Download III. 3-phase Active Shunt Filter

Active Shunt Filter for Harmonic Mitigation in Wind Turbines Generators
Fernando Soares dos Reis - Jorge Antonio Villar Alé
Fabiano Daher Adegas - Reinaldo Tonkoski Jr.
Pontifical Catholic University of Rio Grande do Sul
Av. Ipiranga 6681, Porto Alegre, RS, CEP 90619-900, Brazil
Email: [email protected]
Syed Slan - Kevin Tan
Curtin University of Technology
School of Electrical and Computer Engineering
Kent Street, Bentley, WA 6102 GPO box U1987, Australia
Email: [email protected]
Abstract—One of the preferred technologies in variable speed
wind turbines (VSWT) is formed by a wind rotor, permanent
magnet synchronous generator (PMSG), three-phase bridge
rectifier (BR) with a bulky capacitor, and power electronics
converter for grid interface. High-intensity, low-frequency
harmonic currents flows into the PMSG as electric load has a
non-linear characteristic.
This paper presents an analysis and simulation of an active
shunt filter (ASF) for harmonic mitigation in wind turbines
generators. Currents are represented in d-q synchronous
reference frame (SRF) and PWM carrier strategy is used to
control the active filter. A new scheme to synchronize d-q
currents using mechanical rotor angular speed is adopted.
A dynamic wind turbine model and the active filter are
implemented on software PSIM©. Representative waveforms
and spectral analysis is presented. Simulations show that the
proposed active filtering configuration can mitigate harmonic
content into the PMSG.
(PMSG), three-phase bridge rectifier with a bulky capacitor,
and current-controlled voltage source inverter (CC-VSI) or
line-commutated SRC with active harmonic compensation
for grid interface [4]. Three-phase bridge rectifier with bulky
capacitor presents a non-linear characteristic and
consequently harmonic current content flows into the
PMSG. Asynchronous components in the air-gap field
induces eddy currents in the solid rotor iron, increasing
PMSG losses and temperature [5]
An alternative to mitigate harmonic content into PMSG is
to use power electronics converter that actively cancel
harmonic currents, providing a sinusoidal waveform. One of
the ways to compensate harmonic content is to use an active
shunt filter (ASF). ASF is being used with success to reduce
harmonic content in industry and distribution lines [6]. The
use of ASF in wind turbines must be investigated.
This paper presents an analysis and simulation of an
active shunt filter (ASF) for harmonic mitigation in wind
turbines generators. Currents are represented in d-q
synchronous reference frame (SRF), and PWM carried
strategy is used to control the active filter. A new scheme to
synchronize d-q currents using rotor mechanical angular
speed is adopted.
A dynamic wind turbine model and the active filter are
implemented on software PSIM©. Representative
waveforms and spectral analysis is presented. Simulations
show that the proposed active filtering configuration can
mitigate harmonic content into the PMSG.
Index Terms—Active shunt filter, wind turbines, permanent
magnet synchronous generator, wind energy conversion
systems.
I. INTRODUCTION
W
ind power is the most rapidly-growing means of
electricity generation at the turn of the 21st century
Global installed capacity has raised 20% in 2004 [1].
Developments in wind turbine technology follow this grown.
Fixed speed wind turbines (FSWT) with passive power
control are now giving place to variable speed wind turbines
(VSWT) with active power control. VSWT has some
advantages when compared to FSWT, e.g. lower mechanical
stress, increased energy capture, active reactive power /
voltage control [2].
Operation principle of VSWT is to decouple system
electrical frequency from mechanical frequency. Power
electronics has a main role on this task. Two VSWT
topologies are emerging as preferred technologies.
Doubly-Fed Induction Generator (DFIG) wind turbines
utilize a wound rotor induction generator, where the rotor
winding is fed through back-to-back variable frequency,
voltage source converters [3].
Developments in gearless, variable-speed generators with
power electronics grid interface leads to a generation of
quiet, reliable, economical wind turbines. The most usual
technology of this direct-driven wind turbine is composed by
a multi-pole permanent magnet synchronous generator
II. WIND ENERGY CONVERSION SYSTEM MODEL
The basic diagram of the wind energy conversion system
to be analyzed on this paper is illustrated in Fig. 1. The
system is composed by a wind rotor which transforms the
kinetic energy from the wind with uwind speed in mechanical
torque in the shaft. The shaft drives directly the PMSG,
which generates power with variable-frequency and alternate
current. A rectifier bridge with a bulky capacitor Clink is
responsible for AC-DC conversion to form the DC link. Grid
interfacing DC-AC power converter is represented by a
equivalent resistance Rload.
The ASF is connected on main bus between generator and
bridge rectifier. It consists of a six-switch, three-phase
voltage source inverter (VSI), a CDC capacitor on the DC
side of the inverter, and a LF to suppress high-frequency
currents originated by the switching of the VSI. A bank of
capacitors C is used for filter high-frequency voltage
occasioned by the inverter.
ωe is the electrical angular speed of the generator; λm is the
amplitude of the flux linkages established by the permanent
magnet viewed by the stator windings, and ρ is the operator
d/dt.
0,08
0,07
Fig. 1. Basic diagram of the wind energy conversion system.
A. Wind Rotor
The fundamental dynamics of VSWT can be expressed by
this simple mathematical model:
d m
J
 Ta  T f  Te
dt
1
D
2
CT ( ,  ) A u wind
2
2
m  D 2
(2)
(3)
u wind
For a fixed-pitch blade rotor, CT is a function of  only.
The CT( curve to be used on this work is illustrated on Fig.
2.
Friction torque is determined by:
(4)
T f  B m
where B is the friction coefficient.
B. PMSG
Dynamic modeling of PMSG can be described in d-q
reference system [7]:
(5)
v q   R  pLq iq   e Ld id   e m


v d  R  pLd i d   e Lq i q
0,04
0,03
0,02
0,01
0
2
where CT is the rotor torque coefficient;  is the air density;
A is the rotor swept area; D is the rotor diameter; and uwind is
the wind speed. Torque coefficient is a non-linear function
of the tip-speed ratio and blades pitch angle β. This
relation can be found by computational simulations or
experimentally. Tip-speed ratio is expressed by:

0,05
4
(1)
where J is the moment of inertia (rotor inertia plus generator
inertia), ωm is the mechanical angular speed, Ta is the
aerodynamic torque; Tf is the friction torque (rotor fiction
plus generator friction); and Te is the electrical load torque
from wind turbine.
Aerodynamic torque Ta is determined by:
Ta 
Torque Coefficient
0,06
(6)
where R is the stator winding resistance; Ld and Lq are stator
inductances in direct and quadrature axis, respectively; id e iq
are the currents in direct and quadrature axis, respectively;
6
8
10
12
Tip Speed Ratio
Fig. 2. Torque coefficient CT versus tip-speed ratio 
The expression for the electromagnetic torque can be
described as:

 3  P 
Te     Ld  Lq iq id  m iq
 2  2 

(7)
where P is the number of poles. The relation between
electrical angular speed ωe and mechanical angular speed ωm
is expressed by:
e 
P
m
2
(8)
C. Bridge Rectifier and DC Load
The WECS uses the well-known three-phase six-pulse
bridge rectifier. The DC link is formed by the capacitance
Clink Load characteristics applied to the wind turbine can be
easily represented by changing the value of the resistor Rload,
seen on Fig. 1.
High-intensity, low-frequency harmonic currents flows
into the PMSG as BR has a non-linear characteristic. A
study case is presented showing the PMSG output currents at
WECS full load condition (20 kW resistive load,
Clink=5000uF, RL=6.5 Ω, VL=360 V) using a conventional
BR, at steady-state operation. The wind speed in this case is
12 m/s. A detail of the PMSG WECS simulated output
current and line-to-line voltage (divided by 4), for the rated
power deliver situation at 12 m/s wind speed, is shown in
Fig. 3. The harmonic content and the total harmonic
distortion (THD) of the output PMSG current and voltage
were obtained using Fourier analysis. The results are
summarized in Fig. 4 and Fig. 5.
determined as:
i F  i PMSG  iC  i NL
(9)
where iPMSG is the current supplied by the PMSG, iC is the
current drained by the filter capacitor C and iNL is the non
linear current drained by the load.
Fig. 3. PMSG output currents and line to line voltage div. by 4.
A. ASF Control Circuit
Control circuit of ASF has three main objectives: to
calculate harmonic currents that must be compensated; to
regulate voltage on the capacitor CDC; and to control current
iF in order to inject as close as possible the calculated
reference currents.
1) Reference Currents: The blocks diagram on Fig. 6
illustrates the harmonic currents calculation and voltage vDC
control of the capacitor
Fig. 4. Harmonic content of the PMSG output current.
Fig. 5. Harmonic content of the PMSG output voltage.
The fundamental component was omitted in these figures
in order to remark the harmonic content. From these figures
it is possible to observe that the 5th, 7th, 11th, 13th, 17th and
19th harmonics are significant. The obtained total harmonic
distortion was THD = 10.68 % and 29.15 % for current and
voltage respectively, which are quite high. At full load, the
harmonic content of the output current is minimized by the
influence of the machine stator equivalent inductance and
resistance which are Ls = 3 mH and Rs = 0.432 
respectively. Unfortunately this effect is not so noticeable
when the available wind decreases and, therefore, the
maximum power output decreases and the THD increases.
III. 3-PHASE ACTIVE SHUNT FILTER
The basic compensation principle of the ASF is to control
filter current in a closed loop manner to actively shape the
source current is into the sinusoid. [8]
Applying Kirchoff’s law on the coupling point of the ASF
to the main bus as seen on Fig. 1, current iF can be
Fig. 6. Block diagram of the ASF harmonic currents calculation and vDC
voltage control
Calculation of compensating currents is done by
transforming three-phase load currents in the directquadrature synchronous reference frame (d-q SRF). For this,
phase currents iNLa, iNLb and iNLc are measured and
transformed in α-β coordinates:
i 
i  

1
 1  ia 

2 1
2
2  i 
3
 3  b 
3 0
2
2  ic 

(10)
α-β currents is transformed in d-q SRF coordinates by
using a matrix of unitary amplitude sinus and cosines:
id   cos( SRF ) sin(  SRF )  i 
i   
 
 q   sin(  SRF ) cos( SRF ) i 
(11)
where θSRF is the synchronous reference frame angle.
The θSRF, when ASF is applied to industry or distribution
lines, is usually determined by phase voltage detection and
using a phase-locked-loop (PLL) system. To obtain θSRF in
this work it was used the mechanical angular speed ωm. The
idea is to use the relation between ωm and ωe expressed on
Eq. (8) and integrate ωe, obtaining the SRF angle θSRF. In
frequency domain:
 SRF 
1P
 m (s)
s 2
ASF current.
(12)
where s is the Laplace operator.
id contains fundamental and harmonics information of
active current, and iq contains fundamental and harmonics
information of reactive currents. A first order low-pass filter
with unit gain is used to obtain the DC part of id, idDC, and iq,
iqDC:
G ( s) 
k
sk
(13)
where k is the pole of the filter. idDC and iqDC contains
information of the current’s fundamental frequency.
The DC bus nominal voltage vDC must be greater than or
equal to line-to-line voltage peak to actively control iF. In
order to maintain the vDC voltage on the capacitor, an
amount of active current must be delivered to the ASF. The
vDC is regulated by a closed-loop Proporcional-Integral (PI)
control. The PI control signal Δid is summed with idDC,
adjusting the amount of active fundamental current handled
by the ASF.
The DC currents idDC+ Δid and iqDC returns to α-β
coordinates using the inverse transformation of Eq. 11:
if  cos( SRF )  sin(  SRF ) id 
i   
 
 f   sin(  SRF ) cos( SRF )  iq 
(14)
The fundamental current components on 3-phase a-b-c
coordinates, iaf, ibf, icf are obtained by the inverse
transformation of Eq. 10:


i af 
0 
 1
2  1
 
3  i 
ibf   3  2
2  i  
 
icf 

1
 3 

 
2
2

i * Fa  i NLa  iaf
i
Fc
t
C DC 
The reference currents to the ASF per phase, i*Fa, i*Fb and
are determined by the subtraction of non-linear currents
iNLa, iNLb, iNLc and fundamental currents iaf, ibf, icf:
*
2) Circuit Design: The selection of the filter inductance
LF must consider the ability to track the desired source
current. The ability improves as the filter inductance is
smaller. However, a higher switching frequency is required
to keep the ripple in the line current acceptably small. A
practical choice of LF guarantees that the active filter can
generate a current with a slope equal to the maximum slope
of the load current [9]. The upper bound on filter inductance,
for the switching scheme used in this work, is:
VDC  Vn
(17)
LF 
di (t )
max NLn
dt
where Vn is the line-to-neutral voltage and iNLn is the load
current of phase n, respectively.
The capacitor size CDC can be estimated based on filter
current iF and maximum accepted voltage ripple ΔvDCmax:
(15)
i*Fc
i * Fb  i NLb  ibf
Fig. 7. PWM carrier control for ASF current
(16)
 i NLc  icf
Just harmonics and vDC control current information is
contained on the reference currents.
2) Current Control by PWM Carrier Strategy: The filter
current is controlled by a PWM carrier strategy. Reference
currents i*Fa, i*Fb and i*Fb and measured currents iFa, iFb and
iFc are used in a PI loop control. Control signal is limited and
then compared to a triangular PWM carrier signal in order to
command VSI switches. Fig. 7 illustrates PWM control for
max  i F (t )dt
0
(18)
v DC max
From ASF output voltage to PMSG output voltage, the
inductance LF and capacitance C forms an LC filter which
cutoff frequency is:
1
(19)
 cutoff 
LF C
The value of LF, CDC and C can be adjusted based on
simulation results.
IV. POWER LOSSES CALCULATION
1) PMSG Losses: Basically the total power losses
generated into the machine can be divided into two big
groups: copper losses and core losses. The copper power
losses PCU are produced in the stator winding as function of
the RMS current, according to:
PCU  3R A

 I Ai
(20)
software was used. Table I is a summary of the parameter
values.
TABLE I – SIMULATION PARAMETERS
i 1
where IAi is the RMS value of the ith harmonic component of
the current IA and RA is stator equivalent resistance. [10, 11].
However, operating at higher current level resulted to have
temperature rise. The change of Ra due to temperature rise
was not included in the calculations. The high frequency flux
changing generated by the harmonics causes hysteresis Ph
and eddy current power losses Pe in the core, represented by
[11]:
Pcore  Pe  Ph  (ke f 2 Bmax  k h fBmax )  weight (21)
2
2
where: ke and kh are constants, Bmax is peak flux density, f is
the rated frequency, weight represents the core and copper
weight.
The influence of the voltage harmonic content in magnetic
losses may be evaluated using Eq. 22 and 23 proposed by
Kaboli et al in [10]:

V 
Pe
   i 
Pe1 i 1  V1 
Parameter
LF
C
fPWM
CDC
vDC
Clink
Rload
D
J
B
Ld
Lq
Ra
Description
Value
Inductor Filter
Capacitor Filter
PWM carrier Frequency
ASF DC capacitor
ASF DC voltage
Rectifier Bridge Link Capacitor
Resistance Load
Turbine Rotor Diameter
Turbine Inertia
Friction Coefficient
d-axis inductance
q-axis inductance
Stator Resistance
1.5mH
3.9F
20 kHz
10000F
500 V
5000F
6.5 Ω
10 m
1500 kg.m2
20 N s/rad
5.24 mH
5.24 mH
0.432 Ω
The waveforms of steady-state simulation at WECS full
load condition (20 kW resistive load, Clink=5000uF, RL=6.5
Ω, VL=360 V) with wind speed of 12 m/s is shown on Fig. 8.
2
(22)
2

V  1
Ph
   i 
Ph1 i 1  V1  i
(23)
Ph1, Pe1 and V1 are the hysteresis and eddy current power
losses and the PMSG line to line output voltage respectively
at the nominal condition resistive load without harmonics, i
is the harmonic order and Vi are the amplitude of the
harmonic components of the PMSG line to line output
voltage.
2) ASF Converter Losses: Losses generated by the ASF
consists of passive and active component losses. For one
passive component (e.g. capacitor, inductor), losses can be
determined by:
Ppc  I pcRMS ESR
(24)
where IpcRMS is the passive component RMS current and
ESR is the component series equivalent resistance.
For one IGBT switch current, PIGBT loss can be obtained:
(25)
PIGBT  VCESAT I IGBT _ AVG
where VCESAT is the collector-emitter voltage during
conduction and IIGBT_AVG is the IGBT average current.
Fig. 8. Main waveforms of WECS with ASF at full load condition .
3) Bridge Rectifier Losses: For the bridge rectifier, losses
can be determined by:
PBR  6V D I D _ AVG  rD I D _ RMS 
(26)
where VD is the diode voltage drop under conduction, ID_AVG
and ID_RMS is the average and RMS current of diode
respectively, and rD is diode resistance under conduction.
V. SIMULATION RESULTS
For simulation of the proposed configuration, PSIM®
Harmonic content in percent of fundamental component
using ASF, for PMSG output current and voltage, is
illustrated on Figs. 9 and 10 respectively. The ASF filter
reduces considerably the total harmonic distortion of current,
from 10.68% to 2.60%.Voltage THD got better as well,
from 29.15% to 20.77%. The lower harmonic content of
voltage diminishes the core losses. Due to ASF voltage vDC
control, a larger amount of fundamental current is required
from the PMSG, implying in larger copper losses.
1,2
THD=2.60 %
1,0
0,8
% 0,6
0,4
0,2
0,0
2
7
12
17
22
27
32
37
42
47
52
57
Order
Fig. 9. Harmonic content of the PMSG output phase current using ASF.
14
13
12
11
10
9
8
% 7
6
5
4
3
2
1
0
systems for harmonic mitigation was analyzed and
computationally simulated. The ASF is able to mitigate
harmonic content of current that flows on the permanent
magnet synchronous generator. A capacitor bank filter was
used to suppress high-switching frequency voltage
component generated by the ASF on PMSG terminals. The
d-q SRF synchronization using the angular rotor speed had
worked, and its physical implementation using sensors must
be investigated.
The ASF could diminish voltage core losses. Although,
PMSG efficiency is lower because copper losses are higher
when using ASF. Overall wind energy conversion system
efficiency is lower as well, so the use of ASF could be
justified if only the PMSG could have a larger life cycle.
VII. REFERENCES
THD=20.77 %
GWEC, “Global Wind Power Continues Expansion”, Global
Wind
Energy Council Release, march 4th, 2005.
[2] Spera, David A., ed. (1994). Wind Turbine Technology. New York,
NY: The American Society of Mechanical Engineers.
[3] J.B. Ekanayake, L. Holdsworth, N. Jenkins, “Comparison of 5th
order and 3rd order machine models for doubly fed induction
generator (DFIG) wind turbines” Electric Power Systems Research,
vol. 67, pp. 207-215, April 2003: Elsevier.
[4] Z. Chen, E. Spooner, “Wind Turbine Power Converters – A
2
7
12 17 22 27 32 37 42 47 52 57
comparative study”, IEE Conference on Power Electronics and
Variable Speed Drives, 21-23 September 1998, publ. no456.
Order
Fig. 10. Harmonic content of the PMSG output line-to-line voltage using
[5] J.L.F.van der Veen, L.J.J.Offringa, A. J .A. Van den put, “Minimising
ASF.
rotor losses in high-speed high-power permanent magnet synchronous
generators with rectifier load” IEE Proc-Electr. Power Appl., Vol.
144, No. 5, September 1997.
The WECS system and its subsystems power losses and
[6] Hirofumi Akagi, “New Trends in Active Filters for Power
efficiencies are summarized in Tab. II.
Conditioning” IEEE Transactions on Industry Applications, vol 32,
no 6, November 1996.
[7] Borowi, B. S., Salameh, Z. M., “Dynamic response of a stand alone
TABLE II – WECS COMPONENT LOSSES AND EFFICIENCIES
wind energy conversion system with battery energy storage to a wind
PMSG LOSSES
gust” IEEE Transactions on Energy Conversion, vol. 12, no 1,
Friction
Copper
Core
March 1997.
&
Total
Topology
Losses
Losses
η (%) [8] Akagi, H., Nabae, A. Atoh, S., “Control Strategy of Active Power
Windage
(W)
(W)
(W)
Filters Using Multiple Voltage-Source PWM Converters” IEEE
(W)
Transactions on Industry Applications, vol. IA-22, No. 3, May 1986 .
BR
2318.93
180.82
120
2619.75
88.42
ASF
2790.24
150.73
120
3060.97
86.73 [9] Al-Zamil, A. M., Torrey, D. A., “A Passive Series, Active Shunt
Filter for High PowerApplications” IEEE Transactions on Power
Electronics, vol. 16, no. 1, january 2001.
ASF LOSSES
[10] Kaboli, Sh.; Zolghadri, M.R.; Homaifar, A., “Effects of sampling
IGBT
LF Losses
C Losses
CDC Losses
time on the performance of direct torque controlled induction motor
Total (W)
Losses (W)
(W)
(W)
(W)
drive”, IEEE International Symposium on Industrial Electronics,
2003. ISIE '03, Volume: 2 , June 9-11, 2003, pp.:1049 – 1052.
199.44
284.66
0.2166
116.00
600.33
[11] Yao Tze Tat, "Analysis of Losses in a 20kW Permanent Magnet
Wind Energy Conversion System", in the Department of Electrical
ELECTRICAL SYSTEM LOSSES
and Computer Engineering. Western Australia: Curtin University of
Topology
PMSG
ASF Total
Rectifier
Efficiency
Technology, October 2003. pp. 101.
Total (W)
(W)
Total (W)
(%)
BR
2619.75
0
95.16
88.05
VIII. ACKNOWLEDGEMENT
ASF
3199.92
603.03
211.82
84.74
The authors want to thanks CAPES and CNPq for sponsoring this work.
WECS EFFICIENCY
Topology
Aero dynamical
Electrical (%)
Overall (%)
(%)
BR
ASF
43.26
43.88
88.05
84.74
38.09
37.18
VI. CONCLUSION
The use of active shunt filter in wind energy generation
[1]