in the negative-sequence d–q frame using
cross-coupling control of negative-sequence current. Simulation
results using the SIMULINK power system blockset show good
performance of the proposed control strategy for a 300-MW
300-kV dc VSC transmission system during both balanced conditions and unbalanced conditions as may be caused by a solid
single-phase-to-ground fault.
Index Terms—Control design, converters, modeling, power
transmission, unbalance.
NOMENCLATURE
,
,
,
,
,
,
,
,
Network voltage.
Fundamental frequency voltage of converter output.
Source current.
AC side inductance, resistance.
DC side capacitance.
Source voltage angular frequency.
Modulation index.
AC active, reactive power inputs.
DC side voltage, current, power.
Superscripts
Positive, negative d-q reference frame.
Reference value for controller.
Subscripts
Stationary – axis.
Synchronous d–q axis.
Positive, negative components
Manuscript received April 29, 2003. Paper no. TPWRD-00193-2003.
L. Xu was with ALSTOM T&D Ltd., Power Electronic Activities, Stafford,
ST17 4LN U.K. He is now with the School of Electrical and Electronic
Engineering, Queen’s University of Belfast, Belfast, BT9 5AH U.K. (e-mail:
l.xu@ee.qub.ac.uk).
B. R. Andersen was with ALSTOM T&D Ltd., Power Electronic Activities,
Stafford, ST17 4LN U.K. He is now with Andersen Power Electronic Solutions
Ltd. Stafford, ST16 1BW U.K. (e-mail: Bjarne@andersenPES.com).
P. Cartwright was with ALSTOM T&D Ltd., Power Electronic Activities,
Stafford, ST17 4LN U.K. He is now with Areva T&D Technology Centre,
Stafford, ST17 4LN U.K. (e-mail: phill.cartwright@areva-td.com).
Digital Object Identifier 10.1109/TPWRD.2004.835032
I. INTRODUCTION
H
Vdc schemes employing line-commutated, current
source converters with thyristors have been widely used
for power transmission and its control strategies have been well
established. On the other hand, voltage-source converter (VSC)
transmission using state-of-the-art insulated-gate bipolar transistor (IGBT) technology has attracted increasing attention and
a number of installations are now in operation. The principle
characteristics of VSC transmission are that it needs no external
voltage source for commutation, that it can independently control the reactive power flow at each ac network, and that reactive
power control is independent of the active power control. These
features make VSC transmission attractive for connection of
weak ac systems, island networks, and renewable sources to a
main grid. However, VSC transmission does have high power
loss and high cost compared to conventional HVdc systems [1].
To take full advantages of VSC transmission and to enable it
to compete with conventional HVdc, a number of advances in
technology are required. One such requirement is the ability to
operate in severe unbalanced network conditions.
Reference [2] presents an equivalent continuous-time averaged state-space model of a VSC transmission system and a control system based on decoupling control. This control strategy
can be applied only to balanced network conditions. References
[3] and [4] study STATCOM control under unbalanced network
conditions, and separate loops for the positive- and negative-sequence components are used. A similar approach is used for
controlling a VSC feeding an unbalanced load [5]. In [6], the
control principles are used to control a pulsewidth-modulated
(PWM) rectifier taking into account unbalanced network conditions. However, within a VSC transmission system, it is necessary to consider the interaction of at least two ac networks and
this makes more demands on dynamic response. Simply separating the controller into positive- and negative-sequence loops
as used in [3]–[6] may not achieve satisfactory performance due
to the delays introduced by decomposing the positive- and negative-sequence components of the voltage and current.
This paper presents an analysis and a new control strategy for
a VSC transmission system under balanced and unbalanced network conditions. The VSC transmission system under balanced
and unbalanced condition is analyzed first. The control design
for balanced condition is briefly outlined and then the principles
of the proposed approach for unbalanced network are described.
Finally, simulation results are provided to demonstrate the feasibility of the proposed controller.
0885-8977/$20.00 © 2005 IEEE
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Fig. 1. Schematic diagram of the VSC transmission system.
Fig. 2. Simplified circuits of one end of the VSC transmission system: (a) AC
side. (b) DC side.
II. ANALYSIS OF VSC TRANSMISSION SYSTEM
The schematic diagram of a typical VSC transmission scheme
is shown in Fig. 1. The simplified equivalent circuits on the ac
and dc sides are shown in Fig. 2.
where
and
lation indexes at - and -axis.
A. Balanced Condition
Detailed model of a VSC transmission scheme under balanced network conditions has been studied in [2]; therefore,
only a brief description is given here. As no negative-sequence
components exist when the network is balanced, the voltage/current variables in this subsection are all positive-sequence components expressed in the positive-sequence reference frame.
Referring to Fig. 2, the system on the ac side can be expressed
in the synchronous d–q reference frame, where the d-axis is
fixed to the source voltage , as [2] and [7]
(1)
where
Fig. 3. Relationships between the
(dq) reference frames.
.
Using the power-balancing equation, the dc side system of
one end as shown in Fig. 2(b) is expressed as
(2)
reference frame and the (dq)
and
are the modu-
B. Unbalanced Condition
Assuming no zero-sequence component, the three-phase
voltage and current may be decomposed into positive- and negative-sequence components when the network is unbalanced. In
reference frame, the three-phase voltages and
the stationary
currents are decomposed into positive- and negative-sequence
components as
(5)
where represents either voltage or current and
and
are
the respective phase shift for positive- and negative-sequence
components.
There are various methods which can be used to separate the
positive- and negative-sequence components. One technique is
to delay the input signal by a quarter of the fundamental frequency period as shown in the following equation [8]:
(3)
Assuming an ideal converter model, the ac and dc side systems can be expressed as
(4)
(6)
The positive- and negative-sequence components in the stationary
reference frame are then transformed into
and
reference frames rotating at angular speeds of and
,
respectively. Fig. 3 shows the spatial relationship of the three
reference frames.
XU et al.: VSC TRANSMISSION OPERATING UNDER UNBALANCED AC CONDITIONS—ANALYSIS AND CONTROL DESIGN
According to Fig. 3, the transformation between
reference frames is given by
and
(7)
and
Therefore, in the
be expressed as
429
not square [7]. One way to overcome this difficulty is to consider the model in (4) and divide the control into two separate
loops—an inner fast current loop and an outer slow dc voltage
loop. The interaction between the two loops is avoided by adequately separating their respective dynamics [2], [7]–[9].
The auxiliary inputs are defined as follows:
reference frames, (1) can
(11)
The current
and
can be controlled independently by
and , respectively. Furthermore,
acting upon the inputs
by using integral control, the tracking errors will be minimized.
Therefore, the controller is designed as follows:
(8)
(12)
The active and reactive power inputs at the point of common
coupling (PCC) are expressed as [6]
where
and
are the proportional and integral gains of the
current controller.
and
are given by
Therefore, the control variable
(9a)
where
,
,
, and
are given by
(13)
(9b)
Therefore, using the power-balancing equation, the dc side
equation for the unbalanced condition can be expressed as
(10)
now is given by (9a) and (9b).
where
Thus, (8) and (10) represent the ac and dc side system model
for one end of a VSC transmission scheme under unbalanced
network conditions.
Similar to the current loop, the controller for the dc voltage
loop is designed as
(14)
and
are the proportional and integral gains of the
where
dc voltage regulator.
is then
The control input of the d-axis current reference
derived as
(15)
III. CONTROL DESIGN
In this section, the control design for the balanced condition
will be briefly described first and then the proposed design for
the unbalanced condition will be provided.
A. Balanced Condition
The system model represented by (4) is nonlinear because of
the existence of multiplication terms between the state variables
) [2], [7].
( , ) and the input ( ,
The operation of the VSC transmission scheme requires the
state variables and to follow varying reference points. In
also has to be maintained at a
addition, the dc voltage level
set value. However, the model has only two independent inputs
and
. Hence, the exact feedback linearization technique
is not applicable since the corresponding decoupling matrix is
B. Unbalanced Condition
As the model shown in (8) indicates, the inner current loop
is normally separated into two controllers (i.e., a positive-seframe and a negative-sequence current controller in the
quence current controller in the
frame [3], [4]). Each controller uses (12) and (13) to achieve dynamic tracking of the positive/negative-sequence current references.
and
The positive and negative current references
are generated according to various control objectives and they
and
are normally generated according to the requirement of
. For the transmission scheme, it may be preferred to eliminate second harmonic power input to (or output from) the converter such that there will be no second-order harmonic on the dc
side. Therefore, according to (9b), the power oscillation terms
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 1, JANUARY 2005
and
need to be zero. It should be noted that (9b) represents the active and reactive power seen from the transformer
primary side (PCC); therefore, (9b) needs to be modified to take
into account the influence of the transformer leakage inductance
as
Therefore, in the
is expressed as
frame, the system represented by (1)
(18)
(16)
.
where
The
and
can then be calculated according to the
values of , ,
, and
.
The issues associated with this conventional approach of controlling the positive- and negative-sequence currents are of the
following.
• Good performance of this control strategy is based on the
accurate decoupling of the d-q component and the removal
of the impact of the network voltage. However, as the
process of extracting the positive- and negative-sequence
components (both current and voltage) involves considerable time delay, the system cannot be decoupled under
transient conditions. Therefore, the system performance is
degraded and the stability of the system is reduced.
• If the active power is generated from an outer dc voltage
control loop based on the controller expressed in (15),
any second-order harmonic in the dc voltage or current
will result in second-order harmonic in the active power
or the positive current reference
. This
reference
indicates
actually contains negative-sequence current components. Therefore, the two sets of positive/negative-sequence controllers interact with each other and,
thus, the performance is less satisfactory.
In order to overcome the problems highlighted, a new control strategy is proposed in this paper. The strategy is to have
two current controllers, namely a main controller and an auxiliary controller. The main controller is implemented in the
frame which rotates at an angular speed of . The controller
is designed using the same principles as shown in (12) and
(13). However, it does not involve any positive- and negative-seand as used in the conventional apquence separation of
proach. The auxiliary controller is specially designed for controlling the negative-sequence current and is implemented in the
frame. In order to avoid the problem associated with inadequate decoupling, the so-called “cross coupling control” is
used for the auxiliary controller [10]–[12]. The design of these
two controllers is discussed below.
According to Fig. 3 and (8), the current and voltage in the
frame can be expressed as
(17)
where
and
refer to the converter outputs controlled
by the main and auxiliary controllers, respectively.
Using decoupling control described in (13) and without
involving any positive- and negative-sequence decomposition,
is controlled as
(19)
where
is given by
(20)
As previously described,
may contain negative-sequence
components and it is expressed as
(21)
represents the negative-sequence components in
where
the current references of the main controller. For simplicity,
is assumed to be zero for the following analysis and its
impact will be described later.
Substituting (17), (19), and (20) into (18), and splitting into
a positive-sequence subsystem and a negative-sequence subsystem yields
(22)
(23)
Equation (22) represents the dynamics of the positive-sequence current components and appropriate selection of
and
of the main controller can give good control of the
system. Alternatively, (23) gives the dynamics of the negative-sequence current with the auxiliary controller. Without
causing significant impact on the system dynamic performance,
(23) can be simplified by neglecting the integral term as
(24)
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431
Fig. 4. One terminal of the simulated VSC transmission scheme.
In the
reference frame, extracting the negative-sequence current components and using the so-called cross
is given by
coupling control [9], [10],
TABLE I
LIST OF PARAMETERS OF THE SYSTEM STUDIED
(25)
Substituting (25) into (24) and transforming it into the frequency domain, the dynamics of negative-sequence currents are
then given by
(26)
where
represents
in the
reference frame.
Consequently, there will be an extra term
on the
right-hand side of (26) and it is given by
Equation (25) indicates that the negative-sequence currents
follow a second-order system. In reality because of the use of
PI controllers, the system is no longer a second-order system.
However, the existence of the integral part does not cause significant difference on the system dynamic performance, but it
does reduce the steady-state error of the current controller. As
, according to (26),
and
follow their respective references and the interaction between the negative-sequence d- and q-axis currents is small.
which was previously neNow consider the impact of
glected. Please note
which is the negative component
contained in the current reference of the main controller while
is the negative-sequence current reference for the auxiliary controller. Taking into account
, an extra term on the
right side of (24) appears and this term is given as
(28)
where
(27)
Comparing (28) to (26), it can be seen that all terms on the
right-hand side of (28) tend to zero. This indicates that the influence of
is rejected by the auxiliary controller.
Therefore, with the combination of the two controllers, both
the positive- and negative-sequence currents are controlled precisely. The d–q positive and negative current references are generated using the same approach as previously described.
IV. SIMULATION RESULTS
A VSC transmission system employing the aforementioned
control principle was simulated in SIMULINK. Fig. 4 shows
one terminal of the simulated system. Four-level Foch converters were used in this study which leads to reduced power
loss and voltage harmonic contents [1]. The parameters of the
simulated system are listed in Table I.
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 1, JANUARY 2005
Fig. 5. Simulation results under balanced conditions. (a) DC voltage controller d–q current references and responses. (b) Power controller d–q current references
and responses. (c) Active power inputs at the two ends. (d) Main dc and floating capacitor voltages.
An ac voltage controller, which may be implemented by controlling the reactive power, is not included in the system. Instead,
the model simply uses q-axis current order to directly give reactive power reference. The two converters were implemented
with one converter controlling the dc voltage (namely, the dc
voltage controller) and the other controlling the active power
(namely, the power controller). The location of the two controllers is independent of the power transfer direction. Therefore, the dc voltage controller can operate as a rectifier or an
inverter and the same can be applied to the power controller. As
the aim of this study is to develop a suitable control strategy,
the energization sequence of the converter is not studied here.
It is assumed that the main dc capacitor was initially charged at
300 kV and the floating capacitors
and
were charged at
200 and 100 kV, respectively, prior to the deblock of both converter stations.
First, system operation under balanced network conditions is
tested with active and reactive power variations. Fig. 5 shows
the simulation results of the current references and responses for
the two converters. Both converters were deblocked at a time of
0.05 s and then various active power orders were set at the power
controller (at a rate of 100 MW/20 ms) and q-axis current orders
were set for both ends of the scheme. As can be seen from Fig. 5,
the system responses are satisfactory and the main dc and the
floating capacitor voltages are well controlled under transient
conditions.
Unbalanced conditions were simulated using a solid
single-phase-to-ground fault applied directly at the transformer primary side. A fault on each side of the converters
was studied with active power flow in either direction. During
the simulation, faults were applied at 0.4 s and cleared at 0.6
s. Before the fault, the transmitted power is 200 MW. The
negative-sequence currents
were controlled to ensure
clean active power input/output to the converter, (i.e., no
second-order dc power oscillation). The maximum converter
current was set at 2 kA and the positive-sequence d-axis cur-
XU et al.: VSC TRANSMISSION OPERATING UNDER UNBALANCED AC CONDITIONS—ANALYSIS AND CONTROL DESIGN
433
Fig. 6. Simulation results under single-phase-to-ground fault on the power controller side. (a) DC voltage controller d–q current references and responses. (b)
Power controller positive-sequence d–q current references and responses. (c) Power controller negative-sequence d–q current references and responses. (d) Active
power inputs measured at the PCC and converter side of the power controller. (e) AC voltage THD on both sides. (f) Main dc and floating capacitor voltages.
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 1, JANUARY 2005
rent is automatically limited to ensure the overall current is
within this range.
Fig. 6 shows the simulation results under single-phase-toground fault on the power controller side when the power controller operates as an inverter. The performance when the power
controller operated as a rectifier is very similar to those shown
in Fig. 5 and is not shown due to space limitations.
Fig. 6(a) shows the d–q current reference and response
of the dc voltage controller while the positive- and negative-sequence current references and responses of the power
controller are shown in Fig. 6(b) and (c). It can be seen that
under the single-phase fault condition, both the positive- and
negative-sequence currents are well controlled. Fig. 6(d) shows
the power measured at the transformer primary (PCC) and
secondary (converter) sides, respectively. As can be seen, the
output power from converter does not contain second harmonic
while the power measured at the transformer primary side
does contain second harmonic due to the transformer leakage
inductance. The common bus ac voltages and their THD of the
two ends are shown in Fig. 6(e), respectively. It can be seen,
apart from transient, that the THDs for both ends are below
2% even during the fault. The main dc and floating capacitor
voltages for both ends are shown in Fig. 6(f). It can be seen that
the dc is regulated at its nominal value with little second-order
harmonics even under single-phase fault conditions. During
the whole operating period, the floating capacitor voltage is
well balanced. The increase of the floating capacitor voltage
ripple at the power controller side is due to the increase of the
converter current (i.e., the converter is operated at its current
limit of 2 kA during the fault).
Simulation results when single-phase-to-ground fault applied
to the dc voltage controller side have shown similar performance
as those depicted in Fig. 6.
[3] S. Chen, G. Joos, and L. T. Moran, “Dynamic performance of PWM
STATCOM’s operating under unbalanced and fault conditions in distribution systems,” in Proc. IEEE Power Eng. Soc. Winter Meeting, 2001,
pp. 950–955.
[4] C. Hochgraf and R. H. Lasseter, “STATCOM controls for operation
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538–544, Apr. 1998.
[5] C. B. Jacobina, M. B. de R. Correa, R. F. Pinheiro, E. R. C. da Silva,
and A. M. N. Lima, “Modeling and control of unbalanced three-phase
systems containing PWM converters,” IEEE Trans. Ind. Appl., vol. 37,
no. 6, pp. 1807–1816, Nov./Dec. 2001.
[6] P. Rioual, H. Pouliquen, and J. Louis, “Regulation of a PWM rectifier in
the unbalanced network state using a generalized model,” IEEE Trans.
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[9] N. Mendalek, K. Al-Haddad, L. A. Dessaint, and F. Fnaiech, “Nonlinear
control strategy applied to a shunt active power filter,” in Proc. IEEE
Power Electron. Specialist Conf., 2001, pp. 1871–1882.
[10] Q. Yu, S. D. Round, L. E. Norum, and T. M. Undeland, “Dynamic control
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V. CONCLUSION
A VSC transmission system operated under unbalanced
ac conditions has been analyzed in this paper. A new control
design for improving VSC transmission system performances
during unbalanced network conditions has been proposed.
The proposed approach uses two sets of controller (i.e., a
main controller and an auxiliary controller). The main controller is implemented in the positive-sequence d–q frame
using decoupling without getting involved in positive- and
negative-sequence decomposition. Alternatively, the auxiliary
controller is implemented in the negative-sequence d–q frame
with cross coupling control of the negative-sequence current.
Simulation results have shown good performance of the proposed system under balanced conditions and unbalanced fault
conditions.
REFERENCES
[1] B. R. Andersen, L. Xu, P. Horton, and P. Cartwright, “Topology for
VSC transmission,” Inst. Elect. Eng. Power Eng. J., vol. 16, no. 3, pp.
142–150, Jun. 2002.
[2] J. L. Thomas, S. Poullain, and A. Benchaib, “Analysis of a robust
DC-bus voltage control system for a VSC transmission scheme,” in
Proc. 7th AC/DC Transmission Conf., Nov. 2001.
Lie Xu (M’03) received the B.Sc. degree in electrical
and electronic engineering from Zhejiang University,
Hangzhou, China, in 1993, and the Ph.D. degree in
electrical and electronic engineering from the University of Sheffield, Sheffield, U.K., in 1999.
Currently, he is with the School of Electrical
and Electronic Engineering, Queen’s University of
Belfast, Belfast, U.K. Previous to this, he was with
ALSTOM T&D Ltd., Power Electronic Activities
(PEA), Stafford, U.K. He was with the Centre for
Economic Renewable Power Delivery (CERPD),
University of Glasgow, Glasgow, U.K., from 1999 to 2000. His main interests
are power electronics, renewable energy, and application of power electronics
to power systems.
Bjarne R. Andersen (SM’02) was born in Copenhagen, Denmark, in 1948. He received the M.Sc. degree in electrical power engineering and the Ph.D.
degree in high-voltage technique from the Technical
University of Denmark, Copenhagen, Denmark.
He is now with Andersen Power Electronic
Solutions Ltd. Stafford. Previously, he was Special
Projects Director with ALSTOM T&D Ltd., Power
Electronic Activities (PEA), Stafford, U.K., where
he spent most of his career working on HVdc, SVC,
and flexible ac transmission systems (FACTS).
Dr. Andersen is a Fellow of the IEE, U.K. He is a member of IEEE Working
Group I5 and I8 of the Substation Committee. He is the Convenor of CIGRE
Working Group B4-37 VSC Transmission and the Regular Member for U.K. of
Study Committee B4.
Phillip Cartwright received the B.Eng. (Hons.)
degree in electrical engineering from Staffordshire
University, Stafford, U.K., in 1995, and is currently
pursuing the Ph.D. degree at the University of
Manchester Institute of Science and Technology,
Manchester, U.K.
Currently, he is with Areva T&D Technology
Centre, Stafford. Previously, he was with Alstom
T&D Ltd., Power Electronic Activities, Stafford,
where he contributed to the development, design,
implementation, and testing of several HVdc systems. His main research interests include doubly fed induction machines using
VSCs and their application within wind farm applications.