A study of converter rating for brushless DFIG wind turbines

Abstract

This paper studies the converter rating requirement of a Brushless Doubly-Fed Induction Generator for wind turbine applications by considering practical constraints such as generator torque-speed requirement, reactive power management and grid low-voltage ride-through (LVRT). Practical data have been used to obtain a realistic system model of a Brushless DFIG wind turbine using steady-state and dynamic models. A converter rating optimization is performed based on the given constraints. The converter current and voltage requirements are examined and the resulting inverter rating is compared to optimization algorithm results. In addition, the effects of rotor leakage inductance on LVRT performance and hence converter rating is investigated.

Full text

A Study of Converter Rating for Brushless DFIG
Wind Turbines
A. Oraee*, E. Abdi†, S. Abdi*, R.A. McMahon*,
*Electrical Engineering Division, Cambridge University, 9 JJ Thomson Avenue, Cambridge CB3 0FA, UK
†Wind Technologies Ltd, St John’s Innovation Park, Cambridge CB4 0WS, UK
Keywords: Brushless DFIG, DFIG, MSI, GSI, Converters,
LVRT, Wind Turbines.
Abstract
This paper studies the converter rating requirement of a
Brushless Doubly-Fed Induction Generator for wind turbine
applications by considering practical constraints such as
generator torque-speed requirement, reactive power
management and grid low-voltage ride-through (LVRT).
Practical data have been used to obtain a realistic system
model of a Brushless DFIG wind turbine using steady-state
and dynamic models. A converter rating optimization is
performed based on the given constraints. The converter
current and voltage requirements are examined and the
resulting inverter rating is compared to optimization
algorithm results. In addition, the effects of rotor leakage
inductance on LVRT performance and hence converter rating
is investigated.
1 Introduction
The Brushless DFIG is a promising replacement for the
widely used conventional DFIG offering improved reliability,
reduced capital and maintenance costs and has significantly
greater LVRT capability [1,2]. It is intrinsically a medium-
speed machine, enabling the use of a simplified one or two
stage gearbox, hence reducing the weight of the overall
drivetrain and further improving reliability [3]. It also retains
the low-cost advantage of the DFIG system as it only requires
a fractionally rated converter and does not use permanent
magnet materials. The size of the converter is determined not
only by generator design but also by grid requirements on
reactive power and LVRT. However, little attention has been
devoted to the optimization of converter rating for the
Brushless DFIG [4].
The converter comprises a machine-side inverter (MSI) and a
grid-side inverter (GSI). The optimization method minimizes
the sum of the MSI and GSI ratings, hence the total cost. The
Brushless DFIG’s per phase equivalent circuit, which offers a
straightforward way of calculating efficiency, power factor
and other steady-state measures of the machine is used to
analyse the effects of machine design and reactive power
management on converter rating, whilst the coupled-circuit
dynamic model is used for LVRT effects.
This paper examines the effect of speed range on the inverter
rating using simulation. Sources of reactive power generation
and consumption with expressions derived for the MSI, GSI
and the total inverter rating in terms of the power winding
(PW) and control winding (CW) reactive and active power
are determined. Total inverter rating optimization based on
the equivalent circuit model considering a number of
constraints is performed.
The rotor inductance, Lr significantly affects the machine’s
performance as well as the converter rating since higher
inductance values can limit the LVRT transient currents,
hence reducing converter size. However, a large MSI voltage
range is then required for controlling reactive power. The
Brushless DFIG has an intrinsically larger ‘series’ inductance,
hence experiences a reduced transient current in the MSI
compared to that of an equivalent DFIG [2]. As a result, the
system complexity and cost can be reduced and the MSI can
be utilized to support the supply of reactive current during the
entire fault cycle, giving fast dynamics. Therefore, the
assessment of Lr in system optimization is important and this
paper investigates its effects on converter rating and machine
efficiency.
2 Operation of the Brushless DFIG
The Brushless DFIG as a variable speed drive or generator
comprises two electrically separate stator windings, the Power
Winding (PW) connected directly to the mains and the
Control Winding (CW) fed by a variable voltage and
frequency converter. For variable speed operation, the shaft
speed of a Brushless DFIG is given by:
N
r
=60 f
1
+f
2
p
1
+p
2
(1)
where f1 and f2 are PW and CW supply frequencies and p1
and p2 are their pole pair numbers, respectively. With the CW
shorted (f2 is zero), the shaft speed is defined as the natural
speed. For a 4/8 pole machine this is 500 rpm at 50 Hz. The
Brushless DFIG’s simplified per phase equivalent circuit is
shown in Fig. 1 with parameters listed in Table I. The slips
are defined as follows:
s
1
=
ω
1
+p
1
ω
r
ω
1
(2)
s
2
=
ω
2
+p
2
ω
r
ω
2
(3)
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where ω1 and ω2 are the angular frequencies of the PW and
CW, and ωr is the shaft angular frequency.
Fig. 1. Referred per phase equivalent circuit of Brushless
DFIG
Parameters Power
winding
Control
winding Rotor
Resistance R1 R
2 R
r
Leakage inductance L1 L
2 L
r
Magnetizing inductance Lm1 L
m2 -
Table I Definition of equivalent circuit parameters
3 Brushless DFIG System
Fig. 2 illustrates the basic configuration of a Brushless DFIG
for a wind turbine. The real and reactive power of the PW is
controlled by the MSI. The GSI stabilizes the DC-link voltage
and is able to provide reactive power directly to the grid. A
capacitor bank may be utilized at the grid terminals to provide
a contribution to reactive power generation. A torque profile
over the generator speed range is assumed based on available
data from practical wind turbines. The E.ON grid code
requirements have been used to investigate compatibility with
the grid. The converter optimization has been carried out on
the 180 frame Brushless DFIG with specifications given in
[1].
Fig. 2. Brushless DFIG wind turbine
The CW rating is calculate as,
S
2
=−3V
2
I
2
*
(4)
and is equal to the MSI rating, SMSI,
2
SS
MSI
=
(5)
The PW real and reactive powers, P1 and Q1, can be
controlled by a vector control algorithm, implemented using a
d-q model for the Brushless DFIG [5]. A block diagram of the
control system is shown in Fig. 3 and the principles of the
controller design are presented in [5]. The CW voltage d-q
components v2q and v2d are regulated by i2q and i2d which are
determined by i1q and i1d, respectively [5]. Since there are
linear relationships between P1 and i1q, and Q1 and i1d, P1 and
Q1 can be controlled by the CW voltage, supplied by the MSI.
The control chain is therefore summarized as,
(6)
(7)
Fig. 3. Control scheme of the PW real and reactive power
From (6) and (7), the MSI is used to control the PW real and
reactive power, hence reactive power management directly
affects the size of the MSI. The GSI is generally used to
stabilize the DC-link voltage by handling the real power of
the CW. However, it can also be used to provide reactive
power directly to the grid and the total inverter rating, i.e. the
sum of MSI and GSI can then be optimized. At a grid power
factor of cosϕ, the total reactive power output, Qtot, is written
as
Q
tot
=P
tot
tan
φ
=(P
1
+P
2
)tan
φ
(8)
Qtot includes the reactive power of the PW, Q1, as well as the
reactive power provided by the GSI, QGSI. Therefore, QGSI is
written as,
Q
GSI
=Q
tot
−Q
1
(9)
and its rating, SGSI, is given by,
SGSI =P
2+QGSI
2
(10)
When unity power factor is required, (10) becomes,
S
GSI
=P
2
+Q
1
2
(11)
The total inverter rating, Stot, is the sum of GSI and MSI
ratings, given by,
S
tot
=S
GSI
+S
MSI
(12)
4 Converter Rating Minimization for Reactive
Power Management
The optimization of the total inverter rating comprising the
sum of the MSI and GSI ratings is studied using simulations
at different operating points. Measurements were made on a
prototype D180 4/8 Brushless DFIG, shown in Fig. 4, to
verify the results [5]. The equivalent circuit parameters of the
machine are shown in Table II. During all the tests shown in
this paper the PW is supplied at 240 V and 50 Hz.
P
1
⇒i
1q
⇒i
2q
⇒v
2q
Q1⇒i1d⇒i2d⇒v2d
I
1
R
1
j
ω
1
L
r
R
r
/
s
1
I
r
R
2
s
2
s
1
I
2
s
2
s
12
V
j
ω
1
L
m
2
j
ω
1
L
m
1n
V
1
,
ω
1
nnn
n
nn
n
BDFM
GSIMSI
P
2
,Q
2
Q
GSI,
P
GSI
Capacitor
Bank
Q
c
P
1
,Q
1
Wind
Gearbox
P
Grid,
Q
Grid
Grid
DC-Link
P
I
PI P
I
PI
P
I
PI P
I
PI
*
1
P
1
P
+
+
+
+
−
−
−
−
1
Q
*
1
Q
*
2q
i
+
*
2d
i+
*
2q
v+
*
2d
v
+
2q
i
+
2d
i+
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Fig. 4. Prototype Brushless DFIG
R1
(Ω)
Lm1
(mH)
Rr
’
(Ω)
Lr
’
(mH)
R2
”
(Ω)
Lm2
”
(mH)
2.3 350 1.69 50 1.97 179
Table II: Equivalent circuit parameters of D180 Brushless
DFIG [5]
The sum of the MSI and GSI ratings is minimized for given
constraints on generator reactive power. It is assumed that the
reactive power can be generated by the stator PW and GSI
independently. The former is performed through controlling
the excitation of the CW by the MSI. Thus generation of
reactive power by either means affects the converter size. The
sum of the MSI and GSI ratings at any given speed and power
factor is minimized by varying the CW excitation to identify
the CW voltage at which the sum is minimum.
Using the method proposed, the inverter rating optimization
has been performed for a Brushless DFIG wind turbine with a
practical power curve shown in Fig. 5 [7]. The wind turbine
power curve and corresponding generator shaft speed shown
in Fig. 5 are for the D180 Brushless DFIG, scaled from the
ones provided by [7] for a practical 5 MW wind turbine. As
can be seen, the speed range is symmetrical around the
natural speed and the generator operates at its maximum
speed i.e. 650 rpm from about half of the rated power. The
rated output power of the generator is 5.7 kW at which the
input torque is 105 Nm.
Fig. 6 shows the converter rating requirement to achieve unity
power factor over the entire speed range.. The corresponding
MSI and GSI ratings are also shown. As can be seen, greater
converter rating is required at either ends of the speed range,
and the split between MSI and GSI is not equal. Since higher
torques and inverter currents are required at the higher end of
the speed range, operation at the maximum speed typically
determines the inverter rating.
Fig. 5. Power versus generator speed
Fig. 6. Converter ratings for D180 Brushless DFIG
5 LVRT Performance and the Effect of Rotor
Inductance
In most recent grid codes, wind generators are required to
stay connected and be able to ride through low voltage faults
and meet the reactive current demanded by the grid. Low-
Voltage Ride-Through (LVRT) capability is therefore
important for wind generators which are integrated into the
grid. According to the by E.ON grid code, when the grid
experiences a symmetrical low voltage fault, wind turbines
need to 1) ride through a period of zero voltage up to 0.15 s
and a further period of grid voltage recovery up to 1.35 s; 2)
inject reactive current to the grid up to the rated current
during the entire 1.5 s, as shown in Fig. 7.
Fig. 7. LVRT requirement by E.ON grid code
In order to assess the LVRT performance of the Brushless
DFIG, a coupled-circuit model is utilized [2]. The simulation
results for a symmetrical three-phase short-circuit is shown in
Fig. 8. The machines is run at 650 rpm at nominal torque of
100 Nm. When a grid fault occurs, the CW current and the
MSI current rise rapidly due to loss of magnetization [2]. The
IGBTs in a converter can typically tolerate a transient peak
current up to 2 p.u. but above this level, an additional
hardware such as a crowbar is necessary to protect the
converter. It is shown in [2] that the rotor inductance Lr has
an important effect on limiting the transient current.
Fig. 9 shows the variation of MSI rating against variation of
Lr to enable grid LVRT without a need for crowbar. In the
same figure, the MSI rating required to achieve unity power
factor during steady-state operation is also shown. As
expected, an increase in Lr reduces the MSI rating needed to
ride through grid faults, but comes at the price of limited
0 5 10 15 20 25
0
1
2
3
4
5
6
Generator Output Power (kW)
Wind Speed (m/s)
0 5 10 15 20 25
350
400
450
500
550
600
650
Generator Shaft Speed (rpm)
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capability in reactive power management. The increase in Lr
leads to higher MSI voltage requirement for the control of the
PW reactive power, hence increasing its rating. It can be seen
from Fig. 9 that there is a crossover which shows the rotor
inductance at which MSI rating is minimum while satisfying
both requirements.
The rotor inductance may also affect other performance
measures of the Brushless DFIG, such as efficiency. Fig. 10
shows the effect of Lr on full load efficiency. As expected, the
efficiency declines slightly with increase in Lr. This is due to
the increase in the MSI voltage and current as the leakage
inductance is increased.
Conclusions
The converter rating for the Brushless DFIG wind turbine has
been studied with respect to reactive power management and
grid LVRT requirements. The optimization procedure takes
into account the ratings of MSI and GSI to achieve a
minimum sum to satisfy steady-state and transient operating
constraints. Though the speed deviation is smaller above the
natural speed, the total inverter rating is determined by the
operation at the maximum speed due to the rated power being
delivered at this speed. Once the minimum requirement for
MSI and GSI ratings is established by the optimization
algorithm, the ultimate choice of the inverters is made based
on commercially available converters.
It has also been shown that a higher rotor inductance limits
the LVRT currents but comes at a price of more difficult
reactive power management and reduced overall efficiency.
References
[1] R. A. McMahon, P. C. Roberts, X. Wang, and P. J.
Tavner, “Performance of BDFM as generator and motor”,
Electrical Power Applications, IEE Proceedings, 153(2):289-
299, 2006.
[2] Long, T., Shao, S., Abdi, E., Malliband, P., Mathekga,
M.E., McMahon, R.A. and Tavner, P. J.: ‘Symmetrical low
voltage ride-through of a 250 kW Brushless DFIG’, 6th IET
Int. Conf. on Power Electronics, Machines and Drives
(PEMD), Bristol, UK, March 2012, pp. 1-6.
[3] Polinder, H., van der Pijl, F.F.A., de Vilder, G.-J. and
Tavner, P.J.: ’Comparison of direct-drive and geared
generator concepts for wind turbines’, IEEE Trans. On
Energy Conversion, 2006, 21, (3), pp. 725-733.
[4] X. Wang, P. Roberts, and R. McMahon, “Studies of
inverter ratings of BDFM adjustable speed drive or generator
systems”, International Conference on Power Electronics and
Drives Systems, 2005. PEDS 2005, Vol: 1, pp. 337 – 342,
2005.
[5] Shiyi Shao, E. Abdi, and R. McMahon, “Dynamic
analysis of the brushless doubly-fed induction generator
during symmetrical three-phase voltage dips”, International
Conference on Power Electronics and Drive Systems, PEDS
2009, 2009.
[6] R. Carlson, H. Voltolini, F. Runcos, P. Kuo-Peng, and
N.J. Batistela. Performance analysis with power factor
compensation of a 75 kw brushless doubly fed induction
generator prototype. In IEEE International Electric Machines
& Drives Conference, 2007. IEMDC ’07., 2007.
[7] Rain Byars, Power System Architecture: Finding the Best
Solution for a 5MW Wind Turbine. EWEA Offshore Wind
Conference, Amsterdam, November 30, 2011.
Fig. 8. Converter peak current under LVRT performance
Fig. 9. MSI rating against rotor leakage inductance
Fig. 10. Efficiency variation with rotor leakage inductance
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