Xavier Bracke with a Full Active Rectifier Maximum Power Point Tracking of Small Wind Turbines Academic year 2013-2014 Faculty of Engineering and Architecture Chairman: Prof. dr. ir. Jan Melkebeek Department of Electrical Energy, Systems and Automation Master of Science in Electromechanical Engineering Master's dissertation submitted in order to obtain the academic degree of Counsellors: Ir. Jeroen De Kooning, Ir. Jan Van de Vyver Supervisor: Prof. dr. ir. Lieven Vandevelde
Transcript
Xavier Bracke
with a Full Active RectifierMaximum Power Point Tracking of Small Wind Turbines
Academic year 2013-2014Faculty of Engineering and ArchitectureChairman: Prof. dr. ir. Jan MelkebeekDepartment of Electrical Energy, Systems and Automation
Master of Science in Electromechanical EngineeringMaster's dissertation submitted in order to obtain the academic degree of
Counsellors: Ir. Jeroen De Kooning, Ir. Jan Van de VyverSupervisor: Prof. dr. ir. Lieven Vandevelde
Xavier Bracke
with a Full Active RectifierMaximum Power Point Tracking of Small Wind Turbines
Academic year 2013-2014Faculty of Engineering and ArchitectureChairman: Prof. dr. ir. Jan MelkebeekDepartment of Electrical Energy, Systems and Automation
Master of Science in Electromechanical EngineeringMaster's dissertation submitted in order to obtain the academic degree of
Counsellors: Ir. Jeroen De Kooning, Ir. Jan Van de VyverSupervisor: Prof. dr. ir. Lieven Vandevelde
Preface
In this preface, I would like to thank everyone that has contributed to the realization of thisthesis.
First, I want to thank my two supervisors ir. Jeroen De Kooning and ir. Jan Van de Vyver fortheir never ending support during the many hours I have spent in the laboratory. Jeroen, thankyou for your new design of the half bridge module and your help during their construction. Itwas also you who forced me to think innovative and always tried to push me to a new frontier.Jan, thank you for helping with the construction of the new wind turbine emulator and themany hours you spent in reading and correcting the little mistakes in my text. Secondly, Iwant to thank my promotor prof. dr. ir. Lieven Vandevelde for offering me the opportunityand accommodation for executing this research at EELAB. During his lessons, I gained a lotof knowledge which seemed very useful during this thesis.
I also would like to thank Tony Boone and Stephan D’hondt for helping me with the mechanicalconstruction of the new wind turbine emulator and the active rectifier. Also thanks to my fellowstudents Jonas, Freek, Pieter D., Dries and Pieter D.B. for the many amusing talks we havehad in the lab.
At last, I would like to thank my family for their support during this period. It wasn’t an easytime for all of us and I would like to dedicate this text to my father, who got severely ill duringthe period I was working in the lab. Thanks to both my parents for encouraging and helpingme during the past five years of my studies.
Xavier Bracke, June 2014
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Permission for consultation
“The author gives permission to make this master dissertation available for consultation andto copy parts of this master dissertation for personal use.In the case of any other use, the limitations of the copyright have to be respected, in particularwith regard to the obligation to state expressly the source when quoting results from thismaster dissertation.”
Xavier Bracke, June 2014
vii
Maximum Power Point Tracking
of Small Wind Turbines with
a Full Active Rectifier
by
Xavier Bracke
Thesis submitted to obtain the academic degree of
Master of Science in Electromechanical Engineering:
Electrical Power Engineering
Academic year 2013–2014
Supervisor: Prof. dr. ir. L. Vandevelde
Counsellors: ir. J.D.M. De Kooning, ir. J. Van de Vyver
Faculty of Engineering and Architecture
Ghent University
Department of Electrical Energy, Systems and Automation
Chairman: Prof. dr. ir. J. Melkebeek
Keywords
Maximum power point tracking (MPPT), Permanent magnet synchronous generator (PMSG),Active rectifier, Field oriented control, Wind energy conversion system (WECS)
Summary
Maximum Power Point Trackers controls a wind turbine’s rotor speed to maximize its poweroutput. Several MPPT control strategies exist in literature of which four different ones aredescribed and tested in this thesis. These are examined both by executing simulations andby implementation in a practical setup. As power electronic converter, an active rectifier isdesigned which controls the wind turbine generator torque and rotor speed by using field ori-entation. The active rectifier has some particular advantages compared to the passive rectifieraccording to generator efficiency and MPPT performance. Finally, a new application of theactive rectifier is proposed for improved wind energy conversion during wind gusts. Here, thegenerator operates shortly as motor to help the turbine to start and accelerate to improve theMPPT.
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Maximum power point tracking of small windturbines by using a full active rectifier
Xavier Bracke
Supervisor(s): Prof. dr. ir. Lieven Vandevelde, ir. Jeroen De Kooning, ir. Jan Van de Vyver
Abstract— Maximum power point tracking algorithms control a windturbine’s rotor speed to maximize the power output for a given wind speed.They are widely adopted in wind energy conversion systems, but researchhas shown that the tracking performance of today’s commercial small-scalewind turbines can still be improved. The active rectifier controls the gen-erator torque by using field orientation which results in a faster and moreefficient speed control. With this converter, four different MPPT strategiesare investigated by simulations and by implementation in a lab setup. At theend, a new wind gust capture strategy is presented which uses the ability ofthe active rectifier to operate the generator as motor.
Keywords— wind energy conversion system, maximum power pointtracking, active rectifier, permanent magnet synchronous generator
I. INTRODUCTION
During the last few decades, wind turbines have become oneof the most popular methods for the generation of renewableenergy, proved by the installation of numerous MW-turbines.Small turbines with a rated power between 1 and 30 kW arehowever less popular. The problem of these turbines is the lowerheight of the nacelle, where the wind speed is less stable dueto turbulences. In order to maximize the power output dur-ing fluctuating wind conditions, variable speed wind turbinesare necessary with an adequate maximum power point tracker(MPPT). Commercialised systems are already available with acost-performance ratio that is comparable with photovoltaic sys-tems. However, research shows that there is still margin for im-provement because this market segment is not mature yet [1].Small wind turbines have a great potential as they are ideal forinstallation in both densely populated as rural regions. They arealso suited to be used as distributed generators (DGs) in micro-grids.
II. ACTIVE RECTIFIER
The active rectifier is the first part of the back-to-back con-verter topology presented in Figure 1. This converter connectsthe generator to the grid and controls the rotor speed indepen-dently from the grid frequency. The active and reactive power,injected to the grid, can be controlled to ensure grid voltage sta-bility [2]. The generator creates an ac voltage with a variablefrequency corresponding to the rotor speed. This ’wild’ ac isrectified into a dc current which goes through a DC-bus to thegrid-coupled inverter, which converts the dc current back intoan ac current of 50 Hz for injection in the grid. The active recti-fier can control the generator current to have any waveform. Bycontrolling the stator current sinusoidally in phase with the elec-tromotive force (EMF), field orientation is established by whichthe generator torque is at any moment proportional to the statorcurrent amplitude.
A permanent magnet synchronous generator (PMSG) is acompact machine with high efficiency and easy controllabil-
PMSG ActiveRectifier Inverter
Grid
DC-bus
Fig. 1: Back-to-back converter
ity, ideal to be suited in small wind turbines. The permanentmagnets allow a high number of rotor poles which reduces therated speed of the generator. This eliminates the installation ofa gearbox between turbine and generator, improving reliabilityand cost-efficiency.
The PMSG is the perfect machine to be driven with field ori-entation (FOC). The rotor position can be measured by an en-coder and gives the instantaneous position of the flux linkageΨPM and the corresponding EMF. In a synchronous referenceframe (d,q), the EMF phasor needs to be along the q-axis, sothe d-axis stator current Id is controlled to zero. The q-axis cur-rent Iq determines the stator current amplitude and the resultinggenerator torque:
Tg =3
2NPΨPMIq (1)
with NP the number of pole pairs.The control scheme is presented in Figure 2. The measured
stator currents are transformed to the d,q-frame by using the ro-tor position θ. These two currents are controlled to their respec-tive reference values, resulting in voltages (Vq, Vd) which areapplied to the stator by using pulse width modulation (PWM).The q-axis reference current is determined by an outer speedcontrol loop. The desired rotor speed is determined by theMPPT controller [3].
III. MPPT CONTROL
The power output of a wind turbine can be modelled by theCP(λ)-curve, shown in Figure 3. The dimensionless power co-efficient CP is related to the turbine power:
Pt =1
2ρAv3CP(λ) (2)
where ρ is the ambient air density, A the turbine blade sweptarea and v the wind speed. The tip speed ratio (TSR) λ is thedimensionless version of the rotor speed:
λ =rΩ
v(3)
PI
PI
PI
abc
abc
dq
0
Irefd
Irefq
Id
Iq
Ωref
Ω
Vd
Vq
θ
Ω
NP
dqPMSG
+
-
+- Ia Ib Ic
+-
Fig. 2: Field oriented control scheme.
This curve has a maximal valueCP,max for a given optimal TSRλopt, the maximum power point (MPP). This means that for ev-ery wind speed, an optimal rotor speed exists at which the poweroutput is maximal. The MPPT has the purpose to find the opti-mal rotor speed and to control the wind turbine to it.
CP(λ) CP,max
TSRλopt
Fig. 3: Wind turbine characteristic: power coefficient versus tipspeed ratio.
Four different MPPT strategies have been investigated:1. Tip Speed Ratio controlThe controller measures the wind speed and calculates the opti-mal rotor speed by using the optimal tip speed ratio λopt:
Ωopt =vλoptr
(4)
This is the fastest MPPT if an accurate value of the wind speedis available. However, correct wind speed measurements aredifficult to obtain, especially in small wind turbines which suf-fer harder from turbulences. Other MPPT strategies will try toeliminate these wind speed measurements. Another drawbackof this method is that the optimal TSR needs to be known.2. Power controlFor every rotor speed within its allowed range, an optimal poweroutput exists. The relationship is determined by the optimalpower coefficient Kopt. The generator power is controlled ac-cording to the relationship: Popt = KoptΩ
3. Due to an iterativeprocess, the wind turbine will go to the MPP. The drawback isthat this is a quite slow process and thatKopt needs to be known.3. Hill Climb Search controlThis is a perturb and observe method, which detects the varia-tion of the rotor speed and the generator power and determineswhether a positive or negative fixed step has to be added to the
previous rotor speed reference in accordance with the CP(λ)-curve. This method does not require any experimental informa-tion about the turbine, but results in hysteresis around the MPP.4. Mode controllerThis is an advanced MPPT control scheme that combines a hillclimber with variable step with the ability of keeping the rotorspeed fixed at the MPP. The algorithm is based on [4] and hasbeen adapted to be used with the active rectifier. This results ina performant behaviour comparable with the TSR control.
IV. RESULTS
The four MPPT strategies are implemented in the controllerof the active rectifier. By applying wind speed steps with thewind turbine emulator, the dynamic behaviour can be investi-gated. In Figure 4, the rotor speed and generator power re-sponses are shown, together with the wind turbine character-istics of the wind speeds at start and end. For the four methods,the controller is able to reach the desired MPP. Regarding to thesettling times, the TSR control is the fastest method if accuratewind speed measurements are possible. The mode controller re-sults in comparable settling times without the need of any windspeed measurement. The power control and HCS control resultin much slower behaviour with settling times which are three tofour times longer than for the TSR control. Additionally, theHCS controller experiences hysteresis around the MPP, whilethe other methods keep the rotor speed fixed at constant windspeed.
As alternative, often a low-cost passive rectifier is used, whichintroduces stator current harmonics and a high torque ripple.The active rectifier eliminates these low order harmonics and thetorque ripple due to the sinusoidal current control, resulting in areduction of the generator losses. The additional power outputcan however not compensate the higher converter cost.
V. WIND GUST CAPTURE
During the standard MPPT control, the permanent magnetmachine only operates as generator. The active rectifier is alsoable to operate the generator as motor. This way, the MPP can bereached faster while electric energy from the grid is consumed.In combination with the TSR control, the energy output is nearlythe same as when no motoring is used. The extra energy that is
0 5 10 15 20 25 30 35 40 45 500
20
40
60
80
100
120
Rotor speed Ω [rad/s]
Gen
erato
rpower
Pg
[W]
v = 5 m/s
v = 4 m/s
(a) TSR control
0 10 20 30 40 500
10
20
30
40
50
60
70
80
90
100
110
Rotor speed Ω [rad/s]
Gen
erato
rpow
erP
g[W
]
v = 4 m/s
v = 5 m/s
(b) Power control
0 5 10 15 20 25 30 35 400
10
20
30
40
50
60
70
80
Rotor speed Ω [rad/s]
Gen
erato
rpower
Pg
[W] v = 4.5 m/s
v = 3.5 m/s
(c) HCS control
0 5 10 15 20 25 30 35 400
20
40
60
80
100
120
Rotor speed Ω [rad/s]
Gen
erato
rpow
erP
g[W
]
v = 5 m/s
v = 4 m/s
(d) Mode control
Fig. 4: Generator power in function of rotor speed after wind speed step for four different MPPT strategies
generated by reaching the MPP faster is nearly completely com-pensated by the energy used for the improved acceleration.
However, this method is profitable to capture wind gusts whenthe turbine is initially at standstill. As wind turbines have a rel-atively large rotor inertia and a very small starting torque, theyhave a long and unpredictable start-up. By helping the wind tur-bine to accelerate from the moment a wind gust is detected, theMPPT is better able to track the optimal rotor speed. Figure 5presents the rotor speed response for a wind gust with and with-out additional acceleration. The relative captured energy is thelargest for long wind gusts with a high peak value. This windgust capturing is described in the conference paper [5].
VI. CONCLUSION
The FOC control of a PMSG and four different MPPT controlstrategies have been simulated and implemented in a lab setup.The active rectifier, in combination with these MPPTs, is able tocontrol the rotor speed and follow wind speed variations prop-erly. Also, a comparison is made with the passive rectifier. Fi-nally, a new wind gust capture strategy has been proposed whichincreases the power output during wind gusts.
REFERENCES
[1] J.D.M. De Kooning, B. Meersman, T. Vandoorn and L. Vandevelde, ”Eval-uation of the maximum power point tracking performance in small windturbines”, Proceedings of 2012 IEEE PES general meeting, pp. 1-8, (2012)
0 1 2 3 4 5 60
5
10
15
20
25
Time [s]
Ω[r
ad/s]
Fig. 5: Optimal (dotted), unmotored (normal) and motored (full)rotor speed in function of time.
[2] Z. Chen, J. M. Guerrero and B. Frede, ”A review of the state of the art ofpower electronics for wind turbines”, IEEE trans. on Industrial Electronics,vol. 24, no. 8, pp. 1859-1875, (2009)
[3] M. Chinchilla, S.Arnaltes and J.C.Burgos, ”Control of permanent-magnetgenerators applied to variable-speed wind-energy systems connected to thegrid”, IEEE trans. on Energy Conversion, vol. 21, no. 1, pp. 130-135, (2006)
[4] S. Kazmi, e.a. , ”A novel algorithm for fast and efficient speed-sensorlessmaximum power point tracking in wind energy conversion systems”, IEEEtrans. on Industrial Applications, vol. 58, no. 1, pp. 29-36, (2011)
[5] X. Bracke, J.D.M. De Kooning, J. Van de Vyver and L. Vandevelde, ”Ef-fective capture of wind gusts in small wind turbines by using a full activerectifier”, IET RPG 2014 conference, (2014)
Contents
1 Introduction 1
1.1 Energy landscape in Belgium and Europe . . . . . . . . . . . . . . . . . . . . . 1
1.2 Differences between small and large wind turbines . . . . . . . . . . . . . . . . 3
7 Advanced applications of the active rectifier 827.1 Comparison between passive and active rectifier . . . . . . . . . . . . . . . . . . 827.2 Influence of current waveform on the generator efficiency . . . . . . . . . . . . . 857.3 Improved MPPT by acceleration of the wind turbine using the PMSG . . . . . 89
On the 19th September of 2013, ’De Standaard’ reported that in Flanders 40 percent moregreen energy was produced than the year before [9]. The word ’green energy’ is in fact verygeneral and refers to all methods of producing energy relying on renewable energy sources.These comprise solar energy, hydropower, wind power (which is a result of solar energy),biomass, biofuel and geothermal energy. Of all these energy sources, solar energy has thegreatest potential. The amount of solar energy that reaches earth during 40 minutes is equalto the annual world energy consumption. The solar irradiation of the planet makes water inthe oceans vaporize which falls back as rain in the mountains when it has been cooled down.This water can be stored in reservoirs by constructing dams and used at later moments togenerate electricity. A similar cycle exists for wind. Solar radiation heats up air so it starts torise which creates a low pressure region. When the air flow cools down again, it descends anda high pressure region arises. Air flows then back from the high pressure to the low pressureregion so the cycle is closed. By using wind turbines, this air flow is converted into electricity,which illustrates that both hydro power and wind power are an indirect consequence of solarpower.
In the beginning of the year 2013, 299 wind turbines were installed in Flanders with a totalcapacity of 423 MW. These have each a nominal power varying from 400 kW to 2.5 MW andare horizontal axis wind turbines (HAWT), rotating at a low shaft speed in order to reduce thetip speed and noise [7].
In recent years, there has been enormous investments in offshore wind farms which are installedon the ’Thorntonbank’ in the North Sea along the coast of Zeebrugge. 91 turbines were alreadyinstalled in 2012 at this location with a total capacity of 380 MW [11].
If perspective is broadened, the European Union is forcing to expand the capacity of windenergy generation. In Table 1.1, the evolution of installed capacity in the European Union(offshore+onshore) is shown. In 2012, this number has become larger than 100 GW. At theend of 2013, a total capacity of 117 GW has been installed of which 6.6 GW is placed offshore.The EU now wants to reach a next level and create a pan-European offshore grid instead ofeach country operating its own turbine parks. The objective for 2020 is to have an installedcapacity of 40 GW offshore, which grows to 150 GW in 2030. A European transnational gridwould smooth the variability in production and contribute to the development of one singleEuropean grid. [11]
1
1.1. Energy landscape in Belgium and Europe
This strategy fits in the ”20-20-20” targets in which the European Union has set three keyobjectives for 2020 [12]:
• a 20% reduction of the EU greenhouse emissions compared to 1990 levels.
• a 20% increase in the share of renewable energy resources in the EU energy consumption.
• a 20% improvement in the EU’s energy efficiency.
Year Installed capacity [GW]
2009 75.32010 85.02011 94.52012 106.42013 117.3
Table 1.1: Installed capacity of wind energy production in European Union (EU-28), offshore andonshore.
In January 2014, the European commission presented its new goals for 2030. In that year, thegreenhouse gas emissions should be reduced by 40% and the share of renewable energy shouldbe at least 27% of the total European energy consumption. Also actions are proposed toenhance the stability and power quality of the interconnected European transmission networkas more and more distributed generators (DGs) arise in it. Electricity generation from solar PVunits and wind turbines gives problems for grid stability as their operation is not dispatchable:the production is not adapted to the demand profile. Also, most DG units don’t contributeto primary frequency control, such that other electric power plants have to be more flexible tocompensate variations in demand and production.
In Belgium, the share of wind energy has grown to 3.75% in a situation where 10.04% of theelectricity is produced with renewable energy sources, according to the data in Table 1.2 fromthe year 2012. For the moment, nuclear energy is still our largest energy source, but thisshare is expected to shrink in the following years due to political and environmental issuesresulting in a planned closure of Doel 1 and 2 in 2015. For Tihange 1, there is still no decissionwhether the closure will take place in 2015 or the plant will be updated to run until 2025 [5].In March 2014, the nuclear reactors Doel 3 and Tihange 2 were closed again after the discoveryof microscopic cracks in the reactor vessels. Whether these reactor will be restarted soon isunknown but rather unlikely. This means that a large part of our basic load capacity will haveto be replaced in the next years in order to prevent a possible black-out during the winterseason. However, no investments in new power plants have been made during the last years.
Another phenomenon which is having a large impact on our energy landscape, is the exploita-tion of shale gas in the US. This source of non-conventional gas makes that the US is becomingone of the largest producers of gas and oil in the world. The result is that gas prices areincreasing due to the expensive exploitation so coal, imported from overseas areas, becomescheaper. Power plants in Belgium are now consuming more coal, causing high efficient CCGTplants (’Combined Cycle Gas Turbines’) with an efficiency of more than 60% to shut down.
To investigate the market share of green electricity in the total Belgian electricity production,Figure 1.1 shows the evolution of different technologies through the years by showing the
2
Chapter 1. Introduction
Electricity from: GWh %
Fossil Fuels 28807 37.59- Hard coal 2307 3.01- Oil 8 0.01- Natural gas 22689 29.61- Mixed fuels 1780 2.32
Nuclear energy 38465 50.20
Renewable energy 7690 10.04- Water 1667 2.18- Solar 1628 2.12- Wind 2879 3.76- Other resources 3183 4.15
Total production 76629 100
Table 1.2: Belgian electricity production [6]
amount of green certificates distributed for that technology. Originally, 1 green certificatewas equivalent to a production of 1000 kWh. Now, a banding factor is introduced to reducethe subsidies. These certificates have to be bought by the distribution or transmission gridoperator at a minimum price of 90 euro for onshore installations and 107 euro for new offshoreinstallations [8]. Large electricity producers state that this system of incentives is blockingnew investments in the construction of new power plants, which is endangering the security ofsupply in Belgium.
Figure 1.1: Number of distributed green certificates in Flanders [8]
1.2 Differences between small and large wind turbines
In the evolution of wind energy that has been outlined, only large wind turbines with a nacelleheight of more than 50 m and a rated power of a few MW have been discussed. As Flandersis a densely populated area, the appropriate locations to install such turbines are rare. It iscommon that action committees protest against their installation. So-called drawbacks are thenoise, the blade shadow, risk for birds, etc.
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1.3. Justification of this thesis
There is a great potential in Flanders for the installation of small and medium sized turbines.Small turbines have a shaft height smaller than 15 m and a rated power smaller than 30 kW.These exist both with vertical and horizontal axes. In Schoondijke (Zeeland, NL), a test farmis located where the operation of ten different types of commercial wind turbines is compared.Wind turbines with both horizontal and vertical axes have been installed. One of the resultsof this research is that there is still a lot of variability in the performance of these differentturbines, which indicates a market that is not mature yet. However, the cost-benefit ratio of thebest performing turbines is close to the one of solar panels. If the market share would increaseand be supported by regional or European governments, it is expected that investments willresults in further improvement of the efficiency [24].
It is often the question why the technology of large wind turbines can not be copied to thesmaller types. There are quite a few differences according to both construction and operation[13]:
1. On a height of 10 to 15 m above the ground, wind is less stable than at 50 m. As thecaptured power depends on the wind speed by the third power, this causes a lot ofvariation in the produced power. This is why small turbines have to change their shaftspeed as quickly as possible so the wind turbine rotates at an optimal speed to maximizethe aerodynamic performance.
2. Of course, the rated power of small turbines is lower. Therefore, it is easier for the powerelectronics to convert the full rated power and inject it into the grid. The back-to-backconverter is perfectly suited for this purpose and offers full control of the turbine speed.
3. For large wind turbines, the nacelle is at a relatively large height where wind speeds arequite stable. For these turbines, wind maps can be used to estimate the expected poweroutput. Smaller wind turbines suffer more from turbulences caused by the surroundings,such as houses, trees, etc. In this case, these wind maps are not reliable anymore andwind speed measurements on location are essential but rarely executed. Most of thetime, an overestimation of the wind speed is made, resulting in the installation of a windturbine which is too large and too expensive (economic efficiency smaller), together withthe fact that the resulting power output and efficiency will be lower than expected.
1.3 Justification of this thesis
Recently, research at the University of Ghent [14] has been executed in which the performanceof different existing small wind turbines was investigated relying on measurement data fromliterature. This has shown that existing commercial types are not very good in reaching theiroptimal operating point during steady state conditions. The average procentual improvementis around 5% at 5 m/s. At a lower average wind speed of 4 m/s, this value is even 6.2%.
This paper shows that there is still an opportunity to improve the tracking algorithms whichare used in small wind turbines. In this thesis, a lab setup will be built consisting of an electricmotor coupled with a generator. The motor is a wind turbine emulator which will simulate thedynamic behaviour of a wind turbine in function of the wind speed. The generator is controlledby an active rectifier. The MPPT controller inside the rectifier will drive the generator to theoptimal rotor speed at which the wind turbine produces its maximal power output for thatwind speed. The performance of four different MPPT strategies will be discussed. Finally,the active rectifier is compared to the less complex passive rectifier and a new strategy for theeffective capture of wind gusts is proposed.
4
Chapter 1. Introduction
1.4 Overview
In this introduction, the possibilities and perspectives of wind energy and small wind turbineshave been outlined in order to understand that this technology still has an interesting potential.
In Chapter 2, some theoretical principles about wind turbines with the associated power con-verters and generators will be discussed.
In Chapter 3, the modelling of a wind turbine, permanent magnet synchronous generator andactive rectifier will be discussed together with their implementation in Matlab Simulink inorder to perform simulations of the different MPPT control strategies.
Chapter 4 discusses four different MPPT strategies which are introduced and simulated byusing the Simulink models.
In Chapter 5, the construction of the active rectifier is discussed together with the way itoperates in combination with the wind turbine emulator. The operation of the field orientedcontrol is validated.
In Chapter 6, the four MPPT strategies which were introduced in Chapter 4 are implementedin the active rectifier and the results are discussed.
Chapter 7 discusses the benefits of using an active rectifier compared to the passive rectifier. Italso discusses how the generator can be used as motor to improve MPPT and allow for effectivewind gust capture.
Chapter 8 gives the conclusion of this thesis and some perspectives for further research.
The appendices give extra information about components used in the lab setup such as thegenerator data sheet, torque sensor, CAN communication and also the DSP programming codeis given. Finally, also the paper that has been submitted for the IET RPG 2014 conference isadded.
5
Chapter 2
Wind energy conversion systems
2.1 General description
The purpose of the wind turbine is to capture the kinetic energy contained in the wind andconvert it into useful electric energy. Wind energy is a direct cause of solar energy because thesun heats the atmosphere unequally. As layers of air can have different temperatures, regionsof different atmosphere pressure arise and air starts moving from high to low pressure regionscausing the phenomenon wind.
In general, there are two types of wind turbines: the ones with a horizontal axis (HAWT) andthe ones with a vertical one (VAWT) (see Figure 2.1). It is generally accepted that turbineswith horizontal axis are the most efficient and also the most common ones. The followingtheories and control strategies are valid both for HAWTs and VAWTs.
When wind flows around turbine blades, it creates an aerodynamic lift on them. This resultsin a torque on the rotor which can drive a load. The power contained in the wind flow is theproduct of the mass flow with the kinetic energy:
P0 = Av · 1
2ρv2 =
1
2ρAv3 (2.1)
in which A is the turbine blade swept area of the turbine, ρ the density of air and v the windspeed.
Of course, not all the available power contained in the flow can be captured and transferredto the generator. The power output of the turbine is determined by the power coefficient CP,which is the ratio between turbine power Pt and the power P0 contained in the air flow:
CP =Pt
P0=
Pt12ρAv
3(2.2)
There is a limit to this factor which is an absolute maximum, the so-called Betz limit. Thisvalue is calculated in [3], using aerodynamic principles.
CP,max =16
27= 0.593 (2.3)
In common, modern wind turbine systems, the maximum power coefficient is about 0.45.
The higher the power coefficient, the higher the aerodynamic efficiency of the blades. Theblades of a wind turbine are designed such that the system operates optimal at a certain tip
6
Chapter 2. Wind energy conversion systems
(a) Horizontal axis (b) Vertical axis
Figure 2.1: Difference between horizontal and vertical axis wind turbine
speed ratio λ (TSR). This is the ratio of the blade tip speed to the wind speed:
λ =vtip
v=r Ω
v(2.4)
in which r is the turbine rotor radius and Ω the angular shaft speed in rad/s.
The power coefficient depends on the tip speed ratio and has a maximal value for a certainλopt. For large wind turbines the optimal TSR value is about 6. Such turbines are alsocapable to change the pitch angle of their rotor blades. The pitch angle β influences the powercoefficient and is adapted by the controller to limit the power output at high wind speeds. Forsmall turbines, this control is often not available because of its mechanical complexity and itsadditional cost. Because in this thesis only small turbines are investigated, β will be set tozero in the next equations.
The relationship CP(λ, β) can be determined experimentally, but there exist also many correla-tions in literature based on curve fitting of experimental data. These correlations depend on theapplication, but globally the curves all have the same shape. An example of such CP(λ)-curveis shown in Figure 2.2.
A wind turbine can only operate in a limited range of the wind speed. Below a certain windspeed, the cut-in speed vci, the turbine will not be able to start because of static friction andthe magnetic cogging torque1 of the generator. The machine stays at stand-still and λ is zero.When the wind speed increases above vci, the turbine starts rotating and the system produceselectricity. To operate at the optimal power coefficient CP,max, the control mechanism shouldget the turbine at its optimal value λopt. The rotor speed will now increase linearly with thewind speed. If the wind is too strong with wind speeds larger than the rated wind speed vnom,the shaft speed will be limited because otherwise centrifugal forces would damage the rotor.The shaft speed will be held constant at its nominal value Ωnom, which results in the followinglimit for λ:
λ =r Ωnom
v(2.5)
1In permanent magnet machines, the rotor will try to align itself during standstill with the stator in fixedpositions of minimal saliency. During startup of the machine, an additional torque needs to be applied, thecogging torque, to overcome the static magnetic forces.
7
2.2. Conversion to electric energy
0 2 4 6 8 10 120
0.1
0.2
0.3
0.4
0.5
Tip Speed Ratio λ [-]
Power
Coeffi
cien
tCP
[-]
Figure 2.2: Relation between power coefficient and tip speed ratio
If the wind speed is higher than the cut-out speed vco, the rotor is braked both electrically andmechanically to stand-still to prevent any damage on the wind turbine due to overspeed. Ifpossible, also the nacelle will be turned such that the rotor is not longer pointing to the winddirection.
For each region of the wind speed, another optimal TSR value exists which can be shownschematically in Figure 2.3.
TSR
λ = 0
vci vnom v
λ = λopt
λ = RΩnomv
vco
Figure 2.3: Control strategy for TSR in function of wind speed
2.2 Conversion to electric energy
In Figure 2.4, the general layout of a wind turbine system is shown. The first part, the rotor ofthe wind turbine, has been discussed in the previous section. The following parts are essentialto convert the mechanical energy provided by the shaft of the turbine to electric energy. Eachpart has its own losses, which results in a global efficiency of the system. Between the rotorand the generator, an optional gearbox can be installed which increases the turbine rotor speedto the appropriate speed range of the generator. The presence of a gearbox depends on thenumber of poles in the generator, which determines its synchronous speed. Both inductionand synchronous machines can be used as a generator, each with their specific characteristicsand typical applications. The generator can be connected to a power converter depending on
8
Chapter 2. Wind energy conversion systems
whether the wind turbine is designed to rotate at fixed or variable speed. Fixed speed turbinesare simple and cheap, but are not able to operate continuously at their optimal power output.In variable speed turbines, the converter changes the shaft speed in function of the wind speedto drive the wind turbine continuously to its optimal operating point. Beside the aerodynamicefficiency of the turbine, the converter is the main component that greatly determines theefficiency of the whole system, because it is this component that will determine the operatingpoint of the wind turbine. It has also large influence on the generator efficiency because itcontrols the stator current. Next, the energy from the converter can be injected in the grid, ifnecessary, by using a transformer.
Figure 2.4: Main components of a wind turbine system [16]
In [16], a classification of different wind turbine systems is made, based on the type of generator.
2.2.1 Wind turbines with induction generator
Induction machines exist either with a cage rotor or with a wounded rotor and brushes. Tooperate as a generator, the machine has to rotate supersynchronously: this means at a speedlarger than the synchronous speed (determined by the applied frequency of the grid or theconverter). Cage rotor generators are often used in fixed speed wind turbines, the so-called’Danish concept’. The generator is connected to the grid via a transformer and the shaft speedis determined by the frequency of the grid and the number of pole pairs of the machine. Theadvantage of this method is the cheap and simple construction together with the fact that nosynchronization device is required. Major drawback of this configuration is that the powercoefficient is almost never equal to its optimal value, resulting in less energy output. Otherdisadvantages are the need for a stiff power grid to have a stable operation and the moreexpensive mechanical construction, because of high mechanical stresses by torque pulsationsat wind gusts.
In induction machines with wounded rotors, external variable resistors can be connected tothe rotor. The variation of the rotor resistance changes the slip-torque characteristic of theinduction machine and provides a limited speed control. The machine still needs to operate atsupersynchronous speed. The rotor can also be connected to the grid by using a converter whichcontrols the frequency of the rotor currents. This topology is called the ’Double Fed InductionGenerator’ (DFIG). In contrary with the full rated power converters mentioned later, hereonly part of the generated power goes through the converter. The speed range of the controlremains limited from −30% to +30% of the nominal speed. Another general disadvantage ofinduction machines is their need for reactive power to magnetize the magnetic circuit suchthat the power factor is always less than one. This reactive power is retracted from the gridwhich may require compensation devices, such as capacitor banks or FACTS devices, to ensure
9
2.2. Conversion to electric energy
power quality. The slip rings and the wounded rotor also makes this a more complicated andexpensive machine than the cage rotor induction machine.
The main advantage of variable speed operation is that the turbine can adapt the rotor speed infunction of the wind speed to obtain a higher power coefficient and thus a larger power output.Another result is the reduction in fluctuations of the power production and its injection in thegrid. Due to the variable speed, torque pulsations can be smoothed which results in less wearand stress in the drive train.
2.2.2 Wind turbines with synchronous generator
A synchronous generator has the advantage of generating its own magnetic rotor field whichmakes the machine capable to produce reactive power. For this purpose, a DC voltage sup-plied winding in the rotor can be used. This has the advantage that the excitation field canbe varied, but on the other hand it increases the complexity of both machine and control. Forthis reason, another type of synchronous machine exists, in which the field winding is replacedby permanent magnets producing a constant magnetic field, called a ’permanent magnet syn-chronous machine’ (PMSM). This type of generator can be constructed with a large number ofpole pairs which reduces the mechanical synchronous speed. Due to these smaller rotor speeds,the generator can be directly driven by the turbine. This saves an expensive and maintenanceintensive gearbox. Due to its simple control possibilities, these generators are especially suitedto operate at variable speed, such that a converter for the full rated power needs to be used.
As in this thesis a PMSG at variable speed is used, only this type of generator and associatedconverter topologies will be discussed further on.
2.2.3 Full rated power converters
To make a wind turbine operating at its maximal power point, there exists an optimal TSR.Therefore the generator needs to operate at variable frequency, decoupled of the grid. Differentconverter topologies exist for this purpose. The wild AC current (with variable frequency andamplitude) produced by the generator is first rectified to a DC current and delivered to aDC-bus. Both a passive rectifier with boost chopper as an active rectifier can be used for thispurpose. The DC current is then converted back to an AC current of fixed frequency by usinga ’Voltage Source Inverter’ (VSI). The converter at the machine-side changes the turbine rotorspeed by controlling the generator current (and consequently the torque). The grid-side ofthe converter needs to provide a constant DC-bus voltage and controls the injected active andreactive power to ensure grid voltage stability.
In Figure 2.5, different converter topologies are listed. In the three cases a rectifier, an inverterand a DC-bus capacitor are present. The first topology uses an ordinary diode rectifier. Thereis no control of the generator current nor the voltage. The operating point of the wind turbinecan thus not be influenced. In the second topology, the diode rectifier is extended with a boostchopper which provides a constant DC-bus voltage. The generator voltage can be changed suchthat the operating point is influenced. Additionally, a current control can be added to regulatethe generator power. This way, the system can be easily controlled to the optimal operatingpoint.
10
Chapter 2. Wind energy conversion systems
(a) Diode rectifier
(b) Diode rectifier + chopper
(c) Active rectifier (back-to-back converter)
Figure 2.5: Different types of converters used with a PMSG
The third topology is the ’back-to-back converter’. It consists of two voltage source converters(VSC) with a common DC-bus. The machine-side VSC is the active rectifier which controlsthe generator current. By using advanced techniques such as field oriented control or directtorque control, the generator torque can be precisely controlled. An additional speed controlloop uses the controllable generator torque to control the wind turbine rotor speed to the MPP.
The main advantage of the passive rectifier with the chopper is that only one switching compo-nent is used while the active rectifier uses six of them. This reduces costs and complexity. Thepassive rectifier offers however no control of the power factor and provides a lot of harmonicdistortion in the generator current resulting in torque oscillations. This results in a lower effi-ciency of the generator. The active rectifier can solve these problems. By using field orientedcontrol, the angle between voltage vector and current vector can be controlled close to zero,resulting in a power factor of the generator that is around one. Three-phase ’Pulse WidthModulation’ (PWM) can be used to apply the generator voltage, resulting in a lower harmoniccontent if a sufficiently high switching frequency is used. This rectifier is able to fully controlthe stator current, which means that both the waveform as the magnitude and direction canbe changed. This way, the stator current can be controlled to a sinusoidal waveform which
11
2.2. Conversion to electric energy
improves the generator efficiency and the direction of the current can be controlled in bothdirections such that the machine can operate both as motor or generator. This offers newpossibilities for MPPT control.
2.2.4 Introduction to the PMSM
In recent years, the use of synchronous machines with permanent magnets is strongly increased.They have some specific advantages which make them very suitable to be used in small windturbines. First, no external DC source is required for a field winding in the rotor because theinternal magnets create a constant magnetic field. The absence of rotor windings, slip ringsand brushes eliminates electric rotor losses, reduces noise, increases the reliability and efficiencyand makes the rotor inertia smaller. Because PMSGs are much more compact, they are verysuitable for small-scale applications. Second, the fact that the magnetic flux is constant in timeresults in a simpler but more limited control.
Disadvantages are the high costs of the rare earth materials used to make permanent magnets,such as neodymium and samarium. Rare earth material prices have been increasing during thelast years. Ferrite is an inexpensive but less magnetically strong alternative that is frequentlyused [42].
There exist different types of electrical machines with permanent magnets of which an overviewis given in Figure 2.6. Mainly, there are two categories: the PMDC and PMAC machines. ThePMDC is similar to the DC commutator machine in which the field winding in the stator isreplaced by permanent magnets. The mechanical commutator sets the current spacial distribu-tion perpendicular with the magnetic field spacial distribution. In the PMAC, the permanentmagnets are located in the rotor and the commutator with the brushes is disappeared. Thisresults in an easier construction of a machine which requires less maintenance and is less ex-pensive. The disadvantage of this type of machine are the advanced controlling techniques toperform the commutation electronically. PMACs can be divided in two types of machines:
Brushless DC motors (BLDC) have due to their construction a trapezoidal flux distribution inthe air gap which requires a rectangular current distribution in a concentrated winding. Theircharacteristics are very similar with the brushed DC motors. The control is quite easy as thestator currents are blocks with constant amplitude and duration of 120. Hall sensors are usedto execute the electronic commutation.
Permanent magnet synchronous motor (PMSM) are machines that produce a sinusoidal back-EMF distribution. If this machine is supplied with a sinusoidal current, this results in aconstant torque without any ripple. More advanced controlling such as field oriented controlis required which needs an accurate rotor position measurement. According to the placementof the magnets in the rotor, a new subdivision can be made:
• Surface mounted magnet type (SPMSM): in this machine, the radially magnetizedmagnets are placed along the circumference of the rotor (see Figure 2.7a). The rotoris made of iron on which the magnetic materials are glued with strong adhesives. Thismachine is easy to build and is used for low speed applications because the centrifugalforces on the magnets need to be limited. The permeability of magnetic materials isclose to the one of air. The difference in reluctance for the the direct (d) and quadrature(q) axis is negligible, so the inductances in both axes are almost equal to each other:Ld = Lq. This results in a small reluctance torque.
12
Chapter 2. Wind energy conversion systems
• Interior magnet type (IPMSM): in these machines, the magnets are placed insidethe rotor (see Figure 2.7b). Because the magnets can be seen as air due to its lowpermeability, the reluctance in the d-axis is larger than the one in the q-axis. Thisresults in saliency with a d-axis inductance which is smaller than the inductance alongthe q-axis: Ld < Lq. This results in a reluctance torque. Due to its construction, thismachine is more appropriate for high speed control.
PM electric machines
PMDC machines PMAC machines
Trapizoidal EMF Sinusoidal EMF
SPMSM IPMSM
BLDC PMSM
Surface mounted magnets Interior magnets
Figure 2.6: Classification of machines with permanent magnets
(a) (b)
Figure 2.7: Typical PMSM rotor mount configuration: (a) surface mount, (b) interior mount [42]
13
Chapter 3
Control of an active rectifier andsimulations
3.1 Overview of the system
As discussed in the previous chapter, a permanent magnet synchronous generator (PMSG) isused in combination with a back-to-back converter, as shown in Figure 3.1. The power directionin the figure is from the left to the right. As the gearbox is not considered here, the wind turbineis directly coupled to the generator. The generator is connected with the machine-side converterwhich controls the turbine to its optimal operating point. The machine-side converter is thenconnected to the grid-side converter by means of a DC-bus. This second converter controlsthe voltage of the DC-bus and injects a controlled amount of active and reactive power at aconstant voltage and frequency in the grid. As the scope of this thesis focuses on the machine-side converter, the grid-side converter will not be considered further on. In the practical setup,the DC-bus will be replaced by a DC voltage source with a power resistor in parallel to dissipatethe generated energy.
In the next sections, theoretical principles will be introduced and implemented into a MatlabSimulink simulation model. Next, a speed controller is designed which uses field orientedcontrol (FOC). As FOC directly controls the generator torque, the result is a high qualityspeed control.
The simulation model consists of different model blocks, each containing a component of the
PMSGActive
RectifierInverter
GridDC-bus
Figure 3.1: Schematic view of the back-to-back converter.
14
Chapter 3. Control of an active rectifier and simulations
complete system. The first block simulates the wind turbine and the drive train. The secondblock models the generator based on the electric equations of the PMSG. Next is the converter,which contains a model of the IGBT voltage source converter and the field oriented control. TheMPPT block contains the actual control mechanism which controls the speed of the turbine.All these blocks are interconnected to each other to compose one system, as shown in Figure3.2. Simulation models of a wind turbine, a PMSG and a three-phase inverter were given bythe supervisors. These model blocks are adapted and expanded with the FOC and MPPT.
Figure 3.2: Simulink model of the complete system.
3.2 Modelling of a wind turbine
3.2.1 Wind turbine simulation model
The wind turbine model block is shown in Figure 3.3. It consists of two parts. The main partcalculates the turbine torque Tt from the wind speed v:
Tt =Pt
Ω=
1/2 ρπr2 CP(λ) v3
Ω(3.1)
The other part models the inertia and friction of the turbine-generator assembly and calculatesthe shaft speed starting from the turbine and generator torque Tg. The mechanical equationcan be written as:
JdΩ
dt= Tt − Tg − FΩ (3.2)
where J is the total inertia (turbine + generator) and F the friction coefficient.
3.2.2 Wind turbine parameters
In appendix A, the data sheet of the generator that is used in this project (Ziehl- AbeggMK106-CKK-14N) can be found. The aim is to design a fictive wind turbine in such way that
15
3.2. Modelling of a wind turbine
Figure 3.3: Simulink model of a wind turbine
the rated power of the turbine is adapted to the rated power of the generator. The datasheetgives the following rated power and speed.
Pnom = 356 W (3.3)
nnom = 500 rpm (3.4)
To model the wind turbine, a correlation equation from literature is used for calculation ofthe power coefficient. In [19], the following general equation for variable speed turbines ispresented:
Cp(λ, θ) = 0.73
(151
λi− 0.58 β − 0.002 β2.14 − 13.2
)exp
(−18.4
λi
)(3.5)
with
λi =1
1λ−0.02β − 0.003
β3+1
(3.6)
This equation is used for turbines with variable pitch angle β. As in small turbines such systemsare expensive and the construction is quite complex, the pitch angle is most of the time fixed.This means that β can be set to zero, so the equation only depends on λ:
CP(λ) = 0.73
(151
λ− 13.653
)exp
(−18.4
λ+ 0.0552
)(3.7)
This relationship is shown in Figure 3.4. The curve has a maximum at λopt:
CP,max = 0.4412 (3.8)
λopt = 6.9077 (3.9)
16
Chapter 3. Control of an active rectifier and simulations
0 2 4 6 8 10 120
0.1
0.2
0.3
0.4
0.5
Tip Speed Ratio λ [-]
Power
Coeffi
cien
tCP
[-]
Figure 3.4: Relation between power coefficient and tip speed ratio
As the rated turbine power, described by
Pnom =1
2ρπr2CP
(rΩnom
vnom
)v3
nom (3.10)
has to be equal to the rated generator power, the nominal wind speed, shaft speed and theturbine radius can be calculated:
vnom = 5
√2PnomΩ2
nom
ρπλoptCP,max= 7.523 m/s (3.11)
Ωnom =2πnnom
60= 52.36 rad/s (3.12)
r =λoptvnom
Ωnom= 0.992 m (3.13)
To calculate the mass of the rotor, linear interpolation is used on data from existing types ofFortis turbines (see Table 3.1) [10]:
Passaat Montana Alize
Power [kW] 1.4 5.0 13.0
Rotor mass [kg] 11.8 30.0 70.0
Table 3.1: Power and rotor mass of Fortis turbines
For a rated power of 356 W, the rotor mass is:
mrotor = 6.624 kg (3.14)
The turbine inertia is approximated as [20]:
Jt =1
9mrotorr
2 = 0.724 kgm2 (3.15)
17
3.2. Modelling of a wind turbine
3.2.3 Instability of wind turbine system
Due to the characteristic shape of the CP(λ)-curve of the wind turbine, the possibility existsthat some operating points cannot be reached due to unstable operation. Instability meansthat a small change in speed will cause the turbine to run away from its operating point until itstops rotating or goes to its maximum speed. To determine in which area of the characteristicinstability occurs, not the power but the torque needs to be investigated. For this purpose, inanalogy with the power coefficient, a torque coefficient CT is defined:
CT =CP
Ω(3.16)
The CT(λ)-curve is shown in Figure 3.5. The torque coefficient determines the turbine torqueas:
Tt =1
2ρπr2CT(λ)v3 (3.17)
Instability can occur if the generator is connected to a resistive load. In [20], the generatoris modelled as a three phase voltage source, the EMF, in series with an inductance and aresistor. This results in the fact that the torque versus speed characteristic of the generatorwill always be a parabolic function. In Figure 3.6, the turbine torque for a specific wind speedand the generator torque for a specific resistive load are shown. The intersection between thetwo curves determines the possible operating points. In this case there are two possibilities.
The operating point at the right will be the stable one. For example: if the speed increases alittle, the generator torque increases while the turbine torque decreases. This will slow downthe turbine again, by which the operating point returns to its original setting. A point at theother side of the maximum of the torque characteristic will result in unstable behaviour. Thismeans that in order to guarantee stable operation, the TSR has to be larger that the TSRvalue at which the torque coefficient is maximal. In this case with the power coefficient curvein Eq. 3.7, this TSR value is equal to:
λT,opt = 5.87 (3.18)
In this thesis, a speed controller will be used for some MPPT control strategies which is ableto control the rotor speed to any value independent of the turbine torque. In these cases,instability does not have to be taken into account.
0 2 4 6 8 10 120
0.02
0.04
0.06
0.08
Tip speed ratio λ [-]
Torq
ue
coeffi
cien
tC
T[-]
Figure 3.5: Torque coefficient versus tip speed ratio.
18
Chapter 3. Control of an active rectifier and simulations
Rotor speed Ω
Tu
rbin
eto
rqu
eT
t GeneratorTurbine
STABLEUNSTABLE
Figure 3.6: Turbine torque and generator torque versus rotor speed.
3.3 Modelling of a PMSG
3.3.1 Mathematical model of the PMSG
The electric equations of the permanent magnet generator are written in a synchronous ref-erence system. This is a frame that is fixed with the rotor and consists of a direct (d) andquadrature (q) axis. The d-axis is coincident with a north pole of the permanent magnet. Theq-axis lags 90 electric degrees behind the d-axis. Mechanically, the q-axis is situated betweentwo subsequent poles in the rotor. To describe the phase variables (a,b,c) in this referencesystem, they first have to be converted into the components (α, β) in a fixed stator referenceframe by means of the Clarke transformation:
Vα =2
3
(Va −
1
2Vb −
1
2Vc
)(3.19)
Vβ =1√3
(Vb − Vc) (3.20)
For the conversion of the stator reference system to the synchronous reference system, theelectric angle θe has to be known. This is determined from the mechanical rotor angle θm andthe number of pole pairs NP:
θe = NP θm (3.21)
Next the components (α, β) are transformed to components (d,q) by using the Park transfor-mation.
Vq = Vα cos θe + Vβ sin θe (3.22)
Vd = −Vα sin θe + Vβ cos θe (3.23)
The different voltage components in the three different reference frames are schematically shownin Figure 3.7.
The stator voltage equations of a PMSG in the synchronous, generator reference system are[4]:
Vq = −RsIq − LqdIq
dt+ ωΨPM − ωLdId (3.24)
Vd = −RsId − LddId
dt+ ωLqIq (3.25)
19
3.3. Modelling of a PMSG
αa
β
q
b
c
d
V
Vc
Vq
Va Vα
Vβ
Vb
Vd
θ
Figure 3.7: Voltage vector in fixed and synchronous reference system
in which Rs is the stator resistance, Lq and Ld respectively the stator inductances in the q andd-axis, ΨPM the permanent magnet flux linkage and ω the electric angular speed:
ω =dθe
dt(3.26)
The accompanying schemes for the two axes are given in Figure 3.8.
RsωLqIq
Ld
Id
Vd
(a) d-axis
RsωLdId
Lq
Iq
VqωΨPM
(b) q-axis
Figure 3.8: Schemes for d and q-axis of the PMSG
The instantaneous electric power Pe is determined by the stator voltages and currents in thesynchronous reference system:
Pe =3
2(VqIq + VdId) (3.27)
Substitution of the voltage equations gives:
Pe =3
2Rs(I
2q + I2
d) +3
2
(d
dt
(LqI
2q
2
)+
d
dt
(LdI
2d
2
))+
3
2(ωΨPM Iq +ω(Ld−Lq)IdIq) (3.28)
20
Chapter 3. Control of an active rectifier and simulations
The first term are the Joule losses in the stator, the second one the difference in energy conservedin the magnetic field and the third one gives the electromagnetic power Pem.
Pem =3
2(ωΨPM Iq + ω(Ld − Lq)IdIq) (3.29)
In order to calculate the electromagnetic torque, the electric angular speed has to be convertedto the mechanical angular speed by:
ω = NP Ω (3.30)
The electromagnetic torque Tem is then:
Tem =Pm
Ω=
3
2NP(ΨPM Iq + (Ld − Lq)IdIq) (3.31)
The mechanical equation is determined by the drive train:
JdΩ
dt= Tl − Tem − F Ω (3.32)
in which J is the total inertia (generator + turbine), F the viscous friction and Tl the loadtorque.
3.3.2 PMSG simulation model
The model that is used during the simulations is based on the two schemes of Figure 3.8. Theseare implemented using the SimPowerSystems toolbox and the complete PMSG simulation blockis shown in Figure 3.9. One of the inputs of this model block are the stator phase currentsIs (a,b,c). These are transformed to the synchronous reference system (d,q) using the Clarke-Park transformation which uses the integral of the second input of the model block, namelythe angular rotor speed. The (d,q) currents are then applied in each circuit by using currentsources. Notice in these schemes the inductances, the decoupling terms and the EMF in theq-axis. The magnetic losses are modelled by a parallel equivalent resistor Rc. As these lossesare neglected, the resistance value is set to infinity.
The electromagnetic power is calculated as:
Pem =3
2(EqIoq + EdIod) (3.33)
The electromagnetic torque is an output of the block together with the stator EMFs.
3.3.3 Determination of the generator parameters
To determine the parameters in the equivalent schemes, mentioned above, some measurementsare executed. First the stator resistance is measured in the three phases by using a multimeter.This gives following results:
Rsa = 28.6 Ω (3.34)
Rsb = 28.7 Ω (3.35)
Rsc = 28.6 Ω (3.36)
The stator resistance in d and q-axis is equal to the mean of these three measured statorresistances:
Rs =Rsa +Rsb +Rsc
3= 28.6 Ω (3.37)
21
3.3. Modelling of a PMSG
Figure 3.9: Simulink model of a permanent magnet synchronous generator
22
Chapter 3. Control of an active rectifier and simulations
The inductances are obtained by measuring the stator inductance for each phase using an LCRmeter. These measurements have been executed at 50 Hz and 1V, in function of the rotorangle. Measurements have been made for rotor positions varying from 0 to 1.2 radians, sotwo pole pitches are covered as the generator has 12 poles. This pattern will repeat six timesfor a complete revolution of the rotor. For a sinusoidal PMSG, the inductance should form asinusoidal pattern with a period of 2π
NPradians and an amplitude Ls2 indicating the reluctance
effect. The mean value is then Ls. The patterns of the three phases should be shifted by 2π3NP
radians [4].
Lsa = Ls − Ls2 cos(2θ) (3.38)
Lsb = Ls − Ls2 cos
(2
(θ − 2π
3
))(3.39)
Lsc = Ls − Ls2 cos
(2
(θ − 4π
3
))(3.40)
The mutual inductance is equal to:
Ms = −1
2Ls (3.41)
The equivalent d and q-axis inductances Ld and Lq are then:
Ld = Ls −Ms +3
2Ls2 (3.42)
Lq = Ls −Ms −3
2Ls2 (3.43)
Results of the inductance measurements are shown in Figure 3.10. The measured values arefitted with a sinusoidal curve. The pattern of the inductances itself is not quite sinusoidal,but is periodic and shifted over 2π/3 electric radians for the three phases. The conclusion isthat the stator inductances have a mean value Ls equal to 65.1 mH. As the amplitude of thefitted sinusoidal curve is relatively small (equal to about 1.5 mH), it can be concluded thatthe reluctance effect in the rotor is quite negligible. As a consequence, Ls2 is set to zero. Theinductances are now:
Ld = Lq = Ls −Ms =3
2Ls = 97.7 mH (3.44)
As the inductances in d and q-axis are equal, there is almost no saliency in the rotor. Thegenerator used in this setup is thus a surface magnet PMSG. In this type of machine, thepermanent magnets are installed close to each other along the circumference of the rotor. Inthis way, a high number of poles can be achieved on a relatively small area.
Finally, also the amplitude of the flux of the permanent magnets ΨPM is determined. For thispurpose, the relationship between the stator voltage at no-load condition and the flux linkageis used:
V a = −dΨPM,a
dt(3.45)
The voltage is measured between each phase and the neutral at different rotor speed using amultimeter. This gives the RMS value of the stator voltage for each phase. The next equationscalculate the flux for a given rotor speed Ω.
Vrms =Va,rms + Vb,rms + Vc,rms
3(3.46)
ΨPM,rms =Vrms
ΩNP(3.47)
ΨPM =√
2 ΨPM,rms (3.48)
23
3.3. Modelling of a PMSG
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.262
64
66
68
Rotor position [rad]
Lsb
[mH
]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.262
64
66
68
Rotor position [rad]
Lsa
[mH
]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.262
64
66
68
Rotor position [rad]
Lsc
[mH
]
Figure 3.10: Measured stator inductance and fitted curve in function of rotor position for three phases
24
Chapter 3. Control of an active rectifier and simulations
The results are shown in Table 3.2 for four different rotor speeds. Conclusion is that:
ΨPM = 0.705 Wb (3.49)
n [rpm] Ω [rad/s] Vrms [V] ΨPM [Wb]
200 20.94 61.6 0.693
300 31.42 94.0 0.705
400 41.89 125.5 0.706
500 52.36 156.7 0.705
Table 3.2: Calculation of flux linkage of permanent magnets for different rotor speeds.
3.4 Voltage source converter
3.4.1 General description
The back-to-back converter consists of two elements. At the grid-side, there is a voltage sourceconverter (VSC) that produces an AC current from the DC current of the DC-bus. Thiselement is called an inverter. At the machine-side, there is another VSC that converts the ACcurrent from the machine to DC current for the bus. This element is the active rectifier. BothVSCs have the same topology as shown in figure 3.11, only the power direction is different.
The VSC consists of three legs with each two switches. These switches are IGBTs (InsulatedGate Bipolar Transistors) and are widely used in power electronics for mid-range power appli-cations. They can be easily switched on and off at relatively high frequencies (max. 20 kHz)by applying small gate voltages. For each leg, only one switch can conduct at the same time,otherwise short circuit of the DC-bus would occur. Each point A,B or C is thus at any momentconnected to either the positive or negative terminal of the DC-bus. The duration at which apositive switch of each phase is conducting during one switching period Ts, is determined bythe duty ratio δ, eg. for phase A:
δa =TS1
Ts(3.50)
where TS1 is the conducting time of switch S1 during one switching period.
AB
CO
N
Vdc2
−Vdc2
S1
S2
S3
S4
S5
S6
Figure 3.11: Scheme of voltage source converter
25
3.4. Voltage source converter
The three legs are phase shifted over 2π/3 such that a three phase positive sequence voltagearises. It is very important to insert a dead-time between the opening and closure of twoswitches in the same leg. Otherwise, an accidental short circuit of the DC-bus is possiblebecause the switching happens not infinitely fast. The opening and closure of the IGBT isdetermined by a certain rise time and fall time respectively. Most of the time, a dead-time of2µs is sufficient.
The diodes in parallel with the IGBTs allow to switch voltages of inductive loads. The momentthe IGBT switches off, the current wants to keep flowing due to the inductance. The diode thenprovides a path for this current, while the IGBT can close safely. In reality, the anti-paralleldiode is included in the same package of the IGBT.
At the DC side, a voltage Vdc is applied. Because the generator is connected in a Y-configurationwith neutral point N, the voltage across the machine windings are Van, Vbn, Vcn. A fictive pointO (a virtual neutral point of a DC source) is introduced in the DC-bus, so following relationscan be written:
Van = Vao − Vno
Vbn = Vbo − Vno
Vcn = Vco − Vno
(3.51)
According to Kirchoff’s law:Van + Vbn + Vcn = 0 (3.52)
summing of the three equations (3.51) gives:
Vno =Vao + Vbo + Vco
3(3.53)
After substitution of Vno in (3.51):
Van
Vbn
Vcn
=
1
3
2 −1 −1−1 2 −1−1 −1 2
Vao
Vbo
Vco
(3.54)
Because the duty ratio is defined as the ratio of the conducting time of the positive switch(S1,S3,S5) to the switching period, the relationship between Vao and δa can be derived fromFigure 3.12.
Vao = δa
(Vdc
2
)+ (1− δa)
(−Vdc
2
)=
2δa − 1
2Vdc (3.55)
(1− δ)Ts
δTs
+Vdc2
−Vdc2
Vao(t)
tV ao
Figure 3.12: Output voltage Vao of VSC.
26
Chapter 3. Control of an active rectifier and simulations
Other phases are equivalent. Finally, the relationship between the line-to-neutral voltages andthe duty ratios is:
Van
Vbn
Vcn
=
Vdc
3
2 −1 −1−1 2 −1−1 −1 2
δaδbδc
(3.56)
3.4.2 Pulse width modulation (PWM)
To calculate the duty ratios at which the different phases in the converter have to switch, pulsewidth modulation (PWM) is used. There exist a lot of different strategies but here the uniformsampled symmetrical on-time triangle modulation will be used [2]. A sampled reference signalis compared with a symmetric triangular signal. When the reference signal is larger than thecarrier signal, the PWM output is set high. For the other case, the output is low (see Figure3.13). Uniform sampling means here that the sampling frequency is equal to the switchingfrequency fs (= 1/Ts).
The sequence starts with an analog-to-digital conversion (ADC) of the current at the bottomof the triangle. With this measurement, a new duty ratio is calculated that is given to thePWM module at the next top of the triangle. The advantage of this method is that transientsresulting from switching will have faded out at the moment a new ADC conversion starts.Additionally, the current is at that moment equal to its mean value, by which harmonics dueto the switching frequency will not be visible [21].
In Figure 3.14, the implementation of the voltage source converter in Matlab Simulink is shown.Note that the usual power direction is from the right to the left. The stator emf Es is appliedby three voltage sources. The stator resistances are added in order to have the stator voltagesat the AC terminals of the three-phase VSC. The three stator currents are measured to be used
27
3.5. Field oriented control
as input for the PMSG model and the current controller. The inverter block contains the modelof a three-phase IGBT bridge. Several parameters are used, such as the on-time resistance,forward voltage and rising time. Power is leaving the bridge at the left side of the converterwhere a DC voltage source is placed which can absorb the electric power. The switching signalsat the gates of the VSC are generated by the current controller, which will be explained next.
Figure 3.14: Simulink model of voltage source converter
3.5 Field oriented control
3.5.1 Theoretical background
Field oriented control (FOC) is a controlling technique to make an AC motor behave like a DCmotor. The DC machine has the interesting property of providing a constant torque which isproportional with the armature current at a speed which is proportional to the armature EMF,if the magnetic flux linkage is kept constant. Additionally, this torque is the maximum of whatcan be produced for a given armature current. This is due to the mechanic commutator, whichensures that the current distribution in the rotor is always perpendicular to the magnetic fluxdistribution resulting from the field winding.
In three-phase machines, a sinusoidal field distribution has to interact with a sinusoidal currentdistribution in order to produce the torque. Similar to the DC motor, the torque is maximalwhen the maximum of the current distribution coincides with the maximum of the flux distri-bution. In a phasor representation (see Figure 3.15 in the generator reference system (GRS)),this means that the current phasor Is needs to be aligned with the EMF phasor Ep, which isthe induced voltage in the stator windings due to the rotating magnetic field of the permanentmagnets. The angle ψ between these two phasors, the so-called torque angle, has thus to bezero to obtain the maximal torque for a given current.
Another angle indicated in the figure is φ, the angle between the voltage and the current phasorwhich determines the power factor cosφ. If the voltage phasor is lagging the current phasorin the generator reference frame, this means that machine consumes reactive power. For theother case, reactive power is produced by the PMSG. For φ with an absolute value greaterthan 90, the PMSG will operate as motor. β = ψ− φ, is the angle between the EMF and thevoltage phasors.
28
Chapter 3. Control of an active rectifier and simulations
By definition, the flux linkage of the permanent magnets ΨPM is along the direct axis, thus Ep
is along the positive q-axis. This means that for field oriented control also the current phasor,which consists of a q and a d-part, has to be along the quadrature axis. The d-axis part Id hasthus to be equal to zero. The torque equation of the PMSG (Eq. 3.57) is then:
Tem =3
2NPΨPMIq (3.57)
As the magnetic flux is constant, the electromagnetic torque is now only proportional to theq-axis current, analogue to the DC motor. A variation of the stator current will result in animmediate torque variation with minimal transient behaviour. This allows for high dynamicspeed control. Another result is that the voltage phasor is always lagging the current phasor,which means that the generator will always be a consumer of reactive power due to the fieldoriented control.
q
d
Ep
VI
Iq
Id
βφψ
ΨPM
(a) Normal operation
q
d
Ep
V
I
φ
ΨPM
(b) Field oriented control
Figure 3.15: Phasor schemes for normal generator operation and field oriented control of a PMSG.
Thanks to the Clarke and Park transformation, the phase currents can be converted to thesynchronous reference system and vice versa. Including these transformations in the controlstrategy, the following scheme arises in Figure 3.16.
The first part of the control strategy is to measure the stator currents from the generator. Infact, the measurement of only two phases is sufficient as the sum of the three currents is alwayszero due to the lack of any zero sequence currents (the neutral point in a Y-configurationis usually not connected). By using the Clarke and Park transformation, in which the rotorposition angle θ is used, the measured currents in q and d-axis are obtained. These two are
29
3.5. Field oriented control
compared with their reference values Irefq and Iref
d and the difference goes to their respectivePI controllers (Proportional-Integral controller).
The resulting stator voltages Vq and Vd are transformed back to phase voltages and then thevoltages are converted to duty ratios by using Eq. 3.55. These duty ratios then goes to theVSC which translates them into PWM stator voltages for the generator. The current controlloop is closed now.
Beside the fast current control loop, a third, slower control loop is added in order to controlthe rotor speed. As the generator torque is determined by Iq, a PI controller calculates thereference value Iref
q from the difference of the reference speed Ωref and the measured rotor speedΩ.
As the q and d-axis current can be controlled to any value (within certain limits), differentcontrol strategies exist:
• Constant torque angle controlThis is the strategy that has been previously explained and is easy to implement. Con-trolling the torque angle to zero results in minimal current for maximal torque and thusminimizes the resistive losses [25]. A drawback is that a position encoder is necessaryto know the rotor position in order to execute the Park transformation. This decreasesthe reliability of the system and increases its complexity. However, also sensorless fieldorientation techniques exist which omit the position sensor. Some of them are introducedin Chapter 8.
• Constant power factor controlAnother possibility for avoiding the position sensor, is to control the angle between thevoltage phasor V s and the current phasor Is to zero, resulting in a power factor equal toone. This control strategy can no longer be called field orientation, because the EMF andthe current phasor are not longer perpendicular to each other. The name ’vector control’is used now.
• Minimizing the core lossesAccording to [27], the d-axis current can be controlled to a non-zero value in order toreduce stator flux and minimize the iron core losses. In this method, the value of thedesired Id is tabulated in function of the shaft speed.
PI
PI
PI
abc
abc
dq
0
Irefd
Irefq
Id
Iq
Ωref
Ω
Vd
Vq
θ
Ω
NP
dqPMSG
+
-
+
- Ia Ib Ic
+-
Figure 3.16: Field oriented control scheme.
30
Chapter 3. Control of an active rectifier and simulations
3.5.2 Current PI controller
Design of the PI controller
Because the d and q-axis have the same dynamics (Ld = Lq), the PI controller design is onlyexecuted for the q-axis. The control is performed in discrete time by means of a DSP (DigitalSignal Processor) so the design will be done in the z-domain.
The control loop is determined by the stator winding of the PMSG, containing both an in-ductance Lq and resistance Rs. As this behaves like a first-order system, the transfer functionfrom voltage to current is in the continuous Laplace domain equal to:
Fi(s) =Iq(s)
Vq(s)=
1
Lqs+Rs(3.58)
To convert this continuous time transfer function to a discrete time one, the bilinear transfor-mation is used (more specifically the trapezoidal approximation):
s =2
Ts
z − 1
z + 1(3.59)
in which Ts is the sample frequency. Substitution gives the discrete time transfer function ofthe stator winding:
Fi(z) =I(z)
V (z)=
Ts(z + 1)
(2Lq + TsRs)z − (2Lq − TsRs)(3.60)
According to [27], the controller itself is approximated as a delay of one sample period Ts, thetime that is needed to perform the calculations inside the DSP. In the z-domain this correspondsto a transfer function equal to z−1.
The PI controller can be modeled in the discrete domain by the next transfer function, whichis the conversion of the error E(z) at the input to the output voltage V (z):
Ci(z) =V (z)
E(z)= Ki
z − ai
z − 1(3.61)
in which Ki is the proportional parameter and ai the integration parameter. This correspondswith the following difference equation:
V (n) = V (n− 1) +Ki[e(n)− aie(n− 1)] (3.62)
which can be directly implemented in the DSP. The actual value of the output and the errorneed to be stored in the memory, so it can be used in the next cycle to calculate a new outputvalue.
These three blocks are combined in one closed loop system in Figure 3.17, with the open looptransfer function G(z):
G(z) = Kiz − ai
z − 1· 1
z· Ts(z + 1)
(2Lq + TsRs)z − (2Lq − TsRs)(3.63)
The closed loop transfer function H(z) is given by:
H(z) =Iq
Irefq
=G(z)
1 +G(z)(3.64)
31
3.5. Field oriented control
Fi(z)z−1Ci(z)
Irefq
PI CONVERTER PROCES
IqVq
Figure 3.17: q-axis current control loop.
In Matlab, Sisotool is used to design the PI controller. Following system parameters have beenused:
Rs = 28.6 Ω (3.65)
Lq = 97.7 mH (3.66)
fs = 16 kHz (3.67)
In order to have a fast response with a limited overshoot, the following design has been obtained:
Ki = 765.22 (3.68)
ai = 0.83 (3.69)
The open loop frequency response of this controller (Figure 3.18) shows that this controllerhas a bandwidth of 3772 Hz. This is the frequency at which the open loop gain becomes lowerthan 0 dB. This frequency is large enough to react at signals with high frequency. It is alsonot too high in order that the controller will not react at high frequency noise signals. Thephase margin is equal to 44.1, which is a good value for robust operation. The result of a stepresponse of the closed loop is presented in Figure 3.19.
−100
−50
0
50
Magnitude(d
B)
101
102
103
104
−270
−225
−180
−135
−90
Phase
(deg)
B ode DiagramGm = 12.2 dB (at 2.37e+04 rad/s) , Pm = 44.1 de g (at 7.54e+03 rad/s)
Fre q uency (rad/s)
Figure 3.18: Phase and gain margin of the current open control loop
32
Chapter 3. Control of an active rectifier and simulations
Simulink simulation model
In Figure 3.20, the implementation of the d and q-axis current controllers in Matlab Simulinkare shown. The stator currents, which are measured at the entrance of the VSC, are theinputs of the current controller together with the rotor position angle which is the result of theintegration of the measured rotor speed.
First, the stator currents are filtered using an RC low-pass filter with a cut-off frequency of25 kHz. Precise current measurements with a high bandwidth are needed in order to performthe field orientation correctly. By means of the rotor position (in electric radians), the fil-tered currents are transformed to the synchronous reference system by using the Clarke-Parktransformation. These two values then go to their respective PI blocks which contain the dis-crete transfer function Ci(z) with the two parameters Ki and ai. The resulting voltages aretransformed back to the stator reference system and converted to duty ratios which go to thePWM generators. The outputs of this block are the six switching signals (three times twocomplementary signals) which go to the VSC.
Simulation results
In Figure 3.19, the simulated step response of the q-axis current is shown together with thetheoretical result obtained from Sisotool. It can be noted that these two responses are verysimilar and that the simple theoretical model approximates nicely the more complex simulationmodel.
It is useful to observe also the generator torque response. This way, the performance of the fieldoriented control and the alignment between current and EMF can be investigated. In Figure3.21, the response of the generator torque as result of the same step in the q-axis current can beobserved. Because the d-axis current is controlled to zero, the torque is linear with the q-axiscurrent. This is validated by the fact that the response in Figure 3.21, is the same as in Figure3.19, while taking into account the different scales. This concludes that the field orientation isoperating properly.
0 0.5 1 1.5
x 10−3
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Time (sec)
q-a
xis
curr
ent
[A]
Figure 3.19: Calculated (full line) and simulated (dotted line) current step response in function oftime.
33
3.5. Field oriented control
Figure 3.20: Simulink model of PI current controller
34
Chapter 3. Control of an active rectifier and simulations
0 0.5 1 1.5
x 10−3
0
1
2
3
4
5
6
7
8
9
Time [s]
Gen
erato
rto
rque
[Nm
]
Figure 3.21: Simulated generator torque step response in function of time.
3.5.3 Speed PI controller
The speed controller is an important element that will be used by some MPPT control strate-gies, explained in the next chapter. This controller measures the rotor speed by means ofan encoder, compares it with a speed reference value and then calculates the q-axis currentreference value which goes directly to the current controller.
Design of speed PI controller
While the current control is executed at a relatively high frequency of 16 kHz, the speed controlis operating much slower. This means that during the design of the speed controller, the currentcontrol can be assumed to control the torque infinitely fast. A certain q-axis reference currentwill result immediately in the desired torque. The resulting control loop is showed in Figure3.22.
To control the speed, again a PI controller will be used with parameters Ks and as. The inputis the error between the mechanical speed and its reference value. The output is the referencevalue of the q-axis current, which serves as input for the current control.
Cs(z) = Ksz − as
z − 1(3.70)
As in the current controller, again a delay of one sample period is introduced for the durationof the calculations. The current control is idealized by using Eq. 3.57. The electromagnetic
32NPΨPMz−1Cs(z)
ΩrefPI CONVERTER
ΩIrefq −1
Js+F
PROCES
Tt
+-
+ -
CURRENTCONTROL
Tg
Figure 3.22: Speed control loop.
35
3.5. Field oriented control
torque is directly proportional to the reference value of Irefq . The drive train is modeled using
Newton’s equation of motion:
JdΩ
dt= Tt − Tg − FΩ (3.71)
which can be converted to the Laplace domain, resulting in the transfer function:
Fs(s) =Ω(s)
Tg(s)− Tt(s)=
−1
Js+ F(3.72)
Again the bilinear transformation (Eq. 3.59) is used for conversion to the z-domain, with Ts
the sample period of the speed control loop:
Fs(z) =Ω(z)
Tg(z)− Tt(z)=
−Ts(z + 1)
(2J + TsF )z − (2J − TsF )(3.73)
Due to the absence of a gearbox, the friction is low enough to neglect its influence on thedynamics. The controller is designed robust enough to compensate for the presence of somefriction. During the design the turbine torque is also set to zero:
Fs(z) =Ω(z)
Tg(z)=−Ts(z + 1)
2J(z − 1)(3.74)
As the current control is assumed to operate infinitely fast, the reference value of the q-axiscurrent will immediately result in the generator torque:
Tg =3
2NPΨPMIq = KtIq (3.75)
in which:
Kt =3
2· 6 · 0.705 = 6.4 (3.76)
This results in the open loop transfer function G(z):
G(z) = Cs(z)1
zKtFs(z) (3.77)
The PI is again tuned by using ’Sisotool’. As the speed control is operating much slower thanthe current control, the reference value of the q-axis current is recalculated every 100 currentcontrol cycles. Because the FOC is executed at 16 kHz, this means that the speed control willbe executed at 160 Hz:
Ts =1
fs= 6.3 ms (3.78)
This results in a PI controller with the following parameters:
Ks = −4.23 (3.79)
as = 0.938 (3.80)
This controller has a bandwidth of 8.5 Hz and a phase margin of 60. The step response isshown in Figure 3.25 in full line. The response is a discrete, staircase function with a time stepequal to the sampling period of the PI controller. The overshoot is equal to 15%, the settlingtime is 0.22 s.
36
Chapter 3. Control of an active rectifier and simulations
Integral anti-windup circuit
As protection for overcurrent in the PMSG, a saturation block needs to be placed at the outputof the PI block in order to limit the reference value of the q-axis current. The problem is thatwhen a large step in the reference value is applied, the output will saturate while the integratorin the PI keeps integrating the error. This leads to poor response of the controller. To avoidthis problem, an integral anti-windup circuit with back calculation has to be added as shownin Figure 3.23. This eliminates the error at the input of the PI, so the integrator is kept at aproper value and the PI can immediately respond when a change in error appears.
The value Kw must be chosen as small as possible, but a very small value may result in a poortransient response [15]. For this speed controller a value of -5 for Kw has been chosen.
PI
Kw
+-
+
-
Figure 3.23: Integral anti-windup circuit.
Simulink simulation model
The speed control block will be the basis for the MPPT control strategies, which will beexplained in the next chapter. In this block, shown in Figure 3.24, the discrete PI speedcontroller with the anti-windup circuit is located. The inputs are the reference rotor speedvalue and the measured speed value. The output is the reference value for the q-axis currentcontroller. This value goes through a limiter to keep the current control within the safetylimits. The limited and non-limited value then go through the anti-windup circuit. The samplefrequency is equal to 160 Hz.
Figure 3.24: Simulink model of speed control loop.
Simulation results
By adding the mechanical equation of motion to the speed controller, the operation of this con-troller can be verified. The current reference value is multiplied by Kt to obtain the generator
37
3.5. Field oriented control
torque. The turbine torque is set to zero. The generator torque is divided by the rotor inertiaand integrated to obtain the rotor speed, which is then fed back to the PI speed controller.The resulting rotor speed response when a step in the speed reference value is applied, is shownin Figure 3.25 in dotted line. When comparison is made with the calculated step response, itcan be noted that these two are almost identical and that the simulation model corresponds tothe theoretical transfer function.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.2
0.4
0.6
0.8
1
1.2
Time [s]
Roto
rsp
eed
[rad/s]
Figure 3.25: Calculated (full line) and simulated (dotted line) step response of the closed speed controlloop.
38
Chapter 4
MPPT control strategies andsimulations
4.1 Overview
The previous chapter dealt with the control of an active rectifier. It explained how field orientedcontrol can be used to control the generator torque. The last section discussed the design of aspeed controller, which is used to control the rotor speed of the generator to an earlier specifiedreference value. This controller will be used in some of the following MPPT control strategies.
The strategies which will be explained now, all have the purpose to control the wind turbineto its maximum power point, based on measurements of wind speed, rotor speed, generatorvoltage and current. The more measurements a strategy needs, the more equipment needs tobe installed, which increases the cost and the complexity of the control system and reduces itsreliability. Additionally, correct measurements of the wind speed are hard to achieve and mostof the time adequate filtering techniques have to be used. To avoid this, different methodsexist to estimate the wind speed based on measurements which are more easily to achieve. In[28], for instance, the wind speed is estimated from the electric power output while taking intoaccount the losses and the dynamics of the system. This value of the wind speed is then usedto perform the MPPT.
The MPPT controller will also provide some safety aspects. For example, for wind speeds lowerthan the cut-in speed, the controller will stop the turbine to avoid wear of the components.If the rated wind speed is exceeded, the rectifier will keep the turbine at its rated speed andif the wind speed gets higher than the cut-out speed, the turbine will be shut down to avoiddamage.
Different MPPT control strategies have been developed and are extensively discussed in liter-ature. Most of them have their roots in the control of photovoltaic panels, where the outputpower has a maximal value for a certain output voltage and solar irradiance. In general, theseMPPTs can be classified in one of the following categories.
• TSR controlThis method measures or estimates a value of the wind speed and calculates the referencerotor speed for the speed controller using the optimal tip speed ratio λopt. This methodis faster than all other strategies because the location of the MPP is immediately known.The need for a wind speed sensor which provides accurate measurements makes this alsothe most expensive method. As the wind speed sensor is most of the time placed on top
39
4.1. Overview
of the nacelle, this results in inaccurate measurements due to the passing of the blades,both in upwind and downwind turbines [30]. Low pass filtering reduces the noise, butalso reduces the reaction time of the control system. Another problem is that the windspeed variation across the blade span can not be taken into account by a single pointmeasurement [31]. However, this is quite irrelevant for small wind turbines.
• Power controlFor every rotor speed, an optimal value of the output power exists. This power curvecan be calculated and stored in a lookup table in the memory of the controller. Whenthe rotor speed is measured, the corresponding optimal power value can be found in thetable. This defines directly the generator torque and the current reference value, as, dueto the field orientation, torque and current are proportional. The difference between thegenerator and the turbine torque will then slow down or speed up the turbine to its MPP.This method is inherently slower than the TSR control, because the difference betweenthe two torques remains quite limited, especially for small wind changes. On the otherhand, this is an easy method to implement which only requires an encoder. The use of amechanical speed sensor can also be avoided, by using sensorless control techniques. Forexample, in [29], a control method is proposed in which the rotor position and speed isestimated from the measured currents by using a state observer.
A disadvantage of this method is that the optimal power curve needs to be known.This requires some experimental data of the wind turbine. This curve is a third-orderpolynomial so curve fitting can be done with a cubic function.
Another problem, which is also valid for TSR control, is that the wind turbine powercoefficient curve can shift by variations in the blade characteristics. Also variations in airdensity, temperature, generator efficiency and ageing effects can cause the values in thelookup table to variate from the real MPP.
• Hill Climb Search controlHill climb search control (HCS control) observes the variation of the output power androtor speed and reacts on them by adding small increments or decrements to the rotorreference speed. This method eliminates the use of an anemometer and the use of anyexperimental or theoretical data about the wind turbine. This control strategy is anexample of a Perturb and Observe (P&O) method. The problem of the HCS is that it isnot able to detect the location of the MPP. It will keep looking by continuously changingthe rotor speed reference. This results in a rotor speed fluctuation around the actualMPP, called hysteresis.
Like the lookup table, this method is inherently slower because the MPP is not known apriori. The speed at which the tracker searches the MPP can be set by the step size ofthe rotor speed. A high increment will drive the wind turbine faster towards the MPP,but will also result in a stronger hysteresis around the maximum power point.
The electric power is used as input for the hill climber method since it can be easilymeasured by the converter, but it is in fact the turbine power that should be used forthe control strategy. As these two are only equal in steady state condition, there hasto be waited until the transient in the generator power has disappeared. Only then, themeasured electric power can be used to determine the next step of the control.
40
Chapter 4. MPPT control strategies and simulations
Since no data of the wind turbine is required, it is guaranteed that the wind turbine willend up in its real MPP, even during variations of external factors or blade characteristics.
• Mode controlThe three previous basic methods all have their own advantages and disadvantages. Ad-vanced MPPT controllers will combine the best aspects of each of the three methodsto get a hybrid system. Most systems have a master controller which defines in whichmode the controller is operating, depending on wind speed, variations in wind speed,...In this way, the controller can react differently on larger or smaller wind speed variationsor it can hold the rotor speed fixed as long as the wind speed variation does not exceedany dead band limit. Also the possibility for adaptive controllers arises, which are firstoperating in a learning mode to obtain all the necessary parameters in function of acertain wind pattern [32]. In [30], other hybrid HCS methods are mentioned, such asHCS control with dual or variable step size, search-remember algorithms which store theMPPs in the memory during the learning process. In [33], a TSR controller is proposedwith a hysteresis mechanism in the region of the MPP, to adapt to changing turbinecharacteristics.
4.2 Tip speed ratio control
4.2.1 Principle
This is a straightforward method to implement because only the measured wind speed is usedas input for the MPPT controller. The reference rotor speed is then calculated based on theknowledge of the optimal TSR λopt and the turbine radius r:
Ωref =vλopt
r(4.1)
From the CP(λ) in Figure 3.4, the optimal TSR is known:
λopt = 6.9077 (4.2)
It is important to limit the result of the speed control: the q-axis current reference. This valuemust be limited to its rated value as defined in the generator datasheet. Normally, the currentreference can only be positive, which results in a torque in the opposite direction of the turbinetorque (in the generator reference frame). If the turbine has to speed up because the TSR istoo low, the generator torque will be set to zero. The turbine torque will now drive the rotorspeed to its setpoint. Just before the MPP is reached, the generator torque increases again,until the two are equal at the optimal TSR.
In the active rectifier, the current reference can also become positive, by which a motor torqueis created in the PMSG which acts in the same direction as the turbine torque. This way, thegenerator can help the turbine torque to speed up the rotor. The MPP is reached even faster,but electric energy from the grid is used just for the improved acceleration. This advancedapplication will be discussed in Chapter 7.
In the setup that has been built, the wind speed is given as an input for the wind turbineemulator which drives the generator. This value can also be used directly in the TSR control.Although this is not very representative for a real wind speed sensor, it will be used as avalidation to check the performance of the speed control. To make it more realistic, an artificialerror signal could be added to the wind speed value.
41
4.2. Tip speed ratio control
4.2.2 Simulation model
In the previous chapter, the simulation model of the field oriented control was discussed. Asthe current control is a fast process, simulation times were rather small (milliseconds). Becausethe speed control loop is a much slower process (seconds), it is assumed that the torque controloperates infinitely fast in order to reduce simulation time. This means that a certain value ofthe q-axis current reference will immediately result in the desired generator torque. This isa good approximation as, due to the field orientation, the torque is at any time proportionalwith the q-axis current.
In Figure 4.1, the simulation model is shown. The model block at the bottom is the windturbine model. A given value of the wind speed v will result together with the actual rotorspeed in a turbine torque. The PI speed controller calculates the reference value of the q-axisstator current. As input, the measured rotor speed and the reference rotor speed are used. Thelast one is calculated from the wind speed by using the optimal TSR. The current reference isconverted into a generator torque by using the torque constant Kt:
Kt = 6.4 (4.3)
Next, the mechanical system is implemented as an integrator of the torque difference in orderto get the rotor speed, while taking into account the total inertia J (turbine+generator). Therotor speed value is fed back to the PI controller and the wind turbine model. Note thatmechanical friction has been neglected because of the direct drive configuration.
Figure 4.1: Simulink model of the TSR control loop
4.2.3 Simulation results
In Figure 4.2, the simulation result for the TSR control is presented for a steady wind speedequal to about 5 m/s. The optimal rotor speed at this wind speed is equal to 34.8 rad/s. Therotor speed at the start of the simulation is 32 rad/s, so the turbine needs to accelerate toreach its MPP and the controller will set the generator torque equal to zero. The moment theturbine nearly reaches the MPP, the generator torque starts increasing again until it equals
42
Chapter 4. MPPT control strategies and simulations
the turbine torque and the turbine settles at its optimal rotor speed. Because the rotor speeddoesn’t change that much, the turbine torque remains quite constant. The time it takes forthe turbine to reach its MPP is mainly determined by the total inertia.
0 0.2 0.4 0.6 0.8 1 1.24
5
6
Time [s]
v[m
/s]
0 0.2 0.4 0.6 0.8 1 1.26
6.5
7
7.5
Time [s]
TSR
[-]
0 0.2 0.4 0.6 0.8 1 1.232
34
36
Time [s]
Ω[r
ad/s]
0 0.2 0.4 0.6 0.8 1 1.20
2
4
Time [s]
Tg
[Nm
]
0 0.2 0.4 0.6 0.8 1 1.20
2
4
Time [s]
Tt
[Nm
]
Figure 4.2: Wind speed, rotor speed, generator torque and turbine torque at constant wind speed byusing TSR control.
In Figure 4.3, the simulation result is shown for variable wind speed. The same behaviour asfor the constant wind speed arises: the rotor speed follows the wind speed variation with atransient that is mainly determined by the inertia. Also note the limitation of the generatortorque to its rated value when slowing down the turbine, caused by the current limiter at theend of the speed controller.
43
4.2. Tip speed ratio control
0 5 10 15 20 25 304
6
8
Time [s]
v[m
/s]
0 5 10 15 20 25 306
7
8
Time [s]
TSR
[-]
0 5 10 15 20 25 3030
40
50
Time [s]
Ω[r
ad/s]
0 5 10 15 20 25 300
5
Time [s]
Tg
[Nm
]
0 5 10 15 20 25 300
5
Time [s]
Tt
[Nm
]
Figure 4.3: Wind speed, rotor speed, generator torque and turbine torque at variable wind speed byusing TSR control.
44
Chapter 4. MPPT control strategies and simulations
4.3 Power control
4.3.1 Principle
As discussed in the overview, power control is one of the easiest and most frequently usedMPPT control strategies. It is based on the fact that for every rotor speed Ω a maximumpower output Popt exists. This relationship is known as the optimal power curve. Each pointin this curve corresponds to a wind speed that is a priori unknown. This relationship can becalculated if the CP(λ)-curve of the wind turbine is known. If not, an experimental methodneeds to be used, in which the MPPs are determined and fitted with a polynomial function.
In the lab setup, the optimal curve is known from the CP(λ)-curve which is programmed in thewind turbine emulator. The maximum power output will occur when the turbine is operatingat its maximum power coefficient CP,max:
Popt =1
2ρπr2CP,max · v3 (4.4)
Wind speed and rotor speed are related to each other via the tip speed ratio λ. The wind speedis thus known when the turbine is operating in the MPP:
v =rΩ
λopt(4.5)
Substitution of Eq. 4.5 into Eq. 4.4 results in the equation for the maximum power curve:
Popt =1
2ρπr2CP,max
(r
λopt
)3
Ω3 = KoptΩ3 (4.6)
withKopt = 0.002474 (4.7)
This curve is shown schematically in Figure 4.5a.
When the optimal power is known, the optimal generator torque is:
Topt = KoptΩ2 (4.8)
Because of the field orientation, the relationship between q-axis current and torque is:
Topt = KtIq,opt (4.9)
So the current reference value for the speed controller can be directly calculated from themeasured rotor speed:
Iq,opt =Kopt
KtΩ2 (4.10)
Figure 4.5b shows how the MPP is reached. The generator torque will always be on the optimaltorque curve, the turbine torque always on the wind turbine characteristic which is functionof the wind speed and rotor speed. If the wind speed suddenly decreases, the rotor speedinitially remains constant due to the inertia. The generator torque remains constant, but theturbine torque decreases. This difference in torque will decelerate the turbine. As the speed isdecreasing also the generator torque decreases. The turbine torque instead is increasing, so thedifference is getting smaller. At the moment the two torques are equal, the MPP is reached.
45
4.3. Power control
4.3.2 Simulation model
In Figure 4.4, the simulation model for the power control is shown. Again, the wind turbinemodel block is used, which calculates the turbine torque starting from the wind speed v and therotor speed Ω . The generator torque Tg is calculated from the rotor speed by using Eq. 4.8.The difference between these two torques will determine whether the inertia Jt will accelerateor decelerate.
4.3.3 Simulation results
In Figure 4.6, the simulation result for the power control is presented. First, the wind speedis set at 5 m/s and the wind turbine accelerates until the optimal TSR is reached. After 15seconds, the wind speed suddenly decreases to 4 m/s. Again, the TSR goes to its optimal valueafter a quite long transient. The overall conclusion is that the settling time is much larger thanthe one that was observed during the TSR control. A wind speed step of only 1 m/s results in asettling time of about 15 seconds. This is very slow for such small wind turbine. However, theTSR is already within reasonably limits around the MPP after 5 seconds. The slow reactioncan be explained as follows: after the step in the wind speed is applied, the turbine torqueimmediately increases. The generator torque, on the other hand, remains constant becausethe rotor speed doesn’t change immediately due to the inertia. The difference between thesetwo torques is relatively small such that also the acceleration is limited. This is contrary withthe TSR control, where the generator torque was immediately set to zero. Additionally, thelimited torque difference gets still smaller and smaller as the rotor speed is approaching theMPP so the settling time is increased even more.
The fact that the generator torque is a quadratic function of the rotor speed can be clearlyobserved in the results. Also the turbine torque changes likewise the rotor speed because thewind speed is held constant. During the transient, the difference between the torques getsgradually smaller until they are equal. At that moment, the wind turbine has reached itsMPP.
Figure 4.4: Simulink model of power control
46
Chapter 4. MPPT control strategies and simulations
Rotor speed Ω
Mec
han
ical
pow
erP Optimal power curve
v1
v2
v3
v4
(a) Optimal power curve
Rotor speed Ω
Tor
qu
eT
Optimal torque curve
v1
v2
v3
v4
(b) Optimal torque curve
Figure 4.5: Power and torque versus speed characteristics of wind turbine at various wind speeds andoptimal torque curve.
0 5 10 15 20 25 30
4
5
Time [s]
v[m
/s]
0 5 10 15 20 25 306
7
8
9
Time [s]
TSR
[-]
0 5 10 15 20 25 3025
30
35
Time [s]
Ω[r
ad/s]
0 5 10 15 20 25 300
2
4
Time [s]
Tg
[Nm
]
0 5 10 15 20 25 300
2
4
Time [s]
Tt
[Nm
]
Figure 4.6: Wind speed, TSR, rotor speed, generator torque and turbine torque at variable wind speedby using power control.
47
4.4. Hill climb search control
4.4 Hill climb search control
4.4.1 Principle
The hill climb search control is a MPPT control algorithm that doesn’t require any informationabout the wind turbine to locate the MPP. It can also compensate for variations in the windturbine characteristics and external variations such as temperature and air pressure variations.The main strategy is that the controller observes the generator power and rotor speed variations.In function of the sign of those differences, it determines in which part of the CP(λ)-curve theturbine is operating at that moment. Depending on whether the operating point is left or rightfrom the MPP, the reference value for the speed controller will be varied in small steps. This isshown schematically in Figure 4.7. If, for instance, both power and rotor speed are increasing,the controller knows that the turbine is moving towards its MPP. To accelerate the turbine, itwill increase the rotor speed reference with a small step and a new cycle can start. The largerthese steps, the faster the controller will react, but the more nervous the system will be in theneighbourhood of the MPP.
Inside the controller, the following equation is implemented.
∆Ωref = β · sign(∆Ω) · sign(∆P ) (4.11)
Ωref(n+ 1) = Ωref(n) + ∆Ωref (4.12)
The only parameter that can influence the operation of the HCS controller is β. A good valueneeds to be chosen in order to have a small settling time with limited hysteresis around theMPP.
The CP(λ)-curve describes the relationship between the rotor speed and the turbine power, fora fixed wind speed value. However, in most wind turbine system only the electric generatorpower can be measured. In steady state, the generator power is close to the turbine powerand the difference is only determined by the generator efficiency and the mechanical friction.The friction is very low due to the direct drive configuration and only influenced by bearingsand seals. Additionally, the PMSG has a relatively high efficiency such that differences in thetwo power values are limited. The electric power is determined from the three measured phasecurrents which are also used for the field oriented control. These are multiplied with the voltagevalues which are applied by the three phase VSC.
Every time a new speed reference value is set, the electric power will have a transient of afew seconds until the rotor speed is settled at its new reference level. Only when the electricpower is steady, the system is in regime and the value can be used by the HCS controller todetermine the next step in the rotor speed. This implies that the HCS control will be a slowcontrol method as the time between two calculation cycles can be a few seconds.
To eliminate the hysteresis around the MPP, an additional feature can be added. If the dif-ference in power output is small enough, the new rotor speed reference is set equal to the oldrotor speed. This way, the wind turbine systems can have a stable behaviour at the MPP,instead of oscillating around the optimal TSR. This will however not be considered for thisHCS controller, because a more advanced hill climber with this feature will be discussed in thenext section.
48
Chapter 4. MPPT control strategies and simulations
4.4.2 Simulation model
In Figure 4.8, the Matlab Simulink simulation model for the HCS control is shown. Thecontrol starts with the measurement of the generator power and the rotor speed. These valuesgo through a discrete transfer function block in order to calculate the difference between twotime steps. For instance, for the power signal (analogue for the rotor speed):
∆P = P (n)− P (n− 1) (4.13)
Conversion to the z-domain gives:∆P = P − z−1P (4.14)
which leads to the following transfer function:
∆P
P=z − 1
z(4.15)
These differences then go to the HCS controller where Eq. 4.11 and Eq. 4.12 are executed.These result in a new rotor speed reference value that is going to the same PI speed controllerthat was used in the TSR control. The PI parameters of the speed controller are slightlyadapted for the use in the HCS control. In the TSR control, it was the purpose to reach theMPP as fast as possible. In the HCS control, the additional requirement arises that the q-axisreference value has to be a steady value in regime in order to eliminate large fluctuations inthe electric power. Because a small settling time is less important for the HCS control, the PIcontroller is tuned to have a less fluctuating output signal.
4.4.3 Simulation results
The simulation results are shown in Figure 4.9, where the turbine first goes to its MPP ata wind speed of 5 m/s and then a step of 0.5 m/s is applied. First, it can be noted that thesettling time is much larger than for the two previous methods. The frequency of the HCScontroller is equal to 0.5 Hz, which means that rotor speed and electric power are sampled every2 seconds after a new rotor reference speed is set. Second, the TSR is now oscillating aroundits optimal value. The rotor speed step is equal to 0.9 rad/s in order to have a step size whichis large enough such that the power difference can be detected properly, but small enough tolimit the hysteresis around the MPP. In this algorithm the speed step is fixed, but there alsoexist hill climbers with a variable step which exhibit no hysteresis [34].
In Figure 4.10, a detail of Figure 4.9 is showed. Here, it can be clearly seen that after atransient of one second, the rotor speed and electric power settles into regime. The electricpower is varying heavily due to the action of the speed controller. If the turbine has to speedup, the generator torque will be set to zero so the electric power will become zero. If the turbineneeds to slow down, the generator torque will be limited to its rated value, which explains theflattening of the tops in the power output.
Considering Figure 4.10, the comment can be made to decrease the sampling period. This willeither lead to overshooting and longer settling times during variable wind speed, as the outputpower cannot reach its regime value within the sampling time and the controller gets erroneousbehaviour. Smaller sampling times will also result in faster fluctuations around the MPP whichis energetically less efficient.
49
4.4. Hill climb search control
∆Ω > 0 ∆Ω < 0
∆P > 0 ∆P < 0 ∆P < 0 ∆P < 0
Accelerate
∆Ωref > 0
Decelerate
∆Ωref < 0
Decelerate
∆Ωref < 0
Accelerate
∆Ωref > 0
∆P
∆Ω
P
Ω
1
2
Figure 4.7: Scheme of the HCS control strategy.
Figure 4.8: HCS control simulation model.
50
Chapter 4. MPPT control strategies and simulations
0 50 100 150 200 250 3004.5
5
5.5
6
Time [s]
v[m
/s]
0 50 100 150 200 250 3006
7
8
9
Time [s]
TSR
[-]
0 50 100 150 200 250 30030
35
40
45
Time [s]
Ω[r
ad/s]
0 50 100 150 200 250 3000
100
200
Time [s]
Pg
[W]
Figure 4.9: Wind speed, TSR, rotor speed and generator power at variable wind speed by using HCScontrol.
51
4.4. Hill climb search control
92 94 96 98 100 102 104 106 108 110
4.8
4.9
5
5.1
Time [s]
v[m
/s]
92 94 96 98 100 102 104 106 108 110
6.6
6.8
7
7.2
Time [s]
TSR
[-]
92 94 96 98 100 102 104 106 108 110
34
35
36
Time [s]
Ω[r
ad/s]
92 94 96 98 100 102 104 106 108 110
50
100
150
Time [s]
Pg
[W]
Figure 4.10: Detail of Figure 4.9.
52
Chapter 4. MPPT control strategies and simulations
4.5 Mode control
4.5.1 Introduction
As discussed in the previous section, the behaviour of the basic hill climber is not very perfor-mant during variable wind conditions. Also the power control method results in long settlingtimes to reach the desired MPP. As mentioned previously, each of the three discussed MPPTstrategies has its own advantages and disadvantages. During the past years, a lot of researchhas been done about combining these methods into one hybrid MPPT control strategy withexcellent characteristics. Especially, variations of the HCS method are very popular as theydon’t need any wind sensor nor any experimental information of the wind turbine. Also thefact that it can compensate variations in turbine characteristics is an advantage.
To demonstrate the operation of these strategies, one particular example has been chosen fromliterature. In [34], a hill climber based control strategy in combination with a power controlstrategy has been proposed. The main feature is that the hill climber uses a variable step forthe rotor speed, in function of the difference between the actual rotor speed and the rotor speedin the optimal power curve. This way, the step size is large at the beginning when the windturbine is far away from the MPP, but gets smaller and smaller when it reaches the optimalpower point.
The proposed MPPT control was originally designed for a passive rectifier with a DC/DCchopper. In this section, the strategy has been changed for the active rectifier.
The control strategy is shown schematically in Figure 4.11. It consists of three different oper-ating modes. Initially, the controller operates in mode 2, in which the hill climber is active.First, the rotor speed Ω∗ is calculated from an initial value of the optimal power coefficientkopt and the measured generator power:
Ω∗(k) =
(P (k)
kopt
)1/3
(4.16)
Next, the new reference value for the rotor speed is calculated:
Ωref(k) = Ωref(k − 1)− β(Ω(k)− Ω∗(k)) (4.17)
in which β is a positive value which determines the sensitivity of the variable speed step. Therotor speed approaches the MPP with a variable step that gets smaller and smaller (see Figure4.12).
From the moment the rotor speed gets close to its optimal value, the controller goes into mode0 where it will start searching for the exact location of the MPP. As soon as this is detected,it is stored in the controller by the calculation a new value for kopt.
After mode 0, the controller goes directly to mode 1 where the rotor reference speed is kept at afixed value value which corresponds to the MPP. This way, the hysteresis around the maximumpower point, is completely eliminated. As long as no variation in the wind speed is detected,the controller will remain in mode 1. From the moment a variation is detected, the controllergoes back to mode 2 and the whole cycle is repeated.
This strategy is a hill climber which can detect an MPP and store it by calculating the optimalpower coefficient. This is an example of an adaptive controller. It compensates variations in
53
4.5. Mode control
the wind turbine characteristics contrary to other static MPPT strategies like the TSR controland the power control.
It should be noted that no anemometer for wind speed measurement is necessary. A windspeed variation is detected if the following conditions are not true:
|Ω(k)− Ω(k − 1)| ≤ ε (4.18)
sign(Ωref(k)) = sign(Ω(k)) (4.19)
Otherwise, a wind speed variation can also be detected if both next conditions are true:
Figure 4.11: Flowchart of the adaptive, mode controlled MPPT.
4.5.2 Simulation model
The Matlab Simulink model is shown in Figure 4.13. The center of the controller is the blockwhich contains the scheme from Figure 4.11. As input, it uses previous values of rotor speed,generator power, reference rotor speed, optimal power coefficient and the current mode it isoperating in. The main output is the reference rotor speed which goes to the speed controller.The other outputs are fed back to the input to be used for a new calculation cycle. Thecontroller itself operates at a frequency of 2 Hz while the speed controller keeps operating at160 Hz.
54
Chapter 4. MPPT control strategies and simulations
ΩΩoptΩ∗
P
Tu
rbin
ep
ower
Rotor Speed
Figure 4.12: Principle of hill climber MPPT with variable step.
The coefficient β which determines the sensitivity of the hill climber has been chosen equal to:
β = 0.15 (4.22)
A large value will result in a fast response to wind speed variations, but if it is too large, it willcause overshooting especially when the wind speed decreases suddenly. The limits in whichbetween the difference in rotor speed and generator power may variate in order to keep thecontroller in mode 1, are 0.5 rad/s and 5 W. If these limits are exceeded, the controller will seethis as a deviation from the MPP and it will go directly to mode 2.
4.5.3 Simulation results
The simulation results are presented in Figure 4.14 for a variable wind speed between 5 and5.5 m/s. From the TSR, it can be observed that the steady state value is not exactly equal tothe known optimal TSR of 6.91. This is due to the adaptive character of the controller whichdetermines itself the optimal power coefficient. The settling time for the rotor speed is nowequal to about 5 s, which is 30% of the settling time of the normal hill climber in the sameconditions. These values come close to the settling times which were observed during TSRcontrol.
Also the variation of the mode in function of time is interesting to note. First, the controlleris in mode 2, which means that it uses the hill climber with variable step. From the momentthe controller detects that it is close to the new MPP, it goes to mode 0 and searches for theMPP location. Then it enters mode 1 in which a new value for the optimal power coefficientis calculated and the controller keeps the wind turbine in its MPP.
55
4.5. Mode control
Figure 4.13: Simulink model of mode MPPT controller.
56
Chapter 4. MPPT control strategies and simulations
0 5 10 15 20 25 304.5
5
5.5
6
Time [s]
v[m
/s]
0 5 10 15 20 25 306
7
8
Time [s]
TSR
[-]
0 5 10 15 20 25 30
35
40
Time [s]
Ω[r
ad/s]
0 5 10 15 20 25 300
100
200
Time [s]
Pg
[W]
0 5 10 15 20 25 300
1
2
3
Time [s]
Mode
[-]
Figure 4.14: Wind speed, TSR, rotor speed, generator power and mode in function of time at variablewind speed for adaptive mode controller.
57
Chapter 5
Construction of full active rectifier
5.1 General description
The practical setup that is used in this thesis is shown in Figure 5.1 and consists of two largeparts. First, there is the wind turbine emulator, which is an induction motor that simulatesthe dynamic behaviour of the wind turbine. The induction motor is driven by an advancedmotor drive which controls the motor torque without speed or torque feedback. On the otherside, there is the generator which is controlled by the active rectifier. Motor and generator aredirectly connected with each other (this means that there is no gearbox in between) by usingBellow couplings (see Figure 5.2). These couplings compensate for radial misalignment, butare very stiff in torsion. Between motor and generator, a torque sensor is placed to measurethe steady state torque which can be used for mechanical power measurement. The electricpower generated by the PMSG goes through the rectifier to the DC-bus which is connected toa high voltage DC-source. As most of these supplies cannot dissipate the energy coming fromthe generator, a power resistor is placed in parallel with the DC-source to convert the electricenergy into heat.
First, a short description of the wind turbine emulator will be given. Second, the constructionof the active rectifier will be discussed and finally some validation results are given which provesthe correct operation of the field oriented control.
5.2 Wind turbine emulator
For this thesis, a new wind turbine emulator has been constructed, which is similar to aprevious wind turbine emulator, designed and built by ir. Jan Van de Vyver. The maindifference between these two is that in the newer one an induction motor with more pole pairsis used so the reduction gearbox can be omitted. The rated power of the setup is also lower.In the new emulator, the motor has a rated power of 500 W, where the older one had 2.2 kW.
In the new version, also a communication feature has been added, where values like windspeed, rotor position, etc. can be transmitted to other appliances. The communication isestablished by using a Controller Area Network (CAN). This is a two-wire (LOW and HIGH)communication protocol that is very popular in industry because of its robustness during datatransfer. More information about the CAN bus can be found in Appendix B.
58
Chapter 5. Construction of full active rectifier
Figure 5.1: Experimental setup
Figure 5.2: Bellow coupling
5.2.1 Theoretical principle
The torque produced by a wind turbine is the turbine torque Tt. Its value can be determinedby using a CP(λ)-curve, programmed inside the microcontroller. First, a value of the windspeed v has to be given. Next, the rotor speed Ω is measured by using an encoder to calculatethe TSR. With this value, the power coefficient can be calculated and so the turbine torque isknown:
λ =rΩ
v(5.1)
CP = 0.73
(151
λ− 13.653
)exp
(−18.4
λ+ 0.0552
)(5.2)
Tt =1
2ρπr2 CP
v3
Ω(5.3)
During the calculation of the turbine torque, it is also possible to take wind shear and towershadow into account. Wind shear is the result of the fact that the wind speed varies withheight. When the blade is at its top position, the wind speed is higher than when the blade isat its lowest point. This means that the torque on a blade varies during the rotation. As the
59
5.2. Wind turbine emulator
most common wind turbines have three blades, this means that the turbine torque will pulsatewith three times the rotation frequency due to wind shear. By taking into account the rotorposition θ, a corrected wind speed can be calculated by adding a term vws which is dependentof θ, to the wind speed at nacelle height Vh.
v(t, θ) = Vh + vws (5.4)
Previously, there has always been assumed that the wind flow pattern is the same for the wholefront area of the turbine. As the turbine has to be placed on top of a tower, this means thatthe wind is diverted from its normal path because it has to flow around the tower. The resultis that the torque on a blade will decrease at the moment it passes in front of the tower. Thiseffect is called tower shadow. Analogue to the wind shear effect, an extra term vts can be addedto the nacelle wind speed which is again dependent on the rotor position:
v(t, θ) = Vh + vts (5.5)
As the inertia of the rotor of a real wind turbine is much larger than the inertia of a smallinduction machine, a compensation torque needs to be added. This is important to simulatethe dynamic behaviour of a wind turbine. The extra torque, that is applied, is calculated asfollows [20]:
Tin = (Jm − Jt)dΩ
dt(5.6)
in which Jm is the actual motor inertia and Jt is the turbine inertia that wants to be achieved.
If a gearbox was present, also a gearbox compensation torque should have been added. As extralosses due to friction are introduced, the torque at the end of the gearbox will be lower thanthe set value. By measuring the friction coefficient, the compensation torque can be calculatedand added with the other torque terms.
The sum of all these torque terms determines the reference torque for the Danfoss drive. First,it goes through a limiter which limits the turbine torque between zero and the rated torque ofthe induction motor.
The wind speed can be set either by using the debug mode of the DSP or by using the twobuttons placed on the case of the emulator, which changes the wind speed in predefined steps.
5.2.2 Induction motor and drive
The induction motor used in this setup is a WEG AL90S and has the following characteristics:
• Vnom = 2 20/ 380 V
• fnom = 50 Hz
• Pnom = 0.55 kW
• nnom = 665 rpm
This motor is driven by a Danfoss VLT 302 automation drive, which is operated in openloop torque control. After the machine parameters are automatically measured during aninitialisation cycle, the drive can control the motor torque without any feedback.
60
Chapter 5. Construction of full active rectifier
The reference value of the torque is calculated by a DSP (Digital Signal Processor) of TexasInstruments. The torque is given as a duty ratio to the PWM modulator. By using a low-passfilter, this is converted to an analogue signal between 0V and 10V. This signal then goes to ananalog input of the Danfoss drive.
5.2.3 Absolute encoder
To calculate the turbine torque, the rotor speed has to be known. For this purpose an absolute13-bit encoder (Lika Rotacod Absolute multi-turn encoder HSCT, see Figure 5.3) isused. The encoder has a resolution of 8192 positions per revolution. The position angle istransmitted in Gray code by using the SSI communication protocol with differential signalsin order to reduce noise. The Gray code is first converted into binary code and then into adecimal rotor angle expressed in radians. This angle is numerically differentiated and digitallyfiltered by using a moving average of five values. The result is the measured rotor speed. Fromthe rotor speed, also the rotor acceleration needs to be calculated for the inertia compensationtorque. To obtain an acceptable value of the acceleration, adequate filtering has been executed.
Because the value of the rotor angle is needed for the field oriented control of the generatorand the value of the rotor speed and wind speed is necessary for the MPPT control, these threevalues are transmitted to the active rectifier by using the CAN bus.
5.3 Active rectifier
The main components of the active rectifier are three half bridge IGBT modules (HBM2013)which are a new design of ir. Jeroen De Kooning. Each half bridge module consists of twoIGBTs placed in series between the two DC terminals. By using three of these modules inparallel, a three-phase voltage source converter arises. The six IGBTs are controlled by a DSPin which the algorithms for current, speed and MPPT control are programmed. First, the halfbridge modules will be discussed briefly, next the DSP.
5.3.1 Half bridge module
The half bridge module has two main purposes. The most important one is the control andthe protection of the two IGBTs. Additionally, there are two measuring circuits installed toallow measurements of voltages and currents which may be necessary for the control of theconverter. The different parts of the HBM are:
1. IGBT circuitIn Figure 5.4, the schematic layout of the IGBT circuit is shown. There are two IGBTs:
Figure 5.3: Lika Rotacod HSCT
61
5.3. Active rectifier
the high one (DH) and the low one (DL), which are connected with the positive andnegative DC terminals respectively. Their common connection point in the middle is theoutput terminal VS. Each IGBT is controlled by an intelligent gate driver which appliesthe gate voltage. The chip needs a 15 V supply in order to have a sufficient voltage levelto turn on the gate terminal. The driver also provides several protection mechanismssuch as under-voltage lockout, a saturation protection and anti-miller clamping. If thedriver detects a problem, its fault output is set low and the incoming duty ratio signalto the drivers are blocked.
2. Current measurementBetween the common output of the two IGBTs and the output terminal VS, the outputcurrent flows through a LEM CASR Hall effect current sensor. This type of sensor canmeasure AC currents with a maximum amplitude of 2 A. As the sensor is fed at 5 V,the output voltage varies linearly around an offset voltage of 2.5 V, with a sensitivity of104.2 mV/A. This measured voltage is directed to the DSP where it is read by the ADC.The ADC can measure voltages up to 3 V and as the LEM produces voltages up to 5 Va voltage divider is placed in between. At the end of the circuit, a low-pass RC filteris placed with a cut-off frequency of 22 kHz. This value is chosen to be larger than theswitching frequency of the IGBTs which is 16 kHz, such that this frequency componentis passed to allow the current control.
3. Voltage measurementOn the HBM board are two terminals between which the differential voltage can bemeasured. The module can measure voltages up to 1275 V. Like the current measurement,the output voltage is directed to the DSP and has an offset voltage of 1.5 V, so AC voltagescan be measured. Also in this circuit, a low-pass filter is placed with the same cut-offfrequency as for the current measurement.Because there are three HBMs, there are three voltages which can be measured. One isused to measure the DC-bus voltage, the other two are used to measure two phase voltagesof the generator. The third phase voltage can be calculated from the other two as there areno zero sequence voltages because the generator is connected in Y-configuration withoutneutral connection.
4. Protection circuitA small protection circuit is installed to allow the HBM to block the duty ratios when afault is detected. The circuit watches the fault output of the IGBT drivers, but also looksfor external fault inputs coming from the DSP. Additionally, this circuit also provides areset feature, which can be executed either by pushing a reset button in the circuit, orby an external trigger coming from the DSP. Reset and error states are looped betweenthe three HBMs so they all react at the same time on faults and resets.
5.3.2 Generator
In Figure 5.5, the generator of Ziehl-Abegg is shown which is a permanent magnet generatorwith an external rotor. This means that the stator windings are placed at the inside and thatthe permanent magnets are placed at the outside. To protect the environment from accidentalcollision, a casing with ventilation holes is placed around the rotor. The generator is mountedvia its outer casing, on which also the terminal connectors are located. The stator windings arein Y-configuration with neutral connection. Although this neutral is not connected with the
62
Chapter 5. Construction of full active rectifier
DH
DL
VB+
VB-
VS
Figure 5.4: Schematic layout of IGBT circuit.
converter, it is used inside the converter to measure the phase voltages. The electric parametersof the generator were already given in Chapter 3.
The purpose of the DC-bus is to buffer the electric energy between the DC voltage source andthe converter, while providing a constant voltage level. Four electrolytic capacitors are used.Each has a capacitance of 470 µF and can withstand a voltage level of 500 V. As the DC voltagelevel is 700 V, a configuration needs to be used as shown in Figure 5.6. Now, the equivalentcapacitance is 470 µF and the DC-bus is suited for voltages up to 1000 V. The capacitors areconnected to each other by means of copper bars in order to keep the parasitic inductancebetween the capacitors and the converter terminals lower than 1 µH. The bleeder resistancesare necessary to keep the bus voltage nicely distributed over each individual capacitor. Theyalso remove the voltage from the capacitors after the DC supply has been removed.
5.3.4 DSP
The logic center of the active rectifier is the Digital Signal Processor (DSP) Delfino F28335of Texas Instruments (Figure 5.7). The microcontroller is placed on an experimenter’sboard and communicates with the computer via USB. The program is written in C and can be
63
5.3. Active rectifier
VB+
VB-
+
+ +
+
Figure 5.6: Schematic layout of DC-bus.
uploaded to the processor by Code Composer Studio. This program also provides an extensivedebug feature in which variables can be acquired and manually adapted in real-time. Data canalso be processed directly into graphs. The microcontroller exists of different modules. Themost important ones used for the converter control are:
• General purpose I/O: these pins can be used both as logic input or output. Themaximal voltage on a pin is 3.3 V. These pins are used to execute reset commandos andread fault states from the HBM’s.
• ADC module: this module can measure analogue voltages between 0 and 3 V andconverts it into a 12-bit digital value (value between 0 and 4096) which can be processedfurther on. This module is used to read the measured voltages and currents from eachHBM.
• PWM module: this module can generate pulse width modulated signals on 8 channels.The amplitude of these signals is 3.3 V and the duty ratios can be set in the appropriateregisters. Three PWM channels are used, one for each HBM, with a switching frequencyof 16 kHz. This results in 6 PWM outputs, as each channel generates two complementaryPWM signals DH and DL with a dead time of 1 µs. The PWM output of phase A alsofunctions as the trigger for the interrupt service routine in which the current control isexecuted. A fourth PWM channel is initialized with a switching frequency of 160 Hz, forthe triggering of the speed control interrupt service routine.
• CAN module: this module manages the communication between several microproces-sors. The module can with different mailboxes in which messages can be sent and received.In this setup, the wind turbine emulator sends its values as soon as these are calculated.This produces an interrupt in the DSP of the active rectifier and the receiving functionis executed. The variables in the active rectifier are now updated with the variables fromthe emulator. This communication is executed at a frequency of 2.94 kHz, which meansthat by approximation after 5 current control cycles, the rotor position value is updated.More information about the CAN communication can be found in Appendix B.
5.3.5 Torque sensor
As mentioned earlier, the torque sensor (Metil DR2477, Figure 5.8) is placed between thegenerator and the motor. Its purpose is to measure the steady state generator torque which canbe used for verification of the MPPT control strategies. The problem with torque measurements
64
Chapter 5. Construction of full active rectifier
Figure 5.7: Delfino F28335 experimenter’s kit of Texas Instruments.
is that they are not very accurate and need to be filtered adequately in order to obtain usefulvalues. The sensor is fed by a 15 V DC source and has a measurement output voltage that liesbetween −5 V and +5 V. This value is read by the ADC after been going through a voltagedivider and low pass filter. The measuring torque range of the sensor is between −15 Nm and+15 Nm. More information about the torque sensor and its measurement circuit can be foundin Appendix C.
5.4 DSP program and start-up
The program which is uploaded in the DSP of the active rectifier consists of different functionsand subroutines. The most vital functions are located in interrupt functions for which prioritiesare set. The most important interrupt has the highest priority, in this case the interrupt thatis executed the most frequent: the current control. This means that no other interrupt requestcan disrupt this function until it is fully completed. The function that is called first afterresetting the microcontroller is the ’main’ function. This initializes all the necessary modulesand starts the interrupt routines. The most important functions and interrupt routines aredescribed now, starting with the main function.
Main function
The main function is the very first function that is executed. First, the internal processor(CPU) will be initialized. The clock frequencies are set, system clocks are enabled and the
necessary registers are loaded. The next step is the configuration of the I/O-pins. The PWMand ADC registers are loaded and the CAN module is initialized. Then, the initialization ofthe converter is started. First it checks if there aren’t any faults. Next, the DC-bus voltage ischecked whether it is at a sufficient level to start switching. Next, a trigger on the reset pin willstart the converter, but the duty ratios are still at zero for the three phases. Finally, the mainfunction goes into a never-ending loop. Then, the current control ISR is executed for the firsttime. The converter is now switching and controlling the current to zero. When the currentcontrol is started, also the speed control ISR can start, as soon as the wind turbine is rotatingat a minimal TSR . The current reference value is not longer held constant at zero and powerfrom the generator is now delivered to the DC-bus. The complete controller is active and theMPPT control, which is located in the speed control, can start operating.
Current control ISR
The current control ISR is the most important and most critical function of the controller and isthe same for all the MPPT strategies. It calculates for each PWM period the new duty ratiosfrom the measured currents and the rotor position. Additionally, it provides the importantover-current protection. As the HBM has no internal protection for over-current, it is the DSPthat observes the value of the three phase currents and blocks the IGBT drivers, if necessary.
Each new cycle starts with the ADC module that measures the three phase currents. Next,the current protection checks whether these currents are in between the safety limits. If not,the duty ratios of the three phases are set to zero and the DSP goes into an infinite loop. Theconverter is now shut down. If the current values are within these limits, they are transformedto the synchronous reference frame by using the Clarke and Park transformation. For thisconversion, the rotor position is needed which is transmitted from the wind turbine emulator.These currents then go to the PI current controllers, which calculate the new phase voltagesin the synchronous reference frame. After transformation to the stator reference, these arechanged into duty ratios with values between 0 and 1. Finally, the generator power is calculatedby using the measured currents and the applied phase voltages. This value is filtered with amoving average filter to obtain an useful value for the MPPT controller. These are loaded intothe PWM registers and the ISR is finished.
Speed control ISR
This interrupt routine contains the actual MPPT algorithm. The content varies with thecontrol strategy itself, but they all have the same purpose: calculating a new value of thecurrent reference which can be used by the speed controller. This is a PI controller which issimilar to the ones used for the current control.
Additionally, also the measured torque is read from the ADC registers, filtered and used tocalculate the mechanical power for evaluation purposes.
Receive ISR
This interrupt routine is triggered every time a new message from the wind turbine emulatorarrives. It reads the wind speed, rotor position and rotor speed from the message and stores itinto their respective variables. These values then can be used by the other functions.
66
Chapter 5. Construction of full active rectifier
5.5 Verification
In this section, the basic functions of the active rectifier are tested. First, there is checkedwhether the current controller is able to produce a sinusoidal current. Second, the alignmentbetween the EMF and the stator currents is investigated. For these two tests, the generatoris rotating unloaded to provide the rotor position and the converter is connected to a genericthree phase inductive load. As soon as the alignment is correct, the converter can be connectedto the generator. From that moment, the step response can be verified when the generator isrotating at constant speed.
5.5.1 Sinusoidal current control
In Figure 5.9, the result of the current controller is shown. Both the reference and the measuredcurrent values are shown in the stator reference frame. The q-axis reference current is set to afixed value of 0.2 A, which will result in a sinusoidal phase current with an amplitude of also0.2 A and with a frequency that corresponds to the rotor speed.
Figure 5.9: Measured and reference value (dotted line) of current through three-phase inductive loadin function of time.
5.5.2 Alignment
To establish the alignment between the stator EMF and the stator currents, which is essentialfor the field oriented control, generator and converter are disconnected. The current control isexecuted with a separate three phase load by using the actual rotor position from the generator.Because the generator is at no-load condition, the phase voltage is equal to the EMF. Thecurrent through the inductors and the EMF are plotted together on an oscilloscope. Thenthe offset of the rotor position is changed manually until the current and EMF of each phaserespectively are aligned with each other. From the moment this value is determined, it remainsfixed as long as motor and generator are not mechanically disconnected from each other. Theresult after the alignment procedure is shown in Figure 5.10.
5.5.3 Field oriented control
Once the alignment is correct, generator and rectifier can be connected. The field orientedcontrol is now operational so the currents in the stator windings are controlled sinusoidal inphase with their respective EMF. The stator currents as measured by the active rectifier in
67
5.5. Verification
−0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1−0.1
−0.05
0
0.05
0.1
Curr
ent
[A]
Time [s]−0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1
−100
−50
0
50
100
EM
F[V
]
Figure 5.10: Measured current through three-phase inductive load and measured EMF in function oftime at constant generator speed.
each phase are shown in Figure 5.11. It is observed that these currents have indeed a three-phase positive sequence sinusoidal waveform. Also the stator voltages, as calculated by the PIcontroller and applied to the PWM modules, are presented. Because the current amplitude isquite low, the voltages are nearly equal to their EMFs, both in phase and magnitude.
As validation, the voltage phasor is also calculated by hand. The generator is rotating at amechanical speed of 34.8 rad/s. At that speed, the EMF has an amplitude of 147 V (see Table3.2) and the current amplitude is equal to 0.4 A. Together with the measured stator resistancesand inductances from Chapter 3, the voltage phasor V s with respect to the EMF phasor Ep
during field orientation can be calculated as:
V s = Ep − (Rs + j ωLs)Is (5.7)
= 147 V − (28.0 Ω + j 6 · 34.8 rad/s · 0.0651 H) · 0.4 A (5.8)
= 135.6 exp−j2.3
V (5.9)
This corresponds to the voltage amplitude of Figure 5.11. The power factor is equal to 0.99.
To investigate the performance of the current controller, also the step response of the q-axiscurrent is investigated with the generator rotating at constant speed. In Figure 5.12, boththe results from the simulation model and the step response, as measured by the rectifier, areshown. It is noted that the overshoot (15%) and the settling time 1 ms) are almost equal tothe values that could be expected from the simulations. The overshoot of the real response isslightly larger than the one from the simulations. At steady state, the measured q-axis currentis a little fluctuating due to the noise of the current sensor.
68
Chapter 5. Construction of full active rectifier
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08−0.5
0
0.5
Time [s]
Curr
ent
[A]
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08−150
−100
−50
0
50
100
150
Time [s]
Volt
age[
V]
Figure 5.11: Three-phase stator currents and voltages in function of time during field oriented control(measured in consumer reference frame).
0 0.5 1 1.5 2 2.5
x 10−3
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Time [s]
q-a
xis
curr
ent
I q[A
]
Figure 5.12: Measured and simulated step response of q-axis current in function of time during fieldoriented control.
69
Chapter 6
Maximum power point tracking:results
6.1 Introduction
In the previous chapter, the construction of the active rectifier was explained together with theimplementation of the field oriented control. In this chapter, the different MPPT strategiesthat were introduced and simulated in Chapter 4 are implemented in the controller of therectifier. The experimental results are discussed and checked with the simulation results. Notonly the step responses of the rotor speed and tip speed ratio are presented to verify whetherthe correct MPPs are achieved, also the generator power response is discussed to see how thepower fluctuates during wind speed variations.
First, the three basic MPPT strategies are discussed: TSR control, power control and HCScontrol. Next, also the performance of the MPPT mode control is investigated.
6.2 Tip speed ratio control
The TSR control is the simplest and most effective MPPT strategy that is used and illustratesnicely the operation of the speed controller. Both a positive and negative change in the windspeed are applied in order to show how the controller reacts.
In the beginning, the same parameters for the PI speed controller have been implemented in thelab setup as were used during the simulations. This resulted in a similar behaviour during stepresponses as was observed in the simulation results, only the settling times were much smaller.Finally, the conclusion was made that the inertia compensation in the wind turbine emulatoris not able to operate properly in combination with the speed controller. The calculation ofthe acceleration from the rotor position and the calculation of the inertia compensation torqueare executed correctly, together with the output signal that serves as analog input for thedanfoss drive. It seems that the drive itself does not succeed to apply the compensation torquesufficiently fast. The result is that the speed controller only operates with the physical inertiaof motor and generator itself. The installation of additional inertia on the same rotor shaft, bymeans of a steel cylinder, did not solve the problem.
Finally, a more correct step response was achieved by lowering the sampling rate of the digitalPI controller. While the speed controller in the simulations was operating at a samplingfrequency of 160 Hz, the frequency is now lowered to 16 Hz. This makes the reaction of the
70
Chapter 6. Maximum power point tracking: results
speed controller relatively slow which gives the inertia compensation more time to react. Theacceleration is now corresponding with the virtual turbine inertia, but the slower control alsoenlarges the overshoot and the settling time. Due to the new sampling rate, new parametersfor the PI controller had to be determined:
Ks = 0.2 (6.1)
as = 0.85 (6.2)
This speed controller will also be used in the HCS and the mode controller.
In Figures 6.1 and 6.2, the result for an increase in wind speed from 4 m/s to 5 m/s is shown.In order to track the MPP, the rotor speed has to vary from 27.9 rad/s to 34.8 rad/s. Fromthe rotor speed response, it can be noted that the new MPP is achieved after a transientwith some overshoot. Also the simulated response of the rotor speed is shown in the samefigure and it can be noted that settling times for both are equal to 3 s. The only problem isthat the acceleration immediately after the step in wind speed is too large, because the windturbine emulator did not have enough time to create the correct compensation torque. Theinertia compensation works reactive. This means that first a change in speed has to occurbefore the system can start to compensate. In this lab setup, the rotor speed is calculatedby differentiation of the rotor position. Next, the rotor speed is differentiated to know theacceleration. By consequence of the two differentiations, the noisy acceleration signal needs tobe strongly filtered in order to have an useful value for the inertia compensation. This filteringintroduces also a phase lag which slows down the compensation. Next, the compensation torqueis transferred to the Danfoss drive as a PWM modulated signal where it is filtered again inorder to get an analog input value. All these measurements and conversions take some timebefore the wind turbine emulator can react in order to have a correct response behaviour. Soat the beginning of the step, the generator torque is lowered to accelerate the wind turbine.The turbine torque is however still at the value that corresponds to the previous MPP and willaccelerate the turbine. Now, the inertia compensation should react by lowering the turbinetorque in order to have correct transient behaviour, but this happens too late. Additionally,due to the late response of the inertia compensator, the inertia torque gets larger and largerin magnitude which finally results in a negative total torque which means that the inductionmotor should brake the PMSG in order to get the right response. The problem is that theDanfoss drive cannot handle these negative torque inputs. The conclusion is that the turbineinertia compensation is not able to operate properly in combination with the designed speedcontroller of the active rectifier.
It can be noted that only after one second, the inertia compensation starts reacting by whichthe acceleration is slowed down. At that moment, the turbine is already close to its new MPPand the generator torque starts rising again to slow down. Again, the inertia compensationdetects this deceleration and will increase the turbine torque in order to lower the deceleration.Finally, the system settles around the new MPP.
In Figure 6.2, the response of the generator power in function of the rotor speed is shown.The power follows a trajectory which starts from the MPP at the low wind speed and arrivesat the MPP of the high wind speed. The generator power first decreases to accelerate theturbine. This corresponds to the decrease of the generator torque, as explained earlier. Fromthe moment the new optimal rotor speed is reached, the generator power starts increasing againto slow down to its new operating point.
In Figures 6.3 and 6.4, similar conclusions can be made for a decrease in wind speed from
71
6.2. Tip speed ratio control
5 m/s to 4 m/s. The rotor speed settles at the appropriate value, just like the generator power.Again, the (negative) acceleration at the beginning of the step is too large due to the incorrectinertia compensation. The settling time is now around 4 s which is larger than the positivewind speed step. This is logic as the generator torque will go to its maximal value to slowdown the turbine. As the difference with the turbine torque is smaller than when the generatortorque is set to zero, the acceleration will be smaller. Figure 6.3 shows how the generator power(and torque) first increases to slow down the turbine towards the new MPP. Then the powerdecreases again to go to its steady state value.
0 1 2 3 4 5 6 7 8 9 1027
28
29
30
31
32
33
34
35
36
Time [s]
Rot
orsp
eed
Ω[r
ad/s
]
Figure 6.1: Measured and simulated step response of rotor speed in function of time when positivestep in wind speed is applied during TSR control.
0 5 10 15 20 25 30 35 40 45 500
20
40
60
80
100
120
Rotor speed Ω [rad/s]
Gen
erato
rpow
erP
g[W
]
v = 5 m/s
v = 4 m/s
Figure 6.2: Trajectory of the generator power in function of the rotor speed for a positive step in thewind speed, together with the according wind turbine characteristics during TSR control.
72
Chapter 6. Maximum power point tracking: results
0 1 2 3 4 5 6 7 8 9 1026
27
28
29
30
31
32
33
34
35
36
Time [s]
Roto
rsp
eed
Ω[r
ad/s]
Figure 6.3: Measured and simulated step response of rotor speed in function of time when a negativestep in the wind speed is applied during TSR control.
0 5 10 15 20 25 30 35 40 45 500
20
40
60
80
100
120
Rotor speed Ω [rad/s]
Gen
erato
rpow
erP
g[W
]
v = 4 m/s
v = 5 m/s
Figure 6.4: Trajectory of the generator power in function of the rotor speed for a negative step in thewind speed, together with the according wind turbine characteristics during TSR control.
73
6.3. Power control
6.3 Power control
In the power control strategy, the generator power needs to be controlled to the optimal valuedetermined by the cubic optimal power curve.
Popt = KoptΩ3 (6.3)
This means that the generator torque needs to be controlled according to a quadratic functionof the rotor speed:
Topt = KoptΩ2 (6.4)
As the difference between the turbine and the generator torque remains relatively small, it canbe concluded that this is a slow control strategy with large settling times.
The performance is investigated by applying a step in the wind speed from 4 m/s to 5 m/s. Theeffect on the rotor speed is shown in Figure 6.5. The speed varies from the MPP at 4 m/s toa rotor speed of 34.8 rad/s which corresponds to the MPP at 5 m/s. The final rotor speed canbe easily verified by using the optimal TSR which is equal to 6.91. The settling time is about15 seconds. In the same figure, also the result from the simulation is shown. It can be notedthat the two responses are quite the same. The variation of the rotor speed around the finalMPP is only due to noise from the encoder signal. Because only the absolute rotor position ismeasured, its speed needs to be calculated by differentiation, which increases the noise.
In Figure 6.6, the generator power is shown together with the simulated result. The responsehas the same shape as the rotor speed. This is logic because the generator power is a cubicfunction of the rotor speed. The same settling time of the rotor speed is necessary for thegenerator power to reach the maximal power output that corresponds to the new wind speed.The optimal value is shown as a dotted line.
An interesting figure is the plot of rotor speed Ω versus generator power Pg, together with thespeed/power characteristics of the wind turbine. The result is shown in Figure 6.7. The lowestcharacteristic corresponds to the initial wind speed. The trajectory of the operating point ofthe generator is shown as dots. The first point is the MPP at the initial wind speed. Fromthe moment the step in wind speed is applied, the operating point starts to follow the cubicoptimal power curve until it finally reaches the MPP that corresponds to the new wind speed.This way, it is verified that the control strategy is operating properly.
It should be noted that the generator power that is shown in the figures is the electric generatorpower measured at the stator terminals of the PMSG, corrected with the generator efficiency inorder to get the mechanical power that can be compared with the wind turbine characteristics.This way, it can be verified whether the generator power corresponds to the MPPs programmedin the wind turbine emulator. As generator efficiency, the value from the datasheet in AppendixA is used which is equal to:
ηg = 80.2% (6.5)
An efficiency value is not a constant value but depends on the operating point of the generator.In general, the maximal efficiency is only reached at the rated power. However, in order tocompare the different MPPT strategies with each other and with the theoretic wind turbinecharacteristics, the same efficiency value is used for all the power measurements in this thesis.
74
Chapter 6. Maximum power point tracking: results
0 5 10 15 2027
28
29
30
31
32
33
34
35
36
Time [s]
Roto
rsp
eed
Ω[r
ad/s]
Figure 6.5: Measured and simulated step response of rotor speed in function of time when a step inthe wind speed is applied during power control.
0 5 10 15 2050
60
70
80
90
100
110
Time [s]
Gen
erato
rpow
erP
g[W
]
Figure 6.6: Measured and simulated step response of generator power in function of time when a stepin the wind speed is applied during power control.
75
6.4. Hill climb search control
0 10 20 30 40 500
10
20
30
40
50
60
70
80
90
100
110
Rotor speed Ω [rad/s]
Gen
erato
rpower
Pg
[W]
v = 4 m/s
v = 5 m/s
Figure 6.7: Trajectory of the generator power in function of the rotor speed for a step in the windspeed, together with the according wind turbine characteristics during power control.
6.4 Hill climb search control
The hill climber searches for the maximum power point by using the typical shape of the windturbine characteristic. Both the rotor speed Ω and the generator power Pg are sampled atthe end of each MPPT cycle. The difference with their respective values of the previous cycledetermines the next step in the rotor reference speed Ωref by using the following equation:
For instance, if both power and rotor speed are increasing, the MPPT controller knows by theCP(λ)-curve that the operating point is approaching the maximum power point. The parameterβ determines the size of the speed step. Once the new MPP is reached, the controller keepssearching by which hysteresis occurs: the rotor speed reference stays fluctuating around theoptimal rotor speed.
As observed during the simulations, this process is quite slow because the controller needs towait after every step of the rotor speed until the system gets in steady state. When the rotorspeed is settled, the generator torque remains equal to the turbine torque and the generatorpower corresponds to the turbine power (while taking into account the efficiency). The hillclimber in the simulation model has a sample period of 2 seconds and a fixed step size of0.9 rad/s. In the lab setup, these settings need to be altered because the same speed controllerfrom the TSR control is used. The PI controller frequency was lowered to 16 Hz and theparameters Ks and as were adapted to correct the erroneous behaviour of the wind turbineemulator’s inertia compensation. As consequence, the MPPT sample period is now equal to 3seconds, but the step size is enlarged to 1 rad/s in order to keep the reaction sufficiently fast.A larger step size also results in larger hysteresis.
The correct operation of the implemented hill climber is illustrated by applying a positive step
76
Chapter 6. Maximum power point tracking: results
in the wind speed from 3.5 m/s to 4.5 m/s. The reaction of rotor speed and generator powerare shown in Figures 6.8 and 6.9, respectively. The rotor speed increases indeed in little stepsof 1 rad/s and it takes about 25 seconds to reach the new optimal operating point. Around thenew MPP, which corresponds to an optimal rotor speed of 30.8 rad/s, the hysteresis is clearlyshown. The rotor speed keeps fluctuating because the hill climber is not able to detect whetherit is in the MPP or not.
In the generator power response in Figure 6.9, it can be noted that there has to be indeed waitedaround 3 seconds in each MPPT cycle before the generator power reaches its new steady statevalue. The generator power is actually sampled at a rate of 160 Hz, but it is only the valueat the end of the MPPT cycle that is used to determine the new speed step. The staircasefunction (dotted line) shows these power values that are sampled at the end of each period.During a step, the generator power fluctuates quite heavily. This is because the generatortorque has to change quickly in order to accelerate or decelerate the wind turbine towards thenew reference speed. This power fluctuation not only occurs in the transition between twoMPPs, it is also observed during the hysteresis around one MPP. This power fluctuation ata constant wind speed is not ideal for obtaining maximal efficiency. Together with the quiteslow response at wind variations, it can be concluded that the standard hill climber is not thebest MPPT strategy to be used in small wind turbines. For such turbines, the wind variationis larger at lower altitude due to turbulences from the surroundings.
The plot in Figure 6.10 shows the generator power in function of the rotor speed. The operatingpoint jumps from the MPP at the turbine characteristic of 3.5 m/s to the characteristic of4.5 m/s right after the change in wind speed has occurred. It is nicely illustrated how theoperating point follows the new turbine characteristic towards the top. This shows that thehill climber is indeed able to determine the direction towards the new MPP. Because it is notable to locate its precise location, the rotor speed keeps fluctuating around the new MPP.
0 5 10 15 20 25 30 35 4022
24
26
28
30
32
Time [s]
Roto
rsp
eed
Ω[r
ad/s]
Figure 6.8: Measured and optimal rotor speed in function of time when positive step in the wind speedis applied during HCS control.
77
6.5. Mode control
0 5 10 15 20 25 30 35 4020
30
40
50
60
70
80
90
Time [s]
Gen
erato
rpower
Pg
[W]
Figure 6.9: Measured and optimal generator power in function of time when positive step in the windspeed is applied during HCS control.
0 5 10 15 20 25 30 35 400
10
20
30
40
50
60
70
80
Rotor speed Ω [rad/s]
Gen
erato
rpow
erP
g[W
] v = 4.5 m/s
v = 3.5 m/s
Figure 6.10: Trajectory of operating point in speed/power plane for a step in the wind speed, togetherwith the according wind turbine characteristics during HCS control.
6.5 Mode control
The mode controller based on the control scheme of Kazmi [34] is in fact a hill climber witha variable step. During the simulations, the conclusion was made that this MPPT controllerhas superior performance compared to the standard hill climber. By adding a maximum powerpoint detection algorithm, the rotor speed can be held fixed near the MPP so the hysteresis iseliminated.
The MPPT controller consists of three operating modes. Mode 2 is the hill climber with the
78
Chapter 6. Maximum power point tracking: results
variable step in which the next rotor speed reference is calculated as:
Ωref(n) = Ωref(n− 1)− β(
Ω(n)−(P (n)
kopt
)1/3)
(6.7)
where β sets the sensitivity. This mode is used for the main transition between two MPPs.Once the new MPP is reached, mode 0 is initiated where the controller searches for the exactlocation of the MPP and updates the value of the optimal power coefficient. At the MPP,mode 1 is started which holds the rotor speed fixed. If a new wind speed variation is detected,the controller will go back to mode 2 and the procedure is repeated.
In the lab setup, the parameters of the MPPT controller are set as follows, according to thescheme in Figure 4.11:
fhcs = 0.5 Hz (6.8)
β = 0.8 (6.9)
γ = 0.2 (6.10)
Mode 0 is initiated as soon as the rotor speed is within a range of 1.5 rad/s around the optimalrotor speed value and the power is within the range of 5 W around its optimal value.
The result for applying a positive step in the wind speed from 4 m/s to 5 m/s is shown in thefollowing figures. In Figure 6.11, the rotor speed is shown in function of time together with thereference speed (dotted line) that is set by the mode controller. In Figure 6.12, it is presentedin which mode the controller is operating in function of time. Before the change in wind speed,the wind turbine is settled at the initial MPP and mode 1 is active. Once the wind change isdetected, mode 2 is initiated and the hill climber with variable step becomes active. Alreadyafter 6 seconds, the operating point is close to the new MPP. These are settling times thatcome close to the ones that were observed during the TSR control. It can also be noted thatthe steps in the speed reference are indeed no longer fixed. The first step is a large one, whichbrings the wind turbine already near the optimal operating point. Once at the MPP, there isstill noticed a little fluctuation around the optimal rotor speed in mode 2. After 11 secondsboth rotor speed and generator power are close to their optimal values and mode 0 becomesactive. A hill climber with fixed step γ searches for the location of the new MPP. From themoment this is found, the controller goes to mode 1 where the rotor speed is held constantuntil a new change in wind speed occurs.
In Figure 6.13, the resulting generator power is shown for the same situation. The dotted linerepresents the power values that are sampled at the end of an MPPT cycle. It can be notedthat the sampling period is chosen equal to 2 seconds (fhcs = 0.5 Hz). This is quite short forthe generator power to get to its regime value, especially for the first step. In the plot, it canalso be noted that at the end of the first step after the change in wind speed, the generatorpower is not yet stabilised to the correct value. However, this is no big problem for the correctoperation of the controller during the first few steps. In mode 0 where the controller searchesthe exact location of the MPP, the value of the generator power needs to be more correctly.For these smaller rotor speed steps, a sample period of 2 seconds gives enough time for thepower to stabilize at its steady state value.
The plot of the generator power in function of the rotor speed in Figure 6.14 results in a similartrajectory of the operating point as the one that was observed for the standard hill climber.Again, the operating point jumps initially from the first turbine characteristic to the second
79
6.5. Mode control
one and then tries to follow its way up. The only difference is the use of the variable step, bywhich the operating point gets already close to the MPP after one or two steps, while in Figure6.10 a lot of fixed steps where necessary to go to the MPP.
The overall conclusion of comparing these four MPPT control strategies is that the TSR controlindeed offers the best performance, if accurate wind speed measurements are available. Thepower control results in a steady power output and rotor speed at the MPP, but has very longsettling times. The standard hill climber is also quite slow and results additionally in hysteresisof the rotor speed at the MPP and a heavily fluctuating power output. The mode control is acompromise which results in settling times comparable with the TSR control without requiringany experimental data of the wind turbine or any wind speed measurement.
0 5 10 15 20 25 3028
29
30
31
32
33
34
35
36
Time [s]
Roto
rsp
eed
Ω[r
ad/s]
Figure 6.11: Measured (full) and reference (dotted) rotor speed in function of time when a positivestep in the wind speed is applied during mode control.
0 5 10 15 20 25 300
0.5
1
1.5
2
2.5
Time [s]
Mode
[-]
Figure 6.12: Active mode in function when a positive step in the wind speed is applied during modecontrol.
80
Chapter 6. Maximum power point tracking: results
0 5 10 15 20 25 3050
60
70
80
90
100
110
Time [s]
Gen
erato
rpow
erP
g[W
]
Figure 6.13: Measured (full) and sampled (dotted) generator power in function of time when a positivestep in the wind speed is applied during mode control.
0 5 10 15 20 25 30 35 400
20
40
60
80
100
120
Rotor speed Ω [rad/s]
Gen
erato
rpow
erP
g[W
]
v = 4 m/s
v = 5 m/s
Figure 6.14: Trajectory of operating point in speed/power plane for a positive step in the wind speed,together with the according wind turbine characteristics during mode control.
81
Chapter 7
Advanced applications of the activerectifier
Different types of wind energy conversion systems have been designed during the past fewdecades. These can be mainly categorized according to the used type of generator. As discussedin Chapter 2, the back-to-back converter with a permanent magnet generator seems to havesuperior characteristics. In this topology, the generator’s rotor speed is completely decoupledfrom the grid frequency by which the turbine can be controlled to a wide speeds range inorder to maximize the power output. The generated DC power is injected into the grid by theinverter, which is able to control active and reactive power to provide grid voltage stability.
In the back-to-back converter topology, there are two possibilities to rectify the variable threephase AC from the generator to a fixed DC voltage. The first possibility is to use a passivediode rectifier in combination with a boost chopper. The second possibility is the use of anactive rectifier which has been discussed in this thesis. In this chapter, a comparison betweenthese two types will be made by considering cost, complexity, efficiency and control flexibility.Next, some advanced applications of the active rectifier are explained which can improve theMPPT and allow for effective wind gust capture.
7.1 Comparison between passive and active rectifier
In Figure 7.1, the topology of a passive rectifier with boost chopper is shown. The three-phasediode bridge creates a variable DC voltage from the ’wild’ generator AC voltage. The boostchopper is necessary to convert this variable voltage to a higher, fixed DC voltage which canbe used by the grid-coupled inverter.
The inductor Lch is used for controlling the DC current, while the capacitor Cdc has the samepurpose as the DC-bus capacitors in the active rectifier.
The DC voltage created by the diode rectifier is not entirely constant but contains a 6th-orderharmonic. A capacitor Cch is placed at the output of the rectifier to reduce these voltage ripples.Its use is not essential for correct operation, but it has a large influence on the generator currentwaveform and its harmonic content. A small capacitance value will result rather in a squarewave current, illustrated by Figure 7.2a, while a larger capacitor will cause a more sinusoidal,pulsed behaviour (Figure 7.2b). However, both types of waveforms contain a lot of harmonicsand result in large torque ripples. Especially the current waveform from Figure 7.2b results ina clear torque ripple which is mainly determined by a 6th-order harmonic [41]. These ripples
82
Chapter 7. Advanced applications of the active rectifier
PMSG
Passive rectifier
Cch
Lch
Cdc
Vdc
Figure 7.1: Passive rectifier with boost chopper.
may result in increased wear of the ball bearings in the mechanical drive train, larger vibrationsand extra noise. Especially the vibration of the mechanical position sensor may easily resultin wrong position measurements so the machine supports need to be adequately damped. Thecurrent harmonics also have a detrimental effect on the generator efficiency because they resultin extra joule losses without creating more torque.
The active rectifier is able to create any desired current waveform on the terminals of thegenerator. In this thesis, a sinusoidal three-phase current (cf. Figure 7.2c) is applied whichresults in a constant active power and torque during steady state conditions. Large low-ordercurrent harmonics are not longer introduced. This results in a higher generator efficiency. Theactive rectifier also offers the possibility for a controllable power factor which can compensatefor undesired reactive power consumption. In the passive rectifier on the other hand, thepower factor is fixed for a particular operating point so reactive power consumption cannot beexcluded.
The complete control of the generator current by the active rectifier also implies that anydesired amplitude can be imposed, both positive or negative. This means that the directionof the power flow through the rectifier can be inverted. In the generator reference frame, apositive q-axis current will result in a power flow from the generator to the DC-bus. A negativecurrent will result in active power going from the DC-bus to the PMSG so a torque is createdin the same direction as the wind turbine torque. The permanent magnet machine will nowdrive the wind turbine. The passive rectifier does not offer this feature: active power can onlygo from the generator to the DC-bus because the power direction is fixed by the diodes.
Finally, there is also a difference between these two converters concerning cost and complexity.The active rectifier consists of three half bridge modules in order to create a three-phaseconverter. The cost of such a module is about e92. The passive rectifier needs only one half
(a) Passive rectifier withlow capacitance Cch
(b) Passive rectifier withhigh capacitance Cch
(c) Active rectifier
Figure 7.2: Generator current waveforms for active and passive rectifier.
83
7.1. Comparison between passive and active rectifier
bridge module in which one IGBT is installed as boost chopper. The other one is replaced bythe freewheel diode. Also some additional equipment needs to be installed: a diode rectifier, acapacitor Cch and an inductor Lch. For the DC power control, an extra measurement circuitneeds to be installed for measuring the current through Lch.
To make a brief comparison, the costs of these components for the two converters are listedin Table 7.1. The passive rectifier constructed by Freek Withouck [23] is used as referencefor the cost calculation. In his setup, two parallel electrolytic capacitors of 330µF, 450 V havebeen used for Cch. The inductor Lch is constructed by winding an E65 ferrite core with 1 mmcopper wire. The additional measuring circuit is a half bridge module with only the currentmeasurement circuit installed. The four electrolytic DC-bus capacitors (470µF, 500 V) are thesame for both setups.
Table 7.1: Comparison of costs between passive and active rectifier (in euro).
This comparison shows that the total cost for the active rectifier is about 40% higher than forthe passive rectifier. In the active rectifier, the price of the three half bridge modules is thelargest one. For the passive rectifier, the cost is mainly determined by the passive components.This comparison gives only an indication and is not complete. However, all other costs (DSP,casing, cooling, circuit protection, communication, etc.) are equal for both topologies and willnot largely influence the price difference, but they will surely lower the relative price difference.In general, this shows that the difference in cost for the two converters is quite limited andthat it is definitely not proportional with the number of installed IGBTs.
The passive rectifier has only one degree of freedom: the duty ratio of the boost chopper. Thisvalue controls the voltage at the input of the chopper to a desired level and the generatorrotates at a speed that corresponds to that voltage. A PI controller which calculates the dutyratio can be added in order to control the rotor speed or DC power.
The active rectifier, on the other hand, has six controllable switches to create a three-phasePWM modulated voltage. Complex controlling techniques such as vector control, field orienta-tion or direct torque control can be implemented. These result in a fast dynamic control of thegenerator torque and a more effective MPPT control due to shorter settling times and higheraccuracy.
It can be concluded that the active rectifier indeed offers more flexibility and improved generatorcontrol. The total cost of the converter is larger than the cheaper passive rectifier, but thedifference is limited. It is possible that the higher generator efficiency and better MPPT caneven result in a lower lifetime cost for the active rectifier. However, this can only be verifiedby comparing these two converters in combination with real wind turbines in similar testing
84
Chapter 7. Advanced applications of the active rectifier
conditions. In the following section, it is investigated how the generator efficiency is influencedby using an active rectifier. The larger control flexibility also offers new opportunities for theMPPT control. In the last two sections, it is investigated how the inversion of the active powerdirection can be used to improve MPP tracking.
7.2 Influence of current waveform on the generator efficiency
The generator is one of the elements that influences mostly the total efficiency of a wind turbineconversion system. First, the type of electrical machine gives an indication of its efficiency. Asexplained in Chapter 2, the first generators used in wind turbines were induction machines.Because this machine is only able to produce a torque if the magnetic rotor field is slippingrelatively to the stator field, power will be dissipated in the rotor windings. These rotor lossesimmediately result in a lower efficiency. Additionally, this machine consumes reactive powerso compensation techniques may be necessary to ensure power quality.
Second, the synchronous generator has been introduced in wind energy conversion systems,which has an inherently larger efficiency than the induction machine because rotor and statorfield are not longer relatively slipping. If the magnetic rotor field is created by permanentmagnets, even the joule losses due to the current in the DC winding are disappeared. Thepower factor can be varied along a wide range so the machine is also capable to producereactive power for injection to the grid. However, due to the field orientation, the PMSG willalways be a consumer of reactive power.
Not only the type of machine determines its efficiency. It also depends on the type of loador power converter that is connected to the generator. Also the actual operating point isimportant. In small wind turbines, generators are installed with a relatively low rated power.These smaller machines have a relatively large rotor resistance, which results in high Joulelosses compared to the rated power. These losses are mainly determined by the stator current,its waveform and the corresponding harmonics.
The passive rectifier with boost chopper, which has been discussed in the previous section,results in a lower generator efficiency due to the introduced stator current harmonics. Toinvestigate how the generator efficiency is improved by using an active rectifier, first, mea-surements need to be executed with the PMSG connected to a three-phase diode rectifier. Acapacitor of 500µF in parallel with a power resistor of 522 Ω is placed at the output, illustratedby Figure 7.3. The selected resistance corresponds to the MPP at a wind speed of 5 m/s. Atthis speed, the captured power of the wind turbine is:
Pt =1
2ρπr2CP,maxv
3 = 104.4 W (7.1)
The voltage measured at the output of the rectifier is equal to 208 V. The current through theresistor is then equal to 0.398 A (= 208 V/522 Ω) which results in the following DC power:
Pg = 82.9 W (7.2)
which concludes to the following generator efficiency for this particular situation:
ηg =Pg
Pt= 79.4% (7.3)
85
7.2. Influence of current waveform on the generator efficiency
PMSG
Passive rectifier
Cdc
VdcRdc
Figure 7.3: Setup for measuring generator efficiency.
The generator power output is validated by measuring the three phase voltages (Va, Vb, Vc)and currents (Ia, Ib, Ic), presented in Figure 7.4. The stator currents indeed contain a lot ofharmonics which result in the pulsed waveform. The instantaneous power is calculated as:
Pg = VaIa + VbIb + VcIc (7.4)
The generator power is shown in Figure 7.4 and has a mean value equal to 81.8 W which is fairlyequal to the previous power value measured at the DC-bus. The generator power contains a6th-order harmonic which corresponds to the torque ripple. The torque is calculated from theelectric power while the generator was rotating at a speed Ω of 34.9 rad/s (MPP at 5 m/s):
Tg =Pg
ηgΩ(7.5)
The torque ripple Tg is expressed relative to its mean value T g and is shown in Figure 7.5. Thetorque ripple contains clearly a 6th-order harmonic and has a maximum value around 20%.
From the voltage and current measured in one phase, also the power factor can be calculated.First, it is observed that the current waveform is lagging the voltage waveform. This meansthat the generator is consuming reactive power. The time difference between a zero-crossingof the voltage and one of the current is equal to 0.002 s. This corresponds to an angle betweenthe voltage and current phasor equal to 24. The power factor is thus equal to 0.91.
Next, the PMSG is connected to the active rectifier. The operating point is again set to theMPP at 5 m/s and the same measurements are executed. The results are presented in Figure7.6. As the stator voltages are PWM modulated, only the fundamental harmonics which arecalculated by the PI current controller are given. The phase currents are measured by theactive rectifier itself. These currents are indeed three-phase sinusoidal and do not longer havethe large low-order harmonics which were observed during the operation of the passive rectifier.
The instantaneous power is again calculated with Eq. 7.4 and presented in the same figure.The pulses are disappeared and the power signal does only contain some noise due to the PIcontrol action. Its mean value is equal to:
Pg = 84.1 W (7.6)
This value is validated by the power measurement in the active rectifier which gives a value of85.2 W. This value results in a generator efficiency of:
ηg =Pg
Pt= 81.6% (7.7)
86
Chapter 7. Advanced applications of the active rectifier
−0.04 −0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.04−200
−100
0
100
200
Time [s]
Volt
age
[V]
−0.04 −0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.04
−0.5
0
0.5
Time [s]
Curr
ent
[A]
−0.04 −0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.040
20
40
60
80
100
120
Time[s]
Gen
erato
rpow
er[W
]
Figure 7.4: Phase voltage, current and electric instantaneous power in function of time for a PMSGwith passive rectifier.
−0.04 −0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.04−40
−20
0
20
40
Time [s]
(Tg−
Tg)/
Tg
[%]
Figure 7.5: Torque ripple in function of time for a PMSG with passive rectifier.
87
7.2. Influence of current waveform on the generator efficiency
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08−0.5
0
0.5
Time [s]
Curr
ent
[A]
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
−100
0
100
Time [s]
Volt
age[
V]
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080
50
100
Time [s]
Gen
erato
rpow
er[W
]
Figure 7.6: Phase voltage (fundamental harmonic), current and electric instantaneous power in func-tion of time for a PMSG with active rectifier.
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08−40
−30
−20
−10
0
10
20
30
40
Time [s]
(Tg−
Tg)/
Tg
[%]
Figure 7.7: Torque ripple in function of time for a PMSG with active rectifier.
88
Chapter 7. Advanced applications of the active rectifier
Also for the active rectifier, the torque ripple is calculated and given in Figure 7.7. The rippleis not completely disappeared but surely reduced. The maximum ripple value is now equal to10%. The 6th-order harmonic is not longer present, but the signal still contains high frequentcomponents due to the PWM. These harmonics are filtered by the inertia of the drive trainand will not result in rotor speed oscillations.
Due to the field orientation, it is noted that the voltage and current phasor are nearly in phasewith each other. The power factor is now 0.99, which is almost perfect and a lot better thanthe power factor of the passive rectifier which was equal to 0.91.
When the generator was connected to the passive rectifier, the losses were equal to 21.5 W(= 104.4 W − 82.9 W). With the active rectifier, losses were only 20.3 W. The use of theactive rectifier thus results in a reduction of the generator losses with 6%. Of course, this valueonly gives a qualitative indication of the reduction in energy losses because efficiency valuesalways depend on the operating point. Close to the rated power of the generator, losses will berelatively smaller as the efficiency will be larger. The overall conclusion is that the replacementof the passive rectifier by the active one indeed results in an improved generator efficiency, thedisappearance of the large torque ripple and an improved power factor from 0.91 to 0.99 so lessreactive power is consumed. However, as the difference in power output is relatively small, it ishighly uncertain whether this larger efficiency will compensate the larger cost of the converter.As electricity market prices are quite low for the moment (about 50 e/MWh), the rated powerof small wind turbines is limited to a few kWs and wind availability is not larger than 1000hours/year, the break even time can become very large.
7.3 Improved MPPT by acceleration of the wind turbine usingthe PMSG
7.3.1 Introduction
An advantage of the active rectifier is its ability to control the generator power in two directions.In normal conditions, the power flow is from the turbine, through the generator and the rectifiertowards the grid. Due to the topology of the VSC, it is also possible to invert the power flowsuch that power from the grid is used to drive the PMSG because a torque is created in thesame direction as the wind turbine torque.
In the conventional MPPTs that were discussed in the previous chapter, the PMSG onlyoperated as generator. When the turbine had to accelerate, the generator torque was setto zero and only the turbine torque accelerated the rotor. This resulted in relatively longacceleration times due to the large rotor inertia. Especially at low wind speeds, the turbinetorque is relatively small so acceleration takes even longer.
By driving the wind turbine with the PMSG, the maximum power point can be reached muchfaster. Simulations show that acceleration periods can become 50% shorter by motoring withthe PMSG. However, the main disadvantage is that electric power is used from the grid for thisenhanced acceleration. The question is whether the generated energy yield by the improvedMPPT is larger than the amount of energy used from the grid for the faster acceleration.
The purpose of this section is to investigate whether the active rectifier is able to increase itsenergy output by improved acceleration. This concept is first implemented in the simulationmodel of the TSR control. Second, this strategy is implemented in the wind turbine emulator.
89
7.3. Improved MPPT by acceleration of the wind turbine using the PMSG
7.3.2 Principle
The algorithm of the TSR control is used because this shows clearly how the MPPT trackingcan be affected. Of course, this concept can also be implemented for other MPPT strategies.
To determine whether the performance can be improved, a method must be defined whichdescribes how the improvement can be calculated. First, a reference situation needs to bedetermined. This is the basic TSR control where a step in the wind speed is applied and thePMSG is not operating as motor. The expected rotor speed and power output for this situationcan be illustrated schematically in Figure 7.8 in dotted lines. The generator power goes to zeroso the turbine torque can accelerate the rotor towards the new MPP. Next, the generator powerstarts increasing again to its steady state value. From this step response, a time frame can bedefined starting from the moment the step in the wind speed occurs until the generator poweris settled at its steady state value. In this time interval, the generator power can be integratedto obtain the generated electric energy Enm during this transient:
Enm =
Tframe∫
0
Pg,nm dt (7.8)
This value is used as reference for the next situation where the PMSG can operate as motor.
t
t
Pg
Ω
Tframe
Without motoringWith motoring
+
+-
-
+ : gain due to motoring
- : loss due to motoring
Figure 7.8: Concept of enhanced acceleration in MPP tracking.
To allow the active rectifier of producing an accelerating torque in the generator, the currentlimiter at the end of the PI speed controller needs to be adapted. Until now, only positivecurrent reference values were allowed between zero and the rated generator current. From thissection on, the reference value can also be negative. The minimal value of the limiter determinesthe maximal motor torque. This is an important parameter for the MPPT control because it
90
Chapter 7. Advanced applications of the active rectifier
determines how large the acceleration will be, how much the transient will be shortened andhow much power will be used from the grid.
The rotor speed and generator power responses by additional motoring are also shown in Figure7.8 with full lines. Logically, the settling time for both rotor speed and generator power willbe shorter because the acceleration is larger. Because the settings of the current limiter arechanged, the generator power becomes negative during the first period of acceleration. Fromthe moment the rotor speed gets close to the new MPP, the generator power increases stronglyto generate a decelerating torque which slows the rotor down to the new steady state rotorspeed.
To determine whether the energy output is larger than the reference situation, the generatorpower is again integrated over the same time interval. The results is the generated energy Emot
by additional motoring:
Emot =
Tframe∫
0
Pg,mot dt (7.9)
Qualitatively, it is difficult to see whether the new energy output will be larger than its referencevalue. First, there is a large negative part in the power output which represents the energy usedfrom the grid. Second, there is a larger positive part which represents the gain in generatedenergy due to the faster acceleration by which the MPP is reached much sooner. By doingsimulations, the energy integrals can be calculated in the defined time interval. Finally, theperformance is expressed as a percentual improvement ζ:
ζ =Emot − Enm
Enm× 100% (7.10)
7.3.3 Influence of maximal motoring torque
The motor current is limited to Iq,max,mot by the saturator at the end of the speed control loop.To determine which value of Iq,max,mot maximizes the percentual improvement, ζ is calculatedfor a wind speed step from 4 m/s to 6 m/s while varying Iq,max,mot. First, the reference situationis simulated with the maximal motor current set to zero. The simulation result is presentedin Figure 7.10. The settling time for the generator speed is equal to 2.8 s, which becomes thelength of the reference time frame. Integration of the generator power over this time intervalresults in an energy output of:
Enm = 92.9 J (7.11)
Note that a generator efficiency of 90% has been taken into account for the energy calculation.
Next, the motor current limit is set to 0.8 A. The result of this simulation is shown in Figure7.11. The settling time for the generator speed is now 1.9 s. This is a reduction of 32%compared to the reference case which shows clearly that the motor torque indeed results ina larger turbine acceleration and a faster settling at the new MPP. The integration of thegenerator power leads to the following output energy:
Emot = 93.6 J (7.12)
In this case, ζ is equal to 0.75%. The energy output due to motoring is almost equal to thecase in which no motoring was used. If this simulation is however repeated with a generator
91
7.3. Improved MPPT by acceleration of the wind turbine using the PMSG
efficiency of 100%, Enm becomes equal to 98.9 J and the energy output with motoring is equalto:
Emot = 125.2 J (7.13)
Neglecting the generator efficiency results in a percentual improvement of almost 26.6%. Alower efficiency value has thus a tremendous effect on the power output. This is logic becausethis has two effects. First, it results in less generated power during the period the PMSG isoperating as generator. However, this is also valid for the non-motored case. Second, moreenergy is retracted from the grid than is effectively used for acceleration with the PMSGoperating as motor.
For all other values of the maximal motor current, energy outputs can be calculated. Theresults are presented in the following table:
Table 7.2: Energy output and percentual improvement for different maximum values of the motoringcurrent value.
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Iq,max,mot [A]
ζ[%
]
Figure 7.9: Procentual improvement in function of the maximal motor current.
92
Chapter 7. Advanced applications of the active rectifier
0 1 2 3 4 5
4
6
Time [s]
v[m
/s]
0 1 2 3 4 54
6
8
Time [s]
TSR
[-]
0 1 2 3 4 5
30
35
40
Time [s]
Ω[r
ad/s]
0 1 2 3 4 50
5
Time [s]
Tg
[Nm
]
0 1 2 3 4 50
100
200
300
Time [s]
Pg
[W]
Figure 7.10: Reference situation: simulated TSR control without PMSG motor operation.
The same values for the percentual improvement are also shown in Figure 7.9. The maximalmotor current is indeed the factor that mostly influences ζ. ζ is zero for Iq,max,mot equal tozero, but increases quickly from the moment the reference current increases. This particularstep in wind speed gives a maximal improvement of 1.94% when the maximal motor currentis equal to 0.5 A. For larger motor currents, ζ drops again to zero. For currents larger than1.0 A, the percentual improvement is even negative, which means that the system consumedmore energy than it could produce.
93
7.3. Improved MPPT by acceleration of the wind turbine using the PMSG
0 1 2 3 4 5
4
6
Time [s]
v[m
/s]
0 1 2 3 4 54
6
8
Time [s]
TSR
[-]
0 1 2 3 4 5
30
35
40
Time [s]
Ω[r
ad/s]
0 1 2 3 4 5
−5
0
5
Time [s]
Tg
[Nm
]
0 1 2 3 4 5
−200
0
200
Time [s]
Pg
[W]
Figure 7.11: Simulated TSR control with the maximal motor current set to 0.8 A.
In general, these percentual improvements are relatively small so the energy yield will belimited. Second, they are highly influenced by the maximal motor current, which has a differentoptimal value for every different situation. In addition, also the generator efficiency has a verysevere effect on the percentual improvement. Even from the moment its value is lowered to85%, the improvement values become negative for all possible motor currents. The overallconclusion is that using the PMSG as motor during common MPPT control will for most casesnot result in an improved energy output. However, in the next section, an application of usingthe PMSG as motor will be explained, which indeed results in a larger energy output.
94
Chapter 7. Advanced applications of the active rectifier
7.3.4 Experimental results
The concept of accelerating a wind turbine by using the PMSG as motor has also been testedon the wind turbine emulator controlled by the active rectifier. The TSR control that was usedin the previous chapter has been adapted in such way that the reference value for the q-axiscurrent also can become negative, but limited to the value Iq,max,mot. In the generator referenceframe, the stator current is for a negative q-axis current in antiphase with its respective EMF.
The experimental results for applying a step in wind speed from 4 m/s to 6 m/s with a maximalmotor current of 0.8 A, are presented in the following figures. This experiment corresponds tothe same situation that was simulated in Figure 7.11.
Figure 7.12 shows the rotor speed response in full line and the final steady state value in dashedline. The correct rotor speed that corresponds to the MPP at 6 m/s is achieved within a settlingtime that is nearly the same as in the simulations. Only, the overshoot is larger due to the samereason as for the normal TSR control. The speed controller has been slowed down to a lowersampling rate of 16 Hz to compensate the incorrect behaviour of the inertia compensation ofthe wind turbine emulator.
Figure 7.13 shows the generator power response for the same situation, which also settles tothe correct steady state value along the dashed line that corresponds to the new MPP. Thepeak in negative power is narrower than the one from the simulations. This is due to thelarge acceleration immediately after the step in wind speed, caused by the slow reaction of theinertia compensator. Because of this short acceleration period, the maximum motor current isnot achieved.
The plot of the generator power in function of the rotor speed in Figure 7.14 shows that thegenerator power becomes negative during the first part of the trajectory. This indicates thatthe PMSG indeed operates as motor and that energy is consumed from the grid. The generatorpower varies gradually until the desired rotor speed is reached. Next, it increases while therotor speed is overshooting to finally settle both to their optimal operation point.
0 2 4 6 8 1026
28
30
32
34
36
38
40
42
44
46
time t [s]
roto
rsp
eed
Ω[r
ad/s]
Figure 7.12: Rotor speed in function of time during TSR control with motoring.
95
7.3. Improved MPPT by acceleration of the wind turbine using the PMSG
0 2 4 6 8 10−100
−50
0
50
100
150
200
time t [s]
gen
erato
rpow
erP
g[W
]
Figure 7.13: Generator power in function of time during TSR control with motoring.
0 10 20 30 40 50−100
−50
0
50
100
150
200
rotor speed Ω [rad/s]
gen
erato
rpow
erP
g[W
]
v = 4 m/s
v = 6 m/s
Figure 7.14: Generator power in function of rotor speed during TSR control with motoring.
96
Chapter 7. Advanced applications of the active rectifier
7.4 Wind gust capture
The following results are also described in a conference paper [43] that is submitted for theIET RPG 2014 conference. This paper can be found in Appendix E.
7.4.1 Introduction
In general, small wind turbines should start if the wind speed is large enough. If the turbineinitially stands still and the wind speed is larger than the cut-in speed, a starting torque willarise on the blades which is large enough to let the turbine rotating. In literature, there isstill very little known about the starting behaviour of small wind turbines. In [37] however,a qualitative description of this phenomenon is given. In this paper, rotor speed and windspeed are measured during the start-up of a specific turbine with a rated power of 5 kW. Fromthese measurements, it can be concluded that the starting time can vary from 20 to 40 secondsdepending on the used pitch angle and on the mean wind speed during this period. However, asimple relationship between these variables is difficult to find due to the aerodynamic principlesbehind them. When the blades are rotating very slowly, the angle of attack (i.e. the anglebetween the wind flow at the leading edge and the chord line of the airfoil) is close to 90.In combination with the corresponding low Reynolds number at low wind speeds, there arevery little data known about the lift and drag coefficients in this region. Due to the high flowangle, the blades are stalled during the start-up such that very little lift is created. In thesame paper, it is also observed that after an initial acceleration of the rotor, a period of ’idling’occurs. The rotor turns slowly at a nearly constant rate because of the stalled blades. Whena new increase in wind speed occurs, the angle of attack gets large enough in order to producesufficient torque. The rotor will accelerate again and finally go to its steady state operatingpoint.
From this qualitative observation, it can be concluded that the starting torques for many smallturbines are low. If a short wind gust occurs when the rotor stands still, the turbine accelerationwill be limited and almost none of the wind energy will be captured. Not only the small torquecoefficients at small rotor speeds are a problem, also the relatively large rotor inertia results in alimited acceleration. This conclusion is general in wind turbine systems: the rotor inertia is themajor restriction for the performance of the MPPT. If the turbine should have no inertia, therotor speed could be controlled very fast such that the wind turbine would be at any momentin its MPP. The use of lighter composite materials can however decrease the mass of the rotorand thus the mass moment of inertia.
In a WECS which uses a permanent magnet generator, a third phenomenon occurs whichimpedes the starting. In these electric machines, a torque occurs on the rotor which tries toalign the rotor magnets with the stator slots into positions where reluctance is minimal. Thistorque is called the ’cogging torque’. The rotor won’t start to rotate until these static magneticforces are overcome by the turbine’s starting torque.
In this section, the PMSG will again be used as a motor to accelerate the rotor, which initiallystands still, from the moment a wind gust is detected. During this short period, electric energyis used from the grid to supply the PMSG so the turbine is easily started and the operatingpoint of the wind turbine can be brought near the maximum power point. It is the MPPT thatwill switch at the appropriate moment to the generator mode where electricity is producedand injected back into the grid. The energy that was used for acceleration will be largelyrecuperated together with the extra amount of energy captured by the turbine from the windgust.
97
7.4. Wind gust capture
This leads to an optimization problem in which the energy yield can be maximized. A longerperiod of motoring or a larger motor current will result in faster acceleration. However, alsomore electric energy will be used from the grid which can not be fully recuperated due tothe limited efficiency of the PMSG and the rectifier. A smaller motor current results in lessconsumed energy but the rotor speed doesn’t get large enough to allow the MPPT of capturingthe maximal possible amount of energy from the gust.
This trade-off will be investigated in this section. First, by means of simulations for many differ-ent wind gust profiles and different settings of the maximal motor current. Second, this controlstrategy will also be implemented in the real active rectifier to verify the simulation results.Finally, also the capture of wind gusts during normal MPPT operation will be discussed.
7.4.2 Wind gust definition
First, a clear definition must be given of a wind gust. In general, a wind gust is a brief increasein the wind speed. According to the US National Weather Service, gusts are reported whenthe peak wind speed reaches at least 16 knots (8 m/s) and the variation in wind speed betweenthe peaks and lulls is at least 9 knots (4.6 m/s). The duration of a gust is usually less than 20seconds.
This definition, however, gives no description of how the wind speed varies exactly during thegust. For the simulations, the wind speed needs to be described in function of time, such thata certain wind gust profile is necessary. A definition for such wind speed profile can be foundin a paper which discusses a gust-front loading factor that is used in civil engineering [40].
It describes the rapid changes of the wind speed with a non-stationary wind model that de-scribes a wind field varying over height and time:
v(z, t) = vg(z) · vg(t) (7.14)
in which v(z, t) is the gust wind field, vg(z) the vertical profile and vg(t) the time function of thewind gust. Because the rotor diameter of small wind turbines is limited to only a few meters,the wind speed variation across the front area of the rotor can be neglected. The interestingpart is the time function of the gust which is defined as:
v(t) = vmax sin
(π
tgt
)(7.15)
where vmax is the maximum wind speed value of the wind gust and tg the duration. This profileis shown in Figure 7.15.
v(t)
vmax
tg t
Figure 7.15: Wind gust profile.
98
Chapter 7. Advanced applications of the active rectifier
7.4.3 Theoretical concept and simulations
First, the wind gust capture strategy will be implemented in the simulation model to calculatethe energy yield that can be achieved for different sizes of wind gusts. The CP(λ)-profile thatwas used previously has no starting torque: the CT(λ)-curve is zero at the origin cfr. Figure3.5. To determine a starting torque, the data that is given in [38] is used to determine an offsetvalue that can be added to the turbine torque in a region around the TSR equal to zero. Thisway, the wind turbine will be able to start from the moment wind starts flowing around theblades.
In [38], a 600 W wind turbine with a PMSG has been tested. This setup resembles the windturbine system that is used in this thesis. The start-up behaviour is investigated by measure-ments on a real wind turbine. After a time of almost 20 seconds, the turbine has reached arotor speed of 25 rpm. This results in a mean acceleration of 0.13 m/s2. If this accelerationvalue is combined with the turbine inertia of 0.724 kgm2 that is used in this thesis, the startingtorque should be equal to 0.095 Nm. Note that this is a small value compared with the turbinetorques that arise when the turbine is at normal operation within the nominal wind speedrange. Of course, this result only gives a qualitative view of the range of starting torques. Theactual value can only be determined by measurements on a real turbine. However, the mainconclusion is that these starting torques are rather small and that the start-up can take sometime.
In the simulation model, an offset of 0.1 Nm is given to the turbine torque. First, the referencesituation is simulated for a wind gust without using the generator as motor. The result is shownin Figure 7.16. The sinusoidal curve (dotted line) gives the optimal rotor speed that resultsfrom a wind gust with vmax equal to 3 m/s and tg = 5 s. The other line is the resulting rotorspeed. It can be observed that the rotor speed remains very small and doesn’t become largerthan 0.2 rad/s. In other words, the rotor remains almost at standstill and does not captureany power.
0 1 2 3 4 5 6 70
5
10
15
20
25
Time [s]
Roto
rsp
eed
Ω[r
ad/s]
Figure 7.16: Simulated rotor speed and its optimal reference value in function of time for a wind gustwithout motoring.
Similar to the TSR control with the improved acceleration, a clear definition must be given
99
7.4. Wind gust capture
of how the energy yield by motoring during a wind gust can be expressed. The comparisonis directly made with the kinetic energy Egust contained in the wind gust. This value can beobtained by integrating the wind power P0 over time:
Egust =
∞∫
0
P0 dt =
∞∫
0
1
2ρπr2v3 dt (7.16)
The actual electric energy Eelec that is produced by the WECS is calculated by integration ofthe generator power:
Eelec =
∞∫
0
Pg dt (7.17)
With these two values, a capture coefficient ξ can be calculated as the ratio of the generatedelectric energy to the kinetic wind energy, which represents the relative captured amount ofenergy:
ξ =Eelec
Egust(7.18)
In the best scenario, ξ will be equal to 0.44 which is the maximal power coefficient of the windturbine. This means that the active rectifier is able to control the rotor speed at any momentto the optimal speed corresponding with the wind speed profile such that the maximal possibleamount of wind energy has been captured.
To illustrate the operation of the controller, the same wind gust as in the reference situationis applied but now the PMSG is also able to drive the wind turbine with a maximal q-axisstator current equal to the rated current. The result is shown in Figure 7.17. At the start ofthe gust, the generator torque will become negative because the q-axis motor current limit isset different from zero. The generator now operates as a motor and helps the wind turbineto accelerate towards the optimal rotor speed. When the rotor speed gets near its optimalvalue, the MPPT controller sets the q-axis current again to a positive value. The PMSG isnow operating as generator because the generator power is positive. There is a net energyproduction if the integral of the generator power is positive. If not, more energy from thegrid is used for acceleration than could be produced by the generator. Again, it is clear thatthe turbine inertia is the limiting factor which prohibits the rotor speed to follow its optimalsinusoidal trajectory for maximal power output at any moment. The capture coefficient ξis calculated form the wind speed and generator power responses and is 0.18. A generatorefficiency of 90% has been taken into account.
ξ depends on the wind gust profile. Figures 7.18a, 7.18b, 7.18c show the capture coefficientin function of the duration and the peak value of the wind gust for different maximal motorcurrents Iq,max,mot equal to 0.3 Inom, Inom and 3 Inom respectively. Inom is the peak value ofthe rated RMS current from the generator datasheet. Missing values indicate that the capturecoefficient is smaller than zero and thus more power is used to accelerate than could be producedby the wind turbine.
First, it should be noted that ξ is largely influenced by the maximal motor current. It can beconcluded that the larger Iq,max,mot is, the higher the amount of generated electricity will be.The highest capture coefficients are obtained when the maximal value of the current limiter isset equal to the maximal allowed stator current in the PMSM. This current is normally twoto three times higher than the rated current. This operation is allowed for only few secondsbecause otherwise the machine would overheat due to the excess Joule losses.
100
Chapter 7. Advanced applications of the active rectifier
Second, the controller is able to capture most power from long and large wind gusts. The longerthe wind gust, the more time the MPPT controller has to reach the optimal rotor speed. Theexplanation is that the rotor inertia is the most important factor which impedes the MPPTof reaching the optimal rotor speed. The larger the wind speed, the larger the turbine torqueis. This helps the PMSM to accelerate the rotor and reach the MPP faster. The capturecoefficient can never be higher than the maximal power coefficient CP,max equal to 0.44 (forthis turbine). No more energy can be converted by the rectifier than could be captured bythe turbine. The capture coefficients from the simulations however saturate at a lower valuebecause the generator efficiency has been taken into account.
Finally, it is observed that some wind gusts with a small duration tg or peak value vmax resultin negative capture coefficients. For these gusts, the active rectifier may not be started, becausethis would otherwise result in a net consumption of electric energy.
It can be concluded that it is worthy to use the PMSG as motor to start and accelerate thewind turbine to follow the wind gust profile. The larger the peak value vmax, the larger theduration tg and the larger the maximal motor current Iq,max,mot, the more energy from thewind gust can be captured.
0 1 2 3 4 5 6 70
1
2
3
Time [s]
v[m
/s]
0 1 2 3 4 5 6 70
5
10
15
20
25
Time [s]
Ω[r
ad/s]
0 1 2 3 4 5 6 7−150
−100
−50
0
50
100
150
Time [s]
Pg
[W]
Figure 7.17: Wind speed, rotor speed and generator power in function of time for wind gust capturewith motoring.
101
7.4. Wind gust capture
2
4
6
8
10
2
3
4
5
6
7
0
0.1
0.2
0.3
0.4
tg [s]vmax [m/s]
Captu
reC
oeffi
cien
t[-]
(a) Iq,max,mot = 0.3 Inom
2
4
6
8
10
2
3
4
5
6
7
0
0.1
0.2
0.3
0.4
tg [s]vmax [m/s]
Captu
reC
oeffi
cien
t[-]
(b) Iq,max,mot = Inom
2
4
6
8
10
2
3
4
5
6
7
0
0.1
0.2
0.3
0.4
tg [s]vmax [m/s]
Captu
reC
oeffi
cien
t[-]
(c) Iq,max,mot = 3 Inom
Figure 7.18: Capture coefficient in function of wind gust parameters and maximal motor current.
102
Chapter 7. Advanced applications of the active rectifier
7.4.4 Wind gust detection
The discussed wind gust capture strategy only results in net positive energy outputs for windgust which are large enough both in amplitude and duration. From Figure 7.18c, it is concludedthat the minimal peak value is about 2 m/s and the duration has to be larger than 2 seconds.Only in this case, the rectifier is allowed to start the wind turbine by using the PMSG. Becausethe wind gust profile is not known a priori, it has to be estimated by using information that isavailable at the very beginning of the gust (suppose t = 0).
For the wind gust detection strategy, the wind speed first derivative v(0) is used to knowthe initial wind speed change. With this value, a primary separation can be made. A toolarge derivative may indicate a sharp wind gust with high peak value and a small duration.From Figure 7.18c, it can be noted that for these wind gusts no positive energy output can beobtained, so the converter should not be started. Same for too small initial derivative values,which correspond with weak wind gusts.
This first condition can be used to make a separation during the few milliseconds after themoment a wind gust is detected. However, this condition only does not eliminate all gusts forwhich the energy output can be negative. For that purpose, another value κ has to be used toexpress a new condition. κ is equivalent with the product of the wind gust parameters tg andvmax but can not be measured directly. This value is calculated by using the wind speed firstderivatives v(0) at time zero and v(0.5), 0.5 seconds after the start of the wind gust:
v(0) = vmaxπ
tg
v(0.5) = vmaxπ
tgcos
(π
tg0.5
)(7.19)
(7.20)
This system of equations is solved for tg and vmax, of which the product corresponds to:
κ =v(0)
arccos2(v(0.5)v(0)
) (7.21)
This calculation however is executed after the converter is already started to track the windgust. If κ is lower than 18, the wind gust is an inappropriate one and the converter is shutdown again. If the condition is not fulfilled, operation will be continued. This behaviour can beaccepted, as the half of a second is only a very small time in which the wind turbine will hardlybe accelerated due to its inertia. Because the rotor speed is still very small, the consumed (andthus lost) electric power will be limited.
The conditions are obtained experimentally by observing the first derivative at time zero and attime 0.5 for different wind gusts. The resulting conditions can be presented by the decision treein Figure 7.19. First, the condition, which concerns the initial wind speed derivative, is testedby comparing it with two limit values. Next, after 0.5 seconds, the wind speed derivative isagain measured and used to verify the second condition which states that κ needs to be smallerthan 18. In that case, the converter will be shut down again. This results in a value ε equal toone or zero, whether the observed wind gust is an appropriate (1) or inappropriate (0) one.
103
7.4. Wind gust capture
0.5 < v(0) < 7.5
ε = 1ε = 0
ε = 0ε = 1
after 0.5 s
NO
YES
YES
NOκ < 18
Figure 7.19: Decision tree for windgust detection
24
68
10
2
4
6
0
0.2
0.4
0.6
0.8
1
vmax [m/s]tg [s]
ε[-]
Figure 7.20: Windgust detection in function of wind gust peak value and duration.
These conditions are tested for the same array of wind gust amplitudes and durations that wasused in the previous wind gust simulations. The result is shown in Figure 7.20 where it can benoted that the appropriate wind gusts corresponds relatively well to the result of Figure 7.18c.Also some wind gusts with large amplitude and small duration are rejected which could actuallyresult in positive energy outputs. This is however acceptable because these wind gust are quiterare and their capture coefficients are rather small. Additionally, the inertia and response timeof the practical setup will also prohibit to capture the full amount of the simulated energy
104
Chapter 7. Advanced applications of the active rectifier
output for these type of gusts.
The same decision tree is implemented in the controller of the active rectifier. The wind speedis sampled at 160 Hz and the wind speed derivative is calculated as follows:
v(i) = (v(i)− v(i− 10)) · 16s−1 (7.22)
This way, the noise due to the differentiation action can be reduced.
7.4.5 Experimental results
To illustrate that this wind capture strategy can be implemented in the active rectifier, a windgust with a duration of 5 seconds and a peak-value of 3 m/s has been programmed in the windturbine emulator. Together with the active rectifier, it remains in standby until an externalstart signal is received. After the trigger, the wind speed value starts varying along the windgust profile and the value is transmitted to the active rectifier. The active rectifier reacts bysetting the PMSG current to the maximum allowable motor current to accelerate the windturbine. Once, the MPP is reached, the TSR tracking controller switches to the generatormode such that electric power is produced.
First, the wind gust is applied to the active rectifier in which the motoring ability is disabled.The result is shown in Figure 7.21. Note that the rotor speed is not exactly zero, but thatthe rotor is already rotating at a low speed of 2 rad/s before the wind gust is applied. This isbecause the Danfoss drive of the emulator blocks the rotor when it is at full standstill. Fromthe moment the windgust is detected, the active rectifier sets the generator current to zeroby which the rotor can accelerate due to the turbine torque. When the rotor speed crossesits sinusoidal reference value, the generator torque increases again to its maximal value tohave maximal deceleration of the wind turbine. Once the rotor speed gets again lower than2 rad/s, the converter is shut down and the turbine keeps rotating at this low speed. Otherwise,the rotor could start oscillating around its standstill positions. In a normal wind turbine, amechanical brake should stop the wind turbine. The generator power remains all the time equalto zero, until the PMSG starts slowing down the wind turbine because the generator currentgets positive. This results in a small peak of generated power. The small part where thegenerator power gets negative is due to the q-axis stator voltage which gets negative becauseof the small EMF value at low speed and the voltage drop (resistive+inductive) because of thelarge q-axis current.
Figure 7.22 shows the same situation but now the PMSG is able to operate as motor. Theoverall conclusions is that the acceleration is improved, so the rotor speed is able to followthe wind gust profile. This figure can also be compared to Figure 7.17 which shows the samesituation in the simulation. It can be noted that the rotor acceleration in the lab setup is larger.This is because of the inertia compensation which commands the Danfoss drive to produce abraking torque to reduce the acceleration, but the Danfoss drive can only produce positivemotoring torques. The maximal motor current is also limited to 0.6 A, otherwise an internalerror in the Danfoss occurs which blocks the rotor at standstill. The combination of theselimitations of the wind turbine emulator results in the fact that the generator power deviatesfrom the result of the simulation.
105
7.4. Wind gust capture
0 1 2 3 4 5 60
1
2
3
Time [s]
v[m
/s]
0 1 2 3 4 5 60
10
20
Time [s]
Ω[r
ad/s]
0 1 2 3 4 5 6−0.5
0
0.5
1
Time [s]
i q[A
]
0 1 2 3 4 5 6
0
10
20
Time [s]
Pg
[W]
Figure 7.21: Wind speed, rotor speed, stator current and generator power in function of time at windgust capture without motoring.
106
Chapter 7. Advanced applications of the active rectifier
0 1 2 3 4 5 60
1
2
3
Time [s]
v[m
/s]
0 1 2 3 4 5 60
10
20
Time [s]
Ω[r
ad/s]
0 1 2 3 4 5 6−1
0
1
Time [s]
i q[A
]
0 1 2 3 4 5 6
−50
0
50
Time [s]
Pg
[W]
Figure 7.22: Wind speed, rotor speed, stator current and generator power in function of time at windgust capture with motoring.
107
7.4. Wind gust capture
7.4.6 Wind gust capture during normal MPPT operation
Until now, only wind gusts were investigated which occurred at a moment where the rotor wasinitially at standstill. The use of the PMSG as motor seemed very useful not only to followbetter the wind speed profile, but also to help the wind turbine to start up. This advantagedisappears when a wind gust occurs at a moment that the turbine is already rotating. Now,it is investigated how the MPPT controller reacts at such wind gusts. In the previous sectionwhere the TSR control with additional motoring was discussed, the conclusion was that in mostcases the energy output was nearly equal to the respective reference situation. This conclusionwas made for steps in wind speed. Here, the reaction of wind gust profiles is investigated whichcan possibly result in other conclusions.
In analogy with the previous section, the energy yield is again expressed as a percentual im-provement ζ. For the array of values for vmax and tg, each time the non-motored situationand the motored situation are simulated. The energy outputs are calculated by integration ofthe generator power over the same time interval. This interval is determined from the start ofthe wind gust to the moment the generator power is settled at its steady state value. As thisinterval differs for the motored and non-motored situation, the longest one is taken as timeinterval for the integration. For the motored situation, the maximal motor current is set tothree times Inom. From Figures 7.18a to 7.18c, it was concluded that for this value the capturecoefficients were maximal for wind gusts at standstill.
In Figure 7.23, the percentual improvements for different windgusts starting from 2 m/s areshown. The value vmax is the wind gust amplitude and adds with the starting value. tg is stillthe duration of the wind gust. Several conclusion can be made from this figure.
First, it can be concluded that the percentual improvement varies clearly in function of thewind gust parameters. For some types of gusts, the energy output can be increased by a factor3 to 4. For weak wind gusts with a peak value lower than 2 m/s, ζ is negative. Second, it isobserved that the improvement is maximal for wind gusts with a duration around 4 seconds.For longer gusts, ζ decreases again. This contradictive observation can be explained as follows.Besides the motor torque of the PMSG, the turbine torque of the wind turbine itself is stillpresent. For the non-motored situation, the energy output is already high due to the fact thatthe turbine torque has time enough to accelerate the rotor towards the optimal rotor speed. Bymotoring, the MPP tracking is improved, but the additional output energy is relatively smallcompared with the reference situation. This results in a smaller percentual improvement forthese gusts.
In Figure 7.24, the result of the active rectifier operation without motoring during normal TSRcontrol is shown when a wind gust is applied with an amplitude of 3 m/s and a duration of 5seconds starting from 2 m/s. During the largest part of the gust, the stator current remainsequal to zero. The rotor accelerates only due to the turbine torque of the wind turbine emulator.When the optimal rotor speed is reached, the q-axis reference current increases to track theMPP and finally, both the rotor speed and generator power settles to their previous steadystate values.
Next, the same wind gust is applied but the negative limit of the current saturator is set to Inom.The result is shown in Figure 7.25. From the moment the gust starts, the current referencewill now become immediately negative and a motor torque is produced. Now, the MPPT isable to control the rotor speed close to its optimal value. From the moment the top of the
108
Chapter 7. Advanced applications of the active rectifier
gust is reached, the generator power becomes positive again and electric power is injected intothe grid. When the stator current reaches the maximal allowable generator current, it can beobserved that also the inertia compensation comes to action by reducing the deceleration ofthe rotor. Finally, 3 seconds after the end of the wind gust, the rotor speed will be settledagain to its regime value. One second later, also the generator power has reached the steadystate condition.
24
68
10
1
2
3
4
5−100
0
100
200
300
400
500
tg [s]vmax [m/s]
Per
centu
alim
pro
vem
ent
[%]
Figure 7.23: Percentual improvement in function of wind gust peak value and duration for a maximalmotor current equal to 3 Inom and wind gust starting at 2 m/s.
7.5 Conclusion
The active rectifier has some interesting advantages compared to the passive rectifier with boostchopper. The high controllability of the stator current which allows for torque control resultsin a fast and accurate MPPT. Additionally, the generator efficiency increases due to the lowerharmonic distortion in the current. The additional energy output can however not compensatefor the higher converter cost (+40% compared to the passive rectifier).
Besides the improved efficiency, the active rectifier has also the ability to operate the PMSGas motor. This way, the MPPT can be improved by helping the wind turbine acceleratingduring wind increments. This strategy applied during normal TSR control results for somecases in an improved energy output. The percentual improvement is limited to only one or twopercent and is highly affected by the generator efficiency. Additionally, the maximum allowablemotor current which results in the optimal energy output depends on the type and size of windchange, such that a control strategy is difficult to implement. The overall conclusion is that thisimproved MPPT control will be most of the time not beneficial due to the limited generatorefficiency.
109
7.5. Conclusion
0 2 4 6 8 10
2
4
6
Time [s]
v[m
/s]
0 2 4 6 8 1010
20
30
Time [s]
Ω[r
ad/s]
0 2 4 6 8 10
0
0.2
0.4
Time [s]
i q[A
]
0 2 4 6 8 10
0
20
40
Time [s]
Pg
[W]
Figure 7.24: Wind speed, rotor speed and generator power in function of time at wind gust capturewithout motoring.
The motor operation of the PMSG does have a useful application in the energy capture of windgusts. Especially in those situations where the wind turbine is at standstill and a wind gustis applied, the energy output can be largely improved. Here, the maximum motor current hasto be as large as possible to maximize the energy yield. The maximal current (which is twoto three times larger than the rated current) can only be used during a short period of time,without overheating the machine. Only gusts with a sufficiently large duration and peak valueresult in a positive energy yield. A peak detection strategy has been discussed to detect theseappropriate wind gusts. Also for the capture of wind gusts during normal MPPT operation, theenergy yield can be improved, especially for gust with a high peak value and a short duration.
110
Chapter 7. Advanced applications of the active rectifier
0 2 4 6 8 10
2
4
6
Time [s]
v[m
/s]
0 2 4 6 8 1010
20
30
40
Time [s]
Ω[r
ad/s]
0 2 4 6 8 10−1
0
1
Time [s]
i q[A
]
0 2 4 6 8 10−100
0
100
Time [s]
Pg
[W]
Figure 7.25: Wind speed, rotor speed and generator power in function of time at wind gust capturewith motoring.
111
Chapter 8
Conclusions and future research
This final chapter gives a summary of the research that has been performed during this thesis.The most important conclusions and results are discussed. Finally, some possibilities for futureresearch on this topic are proposed.
8.1 Conclusions
Chapter 1 illustrated the installed capacity and energy production of wind turbines in Belgiumand the European Union. Because of the EU policies on energy saving, wind energy willbecome an important energy resource in the near future so research has to be executed in orderto improve efficiency. Especially in small wind turbines, an opportunity for enhanced efficiencyexists by improving the maximum power point tracking. For every wind speed, an optimalrotor speed exists. MPPT has the purpose to control a wind turbine’s rotor speed to thatoptimal speed.
Chapter 2 gave an overview of the different wind energy conversion systems that have beendesigned during the past few decades. Of all these systems, the back-to-back converter incombination with a permanent magnet synchronous generator seems to have superior char-acteristics. With this converter, the generator speed is completely decoupled from the gridfrequency. The rotor speed can be controlled to any value within its operational range. Thecomplete amount of generated active power is rectified and delivered to a DC-bus. Both apassive or active rectifier can be used for this purpose, but the active one has better propertieswhen it comes to control flexibility, generator efficiency and power factor. Next, a grid-coupledinverter converts this DC power back to AC power for injection into the grid while regulatingactive and reactive power independently. The PMSG is the perfect machine to be used with aback-to-back converter because of its high efficiency, compact design and large number of polesby which the use of a gearbox becomes unnecessary. It is also very suited to be used for highdynamic control strategies, like vector control, field oriented control or direct torque control.
Chapter 3 discussed the modelling of the following components of a wind turbine conversionsystem: the wind turbine, the PMSG and the active rectifier. For each of them, a MatlabSimulink model has been described. For the wind turbine model, a specific wind turbinecharacteristic has been selected from literature. The generator is modelled by expressing theelectrical stator equations in a synchronous reference frame. This system offers great advantagesfor the implementation of field oriented control which controls the generator torque. The activerectifier consists of a three-phase voltage source converter with six PWM controlled IGBTs.The field orientation of the PMSG is performed by a current control loop, which consists of
112
Chapter 8. Conclusions and future research
two PI controllers (one for each axis of the synchronous reference frame). These have beendesigned theoretically and are validated by the simulation results. A PI speed control loop isadded to control the rotor speed, which is the basis of the MPPT control strategies.
In Chapter 4, four different MPPT control strategies are discussed. First, there theoreticalconcepts are introduced. Second, they are implemented in a simulation model and the ro-tor speed and generator power responses are given for a step in the wind speed. In thesesimulation models, the field oriented control is assumed to operate perfect and without anydelay. This severely reduced simulation times. The first method, the TSR control, controlsthe wind turbine to the fixed optimal tip speed ratio which is known from the wind turbinecharacteristic. The TSR control results in the fastest response of all MPP trackers but needsan accurate measurement of the wind speed and thus requires an anemometer. The powercontrol method and hill climber do need not any measurement of the wind speed but requiresthe measured generator power. The power control method needs the knowledge of the optimalpower coefficient which expresses the optimal turbine power in function of the rotor speed.The hill climber does not require any knowledge about the wind turbine. The settling timefor these two methods during wind speed steps is three to four times longer than with TSRcontrol. Additionally, the hill climber shows hysteresis around the optimal rotor speed. Thefourth method, the mode controller, is a hill climber which uses a variable step size. Its settlingtime comes close to the one of the TSR control but doesn’t need any measurement of the windspeed or any experimental data of the specific wind turbine.
For this thesis, a lab setup has been designed and constructed for experimental validation ofthe control strategies. Its construction is described in Chapter 5. First, a new wind turbineemulator has been built based on a design of ir. Jan Van de Vyver. This appliance simulatesthe dynamic behaviour of a small-scale wind turbine. This design has been extended witha CAN module for communication with other power converters. By using a motor with alarge pole number, the gearbox could be omitted which results in a so-called direct drive.Next, the active rectifier has been constructed which consists of three half bridge modules.These modules not only contain two IGBTs, its drivers and a protection circuit, also circuitsfor voltage and current measurement are installed. The three module are controlled by adigital signal processor in which the current controller, speed controller and MPPT controllerare programmed. The DSP also provides some protections for over-current, over-voltage andIGBT faults. The correct operation of the field oriented control is validated by investigatingthe current control and the alignment between the electromotive force and the stator current.A step response of the current controller has been acquired and compared with the simulationmodels. The settling times matched with each other. Only the overshoot of the real currentcontroller was larger than the simulated response.
In Chapter 6, the four MPPT strategies, which were simulated in Chapter 4, have been imple-mented in the active rectifier. First, the TSR method is discussed. The active rectifier controlsthe wind turbine emulator to the appropriate rotor speed but the settling time seems shorterthan what could be expected from the simulations. The reason for this phenomenon is theinertia compensation control inside the wind turbine emulator. Because the physical inertia ofthe lab setup is much smaller than the real inertia of a wind turbine, an inertia compensatoris used which applies a compensating torque based on the measurement of the rotor acceler-ation. To eliminate noise due to differentiation, low-pass filters are used which increases thereaction time. The sample rate of the speed controller needed to be lowered in order to give theinertia compensation enough time to react. Now, correct settling times are observed but theovershoot is slightly increased. The power control gives correct results because this is already
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8.2. Future research
a slow method with settling times around 20 seconds compared to 3 seconds for TSR control,both for a step of 1 m/s. Also the hill climber and mode control result in correct behaviourafter lowering the sampling time of the speed controller. Only the power measurement wasquite difficult because the signal needed to be severely filtered in order to get useful values. Thesame conclusion as in Chapter 4 arises: the TSR control is the fastest MPPT, while the modecontrol is the fastest, sensorless control method. The hill climber and power control methodgives correct results but result in long settling times.
Chapter 7 focusses on the differences between the active and the passive rectifier. First, aglobal comparison is made according to the cost, complexity, control flexibility and generatorefficiency. The generator efficiency is measured both in combination with the active and passiverectifier. An active rectifier indeed eliminates the 6th harmonic in the generator torque ripplewhich was observed during operation with a passive rectifier. This results in less generatorlosses and a higher generator efficiency. The cost of an active rectifier is about 40% larger.This higher cost can however not be compensated by the extra energy production due to theimproved generator efficiency. The higher cost can only be justified by the additional controlpossibilities. The active rectifier is able to control the power flow in two directions by which thePMSG can operate both as motor or generator. Standard MPPT can be improved by usingthe PMSG as motor to help the turbine accelerating during positive wind steps. However,the additional energy output is quite limited because most of the extra generated energy isused for acceleration. Second, the percentual improvement due to motoring is optimal for onlyone value of the maximal allowed motor current which also depends on the specific situation.Larger energy yields can be obtained during wind gust capture when the wind turbine is atstandstill. In this situation, the generator helps the turbine to start and accelerate to theoptimal rotor speed. The energy capture is maximal if the maximal motor current reference isequal to the maximal allowable stator current. A net energy output is obtained for wind gustswith a sufficiently large peak value and duration. To make a separation between appropriateand inappropriate wind gusts, a wind gust detection strategy has been proposed which usesthe first derivative of the wind speed.
8.2 Future research
8.2.1 Application in back-to-back converter topology
In this thesis, the active rectifier has been discussed which is only one part of the back-to-backtopology. An inverter needs to be added to supply the generated DC power to the grid. Theinverter topology is shown in Figure 8.1. The active rectifier can be modelled as a current sourceconnected to the DC terminals. The inverter output is connected to the grid by means of a LCfilter to eliminate injection of the switching harmonics. The control strategy is comparable withthe active rectifier control. The grid current is controlled in a synchronous reference frame withthe d-axis along phase A. The voltage phase is determined by using a phase locked loop (PLL).Two PI controllers are used to control the d and q-axis independently. The d-axis current setsthe active power and is determined by the DC-bus voltage regulator. The measured DC-busvoltage is compared with a reference value and a PI controller results in the d-axis currentreference value. The q-axis current can be set equal to zero to have a power factor equal toone or can be set different of zero to control the reactive power.
Such grid-side coupled inverter has been constructed by Jonas De Kooning [22] and can beused in combination with the active rectifier. In extended research, these two converters canbe connected to each other to investigate their combining behaviour. In addition, the feeder
114
Chapter 8. Conclusions and future research
at EELAB can be used to simulate a distribution grid and to investigate power quality issues.The active rectifier in combination with the inverter is then a distributed generator (DG) unitin the grid.
Idc Cdc
a
bc
Lf
Cf
Vdc
Figure 8.1: Grid-coupled inverter topology
8.2.2 Testing with real wind turbine
The active rectifier in this thesis has been constructed to be used in combination with thewind turbine emulator. This emulator gave some complications according to correct transientbehaviour. The inertia compensation control seemed too slow to react on fast speed variationscaused by the rectifier. There are two solutions for this problem. The first one is to disablethe inertia compensation and add additional inertia to the drive shaft, corresponding with thereal turbine inertia. This would imply that an aluminium disk with a radius of 25 cm and athickness of 6 cm should be connected to the shaft with a gear ratio 1:4 such that the rated diskrotation speed would be 2000 rpm. Installing such fast rotating heavy disk needs a complexand strong construction with adequate safety measures.
Better is to connect the active rectifier to a real wind turbine. By this, the inertia compensationissue has disappeared and more realistic measurements can be made. In this real life conditions,it can be investigated how the performance of the different MPPT methods is influenced. Alsolong term measurements can be made which can give an answer to questions on cost and powerefficiency of the complete wind turbine system.
8.2.3 Minimizing core losses and sensorless control
In this thesis, the d-axis current reference of the generator has always been set to zero in orderto have field orientation. This resulted in optimal torque control, but also in a little reactivepower consumption by the generator. The d-axis current can also be controlled in order tohave a power factor equal to one. However, the effect of this control will be negligible as itis observed during this research that the power was already very good during field orientedcontrol. Another possibility is to reduce the core losses in the PMSG by controlling the d-axiscurrent. In [27], an efficiency optimization is given which tries to minimize the stator flux andthe core losses.
Another improvement for the field oriented control is the elimination of the encoder. Theinstallation of such a device results in a larger cost, additional circuitry and increased mainte-nance. This sensor is also very sensible to vibrations which can result in useless output data ifthe machine suspension is not properly damped. Instead of using a position sensor, the rotor
115
8.2. Future research
position can also be estimated by measuring the stator voltages and currents. The necessarymeasurement circuitries are already available on the half bridge modules, thus no additionalcosts have to made. Different position estimation strategies can be used [1]:
• Rotor position estimation based on EMFThis is the most easy and frequent used method. The EMF phasor is calculated basedon the knowledge of the stator resistance and inductance. The EMF space vector corre-sponds directly to the rotor position. The sensibility of these parameters (especially therotor resistance varies due to temperature and skin and proximity effect) results in poorperformance at low speed.
• Rotor position estimation based on stator flux linkageThe rotor postion can also be estimated by calculation of the stator flux linkage in astationary reference frame, which only requires the stator resistance:
Ψα =
∫(Vα −RsIα)dt (8.1)
Ψβ =
∫(Vβ −RsIβ)dt (8.2)
This strategy can have problems with integration drift and resistance variations. Anotherdrawback is that the initial rotor position is unknown.
• Rotor position estimation based on observer methodIn this method, the rotor position is calculated by using the dynamics of the machinemodel which has the same inputs as the real machine. The errors in the states betweenthe modelled and the real machine are used to correct the estimations. This method ishighly dependent on fluctuations of the machine parameters.
116
Appendix A
Datasheet of PMSG
Datasheet of the Ziehl-Abegg MK106-CKN.14L permanent magnet synchronous machine
CAN is the abbreviation of Controller Area Network and is a method to let microcontrollerscommunicate with each other. Originally, it was used in the automotive sector, but now itis widely adopted in industry. It is a serial communication protocol in which 8 bytes can betransmitted in one message with transfer rates up to 1 Mbit/s.
A CAN network consists of different nodes which are connected with each other through theCAN bus. Each node consists of the following elements:
• Central Processing Unit (CPU)The CPU is the heart of the microprocessor and processes the messages that needs to betransmitted or have been received.
• CAN controllerThe CAN controller collects the messages and converts them into a definite subsequenceof bits, the data frame, that is ready to be transmitted. The controller is implementedas a peripheral system inside the DSP.
• CAN transceiverThe CAN transceiver is installed in an external circuit and connects the CAN bus withthe CAN controller. It converts the bits in the data frame into a signal that can be puton the bus and vice versa. In this setup, the MCP2551 CAN transceiver of Microchipis used, which is supplied on 5 V.
A data frame consists of the following elements:
• Identifier: each node has its own identifier. By sending the identifier within the message,the controller knows which message belongs to which mailbox. The value of the identifieralso determines the priority of the message.
• Number of bytes: 6 bits are necessary to define how much bytes will be transmitted.
• Data: contains the actual data.
• Redundancy check: is an error-detecting code to repair accidental faults in the data.
• Acknowledgement: bit in which the receiver acknowledges the receipt of a new message.
In Figure B.1, an illustration of the CAN bus is shown with several nodes connected to it. Thebus consists of two wires: CANH and CANL. It is important to connect the both ends witheach other by using a termination resistor with a value of 120 Ω.
119
Node 1 Node2 ......120Ω 120Ω
CANH
CANL
Figure B.1: CAN bus
The transceiver is a 8-pin chip shown in Figure B.2. It is connected to a 5 V DC voltagesupply. At one end, there are the two terminals for connection with the CAN bus. At theother side, there are the RXD and TXD pins which have to be connected with the DSP. ’Rs’ isconnected to the ground to let the CAN controller operate in high-speed mode. ’Vref’ remainsunconnected.
MCP 2551
Rs CANH CANL Vref
TXD RXD+5 VGnd
Figure B.2: Microchip MCP 2551 CAN transceiver.
The DSP has two CAN controllers: CANA and CANB. In this setup, only the CANA iscontroller used, such that RXD and TXD need to be connected to GPIO30 and GPIO31respectively on the DSP.
First, the CAN controller needs to be initialized after resetting the DSP. Each CAN controllerconsists of 16 mailboxes of which, in this case, only one mailbox is needed. Mailbox 1 is enabledto which an unique identifier is assigned. It has also to be specified whether this is a receivingor transmitting mailbox. If it is a receiving one which is triggered by an interrupt, also thenecessary interrupt registers need to be loaded.
If a message has to be transmitted, the data need first to be loaded into the data register of themailbox. The transmission will be started as soon as the ’transmission request bit’ is set high.From the moment the ’transmission acknowledgement bit’ becomes high, the DSP knows themessage has been transmitted successfully and a new transmission can start.
When a message arrives at the CAN bus, the first thing the controller will do is checkingwhether the identifier in the message corresponds with the identifier of one of the enabledmailboxes. If so, the ’received message pending bit’ gets high, by which the message is loadedinto the mailbox. The bit triggers the interrupt service routine, which can start processing thenew data.
120
Appendix C
Torque sensor
In Chapter 5, it was shown how the torque sensor (Metil DR2477, cf. Figure C.1) is placedbetween the motor and the generator. It is a contactless sensor with digital signal transmissionbetween stator and rotor for the measurement of dynamic torques. The type used in thissetup has a measurement range from −15 Nm to +15 Nm, resulting in an output signal varyinglinearly between ±5 V. The DC voltage supply needs to be between 12 V and 28 V.
Because the analog input voltage for the ADC is ranging from 0 to 3 V, an analog circuit isdesigned to convert the sensor output signal to the ADC input range. An inverting amplifiercircuit with offset voltage and a low pass filter is used, as shown in Figure C.2.
In the DSP, the torque signal is also digitally filtered using high order low-pass filters.
C.1 Inverting amplifier
In this circuit, the main component is the opamp, uA741, with a two-sided voltage supply of+15V and −15V . Because the feedback loop is connected with the negative input, the voltageat the negative input pin is equal to the voltage at the positive input pin which is equal to theoffset voltage Voff , determined by the voltage divider R3/R4.
Because the opamp has high impedance inputs, the input current at terminal Vin is nearly
Figure C.2: Inverting amplifier with offset voltage
equal to the current in the feedback loop:
Vin − Voff
R1=Voff − Vout
R2(C.1)
resulting in the following relationship between input and output:
Vout =
(1 +
R2
R1
)Voff −
R2
R1Vin (C.2)
The desired input-output function needs to be like figure C.3 and is described by the equation:
Vout = 1.5− 0.3Vin (C.3)
Combination of Eq. C.2 and Eq. C.3 , gives the values for R2/R1 and Voff :
R2
R1= 0.3 (C.4)
Voff = 1.15 V (C.5)
This value for the offset voltage determines the relationship between R3 and R4:
R4
R3 +R4=Voff
Vcc=
1.15
15= 0.077 (C.6)
Searching appropriate resistors in the E24 series, gives the following resistor values:
R1 = 91 kΩ (C.7)
R2 = 27 kΩ (C.8)
R3 = 56 kΩ (C.9)
R4 = 4.7 kΩ (C.10)
122
Appendix C. Torque sensor
Vout
Vin+5V-5V 0
3V
Figure C.3: Desired input-output characteristic
C.2 Analog low-pass filter
The measurement signal produced by the torque sensor contains so much noise, such that itcan not be used immediately. First, the signal needs to be directed through an analog low passfilter. Then, the signal goes through the amplifier of the previous section and then to the DSP.Inside the DSP, the signal is filtered digitally until an acceptable value arises.
The analog first-order low-pass filter is implemented by a simple RC circuit, shown in FigureC.4. By means of a jumper, it can be decided whether the signal goes trough the filter or by-passes it. A filter with a low cut-off frequency has been designed to remove the noise sufficiently.This is no problem for the control strategy, because only steady state values are of interest formeasuring the mechanical power.
The following filter has been obtained:
R = 33 kΩ (C.11)
C = 33 nF (C.12)
which results in a cut-off frequency equal to:
fc =1
2πRC= 146 Hz (C.13)
IN OUT
R
C
Figure C.4: RC first order low-pass filter
C.3 Digital filtering
Because only the global variation of the torque is of interest and not the torque ripple due totransients, digital filtering on the input signal has been established inside the DSP. A 3th-order
123
C.3. Digital filtering
Butterworth low-pass filter with a cut-off frequency of 20 Hz is used. In Matlab, the discretetransfer function of the filter is calculated by using a sample frequency of 160 Hz (the torquefiltering is contained in the speed control loop). This results in the following filter:
H(z) =b1 + b2 z
−1 + b3 z−2 + b4 z
−3
1 + a2 z−1 + a3 z−2 + a4 z−3) (C.14)
with
x ax bx1 1 0.0053
2 -2.2192 0.0159
3 1.7151 0.0159
4 -0.4535 0.0053
In the DSP, the output value y is calculated from the previous outputs y and the previous andcurrent inputs x:
The bode plot of this filter is presented in Figure C.5:
−100
−50
0
Mag
nitude
(dB)
100
101
102
−270
−180
−90
0
Phas
e(d
eg)
Bode diagram
Frequency (rad/sec)
Figure C.5: Bode plot of 3th order Butterworth filter
124
Appendix D
DSP code
This appendix gives the programming code of the DSP of the active rectifier, written in C.The different functions and subroutines are described in the order they are executed after therectifier has been powered.
D.1 Main function
The ’main’ function is the first one that is executed from the moment the program in theDSP is started. It initializes the CPU’s clock system, the PWM modules, ADCs and the CANcommunication. A flag is used to indicate in which state the program is at any moment andwhether a module failed to initialize.
void main (void ) DINT;f l a g =1;
// Device L i f e suppor t & GPIODev i c e In i t ( ) ;
// Set Debug por tGpioDataRegs .GPASET. b i t . GPIO16=1;
// I n i t i a l i z e PWM−outputpwmInit ( ) ;f l a g =11;
// Load Sine and Cosine t a b l e ss i n I n i t ( ) ;f l a g =12;
// I n i t i a l i z e ECAN moduleeCANInit ( ) ;f l a g =13;
// Enable INT9 fo r ECANA:IER |= M INT9 ;// Enable g l o b a l I n t e r r u p t s and h i ghe r p r i o r i t y rea l−t ime debug even t s :EINT; // Enable Globa l i n t e r r u p t INTMERTM; // Enable Globa l r ea l t ime i n t e r r u p t DBGM
// I n i t i a l i z e power conver t e rConver t e r In i t ( ) ;f l a g =14;
125
D.1. Main function
// Enable CPU INT3 fo r EPWM1 INT:IER |= M INT3 ;
// Clear debug por t − I n i t i a l i z a t i o n completeGpioDataRegs .GPACLEAR. b i t . GPIO16=1;f l a g =2;
// I n f i n i t e loop . Jus t s i t and loop f o r e v e r :for ( ; ; )
The main function contains the following subroutines:
• DeviceInit(): the CPU and peripheral clocks are enabled and settings like direction andmultiplex function for the GPIOs (General Purpose Input/Output) are loaded. The codeof this function is not showed because the file is too large, but a list of the used IO pinsis given:
– GPIO0 - GPIO5: these pins give the PWM signals to control the IGBTs of therectifier. Each phase has two PWM signals (eg. GPIO0 and GPIO1 for phase A)which are complementary with a deadband time of 1.5µs.
– GPIO12: output pin which is connected to the reset port of the half bridge modules.A positive pulse on this pin will reset the converter.
– GPIO15: input pin which is connected to the error port. If an error occurred inthe IGBT gate drivers, the error pin will be set low and the PWM switching signalsare blocked to the drivers.
– GPIO30: RX (receiver) pin for the CAN module.
– GPIO31: TX (transmitter) pin for the CAN module.
• pwmInit(): the PWM registers with the related interrupts are loaded together with theADC registers. The following ADC pins are used:
– A0: phase A current measurement
– A1: DC-bus voltage measurement
– A2: phase B current measurement
– A3: phase B voltage measurement
– A4: phase C current measurement
– A5: phase C voltage measurement
– A7: generator torque measurement
void pwmInit (void ) // I n i t i a l i z e PWM1 module (16kHz ) − curren t c on t r o lpwm1. PeriodMax = 4688 ; // 4688 pu l s e s up/downpwm1. HalfPerMax = pwm1. PeriodMax ;pwm1. Deadband = 1.5∗CLOCKFREQ; // 1.5 us dead−t imePWM INIT MACRO(1 ,2 , 3 ,pwm1) ;
// I n i t i a l i z e PWM4 module (160 Hz) − speed con t r o lEPwm4Regs .TBCTL. b i t .CLKDIV = 0 ; // CLKDIV = 1
126
Appendix D. DSP code
EPwm4Regs .TBCTL. b i t .HSPCLKDIV = 4 ; // HSPCLKDIV = 16EPwm4Regs .TBCTL. b i t .CTRMODE = 2 ; // up − down modeEPwm4Regs .TBCTL. b i t .SYNCOSEL = 0 ;EPwm4Regs .TBCTL. b i t .PHSEN = 0 ;EPwm4Regs .TBPHS. h a l f .TBPHS = 0 ;
EPwm4Regs .AQCTLA. a l l = 0x0060 ;EPwm4Regs .AQCTLB. a l l = 0x0600 ;
EPwm4Regs .TBPRD = 58594;EPwm4Regs .CMPA. h a l f .CMPA = EPwm4Regs .TBPRD/2 ;
// I n i t i a l i z e ADC module// ADC pin used at SOCint ChSel [ 1 6 ] = 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ;// Acqu i s i t i on window s i z eint ACQPS[ 1 6 ] = 8 , 8 , 8 , 8 , 8 , 8 , 8 , 8 , 8 , 8 , 8 , 8 , 8 , 8 , 8 , 8 ;
ChSel [ 0 ] = 0 ; // Ia − phase A curren tChSel [ 1 ] = 1 ; // Va − phase A vo l t a g eChSel [ 2 ] = 2 ; // Ib − phase B curren tChSel [ 3 ] = 3 ; // Vb − phase B vo l t a g eChSel [ 4 ] = 4 ; // Ic − phase C currentChSel [ 5 ] = 5 ; // Vc − phase C vo l t a g eChSel [ 6 ] = 6 ; // Not usedChSel [ 7 ] = 7 ; // Tm − Generator Torque
ADC MACRO INIT( ChSel , Tr igSe l ,ACQPS) ;
// I n i t i a l i z e I n t e r r u p t s
EALLOW; // Write to EALLOW pro t e c t ed r e g i s t e r sPieVectTable .EPWM1 INT = &CurrentISR ; // Jump to func t i on at INT3 .1PieVectTable .EPWM4 INT = &SpeedISR ; // Jump to func t i on at INT3 .4PieVectTable .ECAN1INTA = &ReceiveISR ; // Jump to func t i on at INT9 .6EDIS ;
// Enable PIE group 3 i n t e r r u p t 1 f o r EPWM1 INTPieCtr lRegs . PIEIER3 . b i t . INTx1 = 1 ; //EPWM1 − i n t e r r u p tPieCtr lRegs . PIEIER3 . b i t . INTx4 = 1 ; //EPWM4 − i n t e r r u p tPieCtr lRegs . PIEIER9 . b i t . INTx6 = 1 ; //ECAN1INTA − i n t e r r u p t
// Event−Trigger Submodule Reg i s t e r s
// Enable EPWM1INT genera t ionEPwm1Regs .ETSEL. b i t . INTEN = 1 ;// Enable i n t e r r u p t CNT zero event when time−base counter = 0EPwm1Regs .ETSEL. b i t . INTSEL = 1 ;// Generate i n t e r r u p t on the 1 s t eventEPwm1Regs .ETPS. b i t .INTPRD = 1 ;// Enable more i n t e r r u p t sEPwm1Regs .ETCLR. b i t . INT = 1 ;
// Enable EPWMINT4 genera t ionEPwm4Regs .ETSEL. b i t . INTEN = 1 ;// Enable i n t e r r u p t CNT zero event when time−base counter = 0EPwm4Regs .ETSEL. b i t . INTSEL = 1 ;// Generator i n t e r r u p t on the 1 s t eventEPwm4Regs .ETPS. b i t .INTPRD = 1 ;// Enable more i n t e r r u p t sEPwm4Regs .ETCLR. b i t . INT = 1 ;
127
D.1. Main function
• sinInit(): load Sine and Cosine tables with 400 values between 0 and 2π.
void s i n I n i t (void ) int i ;for ( i =0; i< SINLENGTH; i++)
s i nu s [ i ] = IQtoF ( IQs in ( IQ ( i /SINLENGTH∗6 .2831853) ) ) ;for ( i =0; i< SINLENGTH; i++)
co s inu s [ i ] = IQtoF ( IQcos ( IQ ( i /SINLENGTH∗6 .2831853) ) ) ;
• eCanInit(): the CAN communication registers are initialized. The used functions canbe found in DSP2833x_ECan.c. Note the use of a shadow register in order to have accessto the 32-bit registers.
void eCANInit (void ) // I n i t CAN−A GPIO pinsInitECanGpio ( ) ;InitECana ( ) ;
// I d e n t i f i e rEALLOW;ECanaMboxes .MBOX1.MSGID. a l l = 0x95555555 ; // Extended I d e n t i f i e r
// Mailbox d i r e c t i o nECanaShadow .CANMD. a l l = ECanaRegs .CANMD. a l l ;ECanaShadow .CANMD. b i t .MD1 = 1 ;ECanaRegs .CANMD. a l l = ECanaShadow .CANMD. a l l ;
// Enable mai lboxECanaShadow .CANME. a l l = ECanaRegs .CANME. a l l ;ECanaShadow .CANME. b i t .ME1 = 1 ;ECanaRegs .CANME. a l l = ECanaShadow .CANME. a l l ;
// Message s i z e 6 b y t e sECanaMboxes .MBOX1.MSGCTRL. b i t .DLC = 8 ;
// Set−up o f i n t e r r u p t s// Set i n t e r r u p t l i n e to 1 f o r a l l mai l boxesECanaShadow .CANMIL. a l l = ECanaRegs .CANMIL. a l l ;ECanaShadow .CANMIL. b i t . MIL1 = 1 ;ECanaRegs .CANMIL. a l l=ECanaShadow .CANMIL. a l l ;// Enable mai lbox i n t e r r u p tECanaShadow .CANMIM. a l l = ECanaRegs .CANMIM. a l l ;ECanaShadow .CANMIM. b i t .MIM1 = 1 ;ECanaRegs .CANMIM. a l l = ECanaShadow .CANMIM. a l l ;
// Set−up i n t e r r u p t c on t r o l r e g i s t e rECanaShadow .CANGIM. a l l = ECanaRegs .CANGIM. a l l ;ECanaShadow .CANGIM. b i t . I1EN = 1 ;ECanaRegs .CANGIM. a l l = ECanaShadow .CANGIM. a l l ;EDIS ;
• ConverterInit(): the start-up sequence of the active rectifier is initiated.
void Conver t e r In i t (void )
128
Appendix D. DSP code
// Check DC−bus v o l t a g e & communicationwhile ( ( Vdc<VDCMIN) | | ( theta==0))
Vdc=−0.3704∗AdcMirror .ADCRESULT1 + 8 3 8 . 5 2 ;// Toggle s tandby l e dGpioDataRegs .GPATOGGLE. b i t . GPIO13 = 1 ;DELAY US(100 .0L) ;
// S ta r t i n v e r t e r : g i v e pu l s e (100 us ) on r e s e t pin when error i s lowwhile ( GpioDataRegs .GPADAT. b i t . GPIO15!=1)
GpioDataRegs .GPASET. b i t . GPIO12 = 1 ;DELAY US(100 .0L) ;GpioDataRegs .GPACLEAR. b i t . GPIO12 = 1 ;DELAY US(100 .0L) ;
// Set s tandby l e dGpioDataRegs .GPASET. b i t . GPIO13 = 1 ;
D.2 CurrentISR
The ’CurrentISR’ subroutine executes the stator current control in the synchronous referenceframe for the implementation of the field oriented control. At the end of the routine, also thegenerator power is measured and filtered by multiplying the measured stator current with theapplied phase voltage.
//∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗//// Current Contro l I n t e r r up t f unc t i on// Executed at PWM1 in t e r r u p t (16kHz )//∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗//
i n t e r r u p t void CurrentISR (void ) DINT;
// Set debug pin GPIO18GpioDataRegs .GPASET. b i t . GPIO18=1;
// DC−bus v o l t a g e measurementVdc=−0.3602∗AdcMirror .ADCRESULT1+818.43;
// Current p r o t e c t i on − at e x t e r na l i n t e r r u p t ( s top2 ) or overcurren td e t e c t i on a l l duty r a t i o s are s e t to zero
i f ( ( stop2 !=0) | | ( iam >IMAX) | | ( ibm >IMAX) | | ( icm > IMAX) | | ( iam < −IMAX)| | ( ibm < −IMAX) | | ( icm < −IMAX) )
// Clear pwm’ spwm1. MfuncC1 = IQ ( duty l im i t ( 0 . 0 ) ) ;pwm1. MfuncC2 = IQ ( duty l im i t ( 0 . 0 ) ) ;pwm1. MfuncC3 = IQ ( duty l im i t ( 0 . 0 ) ) ;PWMMACRO(1 ,2 , 3 ,pwm1) ;
// Set error pin lowEALLOW;GpioDataRegs .GPACLEAR. b i t . GPIO15 = 0 ;
129
D.2. CurrentISR
GpioCtrlRegs .GPADIR. b i t . GPIO15 = 1 ;EDIS ;
f l a g = 5 ;
// S ta r t i n f i n i t e loopwhile (1 )
DELAY US(10000 .0L) ;
// Park transformdouble Cosinus = Cos ( theta ) ;double Sinus = Sin ( theta ) ;
// Duty r a t i o c a l c u l a t i o ndutya = 0.5+Va/ 6 0 0 . 0 ;dutyb = 0.5+Vb/ 6 0 0 . 0 ;dutyc = 0.5+Vc / 6 0 0 . 0 ;
// Limit duty r a t i o s between 0 and 1 and update PWM r e g i s t e r spwm1. MfuncC1 = IQ ( duty l im i t ( dutya ) ) ;pwm1. MfuncC2 = IQ ( duty l im i t ( dutyb ) ) ;pwm1. MfuncC3 = IQ ( duty l im i t ( dutyc ) ) ;PWMMACRO(1 ,2 , 3 ,pwm1) ;
// Measure e l e c t r i c genera tor power ( genera tor r e f e r ence )P = − 1 .5∗ iqm∗Vq;
130
Appendix D. DSP code
// 0.5 Hz f i r s t −order low pass f i l t e rP g f i l t = 0 .0001∗ (P+P g f i l t b u f f e r ) +0.9998∗ P g f i l t ;P g f i l t b u f f e r = P;
// Set f l a g − Current c on t r o l s t a r t e di f ( f l a g ==2)
f l a g =3;
// Clear debug pin GPIO18GpioDataRegs .GPACLEAR. b i t . GPIO18=1;
// Enable more i n t e r r u p t s from t h i s t imerEINT;EPwm1Regs .ETCLR. b i t . INT = 1 ;
// Acknowledge i n t e r r u p t to r e c e i v e more i n t e r r u p t s from PIE group 3PieCtr lRegs .PIEACK. a l l = PIEACK GROUP3;
D.3 ReceiveISR
The ReceiveISR is executed every time a new message of 64 bits from the wind turbineemulator arrives on the CAN bus. The raw data is stored as integers in two 32-bit registers’HI_WORD’ and ’LOW_WORD’. These data is converted back to floating point variables to be usedby the other ISR’s.
//∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗//// Communication In t e r rup t f unc t i on//Executed when new message a r r i v e s at CAN−bus .//∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗//i n t e r r u p t void ReceiveISR (void )
// Set debug por t GPIO22GpioDataRegs .GPASET. b i t . GPIO20=1;
// Read raw dataUint16 theta m1 = ECanaMboxes .MBOX1.MDL. word .LOWWORD;v = (ECanaMboxes .MBOX1.MDL. word .HI WORD) / 1 0 0 . 0 ;sha f t speed =(ECanaMboxes .MBOX1.MDH. word .LOWWORD) / 1 0 0 . 0 ;
// Acknowledge rece ivementECanaRegs .CANRMP. b i t .RMP1=1;
// Ca l cu l a t e e l e c t r i c ro to r p o s i t i o n in rad ianstheta m = theta m1 /10000 . 0 ;double theta2 = Np ∗ theta m + theta0 ;int theta1 = theta2 / (2 . 0∗ PI ) ;theta = theta2 − theta1 ∗2 .0∗ PI ;
// Ca l cu l a t e ro to r speed in rad ians / secondomega = sha f t speed ∗ 2 .0∗ PI / 6 0 . 0 ;
// Clear debug por t GPIO22GpioDataRegs .GPACLEAR. b i t . GPIO20=1;
// Acknowledge i n t e r r u p t & a l l ow new i n t e r r u p t sPieCtr lRegs .PIEACK. b i t .ACK9=1;IER |=0 x0100 ;
131
D.4. SpeedISR
D.4 SpeedISR
The ’SpeedISR’ subroutine contains the speed control loop and the MPPT control. Becausedifferent MPPT strategies have been implemented, each strategy has its own code and specificvariables. In general, the sequence is as follows. First the rotor speed is filtered by using a 20Hz low pass filter for exporting this value to Matlab. Also the mechanical torque is measuredwith the ADC, filtered and multiplied with the rotor speed in order to get the mechanicalgenerator power. Then, the MPPT controller calculates the rotor speed reference by executingits specific algorithm. The PI speed controller uses this value together with the unfilteredmeasured rotor speed to calculate the q-axis current reference. The result goes to through arate limiter to prevent torque shocks and through a saturator to limit the current reference toits rated value. At the end, the DC-bus voltage is checked. The converter will be shut down ifthe wind speed is lowered between 2 m/s.
D.4.1 TSR control
//∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗//// Speed Contro l I n t e r r up t f unc t i on// Executed at PWM4 in t e r r u p t (160 Hz)//∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗//
i n t e r r u p t void SpeedISR (void ) // Set debug pin GPIO22GpioDataRegs .GPASET. b i t . GPIO22=1;
// Torque measurement (3 rd order Butterworth f i l t e r − low pass 20Hz)Tmbufferin [ 0 ] = 0.0077∗ AdcMirror .ADCRESULT7−14.036;
// 20 Hz low pass bu t t e rwor th f i l t e rTm = 0.0053∗ ( Tmbufferin [0 ]+ Tmbufferin [ 3 ] ) +0.0159∗( Tmbufferin [1 ]+ Tmbufferin
omegabuf fer in [3 ]= omegabuf fer in [ 2 ] ;omegabuf fer in [2 ]= omegabuf fer in [ 1 ] ;omegabuf fer in [1 ]= omegabuf fer in [ 0 ] ;
132
Appendix D. DSP code
// TSR ca l c u l a t i o nlambda = R∗omega/v ; // TSR [−]
// Star tup sequencei f ( f l a g ==3)
i f ( ( omegabuf fer in [0 ] >18 .0 )&&(omegabuf fer in [0 ] <20 .0 ) ) f l a g =4;// Set MPPT l edGpioDataRegs .GPASET. b i t . GPIO14 = 1 ;// Clear Standby l e dGpioDataRegs .GPACLEAR. b i t . GPIO13 = 1 ;
// Speed con t r o l (16 Hz)i f ( f l a g ==4)
Pg = Pgtot ;
i f (MPPTcounter==10)//Speed r e f e r ence va lueomw = v/R ∗ LAMBDAOPT;
// Speed PI c o n t r o l l e rdouble om err = omw − omegabuf fer in [ 0 ] − Kw∗( i q b u f f e r −
i q s a t b u f f e r ) ; // Anti windupi q1 = i q b u f f e r + Ks ∗ ( om err − as ∗ om er rbu f f e r ) ;
// doub le ve rw i jderen voor speed con t r o l
om er rbu f f e r = om err ;
// Current ra t e l im i t e ri f ( ( iq1−i q b u f f e r )>I r a t e )
i q1 = i q b u f f e r + I r a t e ;i f ( ( i q b u f f e r−i q1 )>I r a t e )
i q1 = i q b u f f e r − I r a t e ;i q b u f f e r = iq1 ;
// Current Limiter ( on ly nega t i v e v o l t a g e s − genera tor )i f ( iq1 < −IQMAXGEN)
i q1=−IQMAXGEN;i f ( iq1 > IQMAXMOT)
i q1=IQMAXMOT;i q s a t b u f f e r = iq1 ;
i q = iq1 ;MPPTcounter=0;
MPPTcounter = MPPTcounter+1;
Pcounter = 0 ;Pgtot =0;
// Ver i f y DC−bus v o l t a g e ;Dcbuscontrol ( ) ;
// Shut conver t e r down when wind speed i s too low
133
D.4. SpeedISR
i f (v<2.0) i f ( stop==1)
stop2 = 1 ;stop1 = 1 ;
// Clear debug pin GPIO22GpioDataRegs .GPACLEAR. b i t . GPIO22=1;
// Enable more i n t e r r u p t s from t h i s t imerEPwm4Regs .ETCLR. b i t . INT = 1 ;
// Acknowledge i n t e r r u p t to r e c e i v e more i n t e r r u p t s from PIE group 3PieCtr lRegs .PIEACK. a l l = PIEACK GROUP3;
D.4.2 Power control
//∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗//// Speed Contro l I n t e r r up t f unc t i on// Executed at PWM4 in t e r r u p t (160 Hz)//∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗//i n t e r r u p t void SpeedISR (void )
// Set debug pin GPIO22GpioDataRegs .GPASET. b i t . GPIO22=1;
// Ca l cu l a t e TSRlambda = R∗omega/v ;
// 20 Hz low pass bu t t e rwor th f i l t e romega = 0.0053∗ ( omegabuf fer in [0 ]+ omegabuf fer in [ 3 ] ) +0.0159∗( omegabuf fer in [1 ]+
omegabuf fer in [ 2 ] ) + 2.2192∗ omegabuffer [0 ]−1.7151∗ omegabuffer [1 ]+0 .4535∗omegabuffer [ 2 ] ;
// Speed Contro l I n t e r r up t f unc t i on// Executed at PWM4 in t e r r u p t (160 Hz)//∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗//i n t e r r u p t void SpeedISR (void )
// Set debug pin GPIO22GpioDataRegs .GPASET. b i t . GPIO22=1;
// 20 Hz low pass bu t t e rwor th f i l t e romega = 0.0053∗ ( omegabuf fer in [0 ]+ omegabuf fer in [ 3 ] ) +0.0159∗( omegabuf fer in [1 ]+
omegabuf fer in [ 2 ] ) + 2.2192∗ omegabuffer [0 ]−1.7151∗ omegabuffer [1 ]+0 .4535∗omegabuffer [ 2 ] ;
// Speed con t r o l (160 Hz)// Speed PI c o n t r o l l e r wi th ant i−windupdouble om err = OmegaRef − omegabuf fer in [0]− Kw∗( i q b u f f e r − i q s a t b u f f e r
) ;iq1 = i q b u f f e r + Ks ∗ ( om err − as ∗ om er rbu f f e r ) ;
om er rbu f f e r = om err ;
// Current t r an s i e n t l im i t e ri f ( ( iq1−i q b u f f e r )>I r a t e )
i q1 = i q b u f f e r + I r a t e ;i f ( ( i q b u f f e r−i q1 )>I r a t e )
i q1 = i q b u f f e r − I r a t e ;
i q b u f f e r = iq1 ;
// Current Limiter ( on ly nega t i v e v o l t a g e s − genera tor )i f ( iq1 < −IQMAX)
i q1 = −IQMAX;i f ( iq1 > 0)
i q1 =0;i q s a t b u f f e r = iq1 ;i q = iq1 ;
// Measurements [ sample ra t e 10 Hz ]i f ( datcounter2==16)
i f ( ( datcounter<DATMAX) && ( measure==1)) omegaout [ datcounter ] = ( int ) ( omega ∗100 .0 ) ;omegarefout [ datcounter ] = ( int ) (OmegaRef ∗100 .0 ) ;Pgout [ datcounter ] = ( int ) ( P g f i l t ∗10 .0 ) ;Pout [ datcounter ] = ( int ) (Pg∗10 .0 ) ;Pmout [ datcounter ] = ( int ) (Pm∗10 .0 ) ;datcounter = datcounter +1;
datcounter2 =0;
datcounter2 = datcounter2 +1;
// Ver i f y DC−bus v o l t a g e ;Dcbuscontrol ( ) ;
// Clear debug pin GPIO22GpioDataRegs .GPACLEAR. b i t . GPIO22=1;
// Enable more i n t e r r u p t s from t h i s t imerEPwm4Regs .ETCLR. b i t . INT = 1 ;
// Acknowledge i n t e r r u p t to r e c e i v e more i n t e r r u p t s from PIE group 3PieCtr lRegs .PIEACK. a l l = PIEACK GROUP3;
137
D.4. SpeedISR
D.4.4 Mode control
//∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗//// Speed Contro l I n t e r r up t f unc t i on// Executed at PWM4 in t e r r u p t (160 Hz)//∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗//i n t e r r u p t void SpeedISR (void )
// Set debug pin GPIO22GpioDataRegs .GPASET. b i t . GPIO22=1;
// 20 Hz low pass bu t t e rwor th f i l t e romega = 0.0053∗ ( omegabuf fer in [0 ]+ omegabuf fer in [ 3 ] ) +0.0159∗( omegabuf fer in [1 ]+
omegabuf fer in [ 2 ] ) + 2.2192∗ omegabuffer [0 ]−1.7151∗ omegabuffer [1 ]+0 .4535∗omegabuffer [ 2 ] ;
// Speed con t r o l (160 Hz)// Speed PI c o n t r o l l e rdouble om err = OmegaRef − omegabuf fer in [0]− Kw∗( i q b u f f e r − i q s a t b u f f e r
) ; // Anti windupi q1 = i q b u f f e r + Ks ∗ ( om err − as ∗ om er rbu f f e r ) ;
om er rbu f f e r = om err ;
// Current t r an s i e n t l im i t e ri f ( ( iq1−i q b u f f e r )>I r a t e )
i q1 = i q b u f f e r + I r a t e ;i f ( ( i q b u f f e r−i q1 )>I r a t e )
i q1 = i q b u f f e r − I r a t e ;
i q b u f f e r = iq1 ;
// Current Limiter ( on ly nega t i v e v o l t a g e s − genera tor )i f ( iq1 < −IQMAX)
i q1 = −IQMAX;i f ( iq1 > 0)
i q1 =0;i q s a t b u f f e r = iq1 ;i q = iq1 ;
// Ver i f y DC−bus v o l t a g e ;Dcbuscontrol ( ) ;
// Clear debug pin GPIO22GpioDataRegs .GPACLEAR. b i t . GPIO22=1;
// Enable more i n t e r r u p t s from t h i s t imerEPwm4Regs .ETCLR. b i t . INT = 1 ;
// Acknowledge i n t e r r u p t to r e c e i v e more i n t e r r u p t s from PIE group 3PieCtr lRegs .PIEACK. a l l = PIEACK GROUP3;
D.5 Additional functions
These functions are used in one of the previous subroutines.
• Sin(double x) & Cos(double x) give the sine and cosine respectively of a value xbetween 0 and 2π. The result is looked up in two tables of each 400 values which aregenerated by the sinInit() function during the initialization.
double Sin (double x ) int arg = x∗SINLENGTH∗0.1591549i f ( arg>(SINLENGTH−1) )
arg = SINLENGTH−1; else i f ( arg <0)
140
Appendix D. DSP code
arg = 0 ;return s i nu s [ arg ] ;
double Cos (double x ) int arg = x∗SINLENGTH∗0.1591549i f ( arg>(SINLENGTH−1) )
arg = SINLENGTH−1; else i f ( arg <0)
arg = 0 ;return co s inu s [ arg ] ;
• dutyLimit(double duty) limits the duty ratio generated by the PI current controllersto a value between 0 (DUTYMIN) and 1 (DUTYMAX).
double duty l im i t (double duty ) double dutylim = 0 ;i f ( duty >= DUTYMAX)
dutylim = DUTYMAX;else i f ( duty <= DUTYMIN)
dutylim = DUTYMIN; else
dutylim = duty ;return dutylim ;
• Dcbuscontrol() watches the voltage on the DC-bus and controls the corresponding led.
void Dcbuscontrol (void ) i f ( ( Vdc<VDCNOM) && ( l edcounte r ==80) && ( f l a g ==3))
GpioDataRegs .GPATOGGLE. b i t . GPIO11 = 1 ;l edcounte r =0;
l edcounte r = ledcounte r + 1 ;i f (Vdc>VDCNOM)
GpioDataRegs .GPASET. b i t . GPIO11 = 1 ;
• At last, the declaration of constants in the beginning of the program is given. Thedeclaration of variables is not given because the list is too numerous and differs for eachMPPT strategy.
// Dec lara t ion o f cons tan t s#define CLOCKFREQ 150 // Clock f requency [MHz]#define PI 3.1415926535 // De f in i t on o f p i#define ISR FREQUENCY 10 // ISR frequency ( kHz )#define CPU RATE 6.667L //150 MHz#define DELAY US(A) DSP28x usDelay ( ( ( ( ( long double ) A ∗ 1000 .0L) /
( long double )CPU RATE) − 9 .0L) / 5 .0L)
// Turbine and genera tor paramters#define Jt 0 .724 // Turbine i n e r t i a (kgm2)#define R 0.992 // Turbine b l ade rad ius (m)#define LAMBDAOPT 6.9077 // Optimal t i p speed r a t i o
141
D.5. Additional functions
#define Np 6 // Generator number o f po l e pa i r s#define PSI 1 .5 // Generator f l u x l i n k a g e (Wb)#define VDCNOM 580.0 // Nominal DC−bus v o l t a g e (V)#define VDCMIN 50 .0 // Minimal DC−bus v o l t a g e (V)#define IMAX 2 // Maximal a l l owa b l e current (A)#define IQMAXGEN 0.7 // Maximal genera tor q−ax i s curren t (A)#define IQMAXMOT 0.0 // Maximal genera tor q−ax i s curren t (A)#define SINLENGTH 400.0 // Sine t a b l e l e n g t h
#ifde f CDT PARSER#define i n t e r r u p t#endif
142
Appendix E
IET RPG 2014 conference paper
This appendix contains the paper submitted for the IET RPG 2014 conference in Naples, Italyon ”Effective capture of wind gusts in small wind turbines by using a full active rectifier”.
143
Effective capture of wind gusts in small windturbines by using a full active rectifier
Xavier Bracke, Jeroen D.M. De Kooning, Jan Van de Vyver and Lieven Vandevelde
Electrical Energy Laboratory (EELAB), Department of Electrical Energy, Systems and Automation (EESA),Ghent University, Sint-Pietersnieuwstraat 41, B-9000 Ghent, Belgium,
Keywords: Wind energy conversion system, Maximumpower point tracking, Wind gust capture, Permanent-magnetsynchronous generator, Back-to-back converter
AbstractMany small wind turbines have difficulties to start rotating atlow wind speeds due to their relatively large rotor inertia andlow starting torque. When a permanent magnet generator isused, the rotor magnets will cause an additional cogging torquewhich makes starting even more difficult. By using the gener-ator as a motor from the moment a wind gust is detected, theturbine is able to accelerate much faster to reach the maximumpower point. A maximum power point tracking algorithm isused to locate the optimal operating point. At sufficiently largerotor speeds, the controller switches to the generator modewhere the energy used for acceleration is recuperated, togetherwith the additional energy captured from the wind gust. Tocontrol the generator power in both directions, an active recti-fier is used in a back-to-back converter topology. In this paper,this wind capture strategy is simulated. The results show thatthe power output during a wind gust can be largely increasedcompared to common MPPT strategies.
1 IntroductionDuring the last few decades, wind turbines have become one ofthe most popular methods for renewable power production. Atthe end of 2013, the global installed capacity of both on-shoreand off-shore wind turbines was 318 GW, which is an increaseof 12% compared to the year before [1]. Most of these turbineshave a rated power of a few MWs.
Small wind turbines with a rated power in the range of 1 to30 kW are less popular. The main problem of these turbinesis the low height of their nacelle. At heights of only 15 m,the wind speed is less stable due to disturbances from the sur-roundings. In order to maximize the power output, these vari-able speed wind turbines need to be equipped with an adequatemaximum power point tracker (MPPT) to reach the the maxi-mum power point (MPP). Today, commercialised systems arealready available with a cost-performance ratio that is compa-rable to photovoltaic systems. However, research has shown
that there still is room for improvement since this market seg-ment is not mature yet [2].
Small wind turbines have a great potential because they areideal to be used as distributed generation units (DGs) indensely populated regions, on top of residential or industrialbuildings and in microgrids.
However, there is still very little known about the start-up be-haviour of these small turbines. As most of them do not havepitch control, the angle of attack at stand-still is close to 90.In combination with the corresponding low Reynolds number,very little data are known about the lift and drag coefficientsin this region [3]. In [4], the start-up sequence of a small5 kW turbine is described. It was observed that during start-up’idling’ periods of 30 to 50 seconds with slow rotation exist.During this period, the rotor blades are stalled due to the highflow angles and produce little torque. When a new increasein wind speed occurs, the angle of attack gets large enoughin order to produce sufficient torque and accelerate the turbinefurther on. In general, it can be concluded that the startingtorque of a wind turbine is usually very limited and will resultin a long start-up.
In the latest generation of wind energy conversion systems(WECS), the use of permanent magnet synchronous machines(PMSM) has gained popularity. Due to the absence of any ro-tor windings with corresponding copper losses, they offer highefficiency and reliability in a compact machine. As a largenumber of poles can be installed, the rated speed can be cho-sen near the rated speed of the wind turbine. The gearbox canbe omitted, which results in a direct drive generator. The disad-vantage of the PMSG is the cogging torque which tries to alignthe magnets with the stator slots in positions of minimal reluc-tance. The cogging torque impedes the turbine to start rotatinguntil the static magnet forces are overcome. This phenomenonmakes the turbine starting even more difficult.
If a wind gust with a duration of a few seconds occurs whenthe rotor stands still, the turbine will hardly react due to the lowstarting torque. Almost no energy contained in the wind gustwill be captured and converted into electricity. In this paper,a strategy is described which increases the rotor accelerationfrom the moment a wind gust is detected. In the standard situ-ation, the generator is driven by the turbine and electric power
1
is injected in the distribution grid. For the improved start-upand acceleration, electricity is used from the grid so the PMSMoperates shortly as a motor to produce a torque in the same di-rection of the turbine torque. The rotor starts immediately andis driven towards the optimal rotor speed. When the MPP isreached or the wind speed starts to decrease again, the con-troller switches from motor to generator mode and the PMSMstarts to produce electricity. The energy used for the initialacceleration will be largely recuperated (some of it will be dis-sipated due to the limited efficiency) together with the part ofthe wind gust energy that was captured by the wind turbine.The result is a net production of electricity by the WECS.
2 Wind gust definition
The definition of a wind gust is based on the gust front loadingfactor that is used in civil engineering. In [5], the rapid changesof the wind speed during a short period of time are discussed.A non-stationary wind model is introduced which describes awind field varying over height and in time:
v(z, t) = vg(z) · vg(t) (1)
in which v(z, t) is the wind gust field, vg(z) the vertical profileand vg(t) the time function. Because the rotor diameter ofsmall-scale wind turbines is limited to a few meters, the windspeed variation across the height of the rotor front area can beneglected. The interesting part is the time function of the gustwhich can be described as:
vg(t) = vmax sin
(π
tgt
)(2)
where vmax is the maximum wind speed value of the wind gustand tg is the duration. This wind gust profile will be used inthe simulation model and is illustrated in Fig. 1. By adaptingthe two parameters, different types of gusts can be simulated.
v(t)
vmax
tg t
Fig. 1: Wind gust profile in function of time.
3 Back-to-back converter
The considered WECS uses a back-to-back converter topology[6], illustrated in Fig. 2. The wind turbine drives a PMSMwhich generates an ac current with variable frequency and am-plitude. An active rectifier converts this ’wild’ ac into a dccurrent which is injected in the dc-bus with voltage Vdc. A
grid-coupled inverter converts the dc-power back into an accurrent of fixed frequency. The inverter is able to control theinjected active and reactive power independently and controlsthe dc-bus voltage to balance the active power.
PMSG ActiveRectifier Inverter
Grid
DC-bus
Fig. 2: Back-to-back converter
The active rectifier is a three-phase IGBT voltage source con-verter which controls the generator current by using field ori-ented control (FOC): the stator current is in phase or anti-phasewith the electromotive force (EMF) [7]. This way, the machinetorque can be easily controlled as it is proportional to the statorcurrent amplitude in the q-axis:
Tg =3
2NPΨPMiq (3)
in which NP is the number of pole pairs, ΨPM the flux link-age of the permanent magnets and iq the stator current in asynchronous reference frame. The FOC control scheme is pre-sented in Fig. 3. Two PI current controllers are used: one tocontrol the d-axis current to zero for implementing field ori-entation and another PI-controller to control the q-axis currentto a reference value which corresponds with a reference torqueaccording to Eq. 3. The resulting stator voltages are appliedby using pulse width modulation (PWM).
In order to track the MPP, the rotor speed needs to be controlledto a reference value determined by the MPPT-controller. Athird PI-control loop is used to achieve this. The output of thisPI-controller contains a saturator to limit the current referenceto the positive Iq,max,gen and negative Iq,max,mot limit [8]. Inthe generator reference frame, a positive q-axis current resultsin a generator torque opposite to the turbine torque.
As MPPT-strategy, the TSR-control is used to explain the prin-ciples of wind gust capturing ([9], [10]). Each wind turbinehas its own CP(λ)-curve, illustrated by Fig. 4, in which thepower coefficient CP determines the turbine power Pt:
Pt =1
2ρπr2CP(λ)v3 (4)
with ρ the air density, r the turbine radius and v the wind speed.λ is the tip speed ratio (TSR) and is a dimensionless represen-tation of the rotor speed:
λ =rΩ
v(5)
The following equation for the power coefficient is used [11]:
CP(λ) = 0.73
(151
λ− 13.653
)exp
(−18.4
λ+ 0.0552
)
(6)
2
PI
PI
PI
abc
abc
dq
0
irefd
irefq
id
iq
Ωref
Ω
vd
vq
θ
Ω
NP
dqPMSG
+
-
+- ia ib ic
+-
Fig. 3: Field oriented control scheme.
CP(λ) CP,max
TSRλopt
Fig. 4: CP(λ) wind turbine characteristic
The MPP is determined by CP,max at the optimal TSR λopt.For the TSR-control, the wind speed is measured and the opti-mal rotor speed Ωopt is calculated by using λopt:
Ωopt =vλoptr
(7)
At this optimal speed, the maximum power for that wind speedis captured by the wind turbine. The TSR-control is the fastestpossible MPPT but it requires a correct value of the windspeed. Of course, the discussed wind gust capture strategy isalso valid for other MPPT-strategies.
To investigate whether using the PMSM as motor improves theenergy output or not, the kinetic energy contained in the windgust Egust has to be known. It is calculated by integrating thewind flow power over time:
Egust =
∞∫
0
P0 dt =
∞∫
0
1
2ρπr2v3 dt (8)
Also the electric energy Eelec generated by the PMSG is cal-culated by integrating the generator power:
Eelec =
∞∫
0
Pg dt (9)
The ratio of these two values gives the capture coefficient ξ,which represents the relative captured amount of energy:
ξ =Eelec
Egust(10)
First, a situation is simulated for which a wind gust occurs andthe PMSM only operates as generator. Iq,max,mot is thus setequal to zero. The considered wind turbine produces a me-chanical rated power of 360 W at 500 rpm. The used windturbine characteristic has a wind turbine torque of zero aroundstand-still. An offset value must be added to the turbine torquesuch that the turbine is self-starting. From data in [4], an illus-trative starting torque could be calculated, equal to 0.095 Nm.This is a very small value compared to the rated turbine torqueof 6.9 Nm. The simulation result for a wind gust of 5 secondswith a peak value of 3 m/s is presented in Fig. 5. Due tothe low starting torque, the rotor speed does not become largerthan 0.2 rad/s. The turbine remains almost at stand-still. Ingeneral, it can be stated that no significant amount of powercan be captured during short wind gusts when the PMSM onlyoperates as generator. In the next simulation, Iq,max,mot is setto the rated motor current. The same wind gust profile is ap-plied and the result is shown in Fig. 6. At the start of the gust,the generator power Pg first becomes negative. This indicatesthat the PMSM is operating as a motor. The turbine rotor accel-erates significantly and the rotor speed tries to follow its opti-mal value determined by the measured wind speed. When therotor reaches its MPP, the generator power increases and be-comes positive. The active rectifier is switched to the generatormode and power is generated until the rotor has been returnedto stand-still. The capture coefficient ξ is calculated from thewind speed and generator power responses and is 0.18. A gen-erator efficiency of 90% has been taken into account.
3
0 1 2 3 4 5 6 70
5
10
15
20
25
Time [s]
Rot
orsp
eed
Ω[r
ad/s
]
Fig. 5: Rotor speed (full) and optimal rotor speed (dotted line) in function of time for wind gust without motoring.
5 Influence of maximal motor currentThe capture coefficient depends on the wind gust profile andthe maximal allowed motor current. The previous simulationhas been repeated for different values of the wind gust durationtg, the wind gust peak value vmax and Iq,max,mot. The resultsfor three different values of Iq,max,mot, where the capture coef-ficient is expressed in function of the wind gust parameters arepresented in Fig. 7. Missing values indicate that the capturecoefficient is smaller than zero and thus more power is used toaccelerate than could be produced by the wind turbine.
First, it should be noted that ξ is largely influenced by themaximal motor current. It can be concluded that the largerIq,max,mot is, the higher the amount of generated electricitywill be. The highest capture coefficients are obtained when themaximal value of the current limiter is set equal to the maximalallowed stator current in the PMSM. This current is normallytwo to three times higher than the rated current. This operationis allowed for only few seconds because otherwise the machinewould overheat due to the excess Joule losses.
Second, the controller is able to capture most power from longand large wind gusts. The longer the wind gust, the more timethe MPPT-controller has to reach the optimal rotor speed. Theexplanation is that the rotor inertia is the most important factorwhich impedes the MPPT of reaching the optimal rotor speed.The larger the wind speed, the larger the turbine torque is. Thishelps the PMSM to accelerate the rotor and reach the MPPfaster. The capture coefficient can never be higher than themaximal power coefficient CP,max equal to 0.44 (for this tur-bine). No more energy can be converted by the rectifier thancould be captured by the turbine. The capture coefficients fromthe simulations however saturate at a lower value because thegenerator efficiency has been taken into account.
Finally, it is observed that some wind gusts with a small du-ration tg or peak value vmax result in negative capture coeffi-cients. For these gusts, the active rectifier may not be started,because this would otherwise result in a net consumption ofelectric energy.
0 1 2 3 4 5 6 70
1
2
3
Time [s]
v[m
/s]
0 1 2 3 4 5 6 70
5
10
15
20
25
Time [s]
Ω[r
ad/s]
0 1 2 3 4 5 6 7−150
−100
−50
0
50
100
150
Time [s]
Pg
[W]
Fig. 6: Wind speed, (optimal) rotor speed and generator powerin function of time during wind gust capture with ratedmotor current.
4
2
4
6
8
10
2
3
4
5
6
7
0
0.1
0.2
0.3
0.4
tg [s]vmax [m/s]
Captu
reC
oeffi
cien
t[-]
(a) Iq,max,mot = 0.3 Inom
2
4
6
8
10
2
3
4
5
6
7
0
0.1
0.2
0.3
0.4
tg [s]vmax [m/s]
Captu
reC
oeffi
cien
t[-]
(b) Iq,max,mot = Inom
2
4
6
8
10
2
3
4
5
6
7
0
0.1
0.2
0.3
0.4
tg [s]vmax [m/s]
Captu
reC
oeffi
cien
t[-]
(c) Iq,max,mot = 3 Inom
Fig. 7: Capture coefficient in function of wind gust parametersand maximal motor current.
6 Wind gust detection
To prevent the active rectifier to start operating for small andshort wind gusts with a negative capture coefficient, a detec-tion algorithm is proposed which can distinguish appropriatefrom inappropriate wind gusts. To make the distinction, notthe wind speed itself but its first derivative is used. This valueis determined twice: at the beginning of the wind gust (t=0)and 0.5 seconds after its start. The detection algorithm can beillustrated by the decision tree in Fig. 8. The resulting value εindicates whether the detected wind gust is an appropriate (1)or inappropriate (0) one.
From the moment a wind gust is detected, the initial windspeed derivative v(0) is calculated and compared with a min-imal and maximal value to make a first separation. If the firstcondition is not fulfilled, the rectifier won’t start up and thewind gust will be passed. If v(0) is between 0.5 and 7.5, therectifier will start tracking the MPP by applying the maximalmotor torque.
This first condition however does not exclude all possible in-appropriate wind gusts. Therefore, a second separation is nec-essary which is executed 0.5 seconds after the wind gust’s startand uses both the first derivatives v(0) and v(0.5):
v(0) = vmaxπ
tg
v(0.5) = vmaxπ
tgcos
(π
tg0.5
)(11)
(12)
This system of two equations is solved for tg and vmax andtheir product corresponds with the value κ:
κ =v(0)
arccos2(
v(0.5)v(0)
) (13)
Once v(0.5) is known, κ is calculated. If it is smaller than 18,the rectifier operation will be interrupted and the turbine willstop accelerating. Some energy will be lost, but the amount islimited because the half of a second is a small time in whichthe turbine will be hardly accelerated due to its inertia.
The values for the two conditions are determined by meansof trial-and-error and are tested for the same array of windgust parameters for which the result is presented in Fig. 9.When it is compared with Fig. 7c, it is observed that the windgusts with negative capture coefficient are effectively rejected.Also some profiles with small duration and high peak valueare omitted, but this is acceptable because these gusts are quiterare and their capture coefficients are limited.
7 Conclusions
Many small wind turbines encounter difficult start-ups due totheir large rotor inertia and low starting torques. Especially,when wind gusts occur at the moment the rotor stands still,
5
only a very limited amount of the wind energy can be cap-tured. By using a PMSM with an active rectifier, this machinecan be used as a motor which helps the turbine to start and ac-celerate towards the MPP. By applying the maximal allowablecurrent, the capture coefficients are maximized. Some small,short gusts result in a negative power output and should be re-jected. For this purpose, a wind gust detection algorithm isproposed which uses the measured wind speed’s first deriva-tive.
0.5 < v(0) < 7.5
ε = 1ε = 0
ε = 0ε = 1
after 0.5 s
NO
YES
YES
NOκ < 18
Fig. 8: Decision tree for wind gust detection.
24
68
10
2
4
6
0
0.2
0.4
0.6
0.8
1
vmax [m/s]tg [s]
ε[-]
Fig. 9: Wind gust detection in function of wind gust peak valueand duration.
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[3] C. Mayer, M.E. Bechly, M. Hampsey and D.H. Wood,”The starting behaviour of a small horizontal-axis windturbine”, Renewable Energy, vol. 22, pp. 411-417, (2001)
[4] A.K. Wright and D.H. Wood, ”The starting and low windspeed behaviour of a small horizontal axis wind turbine”,University of Newcastle, Australia
[5] L. Wang and A. Kareem, ”Modelling of non-stationarywinds in gust-fronts”, Proc. of the 9th ASCE Joint Spe-ciality Conf. on Probabilistic Mechanics and StructuralReliability, (2004)
[6] Z. Chen, J.M. Guerrero and B. Frede, ”A review of thestate of the art of power electronics for wind turbines”,IEEE trans. on industrial electronics, vol. 24, no. 8, pp.1859-1875, (2009)
[7] M. Chinchilla, S. Arnaltes and J.C. Burgos, ”Control ofpermanent-magnet generators applied to variable speedwind-energy systems connected to the grid”, IEEE Trans.on energy conversion, vol.21, no. 1, pp. 130-135, (2006)
[8] J. Espina, A. Arias, J. Balcells and C. Ortega, ”Speedanti-windup PI strategies review for field oriented controlof permanent magnet synchronous generators”, Compat-ibility and power electronics, CPE 2009, (2009)
[9] M.A. Abdullah, A.H.M. Yatim, C.W. Tan and R. Saidur,”A review of maximum power point tracking algorithmsfor wind energy systems”, Renewable and sustainableenergy reviews, vol. 16, pp. 3220-3227, (2012)
[10] R. Datta and V.T. Ranganathan, ”A method of trackingthe peak power points for a variable speed wind energyconversion system”, IEEE trans. on energy conversion,vol. 18, no. 1, pp. 163-168, (2003)
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