NORDIC WIND POWER CONFERENCE, 1-2 MARCH, 2004, CHALMERS UNIVERSITY OF TECHNOLOGY 1
Simple Control Scheme of PWM Converter Connecting
Wind Turbine with Grid  Simulation Study
Mariusz Malinowski*, Steffen Bernetf&
*
Warsaw University of Technology, Institute of Control&Industrial Electronics,
ul. Koszykowa 75, 00-662 Warsaw, POLAND, [e-mail]
f&
Technical Univesity of Berlin, Institute of Energy and Automation Technology,
Sekr. E2 Einsteinufer 19, D-10587 Berlin, GERMANY, [e-mail]
distortion, what reduce performance of applied converter.
Abstract This paper proposes a simple direct power Only a DPC strategy based on virtual flux instead of the line
control using space vector modulation (DPC-SVM) for three-
voltage vector orientation, provides robust operation.
phase PWM converter connecting wind turbine generator with
Section II presents principles of virtual flux and power
grid. The active and reactive power is used as the pulse width
estimation as well as basic block scheme of DPC-SVM.
modulated (PWM) control variables instead of the three-phase
Moreover, this section is devoted to presentation of
line currents ever used. Moreover, grid voltage sensors are
synthesis of the power controllers and describes influence of
replaced by virtual flux (VF) estimator. Theoretical principle
coupling between active and reactive power. Section III
of this method as well as synthesis of the active and reactive
shows LCL-filter design. Sections IV and V contain
power controllers are discussed. It is shown that proposed
simulation study and final conclusions.
method exhibits several features as: simple and robust
algorithm as well as simple tuning procedure of PI power
controllers. Moreover paper presents LCL-filter design, which
II. CONTROL OF PWM CONVERTER
fulfil IEEE-SCR 20-50 recommendation. Simulation results
Direct Power Control Space Vector Modulated (DPC-
have proven excellent performances and verify the validity of
SVM) is based on the active and reactive power control
the proposed system.
loops [5,8-9,12]. In DPC-SVM there are no internal current
control loops. Therefore, the key point of the DPC-SVM
Index Terms control strategies, energy conversion,
implementation is a correct and fast estimation of the active
power quality, wind energy.
and reactive power (described in section A) as well as fast
PI power controllers (described in sections B and C). Basic
block scheme of control method is shown in Fig. 1. The
I. INTRODUCTION
commanded reactive power qref (set to zero for unity power
ENERATORS and power electronics technology for
factor operation) and (delivered from the outer PI-DC
G
wind turbines become one of most promising
voltage controller) active power pref values are compared
technology. Number of installed wind turbines increasing
with the estimated q and p values, respectively. The errors
every year rapidly and necessity of grid-friendly interfaces
are delivered to PI controllers, where the variables are DC
application between grid and turbine is viable solution [1,2].
quantities, what eliminates steady state error. The output
Modern, high performance PWM converter provides unity
signals from PI controllers after coordinate transformation
power factor and low harmonic distortion of current. It has
from synchronous rotating dq to stationary Ä…² are used for
huge influence for power quality, because non-sinusoidal
switching signals generation by Adaptive Space Vector
current delivered to grid, can introduce additional non- Modulator (ASVM) [10]. ASVM bases on assumption that
sinusoidal voltage drop across the line impedance and as only two phases are modulated, third phase is clamped to
consequence, increase grid voltage distortion supplied many lower or upper DC bus. It gives only one zero state per
sampling time, what provides 33% reduction of average
other loads or affect other generators. This publication will
switching frequency. However, switching losses strongly
consider new control method for PWM converter
depend on power factor angle. Therefore centre of clamped
connecting small power (100kW) Permanent Magnet
(non modulated) regions should be located at the peak of the
Synchronous Generator (PMSG) with grid.
AC side current what can gives 50% reduction of switching
Various control strategies have been proposed in recent
losses [10]. ASVM observe the peak current position by
works on this type PWM converter [3,8]. A well-known
sensing of current, what is shown in Fig.1.
method of indirect active and reactive power control is
based on current vector orientation with respect to the line
A. Virtual Flux, Active and Reactive Power Estimator
voltage vector [3,6-7]. This method guarantees high
dynamics and static performance via an internal current One of the most effective methods to omit AC-line
control loops. However, the final configuration and voltage sensors is implementation of virtual flux
performance of the system largely depends on the quality of estimator. This simple noise robust solution based on
the applied current control strategy [4]. An other less known assumption that the integration of the voltages leads to an
voltage based method based on instantaneous direct active imaginary Virtual Fluxes (VF) [11,13]. Therefore,
and reactive power control is called Direct Power Control following voltage equation:
(DPC) [3]. Both mentioned strategies are sensitive for grid
 NORDIC WIND POWER CONFERENCE, 1-2 MARCH, 2004, CHALMERS UNIVERSITY OF TECHNOLOGY 2
TR
DC/DC LCL-filter
PMSG
PWM
6D
iA iB
SA SB SC
DA
U
dc
DB
P&VF
ASVM
DC
Power&
Adaptive
Space Vector Virtual Flux
iA
Modulation U
Estimation
iB
Udc_ref dc
UA UB UC
URÄ… UR² q p
Å‚¨G
X
dq
Ä… ²
PI PI PI
-
pref + - qref =0
Control
Fig. 1 Direct power control for 3-phase PWM converter connecting permanent magnet synchronous generator with grid.
diG d¨G jÉt d¨G jÉt
d
jÉt
uG = uL + uR = L + uR (1)
uG = ¨G = e + jɨGe = e + jɨG (4)
dt
dt dt dt
can be replaced by virtual flux equation [13], see Fig. 2:
where ¨G denotes the space vector and ¨G its amplitude.
È =È + È (2)
For virtual flux-oriented quantities, in Ä…-² coordinates (Fig.
G R L
2) and using (3) and (4)
d¨G d¨G
(5)
uG = + j + jÉ(¨GÄ… + j¨G ² )
uR
q-axis ²-axis dt dt
Ä… ²
uG²
uG = uGq
Å„Å‚d¨G d¨G
ôÅ‚ ôÅ‚
iGq É (6)
uGiG* = + j + jÉ (¨GÄ… + j¨G²)üÅ‚ (iGÄ… - jiG²)
òÅ‚ żł
dt dt
iG² d-axis
iG ôÅ‚ ôÅ‚
Ä… ²
ół þÅ‚
¨G (rotating)
¨L
That gives
¨G ²
Õ
¨R Å„Å‚d¨G d¨G
ôÅ‚ ôÅ‚
Ä…-axis
(7a)
p = iGÄ… + iG² +É (¨GÄ…iG² -¨G²iGÄ…)üÅ‚
òÅ‚ żł
dt dt
iGÄ… uGÄ… Å‚¨G=Ét
¨G Ä… (fixed) ôÅ‚ Ä… ²
ôÅ‚
ół þÅ‚
iGd
and
Fig. 2 Reference coordinates and vectors: ¨G  virtual flux vector of grid,
¨R  virtual flux vector of converter, ¨L  virtual flux vector of inductor,
Å„Å‚
ôÅ‚-d¨G d¨G
ôÅ‚
uR  converter voltage vector, uG - grid voltage vector,
(7b)
q = iG² + iGÄ… +É (¨GÄ…iGÄ… +¨G²iG²)üÅ‚
òÅ‚ żł
uL inductance voltage vector, iG  vector of current dt dt
ôÅ‚ Ä… ²
ôÅ‚
ół þÅ‚
Using complex notation, the instantaneous power can be
For sinusoidal and balanced voltage the derivatives of the
calculated as follows:
flux amplitudes are zero. The instantaneous active and
reactive powers can be computed as
p = Re(uG Å" iG") (3a)
p = É Å" (¨GÄ…iG² - ¨G²iGÄ… ) (8a)
q = Im(uG Å" iG ") (3b)
q = É Å" (¨GÄ…iGÄ… + ¨G²iG² ) . (8b)
where * denotes the conjugate current vector. The grid
voltage can be expressed by the virtual flux as
Full estimation process of virtual flux and active and
reactive power estimation is presented in Fig. 3
GRID
PCC
G
i
L
É
j
=
L
u
 NORDIC WIND POWER CONFERENCE, 1-2 MARCH, 2004, CHALMERS UNIVERSITY OF TECHNOLOGY 1
PWM Rectifier Voltage Estimation Block Virtual Flux Estimation Block Active and Reactive Power Estimation Block
1
T
_
D
+ q
A +
1
2
_ 3 +"
TN
+
u
RÄ… ¨GÄ…
1
i
GÄ…
i
2 u
GÄ…
dc
É
D
L
B +
i
i G²
+
G²
+
D +
¨G²
u
1 1 p
C
R²
_
_
2 +"
TN
_
1
T
Fig. 3. Block scheme of DPC-SVM estimators (P&VF)
B. Synthesis of the Active and Reactive Power Controllers The active and reactive power controllers are coupled by
the cross therms. The synthesis of the PI parameters should
The synthesis of the active and reactive power controllers
be performed in order to get a good response and to
can be done analytically using a simplified model. In this
minimize coupling effects.
model the switching waveforms created by the PWM
Considering the reactive power null, that is iLd=0, the
converter are replaced by its average value within the
active power control loop becomes disconnected from the
switching period.
reactive power (the influence of the reactive power is
The model in dq coordinates has the form:
analysed later). The block diagram for active power control
diGd
loop is shown in Fig. 5.
uGd = RiGd + L - ÉLiGq + uRd
dt
(9)
p* p
diGq 1+sTn U
-1
uGq = RiGq + L + ÉLiGd + uRq
+ _ sTi - R+Ls
dt
+
With the reference frame defined in Fig. 2.
U
uGq = U
(10)
uGd = 0
Figure 5: Active power control block diagram
and
The line voltage is seen as a constant perturbation, and
should be compensated by the integral part of the PI
p = UiGq
(11)
controller.
q = UiGd
In this way, the zero of the PI controller is placed over the
Introducing (10) into (9) the model simplifies:
pole of the system. So,
diGd
L
0 = RiGd + L - ÉLiGq + uRd
Tn = = Tol (13)
dt
R
(12)
diGq
U = RiGq + L + ÉLiGd + uRq
Where Tol is the system s open loop time constant. With
dt
this synthesis, in closed loop, the system will be as shown in
Fig.6:
Introducing PI controllers for active power p and reactive
power q the block diagram in Fig. 4 is obtained.
p
p*
U
U
uGq
U
+ _ sTiR
- +
+ -
1
PI
Ls+R
pref
-
Figure 6: Closed loop block diagram
ÉL
The closed loop transfer function is:
ÉL
U
Geq sTi R 1
+ - + = = (14)
1
PI U sTi R
1+ Geq 1+
Ls+R
qref - 1+
+
sTi R
U
0
uGd
U
The closed loop time constant Tcl is given by:
Figure 4: Simplified block diagram
 NORDIC WIND POWER CONFERENCE, 1-2 MARCH, 2004, CHALMERS UNIVERSITY OF TECHNOLOGY 2
Ti R perturbation is determined by the open loop time constant.
Tcl = (15)
This is a drawback of this synthesis that can be corrected
U
adopting small values of the closed loop time constant.
and can be a specification for the controller design. So
For the reactive power control loop it is easy to conclude
that a similar formula can be obtained. Effectively equation
UTcl
Ti = (16) (22) is obtained.
R
t t
ÉTcl p0 îÅ‚ - Tol - Tcl Å‚Å‚
(22)
"q(t) = ïÅ‚ - e śł
e
The parameters of the PI controller can be given by:
Tcl ïÅ‚
śł
1 - ðÅ‚ ûÅ‚
Tol
Tn
1 L
k = =
p
Similarly to eq. 21 the eq. 22 can be reduced to form:
Ti U Tcl
(17)
1 1 R
"q(t) = ÉTcl p0 (23)
ki = =
Ti U Tcl
III. LCL FILTER DESIGN
The specification of Tcl should be done in order to get
good response and decoupling between both controllers. The
The reduction of the current harmonics around switching
ratio of kp/ki for different closed loop time constant Tcl is
frequency and multiplication of switching frequency is done
constant and equal to open loop time constant Tol. Because
to achieve compliance with grid codes as IEEE 519-1992
the active and reactive power control loops are similar,
[15]. High inductance values can achieve this goal, however,
equations (17) are valid for both controllers.
inductor is bulky, expensive and will limit the converter
dynamics as well as the total operating range. The voltage
1) C. Influence of Coupling Between the d and q Axis
drop across the inductance is controlled by the fundamental
Considering now a perturbation y on the active power
component of the PWM converter voltage with its maximal
control loop as shown in Fig. 7,
amplitude limited by the DC-link voltage. Consequently, a
high current through the inductance requires either a high
y
+
dc-link voltage or low inductance. The maximal inductance
p* p
1+sTn + U
can be determinate as [3,12]:
sTi R+Ls
+ _
2
u 2
dc
- U
Gm
3
Figure 7: Simplified block diagram
L )# (24)
É I
m
On the active power control loop, equation (12), the
where udc  dc- link voltage, UGm  amplitude of grid
perturbation is given by:
voltage, Im  amplitude of current, É - angular frequency of
the grid.
q
y = -ÉLiLd = -ÉL (18)
U
In practice high performance gives application of LCL
Using the model of Fig. 7 it is possible to determine
low pass filter (see Fig. 8), which at relatively small filter
analytically the influence of the reactive power variation on
size, provide better harmonic attenuation.
the active power. Using Laplace transforms the effects of the
perturbation are determined by:
3xL2 3xL1
iR1
iG1
-s
(19)
"P(s) = ÉQ(s)
iC1
ëÅ‚ öÅ‚ëÅ‚ öÅ‚ iR2
1 1 iG2
PWM
ìÅ‚ ÷Å‚ìÅ‚ ÷Å‚
s + s +
Grid
ìÅ‚ ÷Å‚ìÅ‚ ÷Å‚
Tcl Tol
Converter
íÅ‚ Å‚Å‚íÅ‚ Å‚Å‚
iC2
iR3
iG3
The inverse Laplace transform gives:
iC3
t t
ÉTcl q0 îÅ‚ -Tol -Tcl Å‚Å‚
"p(t) = - ïÅ‚ - e śł (20)
e
Tcl ïÅ‚
śł
1- ðÅ‚ ûÅ‚
3xC
Tol
Fig. 8 Diagram of three-phase LCL-filter
connected between grid and PWM converter
Equation (20) shows that a step variation on the reactive
power of value q0 produces an undesirable variation on the
Table 1 Parameters used in simulation
active power that is approximately given by:
Power P 100kW
Grid voltage UL 230V
"p(t) = -ÉTclq0 (21)
DC link voltage Udc 750V
Current IG 144A(rms)
Note that this equation is approximately valid because the
Switching frequency fs 4kHz/8kHz
closed loop time constant is smaller than the open loop time
Grid frequency fg 50Hz
constant. It can be concluded also that the elimination of the
 NORDIC WIND POWER CONFERENCE, 1-2 MARCH, 2004, CHALMERS UNIVERSITY OF TECHNOLOGY 3
For the filter design a variety of optimization criteria operation), it is possible to calculate cost and weight of the
exist such as minimum cost, losses, volume and weight. filter. At this current level the weight for a three-phase input
Selection was chosen to fulfil IEEE-SCR 20-50
inductor amounts to roughly 1kg/10µH. Prices for a three-
recommendation [15], where SCR describe short-circuit
phase coil were quoted at roughly 60ct/µH, and a price for
ratio of the bus capacity to the ratings of the converter in
three capacitors used in LCL filter application is roughly
MVA. The analysis was done in Matlab/Simulink with
1USD/µF. LCL filter costs and weight comparison are
resonance frequency in range 10fn-0.5fs. The transfer
shown even in Table 2.
functions are given by:
IV. RESULTS
2
L2C s + 1
iR (s)
To study the operation of the DPC-SVM system, the
H1 (s) = = (25)
PWM converter with the whole control scheme has been
uR (s) L1L2C s3 + (L1 + L2 )s
simulated using the MATLAB/SIMULINK software. The
and
main electrical parameters of the power circuit and control
iG (s)
1
data are given in the Table I. The simulation study has been
H (s) = = (26).
2
3
u (s)
L1L2C s + (L1 + L2 )s
performed with two main objectives in mind:
R
" the steady state operation (Fig. 9);
" presenting operation with LCL-filter (Fig. 10);
Based on Eq. 24 and Table 1 the total inductance of the
Presented results have proven excellent performances and
LCL filter should be less then 4,4mH (0.86 in per unit
verify the validity of the proposed system.
notification of the base impedance zB = (UL-L)2/Sn). However
in practice to keep good dynamics and reasonable cost,
p
weight and losses, the inductance should be around or less
40
0
then 0.1 pu. For the IEEE 519-1992 limitations and the
20
0
assumption that iripple,peak not exceeds 40A the converter side,
inductance L1, implemented with iron powder core, can be 0
calculated to be [16]:
-20
0
-40
0
U
0 0 0 0 1 0 1 0 0 2 0 0 3 0 4
.1 .15 .1 .15 .12 .15 .13 .15 .1
G
L =
(27)
1
q
2 6 f i
s ripple , peak
20
0
10
0
Typically L1 is larger than the line side inductance L2, which
0
is implemented as iron steel core, in order to attenuate most
-10
0
of the current ripple. In this case split factor L2/L1 of 0.8 was
-20
0
chosen to obtain ripple attenuation 90%. In order to keep
0 0 0 0 1 0 1 0 0 2 0 0 3 0 4
.1 .15 .1 .15 .12 .15 .13 .15 .1
high power factor, the capacitor is limited as 5% of the
4
x 10
reactive power absorbed in rated conditions [14]. The
5
capacitance of LCL filter (Y-connected) cannot be larger
0
than:
-5
Pn
-10
C d"
(28)
2
120 "Ä„ " f "U
n G
-15
0 0 0 0 1 0 1 0 0 2 0 0 3 0 4
.1 .15 .1 .15 .12 .15 .13 .15 .1
T e
im
The values of the LCL-filter components, and their per unit
values, for PWM converter at 4kHz and 8kHz switching
Fig. 9. Simulated basic signal waveforms for DPC-SVM: From the top:
frequency, in order to attenuate the switching harmonics
grid voltage, converter current, instantaneous active and reactive power.
below IEEE-SCR 20-50 limits, are given in Table 2.
Based on LCL-filter data and assumption that a current
rating for inductor is determined as 160A(rms) (overload
Table 2 LCL filter components used in simulation for fs=4kHz/8kHz together with LCL filter as well as costs and weight comparison
fs L1 C L2 Costs of filter installation Filter weight
mH PU PU mH PU USD kg
µF
4kHz 3 x 0,30 0.059 3 x 100 0.050 3 x 0,24 0.047 424 54
8kHz 3 x 0,15 0.030 3 x 50 0.025 3 x 0,12 0.024 212 27
 NORDIC WIND POWER CONFERENCE, 1-2 MARCH, 2004, CHALMERS UNIVERSITY OF TECHNOLOGY 4
" Simple PI power regulators tuning procedure, what
provide decoupling between active and reactive power
and good dynamics;
ACKNOWLEDGMENT
The first author thanks the Foundation for Polish Science
for granting him its prestigious scholarship, which
supported him during the described research study.
REFERENCES
[1] L. H. Hansen, P.H. Madsen, F. Blaabjerg, H.C. Christensen, U.
Lindhard, K. Eskildsen  Generators and Power Technology for wind
Turbines in proc. IEEE-IECON Conf., 2001, pp.2000-2005.
[2] S. Muller, M. Deicke, R. W. De Doncer  Doubly Fed Induction
Generator Systems for Wind Turbines IEEE Ind. Appl. Magazine,
May/June 2002, pp. 26-33.
[3] Kazmierkowski M. P., Krishnan R., Blaabjerg F.,: Control in Power
Electronics, Academic Press, 2002.
[4] Kazmierkowski M.P., Malesani L.: Current control techniques for three-
phase voltage-source PWM converters: a survey, IEEE Trans. On Ind.
Electronics, Vol. 45, No. 5, 1998, pp. 691-703.
[5] M. Malinowski, M. P. Kazmierkowski, S. Hansen, F. Blaabjerg, G. D.
Marques: Virtual Flux Based Direct Power Control of Three-Phase
PWM Rectifiers, IEEE Trans. on Ind. Appl., vol. 37, No. 4, 2001, pp.
1019-1027
[6] J. Svensson,  Grid-Connected Voltage Source Converter  Control
Principles and Wind Energy Applications , Ph.D. Thesis, Chalmers
University of Technology, Gotebörg, Sweden, 1998.
[7] M. Lindgren,  Modeling and Control of Voltage Source Converters
Connected to the Grid , Ph.D. Thesis, Chalmers University of
Technology, Gotebörg, Sweden, 1998.
[8] M. Malinowski, M. P. Kazmierkowski  Simple Direct Power Control
of Three-Phase PWM Rectifier Using Space Vector Modulation  A
Comparative Study EPE Journal, Vol. 13, No. 2 pp. 28-34, 2003.
[9] M. Malinowski, G. Marques, M.P.Kax
mierkowski -  New Direct
Power Control of three-phase PWM AC/DC converters under distorted
and imbalanced line voltage conditions - ISIE 03, Brasil.
[10] M. Malinowski  Adaptive space vector modulation for three-phase
two-level PWM rectivier/inverters Archives of Electrical Engineering
No 3, 281-295, 2002.
[11] Duarte J.L., Van Zwam A., Wijnands C., Vandenput A.: Reference
frames fit for controlling PWM rectifiers, IEEE Trans. On Ind.
Electronics, Vol. 46, No. 3, 1999, pp. 628-630.
[12] Malinowski M.: Sensorless Control Strategies for Three-Phase PWM
Rectifiers, PhD Thesis, Warsaw University of Technology, 2001
(www.isep.pw.edu.pl/icg).
[13] Weinhold M.: A new control scheme for optimal operation of a three-
phase voltage dc link PWM converter, in proc. PCIM Conf., 1991,
pp.371-3833.
[14] M. Liserre, F. Blaabierg, S. Hansen,  Design and Control of an LCL-
filter based Three-phase Active Rectifiers , Conf. Rec. IAS, Chicago,
USA, 2001.
[15] IEEE Std 519-1992,  IEEE Recommended Practices and Requirements
for Harmonic Control in Electrical Power Systems  .
[16] S. Bernet, S. Ponnaluri, R. Teichmann,  Design and loss comparison
Fig.10. Simulation results of PWM converter with LCL-filter (L1 = 0.3mH;
of matrix converters and voltage source converters for modern ac-
L2 = 0.24mH; C = 100uF; fs = 4kHz). From the top: converter current iR,
grid current iG, and harmonic spectrum of grid current together with IEEE- drives Trans. of Industrial Electronics Society, Special Edition Matrix
Converters, 2002.
SCR 20-50 recommendation.
V. CONCLUSION
Direct Power Control Space Vector Modulated for three-
phase PWM converter system constitutes a viable
alternative to the conventional control strategies and it has
the following features and advantages:
" No line voltage sensors are required;
" Noise resistant and low sampling frequency control
algorithm;