Torque control of a wind turbine using 6-phase
synchronous generator and a dc/dc converter
Johan Björk-Svensson
and
José Oscar Muñoz Pascual
Department of Energy and Environment
CHALMERS UNIVERSITY OF TECHNOLOGY
Göteborg, Sweden 2007
Torque control of a wind turbine using 6-phase
synchronous generator and a dc/dc converter
Johan Björk-Svensson
and
José Oscar Muñoz Pascual
Department of Energy and Environment
CHALMERS UNIVERSITY OF TECHNOLOGY
Göteborg, Sweden 2007
Torque control of a wind turbine using 6-phase
synchronous generator and a dc/dc converter
Johan Björk-Svensson
and
José Oscar Muñoz Pascual
Department of Energy and Environment
CHALMERS UNIVERSITY OF TECHNOLOGY
SE-412 96 Göteborg
Sweden
Telephone + 46 (0)31 772 16 44
Abstract
In this thesis an electrical system for a torque controlled synchronous generator for wind power applications is developed. The setup is made simple with
a diode rectifier and a boost converter where the boost converter provided
the torque control. Two different generators are tested, an EMSG, Electrically magnetized synchronous generator, and a BLDC generator, Brushless
direct current. A comparison is made between them to investigate the best
working machine. The conclusion in this thesis is that the electrical system
works well for both generators in low wind speeds an that the EMSG provides the best results because it is shown that it was easier to filter out the
harmonics when this generator was used.
Keywords: Wind power, synchronous generator, EMSG, BLDC, Torque
control, Dc/Dc converter.
iii
iv
Acknowledgement
We would like to thank our supervisor Torbjörn Thiringer for all the support
during this thesis. Also we are grateful to the rest of the staff and other
students at the department of Electric Power Engineering at Chalmers for
making us feel welcome.
Also we would like to thank Pablo Ledesma for the help with PSCAD.
For the help with Latex we are grateful for all the help from Alejandro Russo,
without his help this report could not have been nicely written.
Johan would like to thank his family Lennart, Elisabeth, Emilia and
Kristian for their great support and interest in my work. I am also grateful
to all my previous teachers at Chalmers. At last I would like to thank Adrian
for all the support during this time.
José Oscar would also like to thank his parents José Muñoz and Julia
Pascual and my sisters Sonia, Gemma and Lilian without their support I
could not write these lines. Also I would like to thank my home university
Carlos III of Madrid and my supervisor Julio Usaola. To finish I am grateful
to all my friends but specially Raúl Dı́az-Zorita and Carlos Redondo, who
have made me feel good in difficult moments.
v
vi
Contents
1 Introduction
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Purpose of the thesis . . . . . . . . . . . . . . . . . . . . . . .
1.3 Thesis Layout . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1
2
3
2 Wind Power
2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
5
3 Synchronous Machines
3.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 6-Phase Synchronous Machines . . . . . . . . . . . . . . . . .
3.3 6-Phase BLDC machine . . . . . . . . . . . . . . . . . . . . .
7
7
7
8
4 Modelling of 6-phase Synchronous
chine
4.1 Software . . . . . . . . . . . . . .
4.2 Modelling of 6-phase Synchronous
4.2.1 Mathemathical Model . .
4.2.2 Design Model . . . . . . .
4.3 Modelling of BLDC Machine . . .
4.3.1 Mathemathical Model . .
4.3.2 Design Model . . . . . . .
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Machine
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5 Overall Controller
5.1 Tip Speed Ratio . . .
5.2 Mechanical Equation
5.3 Current Control . . .
5.4 Speed Control . . . .
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Machine and BLDC Ma-
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6 Rectifier design
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7 DC/DC Converter design
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vii
8 Results
8.1 Speed performance . . . . . . . . .
8.2 Ability to handle wind fluctuations
8.3 Filter performance . . . . . . . . .
8.3.1 Filter performance in EMSG
8.3.2 Filter performance in BLDC
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9 Conclusions and proposals of future work
41
References
43
viii
Chapter 1
Introduction
1.1
Background
The improvement of the traditional wind mill has given rise to modern wind
turbines that take advantage of the energy in the wind to generate electricity.
The wind has been used by us humans in many capacities for a very long
time. Evidence of wind generators have been found in Greece dating back
to the first centuries B.C. During the years it has been used, for example, to
pump water, grained mill and in the last century producing electricity. The
common feature is that the wind harvester convert the kinetic energy in the
wind into something useful to us humans. This energy is inexhaustible and
it does not contaminate the enviroment. The installation of these systems is
relatively expensive but with increasing number of installations the cost per
unit will go down. The wind turbines can be placed isolated or in groups that
produces electric energy to the electric grid. The wind has two characteristics
that is different from other power sources, its unpredictable variability and
its dispersion. It makes it a complex task to extract electricity from the
wind and it demands a high complexity in the design of the blades and the
control system to regulate the speed of the rotor, to avoid excessive speeds
during gales and to orient the rotor towards the most favourable position.
The source of the wind power plant is the wind, or rather, the mechanical
energy that, in form of kinetic energy sets the air into movement. The wind
is generated by the unequal heating of the surface of our planet. The Earth
receives a great amount of energy coming from the sun, and this energy,
in certain places, can be of the order of 2.000 KW h/m2 annual [3]. 2%
of that energy is transformed into wind energy with a value able to give
a power of 1011 GW. The awareness of global heating in recent years has
yield an enormous boost to the wind power industry with an even increasing
1
production of electricity produced by wind turbine.
With a growing amount of installed wind power methods for connecting wind
turbines to the electrical grid has been giving more and more attention. The
inherent intermittent energy production of wind turbines makes it a not just
a straightforward case to connect the generator in the wind turbine to the
grid i.e. how should a wind turbine with is driven by an ever changing
wind be connected to an AC-grid with a constant frequency of 50/60 Hz.
One solution is of course to use wind turbines with gearboxes running with
different constant speeds and then connect the generator to the grid. The
development in the last 10-15 years in power electronics has made it possible
to develop more complex wind turbines with converters making it able to
have variable speed turbines where the generators are connected to the grid
via a DC-link, like the system proposed in [1]. With large wind farm offshore
far from lands, which are likely to be more common in the future, a DC-cable
to shore with a converter station at the land side might be a viable solution.
Previous work has been done in this field for example in [2].
1.2
Purpose of the thesis
The main objective of this thesis is to model a torque controlled generator
for wind power applications. The model is developed in PSCAD/EMTDC.
Two different generators are modeled and a comparison is made between
them. The two generators are a six-phase EMSG and a BLDC generator,
which is a type of permanent magnet machine. The most obvious difference
between both of them are the shape of the back-emf, back electromotive
force. It is sinusoidal in the first case and trapezoidal in the second. The
output voltage from the generator is rectified through a diode rectifier and
the torque control is achieved by controlling the current through a DC/DCconverter that is conected in between the dc-side of the diode rectifier and
the grid side converter. The rectifier, converter and the control structure is
designed with the greatest possible similarity in both cases. The design will
be made for low wind speeds from 3 m/s to 7 m/s with a constant pitch angle
of the blades of the wind turbine.
2
1.3
Thesis Layout
Chapter 2
describes how is possible to generate electricity with the
aid of the wind.
Chapter 3
presents a general concept of the synchronous machines
specially the EMSG and the BLDC generator.
Chapter 4
modelling of both generators proposed in the thesis.
Chapter 5
design of the speed control, current control and tension
control.
Chapter 6
modelling of the DC/Dc-converter.
Chapter 7
conclusions.
3
4
Chapter 2
Wind Power
2.1
General
The wind turbine generator converts mechanical energy into electrical energy.
The amount of electrical energy that the turbine is able to convert into
electrical energy depends on a lot of factors like: the wind speed, the rotor
area, blades and the density of the air. A wind turbine works in a certain
interval of different windspeeds. When the wind speed is around Vcut-in (3
or 4 m/s) the turbine starts to work and stops when the wind speed is below
Vcut-off(25m/s) as shown in Fig. 2.1
Figure 2.1: Wind speed in the turbine
The turbine itself is not the main focus of this report. An Enercon turbine
model E-82 is used to provide data for this thesis [4] it is shown in Fig. 2.2,
which is a three-blade turbine with a variable speed control. This turbine
has a rated power, Pn of 2 MW. E-82 uses a tower version with a hub height
of 108 m and a rotor diameter of 82 m. The speed of the turbine is between
6 and 19.5 rpm.
5
Figure 2.2: Aerogenerator E-82 [4]
In this thesis work a gearbox is introduced to increase the rotational speed
of the generator. The gearbox transforms the low speed (of the turbine) into
high speed (of the generator). The gearbox is placed between the rotor of
the wind turbine and the rotor of the generator, it is shown in the Fig. 2.3
Figure 2.3: Location of the gearbox
Using a gearbox in this is mainly due to the fact that a generator working
with low speed will be very big and therefore expensive. However there are
also disadvantages. There are losses in the gearbox and the gearbox is one
of the most vulnerable component of the wind turbine.
6
Chapter 3
Synchronous Machines
3.1
Definition
Synchronous machines have been widely used in power systems mainly as
generating unit, they are not only the main generation units in large scale
conventional power stations, but also in small and remote stand alone systems. The synchronous generator produces its magnetization or rotor flux
by either a permanent magnet or by electrical magnetization, as opposed to
the induction machine which uses induction to achieve a magnetic flux. It is
named synchronous because the rotor rotates in phase with the flux generated by the stator currents. Various new types of synchronous generators are
being developed like multi-pole machine for wind power conversion systems.
These machines has a very important role to achieve a high efficiency and
a reliable power system with good power quality. A detailed and accurate
model is essential to investigate the performance of a synchronous machine
and its control strategies.
The evolution of the synchronous machine has been and will continue to
be stimulated by parallel advances made in general machine theory, and in
the application of computer-based methods for optimizing engineering design,
manufacturing and systems analysis.
3.2
6-Phase Synchronous Machines
A synchronous machine normally consists of three phases, but in the last
years many investigations related to multiphase machines have been made, a
lot of them towards six phase machines. The interest in multiphase machines
lies mainly in the fact that with many phases the high currents associated
with high power machines can be divided among more phases. Other advan7
tages of six-phase machines compared to three-phase machine [5]
• a low cost for finish equipment
• lower noise than 3-phase system at the same power level
• improved efficiency
• reduced maintenance requirements
• long life time
• low harmonic distortion
• low EMI
• an increase in transmission ability
• an advance of the voltage regulation so the reactive power control
• an increase transmission performance due to them, it has more energy
because they have lower losses
• better stability than other systems (like 3-phase)
In this thesis, a six-phase EMSG is used because of the advantages stated.
Typical values of the stator resistance and stator inductance of an SM are
0.01 to 0.1 p.u. and 0.8 to 2 p.u. respectively [7].
3.3
6-Phase BLDC machine
Brushless direct current, BLDC machines, is a type of synchronous machines
which has gained popularity in recent years. The reason for it being called a
DC machine when it is in fact an AC machine is that it has a speed-torque
characteristic as a traditional brush commutated DC machine. The reason
for the increasing interest in these types of machines is that it has none of
the drawbacks associated with mechanical commutated DC-machines. The
BLDC machine has the permanent magnets on the rotor and the windings
in the stator, one can say that the machine is turned inside out compared
to a PMDC motor. With this topology there is no need for electrifying the
rotor hence there is no need for mechanical brushes. The windings in the
stator are made up from many coils interconnected. The windings are then
evenly distributed around the stator to form an even number of poles. Depending on the winding topology, the back emf (electromotive force) is either
8
of sinusoidal shape or trapezoidal shape. The BLDC generator modeled in
this thesis work has a back-emf of trapezoidal shape and is the only type
considered from here on regarding the BLDC machine. The attachment of
the permanent magnets to the rotor can be of different type depending of the
area of usage and manufacturing considerations. They can be either attached
to the perimeter of the rotor or they can be buried inside the rotor core. The
surface mounted type yields lower leakage flux but on the other side it is not
suited for high speed. [6] The model proposed in this work will have surface
mounted magnets. Typical stator resistance and stator inductance for PM
machines with surface mounted magnets are 0.01 to 0.1 p.u. and 0.2 to 0.4
p.u respectively [7].
9
10
Chapter 4
Modelling of 6-phase
Synchronous Machine and
BLDC Machine
4.1
Software
All modelling and simulations are carried out in PSCAD/EMTDC 4.1, which
is based on the Fortran language. The electrical components of the whole system are built with standard electrical component models from the PSCAD/EMTDC
library. The models of the EMSG and the wind turbine is already developed
in the PSCAD/EMTDC enviroment and is used in this project.
4.2
Modelling of 6-phase Synchronous Machine
There are several ways to modelling of six-phase EMSM. One way is to use
two doubly-star machines with a 30 electric degrees phase-shift between the
two stars. Another way is to use a split phase machine, which can be built
by equally dividing the phase belt of a conventional three-phase machine into
two parts with spatial phase separation of 30 electrical degrees. Finally the
third way uses the doubly-star machines with a star-triangle transformer at
the output of one machine to get a 30 electrical degrees phase-shift between
the two machines. The most used method is the first described.
11
4.2.1
Mathemathical Model
The machine is assumed to be ideal [8], so there is no reluctance effect (uniform air-gap in the machine), no magnetic induced reactance and no saturation effect. The system is split into two sets of 3-phase windings, which are
spatially out of phase by 30 electrical degrees, as shown in the Fig. 4.1. To
obtain simpler equations it is necessary to use Concordia’s or Park’s transformation matrixes, which allow a simple control of n-phase machines, as
described in this chapter.
Figure 4.1: Six phase generator
The space harmonics of the electromotive force are neglected and the
leakage self-inductances have all the same value Lf . In a natural orthonormal
base
βn = (ssA1 , ssA2 , ssA3 , ssB1 , ssB2 , ssB3 ).
(4.1)
Defining the following vectors
js = jsA1 ssA1 + jsA2 ssA2 + jsA3 ssA3 + jsB1 ssB1 + jsB2 ssB2 + jsB3 ssB3 (4.2)
where jsk stator current in the phase number k gives
us = usA1 ssA1 + usA2 ssA2 + usA3 ssA3 + usB1 ssB1 + usB2 ssB2 + usB3 ssB3 (4.3)
where φsk linked flux of the stator phase number k and
12
φs = φsA1 ssA1 + φsA2 ssA2 + φsA3 ssA3 + φsB1 ssB1 + φsB2 ssB2 + φsB3 ssB3 . (4.4)
Now is possible to express the stator self inductance matrix like

L
1 + Lf
−0.5
−0.5
√




6
Ls = L × 
3

2√

 − 3
2
0
−0.5
L
1 + Lf
−0.5
0
√
−
3
2√
3
2
−0.5
−0.5
L
1 +√ Lf
− 23
0
√
3
2
√
3
2
0√
− 23
L
1 + Lf
−0.5
−0.5
√
−√ 23
3
2
0
−0.5
L
1 + Lf
−0.5

0√
−√ 23 


3

2

−0.5 

−0.5 
L
1 + Lf
(4.5)
Where the solution of the characteristic equation det([L6s ] − λ[J6 ]) = 0
have two eigenvalues,
Lc = 3L + Lf and Lf .
(4.6)
Being the order of multiplicity of Lc is two and the order of Lf is four. Lc is
associated a 2-dimensional eigenspace δ and Lf is associated a 4-dimensional
space κ. So vector x is the sum of two vectors, one per eigenspace. The
descomposition, achieved by creating two orthogonal projections onto the
two eigenspaces, gets
x = x4h + xdq with x4h ∈ κ and xdq ∈ δ
(4.7)
Doing relations between flux and current vectors
φs4h = Lf jsAh + φsr4h
(4.8)
φsdq = Lc jsdq + φsrdq
(4.9)
Applying twice the 3-phase Concordia´s transformation it is possible to
get the characteristic matrix T
 1

√
√1
√1
0
0
0
2
2
2
 1 −0.5 −0.5
0
0
0 


√
√
√


3
3
2  0
−2
0
0
0 
t
2
L =
×
(4.10)

√1
√1
√1
0
0
 0

3
2
2
2 

 0

0
0
1
−0.5
−0.5
√
√
3
3
−2
0
0
0
−0.5
2
13
There is still coupling between the equations because the vectors are
not eigenvectors of Ls6 . So the following matrix allows the definition of an
orthonormal base of eigenvectors


1
1
1
0
0
0
√
√
3
3
 1 −0.5 −0.5
−
0 


2
2
√
√


3
3
1
0
−
0.5
0.5
−1


t
2
2
Tr6
= √ ×
(4.11)

0
0
0
1
1
1


3 
√
√

3
 1 −0.5
−0.5
− 23
0 
2
√
√
3
0.5
0.5 −1
0 − 23
2
t
Each line of Tr6
gives the coordinates, in the natural base, of eigenvectors,
which make up an orthonormal base noted
cs cs cs cs cs
ǫs = (dcs
1 , d2 , d3 , d4 , d5 , d6 )
(4.12)
With (xhA , xd1 , xq1 , zhB , xd2 , xq2 ) the coordintates of a vector x in this
base, it is possible to get finally six equations relative to the statot flux

 φshA = Lf jshA + φsrhA
φsd1 = Lc jsd1 + φsdr1
(4.13)

φsq1 = Lc jsq1 + φsqr1

 φshB = Lf jshB + φsrhB
φsd2 = Lc jsd2 + φsdr2
(4.14)

φsq2 = Lc jsq2 + φsqr2
These equations are the same Equations 4.8 and 4.9 again.
4.2.2
Design Model
The parameters of the two generators making up the 6-phase generator are
the same and all of lies in the interval for high power machines as shown in
Table 4.1 [9]. The electromagnetic field is constant and the stator inductance
is high due to the fact that it is a high power EMSM [7]. A battery of
capacitors are always necessary (due to their capacitive nature) to produce
reactive power. They stabilize and optimize the sizing and the yield of the
installation.
4.3
Modelling of BLDC Machine
The model of the BLDC machine in this work is a y-connected 6-phase machine. Each phase is displaced by 60 degrees compared to the one preceding.
14
Table 4.1: Parameter of the EMSG
Rated power
Rated voltage
Rated current
Armature resistance
Potier reactance
Unsaturated reactance
Unsaturated transient reactance
Unsaturated sub-transient reactance
Unsaturated reactance
Unsaturated transient time
Unsaturated sub-transient time
Ra
Xp
Xd
Xd′
Xd′′
Xq
′
Tdo
′′
Tdo
2MW
0.69KV
0.893KA
0.02sec
0.09p.u.
1.8p.u.
0.15p.u.
0.1p.u.
0.7p.u.
0.6p.u.
0.035p.u.
Each phase is modeled with a source producing the back-emf, a stator resistance and stator inductance. Fig. 4.2 shows one phase. The chosen value
of Rs and Ls is derived from the the typical value stated in the previous
chapter.The mutual inductance is neglected in this model.
0.024
0.095
Rs
Ls
R=0
V
v
e
Figure 4.2: Scheme of one BLDC-phase
4.3.1
Mathemathical Model
The back-emf is calculated for each phase is calculated according to
ke
ωm F (θe )
2
(4.15)
eb =
ke
π
ωm F (θe − )
2
3
(4.16)
ec =
ke
2π
ωm F (θe −
)
2
3
(4.17)
ke
ωm F (θe − π)
2
(4.18)
ea =
ex =
15
ey =
ke
4π
ωm F (θe −
)
2
3
ke
5π
ωm F (θe −
)
2
3
The function F is given in Eq. 4.21 and is of trapezoidal shape.

1
0 ≤ θe < π3



3
π
1 − π (θe − 3 ) π3 ≤ θe < π
F (θe ) =
−1
π ≤ θe < 4π

3


4π
−1 + π3 (θe − 4π
)
≤
θ
<
2π
e
3
3
ez =
(4.19)
(4.20)
(4.21)
where θe is the electrical angle and it is depending on the pole number
according to (θe = p2 θe ). The torque of the BLDC generator is given in
Eq. 4.22.
Te = ea ia + eb ib + ec ic + ex ix + ey iy + ez iz
4.3.2
(4.22)
Design Model
The parameters stated in Table 4.2. is the ones used in the simulation of the
proposed BLDC generator.
Table 4.2: Parameter of the BLDC
Rated power
Rated voltage
Rated current
Stator resistance,
Rs
Stator inductance, Ls
Back-emf constant, ke
Number of poles
16
2 MW
0.69 kV
2.9 kA
0.024 Ω
0.0095 mH
345 Vs/rad
72
Chapter 5
Overall Controller
The main focus of this thesis will be the control of the machines. The whole
system is described in Fig. 5.1. The TSR block, tip speed ratio, calculates
the speed reference ωref , the speed controller then calculates the reference
current, ıref , The current controller calculats the error between the ıref and
the input current to the boost converter and calculate the control voltage
an the PWM block calculate the switching signals to the converter The control scheme is the same for the EMSG and for BLDC generator, the only
differences is in the calculated values.
Figure 5.1: Control scheme of overall controller
5.1
Tip Speed Ratio
The wind turbine works in three different regions depending on the wind
speeds. The first region is approximatly between 4 m/s to 8 m/s and the
turbine works with variable speed, the next region is between 9m/s and
12m/s the machine works near the maximum speed of the rotor and finally
the last region which is between 13m/s and 22m/s where the turbine works
at contstant speed and at rated power. Each region demands a different
17
approch to the control system. In this thesis the first region is considered.
Wind turbines with variable speed are normally pitch regulated, however in
this thesis project the pitch is kept constant, as said before, for constraint
reasons.
The wind turbine is characterized by its mechanical power, which is given
by [10]
2
3
Pm = 0.5ρπRblade
Cp Wspeed
(5.1)
Where ρ is the air mass density, and Rblade is the blade length, and Wspeed
is the wind speed seen by the wind turbine. The aerodynamic efficiency
Cp (β, λ) of the turbine depends on two parameters, the pitch angle of the
blades β and the tip speed ratio λ, being [10]
λ=
tipspeed
Vspeed
(5.2)
In order to obtain the maximum yield in the turbine these two parameters
must be varied at every time instance as the wind change its speed. In order
to work in low speeds λ can be considered to be constant, so the maximum λ
will be used to get the best efficiency in this project. With lambda according
to the Equation 5.2 the reference speed can be calculated as
λmax Wspeed
(5.3)
Rblade
where λmax is the parameter that together with β = 1 give the highest
aerodynamic efficiency Cp , and Wspeed is the wind speed seen by the turbine.
So with all this concepts we can develop the circuit to get the speed reference,
that is shown in the Fig. 5.2.
ωref =
5.2
Mechanical Equation
The dynamic equation of an electrical machine system is well-known and will
not be explained in depth. It is stated as:
dωm
= Tm′ + bwr − Te
(5.4)
dt
J is the inertia of the machine, Te is the electrical torque, Tm′ is the load
torque and b the viscious damping constant. The constant and a proportional
part of the mechanical torque can be summarized according to Eq. 5.4. The
model of the wind turbine in PSCAD gives as output the total mecanical
torque.
J
18
Figure 5.2: Scheme of reference speed
Tm = bwr + Tm
(5.5)
Comparing Eq. 5.4 and Eq. 5.5 yields the mechanical equation used in
this project Eq. 5.6. and shown in Fig. 5.3.
J
dwr
= Tm − Te
dt
(5.6)
Figure 5.3: Scheme of mechanical dynamics equations
5.3
Current Control
The current control is made with two degrees of freedom with antiwindup.
The method of deriving the current controlled, as well as the speed controller
later is proposed in [7]. In this control an active resistance is used, depending
19
on its value the error will be greater or smaller, so if the active resistance
increases the error decreases. The terminal voltage is limited to an upper and
a lower value Vmax and−Vmax , because the rated voltages of the generators
are 690 V. The current control scheme is shown in the Fig. 5.4.
Figure 5.4: Current control loop
Where CC is the close-loop current control, as shown in Fig. 5.5. The
current controller Fc function has a proportional and an integral part. The
transfer function of the controller is stated in Eq. 5.7.
Figure 5.5: Current controller loop
kic
(5.7)
s
The electrical dynamics is given in Eq. 5.8. The active damping, Ra is
introduced to enhance the stability of the system.
Fc (s) = kpc +
1
(5.8)
sL + R + Ra
To be able to calculate the value of kpc and kic a method called loop
shaping is used. Ideally the Gce , the closed-loop transfer function from iref
to i should be as:
Ge (s) =
Gce (s) =
20
αe
s + αe
(5.9)
where αc s the closed-loop system bandwidth but
Gce (s) =
Fc (s)Ge (s)
1 + Fc (s)Ge (s)
(5.10)
so
αe
s
clearing Fc and comparing it with Equation. 5.7 yields:
Fc (s)Ge (s) =
kpc = αe L and kic = αe (R + Ra )
(5.11)
(5.12)
As said before a limiter is used to prevent the control voltage from going
above Vmax . However this can cause the integrator part of the CC to wind
up. To avoid this back calculation is used. The controller can be described
as:
dI
=e
dt
(5.13)
u = kpc e + kic I − Ra i
(5.14)
v = s(u)
(5.15)
where I is the integrator state variable and v is according to:

 Vmax u > Vmax
u
−Vmax ≤ u ≤ Vmax
v = s(u) =

−Vmax u < −Vmax
(5.16)
The back-calculated error e is chosen such that:
v = kpc e + kic I − Ra i
(5.17)
comparing Equation 5.14 is compared with the Equation 5.17 the error
can be cleared:
e=e+
1
(v − u)
kpc
(5.18)
we thus get the control with antiwindup function implemented according
to Equation 5.19-5.21 and as shown in Fig. 5.5
dI
= e + kic I − Ra i
dt
21
(5.19)
5.4
u = kpc e + kic I − Ra i
(5.20)
v = s(u)
(5.21)
Speed Control
The speed controller is the most important part in this thesis because it
regulates the iref for the current controller. Fig. 5.6 shows a simplified scheme
of the speed controller.
Figure 5.6: Speed controller loop
The controller is made easy and resembles much the current controller,
however no limiter or active damping is implemented. The transfer functions
is defined as:
Fw (s) = kpw +
kiw
s
(5.22)
1
(5.23)
sJ + b
The parameters of the speed controller are obtained with the same method
used for the current controller:
Gw (s) =
kpw = αw J and kwi = αw b
(5.24)
The closed-loop bandwidth of the speed dynamics αw are typically related
to the bandwidth of the electrical dynamics according to:
αw < 10αe
22
(5.25)
Chapter 6
Rectifier design
The output alternating voltages from the EMSG or the BLDC generator are
rectified through a six phase diode bridge rectifier. This rectifier is made up
of twelve diodes, grouped in six pairs. The rectifier is located between the
generators and the converter as we can see in Fig. 6.1.
Figure 6.1: Scheme of the 6-phase rectifier of diodes
The diodes are numbered in the in the same order that they conduct in the
sequence 1, 2, 3... (see Fig. 6.1. The commutation of current from one diode
to the next is not instantaneous, due to the inductances of the generator.
Each of the diode pairs are conducting during 60 electrical degrees.

When diode 1 is conducting
 Id
0
When to neither diode 1 or 6 is conducting
ir =

−Id When diode 6 is conducting
23
The voltage of the output of the rectifier is not a true DC voltage. The
diode rectifier creates a lot of harmonic distortion causing ripple in the output
voltage. To avoid this a big capacitor is introduced to get a nearly stiff DC
voltage as input to the DC/DC-converter.
24
Chapter 7
DC/DC Converter design
The boost (step-up) converter is placed after the 6-phase diode rectifier. The
DC/DC-converter controls the Id current, which is directly related to currents
in the generators. Hence the electrical torque of the generator is controlled.
The control of the converter is done by the control circuit derived in the
previous chapter. The boost converter scheme is shown in Fig. 7.1. The
output capacitor is large so it is possible to assume vout (t) = Vout . The value
of the input inductor is made large enough for the converter to always work in
CCM, Continues Conduction Mode. To make sure the converter always works
in CCM Equation 7.1. is used describing the boundary conditions between
CCM and DCM, Discontinues Conduction Mode. I0max is the maximal load
current through the inductor and Ts s is the switching time period.
Figure 7.1: Boost Converter
Ldc =
Ts Vout
D(1 − D)2
2I0max
25
(7.1)
An IGBT (Insulated Gate Bipolar Transistor) is used as switch in the
converter. IGBT switches are state of the art in the switching elements.
Some of its desired advantages are: It can be totally controlled by a low
voltage, has low on-state losses and large blocking voltages [11]. When the
IGBT is turned on, ton , the energy of the generator is being stored in the
inductor. During this time the diode is reversed biased, hence it does not
conduct any current. When the IGBT is turned off, tof f , the stored energy
in the inductor flows through diode transferring it to the load. To calculate
the switching periods of the IGBT a method proposed in, among others, [12]
and [13]. It is assumed that the input voltage Vin an the output voltage
Vout stays constant during each switching periods. The increase in the input
current to the converter is stated as:
∆Iin = it0 +Ts − it0 =
Ts
(Vin − Vout (1 − D))
Ldc
(7.2)
The control signal is selected as
Ldc ∆Iin
Ts
Equation 7.2 together with Equation 7.3 yields the duty ratio:
Vcontrol = it0 +Ts − it0 =
(7.3)
1
(Vcontrol − Vin ) + 1
(7.4)
Vout
The control signal is compared with a periodic triangular pulse with a
constant switching frequency of 2 kHz hence a PWM signal is produced
controlling the IGBT switch. The Fig. 7.2 shows the topology of the PWM
generating circuit.
D = it0 +Ts − it0 =
Figure 7.2: Converter Controller
In this thesis work we use a varible resistor acting as a DC load, this is
to get a constant output voltage Vout , although the PWM calculating circuit
works for all output voltages within the limit 0 ≤ Vmax .
26
Chapter 8
Results
The systems described and modeled in the previous chapter are simulated in
different manners to show the overall performance. Firstly the performances
is verified by exposing the systems to different steps in the wind and then
by exposing the systems to more fluctuating wind speeds, wind speeds that
are more close to reality. In the last part of this chapter the systems are
equipped with different passive filters to be able to find the best solution for
filtering away unwanted harmonics. For all the simulations the inertia J is
6.3 M kgm2 and a viscous damping constant of 0.5 M kgm2 /s. With these
value the value of the speed controller is calculated as proposed in chapter
5.4, yielding an value of Kpw of 500000 and Kiw of 40000. These values of
the speed controller are used throughout all simulations.
8.1
Speed performance
To show the overall performance of the proposed systems different steps in
the wind speeds will be exposed to the system. These steps are 3 m/s, 5 m/s
and 7 m/s and the response are shown in Fig. 8.1 for the EMSG and in Fig.
8.2 for the BLDC where it is possible to see the speed response and current
response for each generator.
The results for the two different generator are similar but not equal, which
is to be expected. The two generators are using different values in the current
controller because the internal resistance and inductance are different. The
values of Kpe and Kie were found with a combination of analytical work and
trial and error, the parameters shown in Table 8.1 were found to be the best
working. The method proposed in chapter 5.3 to calculate these values was
used but the R and L value had to be assumed since they were not known
because the rectifier and boost converter circuit also effect these values.
27
Figure 8.1: Speed and current control EMSG
Figure 8.2: Speed and current control BLDC
28
Table 8.1: Parameters of current controller
Generator Kp
Ki
EMSG
15
0,3
BLDC
3,75 1,41
In both simulations a gearbox is used to increase the speed of the generators. The gearbox has an efficiency of 0,94 % and a gear ratio of 0.73
(Machine/Turbine). The values of the dc/dc converter are equal in both
systems and shown in table 8.2.
Table 8.2: Parameters of boost converter
L
C
5.5 µH 0,7 F
As seen in the graphs the current controller works really well in both
systems. The speed response is in the region of several seconds which is
only to be expected for this big wind turbine. Also noticeable is that the
performance is a bit poorer for decreasing wind speeds. This is of course
due to the fact that it is impossible to break the turbine electrically with
this kind of setup i.e. it is impossible to have the current running in two
directions through a diode rectifier
8.2
Ability to handle wind fluctuations
In this section the response of both generators to fast wind fluctuations are,
althogh it will continue to vary between values from 3 m/s to 7 m/s. This
simulation resembles much more the reality due to the characteristics that
the wind has. Both generators respond to major wind changes but the fast
fluctuations are responded upon which. The responses are shown in Fig. 8.3
for the EMSG and in Fig. ?? for the BLDC. As seen the response of the
current is still good which of course will yield hih torque oscillations.
29
Figure 8.3: Speed and current control EMSG
Figure 8.4: Speed and current control BLDC
30
8.3
Filter performance
The behaviour of the system with passive harmonic filters re simulated in
this chapter. The passive filters are used to eliminate or at least reduce
the produced harmonics in the electrical system. The existence of harmonics
generates adverse effects (like bad behavior of the machine, excessive heating,
loss of life utility. . . ) in the system and the reduction of harmonics is a higly
prioritized area. The filters are made up of single passive elements: resistance
(R), inductor (L) and capacitor (C). Several kind of filters will be studied.
First a pair of passive filters to eliminate the 5th and 7th harmonics together
with a high pass filter between the generator and the rectifier as seen in Fig.
8.5 will be simulated. The second setup with a a capacitor bank between
generator and rectifier Fig. 8.6 will be simulated. The last setup that is
simulated is the setup with no filters between the rectifier and generator to
compare it with the filter performance. Fig. 8.7. Finally a simulation with
the best filters for each generator (Fig. 8.8) is run. All filter setups are
simulated using two different wind conditions. First with a constant wind
speed and then with a fluctuating wind speed which is the one closest to
reality.
Figure 8.5: Scheme with passive filter between generator and rectifier
8.3.1
Filter performance in EMSG
All the the results shown in this section are from the simulations of the
EMSG, the first four graphics describes the situation using a constant wind
speed of 5 m/s and the other four are with fluctuating wind speeds between
3 m/s and 7 m/s.
Analyzing the graphs, the system responds good when the wind is constant except in the third case, Fig. 8.11. The harmonics are reduced to a
31
Figure 8.6: Scheme with one capacitor between rectifier and DC/DC converter
Figure 8.7: Scheme with a capacitor bank between generator and rectifier
Figure 8.8: Scheme with a capacitor bank between generator and rectifier
and one capacitor between rectifier and DC/DC converter
32
Figure 8.9: Passive filter between EMSG and rectifier
Figure 8.10: Capacitor bank between EMSG and rectifier
33
Figure 8.11: One capacitor between rectifier and converter (EMSG)
Figure 8.12: Capacitor bank between EMSG and rectifier and one capacitor
between rectifier and converter
34
Figure 8.13: Passive filter between EMSG and rectifier
Figure 8.14: Capacitor bank between EMSG and rectifier
35
Figure 8.15: One capacitor between rectifier and converter (EMSG)
Figure 8.16: Capacitor bank between EMSG and rectifier and one capacitor
between rectifier and converter
36
Figure 8.17: Passive filter between BLDC and rectifier
fairly high extent in the first two setups Fig. 8.9 and Fig. 8.10, although the
use of passive filters yields greater loss because of the use of many passive
components. The problem is that the passive filters do not work well when
the wind is not constant (as in reality), for that reason a bank of capacitors works better to reduce a great part of the harmonics Fig. 8.12. The
performance of the best setup is shown in Fig. 8.16
8.3.2
Filter performance in BLDC
As in the previous section the first four graphics shows the result of the
simulations using constant wind speeds of 5 m/s and the other four are when
using fluctuating wind speeds between 3 m/s and 7 m/s.
Analyzing the graphs, it can be seen that the behavior for the BLDC is
different from the EMSG, which is to be expected. Since the back-emf of the
BLDC is trapezoidal there is much more harmonics in the BLDC than in the
EMSG with in sinusoidal back-emf. As can be seen in the simulations the
topology with no passive filters between the rectifier and the generators, Fig.
8.22, works the best although the behavior is far from that of the EMSG.
37
Figure 8.18: Capacitor bank between BLDC and rectifier
Figure 8.19: One capacitor between rectifier and converter (BLDC)
38
Figure 8.20: Passive filter between BLDC and rectifier
Figure 8.21: Capacitor bank between BLDC and rectifier
39
Figure 8.22: One capacitor between rectifier and converter (BLDC)
40
Chapter 9
Conclusions and proposals of
future work
The aim of this thesis was to model a torque controlled EMSG and a BLDC
generator working at low wind speeds. The control system was made similar
for the two generators so a comparison could be made between them. As
shown in the previous chapter the control system responded well for both
generators when exposed to different wind changes. The dynamic response
of the system was several seconds which was to be expected because the
large inertia of these big wind turbines. The different filters that were tested
showed different behavior depending on the generator used. The EMSG
machine showed the best performance with a filter topology with a capacitor
per phase between the rectifier and generator and a big capacitor between
the rectifier and converter worked the best. Although the setup with 5th
and 7th harmonic filter together with a high pass filter also worked except
fairly high losses. Together with the fact that in a variable speed drives the
frequency of the harmonics keeps changing. These two drawbacks together
with higher installations costs for this type of filter, a lot of more passive
components are used, the conclusion can be made that the capacitor bank
setup is the best.
For the BLDC generator it was found that that the setup with no extra
filters where the best solution with the lowest torque ripple although the
performance was far from that of the EMSG. With this topology, rectifier
and boost converter, the normal procedure with the BLDC when the phase
currents are switched on depending on the placement of the magnetic field is
bypassed and this is the major source of all the current harmonics and hence
a high torque ripple. With the system proposed in this thesis the conclusion
can be drawn that the EMSG with its sinusoidal back emf works better than
the BLDC with the trapezoidal back emf because it is shown that it is easier
41
to filter away the harmonics which leads to lower torque ripple and hence
lower losses in the machine.
To conclude this work some suggestions for future work is given. The
obvious way forward from this work is of course to implement the torque
control method together with a pitch control for the wind turbine and simulate the performance of the system working in the whole wind speed range.
To further improve the model of the EMSG field control can be implemented
to further enhance the performance.
Further investigations should be done on the BLDC generator. A comparison between the setup in this thesis and a setup with switching elements
switching on and of the phase currents according to the placement of the
magnetic field would be interesting. The latter setup will of course yield
higher installation costs and the question is if the cost can be compensated
by the lower losses that this set ought to give. Further investigation can be
done on different motor topologies to find out how they affect the behavior of
the system i.e. what is the best number of poles, how many windings should
one have for example. This can of course also be done for the EMSG.
42
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44