HARMONIC MITIGATION IN WIND TURBINE ENERGY
CONVERSION SYSTEMS
Fernando Soares dos Reis, Member, IEEE, Kelvin Tan Student Member, IEEE, and Syed Islam, Senior Member, IEEE
Department of Electrical and Computer Engineering, Curtin University of Technology, Perth, Australia. f.dosreis@ieee.org
Abstract—Permanent magnet synchronous generators
(PMSG) wind energy conversion system (WECS) using
variable speed operation is being used more frequently
in low power wind turbine application. Variable speed
systems have several advantages over the traditional
method of operating wind turbines, such as the
reduction of mechanical stress and an increase in
energy capture. To fully exploit the last mentioned
advantage, many efforts have been made to develop
maximum power point tracking (MPPT) control
schemes for PMSG WECS. To allow the variable speed
operation of the PMSG WECS a conventional threephase bridge rectifier with a bulky capacitor associated
with voltage source current controlled inverter (VSCCI) is used. This simple scheme introduces a high
intensity low frequency current harmonic content into
the PMSG and consequently increases the total loses in
it. Subsequently, decreases the power capability of the
system. This paper presents a comparative simulation
study between three different approaches applied to
harmonic mitigation on PMSG WECS. The studied
techniques are: a) harmonic trap filters, b) single-switch
three-phase boost rectifier and c) three-phase boost type
PWM rectifier.
I.
INTRODUCTION
The amount of energy captured from a WECS depends not
only on the wind at the site, but depends on the control
strategy used for the WECS and also depends on the
conversion efficiency. Permanent magnet synchronous
generators (PMSG) wind energy converters system
(WECS) with variable speed operation is being used more
frequently in low power wind turbine applications.
Variable speed systems have several advantages such as the
reduction of mechanical stress and an increase in energy
capture. In order to achieve optimum wind energy
extraction at low power fixed pitch WECS, the wind
turbine generator (WTG) is operating in variable-speed
variable-frequency mode. The rotor speed is allowed to
vary with the wind speed, by maintaining the tip speed ratio
to the value that maximizes aerodynamic efficiency. The
PMSG load line should be matched very closely to the
maximum power line of the WTG. MPPT control is very
important for the practical WECS systems to maintain
efficient power generating conditions irrespective of the
deviation in the wind speed conditions. To achieve optimal
power output, a sensor-less scheme developed by Tan et al
in [1] will be used in this work for extracting desired output
power from the WTG over a wide range of wind speeds. In
spite of, all this complex control theory to get MPPT on
PMSG WECS the standard way to implement a grid
connected PMSG WECS at variable speed is using two
power conversion stages: the first one an AC-DC stage and
the second one a DC-AC stage. To realize the first one a
classical three phase full bridge rectifier associated to a
bulky capacitor is used and the second stage could be
implemented by two types of converters schemes Voltage
source current controlled inverter (VS-CCI) and Line
commutated inverter (LCI) as shown in Fig. 1.
Fig. 1. Wind Energy Conversion System
This paper has the main focus in the first energy conversion
stage the AC-DC converter, which is responsible by an
injection of a high harmonic current content into the
PMSG. The circulation of harmonic currents into the
generator will produce significant additional power losses.
Normally, the useful life of an electrical machine is
specified based on the assumption of operation under rated
load. When considering the proper rating for a machine the
voltages and load currents are usually assumed to be
sinusoidal. Therefore, the additional increase in the steadstate temperature caused by the harmonics can lead to
premature ageing of the insulation and breakdown. Also the
mechanical stress due to harmonics can reduce the useful
life of the machine [2]. This work applies three well-known
approaches to harmonic mitigation in three-phase AC-DC
energy conversion systems: a) harmonic trap filters, b)
single-switch three-phase boost rectifier and c) three-phase
boost type PWM rectifier [3, 4, and 5]. Using these
approaches is possible to minimize or to eliminate the
current harmonic content. A software simulation model
developed in [1] using PSIM software, which allows easy
performance evaluations is used to estimate the behaviour
of these three different schemes associated with the PMSG
WECS. Simulation results showed the possibility of
achieving maximum power tracking, output voltage
regulation and harmonic mitigation simultaneously.
II.
WECS MODEL
The WECS considered in this work consists of a PMSG
driven by a fixed pitch wind turbine; an AC-DC energy
conversion stage implemented using two different power
factor rectifiers; and a VS-CCI. The entire system is shown
in Fig. 1. A brief description of each element of the system
is given below.
A. Power from wind turbine
The output mechanical power of the wind turbine is given
by the usual cube law equation (1). Where Cp is the power
coefficient, which in turn is a function of tip speed ratio .
This relationship is usually provided by the turbine
manufacturer in the form of a set of non-dimensional
curves, the Cp curve for the wind turbine used in this study
is shown in Fig. 2. The tip speed ratio is given by equation
(2). A= wind turbine rotor swept area [m2], Uw= wind
speed [m/s], = air density [kg/m3], r= radius of the rotor
[m], m= mechanical angular velocity of the generator
[r/sec].
1
3
P  ρC AU
Watts
m 2
p
w
λ
rω m
(1)
(2)
Uw
decrease until the turbine stops. Therefore, the controller
has to be designed to keep the operating point inside the
desired region. For a variable speed wind turbine with pitch
control, optimum power can easily be obtained using
appropriate control. However, for small machines that use a
fixed pitch, this mechanism is not possible. The current
paper looks at fixed pitch machines. The use of pitch
machines control may, however, interfere with the control
system modelled in this paper.
B. PMSG model
Theoretical models for generator producing power from a
wind turbine have been previously developed [6, 7]. The
outer rotor 20kW CRESTA PMSG described in [8] is used
in this WECS mathematical model. The model of electrical
dynamics in terms of voltage and current can be given as
(4) and (5) [6]:
v
di
q
  Ri  L
ω L i ω λ
q
q
q dt
r d d
r m
di
d
v d   Ri d  L d
 ωr Lqiq
dt
Fig. 2. Power coefficient vs. Tip seed ratio with =0
It can be seen that if the rotor speed is kept constant, then
any change in wind speed will change the tip-speed ratio,
leading to change of Cp as well as the generated power out
of the wind turbine. If the rotor speed is adjusted according
to the wind speed variation, then the tip-speed can be
maintained at the optimum points, which yield maximum
power output from the system. Cp max is the maximum
torque coefficient developed by the wind turbine at the
optimum tip-speed ratio max. The rate of the rotor speed is
proportional to the inverse of the inertia and difference
between mechanical torque (Tm) produced by the wind
turbine and the electrical torque (T e) load from the
generator.
dω m
dt

1
J
Tm  Te
(3)
The wind turbine output mechanical torque is affected by
the Cp. In order to maximize the aerodynamic efficiency,
the Te of the PMSG is controlled to match with the wind
turbine Tm to have maximum possible Cp max. With a power
converter, adjusting the electrical power from the PMSG
controls the Te; therefore, the rotor speed can be controlled.
For the system to operate at maximum power at all wind
speeds, the electrical output power from the power
converter controller must be continuously changed so that
under varying winds speed condition the system is matched
always on the maximum power locus. From the power
curve of the wind turbine, it is possible to operate the wind
turbine at two speeds for the same power output. In
practice, the operating range at region 1 is unstable as the
rotor speed of the WTG belongs to the stall region. Any
decrease in the tip speed region will cause a further
(4)
(5)
Where, R and L are the machine resistance and inductance
per phase. vd and vq are the 2-axis machine voltages. id and
iq are the 2-axis machine currents. m is the amplitude of
the flux linkages established by the permanent magnet and
r is the angular frequency of the stator voltage. The
expression for the electromagnetic torque in the rotor is
written as:
Te 
 3  P 
  
 2  2 
Ld  Lq  i qid  λ miq 
(6)
The relationship between r and m may be expressed as:
ωr 
p
2
ωm
(7)
C. Input Bridge Rectifier (AC-DC converter)
The complete grid connected sensor-less PMSG WECS
scheme using a well-known three-phase six-pulse bridge
rectifier and two bulky capacitors are shown in Fig. 3.
Fig. 3. Implemented sensor-less VS-CCI WECS
D. Power Variation of the PMSG Wind Turbine
The loading characteristic of the PMSG WECS can be
easily simulated by connecting an adjustable load resistor
to the PMSG and rectifier terminal. Fig. 4 shows the
calculated corresponding output power of the PMSG for
wind speeds ranging from 4 to 12m/sec, where the
generator maximum power curves show the different
operating dc voltages and currents over a range of wind
speeds. In order to extract the peak power from the WTG at
a given wind speed, the WECS has to match closely to the
maximum power curve.
Fig. 5. Three phase PMSG output current at 20 kW.
Fig. 4. Predicted DC power characteristics the WECS.
III.
HARMONIC ANALYSIS
Fig. 6. Harmonic content of the PMSG output current.
First of all it is necessary to understand why this study is
important. Therefore, a briefly remark of the problem is
presented. To do this job a study case is presented showing
the PMSG output currents at full load condition using a
conventional six-pulse rectifier shown in Fig. 3 which, is
normally employed in PMSG WECS is presented, the wind
speed in this case is 12 m/s. Harmonic characterization of
these abnormal currents is obtained and the results are
presented in the following section. A complete harmonic
analysis of the two three-phase PFC presented previously
will be presented in the final paper.
IV.
In Fig. 7 a detail of the harmonic content amplitude of the
PMSG output current in percent of the fundamental is
shown. The fundamental component was omitted in this
figure, in order to, remark the harmonic content.
THREE-PHASE FULL BRIDGE RECTIFIER
A detail of the PMSG WECS output currents, for the
maximum power deliver situation at 12 m/sec wind speed,
is shown in Fig. 5. In order to evaluate the quality of these
currents an objective study was made using the Fourier
analysis, the harmonic content and the total harmonic
distortion (THD) of the output PMSG current were
obtained, the results are summarized in Fig. 6 and Fig. 7.
From these figures it is possible to observe that the 5 th, 7th,
11th, 13th, 17th and 19th harmonics are significant. The
obtained total harmonic distortion was THD = 13.47 %
which is 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 L_F1 = 3 mH and R_S1 = 0.432  respectively.
Unfortunately this effect is not so noticeable when the
available wind decreases and therefore, the maximal output
power decreases and the THD increases.
Fig. 7. Harmonic content of the PMSG output current.
The amplitude of the 5th harmonic is 12.4% of the
fundamental, which is greater than the 10% allowed by
IEEE 519 standard. Of course, the IEEE 519 standard it is
not applicable to this situation but it is a guideline.
V.
HARMONIC MITIGATION
The classical passive trap filters are always associated to
the idea of harmonic mitigation. Also the PFC schemes will
need high frequency filters to mitigate the high frequency
current ripple generated by them selves. A high frequency
filter design criterion will also be presented.
A.
active power filters. The study of the active power filters
applied to PMSG WECS is out of the scope of this paper.
However, is under study at the moment.
Passive Harmonic Trap Filters
Looking for this classical power electronics problem the
first solution is to use passive harmonic trap filters as
shown in Fig. 8 in fact a reduction of the 5th and 7th
harmonic could be enough to turn the THD to acceptable
levels. If the main idea is to found a compromise solution
to track maximum power at the best wind condition the trap
filters could be used.
Fig. 10. Harmonic content of the PMSG output current
using 5th and 7th harmonic trap filters.
B.
Fig. 8. Passive harmonic trap filters.
A design of two trap filters was made to minimise the 5th
and 7th harmonic the results are shown in Figs. 9 and 10.
Fig. 9. Three-phase PMSG output current at 20 kW using
5th and 7th harmonic trap filters.
A remarkable improvement in the current waveform was
obtained using this simple solution. A THD less than 3%
was obtained as shown in Fig. 10. The fundamental
component was omitted in this figure, in order to, remarks
the low harmonic content. Note that this solution implies in
bulky components and is matched only for the maximum
power condition, which occurs at 12 m/s wind speed.
Unfortunately in the real WECS, the wind speed is
constantly varying and hence the PMSG produces variablevoltage and variable-frequency output. Therefore, an
infinity number of the trap filters would be necessary. To
solve this problem an active solution is needed, there are
basically two actives approaches to solve this power
electronics problem the first solution have different names
as: power factor correctors (PFC), power factor rectifiers
(PFR), power factors preregulators (PFP), PWM rectifiers
or resistor emulators the second possible solution is to use
Single-Switch Three-Phase Boost Rectifier
(AC-DC converter)
One of the selected power factor corrector (PFC)
approaches, suitable to implement the input rectifier, the
black block shown in Fig. 3, was the three-phase DCM
boost rectifier proposed by Prasad and Ziogas [3]. Because
this converter presents many advantages such as: a very
low THD in the input current, a simple structure using just
one controlled device and could be controlled using a
simple control strategy easily implemented with generalpurpose PWM integrated circuits (IC) controllers. The
transistor can operate at constant switching frequency. The
control of the DC output power is easily made by duty
cycle control. Only a single active device such as a
MOSFET or IGBT is needed [3, 4]. The main
disadvantages of this implementation is the increasing of
the power losses in the devices in comparison with the
conventional three-phase AC-DC converter and the need of
additional input capacitors for proper operation of the
converter due to the PMSG stator inductance. Therefore,
the implementation of the input rectifier using a singleswitch three-phase boost rectifier resulting in harmonic
mitigation on the PMSG output currents. The complete
schematic diagram of the three-phase DCM boost rectifier
is shown in Fig. 11.
Fig. 11. Single-switch three-phase boost rectifier.
Inductors L1, L2, and L3 have the some small value, such
that they operate in the discontinuous conduction mode in
conjunction with diodes D1 – D6. At the end of the
transistor Q1 conduction subinterval, the inductor currents
reach peak values, which are also proportional to the
applied three-phase line-to-neutral voltages. When
transistor Q1 turns off, then diode D7 becomes forwardbiased and the inductors release their stored energies to the
DC output. Since the peak input currents are proportional
to the applied input line-to-neutral voltages, then the
average values of the input currents are also approximately
proportional to the input line-to-neutral voltages.
Approximate three-phase input resistor emulation is
obtained. The three-phase DCM boost rectifier does
generate a modest amount of low frequency input current
harmonics. But, increasing the DC output voltage is
possible to reduce the THD [4].
C.
Three-Phase Boost type PWM Rectifier (ACDC converter)
As mentioned before the behavior of the two PFC
associated to PMSG WECS are studied in this work
focused in losses reduction on PMSG by harmonic
mitigation. The three-phase boost type PWM rectifier has
the capability of to work as an ideal PFC, with very low
THD at any operation point. Hence, it is investigated in this
work in order to overcome the disadvantages presented by
the single-switch three-phase boost rectifier. The converter
topology has six two-quadrant controlled switches each one
implemented by an active device associated to a diode. The
inductors and capacitor filter the high-frequency switching
harmonics, and have little influence on the low frequency
AC components of the waveforms. The switches of each
phase are controlled to obtain input resistor emulation. To
obtain undistorted line current waveforms, the DC output
voltage V must be greater than or equal to the maximal
peak line-to-line AC PMSG output voltage. The threephase boost type PWM rectifier shown in Fig. 11 has
several attributes the AC input currents are non-pulsating
because the converter works in continuous conduction
mode (CCM), and hence very little additional input EMI
filtering is required. The converter is capable of
bidirectional power flow. This converter also has some
disadvantage like: requirement for six active devices when
compared with the previous circuit shown in Fig. 11 which
uses just one active device, the active semiconductor
utilization is low, since the rectifier has a boost
characteristic and requires a much more complex control
scheme using either a multiplying controller scheme
employing average current control, or with some other
approach like estimation [4, 5].
harmonic component of the current Ia and Ra is stator
equivalent resistance. [9]. However, operating at higher
current level resulted in 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 and eddy current power
losses in the core the equation (9) represents these losses
[9, 10].
PCu  3 R
a
Pcore  Pe  Ph  (k e f 2 B 2 max  k h f B
VI.
PMSG POWER LOSSES CALCULATIONS
VII.
max )  Weight
(9)
EMI FILTER DESIGN CONSIDERATIONS
The design of a suitable EMI filter can be done according
different approaches. Usually a high-order filter is used to
reduce inductance and capacitance values. Ideally it could
be considered that no harmonic components exist in the
frequency range between the line and the switching
frequencies. This fact would allow centring the filter
resonance at a suitable frequency in order to guarantee the
required attenuation. In this ideal situation the filter could
be undamped. In the Continuous Conduction Mode the
input rectified voltage is usually used to create the current
reference waveform. In this case the presence of
instabilities in the filter output (converter side) can lead to
severe converter malfunction. As the input voltage
waveform is not so important for the proper operation of
the PFC in the Discontinuous Conduction Mode, some
damping effect is necessary to avoid oscillations in the
average input current produced by transient situations, like
load or wind changes. The maximum capacitance should be
used to minimise the inductance value. Let us consider the
damped second order filter topology shown in Fig. 13. This
filter attenuates 40 dB/dec [11]. For a given necessary
attenuation, the cut-off frequency is given by:
fx
fc 
A1
A2
(10)
Where fc is the cut-off frequency, fx is the frequency in
which the required attenuation (A1) is determined. A2 is the
filter characteristic attenuation. The inductance value is
given by:
1
Lf  2
4 C1f c2
(11)
The maximum C1+C2 value is 2.2 µF, and for a proper
damping effect, C2=10C1. The damping resistance can be
calculated as:
Rd 
Basically the total power losses generated into the machine
can be divided into two big groups: a) copper losses and b)
core losses. The copper power losses are produced in the
stator winding as function of RMS current in it according
to equation (8), where Ia_I is the RMS value of the ith
1.5 to 2.5
(8)
In order to evaluate the influence of the different
harmonic mitigation approaches in the PMSG power losses
a normalized study is presented in the final paper.
10
Fig. 12. Three-phase boost type PWM rectifier.

 I2
a_i
i 1
Lf
C2
(12)
[6]
Fig. 13. EMI differential mode filter.
[7]
VIII.
CONCLUSION
This digest presents a review on harmonic mitigation in
three-phase rectifiers using trap filters and PFC applied to
PMSG WECS and preliminary simulation results of a
prototype variable speed PMSG WECS. Three possible
harmonic mitigation solutions were discussed. Using
harmonic trap filters is possible to maximize the PMSG
WECS efficiency by mitigation of the harmonics losses.
Regrettably, this solution is effective just at one specific
operation point since the wind is constantly changing as
well the frequency. The single-switch three-phase boost
rectifier requires a very simple changing in the three phase
rectifier topology as shown in Fig. 11, once the converter
work in the DCM the control is as well very simple.
However, the conduction losses in the switch Q1 Fig. 11 are
high since the high RMS current value caused by the DCM
operation. The problem could be minimized using proper
switches like IGBT or GTO. The full paper will present
design considerations and a complete harmonic mitigation
study for this PFC. An EMI filter must be used for EMI
reduction and for proper operation of the converter, to
avoid CCM once the PMSG stator inductance is high. An
EMI filter design criterion is in addition presented.
IX.
[1]
[2]
[3]
[4]
[5]
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