Examensarbete 30 hp

Comparison between active and passive rectification for different types of permanent magnet synchronous machines

Johannes Örnkloo

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

Comparison between active and passive rectificationfor different types of permanent magnet synchronousmachinesJohannes Örnkloo

When using an intermittent source of energy such as wind power together with asynchronous machine a frequency converter system is needed to decouple thegenerator from the grid, due to the fluctuations in wind speed resulting in fluctuatingelectrical frequency. The aim of this master's thesis is to investigate how differenttypes of rectification methods affect permanent magnet synchronous machines ofdifferent saliency ratios. A literature study was carried out to review the researchwithin the area and to acquire the necessary knowledge to carry out the work. Twosimulation models were created that include a permanent magnet synchronousgenerator driven by a wind turbine and connected to the grid via a frequencyconverter, where one model utilizes active rectification and one utilizes passiverectification. The simulation models were verified by carrying out an experiment on asimilar setup, which showed that the simulation results coincide well with the resultsof the experiment. The results of the simulation study were then used to comparethe rectification systems as well as investigate the affect that rotor saliency has on thesystem. It was shown that the active rectification provided a higher efficiency than thepassive rectification system, however the saliency of the rotor had little effect on thesystem.

ISSN: 1650-8300, UPTEC ES 18 042Examinator: Petra JönssonÄmnesgranskare: Rafael WatersHandledare: Sandra Eriksson

II

Sammanfattning

Då en synkrongenerator drivs av en intermittent energikälla såsom en vindkraftsturbinvarierar generatorns rotationshastighet med vindhastigheten, vilket medför att denproducerade elektricitetens frekvens och spänningsnivå kommer att variera. Detta in-nebär att en frekvensomriktare krävs för att kunna nätkoppla generatorn. Syftet meddetta examensarbete är att undersöka hur två olika typer av likriktningsmetoder, ochgeneratorns utpräglingsgrad påverkar systemet. De likriktningsmetoder som under-sökts är aktiv likriktning bestående av en IGBT-brygga och passiv likriktning beståendeav en diodbrygga. För att jämföra de olika likriktningsmetoderna skapades simuler-ingsmodeller av systemen i simuleringsverktyget SimuLink. Simuleringsmodellernabestår av en permanentmagnetiserad synkrongenerator driven av en vindkraftsturbindär generatorn är nätkopplad via en frekvensomriktare. En experimentuppställning haräven använts för att verifiera att simuleringsmodellernas beteende efterliknar det av ettverkligt system.

En litteraturstudie genomfördes för att fördjupa kunskapen inom området och ge un-derlag för den teori som krävdes för att modellera systemet. Den matematiska mod-ellen av en synkrongenerator i det stationära trefas-referenssystemet inkluderar mångatidsvarierande termer, vilket leder till hög komplexitet vid numeriska beräkningar.Av den anledningen används ofta Park-transformen för att representera den matema-tiska modellen av en synkrongenerator i ett roterande referenssystem. Detta innebäratt generatorekvationernas tidsberoende försvinner, vilket underlättar de numeriskaberäkningarna. I litteraturstudien undersöktes även vilka kontrollmetoder som vanli-gen implementeras då en permanentmagnetiserad synkrongenerator används med enintermittent energikälla för de olika fallen av aktiv- respektive passiv likriktning.

I kapitlet teori presenteras all nödvändig teori för att modellera de olika systemen somska jämföras. Först presenteras den grundläggande teorin bakom modellering av en vin-dkraftturbin. Sedan presenteras teorin använd för att modellera generatorn. Resterandedelen av teorikapitlet involverar val- och presentation av de olika kontrollsystemen somanvänds för att modellera frekvensomriktaren i simuleringarna.

I kapitlet metod beskrivs hur teorin implementeras i simuleringsmodellerna och simu-leringsmodellerna presenteras i form av blockdiagram. Vidare så beskrevs den experi-mentella uppställningen som använts för att verifiera simuleringsmodellerna, tillsam-

Johannes Örnkloo

III

mans med den utrustning som använts i experimentet.

I kapitlet resultat presenteras de resultat som erhölls av den experimentella verifieringenoch simuleringarna i form av tabeller och diagram. Resultatet från experimentuppställ-ningen jämfördes med simuleringsmodellen och visar att simuleringsmodellen på ettbra sätt reflekterar beteendet av ett verkligt system vilket därmed verifierar simuler-ingsmodellerna.

Jämförelsen mellan modellerna med aktiv respektive passiv likriktning visar att systemetdär aktiv likriktning implementerats har en högre effektivitet, då systemet har sammauteffekt som systemet med passiv likriktning men vid lägre vindhastighet. Detta kanvara en följd av att aktiv likriktning är mer kontrollerbart och därmed på ett bättresätt lyckas kontrollera generatorn till att arbeta vid optimala förhållanden. Systemenjämfördes även med en mindre omfattande jämförelse vid halverad vindhastighet, äveni detta fall visades att systemet med aktiv likriktning lyckades producera en högreuteffekt än systemet med passiv likriktning. Vid jämförelse av generatorns utpräglings-grads påverkan på systemet visades att generatorns utpräglingsgrad har liten effekt påsystemets parametrar både i fallet med aktiv likriktning och fallet med passiv likriktning.

Johannes Örnkloo

IV

Executive Summary

The developed simulation models has been experimentally verified and the relevantconclusions of the simulation study and experimental verification are presented here.The results of the experimental verification show that the results of the simulationscoincide fairly well with the measured values from the experiments. In the case of ratedspeed the voltage level of the simulations was lower than the experimentally measuredvoltage level, this might be due to the frequency dependency of the inductance causinga mismatch in the inductance of the simulations and the experiments. This should beinvestigated further.

The passive rectification system lacks controllability and has higher losses and there-fore performs worse than the system with active rectification. However the passiverectification system has fewer controllable switches and is therefore less expensive. Thedifference in rotor saliency has little to no effect on the system, this might be due to therelatively low inductance of the generator model used for the simulations.

The wind turbine was only implemented for wind speeds between cut-in speed andwind speeds that correspond to rated power output, for future work a pitch angle controlshould be implemented for the wind turbine to work in higher wind speeds. The drivetrain model was simplified, for a more complete analysis a more complex model of thedrive train should be implemented.

Johannes Örnkloo

Table of Contents V

Table of Contents

Sammanfattning III

Executive Summary IV

List of Tables VII

List of Figures VIII

1 Introduction 11.1 Aim of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Theory 42.1 Modelling of wind turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Modelling of permanent magnet synchronous generators . . . . . . . . . 6

2.2.1 PMSG model in the three-phase stationary reference frame . . . . 62.2.2 PMSG model in the dq rotating reference frame . . . . . . . . . . 72.2.3 Saliency ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.4 Power analysis of PMSG . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Modeling the drive train . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4 Converter topology and control using active rectification . . . . . . . . . 10

2.4.1 Control of generator side converter . . . . . . . . . . . . . . . . . 112.4.2 Control of the grid side converter . . . . . . . . . . . . . . . . . . 12

2.5 Converter topology and control using passive rectification . . . . . . . . 132.5.1 DC link boost converter control . . . . . . . . . . . . . . . . . . . . 13

2.6 Space vector pulse width modulation . . . . . . . . . . . . . . . . . . . . 162.6.1 Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.6.2 Space vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.6.3 Implementation of SVPWM . . . . . . . . . . . . . . . . . . . . . . 18

3 Method 203.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.1.1 Wind turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.1.2 Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.1.3 Drive train . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

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Table of Contents VI

3.1.4 Active rectification . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.1.5 Passive rectification . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.1.6 Grid side converter . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.1 Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2.2 Measurement equipment accuracy . . . . . . . . . . . . . . . . . . 25

3.3 Verifying experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4 Results 274.1 Experimental verification . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.2 Simulation study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2.1 Rated wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2.2 Half of rated wind speed . . . . . . . . . . . . . . . . . . . . . . . 39

5 Discussion & Analysis 415.1 Experimental verification . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.2 Simulation study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.2.1 Active rectification . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.2.2 Passive rectification . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.2.3 Half of rated wind speed . . . . . . . . . . . . . . . . . . . . . . . 43

6 Conclusion 446.1 Experimental verification . . . . . . . . . . . . . . . . . . . . . . . . . . . 446.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Literature 46

Appendices 49

A Simulation models 49

Johannes Örnkloo

List of Tables VII

List of Tables

Table 2.1: Space vectors corresponding to switching states [22] . . . . . . . . . . 17Table 2.2: Sector number and corresponding angle interval . . . . . . . . . . . . 18

Table 3.1: Generator parameters [26] . . . . . . . . . . . . . . . . . . . . . . . . . . 25Table 3.2: Accuracy of measurement equipment at rated speed and half of rated

speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Table 4.1: Comparison of system quantities at rated speed . . . . . . . . . . . . . 27Table 4.2: Comparison of system quantities at half of rated speed . . . . . . . . . 27Table 4.3: Comparison of system quantities for active rectification . . . . . . . . 35Table 4.4: Comparison of system quantities for passive rectification . . . . . . . . 35Table 4.5: Comparison of stator dq-axis currents . . . . . . . . . . . . . . . . . . . 39Table 4.6: Comparison of system quantities at half of rated wind speed . . . . . 40

Johannes Örnkloo

List of Figures VIII

List of Figures

Figure 2.1: The power coefficient as a function of tip speed ratio for differentpitch angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Figure 2.2: The three phase stationary reference frame axes and the dq rotatingreference frame axes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Figure 2.3: The equivalent circuits of the generator d-axis and q-axis. . . . . . . 8Figure 2.4: The dq-axis of different types of rotors. . . . . . . . . . . . . . . . . . 9Figure 2.5: An overview of the system with active rectification . . . . . . . . . . 10Figure 2.6: An overview of the system with active rectification. . . . . . . . . . . 13Figure 2.7: Overview of the DC-link boost converter . . . . . . . . . . . . . . . . 15Figure 2.8: Two-level voltage source converter . . . . . . . . . . . . . . . . . . . 16Figure 2.9: Space vector representation of two-level VSC . . . . . . . . . . . . . 17

Figure 3.1: Control system used for the generator side converter, parameterssuperscripted with * are reference values. . . . . . . . . . . . . . . . . 22

Figure 3.2: Control system used for the boost converter, parameters superscriptedwith * are reference values. . . . . . . . . . . . . . . . . . . . . . . . . 23

Figure 3.3: Control system used for the grid side converter, parameters super-scripted with * are reference values. . . . . . . . . . . . . . . . . . . . 24

Figure 4.1: Phase current of measurement and simulation at rated speed . . . . 28Figure 4.2: Phase voltage of measurement and simulation at rated speed . . . . 29Figure 4.3: dc current of measurement and simulation at rated speed . . . . . . 29Figure 4.4: dc voltage of measurement and simulation at rated speed . . . . . . 30Figure 4.5: Load power of measurement and simulation at rated speed . . . . . 30Figure 4.6: Phase current of measurement and simulation at half of rated speed 31Figure 4.7: Phase voltage of measurement and simulation at half of rated speed 32Figure 4.8: dc current of measurement and simulation at half of rated speed . . 32Figure 4.9: dc voltage of measurement and simulation at half of rated speed . . 33Figure 4.10: Load power of measurement and simulation at half of rated speed . 33Figure 4.11: Phase voltage and current for case PDR-S1.67 . . . . . . . . . . . . . 36Figure 4.12: Phase voltage and current for case PDR-S1.0 . . . . . . . . . . . . . . 36Figure 4.13: Phase voltage and current for case PDR-S0.71 . . . . . . . . . . . . . 37Figure 4.14: Grid phase currents for case AIR . . . . . . . . . . . . . . . . . . . . . 37Figure 4.15: Grid phase currents for case PDR . . . . . . . . . . . . . . . . . . . . 38Figure 4.16: Grid active and reactive power for case AIR . . . . . . . . . . . . . . 38

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List of Figures IX

Figure 4.17: Grid active and reactive power for case PDR . . . . . . . . . . . . . . 39

Johannes Örnkloo

Introduction 1

1 Introduction

1.1 Aim of the thesis

In a permanent magnet synchronous generator (PMSG) the excitation field is causedby permanent magnets instead of coils. The rotor of permanent magnet synchronousgenerators can be designed in different ways, the magnets can either be internally placedin the rotor which is often referred to as an interior permanent magnet synchronousgenerator (IPMSG), or the magnets can be mounted on the surface of the rotor whichis referred to as a surface permanent magnet synchronous generator (SPMSG). Thedifferent types of rotor designs leads to different electrical properties, primarily thesaliency of the rotor varies. The saliency refers to how much each pole piece protrudesfrom the rotor shaft.

When using a permanent magnet generator both active rectification and passive rectifi-cation are commonly used [1]. Generators with different saliency are likely differentlyaffected when using active rectification or passive rectification. By examining howdifferent types of generators are affected, an indication of which kind of setup that issuitable for different applications can be achieved.

The goal of this thesis is therefore to create simulation models of systems with a perma-nent magnet synchronous generator and a frequency converter as interface to the grid.By creating a simulation model using active rectification with IGBTs and a simulationmodel using passive rectification with diodes, a comparison of the systems for differentsaliency of the generator rotor will be done. To verify the simulations an experimentalsetup will also be used.

1.1.1 Limitations

In this section the limitations of the thesis are presented.

• Prime mover - a simple wind turbine model will be implemented with a lumped-mass model of the drive train

• Steady state - the system will be analyzed in steady state, quickness of controlsystems is therefore not a priority

• The grid is modelled as an ideal voltage source with constant voltage

Johannes Örnkloo

Introduction 2

• The generator model is a simplified mathematical model, further elaborated insection 2.2

1.2 Layout

In the second chapter the theory used for the thesis work is presented. First the theoryof the wind turbine, which is the prime mover of the system is presented. An advancedmodel of a wind turbine is not the main goal of the thesis, therefore a simple model of awind turbine is presented.

The theory of mathematically modeling a generator is then presented. The model im-plemented in the simulations uses the dq-rotating reference frame as solving machineproblems in the conventional three phase stationary reference frame is very complex,which is further elaborated in the section.

The converter topology and control algorithms used in the simulation models is thenpresented. The control algorithms for the active rectifier are maximum power pointtracking (MPPT) and field oriented control (FOC). The model with passive rectification ispresented, which consists of a diode bridge rectifier and a DC-DC converter, the DC-DCconverter is also controlled on a theory based on MPPT. Furthermore the control algo-rithm voltage oriented control (VOC) used for the grid side converter is presented. Theconverter control is implemented using space vector pulse width modulation (SVPWM),the theory of which is also elaborated in the chapter.

In the third chapter the implementation of the theory used in the simulation models isexplained. Furthermore the experimental setup used for verification of the simulationsis introduced, the equipment used and the accuracy of measurements is presented alongwith a description of the generator which the simulations are customized after.

In the fourth chapter the results of the experimental verification and the simulations arepresented. The measurements done with the experimental setup are compared to theresults of a simulation using the same parameters. The results of the simulation modelsusing active and passive rectification as well as varying saliency are then presented.

In the fifth chapter the results presented in chapter four are discussed and analyzed,which includes a comparison of the active and passive rectification as well as a compari-son of generator with different saliency.

Johannes Örnkloo

Introduction 3

1.3 Background

When implementing a mathematical model of a synchronous generator it is commonto use the Park transform, as seen in [2][3][4][5][6][7][8]. The park transform was de-veloped by Robert H. Park in 1929 [9]. The Park transform, often referred to as thedq-transform, transforms the time-varying dynamic performance equations of the three-phase stationary reference frame into the dq rotating reference frame, thereby removingthe time-variance of the dynamic performance equations [10][7].

The use of a passive rectification system is often coupled with a DC-DC converter suchas a boost converter, to gain controllability of the generator side of the system. Severalcontrol algorithms have been presented for these types of systems, most involving aMPPT algorithm [11][12][13][14]. When using active rectification there are also manymethods of control such as field oriented control and direct torque control. Researchhas been conducted in [15][16][17] comparing the two control methods, after brieflyreviewing these control methods the field oriented control was chosen for this work.

Johannes Örnkloo

Theory 4

2 Theory

2.1 Modelling of wind turbine

The wind turbine extracts the kinetic energy from the wind. To derive an expression forthe amount of kinetic energy in the wind, the air particles passing a swept area of thewind turbine are considered a lumped mass with total mass m. The kinetic energy of thewind can be written as

Ek =mV2w

2(2.1)

where m is the mass of the air particles and Vw is the velocity of the air particles. Thetotal mass of the air particles passing the swept area of the wind turbine during a periodof time, t, is

m = ρAVwt = ρπr2Vwt (2.2)

where ρ is the density of the air, At is the swept area of the wind turbine and r is theradius of the turbine rotor. By substituting equation 2.2 into equation 2.1 the total kineticenergy of the wind passing the turbine during a period of time, t, is acquired

E =12

ρπr2V3wt (2.3)

The amount of power in the wind is given by the rate of change of the energy in thewind

Pwind =dEdt

=12

ρπr2V3w (2.4)

However it is not theoretically possible to extract all of the power from the wind sincethat would require the wind speed after the turbine to be zero. The amount of powertheoretically possible to extract from the wind is [18]

P =14

ρA(v21 − v22)(v1 + v2) (2.5)

where v1 is the wind speed before passing the wind turbine and v2 is the wind speedafter passing the turbine. This leads to the maximum theoretical amount of poweravailable to extract being [18]

P =12

ρAV3w1627

(2.6)

which equates to approximately 59% of the power in the wind and is called the Betzlimit. The ratio of extractable power to the total power in the wind is called the powercoefficient and is commonly denoted as Cp. It is influenced by a number of factors

Johannes Örnkloo

Theory 5

including blade design and tip speed ratio.

The power coefficient can be numerically approximated for given values of the tip speedratio, λ, and the pitch angle of the rotor blades, θp. The approximation used in this thesisis [19]

Cp = 0.22(116γ− 0.4θp − 5.0)e

−12.5γ (2.7)

withγ =

11

λ+0.08θ −0.035θ3p−1

(2.8)

and the tip speed ratioλ =

ωmrVw

(2.9)

where ωm is the angular speed of the wind turbine and r is the radius of the wind turbinerotor blades. The maximum amount of power available to extract from the wind is

Pturbine =12

ρAV3wCp(θp,λ) (2.10)

Figure 2.1 shows the relationship between the power coefficient and the tip speed ratiofor given values of the pitch angle using the numerical approximation from equation 2.7- 2.9.

Figure 2.1: The power coefficient as a function of tip speed ratio for different pitchangles.

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Theory 6

2.2 Modelling of permanent magnet synchronous generators

In this section a mathematical model of the PMSG will be presented. The model willfirst be presented in the natural three phase stationary reference frame. The mathemat-ical model of a PMSG in the natural three phase reference frame contains inductanceterms that vary as a function of the rotor angle, and thereby as a function of time. Thisintroduces a large complexity in solving machine and power system problems [10].Therefore, the PMSG model will also be presented in the dq rotating reference frame.The dq rotating reference frame is the model which will be used in the simulations.

Developing a mathematical model of the permanent magnet synchronous generator isgreatly simplified by implementing the following assumptions [10]

• The stator windings are sinusoidally distributed along the air-gap as far as themutual effects with the rotor are concerned.

• The stator slots cause no appreciable variation of the rotor inductances with rotorposition.

• Magnetic hysteresis is negligible.

• Magnetic saturation effects are negligible.

2.2.1 PMSG model in the three-phase stationary reference frame

The stator voltage equation of a permanent magnet synchronous generator in state spaceform can be written as [7]usausb

usc

=Ra 0 00 Ra 0

0 0 Ra

isaisb

isc

+ ddtψsaψsb

ψsc

(2.11)where usa,usb,usc are the instantaneous stator voltages, isa, isb, isc are the instantaneousstator currents, Ra is the armature resistance and ψsa,ψsb,ψsc are the stator flux linkages.The stator flux linkages are given as [7]ψsaψsb

ψsc

=Laa Lab LacLba Lbb Lbc

Lca Lcb Lcc

isaisb

isc

+ ψr + cos(θe)ψr + cos(θe + 2π3 )

ψr + cos(θe − 2π3

(2.12)where Laa, Lbb, Lcc are the self-inductances of the stator windings, Lab, Lbc, Lca are themutual inductances between the stator windings, θe is the electrical angle and ψr is theflux linkage caused by the permanent magnet, sometimes referred to as the back emfconstant. The self inductances and the mutual inductances are all a function of the rotorangle, which is time-varying, therefore the self inductances and the mutual inductancesare also time-varying [10].

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Theory 7

2.2.2 PMSG model in the dq rotating reference frame

By transforming the stationary reference frame into a rotating reference frame the time-varying inductances become constant, and therefore the time-variance of the dynamicperformance equations is also removed [10]. In the dq reference frame the d-axisis aligned with the magnetic axis of the rotor while the q-axis leads the d-axis by 90electrical degrees [7]. The three phase stationary reference frame axes and the dq rotatingreference frame axes can be visualized as in figure 2.2.

ωet a

b

c

d

q

Figure 2.2: The three phase stationary reference frame axes and the dq rotating referenceframe axes.

The Park transformation can be written in matrix form asdq0

= 23 cos(θe) cos(θe −

2π3 ) cos(θe +

2π3 )

−sin(θe) −sin(θe − 2π3 ) −sin(θe +2π3 )

12

12

12

ab

c

(2.13)The inverse Park transformation is given byab

c

= cos(θe) −sin(θe) 1cos(θe − 2π3 ) −sin(θe − 2π3 ) 1

cos(θe + 2π3 ) −sin(θe +2π3 ) 1

dq

0

(2.14)The above transformations can be applied to the voltages, currents and flux linkages. Thezero sequence is included to give the complete degrees of freedom when the three-phasestationary reference frame is transformed into the dq reference frame. Under balancedconditions the zero sequence is equal to zero.[10]

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Theory 8

By applying the Park transformation to equation 2.11 the stator voltage equations of thePMSG in the dq reference frame is given by

usd =dψsd

dt− ψsqωe − Raisd (2.15)

usq =dψsqdt

+ ψsdωe − Raisq (2.16)

where usd,usq are the stator voltages, isd, isq are the stator currents, Ra is the armatureresistance, ψsd,ψsq are the stator flux linkages and ωe is the electrical angular frequencyof the rotor. The stator flux linkages in the dq reference frame is given by

ψsd = Ldisd + ψr (2.17)

ψsq = Lqisq (2.18)

where Ld and Lq are the dq-axis inductances respectively and ψr is the permanent magnetflux linkage. Using equations 2.15 to 2.18 the equivalent circuits of the PMSG in the dqreference frame are drawn as in figure 2.3.

−

+

usd

isd Ra Ld − +

ωeLqisq

−

+

usq

isq Ra Lq

−+

ωeLdisd

−+ ωeψr

Figure 2.3: The equivalent circuits of the generator d-axis and q-axis.

2.2.3 Saliency ratio

The saliency of the rotor is often presented as the ratio of the inductances in the dq-axes. Furthermore most commonly as the ratio of the d-axis inductance to the q-axisinductance, that is, saliency = Ld/Lq. In figure 2.4 the dq-axes of two different types ofpermanent magnet synchronous machines are presented. In figure 2.4a the dq-axes ofa two pole PMSM are presented, in figure 2.4b the dq-axes of a multipole PMSM arepresented, the geometry of the multipole machine was created by Petter Eklund.

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Theory 9

dq

(a) Dq-axes of a two pole PMSM

d

q

(b) Dq-axes of a multipole PMSM

Figure 2.4: The dq-axis of different types of rotors.

2.2.4 Power analysis of PMSG

The instantaneous power output of the stator in the abc reference frame is

P = usaisa + usbisb + uscisc (2.19)

under balanced conditions and transformed into the dq reference frame the instanta-neous power becomes

P =32(usdisd + usqisq) (2.20)

by inserting equation 2.15 and 2.16 into equation 2.20 instantaneous power output of thestator in the dq reference frame can be expressed as

P =32[(isd

dψsddt

+ isqdψsqdt

) + (ψsdisq − ψsqisd)ωe︸ ︷︷ ︸A

−(i2sd + i2sq)Ra] (2.21)

where second term (A) corresponds to the power transferred across the air-gap [10]. Theelectromagnetic torque can be determined by dividing the power transferred across theair-gap by the mechanical speed of the rotor

Te =32(ψsdisq − ψsqisd)

ωeωr

=32

p2(ψsdisq − ψsqisd) (2.22)

where ωr is the mechanical speed of the rotor and p is the number of pole pairs. By in-serting the flux linkage equations 2.17 and 2.18, a final expression for the electromagnetictorque is acquired

Te =3p4(ψrisq + (Ld − Lq)isqisd) (2.23)

Johannes Örnkloo

Theory 10

2.3 Modeling the drive train

When the drive train is modeled as a lumped mass, the inertia of the turbine and thegenerator is considered as one and connected by a stiff shaft. This assumption neglectsthe torsional effects that occur on the shaft when the aerodynamic torque from theturbine and the mechanical torque of the generator act on respective side of the shaft[2].Under these assumptions the mechanical system of the wind turbine and the generatorrotor can be expressed using the simplified swing equation as[20]

Jtotdωedt

= Tm − Te (2.24)

where Jtot is the total inertia of the generator and the turbine, Tm is the mechanical torqueof the wind turbine and Te is the electric torque of the generator.

2.4 Converter topology and control using active rectification

In this section the converter topology and control schemes are presented for the systemusing active rectification. In figure 2.5 an overview of the system topology with activerectification is presented showing an active rectifier, a DC-link and an active inverter.

PMSG GRID

Tm

Figure 2.5: An overview of the system with active rectification

The control schemes used are:

• Maximum power point tracking (MPPT)

• Generator control to achieve maximum torque per ampere

• Grid side control for the active and reactive power flow as well as DC-link voltagecontrol

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Theory 11

2.4.1 Control of generator side converter

In this section the control scheme of the generator side converter is presented. Two ofthe most common vector control strategies for PMSG systems are direct torque control(DTC) and field oriented control (FOC) [16]. The control method chosen for this thesis isfield oriented control, while the computational effort is higher and dynamic response isslower when using FOC it has shown to produce lower torque ripple and lower currentripple as well as better low speed performance [17][15][21] and is therefore better suitedfor the work in this thesis. The field oriented control will be coupled with maximumpower point tracking (MPPT) based on optimal tip speed ratio for the generator sidecontrol algorithm.

Maximum power point tracking

When the wind speed is in the range between cut-in speed and speed correspondingto rated power the goal is to extract maximum power from the wind. As can be seenin equation 2.10, for any given wind speed, this is achieved by controlling the powercoefficient. The pitch angle is set to zero for maximal power capture, figure 2.1 showsthat for a fixed pitch angle there is an optimal tip speed ratio which corresponds tothe peak power coefficient. Equation 2.9 shows that the tip speed ratio is a functionof the wind speed, the angular speed of the rotor and the radius of the turbine blades,consequently the control of the tip speed ratio is given by controlling the angular speedof the rotor. The maximum power point tracking is implemented by measuring the windspeed and using that information to calculate the reference value for the speed of therotor.

Field oriented control

Field oriented control is a closed loop control system. It is expressed in the dq rotatingreference frame with the d-axis is aligned with the magnetic axis of the rotor. Thus thed-axis current component controls the magnetic flux while the q-axis current componentcontrols the electromagnetic torque, thereby allowing the stator current componentsin the dq reference frame to be independently controlled in two closed loops [22]. Inaddition to using the speed of the rotor for MPPT, FOC also uses the speed of the rotorfor coordinate transformation. The control strategy requires three controllers, an innerloop controlling each of the stator current components and an outer loop controlling thespeed of the rotor.

The expression for the electromagnetic torque is presented in equation 2.23. For anon-salient rotor this expression can be simplified as

Te =3p4

ψrisq (2.25)

Johannes Örnkloo

Theory 12

Since the permanent magnet flux linkage is constant the electromagnetic torque and theq-axis stator current will be directly proportional, and the electromagnetic torque cantherefore be controlled by controlling the q-axis stator current. To achieve maximumtorque per ampere the reference d-axis current is therefore set to zero which means thatthe torque angle is constant. For a salient pole generator the expression of electromag-netic torque can not be simplified as in equation 2.25. To achieve MTPA for a salient polegenerator the torque angle has to be controlled, which is less trivial than the constanttorque angle control (CTA) that results in MTPA for a non-salient rotor. However it wasshown in [23] that for a specific salient pole generator the MTPA control produced only4.6 % more torque than the CTA control.

2.4.2 Control of the grid side converter

The objective of the grid side controller is to control the apparent power delivered to thegrid as well as the DC-link voltage. This can be achieved by using the control algorithmvoltage oriented control (VOC). For implementation the grid phase voltages and gridphase currents are measured, the grid voltage angle θg detected and the grid variablestransformed using the Park transformation. Theoretically, only two of each grid variableneeds to be measured using the assumption of balanced voltages and currents, howeverthe variables may contain harmonics and be unbalanced. A phase-locked loop (PLL) istherefore used to detect the voltage angle. [22]

The active and reactive power of the grid can be calculated asPg = 32 (ugdigd + ugqigq)Qg = 32 (ugqigd − ugdigq) (2.26)where ugd,ugq, igd, igq are the grid dq-axes voltages and currents respectively. To imple-ment the VOC algorithm the d-axis component of the grid voltage is aligned with thegrid voltage vector, meaning that ugd = ug, as a result the q-axis component of the grid

voltage is equal to zero (ugq =√

u2g − u2gd = 0). [22]

The grid active and reactive power in equation 2.26 can then be calculated asPg = 32 ugdigdQg = − 32 ugdigq (2.27)The dq-axis components of the grid currents are cross-coupled, which can be shown bytransforming the state equations of the grid-side circuit into the dq reference frame. Thestate equation of the grid-side circuit in the abc reference frame can be expressed as [22]

Johannes Örnkloo

Theory 13

digadt = (uga − uia)/Lg

digbdt = (ugb − uib)/Lg

digcdt = (ugc − uic)/Lg

(2.28)

where uia,uib,uic denotes the inverter output voltage. The park transform yieldsdigddt = (ugd − uid + ωgLgigq)/Lg

digqdt = (ugq − uiq −ωgLgigd)/Lg

(2.29)

where ωg is the angular frequency of the grid and ωgLgigd, ωgLgigq are induced speedvoltages, which are a result of transformation from the three-phase stationary referenceframe to the rotating reference frame. Equation 2.29 shows the cross-coupling of the dq-axis current components caused by the induced speed voltages, a decoupled controlleris therefore implemented. [22]

2.5 Converter topology and control using passive rectification

The converter topology used for the system utilizing passive rectification is a diodebridge rectifier, a boost converter and an active inverter. The objective of the boost con-verter is to boost the DC-link voltage to its reference value which is done by controllingthe duty cycle of the switch. In figure 2.6 an overview of the system topology withpassive rectification is presented.

PMSG GRID

Ldc

Cin CdcUin Udc

Tm

Figure 2.6: An overview of the system with active rectification.

2.5.1 DC link boost converter control

The boost converter control is based on a MPPT where the rotational speed of thegenerator is to be controlled by the dc voltage and current.

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Theory 14

The terminal voltage of a non-salient permanent magnet synchronous generator is

U = E− I(Ra + jωeLs) (2.30)

where E is the back electromotive force, I is the phase current, Ra is the armature re-sistance and Ls is the synchronous inductance. The back electromotive force is directlyproportional to the rotational speed of the generator for a PMSG, by neglecting theimpedance of the generator the terminal voltage can be assumed approximately propor-tional to the speed of the generator [14]. In a three phase diode bridge rectifier the dcvoltage can ideally be expressed as [24]

Udc =3√

3π

Û (2.31)

where Udc is the output voltage of the diode bridge and Û is the magnitude of the acphase voltage. Using equation 2.31 and proportionality of the back electromotive forceto the generator speed, the dc voltage can be assumed approximately proportional tothe rotational speed of the generator, that is

Udc ∝ ω (2.32)

As can be seen in equation 2.10 and 2.9 the amount of power extracted from the windis proportional to the speed of the wind in cube, and therefore also proportional to therotational speed of the turbine in cube.

Pturbine ∝ V3w ∝ ω3 (2.33)

using equation 2.32 and equation 2.33 the maximum power Pmax is therefore proportionalto the cube of the dc voltage, that is

Pmax ∝ U3dc (2.34)

The dc power can be expressed as

Pdc = Udc Idc (2.35)

For maximum output power the dc voltage squared is then proportional to the dc currentas

U2dc ∝ Idc (2.36)

which was proposed in [13].

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Theory 15

Using the derived relationship from equation 2.36, a control algorithm from [14] ispresented below for control of the boost converter. The DC-link reference current isobtained by

I∗dc = k(Uin −Uin,min)2 + Idc,min (2.37)

where Uin is the input voltage to the boost converter and k is calculated as

k =Idc,max − Idc,min

(Uin,max −Uin,min)2(2.38)

The inductor transient equation for continous current mode is

LdcdIdcdt

= Uin −Us = Uin − (1− D)Udc (2.39)

where Us is the voltage over the switch, Ldc is the boost converter inductor inductanceand D is the duty cycle of the boost converter. Rearranging equation 2.39 for Idc gives

Idc =1

Ldc

∫(Uin − (1− D)Udc)dt (2.40)

with compensation of the feedforward term the duty cycle of the boost converter isthen acquired from equation 2.40 [14]. In figure 2.7 an overview of the boost converterpresented is given.

Figure 2.7: Overview of the DC-link boost converter

It is preferred for the converter to operate in continuous current mode (CCM) for higherefficiency, for the converter to operate in CCM the required size of of the inductor is [24]

Ldc >(1− D)2DR

2 fs(2.41)

where R is the resistance of the load and fS is the switching frequency.

To reduce the output voltage ripple to Ur the minimum capacitance of the boost convertercapacitor needs to be [24]

Cdc =DUdcUrR fs

(2.42)

where Udc is the output voltage of the boost converter.

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Theory 16

2.6 Space vector pulse width modulation

There are several pulse width modulation (PWM) techniques. Two of the most commonPWM techniques for voltage source converters (VSC) are the sinusoidal pulse widthmodulation (SPWM) and the space vector pulse width modulation (SVM). In this thesisthe space vector modulation technique has been used as it has been shown that it resultsin lower current harmonics in the AC output of the converter and achieves a higherpossible modulation index [25].

2.6.1 Converter

For the active rectification and the inverter a two-level voltage source converter can beused. It consists of six IGBT switching devices on three legs. The equivalent circuit of theconverter is presented in figure 2.8. Each switching device has two states, a conductivestate and a blocking state. For each leg of the converter only one of the switching devicescan be conducting, i.e. if switching device 1 is conducting switching device 2 can notbe conducting. The state of the switches is represented by 1 when the upper switch ofthe leg is conducting (and the lower switch of the leg is blocking) and 0 when the upperswitch of the leg is blocking (and the lower switch of the leg is conducting).

SW1

SW2

SW3

SW4

SW5

SW6

Vdc

Figure 2.8: Two-level voltage source converter

2.6.2 Space vectors

For a three-phase two-level converter there are eight switching states, six of which areactive and produce a non-zero output voltage and two that produce zero voltage output.Each active switching state of the converter corresponds to a space vector [22]. In table2.1 each of the space vectors and their definitions are presented

Johannes Örnkloo

Theory 17

Table 2.1: Space vectors corresponding to switching states [22]

Space Vector Switching state Vector definition

U0 (000) 0U1 (100) 23Udce

j0

U2 (110) 23Udcej π3

U3 (010) 23Udcej 2π3

U4 (011) 23Udcej 3π3

U5 (001) 23Udcej 4π3

U6 (101) 23Udcej 5π3

U7 (111) 0

The active vectors divide the plane into six sectors of equilateral triangles as can be seenin figure 2.9.

U1

U2U3

U4

U5 U6

Ure f1

2

3

4

5

6

Figure 2.9: Space vector representation of two-level VSC

The control algorithm used for the converter yields reference phase voltages which aretransformed to the αβ-reference frame to create a reference space vector. The referencespace vector is defined as [22]

Ure f = uα + juβ =23(ua,re f + ub,re f ej

2π3 + uc,re f e−j

2π3 ) (2.43)

where the αβ-components are acquired by using the Clarke transform on the three-phaseinstantaneous voltages. The Clarke transform can be written as [22]

[uαuβ

]=

23

[1 − 12 −

12

0√

32 −

√3

2

]uaubuc

(2.44)A necessary assumption when using the αβ-transform is that the three-phase system isbalanced.

Johannes Örnkloo

Theory 18

2.6.3 Implementation of SVPWM

The reference voltage is synthesized by activating the two space vectors adjacent to thereference space vector for the appropriate amount of time for each switching period, i.ewhen the reference space vector is in sector 1 as in figure 2.9 the space vectors U1 and U2as well as the zero space vectors (U0, U7) are used to synthesize the voltage reference.

The implementation can therefore be divided into three steps

• Determine the magnitude and position of the reference space vector

• Determine which sector the reference space vector is in

• Calculate the dwell time of the active space vectors needed to synthesize thereference space vector.

Space vector determination

When the three phase reference voltages are sampled the αβ-transform is applied toacquire the reference space vector in the αβ reference frame, the magnitude of thereference space vector can then be calculated as

|Ure f | =√

u2α + u2β (2.45)

and the position of the reference space vector can be calculated as

θ = arctan(uαuβ

) (2.46)

The sector in which the reference space vector is can then be determined according totable 2.2.

Table 2.2: Sector number and corresponding angle interval

Sector number Sector angles

1 0°≤ θ < 60°2 60°≤ θ < 120°3 120°≤ θ < 180°4 180°≤ θ < 240°5 240°≤ θ < 300°6 300°≤ θ < 360°

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Theory 19

To determine the dwell time for each switching state the principle of volt-second balanceis used. When the reference voltage vector is in the first sector the space vectors used areU1,U2,U0 resulting in the following system of equations [22]Ure f Ts = U1ta + U2tb + U0t0Ts = ta + tb + t0 (2.47)where ta, tb, t0 are the dwell times for the respective vectors. By inserting the space vectordefinitions from table 2.1 in equation 2.47 and splitting the reference vector in to realand imaginary parts corresponding to the α-axis and β-axis respectively the followingresult is acquired [22] Re : Ure f Ts cosθ = 23UDCta + 13UDCtbIm : Ure f Ts sinθ = 1√3UDCtb (2.48)Using Ts = ta + tb + t0 together with equation 2.48 the dwell time for each of the vectorscan be calculated as [22]

ta =√

3TsUre fUDC

sin (π3 − θ)

tb =√

3TsUre fUDC

sin (θ)

t0 = Ts − ta − tb

(2.49)

Although these calculations are valid only for the first sector, by using a modifiedexpression for the angle θ the calculations can be adapted to all sectors, the expressionfor the modified angle is [22]

θ′ = θ − (k− 1)π3

(2.50)

where k = 1,2, ...,6 for each sector respectively, the resulting angle is then 0 ≤ θ′ <π/3 ∀ k.

Johannes Örnkloo

Method 20

3 Method

3.1 Simulations

In this section the simulation methods are presented and the theory presented in chapter2 is implemented. The simulations were done in the simulation software MatLabSimuLink.

3.1.1 Wind turbine

The implementation of the wind turbine was done using the measured wind speed andgenerator speed to calculate the power coefficient from equation 2.7 - 2.9, whereby themechanical torque input to the generator was calculated using equation 2.10. Since theprime mover is not within the main scope of this thesis the wind turbine is only modeledfor the MPPT range, that is between cut in wind speed and rated power.

3.1.2 Generator

The generator parameters used in the simulations are matched to a generator presentedin section 3.2.1. As the generator phases are not balanced the average value of eachphase quantity is used in the simulations for simplicity.

The d- and q-axis inductance of the generator has not been experimentally determinedin an accurate way, however in the measurements done the saliency has shown to besmall (Ld/Lq ∼ 1). For the case of a non-salient rotor the d-axis and q-axis inductance isset equal to the synchronous inductance of the generator. In the cases with a salient rotorthe d-axis inductance is set equal to the synchronous inductance of the generator andthe q-axis inductance is set to 1.4 and 0.6 times the synchronous inductance respectively.The flux linkage of the generator is calculated as

ψr =UNL,rms

√2

fel2π(3.1)

where UNL,rms is the rms value of the no load phase voltage at rated speed and fel is theelectrical frequency at rated speed.

Johannes Örnkloo

Method 21

3.1.3 Drive train

The drive train model used does not include a gearbox and the generator is thereforedirect driven. The implementation of the drive train is done using the lumped massmodel. The drive train can therefore be implemented using the simplified swing equationpresented in equation 2.24.

3.1.4 Active rectification

The control algorithm for the generator side converter that was presented in section2.4.1 is implemented as in figure 3.1. As stated in section 2.4.1 the d-axis stator currentreference value is set to zero for the non-salient rotor to achieve maximum torque perampere. The d-axis stator current reference value for the salient rotor cases is also set tozero for simplicity as the difference in torque produced when using MTPA control andCTA control has been shown to be low [23]. The q-axis stator current reference valueis acquired by the PI speed controller which uses the error between the reference rotorspeed acquired by MPPT and the actual rotor speed as input. The dq-axis stator voltagereference values are then acquired by two PI current controllers which use the errorbetween the dq-axis stator current reference values and actual values as input. Spacevector pulse width modulation is used to create the gating signal for the converter.

Johannes Örnkloo

Method 22

PIPI

PI

1z

SVPWM

PMSG GRID

dq

abc

abcαβ

dqabc

θ

i∗sdisd

i∗sqisq

ω∗rωr

isa isb isc

isdisq

u∗sβu∗sα

u∗sau∗sbu

∗sc

u∗sdu∗sq

Figure 3.1: Control system used for the generator side converter, parameterssuperscripted with * are reference values.

3.1.5 Passive rectification

The control algorithm from [14] presented in section 2.5.1 is implemented and theresulting system is shown in figure 3.2. The dc current reference value is acquired fromequation 2.37 which is then compared to the actual dc current and the error is sent to aPI controller. Using the output of the PI controller, the input dc voltage and the boosteddc voltage, the duty ratio of the switch is then determined.

Johannes Örnkloo

Method 23

PWM

PI

÷

PMSG GRID

Ldc

Cin CdcUin Udc-

+

-

+

Uin

Udc D

-+

++

I∗dcIdcUin

Figure 3.2: Control system used for the boost converter, parameters superscripted with* are reference values.

3.1.6 Grid side converter

To achieve systems easily comparable the implementation of the grid side converterexplained below was used for the system using active rectification as well as for thesystem using passive rectification.

The control algorithm presented in section 2.4.2 is implemented for the grid side con-verter and presented in figure 3.3. As seen in equation 2.27 the active and reactive powerdelivered to the grid can be independently controlled by controlling the dq-axis gridcurrents respectively. The q-axis grid current reference value is acquired from

igq∗ = −2Q∗g3ugd

(3.2)

where Q∗g is the reference value of reactive power in the grid which is chosen as zero inthe simulations, the reference q-axis grid current is therefore zero. The reference d-axisgrid current value is acquired from a PI controller using the error between the actual andreference voltage on the DC-link as input, thus realizing the DC-link voltage control.

The grid was modeled as an ideal voltage source with a constant rms line-to-line voltageof 490 V.

Johannes Örnkloo

Method 24

PI

PI

ωgLg

ωgLg

PI

÷

PLLSVPWM

PMSG GRID

dq

abc

abcαβ

dqabc

θg

ugq

ugd UDC

U∗DCi∗gd

i∗gq

igd

igq

u∗gd

u∗gqQ∗g

−1.5ugd

iga igb igcuga ugb ugc

igd igq ugqugd

u∗gβu∗gα

u∗gcu∗ga u∗gb

u∗gd u∗gq

C UDC

Figure 3.3: Control system used for the grid side converter, parameters superscriptedwith * are reference values.

3.2 Experimental setup

To verify the results from the simulations an experiment is set up, however only parts ofthe simulated system is verified experimentally. The experimental setup consists of apermanent magnet synchronous generator driven by an electrical motor, the generatoris connected to a diode bridge rectifier, connected to a capacitor bank in parallel with aresistive load.

The equipment used in the experimental setups is:

• Motor: ABB M2AA 200 L

• Permanent magnet synchronous generator

• Diode bridge: SKKD 26/16

• Load resistors: Terco MV1100

• Capacitors: RIFA PEH200ZX4330M

• Differential probes: Pico Technology TA041

• Current probes: Agilent 1146A & Tektronix A622

• Oscilloscope: Pico Technology PicoScope 3425

Johannes Örnkloo

Method 25

3.2.1 Generator

The generator used was designed and built at Uppsala University for a small scalewind power system. The relevant generator parameters are presented in table 3.1, theparameters were determined through measurements presented in [26].

Table 3.1: Generator parameters [26]

Quantity Value

Rated power [kW] 12.02Electrical frequency at rated power [Hz] 33.9

Number of pole pairs 16Phase a b c

No load voltage (rms) [V] 118.2 117.5 118.1Full load voltage (rms) [V] 110.4 110.3 110.4

Resistance [mΩ] 141 154 151Synchronous inductance [mH] 3.1

3.2.2 Measurement equipment accuracy

In all experiments the data was collected using the measurement equipment presentedin section 3.2. In this section the accuracy of the measurement equipment is presentedand the corresponding value in SI-units is calculated for each configuration.

The PC oscillocope accuracy is ±1 % of the range. The differential probe attenuationwas 100:1 for all measurements with a range of ±700 V, the accuracy of the differentialprobe is ±2 % of the range. The current probe accuracy varies with the amplitude of thecurrent measured, below 40 amperes the probe has an accuracy of ±4 % of reading ±50mA, above 40 amperes the probe has an accuracy of ±15 % of reading ±100 mA. In table3.2 the accuracy is presented in SI-units for the settings of each measurement. Howeverin [26] a cross calibration of the voltage and current measurements were performedfor the same experimental setup. It showed that the measurement accuracy was muchhigher than the specified measurement accuracy of the equipment. For the voltagemeasurements the accuracy was approximately ±4 V, while the current measurementaccuracy was ±1.54 in the range of ±58 A [26].

Johannes Örnkloo

Method 26

Table 3.2: Accuracy of measurement equipment at rated speed and half of rated speed

Equipment Accuracy at rated speed

Quantity Voltage CurrentPC oscilloscope ±5 [V] ±1 [A]

Differential probe ±14 [V] -Current probe - ±15 % of reading ±100 [mA]

Equipment Accuracy at half of rated speed

Quantity Voltage CurrentPC oscilloscope ±2 [V] ±0.5 [A]

Differential probe ±14 [V] -Current probe - ±4 % of reading ±50 [mA]

3.3 Verifying experiments

The verification was done by setting up an experiment using the equipment presentedin section 3.2 and then customizing a simulation after the experimental setup. Theexperimental setup corresponds to the generator, diode bridge rectifier and DC-linkof the model from the passive rectification simulation study from section 3.1.5. Thesimulation customization was done by inputting the generator parameters from table3.1 into the generator model in the simulations, adding a capacitor with the samecapacitance as the ones used in the experiment and then tuning the resistance of thesimulations to the resistance of the experiment by matching the power output of bothsystems. The experiment data was measured after the generator had been run at full loadfor approximately 10 minutes, to ensure that the system was in a thermal steady-state.The data was saved in 10 time series of 500 ms each.

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Results 27

4 Results

4.1 Experimental verification

In this section the results from the experimental verification is presented. In table 4.1 themeasured and simulated values as well as the measurement accuracy of relevant systemquantities at rated speed and with a constant load resistance are presented. However themeasurement accuracies are presented with the accuracy of the measurement equipmentas specified by the equipment manufacturer. The accuracy would be significantly higherusing the result of the cross calibration from [26].

Table 4.1: Comparison of system quantities at rated speed

Quantity Simulated value Measured value Measurement accuracy

Phase current (rms) [A] 45.70 45.03 6.81Phase voltage (rms) [V] 104.0 106.9 13.8DC current (avg.) [A] 57.8 57.6 8.80DC voltage (avg.) [V] 231.2 231.5 14.9

Power (avg.) [kW] 13.36 13.35 2.21

In table 4.2 the measured and simulated values of relevant system quantities at half ofthe rated speed and with a constant load resistance are presented. In table 4.1 and 4.2the power is calculated as Pdc = Udc Idc.

Table 4.2: Comparison of system quantities at half of rated speed

Quantity Simulated value Measured value Measurement error

Phase current (rms) [A] 24.25 24.23 0.96Phase voltage (rms) [V] 52.52 55.00 12.9DC current (avg.) [A] 30.47 30.64 1.37DC voltage (avg.) [V] 119.5 120.2 14.1

Power (avg.) [kW] 3.64 3.68 0.46

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Results 28

In figure 4.1 - 4.5 the simulated and measured parameter waveforms are presented atrated speed, the measurement accuracy is only presented in the ac side measurementsdue to the underestimation of measurement accuracy of the equipment presented in [26].In figure 4.1 the measured and simulated phase currents at rated speed are presentedalong with the measurement accuracy. In figure 4.2 the measured and simulated phasevoltages at rated speed are presented along with the measurement accuracy. In figure4.3 the measured and simulated dc currents at rated speed are presented. In figure 4.4the measured and simulated dc voltages at rated speed are presented. In figure 4.5 themeasured and simulated power in the load at rated speed are presented.

Figure 4.1: Phase current of measurement and simulation at rated speed

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Results 29

Figure 4.2: Phase voltage of measurement and simulation at rated speed

Figure 4.3: dc current of measurement and simulation at rated speed

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Results 30

Figure 4.4: dc voltage of measurement and simulation at rated speed

Figure 4.5: Load power of measurement and simulation at rated speed

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Results 31

In figure 4.6 - 4.10 the simulated and measured parameter waveforms are presentedat half of rated speed. In figure 4.6 the measured and simulated phase currents at halfof rated speed are presented along with the measurement accuracy. In figure 4.7 themeasured and simulated phase voltages at half of rated speed are presented along withthe measurement accuracy. In the figure a signal containing harmonics of the 5th and 7th

order is also presented. The harmonic signal is composed of a fundamental componentof amplitude 80 V, and the 5th and 7th order harmonics has an amplitude of 8 V and6 V respectively. In figure 4.8 the measured and simulated dc currents at half of ratedspeed are presented. In figure 4.9 the measured and simulated dc voltages at half ofrated speed are presented. In figure 4.10 the measured and simulated power in the loadat half of rated speed are presented.

Figure 4.6: Phase current of measurement and simulation at half of rated speed

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Results 32

Figure 4.7: Phase voltage of measurement and simulation at half of rated speed

Figure 4.8: dc current of measurement and simulation at half of rated speed

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Results 33

Figure 4.9: dc voltage of measurement and simulation at half of rated speed

Figure 4.10: Load power of measurement and simulation at half of rated speed

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Results 34

4.2 Simulation study

In this section the relevant quantities of the simulation models of the entire systemwith active and passive rectification as well as with different saliency of the rotor arepresented as plotted waveforms as well as in tables containing rms values and averagevalues of relevant quantities.

There are six cases of simulations, two cases of rectification and three cases of saliency,a name for each case will therefore be defined. The data from models using activerectification will be denoted AIR (active IGBT rectification) followed by the saliency ofthe rotor. The data from models using passive rectification will be denoted PDR (passivediode rectification) followed by the saliency of the rotor. The saliency ratios used in thesimulations are 0.71, 1.0 and 1.67 which will be denoted as an S followed by the saliencyratio. An example of a simulation denotation will then be AIR-S1.0.

4.2.1 Rated wind speed

In this section the results of the simulations at a wind speed corresponding to ratedpower will be presented. In table 4.3 and 4.4 system quantities of the simulations arepresented for the case of active and passive rectification as well as for the cases withdifferent saliency of the generator rotor. The goal was to get an average output power of12 kW, which was achieved in the system using active rectification at a wind speed of9.2 m/s and at a wind speed of 9.4 m/s for the system using passive rectification. Alldata is presented in steady state, as the goal was not to implement a fast control systemrather only a system that reaches the set point in steady state. At a wind speed of 9.2m/s the setpoint of the generator speed is 216 rad/s in angular electric frequency. Ata wind speed of 9.4 m/s the setpoint of the generator speed is 220.7 rad/s in angularelectric frequency. Since the grid was modeled as an ideal voltage source with a constantvoltage of VLL,rms = 490V the waveform is not plotted.

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Table 4.3: Comparison of system quantities for active rectification

Quantity Generator side

Case AIR-S1.67 AIR-S1.0 AIR-S0.71Angular electric frequency (avg.) [rad/s] 216.0 216.0 216.0

Phase current (rms) [A] 34.69 34.69 34.69Turbine input power (avg.) [kW] 12.44 12.44 12.44

Copper losses [W] 671.6 671.2 671.2

Quantity DC-link & Grid side

Case AIR-S1.67 AIR-S1.0 AIR-S0.71DC-link voltage (avg.) [V] 1200 1200 1200

Phase current (rms) [A] 14.36 14.22 14.18Active power (avg.) [kW] 12.19 12.07 12.03

Table 4.4: Comparison of system quantities for passive rectification

Quantity Generator side

Case PDR-S1.67 PDR-S1.0 PDR-S0.71Angular electric frequency (avg.) [rad/s] 224.4 224.3 223.2

Phase current (rms) [A] 40.35 40.10 39.97Turbine input power (avg.) [kW] 13.27 13.27 13.27

Copper losses [W] 924.5 904.6 898.8

Quantity DC-link & Grid side

Case PDR-S1.67 PDR-S1.0 PDR-S0.71DC-link voltage (avg.) [V] 1220 1220 1220

Phase current (rms) [A] 14.13 14.14 14.15Active power (avg.) [kW] 12.00 12.01 12.02

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In figure 4.11 the phase current and phase voltage waveforms for the case of passiverectification and a saliency ratio of 1.67 is presented.

Figure 4.11: Phase voltage and current for case PDR-S1.67

In figure 4.12 the phase current and phase voltage waveforms for the case of passiverectification and a saliency ratio of 1.0 is presented.

Figure 4.12: Phase voltage and current for case PDR-S1.0

In figure 4.13 the phase current and phase voltage waveforms for the case of passiverectification and a saliency ratio of 0.71 is presented.

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Figure 4.13: Phase voltage and current for case PDR-S0.71

In figure 4.14 the grid currents for all cases of saliency ratios and active rectification ispresented.

Figure 4.14: Grid phase currents for case AIR

In figure 4.15 the grid currents for all cases of saliency ratios and passive rectification ispresented.

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Figure 4.15: Grid phase currents for case PDR

In figure 4.16 the active and reactive power on the grid side is presented for the case ofactive rectification. The reactive power was calculated in a SimuLink block which statesthat the instantaneous reactive power is accurate only when the three phase currentsand voltages are balanced and free from harmonic content, which can not be assumed ofthe three phase quantities in the simulation models.

Figure 4.16: Grid active and reactive power for case AIR

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Results 39

In figure 4.17 the active and reactive power on the grid side is presented for the case ofpassive rectification.

Figure 4.17: Grid active and reactive power for case PDR

In table 4.5 the mean value and the peak-to-peak value of the dq-axis currents for allcases are presented.

Table 4.5: Comparison of stator dq-axis currents

Case mean id peak-to-peak id mean iq peak-to-peak iq

AIR-S1.67 0.0 1.66 49.1 2.93AIR-S1.0 0.0 1.75 49.1 1.70AIR-S0.71 0.0 1.72 49.1 1.13

PDR-S1.67 21.0 28.4 52.1 15.9PDR-S1.0 24.4 26.6 50.4 9.71PDR-S0.71 21.0 26.1 52.1 7.38

4.2.2 Half of rated wind speed

To examine the behavior of the system at less than rated power simulations were alsorun at half of rated speed, however since the main interest is the behavior of the systemat rated wind speed the data presented in this section will only be from simulations witha saliency ratio of 1.0.

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In table 4.6 the relevant system quantities are presented. At a wind speed of 4.6 m/s theoptimal rotational speed of the generator, according to the MPPT, is 108.0 rad/s. At awind speed of 4.7 m/s the optimal rotational speed is 110.4 rad/s.

Table 4.6: Comparison of system quantities at half of rated wind speed

Quantity (gen. side) Active rectification Passive rectification

Wind speed [m/s] 4.6 4.7Angular electric frequency (avg.) [rad/s] 108.0 100.9

Phase current (rms) [A] 8.68 10.70

Quantity (grid side) Active rectification Passive rectification

DC-link voltage (avg.) [V] 1200 1220Phase current (rms) [A] 1.95 1.54

Active power (avg.) [kW] 1.65 1.30

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Discussion & Analysis 41

5 Discussion & Analysis

5.1 Experimental verification

Figure 4.1 and 4.6 show that the phase current waveforms of the simulated valuescoincide very well with the experimental results.

The phase voltage waveforms in figure 4.2 and 4.7 do not coincide perfectly, it can alsobe seen in table 4.1 and 4.2 that the rms value of the voltage differs by a few percent.Furthermore the phase voltages are clearly not perfectly sinusoidal, however as can beseen in figure 4.7 where the phase voltages are presented along with a signal containing5th and 7th order harmonics, both the simulated waveforms and the experimental showsimilarities with the harmonic signal.

The dc currents from simulations and experimental verification are presented in figure4.3 and 4.8. In magnitude and general waveform they are much alike, however themeasured dc currents have a current spike at every diode commutation, which does notappear in the simulations. A possible explanation for the current spikes is that they arecaused by the transient behavior of the phase voltage for diode rectification.

The dc voltages of the simulations and experimental verification are presented in figure4.4 and 4.9. At half of rated speed the measurements are fairly consistent with thesimulations, at rated speed however the measured value is a higher than the simulatedvalue, for which there can be a few explanations e.g. the speed of the generator might belower in the simulations than in the measurements, it could be a measurement error asit lies within the range of error in the measurements or it might be due to a mismatchin the synchronous inductance of the generator in the simulations and the measurements.

The power in the load is calculated as Pdc = Udc Idc and therefore carries the characteristicsof the previously mentioned dc voltage and dc current, which is noticeable due to thespikes.

5.2 Simulation study

The dc-link voltage setpoint of the simulations was chosen too high. A dc-link voltagemore appropriate would be equal to or slightly higher than the line-to-line voltage of

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Discussion & Analysis 42

the generator at no-load and rated speed. At the point where this error was made clearthe parameter was too deeply embedded in the system to change without having torecalibrate the entire system, which would be too time consuming.

5.2.1 Active rectification

The data presented in table 4.3 and 4.5 shows that the control system for the case ofactive rectification succeeds in keeping the controlled parameters to their setpoints. Asexplained in section 2.4. The setpoint of the d-axis current is zero to achieve maximumtorque per ampere, the control system achieves this setpoint for all cases of rotor saliency.The optimal rotational speed of the rotor, according to the MPPT algorithm, was alsoachieved for all cases of rotor saliency. The copper losses, also presented in table 4.3 and4.4, are lower in the case of active rectification than in the case of passive rectification,this is due to the generator side phase current rms value being lower in the case ofactive rectification, but also due to the waveform of the phase current of the passiverectification being higher in maximum amplitude than in the case of active rectification.

The grid side converter goal was to control the dc-link voltage to the setpoint, as wellas controlling the active and reactive power injected to the grid. The control systemsucceeds in keeping the voltage level to the setpoint for all cases of saliency. Furthermorethe control system succeeds in keeping the reactive power injected to the grid to zero bykeeping the q-axis current to zero as presented in figure 4.16. The system also achievesthe goal of reaching an output power of 12 kW.

The results of the simulations are very similar for different rotor saliencies despite thatthe control system was implemented for MTPA in the case of a non-salient rotor andCTA in the case of a salient rotor, which indicates that the saliency of the rotor has littleeffect on this system. This might be due to the synchronous inductance of the generatorbeing relatively low, a higher impact of the control system difference is expected for agenerator with larger synchronous inductance.

5.2.2 Passive rectification

As the generator parameters cannot be directly controlled when using passive recti-fication the goal of the boost converter control is to indirectly control the generatorparameters by controlling the dc current and dc voltage. The optimal rotational speedof the generator at the wind speed used in the simulations, according to the MPPTalgorithm, is 220.7 rad/s however the control system was not quite able to keep thespeed of the generator at its optimal speed which is shown in table 4.4. A possibleexplanation for this is that the system with passive rectification can not compensate forthe voltage drop in the generator, whereas the control system assumes that the terminal

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Discussion & Analysis 43

voltage is directly proportional to the rotational speed.

Furthermore as mentioned in section 4.2.1, the system utilizing passive rectificationrequired a higher wind speed to achieve the same output power to the grid compared tothe system utilizing active rectification, this could either be a result of the control systemnot being tuned accurately, a flaw in the control system or because of higher losses inthe system. However the system managed to keep the reactive power injected to thegrid at zero as presented in figure 4.17, and the dc link voltage was also controlled to itssetpoint as presented in table 4.4.

When analyzing figures 4.11 - 4.13 it is shown that the harmonic content of the phasevoltage shown in the experimental verification exists also in the model with a completesystem. As shown in table 4.4 there is little impact on the rms value of the phase currentand phase voltage when using generator models with different saliency.

5.2.3 Half of rated wind speed

As in the case of rated wind speed, the active rectification system manages to keep theangular electric frequency to its reference value, as well as keeping the dc voltage levelto its reference value.

However the system using passive rectification was not on its reference value of angularelectrical frequency at rated wind speed, and it was not on its reference value at halfthe rated wind speed either. This results in the turbine extracting less power from thewind due to the tip speed ratio not being at its optimal value. At rated wind speed theangular electric frequency was higher than its reference value, whereas at half of ratedwind speed it is lower than its reference value.

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Conclusion 44

6 Conclusion

6.1 Experimental verification

The simulation model customized after the experimental setup yields results that coin-cide fairly well with the experimental results except for some transient behavior of theexperimental system that does not appear in the simulations and a voltage level of thesimulations that is lower than the measurements for rated speed. However the resultscoincide well enough to draw the conclusion that the simulations present results thatreflect the behavior of a real system.

6.2 Simulations

As discussed in section 5.2 the difference in rotor saliency has little to no impact for mostparameters. There is a slight change in active power injected to the grid, where the mostnotable difference is in the case of active rectification where the saliency ratio of 1.67shows a relevant increase in output power when compared to the other saliency ratios.However the control systems implemented seem to achieve good results for all threesaliency ratios in both rectification cases.

The wind turbine is only modelled in the MPPT-range and the system is therefore notsimulated in wind speeds that exceed rated power. For future work a pitch angle controlcould be implemented that keeps the generated power at 12 kW at higher wind speeds.This is achieved by pitching the blades to lower the power coefficient, and thereforelowering the power extracted from the wind.

The drive train model used in the simulations is a lumped mass model. This modelneglects the torsional effects on the shaft between the wind turbine and the rotor of thegenerator. In reality the torsional effects on the shaft could affect the system and for amore complete analysis of the system a two-mass model should be implemented.

A passive rectification system lacks controllability when compared to an active rectifica-tion system as a frequency converter using passive rectification has fewer controllableswitches than the active equivalent. A lack in controllability results in the system notbeing able to perform as well as a system using active rectification. However the con-

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Conclusion 45

trollable switches are more expensive than the passive devices, leading to the choice ofrectification system being a trade-off between performance and cost.

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Literature 46

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[9] R. H. Park, “Two-reaction theory of synchronous machines generalized method ofanalysis-part i”, Transactions of the American Institute of Electrical Engineers, vol. 48,no. 3, pp. 716–727, Jul. 1929.

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[14] S.-H. Song, S.-i. Kang, and N.-k. Hahm, “Implementation and control of gridconnected ac-dc-ac power converter for variable speed wind energy conversionsystem”, in Eighteenth Annual IEEE Applied Power Electronics Conference andExposition, 2003. APEC ’03., vol. 1, February 2003, 154–158 vol.1.

[15] F. Korkmaz, İ. Topaloğlu, M. F. Çakir, and R. Gürbüz, “Comparative performanceevaluation of foc and dtc controlled pmsm drives”, in 4th International Conferenceon Power Engineering, Energy and Electrical Drives, May 2013, pp. 705–708.

[16] C. Busca, A. Stan, T. Stanciu, and D. I. Stroe, “Control of permanent magnetsynchronous generator for large wind turbines”, in 2010 IEEE InternationalSymposium on Industrial Electronics, Jul. 2010, pp. 3871–3876.

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[19] S. Heier, Grid integration of wind energy: Onshore and offshore conversion systems.John Wiley & sons, inc., 2014, p. 43.

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Simulation models 49

Appendices

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A Simulation models

Figure A.1: Overview of simulation model utilizing passive rectification

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Appendices 51

Figure A.2: Overview of simulation model utilizing active rectification

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SammanfattningExecutive SummaryList of TablesList of FiguresIntroductionAim of the thesisLimitations

LayoutBackground

TheoryModelling of wind turbineModelling of permanent magnet synchronous generatorsPMSG model in the three-phase stationary reference framePMSG model in the dq rotating reference frameSaliency ratioPower analysis of PMSG

Modeling the drive trainConverter topology and control using active rectificationControl of generator side converterControl of the grid side converter

Converter topology and control using passive rectificationDC link boost converter control

Space vector pulse width modulationConverterSpace vectorsImplementation of SVPWM

MethodSimulationsWind turbineGeneratorDrive trainActive rectificationPassive rectificationGrid side converter

Experimental setupGeneratorMeasurement equipment accuracy

Verifying experiments

ResultsExperimental verificationSimulation studyRated wind speedHalf of rated wind speed

Discussion & AnalysisExperimental verificationSimulation studyActive rectificationPassive rectificationHalf of rated wind speed

ConclusionExperimental verificationSimulations

LiteratureAppendicesSimulation models