Download III. 3-phase Active Shunt Filter - Faculdade de Engenharia

Title: Active Shunt Filter for Harmonic Mitigation in Wind Turbines Generators
Authors:
Fernando Soares dos Reis, Member, IEEE
Reinaldo Tonkoski Jr., Student Member, IEEE
Jorge Villar Ale, Dr. Eng.
Fabiano Daher Adegas, Mestrando
**Syed Islam, Senior Member, IEEE
**Kevin Tan, Student Member, IEEE
Address:
Pontifícia Universidade Católica do Rio Grande do Sul
Faculdade de Engenharia
LEPUC – Laboratório de Eletrônica de Potência da PUCRS
Av. Ipiranga, 6681
CEP: 90619-900, Porto Alegre, RS - Brasil.
** Curtin University of Technology
Department of Electrical and Computer Engineering
Tel:
+55 (51) 3320 3686 / 3320 3500
Branch: 4156, 4571, 3686 Sub: 216, 224 and 225
Fax:
+55 (51) 3320 3625
E-mail:
[email protected]
Contact author:
Fernando Soares dos Reis
Topic area:
TPC2- Power Electronics and Electrical Drives
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.
Active Shunt Filter for Harmonic Mitigation in
Wind Turbines Generators
F. S. Dos Reis, Member, IEEE, R. Tonkoski Jr., Student Member, IEEE, J. V. Alé, Dr. Eng.,
F. D. Adegas, **S. Islam, Senior Member, IEEE, **K. Tan, Student Member, IEEE
Pontifícia Universidade Católica do Rio Grande do Sul, Porto Alegre, Brazil.
**Curtin University of Technology, Perth, Australia.
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.
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 (PMSG), threephase bridge rectifier with a bulky capacitor, and currentcontrolled voltage source inverter (CC-VSI) or linecommutated 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.
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 DCAC 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.
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
J
d m
 Ta  T f  Te
dt
(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 
1
D
2
CT ( ,  ) A u wind
2
2
(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. Tipspeed ratio is expressed by

m  D 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 will be illustrated
on Fig. 2 in the full paper version.
Friction torque is determined by
T f  B m
(4)
where B is the friction coefficient.
B. PMSG
Dynamic modeling of PMSG can be described in d-q
reference system [7].
v q  R  pLq iq   e Ld id   e m
(5)
v d  R  pLd i d   e Lq i q
(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; 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.
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.
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 determined as
i F  i PMSG  iC  i NL
Fig. 3. PMSG output currents and line to line voltage div. by 4.
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.
(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.
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
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 direct-quadrature
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,


i af 
0 
 1
2  1
 
3  i 
ibf   3  2
2  i  
 
icf 

1
 3 

 
2
2

(15)
The reference currents to the ASF per phase, i*Fa, i*Fb and
i Fc are determined by the subtraction of non-linear currents
iNLa, iNLb, iNLc and fundamental currents iaf, ibf, icf.
*
id   cos( SRF ) sin(  SRF )  i 
i   
 
 q   sin(  SRF ) cos( SRF ) i 
(11)
i * Fa  i NLa  iaf
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,

1P
 m (s)
s 2
(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
i * Fb  i NLb  ibf
(16)
i * Fc  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
ASF current.
(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. 14
if  cos( SRF )  sin(  SRF ) id 
i   
 
 f   sin(  SRF ) cos( SRF )  iq 
Fig. 7. PWM carrier control for ASF current
(14)
The fundamental current components on 3-phase a-b-c
coordinates, iaf, ibf, icf are obtained by the inverse
transformation of Eq. 15,
2) Circuit Design: 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
LF 
V DC  Vn
di (t )
max Ln
dt
2
(17)
where Vn is the line-to-neutral voltage and diLn is the load
current of phase n, respectively.
The capacitor size CDC can be estimated based on load
current iL and maximum accepted voltage ripple ΔvDCmax,
max  i F (t )dt
0
v DC max
1
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.
(18)
V. SIMULATION RESULTS
From ASF output voltage to PMSG output voltage, the
inductance LF and capacitance C forms an LC filter which
cutoff frequency is
 cutoff 
(23)
2) ASF Converter Losses: Losses generated by the ASF
consists of passive and active component losses. Those losses
will be fully explained in the full paper version.
t
C DC 

V  1
Ph
   i 
Ph1 i 1  V1  i
(19)
For simulation of the proposed configuration, PSIM®
software was used. On full paper version Table I will be a
summary of the parameter values.
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.
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 Eq. 20,
PCU  3R A

I
i 1
Ai
(20)
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].
2
2
Pcore  Pe  Ph  (ke f 2 Bmax  k h fBmax )  weight (21)
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. 17 and 18 proposed by
Kaboli et al in [10].

V 
Pe
   i 
Pe1 i 1  V1 
2
(22)
Fig. 8. Main waveforms of WECS with ASF at full load condition.
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.
The WECS system and its subsystems power losses and
efficiencies are summarized in Tab. II.
1,2
1,0
THD=2.60 %
0,8
% 0,6
0,4
magnet synchronous generator. A capacitor bank filter was
used to suppress high-switching frequency voltage component
generated by the ASF on generator 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 generator could have a larger life cycle.
0,2
0,0
2
7
12
17
22
27
32
37
42
47
52
57
VII. REFERENCES
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
THD=20.77 %
2
7
12
17
22
27
32
37
42
47
52
57
Order
Fig. 10. Harmonic content of the PMSG output line-to-line voltage using
ASF.
TABLE II – WECS COMPONENT LOSSES AND EFFICIENCIES
Topolog
y
BR
ASF
PMSG LOSSES
Core
Friction &
Losses
Windage
(W)
(W)
180.82
120
150.73
120
Copper
Losses
(W)
2318.93
2790.24
Total (W)
η (%)
2619.75
3060.97
88.42
86.73
ASF LOSSES
IGBT
Losses (W)
199.44
LF Losses
(W)
284.66
Topology
PMSG
Total (W)
2619.75
3199.92
C Losses
(W)
0.2166
CDC Losses
(W)
116.00
Total (W)
600.33
ELECTRICAL SYSTEM LOSSES
BR
ASF
Topology
BR
ASF
ASF Total
(W)
0
603.03
Rectifier
Total (W)
95.16
211.82
WECS EFFICIENCY
Aero dynamical
Electrical (%)
(%)
43.26
43.88
88.05
84.74
Efficiency
(%)
88.05
84.74
Overall (%)
38.09
37.18
VI. CONCLUSION
The use of active shunt filter in wind energy generation
systems for harmonic mitigation was analyzed and
computationally simulated. The ASF is able to mitigate
harmonic content of current that flows on the permanent
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