Design of a Permanent-Magnet Assisted Synchronous ...462259/FULLTEXT01.pdf · Design of a Permanent-Magnet Assisted Synchronous Reluctance Machine for a ... a permanent-magnet assisted

Design of a Permanent-Magnet Assisted SynchronousReluctance Machine for a Plug-In Hybrid Electric Vehicle

KASHIF SAEED KHAN

Licentiate ThesisStockholm, Sweden 2011

TRITA-EE 2011:074ISSN 1653-5146ISBN 978-91-7501-166-0

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 systemonsdagen den 14 december 2011 klockan 15.00 i H1, Kungl Tekniska hogskolan, Teknik-ringen 33, Stockholm.

c© Kashif Saeed Khan, December 2011

Tryck: Universitetsservice US AB

To my parents

iv

Abstract

In this thesis, a permanent-magnet assisted synchronous reluctance machine (PMSynRel)design is presented for a plug-in hybrid electric vehicle application. Apart from operatingas a traction machine to propel the vehicle, the machine is also used when the vehicle’sbattery is charged from the grid. This additional functionality puts restraints (that are dis-cussed in the thesis) on the final machine design.The PMSynRel is designed following a classical approach in which initially the machinegeometry is designed to maximize the reluctance torque. Magnets are then introduced toincrease the torque further. Rotor dimensions are calculated alongside the resulting mag-netic model of the machine.A finite-element method (FEM) based parametric study is then performed to maximizethe developed torque. The effect of different design parameters such as, the insulationratio and the number of flux barriers, on the machine performance is investigated withand without the magnets in the rotor. For a given magnet volume, the performance ofthe machine is investigated with different magnet placements in the rotor. A prototypehas been built based on the resulting machine design to verify the simulation results. Atorque map of the prototype machine has been measured for id<0 and iq>0 at constantspeed (1500 rpm). The torque, efficiency and power factor of the machine are measuredat 1500 rpm and rated current. The experimentally obtained results have been compared,with good agreement, with corresponding FEM simulations.Finally, the performance of the prototype machine in terms of developed torque andmaximum speed is compared to alternative designs utilizing surface-mounted or interior-mounted permanent magnets in the rotor.

Index Terms: Electric vehicle, hybrid electric vehicle, integrated charger, interiorpermanent-magnet machine, magnet placement, permanent-magnet assisted synchronousreluctance machine, surface mounted permanent-magnet machine, synchronousreluctance machine.

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vi

Acknowledgements

This research project was fully funded by the Swedish National Energy Agency, withinthe “energisystem i vagfordon” research program, which is gratefully acknowledged.I would like to thank my main supervisor Prof. Chandur Sadarangani for his valuablecomments and support. I would also like to thank my assistant supervisors Dr. OskarWallmark and Lic. Tech. Mats Leksell for providing me with technical knowledge andcontinuous encouragement throughout the project.I am very grateful to my colleagues at KTH who have helped me in several ways. Par-ticularly, Henrik Grop, Alexander Stening, Shuang Zao, Shafigh Nategh, Naveed Malik,Andreas Krings, Antonios Antonopoulos and Dimosthenis Peftitsis for all the good timesat work. To my former colleagues, Rathna Chitroju and Dimitry Svenskaprov for all theencouragement and valuable discussions. I would also like to thank EME’s financial ad-ministrator Eva Petterson and system administrator Peter Lonn for their help.I further would like to thank Viktor Lassila and Jan Folkhammar for their guidance andvaluable inputs to the project and prototype building.Finally, I would like to express my deepest gratitude to may parents, for their tremendoussupport and encouragement. I would also like to thank my friends, Khuram, Shahazad,Ayayz and Ieva for all the travels around the world.

Kashif Saeed KhanStockholm, SwedenDecember 2011

vii

viii

Contents

Abstract v

Acknowledgements vii

Contents ix

1 Introduction 11.1 Background and objective . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 The integrated charger concept . . . . . . . . . . . . . . . . . . . . . . . 21.3 Machine topology selection . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Outline of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.5 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.6 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Analytical design 92.1 Specifications and initial design selections . . . . . . . . . . . . . . . . . 92.2 Rotor design selections . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 Selection of number of flux barriers . . . . . . . . . . . . . . . . 102.2.2 Flux barrier geometrical parameters . . . . . . . . . . . . . . . . 112.2.3 Flux barrier angle . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.4 Insulation ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.5 Flux barrier dimensions along the d-axis . . . . . . . . . . . . . . 122.2.6 Flux barrier dimensions along the q-axis . . . . . . . . . . . . . . 13

2.3 Stator design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.1 Air-gap flux density at no-load . . . . . . . . . . . . . . . . . . . 132.3.2 The d-axis flux linkage . . . . . . . . . . . . . . . . . . . . . . . 152.3.3 The q-axis flux linkage . . . . . . . . . . . . . . . . . . . . . . . 162.3.4 Calculation of ampere-turns per slot . . . . . . . . . . . . . . . . 162.3.5 Summary of the analytical design process . . . . . . . . . . . . . 18

3 FEM aided design 193.1 An evaluation of the analytical design using FEM . . . . . . . . . . . . . 19

ix

Contents

3.1.1 Air-gap flux density . . . . . . . . . . . . . . . . . . . . . . . . 203.1.2 Developed torque . . . . . . . . . . . . . . . . . . . . . . . . . . 213.1.3 d- and q-axis inductances . . . . . . . . . . . . . . . . . . . . . . 22

3.2 Parametric study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2.1 Number of flux barriers . . . . . . . . . . . . . . . . . . . . . . . 233.2.2 Insulation ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2.3 Magnet placement . . . . . . . . . . . . . . . . . . . . . . . . . 263.2.4 Stator skew and short pitch winding . . . . . . . . . . . . . . . . 303.2.5 Mechanical stability . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 Summary of chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4 Experimental evaluation 414.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.2 Open circuit voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.3 Developed torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.4 Power factor and losses at rated current . . . . . . . . . . . . . . . . . . 42

4.4.1 q-axis current study . . . . . . . . . . . . . . . . . . . . . . . . . 434.5 Circulating currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.5.1 Summary of chapter . . . . . . . . . . . . . . . . . . . . . . . . 44

5 Comparison of different rotor topologies 495.1 Surface-mounted PM synchronous machines . . . . . . . . . . . . . . . . 495.2 Interior PM machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.2.1 Single barrier IPM machines . . . . . . . . . . . . . . . . . . . . 505.2.2 Double barrier IPM machines . . . . . . . . . . . . . . . . . . . 53

5.3 Summary of chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6 Concluding remarks 556.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

A Prototype constructional details 57

References 59

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Chapter 1

Introduction

The role of electric drives along with the associated challenges in hybrid and electricvehicles is reviewed and discussed in this chapter. Different ways to connect to the batteryduring charging and different electric machine topology alternatives are explored and aninnovative solution, the integrated charger, is presented.

1.1 Background and objective

In recent years, concerns over global warming and availability of fossil fuels have moti-vated research in the area of hybrid electric vehicles (HEVs) and electric vehicles (EVs).One of the drawbacks of EVs and HEVs in comparison to conventional vehicles is therelatively expensive additional components such as the battery, the electric drive and thecharging system for the battery. In general, the power rating of the drive line should beminimized since the cost for the electric drive increases with its rated power. Apart fromthe cost, the size and the efficiency of the electric drive are also of high importance. TheEV concept is not new but it has this far not been a commercial success due to the batteriesand their inherent limited energy content which result in a short driving range. Therefore,there is a lot of ongoing research focusing on reduction of the costs and improvements inenergy density, power density and lifetime. For the EVs to become a commercial success,the charging of the battery and surely the battery charger has to be addressed. EVs arecompared and have to compete with conventional vehicles in the market which have plen-tiful of energy stored in the form of fuel. The individual user of the EV will not appreciatea short driving range; even less so if the charging time is too long. In this sense, batterychargers play a critical role in the evolution of this technology. Generally, there are twotypes of battery chargers: on-board type and stand-alone (off-board) type. The on-boardtype is available to each individual user and is suitable for charging from a householdutility outlet. On the other hand, the off-board charger can be compared to a gas stationused for an internal combustion engine vehicle. It is aimed at rapid charging. Becausethe on-board type of charger always must be carried by the vehicle, the weight and space

1

Chapter 1. Introduction

are critical parameters and have to be minimized. Of course, it is very important to mini-mize the charger cost also. On-board chargers are the preferred choice of customers dueto their simplicity, but the problem is that a sufficiently high power level can be difficultto achieve due to weight, space and cost limitations. The objective of this project is todesign an electric drive line that integrates the traction motor and the battery charger intoone unit. The resulting system should have a low weight, a wide speed range and a lowcost. The system should also have the ability to operate without a position sensor.

1.2 The integrated charger concept

It was mentioned earlier that in the case of the on-board charger, it can be difficult toachieve high power levels because of weight, space and cost limitations. However, there isa possibility of avoiding these limitations by using the already available traction hardware,mainly the machine and the inverter, for the charger circuit. Thereby, the electric driveand the battery charger are integrated. Different types of integration solutions have beenreviewed in [6].

In this thesis, an innovative integrated charger is considered that can charge thebattery from the grid by using the traction drive system in an ”inverted” power directionscheme. This is achieved by re-arranging the winding of the machine with the help ofa simple switching device in charging mode to realize a three-phase high power batterycharger. The electric machine has then to be designed with a special winding configurationwhich has two modes: motor/generator operation in traction mode and charging operationin charging mode. Depending on the desired mode of operation the system hardware canbe reconfigured for traction or charging operation.

The electric machine has a distributed three phase winding in the stator as shownin Fig. 1.1. In traction mode, the circuit diagram is shown in Fig. 1.2 which correspondsto a normal star connection winding in an electric machine. Now for charging, the threephase winding is divided into two equivalent parts that are shifted (30 electrical degrees)symmetrically around the stator periphery as shown in Fig. 1.3. The winding connectionis similar to a six phase machine with two sets of three phase windings displaced by 30electrical degrees (commonly known as dual stator winding) [9]. During charging, oneset of the three phase winding is connected to the battery through an inverter while thesecond set of the three phase winding is connected to the grid. However, there is a concernabout the voltage matching in the system since the proposed solution splits the windinginto two halves while switching from traction mode to charging mode which reducesthe voltage by half. The grid supplies an rms phase voltage of 230 V while the windingduring traction only need to handle 80 V (rms) (assuming an rms phase voltage of 160 Vin traction mode). On the inverter side, the winding has an rms phase voltage of 80 Vwhile DC bus voltage is 400 V. Voltage adaption is required to solve this problem. Theproposed winding configurations are shown in Fig. 1.4 for traction mode and in Fig. 1.5

2

1.2. The integrated charger concept

for charging mode, respectively.

Fig. 1.1 Winding configuration of the machine.

Fig. 1.2 Initial machine winding connection during traction mode.

Fig. 1.3 Dual stator winding during charging mode: a) Inverter side winding; b) Grid side winding.

During charging, when the machine rotates with grid synchronous speed, the mag-nets will induce voltages in the inverter side windings. The idea is to connect the machineto the grid via the grid side three-phase winding. The inverter side winding will be con-trolled so that a correct voltage is obtained in the grid side winding. The inverter can now

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Fig. 1.4 Final machine winding connection during traction mode.

Fig. 1.5 Machine winding connection during charging mode.

rectify the three phase voltage in order to supply power to the battery. It should also benoted that the proposed charger solution is not strictly dependant on a particular electricmachine topology and different possible alternatives can be considered.

1.3 Machine topology selection

Electrical machines and drives are key components for the development of EVs and HEVs[27]. The main requirements for an electric machine to be used in a traction applicationare:

• High torque density and power density and wide speed range, with a constant poweroperating range of around 3 to 4 times the base speed.

4

1.3. Machine topology selection

• High efficiency over wide speed and torque ranges, including low torque operation.

• Intermittent overload capability, typically twice the rated torque for short durations.

• In addition, low acoustic noise and low torque ripple are important design consid-erations.

For an urban driving cycle, the traction machine operates most frequently at light loadsaround the base speed. Therefore, in general, it should be designed to operate at maximumefficiency and minimum acoustic noise in this region.

It was discussed in the previous section that many different electric machine topolo-gies can be considered for the integrated charger solution. Induction machines (IMs), syn-chronous reluctance machines (SRMs) and permanent-magnet (PM) brushless machineshave all been employed in traction applications and can be designed to exhibit differenttorque/power-speed characteristics [5, 27]. IMs are robust, have a low cost and rely onwell established manufacturing techniques. However the poor performance in terms oftorque and over load capability of IMs compared to SRMs makes it less suitable [15, 26].

Brushless AC (BLAC) machines are relatively easy to control and exhibit excel-lent performance in terms of maximum torque per ampere control and optimal extendedspeed operation [8, 22, 27]. For radial flux BLAC machines, the surface mounted perma-nent magnet machine (SPM) is the most widely used topology. However, since the d- andq-axis stator winding inductances of such machines are the same, they exhibit zero reluc-tance torque. The magnets are exposed directly to the armature reaction field, and, hence,are susceptible to partial irreversible demagnetization. SPM machines also generally havea relatively limited flux-weakening capability.

For interior mounted permanent magnets machines (IPMs), since the d-axis induc-tance is smaller than the q-axis inductance, a reluctance torque exists while the d-axisinductance is high compared to that of an equivalent SPM topology. Therefore, IPMtopologies are eminently appropriate for extended speed and constant power operationin flux-weakening mode [16,22]. By introducing a V-shaped disposition of the permanentmagnets in the rotor, the air-gap flux can be increased which will improve the torque ca-pability further [7]. Multiple layers of magnets may also be employed to further increasethe saliency ratio [27]. A general drawback for PM based machines is the fact that a dra-matic increase in the usage of rare-earth magnet has led to significantly increased magnetprices. It has been reported that the price of Neodynium (used in permanent magnets) inJapan has increased by 5.4 times during 2010 [10]. This only enhances the fact that PMbased machines can become very costly.

The SRMs, which rely on the reluctance of the machine to generate torque areknown to be very cheap and exhibit a reasonable high torque density. However, they areinferior to PM machines in terms of torque density and efficiency and, hence, are notideal for traction applications which requires a high torque density along with a widespeed range.

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By enhancing the saliency of an IPM, the torque contribution due to saliency canbe increased which enables the design to use less permanent magnets. This topology isreferred to as a PMSynRel and can be considered a promising topology. When the magnetsare inserted into an inherently cheap reluctance machine it results in a higher efficiencyand an improved power factor [19, 20] for a reasonable cost increase.

1.4 Outline of thesis

The chapters in this thesis are outlined as follows.

Chapter 2 describes a design for a PMSynRel based on analytical techniques. It providesthe details of the rotor design, barrier dimensions and their placement.

Chapter 3 reports the corresponding FEM simulation results for the designed machine.A parametric study is performed to optimize the machine design in order to maximize thedeveloped torque.

Chapter 4 provides measurement results from an experimental prototype. It also com-pares the measurement results with the corresponding FEM simulations.

Chapter 5 discusses the design of different rotor topologies and the performance of thesetopologies is compared with the prototype machine in terms of torque development andspeed range.

Chapter 6 summarizes the project and some possibilities for the future research are pre-sented.

1.5 Contributions

The list below summarizes the main contributions presented in this thesis.

• A PMSynRel machine has been designed which can act both during the propulsionof a vehicle and during charging of the battery.

• Based on results from a parametric FEM simulation study, it was found that the op-timal insulation ratio of a PMSynRel machine is different with and without magnetspresent in the rotor.

• It was found that for a given insulation ratio, the number of flux barriers does notaffect the average torque but only the torque ripple.

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1.6. Publications

• It was found that for a fixed number of flux barriers and insulation ratio, the torqueripple is different with and without magnets present in the rotor.

• The simulation results showed that for a given magnet volume, it is recommendedto distribute the magnets in the flux barriers along the d-axis.

• The performance of the prototype machine was compared with other alternativetopologies such as SPMs and IPMs and it was found that the PMSynRel conceptwas most suitable for the intended application.

1.6 Publications

The publications originating from this project are:

• K. Khan, M. Leksell, and O. Wallmark, “Design aspects on magnet placementin permanent-magnet assisted synchronous reluctance machines,” in Proc. 5th IETInternational Conference on Power Electronics, Machines and Drives (PEMD’10),2010.

• 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,” in Proc. 19th IEEE International Conference on Elec-trical Machines (ICEM’10), 2010.

• S. Haghbin, K. Khan, S. Lundmark, M. Alakula, O. Carlson, M. Leksell and O.Wallmark, “Integrated chargers for EVs and PHEVs: examples and new solutions,”in Proc. 19th IEEE International Conference on Electrical Machines (ICEM’10),2010.

• S. Haghbin, M. Alakula, K. Khan, M. Leksell, S. Lundmark, O. Wallmark andO. Carlson, “An integrated charger for plug-in hybrid electric vehicles based on aspecial interior permanent magnet motor” in Proc. IEEE International Conferenceon Vehicle Power and Propulsion Conference (VPPC’10), 2010.

• K. S. Khan, W. M. Arshad, and S. Kanerva, “On performance figures of multiphasemachines,” in Proc. IEEE 18th International Conference on Electrical Machines(ICEM’08), 2008.

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8

Chapter 2

Analytical design

This chapter describes the analytical design of a permanent magnet assisted synchronousreluctance machine (PMSynRel) suitable for a traction application. The calculation pro-cedure to determine the size, position and number of flux barriers in the rotor of thePMSynRel is discussed. The last section of the chapter explains the magnetic circuit as-sociated with the PMSynRel based on the calculated dimensions of the rotor. The statorparameters such as number of turns, phase current, flux density, induced EMF and induc-tances are calculated by solving the magnetic circuit.

2.1 Specifications and initial design selections

The given specifications of the machine to be designed are listed in Table 2.1. For theinitial design, it is assumed that the number of poles are four since the higher number ofpoles reduce the reluctance torque [18]. A distributed winding with four poles results in along end winding. Therefore, the active length of the machine is set to 250 mm to providethe space for the end windings. The air-gap height of a PMSynRel should be kept small inorder to achieve a high reluctance torque component [4,18]. In this study, air-gap height isset to 0.35 mm, limited only by manufacturing. The PMSynRel in consideration is a watercooled machine. Therefore, the assumed rms value of the current density J is 10 A/mm2.The stator slot fill factor fs, is 0.6 which is a typical value for a distributed winding [4,13].The number of slots are 24 as motivated by the integrated charger requirements explainedin Chapter 1 and furthermore it is assumed that the width of the stator slot is half of thestator slot pitch τp.

2.2 Rotor design selections

To introduce key definitions related to the rotor design, a schematic rotor is illustrated inFig. 2.1. As seen, the interior of the rotor consists of flux barriers where also the magnets

9

Chapter 2. Analytical design

Table 2.1: Machine specificationValue Unit

Number of phases 3 -Rated torque 170 NmRated speed 1500 rpmOuter stator diameter 180 mmTotal axial length 330 mmMinimum dc link voltage 400 VCooling method Water jacket -

are mounted. Magnet elements are magnetized uniformly and are also defining the d-axis of the rotor. Since the magnets have almost the same permeability as that of air,the flux barriers create a high reluctance path in the magnetic circuit and introduce amagnetic anisotropy of the motor. The rotor iron is divided into the different segmentsseparated by flux barrier in the rotor. These iron segments provide a low reluctance pathfor the q-axis flux. For mechanical stability, these iron segments must be interconnectedto each other. Therefore tangential ribs near the air-gap are introduced in the rotor. Dueto the permanent magnets, these ribs are saturated during normal operation and thereforemagnetically sperate the different iron segments from each other. From a torque producingpoint of view, the leakage flux caused by the introduction of the tangential ribs should beas small as possible. However, due to limits in mechanical strength, the width of thetangential ribs is set to be 1 (mm) (see also Section 3.2.5).

Fig. 2.1 Regions in the rotor of a PMSynRel.

2.2.1 Selection of number of flux barriers

A multiple number of flux barriers can be introduced to even the flux distribution throughthe rotor and increase the average torque [18]. It is also shown in [18] that the averagetorque is not increasing further as the number of flux barriers is increased to more than

10

2.2. Rotor design selections

four or five. The interaction of stator and rotor harmonics is the cause of the torque ripple.Therefore, the torque ripple is influenced by the number of flux barriers. To reduce thetorque ripple it is recommended in [5] to select the number of flux barriers per pole tosatisfy the condition (Q/p±2) where Q is total number of stator slots and p is the numberof poles. As discussed earlier, p=4 andQ=24 are selected to enable charging. Therefore,the number of flux barriers are selected to four.

2.2.2 Flux barrier geometrical parameters

Now the positioning and sizing of the flux barriers in the rotor body should be determined.It will be useful to introduce some geometrical parameters. In Fig. 2.2 a PMSynRel rotorwith four flux barriers is shown where Tm is the thickness of the barrier along the d-axis.Further, Ts represent the thickness of the iron segment along the d-axis. The length of theflux barrier perpendicular to the d-axis is denoted by Wm and the length parallel to theq-axis is denoted as Wb. The thickness of flux barrier along the q-axis is denoted by Tb.The barrier end point angle is denoted by αm.

Fig. 2.2 Regions in the rotor of a PMSynRel.

2.2.3 Flux barrier angle

To place the barriers in the PMSynRel rotor, they should be thought of as rotor slots.Let’s introduce the barrier end point angle αm which can be expressed as (2.1a)where pis the number of poles, k is the number of barriers and αe is the barrier end point angle inelectrical degrees. While a constant rotor slot pitch (barrier ends in the air gap) is assumed.

αm =

π

p

k + 1(2.1a)

αe =p

2αm (2.1b)

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2.2.4 Insulation ratio

For a purpose of comparison between different geometries, different designs and also fortuning of the final design, it is useful to introduce a design parameter called insulationratio which is given as

Kw =Wins

Wiron(2.2)

where Wins, is the total width of all the flux barriers and Wiron, is the total width of the ironsegments. In this study, insulation ratios along the d and q-axis are assumed to be 0.6 and0.3. However later in the parametric study of the motor, influence of the insulation ratiois studied in detail.

2.2.5 Flux barrier dimensions along the d-axis

For a given d-axis insulation ratio Kwd, the total thickness of the iron segments along thed-axis Tsd can be calculated as

Tsd =D/2−Drc/2

1 +Kwd

(2.3)

where D is the outer diameter of the rotor and Drc is the shaft diameter. In order todetermine the relative thickness of each iron segment, it is assumed that the magneto-motive force (MMF) is sinusoidally distributed, there is no flux leakage and the total fluxdue to this MMF is going into the related segment. The expression to calculate the relativethickness of each iron segment is given in (2.4) which has been taken from [12, 18].

TsiTsi+1

=sin [αe(2i− 0.5)]− sin [αe(2i− 1.5)]

sin [αe(2i+ 1.5)]− sin [αe(2i+ 0.5)], i = 1, 2, 3...k (2.4)

Thickness of each segment can be calculated by solving the above equations. The totalthickness of flux barrier Tmd along the d-axis can then be obtained as

Tmd =(D/2−Drc/2)

1 + 1/Kwd

. (2.5)

In order to determine the relative thickness of the flux barriers, it is assumed that thepermeance (pi = Wmi/Tmi) ratio of the flux barriers is constant. This is preferred sinceit results in a sinusoidal flux density distribution in the air gap and a smoother torquewaveform. The relative thickness of the flux barriers are calculated as (2.6a) also presentedin [12, 18].Tm,i+1

Tm,i

=( num

denum

)2

, i = 1, 2, ...k − 1 (2.6a)

num = sin [αe(2i+ 3.5)]− sin [αe(2i+ 2.5)]− sin [αe(2i+ 1.5)] + sin [αe(2i+ 0.5)]

(2.6b)

denum = sin [αe(2i+ 1.5)]− sin [αe(2i+ 0.5)]− sin [αe(2i− 0.5)] + sin [αe(2i− 1.5)]

(2.6c)

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2.3. Stator design

For a given d-axis insulation ratio Kwd, (2.6a) can be used to determine the thickness ofthe flux barriers.

2.2.6 Flux barrier dimensions along the q-axis

The total available thickness in the q-axis for positioning the flux barriers and iron seg-ments can be calculated as

lq =

(D

2

)sin

(π

p

)(2.7)

Where lq is the total available thickness in the q-axis. In the q-axis, the total amount of ironmust be equal or greater than in the d-axis to ensure the higher q-inductance. In this study,it is assumed that the total amount of iron is equal in the d- and q-axis. The total thicknessof the flux barrier along the q-axis (Tbq) can be calculated by subtracting total amountof iron (same as the d-axis iron segment, Tsd) from the total available q-axis length, lq.Insulation ratio along the q-axis,Kwq is different from the insulation ratio along the d-axisKwd and it can be calculated as

Kwq =Tbq

lq − Tbq(2.8)

The relative thickness of the flux barriers along the q-axis can be calculated by followingthe same procedure as described for the barrier dimensions along the d-axis.

2.3 Stator design

2.3.1 Air-gap flux density at no-load

A rotor structure with four flux barriers in which permanent magnets are mounted isshown in Fig. 2.2. A corresponding magnetic circuit is shown in Fig. 2.3 where infinitepermeability of the rotor iron has been assumed. At no-load there is no stator current andthe permanent magnets are the only sources of flux in the magnetic circuit. The flux gen-erated by a permanent magnet φm is related to its dimensions and remanent flux densityBrem,calculated as

φm = BremWmL (2.9)

whereWm is the width of magnet and L is the active length of the machine. The reluctanceof the flux barriers along the d-axis Rm is given in (2.10).

Rm =Tm

µ0µrecWmL(2.10)

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where µ0 is the absolute permeability and µrec is the relative recoil permeability. Wm andTm are the width and thickness of the magnet, respectively. The tangential ribs near theair gap which provide the necessary mechanical strength to the rotor structure and arenormally saturated. These saturated iron ribs are included in the magnetic circuit as sinksφrib which can be expressed as

φrib = BsatWrL (2.11)

where Bsat is the saturation flux density of the iron and Wr is the width of the tangentialrib (see Fig. 2.2). The equivalent flux from the permanent magnets can the be calculatedas:

φm = BremWmL−Nribφrib (2.12)

where Nrib is the number of tangential ribs corresponding to each flux barrier. The rotorstructure in consideration in this thesis has only tangential ribs and there are no radialribs. This implies that number of ribs for each flux barrier should be only two. The air gapreluctance for each segment can be obtained as:

Rg,i =gi

µ0DLαm

, i = 1 (2.13a)

Rg,i =2gi

µ0DLαm

, 1 < i < k. (2.13b)

Rg,i =4gi

µ0DLαm

, i = k + 1. (2.13c)

where gi is the air-gap width corresponding to each rotor segment and αm is the fluxbarrier end point angle also shown in Fig. 2.2. For a specified geometry, the flux passingthe air-gap reluctance can now be obtained by solving the magnetic circuit in Fig. 2.3.The resulting flux density in the air-gap can be obtained as in (2.14). Where Ai is the area

Fig. 2.3 Equivalent magnetic circuit of a rotor with four flux barriers and permanent magnets.

14

2.3. Stator design

corresponding to each rotor segment.

Bi =φi

Ai

(2.14)

2.3.2 The d-axis flux linkage

An equivalent magnetic circuit to compute d-axis flux linkage is illustrated in Fig. 2.4.Here the flux generated by the permanent magnets is ignored and the saturated iron ribsare ignored as well. The air-gap is divided into different segments (see Fig. 2.2) and thereluctance is calculated as described above. The MMF source across the pole has been

Fig. 2.4 Equivalent magnetic circuit used to obtain the d-axis flux linkage.

divided into different parts as well. The MMF across each segment, Usd,i can be obtainedas

Usdi = −Ksd

D

2

sinαe

αe

, i = 1 (2.15a)

Usdi = −Ksd

D

2

sinαe(i+ 0.5)− sinαe(i− 0.5)

αe

, 1 < i < k + 1 (2.15b)

Usdi = −Ksd

D

2

1− sinαe(i− 0.5)π

2− αe(i− 0.5)

, 1 = k + 1 (2.15c)

where k is the number of flux barriers and αe is the flux barrier end point angle in electricaldegrees. While Ksd is the current loading while its peak amplitude is given as (2.16).

Ksd =3Kwqnsi

πD(2.16)

15


Where Kw is the fundamental winding factor and it is assumed that the current i corre-sponds to a pure d-axis current. The flux density in the ith air-gap segment Bsdi and thecorresponding flux φi can now be obtained as:

Bsdi =µ0

g[Usdi − Uri] (2.17a)

φi =DL

PBsdi (2.17b)

where Uri is the MMF across the ith iron segment also shown in Fig. 2.4. The flux linkageis calculated as:

Ψ1d = 0.5KwNφ (2.18)

φ = 2k+1∑

1

φi (2.19)

where φ is the flux per pole. The d-axis inductance Ld can now be found by dividing thed-axis flux linkage by the stator d-axis current i.

2.3.3 The q-axis flux linkage

Also here, only the magnetic field due to the q-axis current is considered and the per-manent magnets and the tangential ribs are ignored. It is further assumed that the fluxlines pass the air gap and then passes through the rotor without entering the flux barrier.Due to the high permeability of the rotor core, the MMF drop across the rotor is zero.MMF across the air-gap along the rotor circumference due to a pure q-axis current can beapproximated as

Usq = −Ksq

D

2sin(π/2) (2.20)

where Ksq and Usq represents the current loading and MMF due to the a pure q-axiscurrent, respectively. The The resulting air-gap flux density can now be obtained as

Bsq =µ0

gUsq. (2.21)

Similar as for the d-axis, the q-axis flux linkage Ψq and inductance Lq can now be ob-tained.

2.3.4 Calculation of ampere-turns per slot

The ampere-turn per slot nsI and the current density J are related as

J =nsI

Aslfs(2.22)

16

2.3. Stator design

Where Asl, is the area of the slot and fs is the slot fill factor which is assumed as 0.6 inthis design calculation. Dimensions of the slot geometry are computed to calculate thearea of the slot. Height of the stator core can be calculated as [4]

Hcs =B1gτsπBcs

(2.23)

where B1g is the maximum no load air-gap flux density calculated in previous section,Bcs is the average flux density in the stator core ( assumed 1.5 T) and τs is the pole pitch.Now, height of the stator slot can be calculated by subtracting the height of the stator coreHcs from the outer diameter of the stator. Width of the slot was assumed to be half of theslot pitch τs in previous sections. The ampere-turn per slot can be computed by insertingarea of the slot Asl in (2.22).

Number of turns

The torque equation for a permanent-magnet assisted synchronous reluctance machinePMSynRel is given as

T =3p

4[ψmiq + (Ld − Lq)idiq] (2.24a)

id = I cos β (2.24b)

iq = I sin β (2.24c)

It can be seen that the d-axis current generates a reluctance torque (last term in equation) inaddition to the permanent magnet torque (first term in equation). The relative componentsof the reluctance and magnetic torque can be controlled by adjusting the current angle βsince the d and q-axis currents depend on angle β. The angle β is chosen so that it givesthe maximum torque for a given current.

dT

dβ= 0 (2.25)

Solving the equations (2.24b) and (2.25) results in the equation (2.26a). However theinductances in (2.26a) depend on the square of the number of conductors per slot whichis unknown at this point. Therefore the above equation is modified as in (2.26b).

2(Ld − Lq)I2 cos2 β + ψmI cos β − (Ld − Lq)I

2 = 0 (2.26a)

2(Ld − Lq)(nsI)2 cos2 β + 0.5pqψm(nsI) cosβ − (Ld − Lq)(nsI)

2 = 0 (2.26b)

Where Ld,Lq and ψm are independent of the number of conductors per slot and dependonly on the dimensions. The value of ampere-turn per slot is calculated from (2.22). Now,(2.26b) can be solved for the current angle β which gives the maximum torque. Knowingthe values of current angle β and ampere-turns per slot, the number of conductors can be

17


calculated as in (2.27) [4, 16]. Whereas E ′ and R′ are induced EMF and resistance perturn and are given in (2.28a) and (2.28b).

ns =V√(

E ′ +R′(nsI) sin β + Ldω(nsI cos β))2

+(nsI

)2

(−Lqω sin β +R′ cos β)2

(2.27)

E =E

ns

= 0.707ωKwqBδLD (2.28a)

R =R

n2s

= ρcupL+ πKcoilq(D +Hss)

fsAsl

(2.28b)

2.3.5 Summary of the analytical design process

The resulting machine design based on the given specifications and analytical models arereviewed in this chapter and are reported in 2.2. In Chapter 3, this design is used as astarting point for additional analysis using the finite element method (FEM).

Table 2.2: Machine design summary.Value Unit

Number of phases 3 -Number of poles 4 -Number of slots 24 -Outer stator diameter 180 mmTotal axial length 330 mmRotor outer diameter 112 mmShaft diameter 51 mmAir-gap height 0.35 mmStator yoke thickness 15 mmSlot area 173 mm2

Thickness of tangential rib 1 mmFundamental winding factor 0.96 -Slot fill factor 0.6 -Magnet material NdFeB -Rated torque 170 NmRated speed 1500 rpmMinimum dc link voltage 400 VCurrent density,(rms) 10 A/mm2

Resistance 0.46 Ohm

18

Chapter 3

FEM aided design

The finite element method (FEM) is an important tool for the design and analysis ofelectric machines. In this chapter, the previously obtained design using analytical methodsis analyzed and refined using a FEM software. The analysis results in a final design whichthen is experimentally evaluated in Chapter 4.

3.1 An evaluation of the analytical design using FEM

The resulting design from Chapter 2 has been implemented using JMAG1. The simulatedmachine model is shown in Fig. 3.1.

Fig. 3.1 FEM model of the resulting analytical design.

1JMAG is a registered trademark of the JSOL Corporation, Tokyo, Japan.

19

Chapter 3. FEM aided design

3.1.1 Air-gap flux density

The radial component of the air-gap flux density at no-load is shown in Fig. 3.2 and thecorresponding harmonic spectrum is shown in Fig. 3.3. It can be seen that the analyticallycalculated results agree reasonably well with the corresponding FEM simulation results.Fig. 3.4 and Fig. 3.5 show the air-gap flux densities due to id and iq, respectively, wherethe influence of the magnets in the rotor has been removed.

0 50 100 150−1

−0.5

0

0.5

1

PSfrag replacements

Rotation angle (deg)

Flux

dens

ity(T

)

AnalyticalFEM

Fig. 3.2 No load air-gap flux density (radial component only).

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 310

0.2

0.4

0.6

0.8

1

PSfrag replacements

Harmonic number (-)

Flux

dens

ity(T

)

FEMAnalytical

Fig. 3.3 No load air-gap flux density harmonic spectrum (radial component only).

20

3.1. An evaluation of the analytical design using FEM

0 50 100 150−1

−0.5

0

0.5

1

PSfrag replacements


Flux

dens

ity(T

)AnalyticalFEM

Fig. 3.4 Air-gap flux density (radial component) due to id only.

0 50 100 150−1

−0.5

0

0.5

1

PSfrag replacements


Flux

dens

ity(T

)

AnalyticalFEM

Fig. 3.5 Air-gap flux density (radial component) due to iq only.

3.1.2 Developed torque

To minimize the resistive losses, the machine should be operated following the maximumtorque-per-ampere (MTPA) trajectory [4]. For each torque level, the current angle thatfulfills the MTPA condition, is affected by saturation and flux leakage and cannot gen-erally be determined using analytical techniques [2, 12]. A number of FEM simulationshave therefore been performed to determine the optimal current angle for each torquelevel. The resulting variation of the developed torque with the current angle β is shown in

21


Fig. 3.6 where the current angle β is referred to the q-axis. At rated current (53 A, rms),the optimal current angle for the simulated machine is around 60 degrees which differsfrom the 45 degrees predicted from the analytical modeling.

0 20 40 60 800

50

100

150

PSfrag replacements

β (deg)

Torq

ue(N

m)

Fig. 3.6 Variation of torque with the current angle β.

3.1.3 d- and q-axis inductances

In the field weakening range, the machine needs to be controlled so that the requiredvoltage is limited by the available dc-link voltage of the inverter (400 V). In the fieldweakening region, the developed torque is strongly influenced by the open circuit voltageand d- and q-axis inductance difference [8, 16, 19]. The open circuit voltage is directlyproportional to the size and remanent flux density of the permanent magnets used andthe inductance difference mainly depends on the rotor design. Hence, the rotor geometryhas to be designed carefully to enable operation at high speeds. The d- and q-axis in-ductances as a function of id and iq are shown in Fig. 3.7 and Fig. 3.8, respectively. Thed-inductance is generally not very dependent on saturation and cross saturation whereasthe q-inductance, on the other hand, is strongly dependent on iq but very little impact ofcross saturation can be seen.

3.2 Parametric study

Using FEM simulations and the design based on analytical techniques as a starting point,a parametric study of the machine has been performed to find final design parameters suchas the selection of number of flux barriers, the d-axis insulation ratio, the optimal currentangle and magnet dimensions.

22

3.2. Parametric study

−500

50

−500

500

0.005

0.01

0.015

PSfrag replacements

id (A)iq (A)

Ld

(H)

Fig. 3.7 The d-axis inductance as a function of id and iq.

3.2.1 Number of flux barriers

As discussed in Chapter 2, a certain amount of air is introduced in the rotor of a PMSyn-Rel to increase the magnetic anisotropy. The total amount of air introduced in the rotoris then distributed into a number of flux barriers to improve the flux distribution throughthe rotor and increase the average value and smoothness of the torque developed. Somerecommendations for the selection of number of flux barriers to reduce the torque rip-ple are given in [5]. For RSMs, it is possible to select a large number of flux barriers.However, for PMRSMs, there is a limitation on the flux barrier width (Wbd in Fig. 2.2)and, consequently, on the maximum number of flux barriers. This is due to the limitationon minimum thickness of commercially available magnets. In this section, the impact ofusing up to four flux barriers is studied. Cross sections of the simulated rotors with oneand four flux barriers are shown in Fig. 3.9. The rotors have been designed followingthe guidelines described in Chapter 2. The d-axis insulation ratio Kwd and magnet crosssectional area are the same for the four cases and correspond to 0.6 and 290 mm2, re-spectively. The average torque and torque ripple for the four cases without magnets areshown in Fig. 3.10 where it can be seen that the average torque is not influenced much byincreasing the number of flux barriers since the torque depends on the anisotropy of therotor which is the same for all four cases. However, the torque ripple varies significantlywith the number of flux barriers. The simulation results show that the torque ripple isminimized for the rotor with four flux barriers which is in line with the formula Q/p± 2

used to select the number of flux barriers introduced in [5] and discussed in Section 2.3.1.With magnets, the average torque and the torque ripple for the four cases are comparedin Fig. 3.11. Comparing, Fig. 3.11 and Fig. 3.10, it can be observed that both the averagetorque and torque ripple increase when the magnets are introduced. It can also be seen

23


−20 −10 0 10 20

−20−10

010

200

0.02

0.04

0.06

PSfrag replacements

id (A)iq (A)

Lq

(H)

Fig. 3.8 The q-axis inductance as a function of id and iq.

that the torque ripple for the case with magnets and four flux barriers is higher comparedto the corresponding case without magnets. It appears that the magnets enhance the har-monic contribution from the rotor. The torque spectrum with four flux barriers with andwithout magnets are compared in Fig. 3.12 a). The values are given in per unit where therespective fundamental components are considered as one per unit. It can be seen thatthe 12th torque harmonic with magnets is significantly higher than without magnets. Thephase voltage harmonic spectrum is compared in Fig. 3.12 b) and it can be observed thatthe 11th and 13th are the dominant harmonics in the voltage spectrum with magnets.

Fig. 3.9 Cross sections of the simulated PMSynRel rotors: a) Single flux barrier; b) Four fluxbarriers.

24


1 2 3 40

20

40

60

80

100

PSfrag replacements

Number of barriers (-)

Torq

ue,t

orqu

eri

pple

(Nm

,%)

Fig. 3.10 Influence of number of barriers without magnets on the average torque (blue bars) andtorque ripple (red bars).

3.2.2 Insulation ratio

As discussed in Chapter 2, the d-axis insulation ratio Kwd is an important design parame-ter which reflects the dimensions of the flux barriers and iron segments in the rotor. It hasa direct influence on the reluctance torque and can be helpful when comparing differentrotor geometries. From (2.2), it can be deduced that when Kwd = 0, the rotor is assumedto be completely made of iron and when Kwd = 1, the width of the total air and ironlamination segments is equal in the rotor. For Kwd > 1, the widths of the air barriers islarger compared to the widths of the iron segments. The practical upper limit of Kwd islimited by saturation in the iron segments since the saliency then starts to decrease.

In this section, rotors with different insulation ratios are designed following theguidelines described in the Chapter 2 and studied with respect to the developed torque.In Fig. 3.13, two rotors without magnets and with four flux barriers but with differentinsulation ratios are shown. The influence of d-axis insulation ratio on the developedtorque is shown in Fig. 3.14.

It can be seen that the variation of the torque with the d-axis insulation ratio hasthree distinct characteristic regions. Initially, the torque increases sharply as Ld decreasesdue to the introduction of air along the d-axis whereas the inductance along the q-axisLq remains almost unaffected. When the d-axis insulation ratio is increased further, theresulting torque is not changed. This is because Ld has reached its optimal value and Lq

is essentially unaffected. The optimal insulation ratio, where maximum reluctance torqueis achieved, lies in this region. Increasing the insulation ratio even further will also reduceLq since the iron segments start to get saturated. This causes a reduction of the inductancedifference and, consequently, also a reduction of the resulting torque [2].

25


1 2 3 40

50

100

150

PSfrag replacements

Number of barriers (-)

Torq

ue,t

orqu

eri

pple

(Nm

,%)

Fig. 3.11 Influence of number of barriers with magnets on the average torque (blue bars) andtorque ripple (red bars).

Influence of magnets

The influence of the the d-axis insulation ratio on the developed torque for rotors withpermanent magnets is now studied and compared with the rotors discussed above. Asmentioned previously, for a fixed number of flux barriers, there is a practical lower limita-tion for the d-axis insulation ratio when magnets are embedded into the flux barriers sincethe magnet should not be made thinner than around 2 mm to avoid problems with mechan-ical brittleness. Cross sections for the rotors in consideration are illustrated in Fig. 3.15where the magnet area has been kept constant (corresponding to a magnet cross sectionalarea of 290 mm2). The developed torque for the different cases are illustrated in Fig. 3.16where it can be seen that the magnets influence the optimal insulation ratio compared tothe cases without magnets (RSM rotors). As seen, the optimal insulation ratio for the PM-SynRel rotors is lower compared to the RSM rotors. However, the optimal current angleis not very sensitive to the variations in the d-axis insulation ratio as shown in Fig. 3.17.

3.2.3 Magnet placement

Dimensioning and placement of the magnets can be a sensitive issue since it affects thedeveloped torque and the maximum attainable speed of the machine under limited invertervoltage. Naturally, it is desirable to reduce the amount of used magnet material to keep thesystem cost as low as possible while still fulfilling the given specifications. The influencesof magnet volume and placement in the rotor on the developed torque is studied in thissection.

26


6 12 18 24 300

0.1

0.2

3 5 7 9 11 13 15 17 19 21 23 25 27 29 310

0.05

0.1

PSfrag replacementsHarmonic number (-)

Torq

ue(p

u)

a)

w magnetsw/o magnets

Harmonic number (-)

Harmonic number (-)

Volta

ge(p

u)b)

w magnets

w magnets

w/o magnets

w/o magnets

Fig. 3.12 Performance comparison with and without magnets for four flux barriers: a) Torquespectrum; b) Voltage spectrum.

Fig. 3.13 Cross sections of the simulated rotors without magnets: a) Kwd = 0.2; b) Kwd = 1.4.

Magnet positioning

The given magnet volume can be distributed in the flux barriers of the rotor in many differ-ent ways. Four alternatives, labeled Case 1 to Case 4, are shown in Fig. 3.18 and Table 3.1compares the magnet volume of the four cases in per unit values where the machine shownin Fig. 3.1 is taken as a reference (corresponding to 1 per unit). The developed torque asa function of the current angle β is shown in Fig. 3.19 where Mv represents the magnetvolume in per unit. The maximum average torque at rated current and the resulting torqueripple for the Case 1 to Case 4 are shown in Fig. 3.20 and Fig. 3.21, respectively. Natu-rally, the developed torque reduces with a reduction of the magnet volume. However, itcan also be seen that it is better to place the magnets in the innermost flux barriers froma torque ripple point of view. While not only reducing the torque ripple, it is also helpful

27


0.4 0.6 0.8 1 1.2 1.4 1.680

90

100

110

120

PSfrag replacements

Torq

ue(N

m)

Kwd (-)

Fig. 3.14 Influence of the d-axis insulation ratio on the torque for the rotors corresponding toFig. 3.13.

Fig. 3.15 Cross sections of the simulated rotors with magnets: a) Kwd = 0.6; b) Kwd = 1.

for protecting the magnets from demagnetization [17].

Magnet dimension

Now, the magnets are distributed in all four available flux barriers but the total magnetarea is changed as specified in Table 3.1. The resulting rotor configurations in considera-tion are illustrated in Fig. 3.22. The developed torque and the resulting torque ripple forthe four different cases shown in Fig. 3.22 are compared with the previously describedconfiguration of Fig. 3.18 in Fig. 3.23 and Fig. 3.24. It can be observed that although thedeveloped torque is the same, the resulting torque ripple can be reduced significantly bydistributing the magnets in all flux barriers.

Magnet material

The developed torque is now investigated using two different magnet materials. In a PM-SynRel, only a small amount of magnets is typically introduced. This is mainly done in

28


0.4 0.6 0.8 1 1.2 1.4 1.60.8

0.85

0.9

0.95

1

1.05

PSfrag replacementsTo

rque

(pu)

Kwd (-)

w magnetsw/o magnets

Fig. 3.16 Influence of the d-axis insulation ratio on the developed torque with and without mag-nets in the rotor.

order to increase the power factor and efficiency of the machine [20,25]. Although ferriteshave a considerably lower remanent flux density Br compared to NdFeB magnets, theyare associated with a significantly lower cost and can often satisfy the role of increasingthe power factor and efficiency very satisfactorily [11]. However, to fulfill the torque re-quirements with the specified outer dimensions, the magnets are also needed to increasethe torque capability of the machine. In this section, the influence of the magnet materialon the torque capability is compared when the rotor is equipped with ferrites and NdFeBmagnets. As previously, it is assumed that the remanent flux density and the coercivity ofthe NdFeB magnets is 1.2 T and 965 kA/m, respectively, whereas for ferrites, 0.4 T and195 kA/m is assumed. The optimal developed torque as a function of the current angleusing these materials is shown in Fig. 3.25. Obviously, the torque produced with the fer-rite magnets is lower compared to the case with NdFeB magnets. However, the optimalcurrent angle is not very different in both cases with only a slightly lower optimal currentangle for the ferrites.

V-shaped magnets

The possibility to place the magnets along the q-axis,as shown in Fig. 3.26, is now investi-gated. The results are compared to Case 3 in Fig. 3.22 which has the same magnet volume.It is found that the developed torque, is slightly higher for the case with the V-shaped mag-nets (140 Nm compared to 136 Nm) which is in line with the results in [1,7,23]. However,it is also found that the torque ripple is significantly higher for v-shaped magnets (46 %)

compared to Case 3 in Fig. 3.22 (16 %). It is, hence, recommended that it is better todistribute the available magnet volume as illustrated in Fig. 3.22.

29


30 40 50 60 70 80100

120

140

160

180

PSfrag replacements

β (deg)

Torq

ue(N

m)

Fig. 3.17 Influence of the current angle β on the developed torque for different d-axis insulationratios for the PMSynRel rotors: Kwd =0.6 (blue line), Kwd =0.7 (green line), Kwd =

0.8 (red line) and Kwd=1.0 (cyan line).

3.2.4 Stator skew and short pitch winding

The PMSynRel is connected in delta during traction mode which can cause circulatingcurrents due to triplen harmonics. The circulating currents can be as high as 5 % of therated current which will increase losses and the risk of overheating the machine. To elimi-nate the triplen harmonics, the winding is short pitched by 2 slots. The fundamental wind-ing factors are 0.965 and 0.835 for the full pitch and short pitch winding, respectively. Theharmonic spectrums of the open circuit voltage for the full pitch and the short pitch wind-ings are shown in Fig. 3.27 where it can be seen that the triplen harmonics are not presentfor the short pitched winding. However, the penalty to use the short pitched winding isa lower average torque (111 Nm) compared to the full pitched winding (127 Nm) and ahigher torque ripple as shown in Fig. 3.28.

To reduce the torque ripple, the rotor geometry can be modified or the stator orrotor can be skewed. For PMRSMs, it is more practical to skew the stator rather thanthe rotor due to the presence of magnets in the rotor which are segmented axially muchless densely than the iron laminations. Fig. 3.29 shows the effect of the stator skew on thedeveloped torque. As seen, skewing the stator corresponding to two stator slots practicallyremoves all torque ripple. However, this reduces the average torque significantly and alsomakes the winding difficult to mount in the stator for short axial lengths. Therefore, forthe prototype PMSynRel built, the stator skew corresponds only to half a stator slot.

30


Fig. 3.18 Different possibilities for placement of the magnets in the flux barriers.

Table 3.1 Magnet placement alternatives.Title Magnet volume Mv (pu)Case 1 0.95Case 2 0.86Case 3 0.70Case 4 0.48

3.2.5 Mechanical stability

One additional important aspect to consider while designing a PMSynRel rotor is themechanical stability. A straight forward solution reported in the literature is to introduceribs along the d-axis in the flux barriers (radial ribs) or tangentially oriented ribs near theair-gap (tangential ribs) [12, 25]. These ribs will normally be saturated by the magnets.Unfortunately, the introduction of these ribs results in a reduction of the average torqueand also increases the cross-saturation of the d- and q-axis flux paths [26]. In general,the torque reduction is proportional to the width of the rib which consequently dependsupon the maximum speed of the machine and the mechanical stress limit of the rotormaterial [12].

The structural strength of the rotor needs to be guaranteed at all operating con-ditions, including maximum speed which is specified to be 6500 rpm. The structuralstrength of the rotor shown in Fig. 3.1 has been evaluated at 6500 rpm and no load us-ing FEM simulations2. The maximum allowable fatigue stress of the used rotor material(M250-35A) is 455 MPa [24]. The result is shown in Fig. 3.30a) from where it can be seen

2The author wants to acknowledge Mr. Viktor Lassila at BAE Systems Hagglunds AB for carrying outthe FEM analysis of the structural strength.

31


30 40 50 60 70 80100

120

140

160

180

PSfrag replacements

β (deg)

Torq

ue(N

m)

Fig. 3.19 Influence of the current angle β on the average torque: Mv =1 (blue line), Mv =0.95

(green line), Mv=0.86 (red line) and Mv=0.76 (cyan line).

that the highest stress (around 280 MPa) occurs in the tangential ribs closest to the q-axis.As illustrated in Fig. 3.30b), radial iron ribs in the flux barriers are therefore introducedon the sides of the three innermost magnets to enhance the mechanical strength. It can beseen that the highest stress has now been reduced to around 160 MPa which occurs in theinnermost radial ribs. The resulting reduction in average torque is around 1 %.

This concludes the parametric study of the machine. For the final design of themachine, however, the tolerances for the magnet placement in the rotor slot are also intro-duced (0.3 mm) which cause a further reduction of the developed torque by around 7 %.The final design is shown in Fig. 3.31.

3.3 Summary of chapter

In this chapter, the resulting machine design from Chapter 2 has been analyzed using FEMsimulations. A parametric study was performed to optimize the design. It was verified thatthe average developed torque is not influenced much by the selection of number of fluxbarriers as long as the d-axis insulation ratio is kept constant. However, the selection ofnumber of flux barriers is critical in terms of the resulting torque ripple. It was also ob-served that introducing magnets in the flux barriers enhances the amplitude of the slotharmonics and, consequently, the torque ripple. It was shown that the average torque isdirectly affected by the insulation ratio and that there exists an optimal insulation ratio interms of the maximum average torque. In view of torque production, the optimal insula-tion ratio found for an RSM rotor was not found optimal when magnets were introducedin the flux barriers. Further, It was shown that for a given magnet volume, the placementof the magnets in the rotor structure is an important variable from a machine performance

32

3.3. Summary of chapter

0.4 0.5 0.6 0.7 0.8 0.9 1100

120

140

160

180

PSfrag replacements

Magnet volume (pu)

Torq

ue(N

m)

Fig. 3.20 Comparison of developed torque for different magnet placement alternatives inFig. 3.18.

point of view. By studying different alternatives of how to place the magnets in the fluxbarriers, it was found to be beneficial to distribute the available magnet volume in the fluxbarriers rather than placing them in a single flux barrier. The mechanical strength of therotor at maximum speed and no load was also evaluated and radial iron ribs were intro-duced which significantly reduced the maximum fatigue stress. A summary of the finaldesign is reported in Table. 3.3. It can be seen that the developed torque of the machine(114 Nm) is significantly lower than the specified torque (170 Nm). Skewing of the statorand the short pitch winding has contributed to the reduction of the average torque. Thelimitation on the active length of the machine which is due to the longer end winding, isalso responsible for the lower torque than required. The length of the end winding canbe reduced by increasing number of poles or increasing number of stator slots. However,number of poles and number of stator slots are fixed for this machine because of therequirements of the integrated charger as specified in Chapter 1.

33


0.4 0.5 0.6 0.7 0.8 0.9 110

20

30

40

50

60

PSfrag replacements

Torq

ueri

pple

(%)

Magnet volume (pu)

Fig. 3.21 Comparison of resulting torque ripple for different magnet placement alternatives inFig. 3.18.

Fig. 3.22 Distribution of a given magnet volume in all available flux barriers.

Table 3.2 Magnet placement alternatives.Title Magnet volume Mv (pu)Case 1 0.95Case 2 0.86Case 3 0.70Case 4 0.48

34


0.4 0.5 0.6 0.7 0.8 0.9 1100

120

140

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ue(N

m)

Fig. 3.23 Torque comparison for different magnet placements. The solid line corresponds to thealternatives in Fig. 3.18 whereas the dashed line corresponds to Fig. 3.22.

0.4 0.5 0.6 0.7 0.8 0.9 110

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Torq

ueri

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Fig. 3.24 Torque ripple comparison for different magnet placements. The solid line correspondsto the alternatives in Fig. 3.18 whereas the dashed line corresponds to Fig. 3.22.

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10 20 30 40 50 60 70 80

60

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β (deg)

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m)

NdFeBFerrite

Fig. 3.25 Average torque as a function of the current angle β for two different magnet materials.

Fig. 3.26 Distributing the magnets in parallel to the q-axis. The arrows denote the direction of themagnetization.

36


3 5 7 9 11 13 15 17 19 21 23 25 27 29 310

5

10

15

PSfrag replacementsVo

ltage

(V)

Harmonic number (-)

Short pitchFull pitch

Fig. 3.27 Phase voltage spectrum for the full pitch and short pitch winding at 1500 rpm and noload. The fundamental peak voltage is 218 V and 186 V for the full pitched and shortpitched winding, respectively.

6 12 18 24 300

0.02

0.04

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0.1

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u)

Short pitchFull pitch

Fig. 3.28 Torque spectrum for the full pitch and short pitch winding. The average torque is127 Nm and 111 Nm for the full pitched and short pitched winding, respectively.

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0 50 100 15090

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Rotor position (deg)

Torq

ue(N

m)

Fig. 3.29 Influence of stator skew on the developed torque: No skew (blue line), half a slot (greenline), one slot (red line) and two slots (cyan line).

Fig. 3.30 Stress analysis at 6500 rpm and no load.

Fig. 3.31 Cross section of the the resulting FEM aided design.

38


Table 3.3: Machine design summary.Value Unit

Winding connection Delta -Number of phases 3 -Number of poles 4 -Number of slots 24 -Outer stator diameter 180 mmActive length 210 mmRotor outer diameter 112 mmShaft diameter 51 mmAir-gap height 0.35 mmStator yoke thickness 15 mmSlot area 173 mm2

Thickness of tangential ribs 1 mmThickness of radial ribs 1 mmMagnet tolerance 0.3 mmFundamental winding factor 0.83 -Lamination factor 0.97 -Slot fill factor 0.45 -Magnet material NdFeB -Total weight 45 kgWeight of active parts 26 kgWeight of magnets 1.9 kgRated torque 114 NmRated speed 1500 rpmMinimum dc-link voltage 400 VCurrent density,(rms) 10 A/mm2

Terminal current,(rms) 53 APhase voltage,(rms) 210 VOpen circuit voltage,(rms) 116 VResistance 0.46 OhmPower factor 0.93 -d-axis inductance 8 mHq-axis inductance 33 mHCooling method Water jacket -

39


40

Chapter 4

Experimental evaluation

In this chapter, sample experimental results are presented and compared to the resultsobtained from FEM simulations.

4.1 Experimental setup

The prototype PMSynRel machine has been extensively evaluated in an experimental set-up, see Fig. 4.1. The PMSynRel machine is connected to an induction machine whichis speed controlled. The shaft torque is measured with a torque transducer. The machineis supplied by a voltage source inverter which uses a switching frequency of 5 kHz. Aposition sensor is mounted on the shaft of the prototype machine to measure the rotorposition. A power analyzer (Yokogawa WT3000) is used to measure the voltage, currentand power of the prototype machine and the efficiency is estimated by taking the ratio ofthe output and input powers.

4.2 Open circuit voltage

The open circuit voltage of is first measured at 1500 rpm and compared with a corre-sponding FEM simulation without the introduction of additional air between the magnetsand the rotor slots due to manufacturing tolerances required for the laser cutting and themagnets. The results are shown in Fig. 4.2 a). It can be seen that there is a substantialmismatch between the measured and the simulated results. The measured fundamentalvoltage (164 V) is around 12 % lower than the result from the simulation (186 V). Theintroduction of the tolerance for the magnet placement in the rotor slots (0.3 mm) in theFEM simulation model improves the agreement of the measured and simulated results asshown in Fig. 4.2 b).

41

Chapter 4. Experimental evaluation

Fig. 4.1 The experimental setup of the prototype machine.

4.3 Developed torque

The torque of the prototype machine has been measured for id < 0 and iq > 0 at a con-stant speed (1500 rpm). The experimentally obtained results are shown in Fig. 4.3 andthe corresponding results obtained using FEM analysis are shown in Fig. 4.4. For themeasurements, the negative d-axis current is limited to 55 A in order to avoid a possibledemagnetization of the magnets. It can be observed by comparison of the two figures thatthe simulation results are in well agreement with the experimentally obtained results. Themaximum developed torque of the simulated machine is 106 Nm while the experimentallyobtained maximum torque of the prototype machine is 104 Nm.

4.4 Power factor and losses at rated current

The impact of the current angle β on the resulting machine losses and power factor is nowexperimentally obtained at rated current which corresponds to a peak fundamental currentof 75 A while the rotor speed is 1500 rpm. The measurement points are represented as redcircles in Fig. 4.3. The experimentally obtained results are compared with results fromthe FEM simulations in Fig. 4.5. It can be seen that the maximum developed torque isachieved at a current angle β≈55 deg and the efficiency and power factor are maximizedat a current angle β≈70 deg. This is in accordance with the results reported in [14].

42

4.5. Circulating currents

0 0.005 0.01 0.015 0.02−200

−100

0

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200

0 0.005 0.01 0.015 0.02−200

−100

0

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a)

MeasuredSimulated

Time (s)

Time (s)Vo

ltage

(V)

Volta

ge(V

)b)

Measured

Measured

Simulated

Simulated

Fig. 4.2 Open circuit voltage: a) Without compensation for magnet tolerance; b) With compensa-tion for magnet tolerance.

4.4.1 q-axis current study

Now, the developed torque, efficiency and power factor are measured at 1500 rpm whilethe q-axis current is increased from zero to the rated peak fundamental current (75 A). Theexperimental data, together with corresponding results from FEM simulations, are shownin Fig. 4.6. It can be seen that while the torque increases with the increasing currentamplitude, the efficiency and power factor of the machine decreases with the increase ofthe q-axis current which is similar to many SPMs.

4.5 Circulating currents

For a delta connected winding, circulating third-order harmonic currents can arise whichare sources of additional losses and over heating of the machine. Therefore, the windingis short pitched to eliminate the third-order harmonics currents as mentioned in Chap-ter 3. The measurement results presented in Fig. 4.7 verify that the circulating currentsare almost negligible around 0.3 % of the rated current.

43


4.5.1 Summary of chapter

The performance of the prototype PMSynRel machine has been experimentally evaluatedand the results were compared with corresponding FEM simulations. The FEM simula-tion model had to be revised by introducing the tolerance for the magnet placement inthe rotor slots which improved the agreement between the experimentally obtained opencircuit voltage and corresponding FEM simulation. An experimentally obtained torquemap was presented as a function of id and iq and was compared with corresponding FEMsimulations. It was verified that the simulation results were in good agreement with theexperimentally obtained results. The maximum developed torque from the FEM simula-tions (106 NM) was close to the experimentally obtained torque (104 Nm). Further, theperformance of the machine was investigated at rated current (75 A). It was demonstratedthat the power factor and the efficiency of the machine vary with the current angle and thatthey are maximized at a higher current angle (β≈ 70 deg) compared to the current anglethat maximizes torque (β ≈ 55 deg). It was also verified that the circulating third-orderharmonic currents in the machine winding were almost negligible around 0.3 % of therated current.

44


−60 −40 −20 00

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id (A)

i q(A

)

Fig. 4.3 Experimentally obtained torque as function of id and iq. The black dots represent mea-surement points. The red circles correspond to the measurement points in Fig. 4.5

−60 −40 −20 00

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id (A)

i q(A

)

Fig. 4.4 FEM simulation: Torque as a function of id and iq.

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0 10 20 30 40 50 60 70 800

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0 10 20 30 40 50 60 70 8075

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0 10 20 30 40 50 60 70 800.4

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Effi

cien

cy(%

)

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β (deg)

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erfa

ctor

(-)

c)

Fig. 4.5 Performance parameters as a function of current angle β at the rated peak current (75 A):a) Torque; b) Efficiency; c) Power factor.

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0 5 10 15 20 25 30 35 40 450

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cy(%

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Pow

erfa

ctor

(-)

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Fig. 4.6 Performance parameters as a function of the q-axis current: a) Torque; b) Efficiency; c)Power factor.

0 0.05 0.1 0.15 0.2−20

−10

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Time (s)

Cur

rent

(A)

Fig. 4.7 Experimentally obtained winding currents: ia (red line), ib (blue line), ic (green line),Circulating current (magenta line).

47


48

Chapter 5

Comparison of different rotortopologies

The electric machine for the integrated charger may be a synchronous reluctance ma-chine (SRM), surface-mounted permanent-magnet synchronous machine (SPM), interiorpermanent-magnet machine synchronous (IPM) or a permanent-magnet assisted syn-chronous reluctance machine (PMSynRel). This chapter discusses and compares thesedifferent rotor types.

5.1 Surface-mounted PM synchronous machines

The SPM topology machine is the most widely used PM rotor topology due to its hightorque and high efficiency [27]. To compare the characteristics of different SPM designswith the prototype PMSynRel presented in Chapters 1–4, a number of basic SPM designsvariations have been studied using FEM simulations. The stator design is kept the sameas for the prototype machine. Hence, the air-gap length is 0.35 mm which is contrary tonormal practice but is done to increase the validity of the comparison. A cross-section ofthe simulated SPM is shown in Fig. 5.1. The magnet angle span αm is varied in order tooptimize the rotor geometry in terms of developed torque. The magnet thickness Tm iskept constant to 3.76 mm which means slightly different magnet volumes in all studiedcases. The results, reported in Table 5.1, show that the torque developed by the SPMmachines does not increase for αm>120 deg. This is mainly due to saturation in the stator.Note that the maximum developed torque is higher (around 5%) than the torque developedby the prototype machine. However, a significantly lower maximum speed (2800 rpm) isreached compared to what obtained with the prototype machine (6000 rpm).

49

Chapter 5. Comparison of different rotor topologies

Fig. 5.1 Cross-section of the simulated SPM machine.

Table 5.1: Effect of magnet angle span on the developed torque.αm (deg) Torque (Nm)160 119140 119120 120110 97100 91

5.2 Interior PM machines

5.2.1 Single barrier IPM machines

In order to obtain a valid comparison, the stator design of the machine is kept the sameas for the prototype PMSynRel machine. Additionally, the air-gap height is kept the sameas for the prototype machine (0.35 mm) and the thickness of the iron bridges is alsokept constant (1 mm). In this study, the rotor is only optimized in order to maximizethe developed torque. The considered rotor geometry is shown in Fig. 5.2. There are fourdesign parameters which can be varied to optimize the rotor of the machine: magnet angleαm, magnet width Wm, magnet thickness Tm and the radial position of the magnet Yr.

Magnet radial position

Now, the radial position of the magnet Yr is varied while the total cross-sectional areaof the magnets is kept the same as for the prototype machine (290 mm2). The magnetradial position Yr, magnet dimensions (Wm and Tm) and resulting torque are reported inTable 5.2. The study shows that the torque is reasonably insensitive to the radial placementof the magnet unless it is very close to the shaft where it affects the q-axis inductance dueto saturation of the rotor iron near the shaft [21].

50

5.2. Interior PM machines

Fig. 5.2 IPM design parameters. The dotted arrow denote the direction of the magnetization.

Table 5.2: Effect of the radial position of magnet Yr on the developed torque.Wm (mm) 35 32 30 27Tm (mm) 4.1 4.5 4.7 5.2Magnet area (mm2) 289 290 288 285Yr (mm) 4 7 9 11Torque (Nm) 106 113 115 115

Magnet angle span

Now, the influence of the magnet angle span in the rotor αm is investigated on the torquecapability. The dimensions of the magnets in the rotor slot are kept the same and themagnet area is the same as for the prototype PMSynRel machine. This is done in order tominimize the effect of the reluctance variation (due to the rotor slots) on the torque whichis important for a valid comparison of the simulated cases. Maintaining similar magnetdimensions while changing αm is achieved by changing the distance from the shaft Yr

which has relatively little impact on the torque (as concluded from the study above). Theresulting torques are reported in the Table 5.3 from where it can be concluded that withthe same magnet area as for the prototype machine and with the same magnet dimensions,the rotor with a magnet angle span αm=130 deg maximizes the torque.

Table 5.3: Effect of magnet angle span αm on the developed torque.αm 150 140 130 120Wm (mm) 30 31 29 28Tm (mm) 4.8 4.7 4.9 5.2Magnet area (mm2) 289 290 288 290Torque (Nm) 102 103 105 97

51


Magnet dimensions

In this study, the effect of magnet dimensions (Wm and Tm) is investigated on the de-veloped torque and the torque ripple. The simulated cases are illustrated in Fig. 5.3. Themagnet area is kept the same for all cases and the magnet dimensions (Wm and Tm) arevaried. The width of the ”rotor slot” is kept to 31 mm for all three cases since a variationwould affect the reluctance of the rotor and increase the cross-coupling effect (if the ro-tor slot width is reduced, the thickness of the tangential ribs would increase which willincrease the leakage flux) [26]. This results in an increase of the magnet thickness and anintroduction of air in the rotor slot (see Fig. 5.3). The radial distance from the shaft Yr iskept constant (7 mm) for all three cases. FEM simulation results are reported in Table 5.4from where it can be concluded that with the same magnet area as for the prototype PM-SynRel machine, it is better to select wide magnets in the rotor slots from torque point ofview which corresponds to the results presented in [21].

Fig. 5.3 Simulated cases for single barrier IPM rotors.

Table 5.4: Effect of magnet cross-sectional dimensions on the developed torque.- Case A Case B Case CWm (mm) 31 28 20Tm (mm) 4.7 5.1 7.2Magnet area (mm2) 289 290 288Torque (Nm) 112 111 102Torque ripple (%) 45 32 36

From the results above, a final optimized (in terms of torque density) design for asingle barrier IPM machine is shown in Fig. 5.4 and the corresponding parameters arereported in Table 5.5. Tolerance for the magnet placement in the rotor is also introduced(0.3 mm) and the torque developed is 98 Nm which is 9% less compared to the prototypePMSynRel machine.

52

5.2. Interior PM machines

Table 5.5: Design parameters of the single barrier IPM machine.αm (deg) Tm (mm) Wm (mm) Yr130 5.1 28 9

Fig. 5.4 Cross-section of the simulated single barrier IPM machine.

5.2.2 Double barrier IPM machines

Multi-layer IPM machines have been used successfully as reported in [3, 27]. In this sec-tion, the developed torque of a double barrier IPM machine is investigated and com-pared with the single barrier IPM and prototype PMSynRel machines. The magnet areais kept the same as for both the prototype PMSynRel and the single barrier IPM machine(288 mm2). The dimensions of the two magnets are selected so that a uniform flux density

Table 5.6: Cross-sectional dimensions of the magnets of the double barrier IPM machinein consideration.

αm (deg) Tm1 (mm) Wm1 (mm) Tm2 Wm2 (mm)130 2.41 25 3.2 29

is maintained in the rotor. This is done by ensuring the same insulation ratio of the rotor asfor the single barrier IPM case (as outlined in Chapter 2). The dimensions of the magnetsare given in Table 5.6. The resulting geometry is shown in Fig. 5.5. The torque devel-oped by this machine is almost the same as for the single barrier IPM machine (98 Nm).This is mainly because both the machines have the same amount of magnets in the rotorand the insulation ratio is also the same. However, the torque developed by the IPM ma-chine is 9% less compared to the prototype machine since the prototype machine is betteroptimized for both reluctance and magnetic torque components. Another factor whichshould be considered for the comparison of these two topologies is the field weakeningperformance. Apparently the IPM machine with this much amount of magnets has a lower

53


maximum speed compared to the prototype machine (6000 rpm). The performance of thedouble barrier IPM machine in terms of the developed torque is reported in Table 5.7.

Table 5.7: Torque-speed characteristics of the double barrier IPM machine.Speed (rpm) Torque (Nm)1500 983000 754000 534500 6

Fig. 5.5 The cross-section of the simulated double barrier IPM machine.

5.3 Summary of chapter

In this chapter, the prototype PMSynRel machine has been compared, in terms of devel-oped torque, with different rotor topologies using the same amount of magnets. The statordesign and the air-gap height were kept the same as for the prototype machine in order toobtain a valid comparison. A number of rotor designs for both SPM and IPM machineswas optimized. The optimized SPM machine generated 5 % higher torque in compari-son to the prototype PMSynRel machine but it had a significantly lower maximum speed(2800 rpm). The torque developed by the single and double barrier IPM machines wassmaller (11 %) compared to the prototype PMSynRel machine. The maximum speed ofthe double barrier IPM machine was also found lower (4500 rpm). From this comparativestudy, it can be concluded that the prototype PMSynRel machine, is optimized for bothits reluctance and magnetic torque components. It generates torque which is comparableto an SPM machine but has a significantly higher maximum speed, also in comparison tothe IPM machines in consideration.

54

Chapter 6

Concluding remarks

This chapter summarizes conclusions and provides some suggestions for further research.

6.1 Summary

This thesis has focused on a recently presented integrated charger concept in which theelectric machine used for traction is also used as a key component when the electric orplug-in hybrid electric vehicle is charging its battery.A PMSynRel was designed and an analytical model for the design of the rotor withoutpermanent magnets was first reviewed.A FEM model was developed to investigate the results from the analytical design whenmagnets were introduced into the rotor. A parametric study was performed to tune thedesign parameters in order to maximize the developed torque. By varying the insulationratio, it was found that there is an upper limit on the insulation ratio from the developedtorque point of view. It was also observed that the optimal insulation ratio in terms of de-veloped torque is different with and without the introduction of magnets in the rotor. Theoptimal insulation ratio with the magnets embedded in the rotor was found to be smallerthan for the corresponding case without magnets. It was further found that the average de-veloped torque of was not significantly effected by the number of flux barriers in the rotor.However, the resulting torque ripple was found to be strongly influenced by number offlux barriers. It was also found that the placement of a given amount of permanent magnetmaterial in the rotor structure was affecting the developed torque significantly. A numberof FEM simulations showed that magnets should be distributed in the flux barriers alongthe d-axis.The voltage adaptation requirements for the integrated charger requires a delta connectedwinding when the machine operates in the traction mode. A delta connected winding canresult in circulating third-order harmonic current which only introduces additional lossesin the winding. Therefore, a short pitched winding was used to eliminate the third or-der harmonics and, consequently, the circulating currents. The stator of the machine was

55

Chapter 6. Concluding remarks

skewed by half a stator slot to reduce the torque ripple. The mechanical strength of therotor was also investigated and radial iron ribs were introduced in the rotor to enhance itsmechanical strength.A prototype PMSynRel machine was built in order to verify the predicted performance.The torque was measured for id < 0 and iq > 0 at 1500 rpm. The measurement resultswere found to agree well with the predicted result. The torque, efficiency and power fac-tor of the machine were measured at 1500 rpm and at rated current. It was found that thepower factor and the efficiency of the machine were maximized at a higher current angle(β≈70 deg) compared to what was optimal for the developed torque (β≈55 deg). Addi-tionally, was experimentally verified that the circulating currents in the machine windingwere negligible.The integrated charger concept can be also be realized with other rotor topologies usingpermanent magnets. Therefore, the performance of the prototype machine was comparedwith a number of SPM and IPM machine designs. It was found that the SPM machinesconsidered had a higher torque compared to the prototype PMSynRel machine but a sig-nificantly lower speed range. Two IPM machines with single and double layers rotor mag-nets were designed and compared with the prototype machine. It was observed that withthe same magnet volume as used in the prototype machine, the IPM machines consideredhad a lower torque and the speed range was also limited in comparison to the prototypePMSynRel machine.

6.2 Future work

For the prototype PMSynRel machine, a distributed winding with four poles resulted inthe long end windings which has been a limiting factor for the developed torque. There-fore, a fractional slot winding or concentrated winding which can have considerably theshorter end-windings, can be investigated for this application. Thermal and acoustic anal-ysis can also be a topic of interest.Since the machine has been designed to operate both in the traction and charging mode.Therefore, the performance of the machine during charging mode should be investigated.Furthermore, It will be interesting to study the behavior of the machine when there is afault on the grid-side winding or on the inverter-side winding.

56

Appendix A

Prototype constructional details

The FEM simulations and measurements presented in this thesis were performed on theprototype PMSynRel machine. The machine was built by BEVI International AB. Theconstructional details of the prototype machine are presented in this appendix.It is a PMSynRel machine with four poles, 4 flux barriers in the rotor, 24 stator slotsand double-layer distributed winding. The stator and the rotor core are laminated, witha lamination thickness of 0.35 mm. The material used for the lamination is non-orientedelectrical steel (M250-35A) supplied and manufactured by Cogent at SURAHAMMARSBRUKS AB. The laminations are pressed together and then weld on the outer side. Themagnets are glued inside the flux barriers in the rotor. The rare-earth permanent-magnets(VACODYM 854 AP) have been used for the prototype machine which have been man-ufactured and supplied by VACUUMSCHMELZE GmbH & Co. The magnets are coatedin order to avoid oxidation and to prevent erosion. The coating layer is less than 10 µm.The prototype machine is used for both the propulsion of the vehicle and charging of thebattery. This is achieved by re-arranging the winding of the machine with the help of asimple switching device. Therefore, all the coil end-connections are brought out to theswitching device. The rotor and stator of the prototype PMSynRel machine are shown inFig. A.1 and Fig. A.2, respectively. The rotor is filled with the epoxy for a better heattransfer. The stator is half a slot skewed as shown in Fig. A.3

57

Chapter A. Prototype constructional details

Fig. A.1 Rotor of the prototype PMSynRel machine; a) Stacked laminations; b) Epoxy filled rotor.

Fig. A.2 Stator of the prototype PMSynRel machine; a) Shaft end; b) Connections end.

Fig. A.3 Half a slot skewed stator of the prototype PMSynRel machine.

58

References

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[2] A.Vagati, G. Franceschini, and G. Troliga, “Design criteria of high performancesynchronous reluctance motors,” IEEE Trans. Ind. Applicat., vol. 1, pp. 66–73, Oct.1992.

[3] N. Bianchi, S. Bolognani, A. Consoli, T. Jahns, R. Lorenz, E. Lovelace, S. Mori-moto, and A. Vagati, “Design, analysis and control of interior permanent magnetsynchronous machines,” in Tutorial lecture notes. IEEE 40th IAS Annu. Meeting,2004.

[4] I. Boldea, Reluctance synchronous machines and drives. Clarendon press, Oxford,1996.

[5] A. Fratta, A. Vagati, and F. Villata, “On the evolution of AC machines for spin-dle drive applications,” IEEE Trans. Ind. Applicat., vol. 28, no. 5, pp. 1081–1086,Jan./Feb. 1992.

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[16] S. Morimoto, Y. Takeda, T. Hirasa, and K. Taniguchi, “Expansion of operating limitsfor permanent magnet motor by current vector control considering inverter capacity,”IEEE Trans. Ind. Applicat., vol. 26, no. 5, pp. 866–871, 1990.

[17] H. Murakami, Y. Honda, Y. Sadanaga, Y. Ikkai, S. Morimoto, and Y. Takeda, “Op-timum design of highly efficient magnet assisted reluctance motor,” in Conf. Rec.IEEE 36th IAS Annu. Meeting, vol. 4, 2001, pp. 2296–2301.

[18] R. Rajabi, “Synchronous reluctance machine design,” Master’s thesis, Royal Inst.Technol., Stockholm, Sweden, Oct. 2007.

[19] R. Schiferl and T. Lipo, “Power capability of salient pole permanent magnet syn-chronous motors in variable speed drive applications,” IEEE Trans. Ind. Applicat.,vol. 26, no. 1, pp. 115–123, Jan./Feb. 1990.

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