LFAC-Transmission Systems for Remote Wind Farms Using a
Three-phase, Six-pulse Cycloconverter
Yongnam Cho, Student Member, IEEE, George J. Cokkinides, Senior Member, IEEE, and
A. P. Meliopoulos, Fellow, IEEE
needed due to the capacitance of the cables. To overcome the
drawbacks of the HVAC (60Hz transmission systems),
high-voltage direct-current (HVDC) transmission systems was
introduced and recently, HVDC systems become well
established transmission technologies. However, HVDC
systems are expensive solutions to connect offshore wind
farms from short and intermediate distances. The converter
substation has to be nearby the offshore wind farms on the sea,
and thus, the initial investment costs for HVDC systems are
more expensive than those of onshore wind farms.
Low frequency alternating transmission systems using a
three-phase, six-pulse cycloconverter are presented for
intermediate distances between 50km and 150km since the
LFAC-transmission systems represent more cost effective
technology for offshore wind forms [2]. The basic concept of
the LFAC transmissions uses a frequency (16.666Hz/20 Hz)
lower than nominal frequency (50Hz/60Hz) by interconnecting
a frequency changer between the point of common connection
(PCC) and nominal-frequency main grids.
In this paper, we present LFAC-transmission systems and a
robust and reliable modeling method that named quadraticintegration method. In following report, the descriptions of the
LFAC-transmission systems and the modeling method of the
three-phase cycloconverter are described, and the test results
are presented with one of the LFAC-transmission systems.
Abstract— This paper presents an alternative transmission
system for remote wind farms to main grids using a
low-frequency AC (LFAC) technology and a robust-modeling
method for analysis of the alternative-transmission systems. The
LFAC transmission system uses a lower frequency
(20Hz/16.666Hz) than nominal frequency (60Hz/50Hz) of main
grids by introducing a three-phase six-pulse cycloconverter. The
benefits of the LFAC transmission system are demonstrated as
follows:
reduced-investment
cost
compared
with
HVDC-transmission systems and increased power transfer
capability as compared with 60Hz-HVAC transmission systems.
In this paper, the economical and technical benefits of LFAC
transmission systems are presented, the modeling method using
the quadratic-integration method is presented, and the superior
properties of the quadratic integration are demonstrated with an
example LFAC- transmission system.
Index Term—Quadratic integration, three phase six-pulse
cycloconverter, cosine wave crossing method, low frequency
transmission, and wind energy transmission.
III. INTRODUCTION
T
increasing cost and environmental restrictions of
non-renewable resources have accelerated the dramatic
innovations and improvements of technologies to use
renewable energy resources including wind energy, solar
energy, hydropower, etc. Especially, wind energy and solar
energy among them have become the most promising
alternative energy resources. However, the solar energy is not
popular for utility levels but for small facilities as individual
homes. Since wind energy is more feasible for mass-power
generation than other renewable resources, plans to install
hundreds of GW of wind-turbine generation from wind in the
next few years are in place in the US, Europe, and China [1].
Since wind power is randomly varying and it has to be
captured over a wide area for stable and reliable operation,
remote wind farms and offshore wind farms have been very
attractive to overcome the space shortage on shore and to
capture high quality wind. That is, the transmission distance
from wind farms to main grid systems is increased and
traditional transmission systems (high-voltage alternatingcurrent (HVAC) transmission systems) are not cost effective
for both the remote-wind energy transmission and
offshore-wind energy transmission in which electrical losses
are huge and inductive compensation for submarine cables is
HE
IV. DESCRIPTION OF THE LFAC-TRANSMISSION SYSTEMS
In this section, we present alternative transmission
topologies operating at low frequency for the purpose of
decreasing the cost of transmission and making the wind farm a
more reliable power source to increase the capacity credit. The
general approach for defining these topologies is illustrated and
the benefits by using these alternative transmission systems are
presented next.
A. The configurations of LFAC transmissions
Since variable speed wind generation systems are attractive
for increasing energy capture and reducing mechanical fatigue
damage [3], we propose two types of LFAC-transmission
systems connected to variable speed wind turbine generators
(WTG): doubly-fed induction generators (DFIG) and
permanent magnet synchronous generators (PMSG) or squirrel
cage induction generator (SCIG) as shown in Figure 3.
The WTG system using a DFIM is controlled by
back-to-back converter system that is placed between the rotor
and the stator of the DFIM. The back-to-back converter
consists of a rotor-side converter (RSC) and a grid-side
A.P Meliopoulos, George J.Cokkinides, and Yongnam Cho are with the
School of Electrical and Computer Engineering, Georgia Institute of
Technology, Atlanta, GA, 30332 USA e-mail:(sakis.m@gatech.edu,
george.cokkinides@ece.gatech.edu, ycho8@mail.gatech.edu)
978-1-4673-1130-4/12/$31.00 ©2012 IEEE
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converter (GSC). The RSC transmits real power and imaginary
power into the rotor of the DFIM, and the GSC is needed to
support the DC voltage level and to offer the controllability of
imaginary power at the grid [4]. The WTG system using PMSG
(SCIG) is based on a full size back-to-back converter system
that is placed between the stator of the generator and the PCC.
The back-to-back converter system consists of a stator side
converter (SSC) and a grid side converter (GSC), and deals
with the full ranges of the generated power from wind turbines.
The configurations of LFAC-transmission systems using
variable frequency topologies are shown in Figure 2 and Figure
3. In the LFAC-configuration 1, the wind generated power
from WTGs is collected by 20Hz AC power at the PCC,
transmitted by using LFAC transmission systems until the
cycloconverter station, and the cycloconverter interconnects
the LFAC transmission system and nominal-frequency systems.
In LFAC-configuration 2, the wind generated power from
WTGs is rectified to DC power, the DC power is collected at
the PCC and inverted to 20Hz-AC power, the 20Hz-AC power
from the inverter is transmitted before the cycloconverter
station, and the cycloconverter interconnects the LFACtransmission system and nominal-frequency systems.
voltages by a combination of converter controls and
transformer tap changes under load. In case that a wind turbine
system ceases to operate, the DC output is shorted via diode.
The control problem can be simplified by providing battery
storage on the DC bus of the DC/AC converter.
B. Technical and economical benefits
Typically, geographic sites for wind power plants are in
remote land locations and offshore locations (tens of mile from
shore), so as to capture strong wind capacity. In these cases, the
transmission of wind energy to main grids is a major issue for
economically suitable connections and stable, robust
integration of wind farms, fluctuating sources [5].
Recently, HVAC and HVDC systems have been researched
and well established for offshore wind farms. However, in case
of the HVAC systems, long submarine cables interconnecting
wind farms suffer from excessive reactive power requirement
due to the capacitance of the cables and associated electrical
losses, and need for inductive compensation. It is impractical
or economically infeasible for submarine cables, since the
breakeven distance is not exceeding 50km via HVAC-cable
systems in economical aspects. HVDC-transmission systems
also have been used for offshore wind farms. Since HVDC
cable transmission is not affected from the capacitance, the
HVDC systems are technically feasible for lengths of hundreds
of kilometers to transmit electrical energy [6][7]. However,
HVDC systems are expensive solutions to connect offshore
wind farms from short and intermediate distances. The
converter substation has to be installed nearby the wind farms
on the sea, and thus the initial investment costs for HVDC
systems are more expensive than those of onshore wind farms.
The LFAC-transmission systems are introduced to be
applied for offshore wind farms of short and intermediate
distances (50km-150km). Using LFAC transmission, The first
advantage is that standard transformers can be used as long as
V/Hz operating value remains the same as the nominal case; for
example, a 13.8kV/230kV, 60Hz transformer can be used for
4.6kV/76.6kV, 20Hz operation. In this case, the rating voltage
of electrical switches in converters can be reduced since the
voltage levels can be regulated either before or after converter
stations. Second, existing technologies such as transmission
line design and protection systems, which are used in 60Hz
networks, can also be used for LFAC-transmission systems.
Third, a converter station is needed nearby wind farms on the
sea for HVDC transmission technologies. LFAC-transmission
technologies, on other hand, can omit the converter station on
the sea and only one cycloconverter station is needed on the
land. The last advantage is that the LFAC transmission can
increase the transmission capability and the capacitance in
submarine cables can be reduced, since the impedance is
practically one third of 60Hz-HVAC systems.
The presented LFAC transmission systems are technically
and economically suitable configurations to transmit electrical
power from remote wind farms to the power grid. The
proposed configuration may generate higher harmonic levels
(as compared with voltage source converters in DC
transmission systems) that can be controlled with appropriate
harmonic filters.
Figure 1. (A) the WTG system using DFIM and (B) the WTG system using
PMSG (SCIG)
Figure 2. LFAC-configuration 1: A LFAC system using 20Hz connections of
WTGs
Figure 3. LFAC-configuration 2: LFAC system using DC-series connections
The DC series connection at the wind farm (Figure 3)
presents a unique but manageable problem when the various
wind turbine systems operate at different speeds and voltages.
It is important that the AC/DC converters at each WTS and the
DC/AC converter at the collection point are operated within
their allowable range of DC voltages, which is general is quite
large. The control system automatically regulates the DC
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V. DESCRIPTION OF MODELING METHOD OF THREE-PHASE,
SIX-PULSE CYCLOCONVERTER
x (t ) − x (t − h ) = A ⋅
The reliable and realistic model of the LFAC-transmission
systems requires an accurate and robust simulation method and
exact models themselves. Quadratic-integration method is
proposed in this section since the method demonstrates several
superior features to ensure higher fidelity and stability
compared with other simulation methods. Here, we present a
reliable modeling process of a core system, three-phase,
six-pulse cycloconverter using the quadratic integration.
x m − x (t − h ) = A ⋅
h/2
h
t−h / 2
t−h
x (τ ) d τ .
(2)
(3)
X (t m ) = [ x1 (t m ) x 2 (t m ) " x n −1 (t m ) x n (t m )]T ,
n is the number of states of a system, and t m =
(t − h) + t
.
2
B. Description of a three-phase, six-pulse cycloconverter
This subsection presents the application of the quadratic
integration to a three-phase, six-pulse cycloconverter. Since
the three-phase, six-pulse cycloconverter in this paper is
operated in a partial circulating current mode, circulating
currents circulate partially via reactors between both
converters (positive and negative converters) [10][11]. By
using these operation modes, abnormal distortions (that are
generated in transitions from the positive converter to the
negative converter or reversely) are eliminated. As shown in
Figure 5, the three-phase six-pulse, cycloconverter consists of
three physical components: three-phase isolation transformers,
electrical switches (thyristors), and circulating-current circuits.
x(t − h)
0
x (τ ) d τ , and
where X (t ) = [ x1 (t ) x 2 (t ) " x n−1 (t ) x n (t )]T ,
x(t )
t
t−h
ª§
5h · º
h º
ª h
A ¸»
¨I +
A
I
A
−
«
(
)
« 24
24 ¹»
3 » ⋅ ª x t º = «©
⋅ x(t − h)
«
2h » «¬ x m »¼ « §
h
h ·»
«I − A −
A»
« ¨© I + 6 A ¸¹ »
6
3 ¼
¬
¬
¼
x m = x (t − h / 2 )
tm =t −h/2
³
t
Upon evaluation and rearrangement of the integrals, the
following matrix equation is obtained (an algebraic companion
form) that can be applied repetitively to provide the solution to
the differential equation:
A. Advance time domain method
The quadratic integration is based on two concepts: (a) The
natural elimination of artificial numerical oscillations exhibited
by the application of the trapezoidal integration; and (b) the
quadratic-integration method performs better during analysis
of complex switching systems in terms of both stability and
accuracy. These properties ensure that LFAC-transmission
systems with switching subsystems can be modeled and
simulated with greater precision.
The quadratic-integration method is a special case of class
of methods known as collocation methods [8][9]. As shown in
Figure 4, the method has three collocation points at x (t − h ) ,
x (t − h / 2 ) , and x (t ) in the integration time interval [t-h ,t].
t −h
³
t
τ
Figure 4. Graphical illustration of the quadratic integration
Assuming that the function x(t), as shown in Figure 4, varies
quadratically in the interval [t-h, t], i.e. x (τ ) = a + b τ + cτ 2 ,
the three parameters a, b, and c can be expressed as a function
of the three collocation points. The results are:
1
a = x (t − h ) , b = (− 3 x(t − h) + 4 xm − x(t ) ) ,
h
2
and c = 2 ( x(t − h) − 2 xm + x(t ) ) ,
h
where xm is the value x at the mid-point, i.e. at time t-h/2. Then,
the integration of the quadratic function is straightforward. The
procedure will be illustrated with the set of general differential
equations:
dX (t )
= AX (t )
(1)
dt
where X (t ) = [ x1 (t ) x 2 (t ) " x n −1 (t ) x n (t )]T , n is the number of
states of a system. Equation (1) is integrated from t-h to t and
from t-h to t-h/2, yielding:
Figure 5. Three phase six-pulse cycloconverter.
Furthermore, a controller is needed to generate switching
sequences for the thyristors on both converters. The
cycloconverter controller controls the magnitude and
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frequency of output voltages by controlling the timing (phase)
of the thyristor firing pulses. In order to control the output
voltages, many control algorithms have been proposed and
studied for the control of the three-phase, six-pulse
cycloconverter. Cosine-wave crossing method is elected
among the control algorithms since this method has been
proven to have the unique property of minimum total distortion
on output-voltage waveform [12].
The three physical components are modeled separately by
differential equations and algebraic equations, and the
application of quadratic integration to the equations leads to an
algebraic-companion form in terms of voltages and currents at
two future points in time. Standard nodal analysis methods are
used to obtain the algebraic-companion form of a three-phase,
six-pulse cycloconverter from the component algebraic
companion forms.
consist of the node currents of the single-phase transformer and
the internal equations are derived with internal states. The
state- space model is given as follows:
0
(22)
r1
L1
7-11
(29-33)
1
(23)
r1
r1
rc
rc
r2
L2
r2
L2
V1(t)
4-8
V2(t)
1
r2
e(t )
6
(28)
2
V3(t)
(11)
(12)
N=
(14)
where:
A=
4
(10)
(13)
G
K
G
K
ª I (t ) º
ª V (t ) º
A ⋅ «G » = B ⋅ « K
» − C ⋅ V (t − h) − D ⋅ I (t − h)
¬«V (tm )¼»
¬«I (tm )¼»
B=
C=
D=
h
h
º ª − 5h M + N º ª 5 h A º
º ª h
ª h
» « 24 s » ,
« − 24 As 3 As » « − 24 M 3 M + N » « 24
»
» « h
» « h
» «h
« h
2h
2h
«
M » « − M + N » « As »
As
As » « M + N
3
¼
3
¼ ¬ 6
¼» ¬« 6
¬« 6
¼» ¬ 6
V (t)
i (t ) 4
tn e(t )
(8)
(9)
The state-space matrix of the single-phase transformer is
reformulated into algebraic-companion forms applying
quadratic integration to the above differential equations. The
transformer algebraic-companion form (ACF) at each time step
[t-h, t] is:
rc L m
im(t)
i2 (t )
(7)
G
I (t ) = [i1 (t ) i2 (t ) i3 (t ) i4 (t ) 0 0 0 0 0]T ,
G
T
V (t ) = [v1 (t ) v 2 (t ) v3 (t ) v 4 (t ) i m (t ) e(t ) λ (t ) i L1 (t ) i L3 (t )]
5
(27)
3
i4 (t ) = −i3L (t )
0 º
0 º ª0 0 0 0 0 0 0 0
ª0 0 0 0 0 0 0 1
» «
»
«
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
−
» «
»
«
«0 0 0 0 0 0 0 0
0 »
1 » «0 0 0 0 0 0 0 0
» «
»
«
0 »
«0 0 0 0 0 0 0 0 − 1 » , « 0 0 0 0 0 0 0 0
«0 0 0 0 r 1 0 − r − r t » «0 0 0 0 0 0 0 0
0 »
c
c
c
» «
»
«
0 »
0 » «0 0 0 0 0 0 0 0
«0 0 0 0 L m 0 − 1 0
«1 − 1 0 0 0 − 1 0 − r 0 » «0 0 0 0 0 0 0 − L 0 »
1
1
» «
»
«
«0 0 1 − 1 0 − t 0 0 − r2 » «0 0 0 0 0 0 0 0 − L2 »
» «
»
«
0 ¼
0 ¼ ¬0 0 0 0 0 0 − 1 0
¬0 0 0 0 0 1 0 0
4
(26)
L 2 i (t)
(6)
M =
Lm
i1(t) r 1 L 1
i3 (t ) = i3L (t )
Where:
3
(25)
(B)
(5)
G
G
d G
I (t ) = M ⋅ V (t ) + N ⋅ V (t )
dt
Lm
L1
17-21
(39-43)
L2
i2 (t ) = −i1L (t )
The compact matrix form is also given as follows:
Lm
L1
12-16
(34-38)
2
(24)
rc
r2
(4)
0 = −rc i1L (t ) − rc t i3L (t ) + rc im (t ) + e(t )
0 = Lm im (t ) − λ (t )
d
0 = v1 (t ) − v2 (t ) − e(t ) − r1i1L (t ) − L1 i1L (t )
dt
d
0 = v3 (t ) − v4 (t ) − t e(t ) − r2i3L (t ) − L2 i3L (t )
dt
d
0 = e(t ) − λ (t )
dt
C. Modeling of the three-phase isolation transformer
The three-phase, six-pulse cycloconverter needs electrical
isolation between the inputs to the individual six-pulse bridges,
since the three-phase, six-pulse cycloconverter doesn’t has any
common connected points between the input and output [12].
Three-phase isolation transformers offer electrical isolation
and magnetic interconnection.
Modeling of the three-phase isolation transformer can be
modeled using three single-phase transformers. First, a singlephase transformer is denoted as algebraic equations and
differential equations, and the quadratic-integration method is
applied to the equations for algebraic companion forms.
Finally, the algebraic companion forms are interconnected to
provide the topology of the-three phase isolation transformer.
Here, we only introduce a wye-delta connected, three-phase
transformer although all the combinations of connections can
be modeled. Figure 6 shows (A) the three-phase isolation
transformer, and (B) a single-phase transformer.
(A)
i1 (t ) = i1L (t )
3
Figure 6. Three phase Y-˂ isolation transformer and single phase transformer.
G
T
I (t m ) = [i1 (t m ) i2 (t m ) i3 (t m ) i4 (t m ) 0 0 0 0 0]
The differential equations and the algebraic equations
describing the single phase transformer model are written in a
state-space form. There are two sets of equations, external
equations and internal equations. The external equations
G
V (t m ) = [v1 (t m ) v 2 (t m ) v 3 (t m ) v 4 (t m ) i m (t m ) e(t m ) λ (t m ) i L1 (t m ) i L 3 (t m )]T
As=diag(1, 1, 1, 1, 0, 0, 0, 0, 0), and tm is the mid-point of the
integration time step.
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The algebraic-companion forms of the three single-phase
transformers are merged to form the three-phase isolation
transformer algebraic companion form. For this purpose it is
noted that each single-phase transformer is connected to
specific nodes of the three-phase isolation transformer. The
connectivity of each single-phase transformer is defined in
terms of the order of the corresponding states. Figure 6 shows
the node numbers on specific nodes. Table I provides the
connectivity pointers of the single phase transformers.
TABLE I Connectivity pointers of single phase transformer
# 1-
Connective node
transformer
1
t
0
3
4
6
7
8
9
10
tm
22
25
26
28
29
30
31
32
2
t
1
3
5
4
12
13
14
15
tm
23
25
27
26
34
35
36
37
3
t
2
3
6
5
17
18
19
20
tm
24
25
28
27
39
40
41
42
circuits are to reduce the electrical stress placed on the
three-phase six-pulse, cycloconverter by state changes of
switches [13].
11
33
16
38
21
43
Figure 7. Electrical single valve model
The valve can be modeled by the set of algebraic equations
and differential equations:
i1 (t ) = G ⋅ [v1 (t ) − vP (t )] + Gs [vS (t ) − v2 (t )] + i L (t )
i2 (t ) = G ⋅ [v P (t ) − v1 (t )] + Gs [v2 (t ) − v S (t )] − iL (t )
The merging of these models into an overall model of the
three-phase isolation transformer is achieved by writing the
Kirchoff’s current law at each internal node of the three-phase
isolation transformer substituting the appropriate equations.
This process is achieved with the algorithm below:
0 = G S ⋅ [v S (t ) − v 2 (t )] + C S
0 = GV ⋅ [v P (t ) − v 2 (t )] + C P
d
[v P (t ) − v 2 (t )] + G ⋅ [v P (t ) − v1 (t )] − i L (t )
dt
d
0 = −v1 (t ) + v P (t ) + L i L (t )
dt
DO WHILE ( i < The Number of ROW1-˓)
(20)
A compact-matrix from can be easily written using equations
from (16) to (20), and the algebraic-companion form is yielded
by the application of the quadratic-integration method to the
compact-matrix form. All processes are the same as in the case
of the single-phase transformer model.
i1 = Valve Pointer [ i ][ itrans ]
( j < The Number of Column1-˓)
j1 = Valve Pointer [ j ][ itrans ]
A3Φ [i1][ j1] = A1Φ [i ][ j ]
B3Φ [i1][ j1] = B1Φ [i ][ j ]
E. Modeling of the circulating current circuit
The discontinuous transactions between positive and
negative converter valves generate abnormal distortions of
output voltages. Here, circulating current circuits are
introduced to avoid the voltage distortions, since the
circulating current circuits can support continuous conduction
of both converters. Figure 8 shows the equivalent circuit of the
circulating-current circuit.
C 3Φ [i1][ j1] = C1Φ [i ][ j ]
D 3Φ [i1][ j1] = D1Φ [i ][ j ]
where i = 1, 2, ..., number of row of each matrix , and
j = 1, 2, ..., number of column of each matrix
itrans = 1, 2, ...., number of 1 − Φ trnsformers .
The end result is the algebraic companion form of the overall
three-phase isolation transformer given by the following
equation:
G
K
G
K
ª I (t ) º
ª V (t ) º
K
A3Φ ⋅ « G
B
=
⋅
»
» − C3Φ ⋅ V (t − h) − D3Φ ⋅ I (t − h)
3Φ «
¬«V (t m )¼»
¬«I (t m )¼»
(18)
(19)
( itrans < Number of 1-˓ transformers)
ࣜ ࣜ ࣜ ࣜ ࣜ ࣜ
d
[v S (t ) − v1 (t )]
dt
(16)
(17)
Figure 8. Circulating current circuit model
(15)
The equations for the circulating-current circuit can be also
denoted by a set of algebraic equations and differential
equations. The model equations are:
where A3Φ and B3Φ are 44 by 44 matrices, and C 3Φ , and D 3 Φ
are 44 by 22 matrices, which are automatically built by using
the computer algorithm above.
i 0 (t ) = y 1 (t )
D. Modeling of the electrical single valve
Electrical single valve consists of an electrical switch
(thyristor) and protection circuits (a snubber circuit and a
limiting-current circuit) as shown in Figure 7. The protection
i1 (t ) = − y 2 (t )
i2 (t ) = − y1 (t ) + y 2 (t )
0 = N1 y1 (t ) + N 2 y 2 (t ) − ℜφ (t )
(21)
(22)
(23)
(24)
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dN 1φ (t )
d
(25)
− Ll
y1 (t )
dt
dt
dN 2φ (t )
d
(26)
0 = v2 (t ) − v1 (t ) −
− Ll
y 2 (t )
dt
dt
Note that ℜ is reluctance, Ll is the leakage inductance, and φ
Figure 10 represents three-phase (a) line-to-line voltages and
(b) currents at the 60Hz AC transmission system connected to
the three-phase six-pulse cycloconverter; three-phase (c)
voltages and (d) currents at the LFAC-transmission system
connected to the three-phase, six-pulse cycloconverter; and the
(e) real power from wind farm and the (f) RMS voltage at
LFAC during 10 seconds. In this simulation, the power demand
changes 6MW into 10MW at 5 second.
0 = v 0 (t ) − v 2 (t ) −
is magnetic flux on core.
A compact-matrix form can be easily written using the
equations from (21) to (26), and the algebraic-companion form
is derived by the application of the quadratic-integration
method to the compact-matrix form. All processes are the same
as the case of the single-phase transformer model.
F. Modeling of the three-phase six-pulse cycloconverter
The algebraic-companion forms of three three-phase
isolation transformers, thirty-six valves, and six circulatingcurrent circuits are merged to form the three-phase, six-pulse
cycloconverter algebraic-companion form. For this purpose it
is noted that each component is connected to specific nodes of
the cycloconverter as in case of three-phase isolation
transformer. The merging of these models into an overall
model of the three-phase, six-pulse cycloconverter is achieved
by applying the Kirchhoff’s current law at each internal node of
the three-phase, six-pulse cycloconverter substituting the
appropriate equations.
Figure 10. (a) three-phase Line-Line voltages and (b) three-phase currents at
60Hz AC transmission connected to the cycloconverter, three phase (c)
voltages and (b) currents at LFAC transmission connected to the
cycloconverter, and the (e) real power from wind farm and the (f) RMS voltage
at the LFAC from 0.0 to 10.0 seconds.
Figure 11 and Figure 12 represent three-phase (a) line-to-line
voltages and (b) currents at the 60Hz AC transmission system
connected to the three-phase, six-pulse cycloconverter, and
three-phase (c) voltages and (d) currents at the LFACtransmission system connected to the three-phase, six-pulse
cycloconverter in steady state. In Figure 11, the power demand
is 6-MW and the operation mode is a partial circulating current
mode of 0.7-pu of the phase currents at the LFAC side. The
Figure 12 shows the results with following conditions: the
power demand is 10MW and the operation mode is a partial
circulating-current mode of 0.4-pu of the phase current at the
LFAC side.
VI. SIMULATION RESULTS
This section presents simulation results on an example wind
farm with a LFAC-transmission system connected to a power
grid, as shown in Figure 9. The wind farm consists of many
wind turbine systems - the example system includes three of
them. The wind-turbine systems are connected in series after
the wind generated power is rectified to DC, and the DC power
is converted to 20 Hz AC power using an inverter. A
transformer boosts the voltage to 46 kV. A LFAC line operated
at 46 kV transmits the power over a distance of 50-miles to the
nearest power grid substation. At that point a cyclo-converter
converts the LFAC power into 60 Hz AC power for the
interconnection and another transformer boost the voltage to
115 kV. The transformer is connected to the power grid which
is a 115 kV, 60 Hz transmission at that point.
Figure 11. (a) three-phase Line-Line voltages and (b) three-phase currents at
60Hz AC transmission connected to the cycloconverter, three phase (c)
voltages and (b) currents at LFAC transmission connected to the
cycloconverter during steady state from 4.846 to 5.0 seconds.
Figure 9: Single line diagram of a power transient test system
The results illustrate the operation of the wind farm
transmission system by using a three-phase six-pulse
cycloconverter. The three-phase six-pulse, cycloconverter is
operating in a partial circulating current mode and the control
algorithm for generating switching pulses is the cosine-wave
crossing method. The detailed parameters of the three-phase,
six-pulse cycloconverter are shown in Table II.
Figure 12. (a) three-phase Line-Line voltages and (b) three-phase currents at
60Hz AC transmission connected to the cycloconverter, three phase (c)
voltages and (b) currents at LFAC transmission connected to the
cycloconverter during steady state from 9.785 to 10.0 seconds.
6
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Figure 13 and Figure 14 represent the results in transient
conditions: (a) three-phase currents at the 60Hz ACtransmission system connected to the three-phase, six-pulse
cycloconverter, three-phase (b) voltages and (c) currents at the
LFAC-transmission system connected to the three-phase,
six-pulse cycloconverter. Figure 13 shows the initial transient
condition from 0.0 to 0.5 seconds. The cycloconverter is
operated in a full circulating-current mode while the maximum
currents at the LFAC side are smaller than 80 A, and otherwise,
the cycloconverter is operated in a partial circulating-current
mode. In Figure 14, the power demand suddenly changes 6MW
to 10MW at 5.0 second. Note that the output power can be
automatically regulated by controlling the power angle . The
transient conditions last longer than 1.0 second.
VII. CONCLUSION
This paper presents an alternative transmission system from
offshore or remote wind farms to the main grid using a
low-frequency AC (LFAC) technology and a robust modeling
and analysis method for the alternative transmission systems.
In this paper, the technical and economical benefits of
LFAC-transmission systems are discussed. A robust and
reliable modeling and analysis method is presented, based on
model quadratization and quadratic integration method.
Simulation results demonstrate the robustness and stability
(free of fictitious oscillations) of the proposed method. The
proposed method has been used to assess the
advantages/disadvantages of LFAC transmission systems for
remote wind farms.
REFERENCES
[1]
[2]
Figure 13. (a) three-phase currents at 60Hz AC transmission connected to the
cycloconverter, three phase (b) voltages and (c) currents at LFAC transmission
connected to the cycloconverter during steady state from 0.0 to 0.500 seconds.
[3]
[4]
[5]
April 2008.
Bahrman, M.P.;"OVERVIEW OF HVDC TRANSMISSION" Power
Systems Conference and Exposition, 2006. PSCE '06. 2006 IEEE PES,
Nov 2006 pp: 18 – 23.
[7] D. Woodford, "HVDC Transmission". Manitoba HVDC Research Centre
Inc. Manitoba, Canada, 1998.
[8] Yongnam Cho, G.J. Cokkinides, A.P. Meliopoulo “Transient simulation
Technique for HVDC systems,” in submitted to the International
conference on Power Systems Transients, Delft, the Netherlands, June
2011.
[9] A. Meliopoulos, G. Cokkinides, and G. Stefopoulos, “Quadratic
integration method,” in Proceedings of the 2005 International Power
System Transients Conference (IPST 2005). Citeseer, pp. 19–23.
[10] W.A.Hill, E.Y.Y. Ho, and I.J. Nuezil, “Dynamic behavior of
cycloconverter system,” IEEE Transactions on Industry Applications, 06
August 2002, pp.750-755.
[11] J. Pontt, J. Rodriguez, E.Caceres, E. Illanes, and C.
Silva,”Cycloconverter Drive System for Fault Diagnosis Study: Real
Time Model, Simulation and Construction,” in Proceedings of Power
Electronics Specialists Conference, 2006. PESC '06. 37th IEEE, pp. 1-6.
[12] R. Pelly, “Cycloconverter Circuits,” in Thyristor Phase-Controlled
Converters and Cycloconverters, New York: Wiley, 1971
[13] N. Mohan, M. Undeland, and W. Robbins, “Snubber Circuits” in Power
Electronics, 3th ed. New York: Wiley, 1995, pp. 668–670.
Figure 14. (a) three-phase currents at 60Hz AC transmission connected to the
cycloconverter, three phase (b) voltages and (c) currents at LFAC transmission
connected to the cycloconverter during steady state from 4.867 to 5.423
seconds.
[6]
As seen from Figures 10 through 14, the simulation results
show that the performance of the quadratic-integration method
and the three-phase, six-pulse cycloconverter models are
robust and accurate even though the power demand suddenly
changes. Furthermore, the simulation is free from artificial
numerical oscillations as to be expected with the quadratic
integration.
TABLE II Major Circuit Parameters of Example System
Equivalent
Source1 and
Source 2
Line-to-Line voltage (RMS)
Inductance ( L )
Resistance ( R )
The parameters
of cycloconverter
Snubber ( C S )
115 kV
2.6 mH
0.1 Ω
1.0 uF
Snubber ( RS )
1200 Ω
Limiting ( L )
Limiting ( R )
Thyristor ( CP )
100 mH
3000 Ω
35 nF
Thyrister( GV at on-state)
100 Mhos
Thyrister( GV at off-state)
0.01 uMhos
R.K. Brenden; W.Hallaj; G.Subramanian; S. Katoch, “Wind energy
roadmap,” Management of Engineering & Technology, 2009. PICMET
2009. Portland International Conference on, Aug. 2009.
Nan Qin, Shi You, Zhao Xu, and Akhmatov, V., ”Offshore wind farm
connection with low frequency AC transmission technology” Power &
Energy Society General Meeting, 2009. PES '09. IEEE, July 2009, pp 1 –
8.
Shuhui Li and Tim Haskew, “Transient and Steady-State Simulation
Study of Decoupled d-q Vector Control in PWM Converter of Variable
Speed Wind Turbines,” in Proceedings of 2007 IEEE Industrial
Electronics Society Annual Conference, Taipei, Taiwan, November,
2007.
Liyan Q., Wei Q., “Constant power control of DFIG wind turbines with
supercapacitor energy storage,” IEEE Transactions on Industry
Applications, vol. 47, pp. 359-367, Nov. 2010.
P. Bresesti, W. L. Kling, and R. Vailati, “Transmission Expansion Issues
for Offshore Wind Farms Integration in Europe”, IEEE PES
Transmission and Distribution Conference and Exhibition, Chicago,
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