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State University This is to certify that the dissertation entitled DESIGN AND OPERATION OF PERMANENT MAGNET MACHINE FOR INTEGRATED STARTER- GENERATOR APPLICATION IN SERIES HYBRID BUS presented by SINISA JURKOVIC has been accepted towards fulfillment of the requirements for the Doctoral degree in Electrical Engineering flw G, Sl’aww V' Major Professor’s SignatureQ Date MSU is an Affirmative Action/Equal Opportunity Employer ..-.-n-c-a-a-a-o-o--o-o-o-o-n-.-.-.-.-.--.-.-.-o---n-.-c---.-u---o-n--u-o-o-o--o-g-.-v-n—-.--.--a-.-.-q-o-c-o--.-o. PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 5/08 K'IPrq/Acc8PrelelRC/DateDue indd DESIGN AND OPERATION OF PERMANENT MAGNET MACHINE FOR INTEGRATED STARTER-GENERATOR APPLICATION IN SERIES HYBRID BUS By Sinisa J urkovic A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Electrical Engineering 2009 ABSTRACT DESIGN AND OPERATION OF PERMANENT MAGNET MACHINE FOR INTEGRATED STARTER GENERATOR APPLICATION IN SERIES HYBRID BUS By Sinisa J urkovic This work focuses on urban mass transportation vehicle, a hybrid electric bus with series powertrain configuration. With respect to hybrid vehicles, integrated starter / alternator configuration has only been seriously explored in so—called mild hybrid topology, while very little has been published on full hybrids and in particular series hybrid configuration. This work is divided into two parts: The first presents an evaluation and design of PMAC machine candidates suitable for starter-generator application in hybrid bus with series powertrain configuration. PMAC machines with interior and surface mount permanent magnets are considered and compared. Different design aspects such as concentrated versus distributed windings, interior and exterior rotor structures and different permanent magnet materials are evaluated. Different slot per pole per phase configurations for concentrated winding PMAC machines are also examined. Comparison and evaluation of the machines is based on their performance which included evaluation of winding and iron losses, magnet losses and maximum torque capability as well as the size and weight of the machines. A 6kW scaled prototype of the designed machine is built and tested. The second part of this work focuses on the operation and control of PMAC machine for the specified application. Various sensorless control algorithms are considered, as well as control with rotor position feedback with the underlining issue of saturation and its effects. Finally, in-depth design and analysis of a new control algorithm, which accounts for the entire operating range of PMAC machine, is presented. Analytical, simulation and experimental results of the designed machine and the controller are presented. To Mirko, Ljubica and Igor J urkovic with my affection and gratitude iv ACKNOWLEDGMENTS I am deeply indebted, to my advisor Professor Elias Strangas for his guidance, support, and immense patience throughout these years. I am thankful for the privilege to work with him as well as professional and personal example he has set- I would also like to thank Professors Hassan Khalil, Feng Peng and Ranjan Mukherjee for their time and effort in being members of the Ph.D. committee. I would like to extend special thanks to those at General Motors Corporation for their support and patience while finishing this dimertation. Special words of thanks go to my lab colleagues Wes Zanardelli, Carlos Nino, John Kelly, Steve Bohan, Sajjad Zaidi and Tariq Abdul for all of their support. I would also like to thank the members of the department whose help was much appreciated, including Brian W'right, Roxanne Peacock, Vanessa Mitchner, Meagan Kroll and Pauline Van Dyke. I owe very special thanks to my friends, Karen, Igor, Pam, Jadranko, Nancy, Marko, Duje and Hrvoje, whose support and encouragement helped make my graduate studies possible and enjoyable. Finally, I owe special thanks to my parents, Mirko and Ljubica, and my brother, Igor without whose support and encouragement none of this would have been possible. TABLE OF CONTENTS LIST OF TABLES .................................. viii LIST OF FIGURES ................................. ix 1 Introduction ..................................... l 1.1 Objectives and Contributions ...................... 1 1.1.1 Design and Analysis ....................... 2 1.1.2 Operation and Control under Saturation ............ 3 1.2 Organization of the Dissertation ..................... 4 1.3 Hybrid Electric Vehicles ......................... 6 1.3.1 Integrated Starter/ Generator .................. 7 1.3.2 Sizing the Generator ....................... 8 1.4 Survey of PMAC Machines for ISG ................... 11 1.5 Operation of SPM Machines Under Saturation ............. 13 2 Permanent Magnet AC Machines ...................... 16 2.1 Overview .................................. 16 2.2 Permanent Magnet Rotor Topologies .................. 17 2.3 Wmdings ................................. 20 2.4 Control of PMAC Machines ....................... 23 2.4.1 Current Vector Control Principle ................ 24 2.5 PMSM Modeling ............................. 25 2.5.1 Vector Control Model ....................... 25 2.5.2 Magnetic Circuit ......................... 22 3 Analysis of Concentrated Winding SPMSM ............... 32 3.1 Resistance Calculation .......................... 33 3.2 Inductance Calculation .......................... 36 3.3 Winding Emotion ............................. 44 3.4 Magnetic Field in the Air-Gap ...................... 49 3.5 Permeance thction ........................... 50 3.6 Back EMF Waveform ........................... 52 3.7 Electromagnetic Torque Calculation ................... 54 3.8 Winding Losses .............................. 56 3.9 Iron Loeses ................................ 56 3.10 Specific Iron Loss under PWM Supply ................. 63 3.11 Magnet Losses ............................... 67 Finite Element Analysis ............................. 4.1 Comparison of Machine Candidates ................... 4.1.1 Rotor Topology Selection ..................... 4.1.2 Comparison of SPM Machines .................. 4.1.3 Torque Capability ......................... 4.1.4 Losses and Efficiency ....................... 4.1.5 Size and Weight Comparison ................... Control of PMAC ................................. 5.1 Back EMF Methods ........................... 5.2 High Frequency Injection Control .................... 5.3 High Frequency Model .......................... 5.4 General Concept of High-Frequency Injection .............. 5.5 Injection of Oscillating Current Space Vector .............. 5.6 Implementation of a Controller without Rotor Position Sensors . . . . Saturation ....................................... 6.1 Theory ................................... 6.2 Nonlinear model approach ........................ 6.3 Error Signal with Saturation Offset ................... 6.4 FEA Characterization of the Machine .................. SPM Machines Control Under Saturation ................. 7.1 High—Gain Observer for Control of SPM Machines Under Saturation without Position Sensors ......................... 7.2 Observer Gains and Tracking Errors ................... 7.3 Eliminating 180° Ambiguity at Startup ................. 7.4 Controller for SPM Machine ....................... 7.4.1 I-ligh-Frequency Injection Methods ............... 7.4.2 Control Based on Back EMF Measurement ........... 7.5 Experimental Results ........................... 8 Conclusion ...................................... BIBLIOGRAPHY ......................................... 73 74 74 78 78 83 84 85 86 86 87 89 91 94 104 103 105 109 110 114 116 121 122 123 123 125 127 137 3.1 4.1 4.2 4.3 4.4 4.5 4.6 7.1 LIST OF TABLES Modulation Index and Correction Factors .................... 67 Specification of the IPM machine .................... 76 Specifications of SPP=2 / 7 Machine ................... 78 Specifications of SPP=1 / 2 Machine ................... 78 Maximum Torque of SPM with Various SPP .............. 81 Summary of losses for the two machines ................ 82 Summary of size comparison ....................... 83 Experimental Results ........................... 127 1.1 1.2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3.1 3.2 3.3 3.4 3.5 3.6 LIST OF FIGURES Series HE Bus ............................... 6 6L Diesel Engine Fuel Map ........................ 8 PMAC with Exterior and Interior Rotor T.J. Miller [46]. ....... 16 Location of the permanent magnets in PMAC, Gieras [7] ........ 18 Wmding layouts: a) Distributed, b) Concentrated ........... 20 End Windings Comparison ........................ 20 A principle block diagram of the current vector control of PMSMs [47] 25 Phasor Diagram of PMSM [28] ...................... 26 SPM Machine Reluctances ........................ 28 Equivalent Circuit of Reluctances in SPM ............... 28 Single layer winding and Coil Boundries [13] .............. 33 Winding placement for mutual inductance calculation [45] . ..... 36 Doubly cylindrical device with arbitrary placement of windings [45] . 37 Full Pitch Concentrated Winding, Lipo [45] .............. 41 Turn and winding fimctions for an Nt-turn, full pitch coil. [45] . . . . 43 Cosine symmetric winding function Nc(¢*). [45] ............ 43 3.7 Turns and winding fimctions for a fractional winding, Lipo [45] . . . . 3.8 Core losses for US. Steel M36, 29 Gauge ....... - ......... 3.9 US. Steel M36, .............................. 3.10 Measurements of a Specific Core Loss [49] .................... 3.11 Specific Core Loss of MlQ Steel Modulation Index = 0.3 ....... 3.12 Outer Rotor SPM Machine ........................ 4.1 SPM and [PM rotor configuration considered in the comparison . . . 4.2 l8—pole, 6kW IPM Machine ....................... 4.3 Torque, Power and THD of 6kW SPM and IPM Machines ...... 4.4 Concentrated Winding SPM with 2/ 7 SPP ............... 4.5 Concentrated Winding SPM with 1/2 SPP ............... 4.6 Power—Speed Curve ............................ 4.7 Torque Vs. load angle for SPM with 24 slots .............. 5.1 d,q -axis equivalent circuits, Ji-Hoon [41] ................ 5.2 Windings and flux paths in two—pole SNIPM machine. Ji-Hoon [41] 5.3 Block diagram of the Signal Processing [41] ............... 5.4 Controller for Rotor Position and Speed Estimation [41] ........ 6.1 Phasor Diagram of Flux Under Load .................. 6.2 Leakage Flux ............................... 6.3 Magnetic Axis Shift Vs. Current 1}, ................... 6.4 FEM Characterization of the Machine ................. 45 59 61 63 67 68 77 77 78 79 80 82 91 99 101 104 104 110 6.5 6.6 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 Flux Distribution of the SPM Machine under No-Load ........ 113 Flux Distribution of the SPM Machine under 50% of Hill-Load . . . . 113 Block Diagram of the SPM Machine Controller ............ 1 16 Popov Criterion Loop ........................... 1 18 Experimental Measurement of Inductance .................... 128 Block Diagram of the High-Frequency Injection Control Algorithm . . 129 Performance Comparison at Rated Current [.1 = 8A .......... 130 Observer Performance Comparison at No-Load Current ....... 131 Observer Performance Comparison at Rated Current 1.1 = 8A 133 Outer Rotor PMAC Machine ...................... 134 State Diagram of the Controller for Entire Speed Range ........ 134 CHAPTER 1 Introduction This chapter will outline the objectives, contributions and organization of this disser— tation, provide an introduction into Hybrid Electric Vehicles (HEV) and a literature survey on PMAC Machines for Integrated Starter-Generator (ISG) Application as well as the literature survey on the operation of Surface Permanent Magnet Machines (SPM) under saturation. 1. 1 Objectives and Contributions The goal of this work is to solve a two-fold problem related to Integrated Starter- Generator (ISG) in Series Hybrid-Electric (SHE) Bus, design and analysis and oper- ation and control. 1.1.1 Design and Analysis The first part deals with analysis, selection and design of the best PMAC machine candidate for this application. The literature survey shows the following shortcom- ings in the PMAC machine analysis for the given application: Little work has been done on comprehensive comparison of various PMAC machines for ISG applications in Series I-IE Vehicles. Size and weight comparison is often neglected in the per- formance assessment even though it is a crucial factor in automotive applications. While ample of literature exists on analysis of PMAC machines, these tools presented are inadequate for concentrated winding tOpologies. Moreover, SPM Machines are usually not considered for ISG applications, because of their poor performance in constant power region i.e. less speed range than IPMs. In [13]. El-Rcfaie compared various Slot / Pole/ Phase combinations of SPM machines, but not the 1/2 SPP topol- ogy. In that work 2 / 7 SPP machine was selected as the most suitable one because of its extended speed range. In the work presented in this dissertation, the 2 / 7 SPP machine designed by El-Refaie, is used as a starting benchmark point in designing and selecting the best suited PMAC machine for ISG application in Series HEV. The contributions of this work are: 1. Comprehensive analysis and comparison of Interior Permanent Magnet Ma- chines vs. Surface Permanent Magnet Machinm for ISG Application C—4. 2. Analysis and comparison of distributed vs. concentrated windings, as well as the analysis of various Slot / Pole / Phase combinations (including 1 / 2 SPP topology) with respect to machine size, minimal losses and highest torque capability C—4. 3. Tools for analytical design and performance assessment of SPM Machines with concentrated windings are derived and discussed. In particular, improved mod- els for core and magnet losses of fractional slot SPM machines are derived C—3. 1. 1.2 Operation and Control under Saturation The second part of this work focuses on the operation and control of a PMAC machine for the given application. In particular the issue of control of SPM Machines under saturation is explored. The major contributions are: 1. Nonlinear model and characterization of SPM Machine under saturation C-6. 2. Design, analysis emd verification of a general algorithm for the control of SPM machines under saturation C—7. First a model of a saturated SPM Machine is presented and the detrimental effects of saturation on machine performance are discussed. The High-Gain Nonlinear Observer of the rotor flux is designed for the entire operating range of the machine, including saturation. To verify the performance and effectiveness of the designed observer, two existing control strategies, one utilizing high-freaquency injection method (for startup and low speeds) and the other utilizing back EMF measurement method (for high speed operation) are implemented in combination with the designed observer. Finally simulation and experimental results of the machine performance with the proposed observer are presented. 1.2 Organization of the Dissertation The balance of this dissertation is divided into the following parts: 0 Chapter 1, introduces the concept of Hybrid—Electric Vehicles, various power train configurations and advantages and challenges associated with each. The concept of Integrated Starter—Generator and its advantages and applications as well as the sizing of the generator unit for SHE vehicle are also discussed. Finally an analytical approach for assessment of the required generator size for the SHE vehicle is derived, based on the vehicle size, driving cycle and engine efficiency map. 0 Chapter 2 prsents an overview of the current PMAC machine technology, from various types of the machines used today, to vector control of the machines to, electromagnetic modeling of PMAC. Various rotor topologies with respect to magnet placement are presented, as well as different stator winding configura- tions i.e. distributed and concentrated windings. 0 Chapter 3 focuses on the development of analytical tools for the design and per— formance evaluation of Fractional Slot SPM Machines. Analytical calculations of winding resistance and inductance, winding ftmction, magnetic field in the air-gap, permeance ftmction, back EMF waveform, electromagnetic torque and c0pper, iron and magnet losses are presented. 0 Chapter 4 presents Finite Element Analysis of the machines under consider— ation and comparison with analytical results. Summary of losses, efficiencies and torquespeed curves for these are also presented. Finally maximum torque performance is evaluated of various Slot / Pole / Phase configurations for SPM machines. Experimental testing of 6kW prototype is also included. 0 Chapter 5 discusses the state of the art in control of PMAC machines. Both high-frequency injection and back EMF methods are analyzed as well as the issues and challenges associated with them. Specifically, the issue of saturation and its effect on both of the control strategies is addressed. 0 Chapter 6 presents an in—depth analysis and a non-linear model of SPM ma- chine under saturation. With the new model in place position-sensorless control of SPM machines is revisited and necessary improvements are discussed to ac- count for saturation induced errors. Finally Finite Element and experimental characterizations of the saturated SPM machine are presented. 0 Chapter 7 presents a controller of SPM machines under saturation without rotor position sensors. The analysis presented in Chapter 6 is used to design a new High-Gain Non—linear Observer for the operation of the SPM machine in saturated region. In-depth design and analysis of the observer performance and stability is presented followed by the experimental verification of the results. 0 Chapter 8 summarizes the work done in this dissertation along with conclusions and future work suggestions. 1.3 Hybrid Electric Vehicles Although it has only been seriously discussed in the last decade, the idea of electric vehicles goes back to nineteenth century. With improvements in internal combustion engines performance and efficiency throughout the last century, and more recent im- provements in electric motors, battery technology, power electronics and increasing Battery DCLinkCap% Figure 1.1: Series HE Bus awareness in ecology and fuel consumption, the idea of combining the two propulsion means appears to be the most reasonable solution. Several variations of the hybrid combinations are available which can all be classified into four categories series, par- allel, series-parallel or mild hybrid powertrain, with each configuration having its advantages and disadvantages and best suited applications as described in [1]. In a Series Hybrid System, the engine is not directly linked to the transmission for me— chanical driving power. All of the energy produced by the engine is converted to electric power by the generator, which recharges the energy storage device in order to provide power to the electric motor as shown in Figure 1.1 The electric motor system provides torque to run the wheels of the vehicles. Be- cause the combustion engine is not directly connected to the wheels, it can be operated at the optimum rate, and can be automatically turned off for temporary all-electric, zero emission operation. Series hybrids are most suitable for commuting vehicles such a transit bus, which frequently stop and go. In a Series Hybrid Electric Vehicle (SHEV) system, by adding an electric motor to provide the power during accel- erations, the engine can be smaller than that of a conventional vehicles [1]. This work focuses on urban mass transpOrtation vehicles, hybrid electric buses with series powertrain configuration. Heavy duty busses present excellent camdidates for hybrid vehicles because of their size, which translates into a capability to store larger batter- ies and electrical machines required. Compared to passenger cars, busses operate at lower speeds, limited acceleration, and usually less road grades; which all contribute to lower demand on the electrical system. Because of frequent stops a significant amount of energy can be recovered through regenerative breaking. 1.3.1 Integrated Starter / Generator In the last several years there has been an increasing interest in integrated starter- generator (ISG). Starting rotating machines from a battery source has been increas— ingly used in a wide range of automotive, household and military applications. More over it is particularly attractive in automotive, aircraft and portable generator indus- tries, where volume and weight reduction are major requirements. In mild hybrids the integrated starter/ generator machine must be designed to have a wide speed range operation, which is why traditionally this role was reserved for induction or interior PMAC machines, because of their excellent field weakening capabilities. In series hybrid vehicles the generator is designed to operate at one fixed speed and variable torque to optimize the engine efficiency according to the fuel map shown in Figure 1.2. Torque [Nm] 0 ; . . ; 0 500 1000 1500 2000 2500 3000 Speed [RPM] Figure 1.2: 6L Diesel Engine Ere] Map x In addition, to be used as a starter, this machine should be capable of producing high torque at zero and low speeds. It is now apparent that with these new redefined requirements a range of different machines can be considered for this purpose. 1.3.2 Sizing the Generator Given the series configuration of the HE bus, the sizing of a generator must take into consideration the most efficient conditions of the IC engine, in terms of fuel consumption and emissions, which in practice can be accomplished by keeping the operating speed constant and allowing small torque variations as shown in Figure 1.2.We define two operating modes of the HE bus; Mode I - Summer Mode i.e. with air conditioning and Mode II - Winter Mode i.e. without air conditioning. Instead of having continuous torque variation we will simply assume that the engine will operate at two discrete operating points, T1 and T2, shown in Figure 1.2, corresponding to two Operating modes I and II respectively. It is obvious that we must size the generator to satisfy the maximum power requirement, which means operation with air conditioning or Mode I. From this point on we can assume that the generated power will be kept constant, independently of the load demand. The most obvious choice of the generator output power in such case would be given by: PGEN = P00 (11) where PDC is the instantaneous required power from the DC bus including both power for propulsion motors and auxiliary electrical loads. In this case the average power required for traction and electrical loads will be supplied by the generator, while the transients will be covered by the battery unit. On board battery recharge from the generator is not possible, but rather only energy used for battery charging will come from the regenerative breaking. This approach may cause the battery SOC to fall very low at times, reducing its lifetime dramatically. In order to avoid this problem initial and final SOC during a drive cycle must be taken into account when designing the electric generator of the series HEV. At the very minimum we must ensure that: SOCEND Z SOCMIN (1-2) or for the upper limit of the generator size SOCEND = SOCSTAR’I' (1-3) Satisfying this condition will ensure the bus availability for the next trip without necessary st0p for "plug in" battery recharge. We can now rewrite the generator power equation (1.1) as: PGEN = P00 + PBAT (1-4) Where the PB AT will ensure recharge of the battery. In the interval when the vehicle operates in fully electric mode, the battery will be the only source of power delivering energy E B AT- During the time when the generator is on, it should deliver energy supplied by the battery and fulfill the requirements of PDCSO we can write the following: r t1 EBAT + [t PDC — 1’01;th aPDC > PGEN EGEN= t (1-5) EBAT .1000 < PGEN where t -— t1 is the time interval the generator is on. So PB AT can be calculated as =EBAT (1.6) 10 1.4 Survey of PMAC Machines for ISG With respect to hybrid vehicles, integrated starter—generator configuration has only been seriously explored in so called mild hybrid topology, while little has been pub- lished on full hybrids and in particular on series hybrid configuration. Cal in [2] presents a comparison of electrical machines for integrated starter—generator appli- cations in mild hybrids, but quickly excludes the SPM machine because of the wide speed range requirement. Friedrich et al. in [3] provided an optimization procedure for the design of PMAC ISA, but only IPM machines are considered, due to excellent field weakening range. Nagorny et al. in [4] compared several different rotor struc- tures for a similar application to conclude that the SPM machine was best suited, based on torque and THD analysis, but no results on distributed and concentrated windings comparison are available. Similar studies were carried out by both Salminen in [5] and Cross in [6], with conclusions that less magnetic material is required for the same size SPM machine compared to the IPM but only for distributed winding ma— chines. No results are given for the concentrated windings machine. Moreover these authors have focused on assessing output torque and power capabilities of the ma- chine while ignoring the analysis of losses, size and weight. Cros and Viarouge in [7] presented a study about the use of concentrated windings in a high-performance PM machines. They identified the various slot / pole combinations that can support three- phase concentrated windings. They also presented a systematic method to determine the optimum concentrated winding layout in both cases of regular and irregular slot distribution. They provided guidelines for identifying the slot / pole combinations that 11 can provide high machine performance and analysis results for sample designs using concentrated windings, showing that the performance of these machines is better than that of traditional machines with one slot / pole/ phase. There is minimization of both copper volume and Joule losses, reduction in the manufacturing cost and improvement in the output characteristics. The effect of the winding factor on the Joule losses has been discussed by the same group. A comparison of the Joule losses, cogging torque and axial length of conven- tional distributed 1 slot / pole/ phase winding, single-layer concentrated winding, and double layer concentrated winding has been presented. It was shown that by choosing the appropriate slot / pole combination, concentrated windings have lower Joule losses and cogging torque compared to distributed windings. Also it was shown that the double-layer concentrated windings has the shortest axial length and hence has the greatest potential to be the most compact unit among the three winding configura- tions under consideration. Ishak, Zhu and Howen in [8] , [9] compared the eddy current losses in the magnets for both winding configurations. It was shown that the single layer winding induces higher eddy current losses in the magnets due to the higher special harmonic content. Libert and Soulard [11] investigated various slot / pole com- binations for surface PM machines equipped with concentrated windings. Among the considered factors were the winding factors, M A! F harmonic content, torque ripple, and radial magnetic forces that cause vibration and noise. Reichert [12] discussed the advantages and disadvantages of using concentrated windings in large synchronous machines for low speed high torque applications. He indicated that the eddy current losses in the magnets might be a limiting factor for using concentrated windings in 12 high speed applications. In [13] El—Refaie proposed a fractional slot PMAC machine with 2 / 7 slot / pole/ phase (SPP) configuration as the best candidate for this appli- cation, however the comparison has not been carried out with respect to 1 / 2 SPP configuration. In this work (Chapter 2—4) a 2 / 7 SPP SPM Machine designed by El—Refaie in [13] is be used as a starting point and the comparison is carried out with a 1/2 SPP machine. 1. 5 Operation of SPM Machines Under Saturation In the last decade, as the efficiency of electric drives has become a more important and desirable characteristic, Permanent Magnet Synchronous Machines (PMSM) are rapidly replacing induction machines. Rotor position information is necessary for Field Oriented Control (FOC) of Permanent Magnet Synchronous Machines (PMSM). It is particularly attractive to obtain the rotor position information without shaft sensors, since they increase the cost of the overall system and degrade the reliability. It is well documented in the literature that the error in the estimate of rotor position increases with the load current [14]. Guglielmi et al. showed in [15] that an error exists in rotor position estimation due to cross-magnetic saturation between d- and q—axes. Stumberger et al. in [16] evaluated the effect of saturation and cross-magnetization for IPM, but offered no compensation for the error. Li et al. in [17] studied modeling of the cross-coupling magnetic saturation in a specific position-sensorless control scheme based on high-frequency signal injection. Zhu et al. in [18] proposed a practical 13 approach for mitigating the rotor position error due to saturation in high-frequency injection method. However, operation and flux position detection in SPM machines is affected by magnetic saturation regardless of the control strategy and requires correction at the model level. Harnefors et al. in [19] studied a general algorithm for control of AC motors and noted the existence of the error in rotor position estimation due to saturation, but the analysis focused only on the unsaturated case. Moreover the error signal was linearized making their conclusions local only. It will be shown here that although this error may be relatively small, it has a significant detrimental effect on the machine performance. In this work we will focus on operation of SPM machines under magnetic satura- tion. The major contributions of this part are nonlinear model and characterization of SPM machine, and design, analysis and verification of a general algorithm for control of SPMAC machines under saturation. It will be presented in three sections: the non-linear model and characterization of the SPM machine under saturation, in-depth analysis of the non-linear observer struc- ture adjusted for the presence of saturation without linearizing the error signal and experimental results validating the derived non—linear model of the machine, impact of saturation induced error on machine performance and validation of performance of the prOposed observer combined with high frequency injection position-sensorless controller presented by Jang et al. in [22]. It is important to note that although the work presented here is focusing on the observer implementation in conjunction with high frequency injection method, it can be used in combination with any control 14 strategy including back EMF methods or methods utilizing position encoder feedback. 15 CHAPTER 2 Permanent Magnet AC Machines This chapter presents an overview and introduction into PMAC machines, rotor topologies with respect to magnet placement and configuration and concentrated and distributed winding configurations. The concept of vector modeling and control as well as the electromagnetic model of the PMAC machine are also presented. 2. 1 Overview In the last decade as the efficiency of electric drives has become a more important and desirable characteristic, Permanent Magnet Synchronous Machines (PMSM) are rapidly replacing induction machines. Moreover PMSM offer high power density, so they are more suitable in the applications requiring volume reduction i.e. automo- tive, aircraft and portable generator industries. A permanent magnet synchronous machine is basically an ordinary AC machine with windings distributed in the stator slots so that the flux created by stator current is approximately sinusoidal. Quite 16 PERMANENT 12 SLOT MAGNET STATOR / ... @000 D C) 00599 ' 4 POLE PM ROTOR a) b) Figure 2.1: PMAC with Exterior and Interior Rotor T.J. Miller [46]. often also machines with windings and magnets creating trapezoidal flux distribution are incorrectly called permanent magnet synchronous machines. A better term is Brushlefi DC (BLDC) machine, since the operation of such a machine is similar to that of a traditional DC machine with a mechanical commutator, with the exception that the commutation in a BLDC machine is done electronically. The work presented here concentrates on permanent magnet synchronous machines (PMSMs) with a si- nusoidal flux distribution. Rotating permanent magnet synchronous machines used today come in two different configuration; interior and exterior rotor as shown in Figure 2.1. 2.2 Permanent Magnet Rotor Topologies The most commonly used construction for the PM motors has the permanent magnets located on the rotor surface. Herein, this motor type will be called surface magnet 17 motor for simplicity. In a surface magnet motor the magnets are usually magnetized radially. Due to the use of low permeability rareearth magnets the synchronous inductances in the d— and q —- axes may be mnsidered to be equal which can be helpful while designing the surface magnet motor. The construction of the motor is quite cheap and simple, because the magnets can be attached to the rotor surface. The embedded magnet motor has permanent magnets embedded ‘ in the deep slots. There are several possible ways to build a surface or an embedded magnet motor as shown in Figure 2.2 from [7], a) surface mounted magnets, b) inset rotor with surface magnets, c) surface magnets with pole shoes producing a cosine flux density, d) buried tangential magnets, e) buried radial magnets, f) buried inclined magnets with cosine shaped pole shoe, and g) permanent magnet assisted synchronous reluctance motor with axially laminated construction. In the case of an embedded magnet motor, the stator synchronous inductance in the q — axi s is often greater than the synchronous inductance in the d — axis. If the motor has a ferromagnetic shaft a large portion of the permanent magnet produced flux goes through the shaft. In order to increase the linkage flux crossing the air-gap, embedded—magnet motor mat have a non-ferromagnetic shaft. Another method to increase the flux crossing the air gap is to fit a non-ferromagnetic sleeve between the ferromagnetic shaft and the rotor cone [7]. Compared to the em- bedded magnets, one important advantage of the surface mounted magnets is the smaller amount of magnet material needed in the design (in integer-slot machines). If the same power is required from the same machine size, the surface mounted magnet machine needs less magnet material than the corresponding machine with 18 Figure 2.2: Location of the permanent magnets in PMAC, Gieras [7]. embedded magnets. This is due to the two facts: in the embedded-magnets—case there is always a considerable amount of leakage flux in the end regions of the permanent magnets and the armature reaction is also worse than in the surface magnet case. Zhu et al. in [26] reported that the embedded magnet structure facilitates extended flux-weakening operation when compared to a surface magnet motor with the same stator design (both machines are equipped with an integer slot winding). They also stated that the iron losses of the embedded magnet machine were higher than that of the machine with surface magnet rotor. However, there are several advantages that favor the use of embedded magnets. Because of the high air-gap flux density, these machine may produce more torque per rotor volume compared to the motor which has surface mounted magnets. This, however, requires usually a larger amount of PM— material. The risk of permanent magnet material demagnetization remains smaller. The magnets can be rectangular and there are less fixing and bonding problems with the magnets: the magnets are easy to mount into the holes of the rotor and the risk of damaging the magnets is small [46] . Because of the high air-gap flux density an embedded magnet low speed machine may produce a higher efliciency than the similar surface magnet machine. 2.3 Windings A permanent magnet machine can have a variety of winding structures as shown in Figure 2.3, a) distributed windings, b) single—layer concentrated windings and c) double-layer concentrated windings [13]. Early and large PMAC machines have used sinusoidally distributed windings, while in the last several years, for smaller machines the concentrated winding structure has been increasingly explored due to their short end windings and simple structure suitable for high volume automated manufacturing. They are not yet frequently used in larger electrical machines, where efficiency and smooth torque production are more important. This can change if the traditional drawbacks of the winding type, i.e. high torque ripple and low fimdamental winding factor, can be mitigated. Cros and Viarouge in [7] discovered that this motor type has a higher performance than the motor type with regular distribution of the slots. The copper volume and copper losses in the end windings are reduced. The end windings of a traditionally wound machine need more space (which, again, requires more copper volume and mass), because different phase coils cross each other. In the concentrated fractional Figure 2.3: Winding layouts: a) Distributed, b) Concentrated slot wound machine the space needed, in the end tumsregion, for the conductors to travel from one slot to the next one is as small as possible, as the example illustrates in Figure ?? b) where the coil is wound around one tooth. However, the two—layer winding type produces the smallest end windings as it is shown in Figure '3? c. There are several attractive advantages that result from the use of concentrated windings around the teeth: 1. Significant reduction of the copper volume used in the end region, especially in the case of short axial-length machines. This is clear comparing Figures ??, a,b and c [46]. 2. Significant reduction in the Joule losses in the end region due to shorter end turns. Murakami et a1. [27]. 3. Improved efficiency compared to the classical distributed winding configuration with one slot per pole per phase [13]. 4. Reduction in cost made possible by simplified manufacturing [13]. 21 5. Easier to fabricate compared to the distributed lap winding, particularly when the stator can be segmented into separate stator poles. 6. Significantly higher slot fill factor (up to 78 %) can be achieved, where slot fill factor is defined as the ratio of the copper area to the total area of each slot compared to typical 60% in distributed windings. Murakami et al. [27] 7. Concentrated windings can be used in the design of modular PM brushless machines with higher numbers of phases to improve fault tolerance. They also can be used in high-phasenumber machines to increase the specific torque [28] . Challenges involved in using concentrated windings are: 1. The spatial Al Al F distributions in the machine air gap that result from con- centrated windings deviate significantly from sinusoidal waveforms, so that d—q transformation loses accuracy. 2. Assumptions needed for classical phasor analysis are not correct. 3. Risks of elevated torque ripple and low winding factors [13] . 4. Potential for higher acoustic noise and vibration [l3] . 2.4 Control of PMAC Machines In order to be utilized to their highest potential, PMACs have to be controlled by employing field oriented vector control techniques. Since all the control is done in the rotor frame of reference, knowledge of the accurate rotor position is necessary. 22 Figure 2.4: End Windings Comparison Shaft position and speed sensors have been used for decades for this purpose; however their employment drives up the cost of the overall syst- and significantly degrades the reliability. Considering these disadvantages of position sensors, it is obvious why researchers and application engineers have been focusing their efforts on developing robust position-sensorless drives for PMSM. 2.4.1 Current Vector Control Principle The earliest vector control principles for AC permanent magnet synchronous machines resembled the control of a fully compensated DC machine. The idea was to control the current of the madrine in space quadrature with the magnetic flux created by the permanent magnets. The torque is then directly proportional to the product of the flux linkage created by the magnets and the current. In an AC machine the rotation of the rotor demands that the flux must rotate at a certain frequency. If the current is then controlled in space quadrature with the flux, the current must be an AC current in contrast with the DC current of a DC machine. The mathematical modelling of an AC synchronous machine is most conveniently done using a coordinate system, which rotates synchronously with the magnetic axis of the rotor, i.e. with the rotor. The x—axis of this coordinate system is called the direct or ”(1" axis and the y-axis is the quadrature or "q" axis. The magnet flux lies on the d — axis and if the current is controlled in space quadrature with the magnet flux it is aligned with the q — axis. This gives a commonly used name for this type of the control, "id = 0" —control. Unfortunately this type of control is not appropriate for all permanent magnet machines. The problem is that the air-gap flux is affected by the flux created by the current and the inductance of the machine. This is called the armature reaction. Moreover, if the magnetic circuit of the machine is not symmetric in the directions of d— and q—axes, the difference in reluctances can be utilized in the torque production. If the direct axis current is zero, this reluctance torque is also zero. Different d— and q— axis inductances are a result of different d— and q — axis flux reluctance. If the magnets are mounted on the rotor surface, both the d — axis and the q — axis fluxes must go through the magnet. The relative permeability of the rare earth permanent magnets is near unity, which means that permanent magnets behave like air in the magnetic circuit. The so called effective air—gap is therefore very large and the inductanca due to the large air-gap are quite low and nearly equal in d— and q - axis. If the magnets are mounted in slots inside the rotor, the magnet flux paths are quite different. Not all the flux has to go through the magnet and a considerable difference between the d — axis and the q — axis inductances is possible. Since the q — axis flux does not always necessarily go through the magnet, usually the q — axis 24 inductance is bigger than the d ~—axis inductance. This is different from the separately excited synchronous machine where the d — axis inductance is bigger. The reluctance torque resulting in the inductance difference can and should be utilized in the control. Analytical expressions for current references which maximize the ratio of the torque and the current were first formulated by J ahns et al. in [3]. This kind of control is generally called the maximum torque per ampere control or minimum current control. In this work the term current vector control is used for all control methods, which control the torque via controlling the currents. Figure 2.5 presents a principle block diagram of the current vector control of PMSMs. The control system consists of separate controllers for the torque and the current. Measurement or estimation of the rotor angle is needed in the transformation of the d— and q — axis current components into fixed coordinate system. 2.5 PMSM Modeling 2.5.1 Vector Control Model As described earlier the polyphase PMSM control is rendered equivalent to that of the dc machine, by decoupling control known as vector control. It is also explained that the performance of the machine can best be understood in dq axis frame. It is therefore sensible to control the machine in this reference frame. In this section the model of the PMSM machine for vector control is derived. Since the interest is in 25 ##— Rectifier :11: Inverter ‘ PMSM Current I Control i e d 1 .1. , Torque dq in 2 Control , “P ——’i 3 lq T p 6 Figure 2.5: A principle block diagram of the current vector control of PMSMs [47] current control, we consider the three phase current inputs as follows: ins = is =1: sin(wrt + 6) (2.1) . - . 27r lbs = 23 * sm(w,~t + 5 — —3- (2.2) ies = is * sin(w,-t + 6 + 23:) (2.3) where w, is electrical rotor speed Md 5 is the angle between rotor field and the stator current phasor Figure 2.6, known as the torque angle. The rotor field is traveling at a speed of car ; hence the q and d axes stator currents in the rotor frame of reference q—axis Vqs Is 4 I’ 8 6’" vds , ’ . r is ‘I 4: 95 \ Ids 1p.“ 0r Stator Frame of Reference Figure 2.6: Phasor Diagram of PMSM [28] for a balanced three-phase system are given by: ias £23 (:06th c05(Wrt — 23E) ms(w,-t + 231: ills sin wrt sin(w,-t — 2371) sin(w,-t + 2375) . ies by simplifying this equation we get: q. . zqs . sm6 = 13 -r ids c066 In addition one phase voltage of the machine can be written as: 27 (2-4) (2.5) dis Us = Rsis +L dt (2-5) and by following the same transformations as above we can write the complete PMSM model in the rotor frame of references with following equations: 12' R + L —w L if 0 ds 5 tip 1' 9 = d’ + (2-7) vgs erd R S + Lqp £sz er p M Additionally the torque of the PMSM is: 3 T62 515’ [APM*i;3+(Ld—Lq)*igs*igs]. (2.8) 2.5.2 Magnetic Circuit The analytical calculation of the operation of SPM motor is based on the reluctance circuit analysis shown in Figure ??. The equivalent reluctance circuit of SPM is represented in Figure 2.7. The stator iron reluctance R Fe consists of the stator teeth R; and yoke R3 re- luctances. p M is the total magnetic flux of the permanent magnets and (In; are additional leakage fluxes in the end regions of the permanent magnets. The air—gap reluctance R52 consists of the air between two magnets and the air-gap reluctance R6 lies in the minimum air—gap between magnet and stator. The reluctances of the air—gap and permanent magnets are calculated from their region and material char- 28 . e A R 5 2 [l RPM R8 2 CD ® PM Figure 2.7: Equivalent Circuit of Reluctances in SPM acteristics. 60 - = 2.9 Rd I‘oTpLi ( ) The reluctance of the air-gap between two magnets is: lm Rd = 2.10 2 #o(7'p - [plLi ( ) Reluctance of the permanent magnets is: l 1 RPM = m t (2-11) + The iron reluctances in the stator teeth and yoke can then iteratively be calculated. The first evaluation of the air-gap flux can be derived from the equivalent reluctance circuit (Figure 2.7). 4’6,PM = epMRPM (2-12) RPM + R6 + RFe(n) + “E;(R6 + RFe(n)) Because of the rectangular air-gap flux density, the flux densities in the stator teeth are constants above the permanent magnets: Li, u " —_ B 2.13 3:1 and become zero elsewhere. The air-gap flux density 85 is derived from the air-gap flux and width of permanent magnets 1,, as well as from the length L,-. ‘1’6,PM 35 = (2.14) The peak value of the first harmonic of the air gap flux density can be calculated as coefficients of Fourier series as shown by Gieras [42] . - 4 1 1r B- = —B P 2.15 a 65in (2.7—p) ( ) so the E IMF per phase induced by rotor excitation flux is calculated as - 4 1 1r Ba: —BJS:(— P ) (2.16) 27? p where C is the winding factor. We can now calculate the direct and quadrature inductances as: 'm8 1 L —— 2. qt:- , “nzmz’padq_m L.-( = fP (3.13) where P is the permeance of the flux of cross-section A and length l and f is the M M F drop across the length 1. Referring to Figure 3.3, the differential flux across the gap from rotor to stator through a differential volume of length 9 and cross section (W) is are = TA(¢)#0RI% (3.14) where .7: A is the M AIF due to winding A. The AIMF drop (and hence flux) is 37 Figure 3.3: Doubly cylindrical device with arbitrary placement of windings [45] considered positive from rotor to stator. ThetotalfluxlinkageofwindinngromcurrentinwindingAisdesired [45]. One can asign the number “1” to the first conductor carrying current into of the page and “1’” to the first conductor encountered defined as carrying current out of the page. Similarly, the second conductor encountered with current into the page is labeled as 2 and the second with current the opposite direction as 2’. One can continue with the procedure until all N B conductors have been accounted for [45]. The last two conductors are “N B” and “N13”. In Figure 3.2 the labeling promdure has been carried out for a simple three turn winding, N B = 3. Consider now the flux linking coil 1 — 1’. If coil side 1 is encountered first around the gap before , then the positive flux linking the one turn coil is [45]: ’ swig] lemmas (3.15) 9 «>1 Alternatively, if coil 1’ side is situated before 1 then the flux linking the coil is in the negative sense so that ' ‘1’14 = "yo—rt: / lJ"'A(<;5)al<1> (3.16) g 31 Either situation can be accounted for if 3 turns function n Bl ((6) is defined which is zero from (b = 0 until $1 or whichever comes first. When ¢ = (b1 (or) the turns function then jumps from O to 1(or —1) and remains at 1(or —1) until (1) reaches at which point n31(¢) abruptly returns to zero. With this definition of the turns function n31(¢), the flux linking turn #1 for either case is <1” I (pl—1’ z I“: All nBl(¢)-FA(¢)d¢ (3.17) Since n Bl(¢) is zero when 45 takes on value outside the span of the integral, it can also be written: 1 Zn ‘ ‘1’1—1' :51??? f0 nBl(¢)-FA(¢5)d¢ (3.18) This process can be continued for all turns. The flux linking the N B th turn is [45]: _ m 21r . q’Nb—Ng- g [0 "Nb(¢)fr(¢)d¢ (3.19) The total flux linking the winding is found by summing all N A fluxes defined as in 39 [45] , or NA porl ABA =. Z‘I’j—j’ = 9 NA 21r 2:; [0 eschew j=l rl 2“ NA = ”g [0 [1; am] new (320) The term in the parenthesis, however, is simply the turns frmction for the A winding [45] . Defining N A "3(9‘5) = 2 am) (3.21) i=1 the flux linkage of winding B due to a current winding A becomes T 2! ABA = a; [0 ”(screw (3.22) The mutual inductance L B A is defined as the flux linkage of winding B divided by the current flowing in winding A so by substituting (3.12) we can write the following 2x LBA = A513 = fl!- / "B(¢)NA(¢5)d¢ (3-23) 13 9 0 It will be shown in the next section that the turns fimction can be expressed as [45]: "3(95) = NEW) + ("Bl (3-24) where n31(¢) is the winding fimction for the B winding and < n B > is the average value of the turns frmction, so we can rewrite (3.23) as [45]: l 27f ' l 211' LBAJ-‘g— [0 NB(¢)NA(¢)d¢+E';i 0 (nB>NA(¢)d¢ (3.25) Since < n B > is simply a constant, it can be removed from inside the second integral. More over, the winding function N A(¢) is periodic with zero average value, so that the second term is zero. Hence, finally [45]: TI 211' LBA = NB(¢)NA(¢)d¢ (326) From (3.23) it is clear that reciprocity holds, since the order of the two winding fimction may be interchanged [45]. Therefore, LAB = L B A- Alternatively, if one had started the problem assuming instead an M M F distribution for winding B and calcu- lated the flux linking winding A, the result would have been the same [45] . Equations (3.23) and (3.26) are equivalent expressions for mutual inductance. Although use of (3.26) is generally preferred, (3.23) will be of use when considering the mutual in- ductance of concentrated windings. Through this analysis, no restrictions were made on winding placement. That is, either winding (or both) can be located on the rotor as well as the stator. Moreover, the results that have been derived are clearly valid for cases where windings A and B are one and the same. Hence, the inductance of winding A associated with flux crossing the air gap (magnetizing inductance) is given by the integral [45]: l 21r LAA = ”g 0 N3(¢)d¢ (3.27) 41 N Figure 3.4: Ell] Pitch Concentrated Winding, Lipo [45] As a simple introduction to the calculation of winding inductances reconsider the case of the nt turn concentrated, full pitched winding shown in Figure 3.4 [45] .The winding function which has been derived has been plotted in Figure 3.5 for a two pole winding. Since N343) is simply a constant equal to N3/4 integration of (3.27) yields [45]: I L M = Bil—NZ: (3.28) Following this example and changing the winding pitch and appropriate winding flmction we can calculate the self and mutual inductance of any concentrated winding machine. 42 3.3 Winding Function Consider initially the cylindrical structure of Figure 3.4 [45] . Here, one continuous winding with at turns is assumed to be concentrated at two points within the machine as shown. It can be noted that the positive coil side is placed diametrically opposite to the negative coil side. Such a winding spanning 1r radians is called a full pitch winding [45] . The reference position for the angle (ii is arbitrarily chosen in the horizontaldirection. Visualizealineintegral 1—2—3—4—1 crossingtheairgap from stator to rotor at the reference point then crossing back over from rotor to stator at an arbitrary angle measured counter-clockwise from the reference position [45] . A typical line integral is shown in Figure 3.4 where 96 = 40°. It should be noted that the line integral 1 — 2 —3 — 4— 1 is taken in the clockwise direction [45]. The number of turns enclosed by the line integral for the case illustrated is clearly zero. When ()5 = 60° the line integral encloses nt turns [45]. Since the line integral is taken in the clockwise direction, by the right hand rule, positive current enclosed by the path are directed into the page. However, since the winding current has been defined as out of the page, the number of turns enclosed is negative and the turns flmction n(¢) abruptly jumps from zero to —nt at d) = 60°. The flmction remains at at until 45 reaches 240° at which point nt positive turns are enclosed so that the function jumps back to zero [45].The resulting function is plotted in Figure 3.5. Since n(¢) is non—zero only over the range 7r/3 < qfi < 47r/3, the average value of n(¢) is l 47r/3 . Nt (n) -- 5; [#3 (—Nt)de = 7 (3.29) 1r/ 3‘ 1r{2 rlr 35/2 2p ’4) -N.— I I a) NW)‘ n/3 2n Nt/Z it I , n l I l 1 ’(l) "Nt/Z' b) N(‘l’*)“ n/Z 21c Nt/Z—I 7.‘ r——. -43. ‘Nt/Zb I I Figure 3.5: Turn and winding flmctions for an Nt-turn, full pitch coil. [45] N :l: C“) ) Nt/Z | W2 | | l— 3* _J _. | J3n/2 | I7n/2 -Nt/2 Figure 3.6: Cosine symmetric winding function Nc(¢*). [45] From (3.12) the winding flmction is simply the turns flmction n(¢) translated by nt / 2. The function has even symmetry if ¢* is chosen such that [45] 45* = ()5 + 1r/6. The unsifted and shifted winding flmctions are plotted in Figures 3.5(b) and (c). In the case of the shifted winding flmction, the subscript “c” has been appended since this function for the case of at turns concentrated in a single slot has a special significance. In order to help facilitate analysis it is useful to express Nc(¢*) in terms of its Fourier components [45] . It is clear that the winding flmction is completely defined over the entire stator periphery when ranges from 0 to 211'. However, it is possible to consider the frmction to be repeated when ¢* ranges over the value 271' to 47r, 41r to 611’, etc [45]. Specifically, it is useful to assume Nc(¢*) as the periodic flmction shown in Figure 3.6. This function can then be described by a Fourier Series and the resulting series is commonly termed the winding series. It can be noted that since the fimction of Figure 3.6 has the desired even symmetry about (3* = 0, that is N(¢*) = N(—q‘>*) and hence the winding series for this function will contain only cosine terns [45]. The winding series for an nt turn, concentrated coil is [45]: 2N 1 1 NC = —t [cos (15* — - cos 395* + 7; cos 5¢*...] (3.30) 1r 3 0 Because the factor at / 2 appears continuously as the amplitude for the winding flmc- tion of a two—pole winding, the coeflicient of (3.30) is sometimes written 71' 7f (3.31) 45 Nil) 3) Nt - N1; /2 — l I l ,¢ n/Z 1t 31t/2 2n N(¢) b) Nt/z — “/2 I I l l .41 “Nt /2___A 8 l(_ LE N(¢*) c) N /2‘ /2 t l’.‘ . ll . 3* ‘Nt/Z _ _)IS I‘— l 2“ Figure 3.7: Turns and winding flmctions for a fractional winding, Lipo [45] where Np = in / 2 is the number of series connected turns per pole. (For this example the winding only has two poles [45]). We will now calculate the winding frmction of a fractional pitch concentrated winding machine by considering it to be a special case of the full pitch concentrated winding machine. The two winding sections are separated by an angle 5.Such a winding is fractional pitch winding [45] . If the reference position is located midway between windings, the resulting flmction n(¢) is shown in Figure 3.7(a) [45]. In this case the average value < n > of n(¢) is nt/2. The flmction N (¢*) is obtained by shifting N (¢) by 7r+s/ 2 radians, that is 43* = (Q' — 1r)—s/2. Figure 3.7(b) and (c) show winding functions for N ((6) and N (¢*) for this case [45] . The Fourier components for this winding distribution are of considerable interest [45] . Again: N (¢*) = —N(¢* + 1r) (332) and since N (915*) = N (-¢*) (333) the Fourier expansion again contains only odd cosine terms. The h harmonic compo— nent can be expressed as the integral [45]: 2 /2—E/2 N}, = _1_V£f cos h¢d¢ (3.34) 7r 2 —1r/2-E/2 sothat .,.._2Nt e ., 1 35 ,, 1 5e ,, Nc(q> )— 1r coszcosgb 3005 2 005395 + 5cos 2 c055¢ "] (3.35) It is useful to express N h in terms of the corresponding harmonic coeflicients for a concentrated winding. That is N h = kthh (3.36) The factors k), are termed the harmonic winding factors and are a means of relat- ing the harmonic components of a winding of arbitrary distribution to a common 47 reference. For the winding under consideration h—l flaws-'2: k), _ h _ 1 (3.37) 7‘3) or simply k), = cos 525- (3.33) It is evident that by the symmetry of the winding placement, all even harmonics have been eliminated. Moreover, if 5 is properly selected, then one additional odd harmonic can be eliminated. For example, for 5 = 1r / 3, then k3 = cos (3°12) => [:3 = 0 (3.39) Similarly it can be shown that for e = 175, then k5 = 0 etc [45]. It can be shown that two odd harmonies can be eliminated with three nt/3 turn coils displaced by unequal values of sland 52. However, since the spacing between windings is uniform, such an arrangement is generally impractical. Another possibility is to utilize unequal spaced slots but vary the number of turns per coil [45] . However, since the number of turns per coil is discrete and space in the slot is limited, specific harmonics can generally be minimized only, but not eliminated. In the case just considered the concentrated winding has been divided into two equal sections. In general, when the winding is separated into 1: sections (or coils) then k — 1 odd harmonics can be limited [45]. 3.4 Magnetic Field in the Air-Gap The magnetic flux density in the air gap is obtained by calculating the magnetic potential distribution in the air gap governed by the Laplacian equation and subject by appropriate boundary conditions as shown in [9], [25] and it is given by 131-(9.1") = Z KB(n)fBr(T)COS(nP9) (3.40) n=l,3,5... 3109.1“): 2 KB(n)fBo(T)Sin(nP0) (3-41) n=l,3,5... B,- (0, r) is the radial component of the magnetic field. 31(0, r) is the tangential component of the magnetic field. r is the radius [m]. 0 is the angular position with reference to the center of a magnet pole. p is the number of pole pairs. _ M n (4312—1)(%)2flp+2(%)nP—l—(A3n+l) Kszrzgp);—pl P +1 R 2"? u -1 R 2"? Rm 2"? art-(e) --::-[(-n) -(e—) ] (3.42) fBr(T) = (£71le + (gyrl (1:3) up“ (3.43) f..e=_(g)"”‘1+(g;)"fl(Jew (3.44) 49 and A3": ("P-5;) 347+; (3'45) This expression assumes the following: o Slotless machine - However in order to account for slotting the expression will be multiplied by the relative permeance function, which will be derived in the next section 0 ExternalrotormachineILn 1:. =8.3.1o—5—WT (3.87) 3 Bml Bm2 Bm3 kgHz T2 The calculations of kh, a h and bh is also straightforward, although somewhat more tedious. A system of three linear equations, formed by substituting D1 , 02 and D3 obtained from the three values of Bm into logarithm of equation (3.85), is to be 62 solved; 1 1n Bml Bbml ln Bml 1 1n Bm2 Bme 111 Bm2 L1 lan3 Bbmglang The system is solved for In k1,, ah and bh. The 1:), is then obtained as: kh=e with the following values obtained for this particular example lnkh kh = 0.023 ah = 1.582 bh = 0.147 3.10 Specific Iron Loss under PWM Supply Ink), ah bh (3-88) (3.89) PMAC machines are considered in this work are supplied by the 3—phase PWM In- verter. It is well documented in the literature that the inverter switching increases the iron losses in the machine. In [49] an experimental study of the specific iron losses on lamination materials was carried out and it was determined that the losses in larninations are affected by PWM supply and modulation index as shown in Figure (3.10). From the same figure it can also e seen that the iron losses are not impacted by the switching frequency, so for the purpose of this analysis, switching frequency will not be considered. In this section, a method for correcting a specific iron loss 2 l ESE mm?— EcD 958nm 25 5 10 15 20 Switching Frequency [kHz] 0 ..anlldanlllwlleulwlln % _ _ _ _ _ $55. $3 280 958mm 1.6 0.8 D [T] ensity Flux Figure 3.10: Measurements of a Specific Core Loss [49] of a material under PWM excitation is presented and applied to SPM machines core loss calculation. An assumption is made that the PWM switching will only influence the eddy-current induced loeses. Consider the equation for eddy current losses as described by Boglietti in [44]: T dB 2 _ peddy = 21rKef / (E) dt (3.90) 0 For non sinusoidal voltage, ignoring winding losses, voltage can be expressed as: dB v(t) = NSE (3.91) where N is the turn number, S is the section of magnet core. The relationship between the Em and the voltage can be expressed as in [44]: T / v(t)dt = 4NSBm (3.92) 0 combining with the equation (3.91) we can rewrite the eddy loss equation (3.90) as: K Peddy_PWM = 2“ mfg—2037113 (393) When the supply voltage is PWM, for Sine-Triangle PWM, the ratio between har- monic voltage vg and fimdamental voltage vcan be written as [44]: ’U _ 71111! (3.94) where: g = nN :l: h (3.95) n = 1,3,5... h = 3(2m — 1) :t l, m = 1,2,3... (3.96) 6m+ 1, m =0,1,... n = 2,4,6... h = (3.97) 6m— 1, m = 1,2,... where (X) J19) = Z (—1)’" 1 (3mm (3.98) m=0 m!I‘(h+m+l) is Bessel function, a is the modulation index, N is the ratio between carrier frequency and modulation frequency. The ratio of voltage rms value between SPWM supply and the fimdamental sinusoidal voltage is [44]: mm 2 ”ms purm SlIl nMih If N is high, the ratio of voltage means value between SPWM supply and sinusoidal supply can be considered equal to one. However at low modulation index values an adjustment is needed to account for the increase in the losses due to switching. Neglecting the increment of the excess loss under SPWM conditions, the eddy com- ponent of the magnetic losses of electric magnetic material with SPWM supply can be calculated as [44]: Peddy_PWM = Peddy_SIN + KPeddy_SIN (3-100) Modulation Index Correction Factor 0.1 0.9756 0.2 0.9053 0.3 0.7975 0.4 0.6645 0.5 0.5209 0.6 0.3807 0.7 0.2562 0.8 0.1564 0.9 0.0878 Table 3. 1: Modulation Index and Correction Factor where n is the adjustment factor defined as: mm 2 _ 2 n _ Z [41,, mm] (3.101) nMih The numerical relationship of n and the modulation index a is shown in the Table 3.1. 3. 1 1 Magnet Losses Several authors have addressed the i$ue of eddy—current losses in the magnets in case of surface and interior PM machines. There are three main sources of the eddy- current losses induced in the magnets. These are the stator winding space harmonics, the stator current time harmonics, and the space harmonics due to slotting effects. In surface PM machines, it can be assumed that the losses due to slotting effects can be neglected due to the large effective air gap. In general magnet losses in ferrates and bonded magnets are much lower compared to sintered magnets since they have 67 120 g / . E 80 (w » IN :3 / PWM 3 4o [ 0.00 1.00 2.00 Flux Density [1'] 400Hz- [ 20 1 :1 15 / '6 b x ..- E: 1° // sm 5,) 5 PWM 3| / 0 O 1 2 Flux Density [T]—-————100H2—4 Figure 3.11: Specific Core Loss of MIQ Steel Modulation Index = 0.3 Figure 3.12: Outer Rotor SPM Machine high resistivity.Atallah ct al. in [29] and later El—Refaie in [13] presented methods for calculating magnet losses in PMAC machines. However the models embed above were developed to include losses caused by the time harmonics of the stator currents and space harmoni 2 111 1.31, 0 S Iq g 2 L4 = (6-33) 1.35 — 0.03751 - iq, iq > 2 Figure 6.4a shows the variation of q — axis inductance & a function of iq. Figure 6.4b shows the variation of d — axis inductance, id = 0 for both cases since we are examining SPM machine. Figures 6.4c and 6.3 show the variation of the mutual inductance qu and magnetic axis shift as functions of iq. Figures 6.5 and 6.6 show the flux paths of the SPM machine, under no-load and 50% of full—load. The change in the flux path due to saturation is clear from the Figure 6.6. 112 q-axis Inductance d-axis inductance 0.510 -5 0 5 10 Cross-Saturation Induced inductance 0.5 -_10 -5 0 5 10 Current I q [A ] Figure 6.4: FEM Characterization of the Machine 113 77/4 5 " Mr?— I - 5% 3‘ i i ii Eff ”CAT": ' ., :Ty/I' l . ~L/y/ : l ' "7.7” . . 1 A .¥"‘ l/ - ‘ ~. 1 ,./ . in 3 l ‘l s - ' 1‘ a 9/ 4' ‘ ‘; M3} . I . , It I , :2 Figure 6.5: Flux Distribution of the SPM Machine under No-Load A r I2.3e-2 2.3e-2 l Figure 6.6: Flux Distribution of the SPM Machine under 50% of Full-Load 114 CHAPTER 7 SPM Machines Control Under Saturation The non-linear model of SPM under saturation derived in Chapter 6 will be used here to design a new ' —gain non-linear observer for position-sensorless control of PMAC machines. The new observer is then combined with control strategies presented in chapter 5 to implement a new controller which accounts for the operation of SPM machine under saturation. As it was shown in chapter 6 and in [14] the rotor position error increases as a function of the load current, however little has been published on techniques to correct for this error. Li et al. in [17] studied modeling of the cross— coupling magnetic saturation in a specific position-sensorless control scheme based on the high-frequency signal injection. Zhu et al in [18] proposed a practical approach for mitigating the rotor position error due to saturation in high-frequency injection method. However operation and flux position detection in SPM machines is affected by magnetic saturation regardless of the control strategy. Harnefors et al. in [19] 115 studied a general algorithm for control of AC motors and noted the existence of the error in rotor position estimation due to saturation, but the analysis focused only on unsaturated case. Moreover error signal was linearized making their conclusions local only. It will be shown here that although this error may be relatively small, it has detrimental effect on the machine performance. In this work we will focus on operation of SPM machines under magnetic saturation. The major contributions of this part are nonlinear model and characterization of SPM machine and design, analysis and verification of a general algorithm for control of SPMAC machines un— der saturation. This chapter is divided into two major parts: in—depth analysis of the non-linear observer structure adjusted for presence of saturation without linearizing the error signal and experimental results validating the derived non-linear model of the machine, impact of saturation induced error on machine performance and valida- tion of performance of the proposed observer combined with high frequency injection position-sensorless controller presented by J ang et al. in [22]. It is important to note that although the work presented here is focusing on the observer implementation in conjunction with high frequency injection method, it can be used in combination with any control strategy including back EMF methods or methods utilizing position encoder feedback. 116 High Gain Observer Feedback Observer BEMF Input Position gzctorl HF INJ. : Error D Observer 31:11:20 : Signal Figure 7.1: Block Diagram of the SPM Machine Controller 7. 1 High-Gain Observer for Control of SPM Ma- chines Under Saturation without Position Sen- SOl‘S A general algorithm for speed and position estimation of AC drives was presented by Harnefors et al. [19], and although they noted the existence of position estimation error as a result of saturation, no details were given on mitigating techniques. The error signal was linearized making their conclusions local only. In this work we will examine the non-linear observer structure adjusted for presence of saturation presented in the previous section. We showed through analysis that the cross-saturation inductance is fimction of the offset angle 00 so it is expected that the error signal will also be a function of the same variable, since the existence of the error is caused by the cross- saturation term. We can see that the cross-saturation induced term will become 0 when 5 = 00 at this point we know i) and as do —-> 00 we can determine both rotor position 0,. and rotor flux position 0. With 9 = 0r — 90 we can write the following error signal for non-salient PMAC 117 machine: a = Ksin(m(6 — 9)) (7.1) where 9 is the estimated position of the rotor flux (9, + 90) and K is the gain which willbedefinedlater. aaOaséoaOOandé—fi. mis lfornon-salientPMmachine and 2 otherwise. This error signal can be used to drive speed and position estimates to their actual values by using the same non-linear high—gain observer topology as: (fir = ’72 ' 5 (7'2) ézar+71-e (7.3) where '11 and 72 are gains of the observer. We also define (I),- = wr — (22,- and similarly ~ A 0 = 0 — 0, so we can write that the estimation errors satisfy the following conditions: d3, = J72 . Ksin(0 — é) (7.4) 0 = a, — 71 - Ksin(0 — 9) (7.5) Note that '71 > 0, 72 > 0 and k > 0. As it was shown in chapter 6 with the non- linear model, the value of K may be uncertain and also may vary with the current iq, so it is necessary to examine the stability of this topology as a flmction of K. Towards that end we make the following assumptions: since the speed change of the rotating machines has relatively slow dynamies we can assume that (2),. = 0. We will use Lyapunov fimction found under Popov criterion as described by Engel and Khalil 118 + G(s>] . % \IJ(Y)[—- Figure 7.2: Popov Criterion Loop in [21] to show the stability of the system. The Popov criterion assumes that the system is divided into two parts in the feedback loop: the linear part 0(3) and the nonlinear one, fly) as shown in Figure 7.2. So we rewrite the system equations as: 9 o 1 6 71K = — u (7.6) (Dr 0 0 (:11- 72K where u = sin(y) (7.7) and for SPM we define: 6 y: [1 o] (7.8) (Dr 0 1 Obviously the system matrix is not Hurwitz. We perform the loop transfor- 0 0 119 mation u = —ay + fly) and obtain . = - 1143/) (7-9) (I),- —-a'y2K 0 (D,- 72K where My) = Sin(y) - 0y. (“W The nonlinearity fly) is memorylees and the system matrix is Hurwitz for all a > 0. We define the observer gains for 0 < p << 1 as 01 02 .2 ,: __ 7.11 11 pK 12 ( ) notingthat00.Thescaledestimationerrorsaren1=5 and 712 = p53,, so the system becomes: pi) = An - Hwy) (712) T Where ’7 = ['71 172] y = 012 (7.13) M3!) = sin(y) - 011- (7-14) —aalK 1 al A: .B= ,0: [1 o] (7.15) —002K 0 02 By Popov criterion the system (7. 12) will be globally asymptotically stable for any 120 nonlinearity rb(y) in the sector [0, 1 — a] if the following condition is satisfied: _1_ + Re[G( 31.1)] — 7wIm[G(jw)] > 0,Vw 6 [—oo, 00] (7-16) l—a with the transfer fimction defined as G(s) = C(sI — ArlB (7.17) or 013 + (12 G = 7.18 (s) s2 + 0018 + 002 ( ) Rewriting equation (7.16) 2 2 2 4 1 + aa2 + 0.2 (cm1 — a2) + 'zyw a] > 0 (7.19) 1 — a (waa1)2 + (002 -— w )2 The condition will be satisfied if Kalman—Yakubovich-Popov lemma is satisfied as shown by Khalil (Lemma 6.3) in [20] and Engel [21], or for this particular case for (010:1)2 > ((1072)2 and '7 > 0. The Lyapunov function for the system is given by: War, 9) = énTPn + 7 [0" WOW (7.20) 121 obviously positive definite making the derivative: War, 5) = Zip [CnTPn - (£0 + wu)T(Ln + wu)] 1 T 1 71/431) [31 - ——1 _ 02/410] (7-21) Hence, Wang) S -2—lp-C71TP17 (72?) negative definite for d: = 0. 7 .2 Observer Gains and Tracking Over a short period of time the rotor position change can be reasonably approximated with a ramp function so (I),- is constant or d), = 1:, so that It will be added to the right side of (7.4). Setting 6:3,. = Z? = 0, we can solve for asymptotic ramp tracking errors with 71 and 72 defined in (7.11) we rewrite (7.4) as: (I),- = n — 72 - K sin(é) (7.23) Hence errors are: 08"“ = sin—'1 (5'3) (7.24) 02 7.25"“ = mg (7.25) 02 These expressions are useful because they allow us to the analyze tracking error 122 of the observers in terms of observer gains and known drive parameters i.e. speed loop bandwidth and maximum acceleration. 7 .3 Eliminating 180° Ambiguity at Startup [24] The rotor position angle, 0,, is defined as the angle between the stationary frame q— axis and the rotor frame q—axis. The estimation methods described above determine 0,- based on the inductance difference between the d and q—axes. The methods do not inherently differentiate between the positive q—axis and the negative q-axis. This is apparent from the current and inductance equations which are proportional to the twice the rotor angle. This means that a rotor position angle of 0 electrical degrees will result in the same negative sequence current as a rotor position angle of 1800. If the rotor position is at 0 degrees and the self-sensing estimate locks onto 180”, the result will be that the machine will spin in the negative direction for a positive speed command. So an initiation test must be performed at start up to determine whether the self-sensing estimate has locked onto the correct angle [24] . The influence of the stator current on the flux-parallel saturation level in the machine is utilized. For this purpose, afier having detected the flux axis (but not knowing the sign of the flux yet) as described above, a flux-parallel stator current component (produces no torque) is applied. Now, a measurement is carried out. This procedure is repeated with the opposite sign of the stator current. Again, a measurement is performed. Comparing the magnitudes of the current changes during the measurements shows which case was the flux-increasing (larger current change 123 per time in flux direction) or flux-decreasing (smaller current change per time since saturation is reduced). Hence, the flux is fully detected now [24] . The initiation test is done as follows. First the rotor is moved to a known posi- tion. This is done by commanding a small dc voltage onto the stator winding which effectively sets up a dc magnetic field in the air gap. The rotor magnets will align with this field and thus the rotor will move to a known position. By commanding a small additional duty cycle to the positive rail switch on phase A of the machine, a dc field is established in the direction of the stator +q-axis. The rotor magnets align with this field which results in a 90° angle between the stator q—axis and the rotor q—axis (ie. 0,- : 90°). The self-sensing algorithm will estimate either 0r=90°or 0,.2-90" for the rotor in this position. If the estimate is equal to -90° , then 180" is added to the self-sensing estimate and that result is used in the control algorithm for 0,». If the estimate is equal to 90", then there is no offset angle added to the estimate before being used in the control algorithm [24] . 7 .4 Controller for SPM Machine 7 .4.1 High-Frequency Injection Methods In this section we will revisit the control strategies described in chapter 5 and use the theory presented in chapter 6 and previous section of this chapter to derive a particular controller for SPM Machine. High-frequency Injection scheme will be considered to derive the error signal. Estimation of the rotor position employing alternating voltage 124 space vector injection is described. Consider the previously derived equation (5.6), from chapter 5, in the actual rotor frame of reference. The high frequency pulsating voltage space vector is injected in the estimated (denoted by 1") d-axis direction. vdh cos(wct) f = 14”,- . (7.26) v qh f 0 Performing the same transformation to the estimated frame of reference as dmcribed chapter 51 and governed by equation(5.10)- (5.18) and error definition as in (6.30) and then measuring the induced current in q — axis. The current in (5.25) can be written as follows: ,. 1 (’47 f f + jthdi f 1')an sin(9r - 90) i = -— , , qshf 2 (rghf + thLghfxrghf + thLghf) cos(whft) (7.27) In the high-frequency impedances the inductances are dominant and sufficiently larger than the resistances, so we can neglect the resistances. Hence the current becomes: Ei'l-i [_ whdeiff sin(whft) r 2'53); f = 2 J SinU-ir - 90) (7-28) 2 “hiLEhquhf The rotor position estimation error can be Obtained if this signal is passed through an LPF with appropriate corner frequency: f(6,.) = LPF [438M sin(whft)] (7.29) 125 Finally q—axis current containing rotor position error is derived: qs T r 4“’szLaququm' sin(5,- —- 00) (7.30) Now that we have an error signal similar to that defined by (7.1) we can write our observer for this machine. Hence, Vindeiff K = -— (7.31) 4whfL2hfLth so we define 71 _ V 'L . ’72 _ p2V 'L . ' P m] diff m] dsz substituting into equations (7.2) and (7.3) the observer will take the following format: 6 0 1 av 2/p __._ _ i (7.33) . . 2 K (411- 0 0 DJ" l/p In next section we will show the implementation of the same observer in the controller based on back EMF measurement. 7.4.2 Control Based on Back ENIF Measurement In this section we will use the theory presented to derive a particular controller for SPM Machine. Back ENE" position-sensorless scheme will be considered to derive the error signal. Consider the previously derived equation (5.18) in the actual rotor frame of reference ignoring the current derivatives in steady state: 126 1’; R3 + er12 “HI/22 if] curl/1; = + (7.34) Transferring the same equation in estimated frame of reference d-axis back EMF term will take the following for: E4 = wry)", sin(5,- — 90) (7.35) where Ed for practical implementation will obtained as follows: Ed = v5 — R‘s-if; + (fly-([4117: + leiZ) (7.36) Now that we have an error signal similar to that defined by (7.1) we can write our observer for this machine. Hence, K = —o,.1pm (7.37) sowedefine _2 —1 ’ _ 1 —1 1 para/z...“ film". 7 (7-38) substituting into equations (7.2) and (7.3) the observer will take the following format: Q) Q p—r Q) N \ 'b E F? (7.39) It is worth noting that this is only one possible way of generating the error signal. A 127 similar error signal could be generated by .ploying high-frequency injection method for sensorless control or even utilizing position encoder. 7 .5 Experimental Results In this section we present simulation and experimental results of the proposed con- trol algorithm. First experimental characterization of the machine is carried out to obtain the inductances under saturated conditions. Figure. 7.3 shows measured SPM machine inductances. The measured inductances are somewhat higher than the values obtained via FE analysis, however this should not have any effect on the con- trol algorithm since the ratio of d- and q- axes inductances remains unchanged.With the machine model in place we now turn to experimental validation of the control algorithm. The block diagram of the control system is shown in Figure. 7.4. The first set of experimental results shows decreased performance of the system if the magnetic axis shift is not taken into account by comparing the transient per- formance of the systems with and without compensation for the saturation induced error. In the compensated system setup angle shift is simply added to the rotor posi- tion measurement from the encoder. A step speed command is applied to both setups with q—axis current limit set at 10A, while constant torque is provided on the shaft by the coupled Induction Machine acting as a load, we measured the actual speed and observed the time needed to accelerate to the reference speed, which in turns provides the information about developed torque in the machine. Figure. 7.5 shows the difference in performance at rated current, while the Table 7. 1 shows performance 128 q-axis inductance r i -10 -5 0 S 10 d-axis inductance 2 0 i -10 -5 0 5 10 Cross-Saturation Induced Inductance 1 10 -3 (3 5 10 Current Iq [A] Figure 7.3: Experimental Measurement of Inducatances 129 Speed _ Cmd l S Integrator HF INJ Figure 7.4: Block Diagram of the High-Eequency Injection Control Algorithm q—axis Axis Current % Torque Increase 2 A 1.4 % 4 A 4.8 % 6 A 6.7 % 8 A 11.8 % 10 A 11.9 % Table 7.1: Experimental Results comparison for the range q—axis current. The second set of experimental results shows the comparison between rotor posi- tion obtained from the encoder feedback corrected by the saturation induced error, and rotor position obtained from our observer for a given speed reference profile and fixed shaft torque. Figure. 7.6 shows that very good agreement is achieved with minimal error. Finally Fig. 7.7 shows the comparison of the performance of the systems with 130 0 Measured & Reference Speed 3'1 3 50 \- ----------------- E 0 Uncompensated“ ‘1 a m -50 i .- 0 5 10 5‘ Id & Iq <fi Uncompensated r E. 10%—F ---------- ‘t-x ------------ - d.) : t 0 5 10 = 0 5 10 Speed Reference-Measured Speed l__'100 : :5 Uncompensated £3. 50- -------------------------- - / ------------------------------- - 13 i. m 0 i 0 5 10 Time [s] Figure 7.5: Performance Comparison at Rated Current L1 = 8A a. .. '77:..2: 77: .l‘r“:',A .137- -:,- -‘ .' . _‘ , .- ‘-‘ "~‘. » ‘ '*., Estimated Speed 0 0.5 i 1.5 2 Rotor Position 100 9 [rad] U] Cf i 0.5 1 1 .5 2 Position Error 9 Error [rad] Figure 7.6: Observer Performance Comparison at No—Load Current 132 rotor position feedback from the encoder and the one with the feedback from the observer for a given speed command profile and constant shaft torque. It is clear that higher q—axis current (around 10% in this case) is required to achieve the same speed and torque if the magnetic axis shift error is not taken into consideration. In other words, by accounting for the magnetic axis shift a performance of the machine can be improved. This translates into higher efficiency for the given torque requirement and higher maximum torque capability. 133 OO O g 60 - a l :40 l“ 3 i (2:20- 0 . 0 q-axis Current 20 . : - 2'! 1 5 — ----------------------------------- i E '3' W/Encoder Feedback g 10% """""""""""" y/ T . W/ Observer Feedback 5 00 2 21 6 8 Time [s] Figure 7.7: Observer Performance Comparison at Rated Current L, = 8A 134 l Magnets Rotor Mount to Shaft Figure 7.8: Outer Rotor PMAC Machine START I/l/l ENABLE HIGH . ~ SPEED MODE pmmmoro f POSITION RI Back EMF HF INJECTION L/IETHOD ENABLE LOW SPEED MODE Figure 7.9: State Diagram of the Controller for Entire Speed Range 135 CHAPTER 8 Conclusion The first part of this work presented design, analysis and comparison of the best PMAC machine candidate for integrated starter—generator application in Series HE bus. Performance capabilities such as maximum torque, power density, size and weight of IPM and SPM machines were addressed and evaluated. Finite element simulation results are provided to support the analytical work. The best machine candidate (SPM with 1 / 2 slot / pole / phase) was proposed and the prototype built for experimental validation of the results presented here. The second part of the work deals with operation and control of SPM machines. Both control strategies utilizing position resolvers and position-sensorless are consid- ered with the effect of saturation on both of them. A non-linear model of the PMAC machine was presented to show the influence of saturation. It was shown both analyt- ically and in FEM simulation that the SPMSM machine under saturation will exhibit magnetic axis shift which causes an error in flux position detection and can have fur- ther ramifications such as: demagnetization of permanent magnet, poor performance 136 of the machine etc. Finally, a new high-gain observer is designed in combination with high-frequency injection methods to account for the entire operating range of the machine, including the saturation. To verify the performance and effectiveness of the designed observer, an existing position-sensorless control strategies utilizing high-freaqency injection (for startup and low speeds) and Back EMF method (for high speed operation) are implemented in combination with the designed observer. Finally simulation and experimental results of the machine performance with the pro- posed observer are presented. The contributions of this work can be summarized as follows: 1. Comprehensive analysis and comparison of Interior Permanent Magnet Ma- chines vs. Surface Permanent Magnet Machines for ISG Application. 2. Analysis and comparison of distributed vs. concentrated windings, as well as the analysis of various Slot / Pole / Phase combinations (including 1 / 2 SPP topology) with respect to machine size, minimal losses and highest torque capability. 3. Tools for analytical design and performance assessment of SPM Machines with concentrated windings are derived and discussed. 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