torque control of a wind turbine using 6-phase synchronous
TRANSCRIPT
Torque control of a wind turbine using 6-phase
synchronous generator and a dc/dc converter
Johan Bjork-Svensson
and
Jose Oscar Munoz Pascual
Department of Energy and EnvironmentCHALMERS UNIVERSITY OF TECHNOLOGY
Goteborg, Sweden 2007
Torque control of a wind turbine using 6-phasesynchronous generator and a dc/dc converter
Johan Bjork-Svensson
and
Jose Oscar Munoz Pascual
Department of Energy and EnvironmentCHALMERS UNIVERSITY OF TECHNOLOGY
Goteborg, Sweden 2007
Torque control of a wind turbine using 6-phasesynchronous generator and a dc/dc converter
Johan Bjork-Svenssonand
Jose Oscar Munoz Pascual
Department of Energy and EnvironmentCHALMERS UNIVERSITY OF TECHNOLOGYSE-412 96 GoteborgSwedenTelephone + 46 (0)31 772 16 44
Abstract
In this thesis an electrical system for a torque controlled synchronous genera-tor for wind power applications is developed. The setup is made simple witha diode rectifier and a boost converter where the boost converter providedthe torque control. Two different generators are tested, an EMSG, Electri-cally magnetized synchronous generator, and a BLDC generator, Brushlessdirect current. A comparison is made between them to investigate the bestworking machine. The conclusion in this thesis is that the electrical systemworks well for both generators in low wind speeds an that the EMSG pro-vides the best results because it is shown that it was easier to filter out theharmonics when this generator was used.
Keywords: Wind power, synchronous generator, EMSG, BLDC, Torquecontrol, Dc/Dc converter.
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Acknowledgement
We would like to thank our supervisor Torbjorn Thiringer for all the supportduring this thesis. Also we are grateful to the rest of the staff and otherstudents at the department of Electric Power Engineering at Chalmers formaking 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 andKristian for their great support and interest in my work. I am also gratefulto all my previous teachers at Chalmers. At last I would like to thank Adrianfor all the support during this time.
Jose Oscar would also like to thank his parents Jose Munoz and JuliaPascual and my sisters Sonia, Gemma and Lilian without their support Icould not write these lines. Also I would like to thank my home universityCarlos III of Madrid and my supervisor Julio Usaola. To finish I am gratefulto all my friends but specially Raul Dıaz-Zorita and Carlos Redondo, whohave made me feel good in difficult moments.
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Contents
1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Purpose of the thesis . . . . . . . . . . . . . . . . . . . . . . . 21.3 Thesis Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Wind Power 52.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 Synchronous Machines 73.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 6-Phase Synchronous Machines . . . . . . . . . . . . . . . . . 73.3 6-Phase BLDC machine . . . . . . . . . . . . . . . . . . . . . 8
4 Modelling of 6-phase Synchronous Machine and BLDC Ma-chine 114.1 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.2 Modelling of 6-phase Synchronous Machine . . . . . . . . . . . 11
4.2.1 Mathemathical Model . . . . . . . . . . . . . . . . . . 124.2.2 Design Model . . . . . . . . . . . . . . . . . . . . . . . 14
4.3 Modelling of BLDC Machine . . . . . . . . . . . . . . . . . . . 144.3.1 Mathemathical Model . . . . . . . . . . . . . . . . . . 154.3.2 Design Model . . . . . . . . . . . . . . . . . . . . . . . 16
5 Overall Controller 175.1 Tip Speed Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . 175.2 Mechanical Equation . . . . . . . . . . . . . . . . . . . . . . . 185.3 Current Control . . . . . . . . . . . . . . . . . . . . . . . . . . 195.4 Speed Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
6 Rectifier design 23
7 DC/DC Converter design 25
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8 Results 278.1 Speed performance . . . . . . . . . . . . . . . . . . . . . . . . 278.2 Ability to handle wind fluctuations . . . . . . . . . . . . . . . 298.3 Filter performance . . . . . . . . . . . . . . . . . . . . . . . . 31
8.3.1 Filter performance in EMSG . . . . . . . . . . . . . . . 318.3.2 Filter performance in BLDC . . . . . . . . . . . . . . . 37
9 Conclusions and proposals of future work 41
References 43
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Chapter 1
Introduction
1.1 Background
The improvement of the traditional wind mill has given rise to modern windturbines 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 longtime. Evidence of wind generators have been found in Greece dating backto the first centuries B.C. During the years it has been used, for example, topump water, grained mill and in the last century producing electricity. Thecommon feature is that the wind harvester convert the kinetic energy in thewind into something useful to us humans. This energy is inexhaustible andit does not contaminate the enviroment. The installation of these systems isrelatively expensive but with increasing number of installations the cost perunit will go down. The wind turbines can be placed isolated or in groups thatproduces electric energy to the electric grid. The wind has two characteristicsthat is different from other power sources, its unpredictable variability andits dispersion. It makes it a complex task to extract electricity from thewind and it demands a high complexity in the design of the blades and thecontrol system to regulate the speed of the rotor, to avoid excessive speedsduring gales and to orient the rotor towards the most favourable position.The source of the wind power plant is the wind, or rather, the mechanicalenergy that, in form of kinetic energy sets the air into movement. The windis generated by the unequal heating of the surface of our planet. The Earthreceives a great amount of energy coming from the sun, and this energy,in certain places, can be of the order of 2.000 KWh/m2 annual [3]. 2%of that energy is transformed into wind energy with a value able to givea power of 1011 GW. The awareness of global heating in recent years hasyield an enormous boost to the wind power industry with an even increasing
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production of electricity produced by wind turbine.With a growing amount of installed wind power methods for connecting windturbines to the electrical grid has been giving more and more attention. Theinherent intermittent energy production of wind turbines makes it a not justa straightforward case to connect the generator in the wind turbine to thegrid i.e. how should a wind turbine with is driven by an ever changingwind 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 withdifferent constant speeds and then connect the generator to the grid. Thedevelopment in the last 10-15 years in power electronics has made it possibleto develop more complex wind turbines with converters making it able tohave variable speed turbines where the generators are connected to the gridvia a DC-link, like the system proposed in [1]. With large wind farm offshorefar from lands, which are likely to be more common in the future, a DC-cableto 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 generatorfor wind power applications. The model is developed in PSCAD/EMTDC.Two different generators are modeled and a comparison is made betweenthem. The two generators are a six-phase EMSG and a BLDC generator,which is a type of permanent magnet machine. The most obvious differencebetween both of them are the shape of the back-emf, back electromotiveforce. It is sinusoidal in the first case and trapezoidal in the second. Theoutput voltage from the generator is rectified through a diode rectifier andthe torque control is achieved by controlling the current through a DC/DC-converter that is conected in between the dc-side of the diode rectifier andthe grid side converter. The rectifier, converter and the control structure isdesigned with the greatest possible similarity in both cases. The design willbe made for low wind speeds from 3 m/s to 7 m/s with a constant pitch angleof the blades of the wind turbine.
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1.3 Thesis Layout
Chapter 2 describes how is possible to generate electricity with theaid of the wind.
Chapter 3 presents a general concept of the synchronous machinesspecially 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 tensioncontrol.
Chapter 6 modelling of the DC/Dc-converter.
Chapter 7 conclusions.
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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 intoelectrical energy depends on a lot of factors like: the wind speed, the rotorarea, blades and the density of the air. A wind turbine works in a certaininterval of different windspeeds. When the wind speed is around Vcut-in (3or 4 m/s) the turbine starts to work and stops when the wind speed is belowVcut-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 turbinemodel 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 turbinehas a rated power, Pn of 2 MW. E-82 uses a tower version with a hub heightof 108 m and a rotor diameter of 82 m. The speed of the turbine is between6 and 19.5 rpm.
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Figure 2.2: Aerogenerator E-82 [4]
In this thesis work a gearbox is introduced to increase the rotational speedof the generator. The gearbox transforms the low speed (of the turbine) intohigh speed (of the generator). The gearbox is placed between the rotor ofthe 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 workingwith low speed will be very big and therefore expensive. However there arealso disadvantages. There are losses in the gearbox and the gearbox is oneof the most vulnerable component of the wind turbine.
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Chapter 3
Synchronous Machines
3.1 Definition
Synchronous machines have been widely used in power systems mainly asgenerating unit, they are not only the main generation units in large scaleconventional power stations, but also in small and remote stand alone sys-tems. The synchronous generator produces its magnetization or rotor fluxby either a permanent magnet or by electrical magnetization, as opposed tothe induction machine which uses induction to achieve a magnetic flux. It isnamed synchronous because the rotor rotates in phase with the flux gener-ated by the stator currents. Various new types of synchronous generators arebeing developed like multi-pole machine for wind power conversion systems.These machines has a very important role to achieve a high efficiency anda reliable power system with good power quality. A detailed and accuratemodel is essential to investigate the performance of a synchronous machineand its control strategies.
The evolution of the synchronous machine has been and will continue tobe stimulated by parallel advances made in general machine theory, and inthe 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 lastyears many investigations related to multiphase machines have been made, alot of them towards six phase machines. The interest in multiphase machineslies mainly in the fact that with many phases the high currents associatedwith high power machines can be divided among more phases. Other advan-
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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 energybecause 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 are0.01 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 machineswhich has gained popularity in recent years. The reason for it being called aDC machine when it is in fact an AC machine is that it has a speed-torquecharacteristic as a traditional brush commutated DC machine. The reasonfor the increasing interest in these types of machines is that it has none ofthe drawbacks associated with mechanical commutated DC-machines. TheBLDC machine has the permanent magnets on the rotor and the windingsin the stator, one can say that the machine is turned inside out comparedto a PMDC motor. With this topology there is no need for electrifying therotor hence there is no need for mechanical brushes. The windings in thestator are made up from many coils interconnected. The windings are thenevenly distributed around the stator to form an even number of poles. De-pending on the winding topology, the back emf (electromotive force) is either
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of sinusoidal shape or trapezoidal shape. The BLDC generator modeled inthis thesis work has a back-emf of trapezoidal shape and is the only typeconsidered from here on regarding the BLDC machine. The attachment ofthe permanent magnets to the rotor can be of different type depending of thearea of usage and manufacturing considerations. They can be either attachedto the perimeter of the rotor or they can be buried inside the rotor core. Thesurface mounted type yields lower leakage flux but on the other side it is notsuited for high speed. [6] The model proposed in this work will have surfacemounted magnets. Typical stator resistance and stator inductance for PMmachines with surface mounted magnets are 0.01 to 0.1 p.u. and 0.2 to 0.4p.u respectively [7].
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Chapter 4
Modelling of 6-phaseSynchronous Machine andBLDC Machine
4.1 Software
All modelling and simulations are carried out in PSCAD/EMTDC 4.1, whichis based on the Fortran language. The electrical components of the whole sys-tem are built with standard electrical component models from the PSCAD/EMTDClibrary. The models of the EMSG and the wind turbine is already developedin the PSCAD/EMTDC enviroment and is used in this project.
4.2 Modelling of 6-phase Synchronous Ma-
chine
There are several ways to modelling of six-phase EMSM. One way is to usetwo doubly-star machines with a 30 electric degrees phase-shift between thetwo stars. Another way is to use a split phase machine, which can be builtby equally dividing the phase belt of a conventional three-phase machine intotwo parts with spatial phase separation of 30 electrical degrees. Finally thethird way uses the doubly-star machines with a star-triangle transformer atthe output of one machine to get a 30 electrical degrees phase-shift betweenthe two machines. The most used method is the first described.
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4.2.1 Mathemathical Model
The machine is assumed to be ideal [8], so there is no reluctance effect (uni-form air-gap in the machine), no magnetic induced reactance and no satura-tion effect. The system is split into two sets of 3-phase windings, which arespatially out of phase by 30 electrical degrees, as shown in the Fig. 4.1. Toobtain simpler equations it is necessary to use Concordia’s or Park’s trans-formation matrixes, which allow a simple control of n-phase machines, asdescribed in this chapter.
Figure 4.1: Six phase generator
The space harmonics of the electromotive force are neglected and theleakage self-inductances have all the same value Lf . In a natural orthonormalbase
βn = (ssA1, ssA2, ssA3, ssB1, ssB2, ssB3). (4.1)
Defining the following vectors
js = jsA1ssA1 + jsA2ssA2 + jsA3ssA3 + jsB1ssB1 + jsB2ssB2 + jsB3ssB3 (4.2)
where jsk stator current in the phase number k gives
us = usA1ssA1 + usA2ssA2 + usA3ssA3 + usB1ssB1 + usB2ssB2 + usB3ssB3 (4.3)
where φsk linked flux of the stator phase number k and
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φs = φsA1ssA1 +φsA2ssA2 +φsA3ssA3 +φsB1ssB1 +φsB2ssB2 +φsB3ssB3. (4.4)
Now is possible to express the stator self inductance matrix like
L6
s = L ×
1 +Lf
L−0.5 −0.5
√3
2−
√3
20
−0.5 1 +Lf
L−0.5 0
√3
2−
√3
2
−0.5 −0.5 1 +Lf
L−
√3
20
√3
2√3
20 −
√3
21 +
Lf
L−0.5 −0.5
−√
3
2
√3
20 −0.5 1 +
Lf
L−0.5
0 −√
3
2
√3
2−0.5 −0.5 1 +
Lf
L
(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 isassociated a 2-dimensional eigenspace δ and Lf is associated a 4-dimensionalspace κ. So vector x is the sum of two vectors, one per eigenspace. Thedescomposition, achieved by creating two orthogonal projections onto thetwo eigenspaces, gets
x = x4h + xdq with x4h ∈ κ and xdq ∈ δ (4.7)
Doing relations between flux and current vectors
φs4h = LfjsAh + φsr4h (4.8)
φsdq = Lcjsdq + φsrdq (4.9)
Applying twice the 3-phase Concordia´s transformation it is possible toget the characteristic matrix T
Lt =
√2
3×
1√2
1√2
1√2
0 0 0
1 −0.5 −0.5 0 0 0
0√
3
2−
√3
20 0 0
0 0 0 1√2
1√2
1√2
0 0 0 1 −0.5 −0.5
0 0 0 −0.5√
3
2−
√3
2
(4.10)
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There is still coupling between the equations because the vectors arenot eigenvectors of Ls6. So the following matrix allows the definition of anorthonormal base of eigenvectors
T tr6 =
1√
3×
1 1 1 0 0 0
1 −0.5 −0.5√
3
2−
√3
20
0√
3
2−
√3
20.5 0.5 −1
0 0 0 1 1 1
1 −0.5 −0.5 −√
3
2
√3
20
0 −√
3
2
√3
20.5 0.5 −1
(4.11)
Each line of T tr6 gives the coordinates, in the natural base, of eigenvectors,
which make up an orthonormal base noted
ǫs = (dcs1 , dcs
2 , dcs3 , dcs
4 , dcs5 , dcs
6 ) (4.12)
With (xhA, xd1, xq1, zhB, xd2, xq2) the coordintates of a vector x in thisbase, it is possible to get finally six equations relative to the statot flux
φshA = LfjshA + φsrhA
φsd1 = Lcjsd1 + φsdr1
φsq1 = Lcjsq1 + φsqr1
(4.13)
φshB = LfjshB + φsrhB
φsd2 = Lcjsd2 + φsdr2
φsq2 = Lcjsq2 + φsqr2
(4.14)
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 arethe same and all of lies in the interval for high power machines as shown inTable 4.1 [9]. The electromagnetic field is constant and the stator inductanceis high due to the fact that it is a high power EMSM [7]. A battery ofcapacitors are always necessary (due to their capacitive nature) to producereactive power. They stabilize and optimize the sizing and the yield of theinstallation.
4.3 Modelling of BLDC Machine
The model of the BLDC machine in this work is a y-connected 6-phase ma-chine. Each phase is displaced by 60 degrees compared to the one preceding.
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Table 4.1: Parameter of the EMSG
Rated power 2MWRated voltage 0.69KVRated current 0.893KAArmature resistance Ra 0.02secPotier reactance Xp 0.09p.u.Unsaturated reactance Xd 1.8p.u.Unsaturated transient reactance X ′
d 0.15p.u.Unsaturated sub-transient reactance X ′′
d 0.1p.u.Unsaturated reactance Xq 0.7p.u.Unsaturated transient time T
′
do 0.6p.u.Unsaturated sub-transient time T
′′
do 0.035p.u.
Each phase is modeled with a source producing the back-emf, a stator resis-tance and stator inductance. Fig. 4.2 shows one phase. The chosen valueof Rs and Ls is derived from the the typical value stated in the previouschapter.The mutual inductance is neglected in this model.
R=
0V
0.024 0.095
e
v
Rs Ls
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
ea =ke
2ωmF (θe) (4.15)
eb =ke
2ωmF (θe −
π
3) (4.16)
ec =ke
2ωmF (θe −
2π
3) (4.17)
ex =ke
2ωmF (θe − π) (4.18)
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ey =ke
2ωmF (θe −
4π
3) (4.19)
ez =ke
2ωmF (θe −
5π
3) (4.20)
The function F is given in Eq. 4.21 and is of trapezoidal shape.
F (θe) =
1 0 ≤ θe < π3
1 − 3
π(θe − π
3) π
3≤ θe < π
−1 π ≤ θe < 4π3
−1 + 3
π(θe − 4π
3) 4π
3≤ θe < 2π
(4.21)
where θe is the electrical angle and it is depending on the pole numberaccording to (θe = p
2θe). The torque of the BLDC generator is given in
Eq. 4.22.
Te = eaia + ebib + ecic + exix + eyiy + eziz (4.22)
4.3.2 Design Model
The parameters stated in Table 4.2. is the ones used in the simulation of theproposed BLDC generator.
Table 4.2: Parameter of the BLDC
Rated power 2 MWRated voltage 0.69 kVRated current 2.9 kAStator resistance, Rs 0.024 ΩStator inductance, Ls 0.0095 mHBack-emf constant, ke 345 Vs/radNumber of poles 72
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Chapter 5
Overall Controller
The main focus of this thesis will be the control of the machines. The wholesystem is described in Fig. 5.1. The TSR block, tip speed ratio, calculatesthe speed reference ωref , the speed controller then calculates the referencecurrent, ıref , The current controller calculats the error between the ıref andthe input current to the boost converter and calculate the control voltagean the PWM block calculate the switching signals to the converter The con-trol scheme is the same for the EMSG and for BLDC generator, the onlydifferences 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 windspeeds. The first region is approximatly between 4 m/s to 8 m/s and theturbine works with variable speed, the next region is between 9m/s and12m/s the machine works near the maximum speed of the rotor and finallythe last region which is between 13m/s and 22m/s where the turbine worksat contstant speed and at rated power. Each region demands a different
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approch to the control system. In this thesis the first region is considered.Wind turbines with variable speed are normally pitch regulated, however inthis thesis project the pitch is kept constant, as said before, for constraintreasons.
The wind turbine is characterized by its mechanical power, which is givenby [10]
Pm = 0.5ρπR2
bladeCpW3
speed (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 efficiencyCp(β, λ) of the turbine depends on two parameters, the pitch angle of theblades 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 parametersmust be varied at every time instance as the wind change its speed. In orderto work in low speeds λ can be considered to be constant, so the maximum λwill be used to get the best efficiency in this project. With lambda accordingto the Equation 5.2 the reference speed can be calculated as
ωref =λmaxWspeed
Rblade
(5.3)
where λmax is the parameter that together with β = 1 give the highestaerodynamic 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.
5.2 Mechanical Equation
The dynamic equation of an electrical machine system is well-known and willnot be explained in depth. It is stated as:
Jdωm
dt= T ′
m + bwr − Te (5.4)
J is the inertia of the machine, Te is the electrical torque, T ′m is the load
torque and b the viscious damping constant. The constant and a proportionalpart of the mechanical torque can be summarized according to Eq. 5.4. Themodel of the wind turbine in PSCAD gives as output the total mecanicaltorque.
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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 inthis project Eq. 5.6. and shown in Fig. 5.3.
Jdwr
dt= Tm − Te (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 controllerlater is proposed in [7]. In this control an active resistance is used, depending
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on its value the error will be greater or smaller, so if the active resistanceincreases the error decreases. The terminal voltage is limited to an upper anda lower value Vmax and−Vmax, because the rated voltages of the generatorsare 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. Thecurrent controller Fc function has a proportional and an integral part. Thetransfer function of the controller is stated in Eq. 5.7.
Figure 5.5: Current controller loop
Fc(s) = kpc +kic
s(5.7)
The electrical dynamics is given in Eq. 5.8. The active damping, Ra isintroduced to enhance the stability of the system.
Ge(s) =1
sL + R + Ra
(5.8)
To be able to calculate the value of kpc and kic a method called loopshaping is used. Ideally the Gce , the closed-loop transfer function from iref
to i should be as:
Gce(s) =αe
s + αe
(5.9)
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where αc s the closed-loop system bandwidth but
Gce(s) =Fc(s)Ge(s)
1 + Fc(s)Ge(s)(5.10)
so
Fc(s)Ge(s) =αe
s(5.11)
clearing Fc and comparing it with Equation. 5.7 yields:
kpc = αeL and kic = αe(R + Ra) (5.12)
As said before a limiter is used to prevent the control voltage from goingabove Vmax . However this can cause the integrator part of the CC to windup. To avoid this back calculation is used. The controller can be describedas:
dI
dt= e (5.13)
u = kpce + kicI − Rai (5.14)
v = s(u) (5.15)
where I is the integrator state variable and v is according to:
v = s(u) =
Vmax u > Vmax
u −Vmax ≤ u ≤ Vmax
−Vmax u < −Vmax
(5.16)
The back-calculated error e is chosen such that:
v = kpce + kicI − Rai (5.17)
comparing Equation 5.14 is compared with the Equation 5.17 the errorcan be cleared:
e = e +1
kpc
(v − u) (5.18)
we thus get the control with antiwindup function implemented accordingto Equation 5.19-5.21 and as shown in Fig. 5.5
dI
dt= e + kicI − Rai (5.19)
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u = kpce + kicI − Rai (5.20)
v = s(u) (5.21)
5.4 Speed Control
The speed controller is the most important part in this thesis because itregulates the iref for the current controller. Fig. 5.6 shows a simplified schemeof 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 functionsis defined as:
Fw(s) = kpw +kiw
s(5.22)
Gw(s) =1
sJ + b(5.23)
The parameters of the speed controller are obtained with the same methodused for the current controller:
kpw = αwJ and kwi = αwb (5.24)
The closed-loop bandwidth of the speed dynamics αw are typically relatedto the bandwidth of the electrical dynamics according to:
αw < 10αe (5.25)
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Chapter 6
Rectifier design
The output alternating voltages from the EMSG or the BLDC generator arerectified through a six phase diode bridge rectifier. This rectifier is made upof twelve diodes, grouped in six pairs. The rectifier is located between thegenerators 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 thesequence 1, 2, 3... (see Fig. 6.1. The commutation of current from one diodeto the next is not instantaneous, due to the inductances of the generator.Each of the diode pairs are conducting during 60 electrical degrees.
ir =
Id When diode 1 is conducting0 When to neither diode 1 or 6 is conducting−Id When diode 6 is conducting
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The voltage of the output of the rectifier is not a true DC voltage. Thediode rectifier creates a lot of harmonic distortion causing ripple in the outputvoltage. To avoid this a big capacitor is introduced to get a nearly stiff DCvoltage as input to the DC/DC-converter.
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Chapter 7
DC/DC Converter design
The boost (step-up) converter is placed after the 6-phase diode rectifier. TheDC/DC-converter controls the Id current, which is directly related to currentsin the generators. Hence the electrical torque of the generator is controlled.The control of the converter is done by the control circuit derived in theprevious chapter. The boost converter scheme is shown in Fig. 7.1. Theoutput capacitor is large so it is possible to assume vout(t) = Vout. The valueof the input inductor is made large enough for the converter to always work inCCM, Continues Conduction Mode. To make sure the converter always worksin CCM Equation 7.1. is used describing the boundary conditions betweenCCM and DCM, Discontinues Conduction Mode. I0max is the maximal loadcurrent through the inductor and Ts s is the switching time period.
Figure 7.1: Boost Converter
Ldc =TsVout
2I0max
D(1 − D)2 (7.1)
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An IGBT (Insulated Gate Bipolar Transistor) is used as switch in theconverter. IGBT switches are state of the art in the switching elements.Some of its desired advantages are: It can be totally controlled by a lowvoltage, has low on-state losses and large blocking voltages [11]. When theIGBT is turned on, ton, the energy of the generator is being stored in theinductor. During this time the diode is reversed biased, hence it does notconduct any current. When the IGBT is turned off, toff , the stored energyin the inductor flows through diode transferring it to the load. To calculatethe 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 voltageVout stays constant during each switching periods. The increase in the inputcurrent to the converter is stated as:
∆Iin = it0+Ts− it0 =
Ts
Ldc
(Vin − Vout(1 − D)) (7.2)
The control signal is selected as
Vcontrol = it0+Ts− it0 =
Ldc∆Iin
Ts
(7.3)
Equation 7.2 together with Equation 7.3 yields the duty ratio:
D = it0+Ts− it0 =
1
Vout
(Vcontrol − Vin) + 1 (7.4)
The control signal is compared with a periodic triangular pulse with aconstant switching frequency of 2 kHz hence a PWM signal is producedcontrolling the IGBT switch. The Fig. 7.2 shows the topology of the PWMgenerating circuit.
Figure 7.2: Converter Controller
In this thesis work we use a varible resistor acting as a DC load, this isto get a constant output voltage Vout, although the PWM calculating circuitworks for all output voltages within the limit 0 ≤ Vmax.
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Chapter 8
Results
The systems described and modeled in the previous chapter are simulated indifferent manners to show the overall performance. Firstly the performancesis verified by exposing the systems to different steps in the wind and thenby exposing the systems to more fluctuating wind speeds, wind speeds thatare more close to reality. In the last part of this chapter the systems areequipped with different passive filters to be able to find the best solution forfiltering away unwanted harmonics. For all the simulations the inertia J is6.3 Mkgm2 and a viscous damping constant of 0.5 Mkgm2/s. With thesevalue the value of the speed controller is calculated as proposed in chapter5.4, yielding an value of Kpw of 500000 and Kiw of 40000. These values ofthe speed controller are used throughout all simulations.
8.1 Speed performance
To show the overall performance of the proposed systems different steps inthe wind speeds will be exposed to the system. These steps are 3 m/s, 5 m/sand 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 currentresponse for each generator.
The results for the two different generator are similar but not equal, whichis to be expected. The two generators are using different values in the currentcontroller because the internal resistance and inductance are different. Thevalues of Kpe and Kie were found with a combination of analytical work andtrial and error, the parameters shown in Table 8.1 were found to be the bestworking. The method proposed in chapter 5.3 to calculate these values wasused but the R and L value had to be assumed since they were not knownbecause the rectifier and boost converter circuit also effect these values.
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Figure 8.1: Speed and current control EMSG
Figure 8.2: Speed and current control BLDC
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Table 8.1: Parameters of current controller
Generator Kp Ki
EMSG 15 0,3BLDC 3,75 1,41
In both simulations a gearbox is used to increase the speed of the gen-erators. 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 bothsystems and shown in table 8.2.
Table 8.2: Parameters of boost converter
L C5.5 µH 0,7 F
As seen in the graphs the current controller works really well in bothsystems. The speed response is in the region of several seconds which isonly to be expected for this big wind turbine. Also noticeable is that theperformance is a bit poorer for decreasing wind speeds. This is of coursedue to the fact that it is impossible to break the turbine electrically withthis kind of setup i.e. it is impossible to have the current running in twodirections 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. Thissimulation resembles much more the reality due to the characteristics thatthe wind has. Both generators respond to major wind changes but the fastfluctuations are responded upon which. The responses are shown in Fig. 8.3for the EMSG and in Fig. ?? for the BLDC. As seen the response of thecurrent is still good which of course will yield hih torque oscillations.
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Figure 8.3: Speed and current control EMSG
Figure 8.4: Speed and current control BLDC
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8.3 Filter performance
The behaviour of the system with passive harmonic filters re simulated inthis chapter. The passive filters are used to eliminate or at least reducethe produced harmonics in the electrical system. The existence of harmonicsgenerates adverse effects (like bad behavior of the machine, excessive heating,loss of life utility. . . ) in the system and the reduction of harmonics is a higlyprioritized 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 togetherwith 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 betweengenerator and rectifier Fig. 8.6 will be simulated. The last setup that issimulated is the setup with no filters between the rectifier and generator tocompare it with the filter performance. Fig. 8.7. Finally a simulation withthe best filters for each generator (Fig. 8.8) is run. All filter setups aresimulated using two different wind conditions. First with a constant windspeed and then with a fluctuating wind speed which is the one closest toreality.
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 theEMSG, the first four graphics describes the situation using a constant windspeed of 5 m/s and the other four are with fluctuating wind speeds between3 m/s and 7 m/s.
Analyzing the graphs, the system responds good when the wind is con-stant except in the third case, Fig. 8.11. The harmonics are reduced to a
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Figure 8.6: Scheme with one capacitor between rectifier and DC/DC con-verter
Figure 8.7: Scheme with a capacitor bank between generator and rectifier
Figure 8.8: Scheme with a capacitor bank between generator and rectifierand one capacitor between rectifier and DC/DC converter
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Figure 8.9: Passive filter between EMSG and rectifier
Figure 8.10: Capacitor bank between EMSG and rectifier
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Figure 8.11: One capacitor between rectifier and converter (EMSG)
Figure 8.12: Capacitor bank between EMSG and rectifier and one capacitorbetween rectifier and converter
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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 capacitorbetween 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 theuse of passive filters yields greater loss because of the use of many passivecomponents. The problem is that the passive filters do not work well whenthe wind is not constant (as in reality), for that reason a bank of capaci-tors works better to reduce a great part of the harmonics Fig. 8.12. Theperformance 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 thesimulations using constant wind speeds of 5 m/s and the other four are whenusing fluctuating wind speeds between 3 m/s and 7 m/s.
Analyzing the graphs, it can be seen that the behavior for the BLDC isdifferent from the EMSG, which is to be expected. Since the back-emf of theBLDC is trapezoidal there is much more harmonics in the BLDC than in theEMSG with in sinusoidal back-emf. As can be seen in the simulations thetopology 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.
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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)
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Chapter 9
Conclusions and proposals offuture work
The aim of this thesis was to model a torque controlled EMSG and a BLDCgenerator working at low wind speeds. The control system was made similarfor the two generators so a comparison could be made between them. Asshown in the previous chapter the control system responded well for bothgenerators when exposed to different wind changes. The dynamic responseof the system was several seconds which was to be expected because thelarge inertia of these big wind turbines. The different filters that were testedshowed different behavior depending on the generator used. The EMSGmachine showed the best performance with a filter topology with a capacitorper phase between the rectifier and generator and a big capacitor betweenthe rectifier and converter worked the best. Although the setup with 5thand 7th harmonic filter together with a high pass filter also worked exceptfairly high losses. Together with the fact that in a variable speed drives thefrequency of the harmonics keeps changing. These two drawbacks togetherwith higher installations costs for this type of filter, a lot of more passivecomponents are used, the conclusion can be made that the capacitor banksetup is the best.
For the BLDC generator it was found that that the setup with no extrafilters where the best solution with the lowest torque ripple although theperformance was far from that of the EMSG. With this topology, rectifierand boost converter, the normal procedure with the BLDC when the phasecurrents are switched on depending on the placement of the magnetic field isbypassed and this is the major source of all the current harmonics and hencea high torque ripple. With the system proposed in this thesis the conclusioncan be drawn that the EMSG with its sinusoidal back emf works better thanthe 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 hencelower losses in the machine.
To conclude this work some suggestions for future work is given. Theobvious way forward from this work is of course to implement the torquecontrol method together with a pitch control for the wind turbine and simu-late the performance of the system working in the whole wind speed range.To further improve the model of the EMSG field control can be implementedto further enhance the performance.
Further investigations should be done on the BLDC generator. A com-parison between the setup in this thesis and a setup with switching elementsswitching on and of the phase currents according to the placement of themagnetic field would be interesting. The latter setup will of course yieldhigher installation costs and the question is if the cost can be compensatedby the lower losses that this set ought to give. Further investigation can bedone on different motor topologies to find out how they affect the behavior ofthe system i.e. what is the best number of poles, how many windings shouldone have for example. This can of course also be done for the EMSG.
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References
[1] Amei, K., Takayasu, Y., Ohji, T., Sakui M., A maximum power controlof wind generator system using a permanent magnet synchronous gen-erator and a boost chopper circuit, Proceedings of the Power ConversionConference, 2002. PCC Osaka 2002., Volume 3, pp. 1447-1452, April2002.
[2] Bresesti, P., Kling, W.L., Hendriks, R. L., Vailati, R., HVDC Con-nection of Offshore Wind Farms to the Transmission System, IEEETransaction on Energy Conversion, Volume 22, pp. 37-43, March 2007.
[3] Marıa Florencia Martinetti, http://www.monografias.com/trabajos//fuentesener/fuentesener.shtml, Energıa eolica.
[4] Enercon, http : //www.enercon.de/en/ home.htm, 2004-2007.
[5] S.E.Abo-Shady, Y.A.Al-Turki, Methodology of asymmetrical fault anal-ysis of a 6-phase synchronous machine, King Abdul-Aziz University,1989.
[6] Hamdi, E.S., Permanent Magnet and Variable Reluctance Drive Sys-tems, ETI Sweden.
[7] Harnefors, L., Control of Variable-Speed Drives, Malardalen University,2002.
[8] E.Semail,A.Bouscayrol, J.P- Hautier, Vectorial formalism for analysisand design of polyphase synchronous machines, The European PhysicalJournal Applied Physics, pp. 207-220, 2003.
[9] Jorma Luomi, Transient Phenomena in Electrical Machines, ChalmersUniversity, Sweden, 1998.
[10] Arkadiusz Kulka, Pitch and torque control of variable speed wind tur-bines, Chalmers University, Sweden, 2004.
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[11] Mohan, N., Undeland, T.M., Robbins, W.P., POWER ELECTRONICS,Converters, Applications and Design, Third edition, John Wiley & Sons,Inc., 2003.
[12] Wall, S., Jackson, R., Fast controller design for practical power-factorcorrection systems, Proceedings of the IECON ´93, Vol. 2, pp. 1027 -1032, November 1993.
[13] Jiao, S., Hunter, G., Ramsden, V., Patterson, D., Control system designfor a 20kW wind turbine generator with a boost converter and a batterybank load, IEEE 32nd annual PESC 2001, Vol. 4, pp. 2203-2206, June2001
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