Modeling and Control of a PMSynRel Drive for a Plug-In ...442423/FULLTEXT01.pdf · An alternative solution, the hybrid electric vehicle (HEV) concept, alleviates these issues by combining

Modeling and Control of a PMSynRel Drive for a Plug-InHybrid Electric Vehicle

SHUANG ZHAO

Licentiate ThesisStockholm, Sweden 2011

TRITA-EE 2011:063ISSN 1653-5146ISBN 978-91-7501-109-7

Electrical Machines and Power ElectronicsSchool of Electrical Engineering, KTH

Teknikringen 33SE–100 44 Stockholm

SWEDEN

Akademisk avhandling som med tillstand av Kungl Tekniska hogskolan framlagges tilloffentlig granskning for avlaggande av teknologie licentiatexamen i elektrotekniska systemfredagen den 21 oktober 2011 klockan 10.00 i H1, Kungl Tekniska hogskolan, Teknik-ringen 33, Stockholm.

c© Shuang Zhao, October 2011

Tryck: Universitetsservice US AB

To my family

iv

Abstract

This thesis presents two transient models for a prototype integrated charger for use in aplug-in hybrid-electrical vehicle application. The models can be useful in order to developcontrol algorithms for the system or to recommend improvements to the machine design.

A flux map based method, obtaining input data from simulations using the finiteelement method (FEM) is used to model the grid synchronization process. The grid sidevoltage can then be predicted by incorporating spatial flux linkage harmonics. The modelis implemented in Matlab/Simulink and compared to stand alone FEM simulations withgood agreement.

The charging process is modeled using an inductance based model also requiringFEM simulations as input data. Since the flux linkages in the grid and inverter side wind-ings are dependent on each other, the presented transient model is linearized around aspecific operating point. This model is also implemented in aMatlab/Simulink environ-ment.

Sensorless control of a PMSynRel drive is also studied in this thesis. Focus is puton operating limits due to magnetic saturation when operating at low speeds. The rotatingand pulsating voltage vector injection methods for sensorless control are studied in detail.A technique to map the feasible sensorless control region isproposed which utilizes theresulting position error signal rather than data of differential inductances. This techniqueis implemented experimentally and compared to corresponding FEM simulations withgood agreement.

The impact of spatial inductance harmonics on the quality ofthe position estimatesis also studied. A method to predict the maximum position estimation error due to theinductance harmonics is proposed based on simplified analytical models. A technique ispresented and experimentally verified which can compensatefor this effect by injectinga modified rotating voltage carrier. Lastly, the impact of saturation in the rotor structureon the initial magnet polarity detection is investigated. The experimental results, in goodagreement with the corresponding FEM simulations, indicate that the impact of satura-tion in the magnet bridges of rotor is the dominant phenomenon at lower peak currentmagnitudes.

Index Terms: Electric drive, feasible region, inductance spatial harmonics, integratedcharger, permanent-magnet assisted synchronous reluctance machine, plug-inhybrid-electric vehicle, polarity detection, saturationand cross-saturation, sensorlesscontrol, signal injection, transient modeling.

v

vi

Acknowledgements

This research project was fully funded by the Swedish HybridVehicle Center (SHC)which is gratefully acknowledged.

First of all, I would like to thank my assistant supervisors Dr. Oskar Wallmarkand Lic. Eng. Mats Leksell for providing me with technical knowledge and continuousencouragement throughout the project. I would also like to thank my main supervisorProf. Chandur Sadarangani for his valuable comments and strong support.

I am very grateful to my colleagues at KTH who have assisted mein several ways.Particularly, Andreas Krings, Antonios Antonopoulos, AraBissal, Dimosthenis Peftitsis,Kashif Khan and Dr. Samer Shisha for all the fun time we had inside but mostly outsidethe office. To my former college Dr. Hailian Xie, I would like to thank you for yourvaluable advice and priceless encouragement. Further, I would like to thank Dr. TommyKjellqvist for his help during the time he worked in the laboratory. Special thanks to theEME’s financial administrator Eva Pettersson and system administrator Peter Lonn forhelping me solve financial and computer problems.

I further would like to thank Dr. Staffan Norrga who was my former supervisorduring my master thesis and now is my colleague in KTH. Thank you for encouraging meto start my Ph.D. studies.

Finally, I would like to express my deepest gratitude to my parents, for their contin-uous support and endless love. Last but certainly not least,I would like to thank my wifeJingjing Liu for always believing me. You mean everything tome.

Shuang ZhaoStockholm, SwedenAugust 2011

vii

viii

Contents

Abstract v

Acknowledgements vii

Contents ix

1 Introduction 11.1 Motivation for Hybrid Electric Vehicles . . . . . . . . . . . . .. . . . . 11.2 Basic HEV Drivetrain Configurations . . . . . . . . . . . . . . . . .. . 21.3 A Plug-In Hybrid Vehicle Equipped with an Integrated Charger . . . . . . 31.4 Permanent-Magnet Assisted Reluctance Machines in HEV Applications . 31.5 Outline of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.6 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.7 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Modeling of PMSynRel Machines 72.1 Principles of a Magnetic Circuit . . . . . . . . . . . . . . . . . . . .. . 72.2 PMSynRel Machines in Charging and Traction Applications . . . . . . . 82.3 An Analytical Model of the Charging Mode . . . . . . . . . . . . . .. . 102.4 Transient Modeling of IC for Simulations . . . . . . . . . . . . .. . . . 17

2.4.1 FEM Analysis of the Charging Mode . . . . . . . . . . . . . . . 172.4.2 Flux Based Modeling for the Grid Synchronization Process . . . . 202.4.3 Inductance Based Modeling of the Charging Process . . .. . . . 23

2.5 Summary of Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3 Position Sensorless Control 273.1 Motivation for Sensorless Control . . . . . . . . . . . . . . . . . .. . . 273.2 Different Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3 High Frequency Continuous Signal Injection . . . . . . . . . .. . . . . . 29

3.3.1 Modeling the PMSynRel Current Dynamics . . . . . . . . . . . .293.3.2 Machine Model for High Frequency Excitation . . . . . . . .. . 303.3.3 Rotating Voltage Vector Injection Method . . . . . . . . . .. . . 32

ix

Contents

3.3.4 Pulsating Voltage Vector Injection Method . . . . . . . . .. . . 323.3.5 Obtaining Speed and Position Estimates . . . . . . . . . . . .. . 33

3.4 Effects of Saturation and Cross-Saturation . . . . . . . . . .. . . . . . . 353.5 Effects of a Non-sinusoidal Field Distribution . . . . . . .. . . . . . . . 44

3.5.1 Spatial Inductance Harmonics . . . . . . . . . . . . . . . . . . . 443.5.2 Spatial Harmonic Compensation . . . . . . . . . . . . . . . . . . 48

3.6 Polarity Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.7 Summary of Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4 Conclusion 574.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.2 Recommendations for Future Research . . . . . . . . . . . . . . . .. . . 58

4.2.1 The Integrated Charger Concept . . . . . . . . . . . . . . . . . . 584.2.2 Sensorless Control . . . . . . . . . . . . . . . . . . . . . . . . . 58

A Laboratory Setup 61

References 63

x

Chapter 1

Introduction

In this chapter, the motivation for hybrid electric vehicles and a schematic description ofthe drivetrain configurations used in such vehicles are presented. An outline of the thesisas well as the scientific contributions related to this work are also presented.

1.1 Motivation for Hybrid Electric Vehicles

Conventional passenger and heavy duty vehicles are typically propelled by internal com-bustion engines (ICEs) which consume oil (in forms of petrolor diesel fuel) and emitgreen-house gas (GHG). As the concerns for global warming, environmental degradationand petroleum shortage continue grow worldwide, more and more rigorous governmentalenvironment regulations have been announced which drive the automobile manufacturesand researchers to find solutions to reduce the oil usage and the associated GHG emis-sions [44]. The electric vehicle (EV) seems like an ultimatesolution provided that theenergy used to charge the battery comes from a clean energy source which, in itself, isnot consuming oil or emitting substantial amounts of GHG. However, compared to ve-hicles equipped with ICEs, issues such as a limited driving range and a time consumingrecharging process (both limited by the present technologyand the infrastructure) makeEVs very rare in the worldwide vehicle fleet [1].

An alternative solution, the hybrid electric vehicle (HEV)concept, alleviates theseissues by combining a conventional ICE propulsion system with an electric propulsionsystem. In an HEV, the electric powertrain is intended to offer advantages over conven-tional ICE equipped vehicles and EVs. With the assistance ofthe electric powertrain, theoperating region of the ICE can be optimized which often means a reduced fuel con-sumption and reduced emissions. Due to the presence of the ICE, HEVs have a largerdriving range compared to EVs. Furthermore, known as regenerative braking, HEVs havethe possibility to convert the kinetic energy gained duringthe braking and utilize it forpropulsion rather than waste it as heat.

1

Chapter 1. Introduction

1.2 Basic HEV Drivetrain Configurations

There are many ways to combine the electric traction and mechanical traction systems inan HEV drivetrain. However, the two most basic configurations are the series hybrid andparallel hybrid drivetrain, which both are illustrated in Fig. 1.1.

Fueltank

El.mach.PE

Trans.ICE

Fueltank

El.mach.PE Trans.

ICEGen.

(a)

(b)

Fig. 1.1 Examples of different HEV drivetrains. The arrows indicatepossible directions of energyflow: (a) Series-HEV configuration; (b) Parallel-HEV configuration.

In series hybrid system, the vehicle is propelled solely by an electric machine. Agenerater converts the mechanical output power from the ICEto electricity which eithercharges the battery or directly powers the electric machine. Due to the decoupling of theICE and the transmission system, the ICE can operate at its optimal operating points to re-duce the fuel consumption. Furthermore, the system provides a high flexibility for locatingthe ICE and generator set. However, the efficiency of series hybrid systems is generallylower compared to the parallel hybrid system described below due to the many power con-versions. Another disadvantage is that all drivetrain components (ICE, generator, electricmachine and power electronics) need to be sized for the maximum sustained power of thevehicle which can make the system more expensive than its parallel counterpart.

Differing from the series HEV, parallel HEV can be propelledby the ICE and elec-tric machine together or individually. The electric machine can be used as a generator tocharge the battery by absorbing power from the ICE or during regenerative braking. Dueto the coupling of the ICE and the electric machine, downsizing of the combination is en-abled provided that the battery is never depleted. Even for long-distance operation, only

2

1.3. A Plug-In Hybrid Vehicle Equipped with an Integrated Charger

the ICE needs to be rated for maximum power and the electric machine may still be of asmaller size compared to what is needed in a corresponding series HEV.

1.3 A Plug-In Hybrid Vehicle Equipped with an IntegratedCharger

Differing from the HEV drivetrains described above, a plug-in hybrid electric vehicle(PHEV) can charge the battery from an external electric power source (either from asingle phase power supply or a three phase power supply [30]). The integrated chargerconcept considered in this thesis was first presented in [29]and a schematic diagram ofthe concept when applied in a parallel PHEV drivetrain is illustrated in Fig. 1.2. Theintegrated charger represents a new type of electric machine which can be operated bothin traction and charging mode. The stator winding of this machine is split into two groupsduring charging: one group is connected to the inverter and the other group is connectedto the three-phase grid. By using proper control, the electric power can be transferredfrom the grid side to the battery while the rotor is mechanically disconnected from thedrivetrain and rotating at synchronous speed (50 Hz). A detailed introduction and analysisof an experimental integrated charger prototype can be found in Chapter 2.

Fig. 1.2 A PHEV equipped with an integrated charger.

1.4 Permanent-Magnet Assisted Reluctance Machines inHEV Applications

The electric machine(s) is a key component in any HEV configuration. It is requiredto have a high torque/power density, a high maximum speed capability and a high ef-ficiency over wide speed and torque ranges [80]. It is challenging to design a machine

3


which fulfills all these requirements at a relatively low cost. Several candidates were sug-gested and compared in [72]: induction machines (IMs), permanent-magnet synchronousmachines (PMSMs) and synchronous reluctance machines (SRMs). Considering an iden-tical stator design, PMSMs provide the highest efficiency and torque density followedby SRMs and IMs. However, due to the high price of rare-earth material, PMSMs areexpensive. Among the three candidates, SRMs provide higherefficiency and torque den-sity (compared to IMs) and better field-weakening capability and lower cost (comparedto PMSMs). The operating performance of SRMs can be further improved by addingpermanent-magnet in the rotor. This resulting electric machine is known as the permanent-magnet assisted synchronous reluctance (PMSynRel) machine [50]. Due to the permanentmagnets in the rotor, the torque density is increased thanksto the additional permanentmagnet torque. Compared to PMSMs, typically a smaller amount of permanent magnetmaterial is used. Therefore, PMSynRels typically have better field-weakening capabilitycompared to PMSMs. Additionally, due to the inherent high saliency, PMSynRel ma-chines are attractive for sensorless control applications. There are numerous referencesthat present PMSynRel designs developed for EV and HEV applications; some examplesare [8,42,51].

1.5 Outline of Thesis

This thesis consists of two major parts: transient modelingof a PMSynRel with inte-grated charger capability and analysis of a deeply saturated sensorless PMSynRel drive.The chapters are outlined below.Chapter 2: The integrated charger is introduced and modeled in this chapter. An ana-lytical model is derived using basic magnetic circuit concepts. Two transient modelingapproaches are proposed to model the grid synchronization process and the charging pro-cess, respectively.Chapter 3: Sensorless control strategies are reviewed and analyzed in this chapter. Theeffects of saturation and cross-saturation are studied by means of analytical methods andFEM simulations. A feasible region mapping method is proposed using the resulting errorsignal containing position information. The experimentaltests are compared with FEMsimulations showing a reasonable agreement. The effects ofspatial inductance harmonicsare also considered and compensated for in this chapter. Last, standstill rotor polarity de-tection is modeled and experimentally implemented to studythe effect of the saturationin the rotor structure.Chapter 4: This chapter summarizes the conclusions of the work and provides proposalsfor further research.

4

1.6. Contributions

1.6 Contributions

In order how they appear, the list below summarizes the main contributions presented inthis thesis.

• A thorough analysis of a prototype integrated charger is presented which takes mag-netic saturation and spatial harmonics into account. The model, which uses data ob-tained from FEM simulations, extends a simplified, inductance based model whichis derived using simple magnetic circuits.

• The current and mechanical dynamics of the integrated charger have been modeledin order to enable accurate simulations of the grid synchronization and chargingprocesses.

• The operating region for a PMSynRel drive operating sensorless at low speeds isanalyzed in detail by experimental investigations and corresponding FEM simula-tions. A method for determining the maximum available torque using the result-ing position estimation error signal is presented and compared with a technique inwhich this limit is obtained by computing differential inductances from FEM (orobtained experimentally). In general, the agreement with the experimental resultsand the corresponding FEM simulations is very good which provides a good basefor future investigations related to different design modifications in order to extendthe operating region when the PMSynRel is controlled without using a positionsensor.

• The impact of spatial harmonics on the performance of the PMSynRel when operat-ing sensorless is analyzed and a technique to compensate forthis effect is proposedfor the sensorless technique known as rotating carrier vector injection.

• The impact of saturation in the rotor structure during initial rotor polarity detec-tion is investigated experimentally and compared, with good agreement, with cor-responding FEM simulations.

1.7 Publications

Thus far, the publications originating from this project are:

1. S. Zhao, O. Wallmark, and M. Leksell, “Analysis of a deeplysaturated sensorlessPMSynRel drive for an automotive application,” inProc. 14th European Conference onPower Electronics and Applications (EPE’11), 2011.

5


2. S. Zhao, S. Haghbin, O. Wallmark, M. Leksell, S. Lundmark,and O. Carlson, “Tran-sient modeling of an integrated charger for a plug-in hybridelectric vehicle,” inProc. 14thEuropean Conference on Power Electronics and Applications(EPE’11), 2011.

The publication below is related in interest but not included in this thesis:

3. S. Nategh, O. Wallmark, M. Leksell, and S. Zhao, “Thermal analysis of a PMaSRMusing partial FEM and lumped parameter modeling,” submitted manuscript.

6

Chapter 2

Modeling of PMSynRel Machines

This chapter thoroughly derives a transient PMSynRel modelsuitable not only for trac-tion applications but also when the machine is functioning as a component of the vehicle’sbattery charging system. To introduce the notation and simplify for the reader, the basicprinciples of magnetic circuits are briefly reviewed at first. Then, the analytical machinemodel is derived and two modeling approaches are introducedto model the grid synchro-nization and charging process.

2.1 Principles of a Magnetic Circuit

Fig. 2.1(a) illustrates a simple magnetic circuit made up ofa magnetic core with a smallair gap and a coil that carries the currentI [13]. The material of the magnetic core is as-sumed to be a ferromagnetic material like iron which has a very high relative permeabilitycompared to air. Therefore, the magnetic reluctance of the magnetic core can be neglected.In this simple magnetic circuit arrangement, the air gap lengthδg is constant and the crosssectional area is denoted byA. Similar as for an electrical circuit, the magnetic circuitcan be represented by an equivalent lumped circuit as illustrated in Fig. 2.1(b). Compared

δg

I

Bδ

Aμrc

μr0

(a) (b)

n

ψ/nψ/n

m

Fig. 2.1 Illustration of a simple magnetic circuit: (a) Magnetic core wound by a conducting coil;(b) Magnetic circuit modeled by an equivalent electric circuit.

7

Chapter 2. Modeling of PMSynRel Machines

to the electrical circuit, the electromotive force (EMF) isreplaced by the magnetomo-tive force (MMF) which drives the flux, rather than the current, that passes through themagnetic path. Further, the electrical impedance is replaced by the magnetic reluctance.According to Ampere’s law, the MMFm can be calculated as

m = nI (2.1)

wheren is the number of turns of the long conducting coil.Now, the magnetic field is assumed to be evenly distributed inthe air gap and per-

pendicular to the cross-sectional surfaceA. The flux linkageψ is simply the integral ofthe flux densityBδ over the surface areaS multiplied by the number of turns. Hence,

ψ = n

∫

S

BδdS = nBδA. (2.2)

The reluctance of the air gap can be calculated as

R =δg

µ0µr0A(2.3)

whereµ0 is the permeability of vacuum andµr0 is the relative permeability of air (whichis 1). From the flux linkage and air gap reluctance, the MMFm can be obtained as

m =Rψ

n. (2.4)

Using (2.1)–(2.4), the flux densityBδ can be obtained as a function of the MMF and theair gap length

Bδ =mµ0

δg. (2.5)

2.2 PMSynRel Machines in Charging and Traction Ap-plications

PMSynRels can be attractive in automotive applications dueto their high efficiency, hightorque density and the potential of using sensorless control in the full speed range [7, 18,26]. The prototype PMSynRel considered in this work can alsobe reconnected so that itis used as a key component when the vehicle’s battery is charged from the electrical grid.Hence, the machine is particularly suitable for PHEVs.

The connection of the winding can be quickly reconfigured from traction mode tocharging mode and vice versa using contactors [37]. The physical winding arrangementof the prototype PMSynRel considered in this thesis is illustrated in Fig. 2.2(a). Similar asfor transformers, a good magnetic coupling between the primary side and the secondary

8

2.2. PMSynRel Machines in Charging and Traction Applications

N

N

S

S a1

d

Φ

θ

Ag

Bg

Cg

A

B

C

Inverter Battery

.

.

.

.

.

.

.

.

.

.

.

.

A

B

C

Inverter Battery

.

.

.

.

.

.

.

.

.

.

.

.

(a)

(b)

c)(

Fig. 2.2 Principle illustration of the PMSynRel prototype: (a) Winding arrangement and stator androtor geometries (the anglesφ andθ are represented in electrical degrees); (b) Windingconnection during charging; (c) Winding connection duringtraction.

9


side windings results in a high efficiency. This is achieved by placing the inverter sidewindings adjacent to the grid side windings. As shown in Fig.2.2(a), the phase shift of thetwo coupled windings is one slot which corresponds to 30 electrical degrees. Fig. 2.2(b)shows the winding connection of the machine in charging modeand Fig. 2.2(c) shows thewinding connection in traction mode, respectively. Using the charging mode connection,voltage adaptation (to the grid voltage) and galvanic insulation can be realized whichmakes an additional transformer unnecessary [29,30].

2.3 An Analytical Model of the Charging Mode

In this section, an analytical model of the prototype when operating in charging modeis thoroughly derived. The derivation extends the work in [64] and [71] to the machineconsidered in this thesis in which the two winding sets are shifted by 30 electrical degreesand connected to the grid and inverter, respectively. An analytical model of an IC withdifferent winding configurations is presented in [28]. However, the work presented hereshows how the model in [28] can be derived using basic magnetic circuit concept and,additionally, how to use it as a base for the transient FEM model of the charging process.

Fig. 2.3(a) and Fig. 2.3(b) depict the slot conductor density and the effective inverseair gap length along the air gap, respectively. As illustrated in Fig. 2.2 (a), the vectora1corresponds to the magnetic axis of the phase windingA1 and is used as a reference todefine the circumferential angleΦ (which is expressed in electrical degrees). The rotorposition angleθ is then defined as the angle (in electrical degrees) between amagneticnorth pole of the rotor and the vectora1. Fig. 2.3(a) illustrates the winding distribution

na

Nε

-

ε

Φ

Nε

δ-1

Φπ4

+θ

δmin

-1-1

δmax

-1-1

(a) (b)

π3

π3

-

2π3

2π3

-

3π4

+θ5π4

+θ

Fig. 2.3 (a) Winding function of phaseA1; (b) Inverse effective air gap function.

which is far from sinusoidal. It is assumed that the conductors are evenly distributed inthe slots and that the effective width of the slotε is very small. To find the inductanceof a phase winding, the characteristics of its coils are firststudied. To further simplifythe analysis, only the fundamental component is considered. Assume that the first coilis shifted from the reference winding by the angleα and that it has a conductor density

10

2.3. An Analytical Model of the Charging Mode

given by

nx(φ) =2√3N

πsin(φ− α) (2.6)

whereN is the number of conductors per coil per slot. The second coilis shifted from thefirst coil by the angleβ which gives a conductor density according to

ny(φ) =2√3N

πsin(φ− α− β). (2.7)

In terms of magnetic permeability, the rotor-magnet material is approximately thesame as that for air. Therefore, a wider effective air gap is “seen” when the rotor magnet isaligned to an arbitrary winding. Fig. 2.3(b) illustrates the effective inverse air gap lengthwhen the stator slotting effect has been neglected and the magnet coverage for one polehas been assumed to be 90 electrical degrees. By a Fourier series expansion, the inverseeffective air gap length can be expressed as a function of thecircumferential angleΦ andthe rotor positionθ as

δ−1(φ, θ) = a− b cos 2(φ− θ) (2.8)

wherea = (δ−1min + δ−1

max)/2 and b = 2(δ−1min − δ−1

max)/π, respectively and additionalharmonic terms have been neglected.

When a currentix flows in the arbitrary windingx, the resulting MMFmx can beobtained as

mx =1

2

φ+π∫

φ

nx(φ′)ixdφ

′ =2√3Nixπ

cos(φ− α). (2.9)

Substituting (2.8) and (2.9) into (2.5), the correspondingair-gap flux density is found as

Bx = µ0δ−1mx =

2√3Nixµ0

πcos(φ− α) [a− b cos 2(φ− θ)] . (2.10)

Thex-phase flux linkage due to the winding current ofx-phase can now be found as

ψxx = rl

π2+α

∫

−π2+α

φ+π∫

φ

ηcnx(φ′)dφ′

Bxdφ

=12µ0rlN

2

πηcix

[

a− b

2cos(2θ − 2α)

]

(2.11)

wherel andr represent the active length and inner radius of the stator, respectively. Due tothe series and parallel connection of the grid and inverter windings, the connection factorηc is introduced to generalize (2.11). The connection factor equals to 1 for the inverter

11


side windings to 2 for the grid side windings. From (2.11), the x-phase self inductance,taking the leakage inductanceLls into account, can be expressed as

Lxx =ηcηiLls +

ψxxηiix

=ηcηi

{

Lls +12µ0rlN

2

π

[

a− b

2cos(2θ − 2α)

]}

(2.12)

whereηi is the ratio of the phase current and the winding current (ηi = 1 for the grid sidewindings andηi = 2 for the inverter side windings) andLls is the leakage inductance.In the same manner, the flux linkage of they-phase winding due to thex-phase windingcurrentix can be expressed as

ψxy =

π2+α+β∫

−π2+α+β

φ+π∫

φ

ηcny(φ′)dφ′

Bxdφ

=12µ0rlN

2

πηcix

[

a cos β − b

2cos(2θ − 2α− β)

]

. (2.13)

Hence, the mutual inductance between thex- andy-phase windings is obtained as

Lxy = Lyx =ψxyηiix

=ηcηi

12µ0rlN2

π

[

a cos β − b

2cos(2θ − 2α− β)

]

. (2.14)

Substituting the corresponding phase displacement anglesα andβ into (2.12) and (2.14),

12


the inductances of each winding is found as:

La1a1 =1

2(Lls + Lm,0 − Lm,2 cos 2θ) (2.15a)

La1b1 = Lb1a1 = −1

4Lm,0 −

Lm,22

cos(2θ − 2π

3) (2.15b)

La1c1 = Lc1a1 = −1

4Lm,0 −

Lm,22

cos(2θ +2π

3) (2.15c)

La1a2 = La2a1 =

√3

2Lm,0 − Lm,2 cos(2θ −

π

6) (2.15d)

La1b2 = Lb2a1 = −√3

2Lm,0 − Lm,2 cos(2θ −

5π

6) (2.15e)

La1c2 = Lc2a1 = Lm,2 cos(2θ −π

2) (2.15f)

Lb1b1 =1

2

(

Lls + Lm,0 − Lm,2 cos 2(θ −2π

3)

)

(2.15g)

Lb1c1 = Lc1b1 = −1

4Lm,0 −

Lm,22

cos 2θ (2.15h)

Lb1a2 = La2b1 = Lm,2 cos(2θ +π

6) (2.15i)

Lb1b2 = Lb2b1 =

√3

2Lm,0 + Lm,2 cos(2θ −

π

2) (2.15j)

Lb1c2 = Lc2b1 = −√3

2Lm,0 − Lm,2 cos(2θ −

π

6) (2.15k)

Lc1c1 =1

2

(

Lls + Lm,0 − Lm,2 cos 2(θ +2π

3)

)

(2.15l)

Lc1a2 = La2c1 = −√3

2Lm,0 − Lm,2 cos(2θ +

π

2) (2.15m)

Lc1b2 = Lb2c1 = Lm,2 cos(2θ +5π

6) (2.15n)

Lc1c2 = Lc2c1 =

√3

2Lm,0 + Lm,2 cos(2θ +

π

6) (2.15o)

La2a2 = 2(

Lls + Lm,0 − Lm,2 cos 2(θ −π

6))

(2.15p)

La2b2 = Lb2a2 = −Lm,0 − 2Lm,2 cos(2θ − π) (2.15q)

La2c2 = Lc2a2 = −Lm,0 − 2Lm,2 cos(2θ +π

3) (2.15r)

Lb2b2 = 2

(

Lls + Lm,0 − Lm,2 cos 2(θ −5π

6)

)

(2.15s)

Lb2c2 = Lc2b2 = −Lm,0 − 2Lm,2 cos(2θ −π

3) (2.15t)

Lc2c2 = 2(

Lls + Lm,0 − Lm,2 cos 2(θ +π

2))

(2.15u)

13


where the notation

Lm,0 =12µ0rlN

2

πa (2.16)

Lm,2 =6µ0rlN

2

πb. (2.17)

In this work, the subscripts “1” and “2” indicate that the quantities are on the inverterside and grid side, respectively. The inductance expressions can now be collected into asymmetric inductance matrixL s,IC as

L s,IC =

La1a1 La1b1 La1c1 La1a2 La1b2 La1c2Lb1a1 Lb1b1 Lb1c1 Lb1a2 Lb1b2 Lb1c2Lc1a1 Lc1b1 Lc1c1 Lc1a2 Lc1b2 Lc1c2La2a1 La2b1 La2c1 La2a2 La2b2 La2c2Lb2a1 Lb2b1 Lb2c1 Lb2a2 Lb2b2 Lb2c2Lc2a1 Lc2b1 Lc2c1 Lc2a2 Lc2b2 Lc2c2

. (2.18)

Due to the physical displacement of the windings, it is evident from Fig 2.2(a) thatthe permanent-magnet flux linkage for each phase can be expressed as

ψm,ph,IC =ψm

[1

2cos θ

1

2cos(θ − 2π

3)1

2cos(θ +

2π

3)

cos(θ − π

6) cos(θ − 5π

6) cos(θ +

π

2)

]T

(2.19)

where the harmonics have been omitted for the sake of simplicity.Similarly, the resistance, phase currents and phase-to-neutral voltages can also be repre-sented in matrix and vector form as

Rs,IC = diag(Rs1, Rs1, Rs1, Rs2, Rs2, Rs2) (2.20)

is,IC =[ia1 ib1 ic1 ia2 ib2 ic2

]T(2.21)

vs,IC =[va1 vb1 vc1 va2 vb2 vc2

]T. (2.22)

Using (2.18)-(2.22), the voltage equations for the multi-phase system can be expressed inmatrix form as

vs,IC =d

dt(L s,IC is,IC + ψm,ph,IC) + Rs,IC is,IC. (2.23)

Eq. (2.23) can also be expressed in a rotor-fixed reference frame using the amplitude-

14


invariant extended Park transformation [28]:

Tdq,IC =2

3

cos θ cos(θ − 2π3) cos(θ + 2π

3) . . .

− sin θ − sin(θ − 2π3) − sin(θ + 2π

3) . . .

12

12

12

. . .

0 0 0 . . .

0 0 0 . . .

0 0 0 . . .

0 0 0

0 0 0

0 0 0

cos(θ − π6) cos(θ − 5π

6) cos(θ + π

2)

− sin(θ − π6) − sin(θ − 5π

6) − sin(θ + π

2)

12

12

12

. (2.24)

Transforming (2.23) using (2.24) yields

vdq0,IC = Tdq,IC

d

dt

(L s,ICT−1

dq,IC idq0,IC + ψm,ph,IC)+ Rs,IC idq0,IC (2.25)

wherevdq0,IC = [vd1 , vq1 , v01, vd2 , vq2, v02 ]T and idq0,IC = [id1 , iq1, i01 , id2 , iq2 , i02 ]

T . Forbalanced operation, the zero-sequence components can be neglected [73]. Using this sim-plification, (2.25) can be reexpressed as

vdq,IC = L dq,IC

didq,ICdt

+ Zdq,IC idq,IC + ωrψm,dq,IC (2.26)

Ldq,IC =

Ld1d1 0 Ld1d2 0

0 Lq1q1 0 Lq1q2Ld2d1 0 Ld2d2 0

0 Lq2q1 0 Lq2q2

(2.27)

Zdq,IC =

Rs1 −ωrLq1q1 0 −ωrLq1q2ωrLd1d1 Rs1 ωrLd1d2 0

0 −ωrLq2q1 Rs2 −ωrLq2q2ωrLd2d1 0 ωrLd2d2 Rs2

(2.28)

ψm,dq,IC =[0 ψm,d1 0 ψm,d2

]T(2.29)

15


where the notation

Ld1d1 =Lls2

+3Lm,04

− 3Lm,24

(2.30a)

Lq1q1 =Lls2

+3Lm,04

+3Lm,24

(2.30b)

Ld2d2 = 2Lls + 3Lm,0 − 3Lm,2 (2.30c)

Lq2q2 = 2Lls + 3Lm,0 + 3Lm,2 (2.30d)

Ld1d2 = Ld2d1 =3(Lm,0 − Lm,2)

2(2.30e)

Lq1q2 = Lq2q1 =3(Lm,0 + Lm,2)

2(2.30f)

ψm,d1 =1

2ψm (2.30g)

ψm,d2 = ψm (2.30h)

has been introduced. In order to complete the derivation andgain further understanding,it is useful to derive an expression of the electro-mechanical torque. Assuming linearmagnetic conditions, the magnetic coenergyW is given by [40]

W =1

2iTs,ICL s,IC is,IC + iTs,ICψm,ph,IC. (2.31)

Hence, the torque expression can be derived according to [40]

Te,IC = np∂W

∂θ= np

(1

2iTs,IC

∂L s,IC

∂θis,IC + iTs,IC

∂ψm,ph,IC∂θ

)

. (2.32)

Transforming (2.32) into the rotor-fixed reference frame yields

Te,IC = np

[1

2

(T−1dq,IC idq0,IC

)T ∂L s,IC

∂θT−1dq,IC idq0,IC +

(T−1dq,IC idq0,IC

)T ∂ψm,ph,IC∂θ

]

.

(2.33)

Expanding and sorting (2.33), the resulting torque expression is found as

Te,IC =3np2

(ψd1iq1 + ψd2iq2 − ψq1id1 − ψq2id2) (2.34)

where the notation

ψd1 = Ld1d1id1 + Ld1d2id2 + ψm,d1 (2.35a)

ψq1 = Lq1q1iq1 + Lq1q2iq2 (2.35b)

ψd2 = Ld2d2id2 + Ld2d1id1 + ψm,d2 (2.35c)

ψq2 = Lq2q2iq2 + Lq2q1iq1 (2.35d)

is introduced. It is evident in (2.34) that the total torque is the sum of the torques producedby the two sets of windings (connected to the inverter and grid, respectively).

16

2.4. Transient Modeling of IC for Simulations

2.4 Transient Modeling of IC for Simulations

In order to obtain a detailed PMSynRel machine (especially when operating in chargingmode), the physical geometry and non-linear material parameters have to be taken intoaccount. Due to this, finite element methods (FEM) have to be used. Although the re-cent FEM software (such as JMAG1) can be linked to other simulation software (such asSimulink2) directly, a simplified model is required due to the long simulation time andlarge amount of data that are following such a modeling approach. Two transient modelsare introduced in this section which both utilize results from FEM simulations to enablesufficient accuracy.

2.4.1 FEM Analysis of the Charging Mode

The integrated charger has six phases that can be divided into two sets: the motor set andthe generator set. Hence, FEM simulations are more complicated than those for a conven-tional three phase machine since the flux linkage is now a function of both the inverterand the grid side windings (id1 , iq1, id2 andiq2). In order to analyze the integrated charger,a number of FEM simulations have been conducted. In each simulation, constant currents(id1 , iq1) and (id2 , iq2) are injected to the inverter side and grid side winding, respectively.The resulting flux linkages for all phases are transformed into thedq-reference frame andstored as “flux maps”. A typical FEM simulation result for oneoperating point is illus-trated in Fig. 2.4(a). Fig. 2.4(b) shows the resulting flux map for inverter side flux linkagein theq-direction when the currents on the grid side are constant.

When the machine is operating in charging mode, it is disconnected from the me-chanical drive-line and running idly to charge the battery.Therefore, the load torque ofan integrated charger is only the friction torque in the steady state. Hence, the operatingpoints in the steady state should be in the vicinity of the zero-torque loci.

From the FEM simulations and by using (2.34), zero-torque loci can be found andplotted against the operating points (id1 , iq1 , id2 , iq2). In order to visualize the results, onlythe inverter side currents are shown in Fig. 2.5 and the corresponding grid side currentsare listed in Table 2.1. To exemplify, case5 in Table 2.1 is considered in Fig. 2.6 whichshows the power flow and power factor (the correspondingid1 and iq1 can be found inFig. 2.5). As seen in Fig. 2.6, the power factor of the grid side is very close to unityand almost not affected by the inverter side currents. However, the power factor of theinverter side is dependent ofid1 and so is the transferred power. The analysis suggeststhat the steady state operating point should be selected carefully to obtain a good balancebetween charging power and efficiency.

1JMAG is a registered trademark of JSOL Corporation, Tokyo, Japan2Simulink is a registered trademark of MathWorks Inc., Natick, Massachusetts, U.S.A.

17


(a)

1015

20

−40

−20

0−0.5

0

0.5

id1 [A]iq1 [A]

ψq1

[Vs]

(b)

Fig. 2.4 One example of FEM simulation whenid2=0 A andiq2=11 A: (a) Flux line; (b) Flux mapof inverter side along q-axis.

10 12 14 16 18 20−25

−20

−15

−10

−5

0

case 1case 2case 3case 4case 5case 6case 7case 8case 9

id1 [A]

i q1

[A]

Fig. 2.5 Zero torque loci.

18


Table 2.1: Simulated operating points on the grid sideCase id2 [A] iq2[A]

1 -2.5 4.02 -2.5 7.03 -2.5 11.04 0.0 4.05 0.0 7.06 0.0 11.07 2.5 4.08 2.5 7.09 2.5 11.0

10 12 14 16 18 20−3000

−2000

−1000

0

1000

2000

3000

Grid sideInverter side

10 12 14 16 18 20

−1

−0.5

0

0.5

1

Grid sideInverter side

(a) (b)

Pow

er[w

]

id1 [A]id1 [A]

Pow

erfa

cto

r[-

]

Fig. 2.6 (a) Power flow from grid to inverter for case 5; (b) Power factor on the grid side andinverter side for case 5.

19


2.4.2 Flux Based Modeling for the Grid Synchronization Process

Before charging can commence, the grid side windings need tobe synchronized to theelectrical grid in terms of both amplitude and frequency. During this synchronization pro-cess, the grid side winding is open circuited and the rotor speed is controlled by the in-verter side winding only. Therefore, from the inverter side, the machine can be consideredas a conventional three phase machine. The grid side voltagecan also be controlled by theinverter side current (iq1 = 0 A at the steady state). Two FEM simulations, when the ro-tor is rotating at rated speed (1500 rpm), are illustrated inFig. 2.7 whereid1 = 0 A andid1 = 11 A, respectively. As seen, the fundamental grid side voltageis dependent on thecurrentid1 . However, the voltage is distorted due to the non-sinusoidal flux distribution.

0 0.005 0.01 0.015 0.02

−200

0

200

1 2 3 4 5 6 7 8 9 100

100

200

t [s]

Harmonic order

v a2

[V]

v a2

[V]

(a)

0 0.005 0.01 0.015 0.02

−200

0

200

1 2 3 4 5 6 7 8 9 100

100

200

t [s]

Harmonic order

v a2

[V]

v a2

[V]

(b)

Fig. 2.7 FEM simulations of the grid side voltage (phaseA2): (a) Whenid1 = 0 A; (b) Whenid1 = 11 A.

As stated above, saturation and cross saturation phenomenashould be taken intoaccount to obtain a precise machine model. Therefore, the flux based modeling methodis used here to develop a model for the synchronization process which includes satura-tion, cross saturation and also the influence of slot harmonics. The modeling method waspresented in [11] for an interior PMSM and is adapted to modelthe synchronization pro-cess. Differing from an interior PMSM, the machine in consideration has three additionalwindings on the grid side. Since the objective of the synchronization controller is to syn-chronize the grid side winding voltage to the grid voltage, the voltage of the grid sidewindings needs to be modeled accurately. To incorporate theeffect of the slot harmonicson the resulting flux linkage, FEM simulations are conductedfor different rotor positions.Fig. 2.8(a) shows the FEM simulation result which is a stack of flux maps ofψd1 andψq1(only ψd1 is shown in Fig. 2.8(a)). Each flux map corresponds to a certain rotor position.

20


Using the stack of flux maps, the impact of slot harmonics is taken into consideration foreach operating point. In Fig. 2.8(b), the variation of flux linkage when the rotor positionis varied is illustrated.

−500

50

−5

0

50

0.5

1

id1 [A]iq1 [A]

ψd1

[Vs]

(a)

0 20 40 600.6

0.7

0.8

0.9

0 20 40 60

−0.5

0

ψd1

[Vs]

Rotor position [el. deg]

Rotor position [el. deg]

ψq1

[Vs]

(b)

Fig. 2.8 (a) Flux stacks obtained using FEM simulation; (b) Effect ofslot harmonics.

ψd1 =

∫

(vd1 − Rs1id1 + ωrψq1) dt (2.36a)

ψq1 =

∫

(vq1 −Rs1iq1 − ωrψd1) dt (2.36b)

vd2 =dψd2dt

− ωrψq2 (2.36c)

vq2 =dψq2dt

+ ωrψd2 . (2.36d)

The resulting transient Matlab/Simulink models of the inverter side and grid side inter-

flux_q1

2-D T(u)

flux_d1

2-D T(u)

flux harmonics on inverter side

theta 6

theta 12

id

iq

psid_harmonics

psiq_harmonics [psiq_har]

[psid_har]

[iq1]

[id1]

[psiq1]

[psid1]

[psiq_har]

[psid_har]

[iq1_ref]

[theta6]

[id1_ref]

[theta12]

f (z) zSolve

f(z) = 0

f (z) zSolve

f(z) = 0

Fig. 2.9 Transient model of the inverter side of the integrated charger.

21


Fig. 2.10 Transient model of the grid side of the integrated charger.

faces are presented in Fig. 2.9 and Fig. 2.10, respectively.In Fig. 2.9, the reference fluxespsid1 andpsiq1 are computed using (2.36a) and (2.36b) [11], respectively.As shown inFig. 2.10, the grid side voltage is calculated using (2.36c)and (2.36d). The slot harmoniceffect is taken into consideration by adding the flux harmonics, which are interpolatedaround the current reference in a lookup table, on top of the fundamental flux linkages. In

0 0.1 0.2 0.3 0.4 0.5

0

5

10

15

id

1

iq

1

t [s]

i d1

&i q

1[A

]

(a)

0.4 0.405 0.41 0.415 0.42−300

−200

−100

0

100

200

300

FEMSimulink

v a2

[V]

t [s](b)

Fig. 2.11 Simulation results during synchronization: (a) Current commands; (b) Grid side voltage.

the simulation shown in Fig. 2.11, the rotor is rotating at synchronous speed (1500 rpmwhich corresponds to 50 Hz) andid1 is slowly increased to increase the amplitude of thegrid side voltage. Fig. 2.11(a) shows the inverter side currents. One cycle of the grid sidevoltageva2 together with a corresponding FEM simulation are illustrated in Fig. 2.11(b).It is evident that the simulink simulation shows a good agreement with the correspondingFEM simulation. However, it can be seen that the grid side voltage is distorted since thequality of the grid side voltage is not controlled in the presented simulation. In order toobtain a sinusoidal grid side voltage with a required amplitude (corresponding to 400 Vline-to-line voltage), further development of the machineand a proper voltage controlloop is required.

22


2.4.3 Inductance Based Modeling of the Charging Process

Unlike during the synchronization process, the grid side windings are connected to thegrid while the inverter side windings are connected to the inverter during charging. Dif-fering from a multi-phase machine, the grid side currents are only indirectly controlledby the inverter side. It is difficult to model the machine using the flux maps since the fluxlinkage does not only depend on the inverter side currents but also on the grid side cur-rents. One way to model the charging process is to linearize the machine model aroundeach operating point.

The analytical model derived in Section 2.3 does not includethe cross couplingbetween thed- andq-axes. However, the effect cannot be neglected in order to model themachine in detail. Adapting the results in [68] to model the charging process, (2.26) isreexpressed as

vdq,IC = Rs,IC idq,IC + L ′dq,IC

didq,ICdt

+ ωrψωr,IC(2.37)

where the notation

L ′dq,IC =

L′d1d1

L′d1q1

L′d1d2

L′d1q2

L′q1d1

L′q1q1

L′q1d2

L′q1q2

L′d2d1

L′d2q1

L′d2d2

L′d2q2

L′q2d1

L′q2q1

L′q2d2

L′q2q2

(2.38)

ψωr ,IC =[−ψq1 ψd1 −ψq2 ψd2

]T(2.39)

is introduced. For a certain operating point, the elements in the matrixL′dq,IC can be

computed (using data obtained from FEM simulation) as

L′d1d1

=ψ∗d1(id1 +∆i, iq1 , id2 , iq2)− ψ∗

d1(id1 , iq1, id2 , iq2)

∆i(2.40a)

L′d1q2

=ψ∗d1(id1 , iq1, id2 , iq2 +∆i)− ψ∗

d1(id1 , iq1, id2 , iq2)

∆i. (2.40b)

The superscript∗ indicates that the quantities are obtained from FEM simulation results.Other differential inductances can be calculated in the same manner.

In order to have a dynamic flux vectorψωr,IC, the integrated charger model is lin-

earized around the reference currents. First, the inductances are computed using (2.30a)-(2.30f) and (2.35a)-(2.35d) in which the current is replaced with its reference value. Sincethe current response should be close to the reference current in order for the linear modelto be valid, it is reasonable to compute the dynamic flux valueusing the inductance andresponding current. Then, the previously computed inductances and the resulting currentare substituted in (2.35a)-(2.35d) in order to computeψωr ,IC . Therefore, the linearizeddynamic model of the integrated charger can be expressed as

idq,IC = L ′−1dq,IC

vdq,IC − Rs,IC idq,IC − ωrψωr ,IC

s. (2.41)

23


Fig. 2.12 is an illustration of the linearized dynamic modelwhere (2.30a)-(2.30f) and(2.35a)-(2.35d) are employed in theOn-line parameter calculationblock and (2.41) isemployed inDynamic model algorithmblock. Using this method, the charging processcan be dynamically modeled around the reference current. Similar as in Section 2.4.2,the harmonics due to the slotting effect can also be added on top of the fundamental fluxlinkage although it is not shown in Fig. 2.12 in order to give aclear visualization of theprocess.

Fig. 2.12 Scheme of the inductance base dynamic modeling when the impact of harmonics due toslotting effects has been neglected.

A simulation model of the machine and control system during charging has beenimplemented in Matlab/Simulink where the charge controller presented in [28] is used tocontrol the charging process. When the simulation commences, the grid side windings aresynchronized and connected to the grid. Then, the power transferred from the grid to theinverter side is slowly increased. The resulting steady state reference current is depictedas a× in Fig. 2.5 and the values, together with the simulation results (transferred powerand power factor), can be found in Table 2.2. It is evident that the simulation results arein close agreement to the FEM analysis illustrated in Fig. 2.6.

Table 2.2: Sample simulation result during chargingid1,ref [A] iq1,ref [A] id2,ref [A] iq2,ref [A] P1 [W] P2 [W] PF1 PF2

12.3 -12.0 0.0 7.0 -2103.0 2238.0 -0.70 0.96

The resulting currents are illustrated in Fig. 2.13(a). As seen, the currents are in-creased slowly from 1 s and the system reaches steady state after around 4.5 s. Fig. 2.13(b)shows the currents and voltages corresponding to phasea1 anda2 when steady state isreached. The grid side phase voltageva2 and phase currentia2 have small a phase shiftwhich yields a high power factor.

24

2.5. Summary of Chapter

0 1 2 3 4 5 6 7

0

5

10

0 1 2 3 4 5 6 7

−10

0

10

i d1&i d

2[A

]

t [s]

i q1&i q

2[A

]

(a)

6 6.005 6.01 6.015 6.02−250

−1000

100

250

6 6.005 6.01 6.015 6.02−20

0

20

6 6.005 6.01 6.015 6.02−250

−1000

100

250

6 6.005 6.01 6.015 6.02−20

0

20

v a1

[V]

i a1

[V]

v a2

[V]

t [s]i a

2[V

](b)

Fig. 2.13 Simulation results during charging: (a) Current response,the inverter side and grid sidecurrents are plotted by blue and green lines, respectively;(b) Phase voltage and phasecurrent on the inverter side and the grid side.

2.5 Summary of Chapter

This chapter has dealt with modeling the grid synchronization and charging process for anintegrated charger. An analytical model was derived using basic knowledge of magneticcircuits. The flux based and inductance based modeling methods which take the magneticnonlinearity and slot harmonics into account were proposedto simulate the grid synchro-nization and charging process, respectively. The modelingmethods were implementedand verified with FEM simulations.

25


26

Chapter 3

Position Sensorless Control

Generally, there are two groups of methods to estimate the rotor position and speed forPMSynRels. The first group consists of fundamental-excitation based methods which arebased on the position detection information found in the back EMF. The second group con-sists of signal injection methods which rely on the detection of the magnetic anisotropies.This chapter briefly reviews both groups and their sub-categories. Based on FEM anal-ysis, the available sensorless operating region for a prototype PMSynRel is determined.The impact of stator slotting and how it can be compensated for is also considered. Ini-tial rotor position detection at standstill is also discussed based on studying the effect ofsaturation in the rotor structure.

3.1 Motivation for Sensorless Control

Nowadays, HEVs are present in the daily life and is a promising mean to reduce green-house gas emissions and lower the fuel consumption. Within the automotive industry,significant efforts have been put into development of different kinds of HEVs to meet therequirements of customers ranging from private cars to light trucks [48]. Mass producedcommercial HEVs have been available in the market since 1997when the Toyota Priusand Honda Civic were launched [3]. However, the initial costof an HEV is a main con-cern for general customers even though several governmentshave announced attractivepolicies and incentives (e.g. a 10 000 SEK rebate on green cars in Sweden [9]) to encour-age consumers to move from conventional vehicles to HEVs. Also, the reliability of thewhole system is an important issue needed to be addressed by the manufacturers.

The electric machine (or machines) is a key component in an HEV since it con-verts the electric power to mechanical power or vice versa. The studies in [26] and [8]indicate that PMSynRels can be an attractive candidate in HEV applications due to theirhigh efficiency, high torque density and large constant power region. However, the con-trol system requires information about the rotor position (and speed) in order to operateproperly. Therefore, a position sensor is typically mounted on the rotor shaft in order to

27

Chapter 3. Position Sensorless Control

detect the rotor position. Apart from the increased cost, the reliability of the whole systemis reduced by the potential failure of the position sensor. As an alternative solution, posi-tion estimation (sensorless control) technology can be implemented instead of mounting aphysical position sensor. Thereby, a reduction of the totalcost and an improved reliabilitycan be realized.

3.2 Different Approaches

As mentioned above, the methods for obtaining estimates of rotor position and speedof AC machines can, in principle, be divided into two groups.The first group is oftenreferred to as fundamental-excitation methods based on information found in the backEMF. These techniques have been developed for more than two decades for inductionmachines [78], synchronous reluctance machines [41], and PMSMs (suitable for non-salient rotors [23,77] and for salient rotors [12,46,49]).In general, they are accurate, withrespect to the position estimation error, in the range of medium to high speeds. However,they fail at low speeds and at standstill, where the back EMF vanishes. Although somework have been proposed towards solving this problem [35, 43, 79], low speed operationis still a challenge with these techniques.

The second group of methods is also known as signal injectionmethods and arebased on the detection of magnetic anisotropy, which occursdue to the geometric con-struction (salient pole character) as in the case of reluctance machines and PMSMs withburied magnets or due to magnetic saturation as in the case ofinductance machines andsurface mounted PMSMs. In principle, signal injection methods can be utilized to esti-mate the rotor position in the whole speed range, including standstill. However, signalinjection, at least to some extent, leads to acoustic noise,torque ripple and additionallosses. Therefore, a combination of a signal injection technique (covering low speeds andstandstill) and a fundamental-excitation technique (covering higher speeds) is often im-plemented.

In signal injection methods, both current [21] and voltage injection can be used.However, the scheme based on voltage injection is considered more practically feasiblethan the current based injection due to the fact that the latter scheme requires a very highbandwidth of the current regulators (much larger than the signal frequency) [52]. Thenumber of publications in this category is vast and the different approaches are brieflyintroduced in this section.

An early method for estimation of the rotor position is knownas the “INFORM”method (“INdirect Flux detection by On-line Reactance Measurement”) and was proposedby Schroedl in [66]. The technique is applicable for induction machines, PMSMs andreluctance machines as long as they possess some form of saliency. This method measuresthe “complex INFORM reactance” in real time which contains rotor position information.This is achieved by applying voltage pulses and measuring the resulting current change.

28

3.3. High Frequency Continuous Signal Injection

Hence, the fundamental operation of the controller needs tobe interrupted which is adrawback of the method. A considerable amount of material has been published related tothis area [53,61,62,65,75] including a description of the technique applied in an industryapplication [63].

Third-harmonic based sensorless techniques for low speed applications was pro-posed by Consoli in [17]. Here, the interaction of the injected high frequency rotatingfield and the main field, which possesses the saturation induced third harmonic flux com-ponent, is utilized. In [17], the zero sequence voltage, which possesses rotor positioninformation, is measured to obtain position estimates. Theamplitude of the resultinghigh-frequency zero sequence voltage is independent of thesignal frequency which is anadvantage with this method at the expense of additional voltage measurements. In [19],a third-harmonic based sensorless technique is implemented for a PMSM and good ex-perimental results are demonstrated. Other activities in this area in the last decade canbe found in [10, 15, 16, 25]. However, due to the requirement of the saturation inducedthird-harmonic flux component, the method is not suitable for all kinds of machines.

Rotating and pulsating voltage vector injection methods, based on a high frequencyvoltage excitation, are different compared to the INFORM method which utilizes discretevoltage pulses. The rotating voltage vector injection method was introduced by Jansen andLorenz in 1994 [34]. A rotating high frequency voltage vector is added on top of the fun-damental excitation in the stator reference frame. The resulting negative sequence currentcomponent, which contains rotor position information, is used to obtain the position esti-mates. In [20], Corley and Lorenz proposed the pulsating voltage vector injection methodbased on injecting a pulsating voltage in the estimated rotor-fixed reference frame. Bothmethods are easy to implement and position estimates of highquality are obtained pro-vided that the machine possesses significant saliency at theconsidered operating point.Comparisons between these two signal injection methods have been made in a number ofpapers, some examples are [39,57,58]. These two signal injection methods are consideredand implemented in this work and will be reviewed in detail inthe following section.

3.3 High Frequency Continuous Signal Injection

3.3.1 Modeling the PMSynRel Current Dynamics

An analytical model of the PMSynRel when used in traction mode can be derived usingthe methods used in Chapter 2. This model will be used to analyze the sensorless controlalgorithms considered in this chapter. For this purpose, the model in the rotor-fixeddq-reference frame offers many benefits compared to that expressed using phase quantities.Therefore, the model here is only presented in thedq-reference frame.

The current dynamics, in thedq-reference frame can be expressed in matrix form

29


as

vdq = Ldq

didqdt

+ Zdqidq + ωrψm,dq (3.1)

wherevdq = [vd, vq]T , idq = [id, iq]

T , ψm,dq = [0, ψm]T and the matrixesL dq andZdq are

found as

Ldq =

[Ld 0

0 Lq

]

(3.2)

Zdq =

[Rs −ωrLqωrLd Rs

]

(3.3)

where the notation

Ld = Lls +3Lm,02

− 3Lm,22

(3.4a)

Lq = Lls +3Lm,02

+3Lm,22

(3.4b)

is introduced. It should be mentioned that this is a simplified model (for control purposes)which neglects saturation effects and harmonics.

3.3.2 Machine Model for High Frequency Excitation

As mentioned above, signal injection methods are often considered only in low speedrange when the back EMF is very low. Hence, the impact of the rotating speedωr canbe neglected. Due to the considerably high signal frequency, the machine behaves as apure inductive load since the stator voltage drop and the back-EMF can be omitted. ThePMSynRel model presented in (3.1) can then be reexpressed as

vdqc = Ldq

didqcdt

. (3.5)

Considering the high frequency injection method, the differential inductances are usedwhich yields

L dq =

[L′d 0

0 L′q

]

(3.6)

where

L′d =

∂ψd(id, iq)

∂id(3.7a)

L′q =

∂ψq(id, iq)

∂iq(3.7b)

30


and the subscript′ denotes that the inductance is a differential inductance. Although notincluded in (3.6) for simplicity, the differential mutual inductance can be calculated as

L′dq =

∂ψd(id, iq)

∂iq(3.8a)

L′qd =

∂ψq(id, iq)

∂id. (3.8b)

In Fig. 3.1, three coordinate systems are defined. The truedq-coordinate system isdefined such that itsd-axis coincides with the magnetic north pole of the rotor. The quan-tities represented using the truedq-coordinates can be transformed to the stationary ref-erence frame (αβ-coordinates) and the estimated rotor-reference-frame (dq-coordinates),or vice versa, using the following transformation matrix

T(θx) =[cos θx − sin θxsin θx cos θx

]

. (3.9)

Then, an arbitrary vectorfs = [fd fq]T can be transformed to vectorfss = [fα fβ ]

T andvectorfs = [fd fq]

T by performing

fss = T(θ)fs (3.10a)

fs = T(θ)fs (3.10b)

or vice versa

fs = T−1(θ)fss (3.11a)

fs = T−1(θ)fs (3.11b)

whereθ is the estimated rotor position angle andθ is the position estimation error definedasθ = θ − θ.

Fig. 3.1 Definition ofαβ-coordinates,dq-coordinates anddq-coordinates.

31


3.3.3 Rotating Voltage Vector Injection Method

The key idea of the rotating voltage vector injection methodis to superimpose a balancedrotating voltage vectorvsc = Vce

jωct on top of the fundamental excitation in the stator ref-erence frame. By using (3.5) and (3.11a), the resulting highfrequency current expressedin αβ-coordinates can be found as

isc =∫

T(θ)L−1dq T−1(θ)vscdt

=Vc

2ωcL′dL

′q

[(L′

d + L′q) sinωct+ (L′

q − L′d) sin(ωct− 2θ)

−(L′d + L′

q) cosωct+ (L′q − L′

d) cos(ωct− 2θ)

]

(3.12)

where the rotor positionθ has been assumed constant. In order to obtain the rotor positionestimation error, (3.12) is modulatedtran as

T(−2θ)T(ωct+ π)isc =Vc

2ωcL′dL

′q

[

−(L′q + L′

d) sin(2ωct− 2θ) + (L′q − L′

d) sin 2θ

(L′q + L′

d) cos(2ωct− 2θ)− (L′q − L′

d) cos 2θ

]

.

(3.13)

Provided that the machine retains saliency, i.e.,L′q−L′

d 6= 0, the first component in (3.13)contains useful rotor position information, due to the termsin 2θ. A suitable error signalεrot is now found by low-pass filtering the first component of (3.13)

εrot = LPF

{Vc

2ωcL′dL

′q

[

−(L′q + L′

d) sin(2ωct− 2θ) + (L′q − L′

d) sin 2θ]}

=(L′

q − L′d)

2ωcL′dL

′q

︸︷︷︸

Krot

sin 2θ (3.14)

whereKrot is the signal injection gain. This error signal can then be used in a trackingobserver to obtain estimates of the rotor position and speed.

The fundamental current also exists in the measured currentand essentially behavesas DC component in the estimateddq-coordinates. After performing the modulation pro-cess in (3.13), however, the fundamental current becomes a high frequency componentwhich is easily filtered out by the low-pass filter in (3.14).

3.3.4 Pulsating Voltage Vector Injection Method

When the pulsating voltage vector injection method is applied, a high-frequency voltage,with the amplitudeVc and angular frequencyωc is injected on top of the fundamentalexcitation in the (estimated)d-direction. The injected voltage vector in the set of estimatedcoordinates can then be expressed as

vc = [Vc cosωct 0]T . (3.15)

32


Using (3.5) and (3.11b), the resulting current in the estimated rotor reference frame cannow be obtained as

isc =∫

T(θ)L−1dq T−1(θ)vscdt

=Vc sinωct

2ωcL′dL

′q

[(L′

q + L′d) + (L′

q − L′d) cos 2θ

(L′q − L′

d) sin 2θ

]

(3.16)

where the estimation errorθ changes slowly (treated as a constant) compared to the in-jected signal frequencyωc. As seen, the resulting current in theq-direction contains theposition error information due to thesin 2θ expression. However, the resulting current ismodulated bysinωct and cannot be used in the position estimation directly. Since the fre-quencyωc is perfectly known, the current vectorisc can be demodulated by multiplyingwith sinωct. The demodulated current contains a DC component possessing the positionerror information sincesin2 ωct = (1 − cos 2wct)/2. Then, the resulting error signal forthe pulsating injection method can be obtained by filtering the demodulated current

εpulse= LPF[

iqc sinωct]

=(L′

q − L′d)

4ωcL′dL

′q

︸︷︷︸

Kpulse

sin 2θ (3.17)

whereKpulse is the signal injection gain. This error signal can then be used in a trackingobserver to obtain estimates of the rotor position and speed.

The fundamental is, of course, also present in the estimateddq-coordinates togetherwith the resulting high frequency current. This can be removed by adding a high pass filterwith a very low cut-off angular frequency. In this way, the fundamental current is alreadyremoved before performing (3.17).

3.3.5 Obtaining Speed and Position Estimates

The rotor position and speed can be estimated using the errorsignals described above asinputs to different forms of tracking observers. A number oftracking observers have beenproposed in the literature which exhibit different properties in terms of algorithm com-plexity, sensitivity to parameter variations and noise [55]. Although not the primary focusin this work, some tracking algorithms are reviewed here. A Luenberger style trackingobserver is based on a mechanical model where the electromagnetic torque reference isfeedforward to achieve zero lag estimation [38, 53]. Reference [55] presents a trackingobserver based on a Kalman filter for estimates of rotor position and speed. The proposedKalman filter is adopted from [4] which is based on a parameterindependent mechani-cal model. The inherent filtering characteristic makes thiskind of tracking observer lesssensitive to measurement noise. Several novel observers have been proposed recently.A sliding mode observer is used in [24] showing high steady-state estimation accuracy

33


and good dynamic properties. An intelligent sensorless PMSM drive system is proposedin [74] in which the extended Kalman filter is used for position and speed estimates andfuzzy control is used for covariance matrix adjustment.

The phase locked loop (PLL) type tracking observer presented in [31] is shown inFig. 3.2, and is used in this work. In state space form, the PLLtype estimator can beexpressed as

˙ωr = γ1ε (3.18a)

˙θ = ωr + γ2ε (3.18b)

whereγ1 andγ2 are gain parameters andε is the error signal containing position infor-mation [31]. Provided thatε = θ, the characteristic polynomialc(s) describing the errordynamics is found as [31]

c(s) = s2 + γ2s+ γ1. (3.19)

In order to obtain a well damped system (avoid oscillations), both poles are placed ats = −ρwhereρ is a positive constant. This is done by selectingγ1 = ρ2 andγ2 = 2ρ [31].

Fig. 3.2 PLL tracking observer.

34

3.4. Effects of Saturation and Cross-Saturation

3.4 Effects of Saturation and Cross-Saturation

The sensorless control strategy considered in Section 3.3 relies on tracking the rotor-position dependent saliency. However, the machine saliency depends on both its geome-try (i.e., a salient rotor design) and magnetic saturation which varies with the operatingpoint [2]. The analysis presented in Section 3.3 only considers a single saliency and thecross-saturation effect is disregarded. However, the cross-magnetization phenomenon inelectrical machines also has great impact on sensorless control application [27,60,67].

In order to study the effects of saturation and cross-saturation, the correspondingdifferential inductances for the prototype machine in consideration are computed usingFEM data and (3.7a)–(3.8b). The result is shown in Fig. 3.3(b)–Fig. 3.3(d). As seen, theeffect of saturation along theq-axis is evident and the differential inductanceL′

q decreasesrapidly whenq-axis current is increased. Relatively, thed-axis differential inductanceL′

d

is less sensitive to saturation due to the fact that saturation in the rotor iron path is morepronounced than saturation in the stator iron. This is the drawback of PMSynRels com-pared to inset PMSMs [6] when applied in low speed range sensorless control applica-tions. It is also evident that our prototype machine possesses differential mutual induc-tances due to the existence of an iron path between thed- andq- axes. The correspondingFEM simulation results are shown in Fig. 3.3(c) and 3.3(d) where the value of the mutualinductances (in mH) are depicted as contour lines.

As shown in (3.14) and (3.17), the error signals degrade whenthe difference ofL′q

andL′d reduces. This difference can be zero and even negative for some operating points

which make sensorless control inapplicable. Thefeasible regionis introduced in [5] anddefined by the loci where the difference of the differentialdq-inductances is zero, whichis shown by the solid line in Fig. 3.4. It can be used as a guide to select feasible operatingpoints for sensorless control. In order to obtain a high efficiency, the operating pointsare often selected based on the maximum torque-per-Ampere (MTPA) trajectory which isshown in Fig. 3.4. However, according to the FEM simulations, the MTPA trajectory isnot always applicable for sensorless control. In order to verify the simulation results, theprototype machine in consideration is experimentally tested at different operating pointswhich are also shown in Fig. 3.4 as black dots.

When cross-saturation is considered, the differential inductance matrixLdq in (3.2)becomes to

Ldq =

[L′d L′

dq

L′dq L′

q

]

. (3.20)

By substituting (3.20) into (3.12) and (3.16), and applying(3.14) (for the rotating voltagevector injection method) and (3.17) (for the pulsating voltage vector injection method),

35


(a)

−80 −60 −40 −20 00

10

20

0 20 40 60 800

100

200id [A]

∂ψd

∂i d

[mH

]

iq [A]∂ψq

∂i q

[mH

](b)

−60 −40 −20 00

10

20

30

40

50

60

−2

−1

0

1

2

3

id [A]

i q[A

]

(c)

−60 −40 −20 00

10

20

30

40

50

60

−2

−1

0

1

2

3

id [A]

i q[A

]

(d)

Fig. 3.3 FEM simulation and inductances: (a) FEM model; (b) Differential self inductances; (c)Differential mutual inductanceL′

dq [mH]; (d) Differential mutual inductanceL′qd [mH].

the error signals are found as

εrot =Vc2ωc

(L′q − L′

d) sin 2θ − 2L′dq cos 2θ

L′dL

′q − L′2

dq

=Vc2ωc

√

(L′q − L′

d)2 + 4L′2

dq sin(2θ − ϕ)

L′dL

′q − L′2

dq

(3.21)

εpulse=Vc4ωc

(L′q − L′

d) sin 2θ − 2L′dq cos 2θ

L′dL

′q − L′2

dq

=Vc4ωc

√

(L′q − L′

d)2 + 4L′2

dq sin(2θ − ϕ)

L′dL

′q − L′2

dq

(3.22)

36


−40 −30 −20 −10 00

10

20

30

40

id [A]

i q[A

]

Fig. 3.4 Operating characteristics in thedq-current plane: Dashed lines indicate constant torque,blue dots indicate the MTPA loci, dotted line is the current-limit circle, solid line indicateswhereL′

q − L′d = 0, black dots indicate selected operating points for the experimental

test.

where [45]

ϕ = cos−1[(L′q − L′

d

)/(√

(L′q − L′

d)2 + 4L′2

dq

)]

. (3.23)

It is evident from (3.21) and (3.22) that the differential mutual inductanceL′dq induces a

phase shift which results in a steady-state position estimation error when the error signalis forced to zero by the PLL. Assuming that the difference ofL′

q andL′d is positive, the

mutual differential inductance induces a steady-state position estimation error given by

θ∗ =ϕ

2=

1

2cos−1

L′q − L′

d√

(L′q − L′

d)2 + 4L′2

dq

. (3.24)

Obviously, the position estimation error is zero only ifL′dq = 0 [27,45]. Assuming a small

estimation errorθ yieldssin 2θ ≈ 2θ andcos 2θ ≈ 1. Eq. (3.22) can then be approximatedas

εpulse≈Vc2ωc

(L′q − L′

d)θ − L′dq

L′dL

′q − L′2

dq

=Vc2ωc

(L′q − L′

d)θ

L′dL

′q − L′2

dq

−Kc (3.25)

whereKc = VcL′dq/

(2ωc(L

′dL

′q − L′2

dq))

which is constant for a certain operating pointand can be identified experimentally. A new error signalε′pulse = εpulse+ Kc can then beused in the PLL to compensate for the cross-saturation effect. This method is implementedfor both the rotating and pulsating voltage vector injection methods in this work.

Another observation from (3.21) and (3.22) is that magneticcross-saturation alsoaffects the amplitude of the error signals. As introduced in[5], the feasible regionis

37


defined as the loci whereL′q − L′

d = 0. This loci can be experimentally determined bymeasuring the differential inductances at each operating point. Alternatively, the resultingposition error signal can also be used to determine the feasible region. However, in theexistence of magnetic cross-saturation, the amplitude of the error signal may be not equalto zero whenL′

q − L′d = 0. Thereby, using the position error signal to map the feasible

region can be challenging. In this work, mapping of the feasible region is carried outusing the resulting error signal based on experimental measurements and comparativeFEM simulations. A factorKe is first defined to map the feasible region, which is givenas

Ke =Vc4ωc

√

(L′q − L′

d)2 + 4L′2

dq

L′dL

′q − L′2

dq

sign(L′q − L′

d

). (3.26)

In (3.26), the absolute value ofKe equals to the amplitude of the position error signal in(3.22) and its sign is determined byL′

q − L′d. According to [5], the feasible region can be

redefined by finding all operating points (in terms ofid andiq) whereKe > 0.The mutual inductanceL′

dq can also be found in the denominator of (3.26) whichmakes analysis ofKe more complicated. Comparison ofL′2

dq andL′dL

′q is shown in Fig. 3.5

in percentage which is based on FEM simulations.

−30 −25 −20 −15 −10 −50

5

10

15

20

25

0.5

1

1.5

2

2.5

3

id [A]

i q[A

]

Fig. 3.5 Comparison ofL′2dq andL′

dL′q: L

′2dq/(L

′dL

′q)[%].

Since only a part of the current span is covered in the experimental measurement(illustrated in Fig. 3.4), the comparison shown in Fig. 3.5 only covers the same operat-ing region. As seen in Fig. 3.5,L′2

dq is negligible compared toL′dL

′q . Hence,Ke can be

38


simplified to

Ke ≈Vc4ωc

√

(L′q − L′

d)2 + 4L′2

dq

L′dL

′q

sign(L′q − L′

d

)

=Vc4ωc

√√√√√√

(L′q − L′

d

L′dL

′q

)2

︸︷︷︸

C1

+

(2L′

dq

L′dL

′q

)2

︸︷︷︸

C2

sign(L′q − L′

d

)(3.27)

whereC1 andC2 denote two key components of (3.27). As seen,C1 is independent ofcross-saturation. However,C2 is the cross-saturation induced component which can makethe amplitude ofKe non-zero even whenL′

q − L′d = 0. These two components are com-

puted based on FEM simulation data and are plotted in Fig. 3.6. As shown in Fig. 3.6(a),the amplitude ofC1 decreases rapidly along theq-axis direction (the contour boundarylines are almost in parallel with each other) due to the reduced saliency. It becomes zerowhenL′

q − L′d = 0 and starts to increase again whenL′

q − L′d changes sign. Relatively,

the change ofC2 shown in Fig. 3.6(b) is smoother, especially whenC2 is small. Hence,the componentC1 dominates the change ofKe. One assumption is made accordingly thatalong theq-axis direction, the amplitude ofKe decreases withL′

q − L′d and reaches its

minimum value whenL′q−L′

d = 0. It starts to increase again whenL′q−L′

d changes sign.This assumption can be used for feasible region mapping based on the resulting positionerror signal.

The resulting error signal when the pulsating voltage vector injection method isadopted has been measured in the experimental setup. In the experimental tests, the po-sition estimation errorθ is varied linearly from0◦ to 180◦ (electrical degrees) while themachine is rotating at the constant speed 150 rpm. The current controller bandwidth isset as low as 100 rad/s in order to reduce the effect of the closed-loop current control.One experimental sample is shown in Fig. 3.7. From the obtained experimental data, theamplitude of the error signal’s fundamental is obtained using a discrete Fourier transform(DFT). In this work, the tests are divided into 13 groups. In each test group, thed-axiscurrent is fixed and theq-axis current is increased by small steps. According to the previ-ous analysis, the absolute value ofKe decreases to the minimum value whenL′

q−L′d = 0

and starts to increase again whenL′q − L′

d changes sign. Therefore, the sign ofKe isdetermined accordingly.

The FEM simulation results, based on (3.26), and the corresponding experimentalmeasurement results are shown in Fig. 3.8 whereKe is plotted as contour face and thefeasible region is defined as the region whereKe > 0. The maximum torque-per-ampere(MTPA) loci is shown by the blue dots in Fig. 3.8(a) and Fig. 3.8(b) and the measuredoperating points are indicated by the small back dots in Fig.3.8(b). As seen in Fig. 3.8, thesimulation results and the experimental results are in reasonably good agreement. It canbe seen that the operating points corresponding to high torque are within the unfeasible

39


sensorless control region. Therefore, those operating points are not possible to obtainwhen sensorless control is applied.

40


−30 −25 −20 −15 −10 −50

5

10

15

20

25

500

1000

1500

2000

2500

3000

3500

4000

id [A]

i q[A

]

(a)

−30 −25 −20 −15 −10 −50

5

10

15

20

25

200

400

600

800

1000

id [A]

i q[A

]

(b)

Fig. 3.6 Key components for evaluation ofKe based on FEM data: (a)C1; (b) C2.

41


0 0.2 0.4 0.6 0.8 10

50

100

150

0 0.2 0.4 0.6 0.8 1−0.5

0

0.5

(a)

θ[e

lec.

deg

.]

(b)

t (s)

t (s)

ε pul

se[A

]

Fig. 3.7 Experimental test for the pulsating method whenid=-30 A andiq=13 A: (a) Forced posi-tion estimation error test; (b) Resulting error signalεpulse.

42


−30 −20 −10 00

10

20

30

40

−0.5

0

0.5

id [A]

i q[A

]

(a)

−30 −20 −10 00

10

20

30

40

−0.5

0

0.5

id [A]

i q[A

]

(b)

Fig. 3.8 Ke as function of (id,iq): (a) FEM simulation; (b) Measurement.

43


3.5 Effects of a Non-sinusoidal Field Distribution

3.5.1 Spatial Inductance Harmonics

As shown in Fig. 3.7(b), the error signalεpulse possesses high order harmonics which areinduced by spatial inductance harmonics [47,56,73]. Thesecan have a significant impacton the quality of the obtained position estimates; especially when the amplitude of theerror signal is small (i.e., near the borders of the feasibleregion). The spatial inductanceharmonics is a well know phenomenon which are induced by the non-sinusoidal fielddistributions [47] and leads to position estimation errors.

Typically the dominating inductance harmonic is the 6th or 12th order harmonicwhen expressed in rotor-fixed coordinates [47, 56, 73]. Higher order harmonics can oftenbe neglected due to their relatively small amplitudes. Therefore, the stator inductancematrix shown in (3.2) can be reexpressed as

L s =

[L′d + L′

6 cos 6θ −L′6 sin 6θ

−L′6 sin 6θ L′

q − L′6 cos 6θ

]

(3.28)

whereL′6 is the amplitude of the 6th order spatial inductance harmonic [56]. Note that the

cross-saturation effect is neglected in (3.28) for simplicity.If spatial harmonics of the permanent magnet flux linkage areconsidered up to the

6th order as well,ψm,dq can be expressed as

ψm,dq =

[ψm + ψd6 cos 6θ

ψq6 sin 6θ

]

(3.29)

whereψd6 andψq6 are the amplitudes of the 6th-order harmonics in thed- andq- axes,respectively [56]. Similarly, the impedance matrixZs in (3.3) can be reexpressed as [73]

Zs =

[Rs − 5ωrL

′6 sin 6θ −ωrL′

q − 5ωrL′6 cos 6θ

ωrL′d − 5ωrL6 cos 6θ Rs + 5ωrL

′6 sin 6θ

]

. (3.30)

Since the injected voltage vector typically has a much higher frequency compared tothe fundamental frequency, the term5ωr shown in (3.30) can still be assumed to be zero.Hence, as seen from the high-frequency carrier signal, all elements inZs can be neglected.Therefore, the resulting current for the rotating and pulsating voltage vector injectionmethods can still be calculated using (3.12) and (3.16), respectively. The resulting positionerror signals for the rotating and pulsating voltage vectorinjection methods are found as

εrot =Vc2ωc

(L′q − L′

d) sin 2θ + 2L′6 sin(6θ − 2θ)

L′dL

′q + L′

6(L′q − L′

d) cos 6θ − L′26

(3.31a)

εpulse=Vc4ωc

(L′q − L′

d) sin 2θ + 2L′6 sin(6θ − 2θ)

L′dL

′q + L′

6(L′q − L′

d) cos 6θ − L′26

. (3.31b)

44

3.5. Effects of a Non-sinusoidal Field Distribution

As seen in (3.31a) and (3.31b), the spatial inductance harmonic introduces a disturbancein the error signal which oscillates at six times of the fundamental frequency.

Now, if L′dL

′q ≫ L′

6(L′q − L′

d) andL′26 ≈ 0 are assumed, (3.31a) and (3.31b)

simplifies to

εrot ≈Vc(L

′q − L′

d)

2ωcL′dL

′q

︸︷︷︸

Krot,1

sin 2θ +VcL

′6

ωcL′dL

′q

︸︷︷︸

Krot,L′

6

sin(6θ − 2θ) (3.32a)

εpulse≈Vc(L

′q − L′

d)

4ωcL′dL

′q

︸︷︷︸

Kpulse,1

sin 2θ +VcL

′6

2ωcL′dL

′q

︸︷︷︸

Kpulse,L′

6

sin(6θ − 2θ) (3.32b)

whereKrot,1 andKpulse,1 denote the amplitudes of the error signals induced by the maininductances (L′

d andL′q), and,Krot,L′

6andKpulse,L′

6denote the amplitudes of the error

signals induced by the 6th-order inductance harmonic (L′6) for the rotating and pulsating

voltage vector injection methods, respectively.Now, (3.32b) is considered only since (3.32a) has a similar format. In the PLL po-

sition estimator, the error signalεpulse is forced to zero which yields the resulting positionestimation error

θ = −1

2sin−1

Kpulse,L′

6sin(6θ − 2θ)

Kpulse,1. (3.33)

The maximum position estimation error is, hence, found as

max θ =1

2sin−1

Kpulse,L′

6

Kpulse,1(3.34)

which can be obtained experimentally. SinceKpulse,1 represents the fundamental ampli-tude of the error signal, it can be replaced byKe if cross-saturation can be neglected.If Kpulse,L′

6is determined experimentally,θ = 0 is set for each measurement (enabled

by controlling the PMSynRel using a resolver but still adding the carrier signal) and theresulting error signal is stored. An example of an experimentally obtained error signalis shown in Fig. 3.9. It is evident that the error signal is induced by a 6th-order induc-tance harmonic. As shown in Fig. 3.9, the error signal contains exactly 10 fundamentalperiods and the 6th-order harmonic is selected asKpulse,L′

6. The predicted position estima-

tion error is calculated by substitutingKe andKpulse,L′

6into (3.34), and is shown for the

experimental PMSynRel in Fig. 3.10.The pulsating voltage vector injection strategy together with compensation for the

cross-saturation is implemented and experimental resultsare shown in Fig. 3.11. It canbe seen that the measured rotor position estimation error isoscillating at 6 times of thefundamental frequency which is induced by the 6th-order spatial inductance harmonic.The maximum value ofθ is close to the prediction shown in Fig. 3.10.

45


0 0.5 1 1.5 2−0.1

0

0.1

0 1 2 3 4 5 6 70

0.02

0.04

0.06

0.08

t (s)

Harmonic order

ε pul

se[A

]ε p

ulse

[A]

Fig. 3.9 Measurement sample for pulsating method whenid=-30 A andiq=18 A, and the funda-mental frequency is 5 Hz.

For the PMSynRel in consideration, the 6th-order inductance harmonics is pro-nounced in the operating points close to the MTPA loci. This potentially will reduce therobustness of the sensorless control strategy and should becompensated for.

46


2

2

4

4

6

6

8

8 101214152535

455565

−30 −20 −10 00

10

20

30

40

10

20

30

40

50

60

id [A]

i q[A

]

Fig. 3.10 Maximum steady-state position estimation error (θ) due to the 6th–order spatial induc-tance harmonic.

0 0.5 1 1.5 2

−10

−5

0

5

10

0 0.5 1 1.5 2

−10

−5

0

5

10

0 0.5 1 1.5 2

−10

−5

0

5

10

0 0.5 1 1.5 2

−10

−5

0

5

10

id = -30 A, iq = 13 A id = -30 A, iq = 15 A

id = -30 A, iq = 16 A

t [s]t [s]

t [s]t [s]

θ[e

lec.

deg

.]

θ[e

lec.

deg

.]

θ[e

lec.

deg

.]

θ[e

lec.

deg

.]

id = -30 A, iq = 18 A

Fig. 3.11 Position estimation errorθ due to the 6th-order spatial inductance harmonic (the PM-SynRel is rotating at 150 rpm).

47


3.5.2 Spatial Harmonic Compensation

Different approaches have been proposed for spatial inductance harmonic (or referredto multiple saliency) compensation in sensorless control.In [22, 32, 70], the effect ofinductance harmonics and their compensation when the rotating voltage vector injectionmethod is applied to an induction machine were studied. The corresponding compensationstrategies are also proposed and one example from [22] is shown in Fig.3.12.

Fig. 3.12 Compensation of 6th-order spatial inductance harmonic forrotating method proposedby Degner and Lorenz.

As shown in Fig.3.12, the spatial inductance harmonic induced error signal is re-moved by subtractingIcn,6ej(6θ+φ6) from the error signal whereIcn,6 is the amplitude ofthe harmonic induced error signal andφ6 is its phase shift. Different approaches can befound in [32] and [70] but the principle is the same.

Another compensation method is proposed in [56] which addresses the pulsatingvoltage vector injection method for PMSMs. The impact of thespatial inductance har-monics is eliminated by injecting a modified pulsating voltage vector to the estimatedd-axis. The method is reviewed here and also extended so that it is suitable also for therotating voltage vector injection method. The basic idea ofthe compensation method pro-posed in [56] is to obtain an ideal error signal by means of modifying the high frequencycarrier voltage. The ideal high frequency current signal, which is identical to (3.16) ifθ = 0, can be found as [56]

is =VcωcL′

d

sinωct

[1

0

]

. (3.35)

The PMSM model considered in the high frequency injection method is

vs = L s

disdt

+dL s

dtis (3.36)

48


wheredL s/dt can be found as

dL s

dt= ωr

[−5L′

6 sin 6θ −L′q − 5L′

6 cos 6θ

L′d − 5L6 cos 6θ 5L′

6 sin 6θ

]

. (3.37)

Substituting (3.35) into (3.36) gives a modified high frequency voltage

vc = Vc cos(ωct)

[1 + (L′

6/L′d) cos 6θ

−(L′6/L

′d) sin 6θ

]

+ωrωcVc sin(ωct)

[−5(L′

6/L′d) sin 6θ

1− 5(L′6/L

′d) cos 6θ

]

. (3.38)

The method described above has been implemented in the experimental setup. As seen in(3.38), the second term on the right hand side can generally be neglected sinceωr/ωc canbe considered small (ωr = 5 Hz andωc = 500 Hz in the experimental test). As shown inFig. 3.13, the effect of the 6th–order inductance harmonic can be effectively compensatedby the proposed method and the rotor position estimation error is reduced significantly.

0 0.5 1 1.5 2−20

−10

0

10

20

0 0.5 1 1.5 2−20

−10

0

10

20

t [s]

Before compensation

t [s]

θ[e

lec.

deg

.]θ

[ele

c.d

eg.]

After compensation

Fig. 3.13 Pulsating sensorless control strategy at 150 rpm whenid=-30 A andiq=18 A.

A similar compensation technique for the rotating carrier injection sensorless con-trol strategy is now derived based on the principle of [56]. When the rotating carriervoltage is superimposed on the fundamental excitation, theresulting carrier current can

49


be expressed in the stator reference frame as

isc =∫

T(θ)L−1T(θ)−1vcdt

= − Vc2ωc

(L′d + L′

q) sin(ωct) + (L′q − L′

d) sin(ωct− 2θ)− 2L′6 sin(ωct+ 4θ)

L′26 − L′

6(L′q − L′

d) cos 6θ − L′dL

′q

−(L′d + L′

q) cos(ωct) + (L′q − L′

d) cos(ωct− 2θ)− 2L′6 cos(ωct+ 4θ)

L′26 − L′

6(L′q − L′

d) cos 6θ − L′dL

′q

.

(3.39)

As seen in (3.39), the resulting carrier current possesses 6th–order inductance inducedharmonics which should be removed. Hence, the ideal resulting carrier current can beobtained by omitting all terms containingL′

6 which yields

i′sc =

Vc2L′

dL′qωc

[(L′

d + L′q) sin(ωct) + (L′

q − L′d) sin(ωct− 2θ)

−(L′d + L′

q) cos(ωct) + (L′q − L′

d) cos(ωct− 2θ)

]

(3.40)

which is identical to (3.12). Then, the modified rotating voltage vector in the stator refer-ence frame can be calculated as

vsc = T(θ)L sT−1θ di

′sc /dt

=Vc

2L′dL

′q

[2L′

dL′q cosωct+ L′

6(L′q − L′

d) cos(ωct− 6θ) + L′6(L

′d + L′

q) cos(ωct + 4θ)

2L′dL

′q sinωct + L′

6(L′q − L′

d) sin(ωct− 6θ)− L′6(L

′d + L′

q) sin(ωct+ 4θ)

]

.

(3.41)

Eq. (3.41) can also be implemented in theabc-coordinate as

vabc = Tabcvsc

= Vc

cos(ωct) +(L′

q−L′

d)L′

6

2L′

dL′

qcos(ωct− 6θ) +

(L′

d+L′

q)L′

6

2L′

dL′

qcos(ωct+ 4θ)

cos(ωct− 2π3) +

(L′

q−L′

d)L′

6

2L′

dL′

qcos(ωct− 6θ − 2π

3) +

(L′

d+L′

q)L′

6

2L′

dL′

qcos(ωct + 4θ + 2π

3)

cos(ωct +2π3) +

(L′

q−L′

d)L′

6

2L′

dL′

qcos(ωct− 6θ + 2π

3) +

(L′

d+L′

q)L′

6

2L′

dL′

qcos(ωct+ 4θ − 2π

3)

(3.42)

where

Tabc =

1 0

−12

√32

−12

−√32

. (3.43)

The proposed compensation method is implemented in the experimental test and a sam-ple result is shown in Fig. 3.14. As seen, the rotor position estimation is significantlyimproved by the proposed compensation method.

50

3.6. Polarity Detection

0 0.5 1 1.5 2−20

−10

0

10

20

0 0.5 1 1.5 2−20

−10

0

10

20

Before compensation

t [s]

t [s]θ

[ele

c.d

eg.]

θ[e

lec.

deg

.]After compensation

Fig. 3.14 Rotating sensorless control strategy at 150 rpm whenid=-30 A andiq=18 A.

3.6 Polarity Detection

The drawback of using the error signals given in (3.14) and (3.17) is that the estimatedposition θ can be equal toθ + kπ, wherek is an integer. Obviously, they provide am-biguous information about the polarity of the rotor magnet which is required during astartup procedure. Some techniques have been proposed to detect the magnet polarity,either being integrated in the position estimation process[33, 36, 59] or being performedstand alone [14,66,69]. Disregarding how it is implemented, the phenomenon of magneticsaturation in the stator iron is typically used to detect themagnet polarity. A typical mag-netization curve of a PMSM is shown in Fig. 3.15 where the horizontal axis representsthe d-axis current and the vertical axis represents thed-axis flux. Thed-axis directioncorresponds to the north pole direction of the permanent magnet andψm denotes the fluxlinkage due to the rotor magnet.

As shown in Fig. 3.15, a stator flux linkage∆ψ is injected to thed-axis being inphase (corresponding toψm + ∆ψ) and out of phase (corresponding toψm − ∆ψ) withthe magnet flux linkage. A positive change of thed-axis flux increases the stator ironsaturation, resulting in a decreasedd-axis inductance and vice versa. As a consequence,the resulting currentid+ is greater than the resulting currentid− in amplitude. This phe-nomenon can be used to detect the north pole of the rotor magnet.

The magnet polarity detection can be implemented by injecting two voltage pulses,equal in amplitude, into the positive and negative estimated d-axis direction. Assuminga negligible position estimation errorθ, the corresponding current inq-direction is verysmall and the produced torque is negligible. A larger current response is expected if the

51


Fig. 3.15 Typical relation betweend-axis current andd-axis flux linkage for a PMSM.

estimatedd-direction is aligned to the magnetic north pole.Fig.3.16 shows FEM simulation results of the polarity detection technique de-

scribed above for the prototype PMSynRel in consideration.The voltage pulses are in-jected into the positive and negative “true”d-direction. The injected voltage pulses andtheir current responses are shown in Fig. 3.16(a) and Fig. 3.16(b), respectively. Differingfrom above, a larger current response is obtained when the voltage pulse is opposite to themagnet flux. The reason can be found in Fig. 3.16(c) and Fig. 3.16(d) which illustrate theflux lines corresponding to the positive and negative peak current responses, respectively.As seen, the flux leakage in the magnet bridges is decreased for the positive pulse testwhich increases thed-axis inductance and decreases the current response (the oppositeis true for the negative pulse test). Hence, saturation in the magnet bridges in the rotorstructure is the dominating effect rather than saturation in the stator core.

In order to experimentally verify the FEM simulations, a polarity test has been im-plemented experimentally. The test results together with corresponding FEM simulationsare shown in Fig. 3.17. It can be seen that the experimental test are in good agreementwith the FEM simulations.

Voltage pulses with different amplitudes were also tested to find out how muchcurrent is required to result in dominating saturation in the stator core. The experimen-tal results are shown in Fig. 3.18(a)–(d). All the FEM simulations show good agreementwith the experimental tests. As seen in Fig. 3.18 (c) and (d),the positive current responseis slightly bigger than the negative current response when the amplitude of the voltagepulse is increased to 35 V. However, a more distinguishable current response difference isrequired to obtain a robust polarity detection due to the signal to noise ratio requirement.To avoid demagnetization, a further increase in voltage magnitude was only consideredusing FEM simulations. The FEM simulations shows that when the amplitude of the volt-age pulse is increased to 40 V, a distinguishable current response difference is obtained,indicating dominating saturation in the stator core.

52

3.6. Polarity Detection

0 0.05 0.1 0.15 0.2 0.25−5

05

1015

0 0.05 0.1 0.15 0.2 0.25−5

0

5

10

v d[V

]

t [s]

t [s]

i d[A

]

(a)

0 0.05 0.1 0.15 0.2 0.25−15−10−5

05

0 0.05 0.1 0.15 0.2 0.25−15−10−5

05

v d[V

]

t [s]

t [s]

i d[A

]

(b)

(c) (d)

Fig. 3.16 Impact of voltage pulses for polarity detection (FEM simulations): (a) Positive voltagepulse and current response; (b) Negative voltage pulse and current response; (c) Fluxlines corresponding to the maximum positive pulse response; (d) Flux lines correspond-ing to the maximum negative pulse response.

53


0 0.05 0.1 0.15 0.2 0.25−5

05

1015

0 0.05 0.1 0.15 0.2 0.25−5

0

5

10

Measurement

FEM simulation

v dre

fere

nce

[V]

t [s]

t [s]

i d[A

]

(a)

0 0.05 0.1 0.15 0.2 0.25−15−10−5

05

0 0.05 0.1 0.15 0.2 0.25−15

−10

−5

0

5

Measurement

FEM simulationv d

refe

ren

ce[V

]

t [s]

t [s]

i d[A

]

(b)

Fig. 3.17 (a) Positive voltage pulse and current response;(b) Negative voltage pulse and currentresponse.

0 0.05 0.1 0.15 0.2 0.25−5

0

5

10

MeasurementFEM simulation

0 0.05 0.1 0.15 0.2 0.25−20

−10

0


(a)

(b)

t [s]

t [s]

i d[A

]i d

[A]

0 0.05 0.1 0.15 0.2 0.25

0

20

40


0 0.05 0.1 0.15 0.2 0.25−40

−20

0


(c)

(d)

t [s]

t [s]

i d[A

]i d

[A]

Fig. 3.18 Current response of polarity detection: (a)vpulse= 20 V;(b) vpulse= −20 V;(c) vpulse=35 V;(d) vpulse= −35 V.

54

3.7. Summary of Chapter

3.7 Summary of Chapter

In this chapter, different rotor position estimation methods covering from zero speed tohigh speed were reviewed. The rotating and pulsating voltage vector injection methods forrotor position estimation at low speeds were studied in detail. The effects of the saturationand cross-saturation were investigated by means of analytical methods and FEM analy-sis. The resulting error signal containing position information was then used to map thefeasible region instead of identifying the feasible regionbased on measurements of thedifferential inductance. A reasonable agreement was obtained between the simulationsand experimental tests. The effect of the spatial inductance harmonics was also investi-gated as well as compensation methods. The results from the experimental setup showedthat the compensation works properly. The effects of the saturation in the rotor struc-ture which influences the polarity detection was also highlighted. The experimental testsand the corresponding FEM simulations showed good agreement indicating that the FEMmodeling was accurate.

55


56

Chapter 4

Conclusion

This chapter summarizes the conclusions and provides suggestions for further researchrelated to the different topics considered in this thesis.

4.1 Summary

In this thesis, two transient models for a prototype integrated charger for use in a PHEVapplication were proposed. The integrated charger conceptwas first proposed in [29] andthe derived transient models can be useful in order to develop control algorithms for thesystem or to recommend improvements to the machine design. The final transient modelswere based on input from a set of FEM simulations but the initial modeling was based onan inductance based model derived using simplified magneticcircuits.

To model the grid synchronization process a flux map based model based on thework in [11] was derived. By incorporating spatial flux linkage harmonics into the model,the grid side voltage could be predicted. The transient model for the grid synchronizationprocess, implemented in Matlab/Simulink, was compared to FEM simulations with goodagreement.

To model the charging process, a FEM based analysis was first carried out in orderto locate possible steady state operating points that provided charging power without pro-ducing a shaft torque. Since the flux linkages in the grid and inverter side windings aredependent on each other, a linearized transient model, valid around a specific operatingpoint, was presented and implemented in a Matlab/Simulink simulation environment.

The second part of this thesis was focused on operating limits related to the proto-type PMSynRel when operating without the use of a position sensor. Focus was put not onpresenting entirely novel position estimation methods butrather on analyzing limitationsand proposing improvements to already existing solutions when applied to the prototypePMSynRel.

The rotating and pulsating voltage vector carrier injection methods for sensorlesscontrol were studied in detail in this thesis. Based on an analysis of the impact of sat-

57

Chapter 4. Conclusion

uration and cross-saturation on the two methods, a technique was proposed to enablemapping of the feasible sensorless control region using theresulting position error signalrather than data of the differential inductances (evaluated experimentally or obtained us-ing FEM simulations). This technique was implemented experimentally and compared tocorresponding FEM simulations with reasonable agreement.

The impact of spatial inductance harmonics on the quality ofthe position estimateswas also studied in this thesis. Based on simplified analytical models, a method to predictthe maximum position estimation error due to the inductanceharmonics was proposedand supported with experimental results. To reduce this effect, a modified rotating voltagecarrier was proposed and experimentally verified. Lastly, an analysis of the impact ofsaturation in the rotor structure during initial magnet polarity detection was carried out.The experimental results, in good agreement with the corresponding FEM simulations,showed that the impact of saturation in the magnet bridges ofthe rotor was the dominantphenomenon at lower peak current magnitudes.

4.2 Recommendations for Future Research

4.2.1 The Integrated Charger Concept

The derived transient models of the integrated charger needs to be evaluated in an experi-mental setup. Fortunately, such an experimental setup is currently being setup at ChalmersUniversity of Technology in Goteborg, Sweden and it will beinteresting to see how wellthe proposed transient models matches actual measurements. Naturally, an interestingtopic for further research would be to develop machine design methodologies for the in-tegrated charger concept so that high performance of the machine in both modes (tractionand charging) can be achieved. Another interesting topic related to integrated chargingwould be to develop sensorless control techniques applicable for the grid synchronizationand charging processes.

4.2.2 Sensorless Control

The analysis and corresponding evaluations presented in Chapter 3 related to the availableoperating region when the PMSynRel is operating sensorlessclearly illustrates the limi-tations resulting from the specific rotor geometry. Hence, although the PMSynRel rotortopology provides an advantage in terms of a high torque density reached using relativelysmall amounts of magnet material, the limitations when operating sensorless at low speedsis a disadvantage which may render the topology less suitable for certain applications. Aninteresting topic for further research would be to optimizethe stator and rotor design sothat the torque levels when operating sensorless at low speeds could be extended. A pos-sible approach to tackle this problem would be to develop a generic non-linear reluctance

58

4.2. Recommendations for Future Research

based network model of the machine with a level of detail so thatdifferentialinductancescan be computed with sufficient accuracy. Such a model has thepotential of being signifi-cantly faster than a FEM based model which means that the optimization of the geometrycan be made with much more rigor than studying a much more limited number of designvariations using FEM. It should be mentioned that machine design approaches to opti-mize the performance when operating sensorless is a growingresearch topic from whicha significant number of publications can be expected during the coming years [54,76].

Another interesting aspect that has received little attention in the research commu-nity is what impact the reduced mechanical bandwidth due to the lack of a position sensorhas when the electric machine is connected to complex mechanical systems such as anHEV driveline. Hence, it would be of interest to develop and experimentally evaluate me-chanical models of the PMSynRel drive system when operatingsensorless and study itsinteraction with available mechanical models of hybrid drivelines. In this way, possiblelimitations such as resulting mechanical oscillations could be predicted and means fortheir mitigation could be proposed.

59

Chapter 4. Conclusion

60

Appendix A

Laboratory Setup

Fig. A.1 shows the laboratory setup used in the experiments.The PMSynRel is connectedto an induction machine which is speed controlled. Both the PMSynRel and the inductionmachine are connected to voltage source inverters (VSIs) which are fed from a single dcsupply (0-600 V). A position resolver is mounted on the shaftof the PMSynRel to measurethe rotor position which is only used as a reference when the PMSynRel is operatingsensorless.

PMSynRel

Induction Machine

Fig. A.1 Experimental Setup.

A dSPACE system is used to control both the PMSynRel and the inductance ma-chine. The control algorithms are written in the C language using floating point arith-metics. The compiled program is then downloaded to the control board DS1005. Thedc-link voltage and phase currents are sampled and sent to the ADC board DS2001 ascontrol input. The voltage references to the VSIs are modulated digitally and sent fromthe digital waveform output board DS5101. The resolver output is converted to digitalsignal and sent to the I/O board DS4001. Regular, asymmetrically sampled pulse width

61

Chapter A. Laboratory Setup

modulation is used and the sampling frequency and switchingfrequency are 10 kHz and5 kHz, respectively.

The nominal values of the PMSynRel and induction machine aregiven in Table A.1and Table A.2, respectively.

Table A.1: Nominal values of the PMSynRelConnection Y

No. of pole pairs np 2Rated current In 30 A

Rated frequency fn 50 HzRated power Pn 21 kWRated Torque Tn 107 Nm

Table A.2: Nominal values of the induction machineConnection ∆

No. of pole pairs np,ind. 2Rated current In,ind. 108 A

Rated frequency fn,ind. 135 HzRated power Pn,ind. 47 kWRated Torque Tn,ind. 110 Nm

62

References

[1] A. S. Al-Adsani, A. M. Jarushi, and N. Schofield, “Operation of a hybrid PM gen-erator in a series hybrid electrical vehicle,” inConf. Rec. 35th IEEE-IECON Annu.Meet., Nov. 2009, pp. 3898–3903.

[2] J. Arellano-Padilla, C. Gerada, G. Asher, and M. Sumner,“Inductance character-istics of PMSMs and their impact on saliency-based sensorless control,” inProc.Power Electronics and Motion Control Conference (EPE/PEMC), 2010 14th Inter-national, 2010, CD-ROM.

[3] M. Barcaro, N. Bianchi, and F. Magnussen, “PM motors for hybrid electric vehicles,”in 43rd International Universities Power Engineering Conference, 2008, Sept. 2008,CD-ROM.

[4] A. Bellini, S. Bifaretti, and S. Costantini, “Identification of the mechanical parame-ters in high performances drives,” inProc. EPE, Gratz, 2001, CD-ROM.

[5] N. Bianchi and S. Bolognani, “Influence of rotor geometryof an interior PM motoron sensorless control feasibility,” inConf. Rec. 40th IEEE-IAS Annu. Meet., vol. 4,2005, pp. 2553–2560.

[6] N. Bianchi, S. Bolognani, and A. Faggion, “Predicted andmeasured errors in esti-mating rotor position by signal injection for salient-polePM synchronous motors,”in Proc. Int. Conf. IEMDC, May 2009, pp. 1565–1572.

[7] G. Bisheimer, M. Sonnaillon, C. Angelo, J. Solsona, and G. Garcıa, “Full speedrange permanent magnet synchronous motor control without mechanical sensors,”in IET Electr. Power Appl., vol. 4, 2010, pp. 35–44.

[8] I. Boldea, L. Tutelea, and C. Pitic, “PM-assisted reluctance synchronous mo-tor/generator (PM-RSM) for mild hybrid vehicles: electromagnetic design,”IEEETrans. Ind. Appl., vol. 40, no. 2, pp. 492–498, 2004.

[9] M. Borup, “Environmental vehicle excise duty in Sweden,” in Proc. Cases in Sus-tainable Consumption and Production: Workshop of the Sustainable ConsumptionResearch Exchange (SCORE!), 2007, CD-ROM.

63

References

[10] F. Briz, M. Degner, P. Garcia, and J. Guerrero, “Rotor position estimation of AC ma-chines using the zero-sequence carrier-signal voltage,”IEEE Trans. Ind. Applicat.,vol. 41, no. 6, pp. 1637–1646, 2005.

[11] L. Chedot and G. Friedrich, “A cross saturation model for interior permanent magnetsynchronous machine. Application to a starter-generator,” in Conf. Rec. 39th IEEE-IAS Annu. Meet., 2004, pp. 64–70.

[12] Z. Chen, M. Tomita, S. Doki, and S. Okuma, “An extended electromotive forcemodel for sensorless control of interior permanent-magnetsynchronous motors,”IEEE Trans. Ind. Electron., vol. 50, no. 2, pp. 288– 295, Apr. 2003.

[13] D. K. Cheng,Field and Wave Electromagnetics. Addison-Wesley Publishing Com-pany, Inc., Massachusetts, USA, 1989.

[14] D. Chung, J. Kang, and S. Sul, “Initial rotor position detection of PMSM at standstillwithout rotational transducer,” inProc. Int. Conf. IEMD, 1999, pp. 785–787.

[15] A. Consoli, G. Scarcella, G. Bottiglieri, and A. Testa,“Harmonic analysis of voltagezero-sequence-based encoderless techniques,”IEEE Trans. Ind. Applicat., vol. 42,no. 6, pp. 1548–1557, 2006.

[16] A. Consoli, G. Scarcella, G. Scelba, S. Royak, and M. Harbaugh, “Implementationissues in voltage zero sequence-based encoderless techniques,” IEEE Trans. Ind.Applicat., vol. 44, no. 1, pp. 144–152, 2008.

[17] A. Consoli, G. Scarcella, and A. Testa, “A new zero frequency flux position detectionapproach for direct field oriented control drives,” inConf. Rec. 34th IEEE-IAS Annu.Meet., vol. 4, 1999, pp. 2290–2297.

[18] ——, “Sensorless control of PM synchronous motors at zero speed,” inConf. Rec.34th IEEE-IAS Annu. Meet., vol. 2, 1999, pp. 1033–1040.

[19] A. Consoli, G. Scarcella, G. Tutino, and A. Testa, “Zerofrequency rotor positiondetection for synchronous PM motors,” inConf. Rec. 31st IEEE-PESC Annu., vol. 2,2000, pp. 879–884.

[20] M. Corley and R. D. Lorenz, “Rotor position and velocityestimation for a permanentmagnet synchronous machine at standstill and high speeds,”in Conf. Rec. 31st IEEE-IAS Annu. Meet., vol. 1, 1996, pp. 36–41.

[21] F. Cupertino, G. Pellegrino, P. Giangrande, and L. Salvatore, “Sensorless positioncontrol of Permanent-Magnet motors with pulsating currentinjection and compen-sation of motor end effects,”IEEE Trans. Ind. Applicat., vol. 47, no. 3, pp. 1371–1379, June 2011.

64

References

[22] M. W. Degner and R. D. Lorenz, “Using multiple saliencies for the estimation offlux, position, and velocity in AC machines,” inConf. Rec. IEEE 32nd IAS Annu.Meet., vol. 1, Oct. 1997, pp. 760–767.

[23] N. Ertugrul and P. Acarnley, “A new algorithm for sensorless operation of permanentmagnet motors,”IEEE Trans. Ind. Applicat., vol. 30, no. 1, pp. 126–133, Feb. 1994.

[24] G. Foo and M. F. Rahman, “Sensorless sliding-mode MTPA control of an IPM syn-chronous motor drive using a sliding-mode observer and HF signal injection,”IEEETrans. Ind. Electron., vol. 57, no. 4, Apr. 2010.

[25] P. Garcia, F. Briz, D. Raca, and R. D. Lorenz, “Saliency tracking-based, sensorlesscontrol of AC machines using structured neural networks,” in Conf. Rec. 40th IEEE-IAS Annu. Meet., vol. 1, 2005, pp. 319–326.

[26] P. Guglielmi, G. Giraudo, G. Pellegrino, and A. Vagati,“P.M. assisted synchronousreluctance drive for minimal hybrid application,” inConf. Rec. 39th IEEE-IAS Annu.Meet., vol. 1, Oct. 2004, pp. 299–306.

[27] P. Guglielmi, M. Pastorelli, and A. Vagati, “Cross-saturation effects in IPM motorsand related impact on sensorless control,”IEEE Trans. Ind. Applicat., vol. 42, no. 6,pp. 1516–1522, 2006.

[28] S. Haghbin, “An isolated integrated charger for electric of plug-in hybrid vehicles,”Licentiate Thesis, Chalmers Univ. Technol., Goteborg, Sweden, 2011.

[29] S. Haghbin, M. Alakula, K. Khan, S. Lundmark, M. Leksell, O. Wallmark, andO. Carlson, “An integrated charger for plug-in hybrid electric vehicles based on aspecial interior permanent magnet motor,” inProc. IEEE Vehicle Power and Propul-sion Conference, Sept. 2010, CD-ROM.

[30] S. Haghbin, K. Khan, S. Lundmark, M. Alakula, O. Carlson, M. Leksell, andO. Wallmark., “Integrated chargers for EV’s and PHEV’s: examples and new so-lutions,” in Conf. Electrical Machines (ICEM), 2010, CD-ROM.

[31] L. Harnefors and H.-P. Nee, “A general algorithm for speed and position estimationof ac motors,”IEEE Trans. Ind. Electron., vol. 47, no. 1, pp. 77–83, Feb. 2000.

[32] J. Holtz, “Sensorless position control of induction motors-an emerging technology,”in Conf. Rec. 24th IEEE-IECON Annu. Meet., vol. 1, Sept. 1998, pp. 1–12.

[33] S. Ichikawa, M. Tomita, S. Doki, and S. Okuma, “Initial position estimation andlow speed sensorless control of synchronous motors in consideration of magneticsaturation based on system identification theory,” inConf. Rec. 39th IEEE-IAS Annu.Meet., vol. 2, Oct. 2004, pp. 971– 976.

65

References

[34] P. Jansen and R. D. Lorenz, “Transducerless position and velocity estimation in in-duction and salient AC machines,” inConf. Rec. 29th IEEE-IAS Annu. Meet., 1994,pp. 488–495 vol.1.

[35] M. Jansson, L. Harnefors, O. Wallmark, and M. Leksell, “Synchronization at startupand stable rotation reversal of sensorless nonsalient PMSMdrives,”IEEE Trans. Ind.Electron., vol. 53, no. 2, pp. 379– 387, Apr. 2006.

[36] Y.-S. Jeong, R. D. Lorenz, T. Jahns, and S. Sul, “Initialrotor position estimation ofan interior permanent-magnet synchronous machine using carrier-frequency injec-tion methods,”IEEE Trans. Ind. Applicat., vol. 41, no. 1, pp. 38–45, 2005.

[37] K. Khan, S. Haghbin, M. Leksell, and O. Wallmark, “Design and performance anal-ysis of a permanent-magnet assisted synchronous reluctance machine for an inte-grated charger application,” inConf. Electrical Machines (ICEM), 2010, CD-ROM.

[38] H. Kim, M. C. Harke, and R. D. Lorenz, “Sensorless control of interior permanent-magnet machine drives with zero-phase lag position estimation,” IEEE Trans. Ind.Applicat., vol. 39, no. 6, pp. 1726–1733, 2003.

[39] H. Kim and R. D. Lorenz, “Carrier signal injection basedsensorless control methodsfor IPM synchronous machine drives,” inConf. Rec. 39th IEEE-IAS Annu. Meet.,vol. 2, 2004, pp. 977–984.

[40] P. C. Krause, O. Wasynczuk, and S. D. Sudhoff,Analysis of Electric Machinery andDrive Systems. Piscataway, NJ: IEEE Press, 1994.

[41] R. Lagerquist, I. Boldea, and T. J. Miller, “Sensorless-control of the synchronousreluctance motor,”IEEE Trans. Ind. Applicat., vol. 30, no. 3, pp. 673–682, June1994.

[42] J. Lee, J. Kim, and D. Hyun, “Effect analysis of magnet onLd and Lq inductanceof permanent magnet assisted synchronous reluctance motorusing finite elementmethod,”IEEE Trans. Magn., vol. 35, no. 3, pp. 1199–1202, Mar. 1999.

[43] M. Leksell, L. Harnefors, and M. Jansson, “Direct sensorless speed control of PM-motors-a simple and effective sensorless method,” inProc. IEEE Conf. PESC, vol. 2,2001, pp. 805–810.

[44] X. Li and S. S. Williamson, “Assessment of efficiency improvement techniques forfuture power electronics intensive hybrid electric vehicle drive trains,” inConf. Elect.Power (EPC), Canada, Oct. 2007, pp. 268–273.

66

References

[45] Y. Li, Z. Zhu, D. Howe, C. Bingham, and D. Stone, “Improved rotor position es-timation by signal injection in brushless AC motors, accounting for cross-couplingmagnetic saturation,” inConf. Rec. IEEE 42nd IAS Annu. Meet., 2007, pp. 2357–2364.

[46] J. Liu, T. A. Nondahl, P. B. Schmidt, S. Royak, and M. Harbaugh, “Rotor positionestimation for synchronous machines based on equivalent EMF,” IEEE Trans. Ind.Applicat., vol. 47, no. 3, pp. 1310–1318, June 2011.

[47] A. Madani, J. P. Barbot, F. Colamartino, and D. Marchand, “An observer for the esti-mation of the inductance harmonics in a permanent-magnet synchronous machine,”in Proc. IEEE CCA, Oct. 1997, pp. 517–521.

[48] T. Moore, “Hybrid EVs: making the grid connection,” inProc. IEEE 16th Annu.Battery Conf. on Applic. and Advances. IEEE, 2001, pp. 37–43.

[49] S. Morimoto, K. Kawamoto, M. Sanada, and Y. Takeda, “Sensorless control strategyfor salient-pole PMSM based on extended EMF in rotating reference frame,”IEEETrans. Ind. Applicat., vol. 38, no. 4, pp. 1054–1061, Aug. 2002.

[50] S. Morimoto, M. Sanada, and Y. Takeda, “Performance of PM-assisted synchronousreluctance motor for high-efficiency and wide constant-power operation,”IEEETrans. Ind. Applicat., vol. 37, no. 5, pp. 1234–1240, 2001.

[51] P. Niazi, H. Toliyat, D. Cheong, and J. Kim, “A low-cost and efficient permanent-magnet-assisted synchronous reluctance motor drive,”IEEE Trans. Ind. Applicat.,vol. 43, no. 2, pp. 542–550, 2007.

[52] S. Øvrebø, “Sensorless control of permanent magnet synchronous machines,” Doc-toral Thesis, Norwigian Univ. Science and Technol, Trondheim, Norway, 2004.

[53] S. Ovrebo and R. Nilsen, “New self sensing scheme based on INFORM, hetero-dyning and luenberger observer,” inProc. Int. Conf. IEMDC, vol. 3, June 2003, pp.1819–1825.

[54] M. Pacas, “Sensorless drives in industrial applications,” Industrial Electronics Mag-azine, vol. 5, no. 2, pp. 16–23, June 2011.

[55] F. Parasiliti, R. Petrella, and M. Tursini, “Sensorless speed control of salient rotorPM synchronous motor based on high frequency signal injection and Kalman filter,”in Proc. Int. ISIE, vol. 2, 2002, pp. 623– 628.

[56] A. Piippo and J. Luomi, “Inductance harmonics in permanent magnet synchronousmotors and reduction of their effects in sensorless control,” in Proc. ICEM, 2006,CD-ROM.

67

References

[57] D. Raca, P. Garcia, D. Reigosa, F. Briz, and R. D. Lorenz,“A comparative analysisof pulsating vs. rotating vector carrier signal injection-based sensorless control,” inProc. IEEE 23rd Applied Power Electron. Conf. and Exp., 2008, pp. 879–885.

[58] D. Raca, P. Garcia, D. D. Reigosa, F. Briz, and R. D. Lorenz, “Carrier-Signal se-lection for sensorless control of PM synchronous machines at zero and very lowspeeds,”IEEE Trans. Ind. Applicat., vol. 46, no. 1, pp. 167–178, Feb. 2010.

[59] D. Raca, M. C. Harke, and R. D. Lorenz, “Robust magnet polarity estimation forinitialization of PM synchronous machines with near-zero saliency,” IEEE Trans.Ind. Applicat., vol. 44, no. 4, pp. 1199–1209, 2008.

[60] D. D. Reigosa, P. Garcıa, D. Raca, F. Briz, and R. D. Lorenz, “Measurement andadaptive decoupling of cross-saturation effects and secondary saliencies in sensor-less controlled IPM synchronous machines,”IEEE Trans. Ind. Applicat., vol. 44,no. 6, 2008.

[61] U. Rieder, M. Schroedl, and A. Ebner, “Sensorless control of an external rotorPMSM in the whole speed range including standstill using DC-link measurementsonly,” in Conf. Rec. 35th IEEE-PESC Annu. Meet., vol. 2, 2004, pp. 1280–1285.

[62] E. Robeischl and M. Schroedl, “Direct axis current utilization for intelligent sen-sorless permanent magnet synchronous drives,” inConf. Rec. 36th IEEE-IAS Annu.Meet., vol. 1, 2001, pp. 475–481.

[63] ——, “Optimized INFORM measurement sequence for sensorless PM synchronousmotor drives with respect to minimum current distortion,”IEEE Trans. Ind. Appli-cat., vol. 40, no. 2, pp. 591–598, 2004.

[64] H. Ryu, J. Kim, and S. Sul, “Synchronous frame current control of multi-phase syn-chronous motor. Part I. modeling and current control based on multiple d-q spacesconcept under balanced condition,” inConf. Rec. IEEE 39th IAS Annu. Meet., vol. 1,2004, pp. 56–63.

[65] M. Schrodl and M. Lambeck, “Statistic properties of theINFORM method forhighly dynamic sensorless control of PM motors down to standstill,” in Conf. Rec.29th IEEE-IECON Annu. Meet., vol. 2, 2003, pp. 1479–1486.

[66] M. Schroedl, “Sensorless control of AC machines at low speed and standstill basedon the “INFORM” method,” inConf. Rec. 31st IEEE-IAS Annu. Meet., vol. 1, 1996,pp. 270–277.

[67] P. Sergeant, F. De Belie, and J. Melkebeek, “Effect of rotor geometry and magneticsaturation in sensorless control of PM synchronous machines,” IEEE Trans. Magn.,vol. 45, no. 3, pp. 1756–1759, Mar. 2009.

68

References

[68] B. Stumberger, G. Stumberger, D. Dolinar, A. Hamler, and M. Trlep, “Evaluationof saturation and cross-magnetization effects in interiorpermanent-magnet syn-chronous motor,”IEEE Trans. Ind. Applicat., no. 5, pp. 1264– 1271, Oct. 2003.

[69] T. Takeshita and N. Matsui, “Sensorless control and initial position estimation ofsalient-pole brushless DC motor,” inProc. Int. Workshop on Advanced Motion Con-trol, vol. 1, 1996, pp. 18–23.

[70] N. Teske, G. M. Asher, M. Sumner, and K. J. Bradley, “Suppression of saturationsaliency effects for the sensorless position control of induction motor drives underloaded conditions,”IEEE Trans. Ind. Electron., vol. 47, no. 5, pp. 1142–1150, Oct.2000.

[71] H. Toliyat, S. Waikar, and T. Lipo, “Analysis and simulation of five-phase syn-chronous reluctance machines including third harmonic of airgap MMF,” IEEETrans. Ind. Applicat., vol. 34, no. 2, pp. 332–339, Apr. 1998.

[72] A. Vagati, A. Fratta, G. Franceschini, and P. Rosso, “ACmotors for high-performance drives: a design-based comparison,”IEEE Trans. Ind. Applicat.,vol. 32, no. 5, pp. 1211–1219, 1996.

[73] O. Wallmark, “Control of permanent-magnet synchronous machines in automotiveapplications,” Doctoral Thesis, Chalmers Univ. Technol.,Goteborg, Sweden, 2006.

[74] J. Wang and H. Liu, “Novel intelligent sensorless control of permanent magnet syn-chronous motor drive,” inICEMI, Aug. 2009, pp. 2–953–2–958.

[75] T. Wolbank and J. Machl, “A modified PWM scheme in order toobtain spatial in-formation of AC machines without mechanical sensor,” inProc. IEEE 27th AppliedPower Electron. Conf. and Exp., vol. 1, 2002, pp. 310–315 vol.1.

[76] R. Wrobel, A. S. Budden, D. Salt, D. Holliday, P. H. Mellor, A. Dinu, P. Sangha, andM. Holme, “Rotor design for sensorless position estimationin permanent-magnetmachines,”IEEE Transactions on Industrial Electronics, vol. 58, no. 9, pp. 3815–3824, Sept. 2011.

[77] R. Wu and G. Slemon, “A permanent magnet motor drive without a shaft sensor,”IEEE Trans. Ind. Applicat., vol. 27, no. 5, pp. 1005–1011, Oct. 1991.

[78] X. Xu and D. W. Novotny, “Implementation of direct stator flux orientation controlon a versatile DSP based system,”IEEE Trans. Ind. Applicat., vol. 27, no. 4, pp.694–700, Aug. 1991.

69

References

[79] L. Ying and N. Ertugrul, “A novel, robust DSP-based indirect rotor position estima-tion for permanent magnet AC motors without rotor saliency,” IEEE Trans. PowerElectron., vol. 18, no. 2, pp. 539– 546, Mar. 2003.

[80] Z. Q. Zhu and D. Howe, “Electrical machines and drives for electric, hybrid, andfuel cell vehicles,”Proc. of the IEEE, vol. 95, no. 4, pp. 746–765, Apr. 2007.

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