Modelling and field-oriented control of a synchronous reluctance motor with rectangular stator current excitation

Transcription

1 University of Wollongong Research Online University of Wollongong Thesis Collection University of Wollongong Thesis Collections 21 Modelling and field-oriented control of a synchronous reluctance motor with rectangular stator current excitation Colin Coates University of Wollongong Recommended Citation Coates, Colin, Modelling and field-oriented control of a synchronous reluctance motor with rectangular stator current excitation, Doctor of Philosophy thesis, School of Electrical, Computer and Telecommunications Engineering, University of Wollongong, Research Online is the open access institutional repository for the University of Wollongong. For further information contact Manager Repository Services: morgan@uow.edu.au.

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3 MODELLING AND FIELD-ORIENTED CONTROL OF A SYNCHRONOUS RELUCTANCE MOTOR WITH RECTANGULAR STATOR CURRENT EXCITATION A thesis submitted in fulfilment of the requirements for the award of the degree DOCTOR OF PHILOSOPHY from UNIVERSITY OF WOLLONGONG by COLIN COATES, B.MATH-B.E. School of Electrical, Computer and Telecommunications Engineering August, 21

4 ABSTRACT The rotor saliency of the axially laminated synchronous reluctance motor (SynRM) produces a rectangular air-gap flux density distribution. Optimal torque / rms ampere is achieved from machine if a rectangular stator current distribution interacts with this flux. The impact o rectangular stator currents on the design and control of the SynRM are considered. A design model is developed that assumes rectangular stator currents. The design model is based on an existing lumped element model of the SynRM magnetic circuit that has been extended to include saturation effects. All stator and rotor dimensions are included in the design model. The key dimensions are identified and a simple iterative algorithm is determi for optimising these values. A 5.kW experimental motor is designed and built with an optimal torque / unit mass ratio. The designed motor has a nine-phase concentrated winding to approximate the ideal rectangul stator current distribution. Finite element analysis and static tests demonstrate the valid the design model. Generalised voltage and torque expressions are developed for the nine-phase machine. An orthogonal transformation is obtained to isolate the direct and quadrature, harmonic components of the stator inductance matrix. This transformation is applied to the standard stator voltage and torque equations to determine the equivalent d-q harmonic component equations. Two field-oriented control strategies are developed for the multiphase SynRM drive. A simpl stator reference frame control strategy is implemented and performance results presented. A transformed frame vector controller is demonstrated to have theoretically superior performa to the stator reference frame controller but could not be implemented due to the excessive computational requirement for this strategy.

5 DECLARATION I, Colin Coates, declare that this thesis, submitted in fulfilment of the requirements for the award of Doctor of Philosophy, in the School of Electrical, Computer and Telecommunications Engineering, University of Wollongong, is wholly my own work unless otherwise referenced or acknowledged. The document has not been submitted for qualifications at any other academic institution. Colin Coates 3 rd August 21

6 ACKNOWLEDG EM ENTS I would like to thank Don Piatt, Vic Gosbell and Sarath Perera for their guidance, assist and encouragement throughout this project. Particular mention must also go to Brian Webb whose mechanical skills turned my ideas in motor, as he does with so many other projects at the University of Wollongong. Finally, I would like to express my love and gratitude to my wife, Charlene, for her pati encouragement and support.

7 TABLE OF CONTENTS Abstract Declaration Acknowledgements Table of Contents List of Figures List of Symbols IV vii Chapter Introduction Overview of Electrical Machine Technology Permanent Magnet Motor Switched Reluctance Motor Synchronous Reluctance Motor 1.2 The SynRM: an Historical Perspective Salient Pole Rotor Segmented Rotor Flux Barrier Rotor Axially Laminated ^isotropic Rotor Stator Winding Considerations 1.3 Project Overview 1.4 Thesis Outline Chapter 2 Magnetic Circuit Modelling and Design Optimization of the SynRM 2.1. Introduction Design Strategy 2.3. Magnetic Circuit Model 2.4. Saturation Effects

8 ii 2.5. Optimization Algorithm Key Independent Dimensions Dependent Dimensions Optimization Algorithm Optimization Results and Analysis Summary Chapter 3 The 5kW Synchronous Reluctance Motor 3.1 Introduction kw SynRM Construction Results and Analysis Summary Chapter 4 Generalized Equations for a Nine Phase SynRM 4.1 Introduction The Stator Inductance Matrix Voltage Equation Torque Equation Summary Chapter 5 Field-Oriented Control of the SynRM 5.1 Introduction Stator Current Controller Stator Current Reference Inverter Switching Strategy Stator Current Controller Simulation Transformed Frame Vector Controller Transformed Frame Current Reference Voltage Vector Selection Transformed Frame Vector Controller Simulation... 84

9 iii 5.4 Summary... 9 Chapter 6 The Nine Phase Inverter and Controller 6.1 Introduction Inverter Power Circuit DSP Controller Controller Interface Circuit Chapter 7 The SynRM Drive Software and Performance 7.1 Introduction Control Software Transformed Frame Vector Controller Stator Current Controller Performance Results Chapter 8 Conclusions References Publications of Work Performed as Part of this Thesis Appendix A 5kW SynRM Schematics Appendix B Inverter Schematics Appendix C Control Program Listing Appendix D Numerical Solution to SynRM Model Differential Equation Appendix E Device Data Sheets Appendix F Control Simulation Source Files Appendix G Derivation of Quadrature Axis Reluctance

10 LIST OF FIGURES Fig 1.1 Diagrammatic representation of a PMM. 3 Fig 1.2 Diagrammatic representation of a SRM. 4 Fig 1.3 Diagrammatic representation of a SynRM. 5 Fig 1.4 SynRM rotor structures. 7 Fig 2.1 Equivalent magnetic circuit model. 23 Fig 2.2 Typical air-gap flux density distribution in a two-pole SynRM. 24 Fig 2.3 Simplified magnetic circuit of SynRM. 25 Fig 2.4 B-H characteristic assumed for iron. 27 Fig 2.5 Air-gap flux density distributions with iron saturation effects with (a) 28 direct axis excitation, (b) quadrature axis excitation, (c) combined direct and quadrature axis excitation. Fig 2.6 Piecewise linear approximation to the air-gap flux density distribution. 29 Fig 2.7 Stator tooth tip detail. 31 Fig 2.8 Block diagram of optimization algorithm. 34 Fig 2.9 Optimum motor dimensions as machine size is varied. 35 Fig 2.1 Sensitivity of machine performance to design parameters. 37 Fig 3.1 Prototype 5kW SynRM. 39 Fig 3.2 5kW SynRM stator lamination. 41 Fig 3.3 5kW SynRM rotor. 45 Fig 3.4 Air-gap flux density distribution in 5kW SynRM. 47 Fig 3.5 Variation of SynRM torque with rotor position. 47 Fig 3.6 Phase winding model. 48 Fig 3.7 Direct axis magnetizing inductance. 49 Fig 3.8 Quadrature axis magnetizing inductance. 49 Fig 3.9 Magnetizing inductance of one phase versus rotor position. 5

11 Fig 3.1 Mutual inductance between two stator phase windings versus rotor 5 position. Fig 4.1 Generalized coils on SynRM rotor. 54 Fig 4.2 Air-gap flux density distribution 55 Fig 4.3 Decomposition of air-gap flux density distribution 57 Fig 4.4 Theoretical and measured (a) self inductance for phase 'a' and (b) 59 mutual inductance between phase 'a' and 'e' for the experimental SynRM. Fig 5.1 Fig 5.2 Fig 5.3 Fig 5.4 Fig 5.5 Fig 5.6 Fig 5.7 Fig 5.8 Fig 5.9 Fig 5.1 Fig 5.11 Fig 5.12 Fig 5.13 Fig 6.1 Fig 6.2 Fig 6.3 Fig 6.4 Fig 6.5 Compensation for slot effects in the stator current reference Phase current adjustments for star connected stator. Typical phase current reference versus rotor position. Stator current controller simulation block diagram. Speed controller including approximation to torque control loop. Step response of torque controller. SynRM current reference in transformed rotor current plane. Voltage vectors from a nine-phase inverter. Voltage vectors from - 2 sector of fundamental plane. Voltage vector relationship to inverter switching configuration. Transformed frame vector controller simulation block diagram. Step response of dq current components Response of torque to step change in currents. Block diagram of the inverter and controller circuit. Inverter hardware. DC link power supply. Circuit diagram for one phase of inverter. Block diagram of gate drive interface circuit

12 VI Fig 6.6 Shaft encoder outputs. 1 Fig 6.7 Block diagram of shaft encoder interface circuit 1 Fig 7.1 Key control functions necessary to implement the transformed frame 13 vector controller. Fig 7.2 Step torque response of transformed frame vector controller at 1kHz. 16 Fig 7.3 Stator current controller software block diagram. 18 Fig 7.4 Typical current and voltage waveforms recorded during magnetization 113 test (I D = 1 A, to = 2rpm) Fig 7.5 Magnetization test results (co = 35rpm) 114 Fig 7.6 Phase current waveforms (a) CO = 8rpm, (b) co = 2 rpm and (c) co = rpm (inverter bus voltage = 25V) Fig 7.7 Phase current waveform detail versus position for (a) co = 8rpm, (b) co 116 = 2 rpm and (c) co = 345rpm (inverter bus voltage = 25V) Fig 7.8 Measured and simulated speed and quadrature current values in 118 response to a step change in speed reference from loorpm to 24rpm. Fig 7.9 Measured and simulated speed and quadrature current values in 119 response to a step change in speed reference from +15rpm to -15rpm. Fig 7.1 Torque versus quadrature current with SynRM at very low speed 12 (<5rpm) Fig 7.11 Torque versus quadrature current for SynRM with (a) VUNK = 2V, (b) 122 VUNK = 4V and (c) V ^ = 56V. Fig 7.12 SynRM phase current (a) Id = 1.8A, L, = IA and (b) L. = 1.8A, Iq = 1.5A. 123

13 Vll LIST OF SYMBOLS A r/ Average surface area of rotor laminations (m 2 ) A s Air-gap surface area of stator slot pitch (m 2 ) B d Air-gap flux density due to direct axis flux (T) B g () Air-gap flux density (T) B q Air-gap flux density due to quadrature axis flux (T) D Stator slot depth (m) g Air-gap length (m) g e Effective air-gap length (m) H r () Rotor magnetic field intensity (A/m) H s {&) Stator magnetic field intensity (A/m) Direct axis component of stator current (A) n'th harmonic direct axis component of stator current (A) l dn. Transformed d-q current vector (A) Quadrature axis component of stator current (A) n'th harmonic quadrature axis component of stator current (A) qn Stator phase current vector (A) Phase 'x' instantaneous current (A) J r max Maximum stator winding current density (A/m 2 ) J s (9) Stator current density distribution (A/m) L Motor axial length (m) L d Direct axis inductance (H) L da Average direct axis length (m)

14 Lfa n'th harmonic component of direct axis inductance (H) L^ Diagonalized stator inductance matrix (H) L dw Scaled difference of direct and quadrature inductance (H) L m Stator phase winding magnetising inductance (H) L q Quadrature axis inductance (H) L^ n'th harmonic component of quadrature axis inductance (H) L T Rotor axial length (m) L s Stator phase winding leakage inductance (H) L^ Stator phase inductance matrix (H) L st Stator axial length (m) I Stator slot pitch (m) L sum Scaled sum of direct and quadrature inductance (H) M^ Mutual inductance between stator coils a and b (H) N Number of turns / coil in stator phase winding N s Number of stator slots R Air-gap radius (m) R c Stator phase winding core loss resistance (Q.) R Quadrature axis reluctance per metre (A/Wb/m) R r Rotor radius (m) R s Stator phase winding resistance (Q) R st Stator inner radius (m) S Slot opening (m) T(a) Transformation matrix T e Electrical torque (Nm)

15 IX T L Rotor iron lamination thickness (m) t rl Ratio of iron : iron + fibre in the rotor n t^ Ratio of fibre : iron + fibre in the rotor v d Direct axis component of stator voltage (V) v^ n'th harmonic direct axis component of stator voltage (V) v d Transformed d-q voltage vector (V) v g Quadrature axis component of stator voltage (V) v n'th harmonic quadrature axis component of stator voltage (V) W s Stator slot width (m) W, Stator tooth width (m) X Tooth tip thickness (m) Y Yoke depth (m) a Angular displacement of rotor axis from coil A axis (rad) /? Angular displacement between two stator coils (rad) j3' Angle between axes of adjacent phase windings (rad) AT Winding temperature rise ( C) 6 Angular displacement from coil A axis around stator (rad) 9 p Rotor pole pitch (rad) A s Stator phase flux linkage vector (Wb) ju Permeability of free space, An x 1" 7 (H/m) p Rotor pole pairs T Rotor torque (Nm) </> (&) Quadrature axis flux (Wb) ( Rotor speed (rad/s)

16 Introduction 1 CHAPTER 1 Introduction 1.1 Overview of Electrical Machine Technology The induction machine was invented in the 188's by Nikola Tesla. Since this time it has g on to become the most commonly used electrical machine in industry. Historically, the induction machine first found use in fixed speed applications where it was supplied direct from the ac mains (possibly in conjunction with some means of reduced voltage starting to transients at start up). The induction machine enjoyed wide spread acceptance due to its s low cost, low maintenance structure compared to other fixed speed machines. Over recent decades the use of the induction machine in variable speed applications has particularly increased. This has been made possible by improvements in variable speed driv technology. These improvements include the availability of new high-speed power electronic switching devices as well as more powerful microcontrollers and digital signal processors (DSP). Speed and torque control matching that of a DC drive is now possible in an induction machine drive. Thus, DC drives which once dominated in this area are being replaced. The induction motor offers a significant price advantage over the DC motor and with no brushes virtually maintenance free. The trend is being further driven by a push towards the social and economic goals of energ efficiency. Many processes that have been traditionally operated with fixed speed machines (blowers, compressors and air conditioners) are being converted to variable speed operatio This allows energy savings during low load operating periods that characterize much of the operating time of these applications. Since its invention the appearance of the induction machine has changed significantly. Thi been most notable in terms of size reduction due to improved construction techniques and

17 Introduction 2 materials [47]. However, the fundamental design methodology has not changed from that originally determined for fixed frequency supplies. One notable exception being the removal the double cage or deep bar rotor, which was previously used to improve fixed frequency starting torque [38]. Given that the design methodology has not changed despite the change in application, the question arises to the possibility of improving on the performance of the induction machine variable speed drive. A starting point might be to define the ideal drive system. One such description has the ideal drive providing high torque density, with minimal losses while operating at a high power factor. It has fast speed and torque dynamics, operates over a wi speed range and has a large peak transient torque density. Finally the rrjachine has a rugg construction, the controller is simple and the entire system is cost efficient [4]. In terms of the ideal drive the major criticism of the induction machine is its relatively efficiency in variable speed applications. In western society, as much as 7% of all electr energy generated is used in motor driven systems [51]. Induction motors form the largest su of this group. Typically an induction motor has an efficiency ranging from 75% (small motor less than lkw) to 95% (large motors, greater than lookw). Any improvement in efficiency would provide economic benefits to the users of the motors as well as economic and environmental benefits to society as a whole. Further, the control of induction motors is relatively complicated. Particularly in high performance applications it is difficult to accurately control induction motor torque [41]. Torque is proportional to the rotor resistance, which varies with temperature. Some type of rotor resistance compensation is required for this value making the controller considerabl complex. There are three main machines frequently suggested as alternatives to the induction motor i variable speed applications. These are the permanent magnet, switched reluctance and synchronous reluctance motors. While they are unsuitable for operating from fixed frequency

18 Introduction 3 supplies, in the context of variable speed drives, supplied by a power electronic device, they all have unique advantages and disadvantages that will be briefly considered PERMANENT MAGNET MOTOR Figure 1.1 shows a diagrammatic representation of a brushless permanent magnet motor (PMM). The PMM has a stator structure similar to that of an induction machine. However, its rotor contains permanent magnets used to set up the air-gap flux. PMMs are recognized as offering the highest power density and efficiency of all motors [3, 38]. Recent improvements in permanent magnet technology, leading to the development and use of neodymium-iron-boron magnetic materials, have allowed the high power density and efficiency values to be achieved. It is estimated that a PMM has 2-5% more output power than a comparably sized induction machine [45]. Distributed s winding rnanent magnets bedded on rotor Figure 1.1 Diagrammatic representation of a PMM The main disadvantage associated with this type of motor is the high cost of magnetic materials. Using permanent magnets is only viable in small machines (less than 2kW), as the cost quickly becomes excessive in larger frame-sized motors [45]. In addition, both operating temperature and peak transient torque have to be restricted to avoid

19 Introduction 4 demagnetization of the magnets. Permanent magnet motor designs generally exhibit cogging torque, caused by the interaction of the magnet and the stator teeth, which lead to output torque ripple, vibration and noise [54]. Nevertheless, despite these problems the PMM is predicted to receive increased use in the future as oil and ener prices increase [38] SWITCHED RELUCTANCE MOTOR Figure 1.2 shows a diagrammatic representation of the switched reluctance motor (SRM The SRM has saliencies on both the rotor and stator, although only the stator contai windings. The windings associated with the individual stator poles are sequentially excited causing the rotor to follow in a synchronous fashion. The SRM benefits from simple rugged rotor structure, which has a comparatively low inertia. As the rotor contains no windings it conducts no currents and has no resistive losses. Thus, the majority of machine losses are on the stator, which is relatively easy to cool. As t no permanent magnets in the machine, operating temperatures are less restrictive. Th SRM's power density and efficiency are generally acknowledged as exceeding those of an induction motor [3,18] but are lower than those of the PMM. Salient pole stator (with windings) Salient pole rotor Figure 1.2 Diagrarnmatic representation of a SRM

20 Introduction 5 The major problem with the SRM is that it suffers from torque pulsations. It is possible to reduce torque ripple over narrow speed ranges to levels comparable to induction motors. However, this level of smoothness cannot be maintained over a large speed range [45]. The torque pulsations can also produce considerable acoustic noise, which increases with motor size. Efforts to reduce the torque pulsations and acoustic noise led to designs with larger air-gaps, which lowers the achievable power density. Conversely, in high power density designs there is a cost penalty due to the small, ai tolerance [41]. Other limitations of the SRM include poor utilization of the active machine iron and copper as well as a transient torque density which is less than that PMM and induction motor [3] SYNCHRONOUS RELUCTANCE MOTOR The synchronous reluctance motor (SynRM) combines a stator structure, similar to that an induction machine, with a salient pole rotor. This structure is represented in Figu The SynRM shares the advantages of the SRM's rugged rotor construction including an absence of rotor copper losses and a comparatively low rotor inertia. However, unlike SRM, it has a cylindrical stator. This alleviates the problems of torque pulsations an acoustic noise associated with the SRM. Distributed winding Lient pole rotor Figure 1.3 Diagrammatic representation of a SynRM

21 Introduction 6 The SynRM contains no permanent magnets. As such, it does not suffer from the demagnetization problems of the PMM, is inherently cheaper and can be operated at higher temperatures. Further, the SynRM only has copper losses on the stator. The stator is substantially easier to cool than the rotor. As such, the SynRM can be operated at low speeds without the need for forced cooling. Induction motors suffer from overheating under similar conditions. The advantages of the SynRM suggest it is well suited for general use in inverter fed variable speed applications. Indeed on this basis the SynRM has attracted significant recent research interest and is the focus of this thesis. Before proceeding with the speci goals of this thesis a review of the existing work on the SynRM will be considered. 1.2 The SynRM: an Historical Perspective The SynRM has a long history. The earliest reference to it is in a paper by Kostko in 1923 Since then several different rotor structures have been proposed. The earliest structures for line start applications and included a starting cage. Recent designs are specifically inverter fed applications where the starting cage can be removed. In either case, the performance of the SynRM is improved by maximizing the ratio of the direct axis inductance L. quadrature axis inductance, (referred to as the saliency ratio), and the difference L d L (sometimes referred to as the torque index) [1, 2, 41, 53]. The different rotor designs re attempts to improve the machine's performance accordingly. Figure 1.4 shows the four-pole variants of the key rotor structures that have been considered. These will be referred to salient pole rotor, segmented rotor, flux barrier rotor and axially laminated anisotropic respectively SALIENT POLE ROTOR The earliest salient pole machines found use in the 195's and 196's. They were made by using special rotor punchings or, more conventionally, by milling away portions of a

22 Introduction 7 normal induction motor rotor so as to achieve saliency [13, 32]. The motors had the advantage of providing cheap, robust and reliable synchronous operation, despite suffering from low power factor and poor torque output. They found application in su diverse areas as the positioning of control rods in nuclear reactors to use in synt spinning plants [3]. In the latter case, the SynRMs synchronous operation allowed produce better fibres than speed regulated dc or induction motors [38]. O Salient pole rotor Segmented rotor Flux barrier rotor Axially laminated rotor Figure 1.4 SynRM rotor structures The salient pole machines were being operated from constant frequency supplies. As such they required starting cages so that induction motor torque brought the rotor speed where it could synchronize with the stator field. Rotor designs had to balanc conflicting requirements of high pull-out torque and power factor against the requi for high pull-in torque [33]. As such the machines exhibited low saliency ratios in range 2-3 [12, 46]. Consequently they performed badly in terms of power factor (.

23 Introduction.55), efficiency (5-75%) and maximum torque (1.5 times rated value). Additionally the machines were only capable of producing a fraction of the power (6% - 65%) of comparably sized induction machines [12, 13,14]. An interesting variation of the salient pole structure was to manufacture the rotor f solid mild steel [6, 7]. This structure did not require a starting cage in line start applications. Eddy currents induce a magnetic field in the rotor. Starting torque is developed by the interaction of the stator and rotor magnetic fields. However, with reported power factors in the range and efficiencies in the range the imchine did not offer any significant improvement in synchronous performance over the conventional design SEGMENTED ROTOR An early alternative to the salient pole machine was the segmented rotor structure. T segmented rotor consists of isolated poles mounted on a non-magnetic shaft. The structure was initially proposed in 1962 by Lawrenson [29]. He actually developed two separate structures. The first was the conventional structure with the poles mounted direcdy on a non-magnetic shaft. The second had the poles separated from an inner sha to reduce the inertia of the rotor [31]. Further work was done to optimize this struc by Lawrenson [3, 33] and later Ramamoorty [49]. The segmented rotor structure did produce larger torque densities at a better power and efficiency than the salient pole structure. Saliency ratios reported were in the to 6 [31, 33, 46, 49, 5]. The higher saliency ratios led to better power factor (.6 and efficiency (6-8%) results for these machines. By comparison the segmented rotors performed better than the salient pole machines. However, the construction of segmented machine was less robust given its greater complexity, due to the necessity non-magnetic discs and bolts to secure the poles to the shaft.

24 Introduction FLUX BARRIER ROTOR A second alternative to the salient pole structure was initially considered in the ear 197's. Flux barriers (specially shaped air openings) are introduced into the rotor structure with the aim of decreasing quadrature axis inductance without reducing direc axis inductance. A common sub-classification is based on the number of flux barriers introduced per pole. Some of the structures considered by various researchers were the double barrier [19, 2, 21, 25], single barrier [6, 7, 44, 53] and essential barrier [ Even the segmented rotor can be viewed as a single barrier type rotor but with a very wide barrier. The flux barrier rotor also offered improved performance over that of the salient pole rotor. Saliency ratios were reported in a range comparable to the segmented rotor with similar performance figures [14, 19, 21]. As these machines were essentially for linestart applications a key concern was the trade-off between pull out torque and stabili Honsinger introduced magnetic bridges along the quadrature axis to achieve a compromise between these goals [21]. The structure made from radial laminations was inherentiy more robust and easy to build compared to the segmental rotor. Despite the performance gains achieved by the segmented and flux-barrier rotor structures, the early SynRMs still did not match the performance of induction machines Consequently, interest in the SynRM waned from the mid to late 197's. This is further attributed to the emergence of dc drives with accurate speed control and later inducti motor drives with similar speed regulation. However, with the development of fieldoriented control techniques interest in the SynRM has been rekindled. SynRMs controlled using field-oriented techniques no longer require starting cages, which hav been a major limiting factor in design improvements.

25 Introduction AXIALLY LAMINATED ANISOTROPIC ROTOR With the reemergence of interest in the SynRM a rotor structure that has attracted considerable focus is the axially laminated anisotropic rotor. The structure can be thought of as combining characteristics from both the segmented and flux barrier rotors Figure 1.4 shows that the rotor laminations are layered axially to act as flux guides f direct axis flux. They are interleaved with non-magnetic material that acts as a flux barrier to quadrature axis flux. Although much of the focus on the axially laminated structure has been recent it does have a long history. Kostko originally suggested the structure in 1923 highlighting the importance of anisotropy of the magnetic material with view to reducing the quadrature inductance without affecting the direct axis inductance [26]. It was not until 1966 tha Cruickshank et. al. proposed their axially laminated structure as a means of implementi this principle [11]. They along with others optimized the structure, for both line-star constant V/f applications, managing to achieve saliencies matching and even exceeding those of other rotor structures [12, 42, 43, 5]. Typical saliency values obtained were the range 4-9. Researchers were restricted from achieving higher values because of the maintained presence of the starting cage and the knowledge that increasing saliency als leads to instability at some frequencies [34, 37]. These limitations were overcome with the application of field-oriented control techniqu to the SynRM. This removed the need for a starting cage on the rotor and allows the rot structure to be optimized for maximum saliency [1, 2, 53]. Several researchers have looked at the problem of optimizing the rotor structure under these circumstances [4, 8 27,28,41,48,53]. Field-oriented controlled axially laminated anisotropic SynRMs have now been reported as matching and exceeding the performance of equivalent induction motor drives. This work includes that by Piatt [48] who proposed a rotor structure that utilized the full

26 Introduction 11 gap surface improving upon the stacked "u" or "v" sections originally proposed by Cruickshank et. al. Although his design was not optimized, he was able to obtain equivalent torque production to a comparably sized induction rmchine. Staton et. al., using a similar rotor structure, also obtained matching performance to an induction machine [53]. Significantly, in this case if the induction motor was derated for variab speed inverter operation the SynRM showed a 2% lower kva requirement and 1-15% lower losses. A key design requirement of high-performance remains achieving a high saliency ratio. Some research effort has focused specifically on this goal. Matsuo and Lipo calculated the optimal ratio of rotor insulation width to rotor iron width to be.5 [41]. In a 3 machine based on this, a saliency ratio of 1.4 was obtained. Boldea et. al using a similar ratio of insulation to fibre, but with thin laminations, demonstrated a salien of 16 with high power factor of.91 in a 1.5kW machine [4]. Chalmers presents the performance results for a 7.5kW machine with saliency of 12.5 [8]. The SynRM is shown to produce 4.3% more output power than that of a comparable induction motor. However, it is also demonstrated that the SynRM has considerably higher no-load iron losses due to eddy currents in the rotor laminations. These could be largely reduced by cutting radial slits in the rotor. While the development of the axially laminated SynRM is far from complete indications are that it has the potential to replace the induction motor drive. Its comparative performance, ability to produce rated torque at low speed and its relatively simple con algorithms are some of the axially laminated SynRMs key advantages. There are of course still some issues that need to be resolved with regard to the SynRM. One questio requiring further investigation is that of no-load losses in the rotor iron due to eddy currents. There are some indications that these can be considerably reduced by cutting radial slits in the rotor as previously cited. Additionally, there are mechanical issue associated with the rotor structure. The axially laminated structure is completely dif

27 Introduction to conventional machine structure and requires new mass manufacturing techniques to be developed. Also means of maintaining the mechanical integrity of the rotor at hi need to be determined and tested STATOR WINDING CONSIDERATIONS The previously cited research has focused on three-phase sinusoidally wound mach stressing the similarity between the proposed SynRM and induction rnachine stator This was necessary for line-start rnachines and was also seen as advantageous to potential manufacturing of the SynRM. However, the SynRMs rotor saliency naturall produces a "rectangular" air-gap flux density distribution. Conventional three-p windings produce sinusoidal magnetomotive force (MMF) distributions, which do not necessarily produce the optimal torque from the machine. Considering that the pr field-oriented controlled SynRM drives are supplied from inverters many of the arguments for a three-phase distributed stator winding are no longer valid. Thus, emerging area of research is focusing on the stator winding and excitation. The advantage of rectangular stator excitation over sinusoidal excitation can be demonstrated by a simple comparison. Consider a two-pole machine with a rotor pol pitch of 2 radians. The machine has an air-gap radius, R, and a stack length, L. machine is run at the saturation limit the air-gap flux density, B, will be cons rotor pole face. For a sinusoidal stator current distribution with a peak curren the torque can be calculated as, I = 1.6S3BLR 2 J T= \BLR 2 Jcos9d6 _x (LI) For a rectangular stator current distribution with the same peak current density is given by,

28 Introduction = 2BLR 2 J 1 T = \BLR 2 Jd i (i.2) Although simplistic in its nature the comparison shows a 2% increase in torque i latter case. A more realistic comparison would have to account for the fact that optimal machine dimensions should be different in each instance as well as includ losses. However, the comparison does highlight the potential gains achievable in rectangular stator currents. Hsu et. al. demonstrate the advantage of adding a third harmonic component to the fundamental component of MMF in the SynRM [22, 23, 36]. The third harmonic component was obtained using a dual three-phase machine with isolated windings. T associated inverter consisted of six single-phase bridges. They show significant in torque per RMS ampere in both a salient pole and segmented rotor machine. Toli et. al. also demonstrate this idea but with a simpler five-phase star connected w from a voltage source inverter. This proposal had the advantage of reducing the p electronic requirement of Hsu's system [56, 57, 58]. Toliyat shows a 1% increase torque achieved by the addition of a third harmonic component of MMF. Again these results were obtained with a salient pole rotor but would be expected with any of common rotor structures. Law et. al. consider another variant of the multiphase SynRM coining the term "fi regulated reluctance machine" [5, 27, 28]. In this case the stator is wound with pitched, concentrated windings. Coils at the rotor pole sides are designated as s the field or direct axis excitation. Coils over the rotor pole face supply the eq armature current or quadrature axis excitation. The individual phase windings are isolated from one another and each requires a full bridge inverter. Consequently, drive as proposed is expensive in terms of power electronic requirements. However

29 Introduction 14 performance gains were quite substantial with a reported 68% greater force density than an equivalent induction machine. Another potential advantage of a higher phase number, in addition to higher torque density, is increased redundancy in the drive. A phase can fail in the inverter and the drive will still function albeit with reduced torque output. In applications where continued operation is critical this is a potential means of increasing drive reliabihty. At this point in time there has only been hrnited research in the area of multiphase SynRMs exploiting non-sinusoidal stator excitation, consisting primarily of the references cited above. There are clear indications of improved performance from the multiphase drives coming at the cost of increased inverter complexity. As the relative cost of power electronic devices reduces, the potential for this class of machines becomes more apparent. A major motivation for this thesis is to investigate the design and field-oriented control of this class of machine. 1.3 Project Overview The broad motivation for this thesis is to investigate and develop the potential of the fiel oriented SynRM drive. As seen in the literature review there are indications that the SynRM offers benefits such as greater torque density, higher efficiency and simpler control algor when compared to the induction machine. The potential advantages associated with realizing any of these benefits in a practical drive system warrant the additional investigation into SynRM. Particular attention will be given to the class of multiphase axially laminated SynRMs. Axia laminated machines have emerged from existing research as possessing the highest saliency ratios when compared to other members of the SynRM family. High saliency ratio is shown to be associated with greater torque density and efficiency.

30 Introduction 15 The majority of existing work on axially laminated SynRM design assumes a standard threephase stator with sinusoidally distributed windings. The reason research has focused in this is because of the perceived advantage of sharing a stator structure with the induction machrn In the context of an inverter fed niachine the need for a certain number of phases disappears the stator can have any number of windings. Allowing more than three, non-sinusoidal, phase windings forces the reevaluation of the questions as to how best design and control the machi The design question will be approached assuming a "rectangular" air-gap flux density distribution, which the rotor saliency of the SynRM naturally produces. Further, a rectangula stator current distribution will be assumed to interact with this flux. This produces the opt output torque per rms ampere from the machine. Implicit in the latter assumption is that the stator has a multiple-phase winding capable of approximating the assumed current distribution The design model will be based on an analytical lumped element model of the machine's magnetic circuit. Lumped element modelling is chosen over finite-element techniques to allow fast performance calculations and hence fast design optimization. Further, it is expected th analytical techniques will offer better insights into the practical performance limits of the machine. The design model is validated through the construction and testing of a 5kW experimental SynRM. This prototype has a nine-phase concentrated stator winding to approximate the ideal stator current distribution assumed in the design model. The choice of phase number was made given the rotor dimensions determined through the optimisation process. Nine was the minimum number of phases necessary to ensure at any time at least one phase would be dedicated to solely supplying direct axis excitation. Implementing a field-oriented controller on the multiphase SynRM presents additional difficulties. To initially approach this problem, the generalized d-q voltage and torque equations will be determined for the nine-phase SynRM. Similar equations have been previously determined for the five-phase machine [57]. However, the methods used become increasingly cumbersome as phase number is increased. A new approach will be considered

31 Introduction 16 which can be readily generalized to any n-phase SynRM. The equations, once formed, will allow the simulation of the drive's dynamic performance and perhaps suggest methods for implementing field-oriented control. The limited research into multiphase SynRM design means that there is even less research focused on multiphase SynRM control. Techniques will be considered for implementing fieldoriented control on the experimental SynRM drive. Existing multiphase drives have been controlled using simple techniques where each phase winding is designated as providing solely magnetizing flux (direct axis excitation) or torque producing current (quadrature axis excita [27, 36, 58]. This method will be explored more fully along with methods based around current transformations that recognise the individual windings contribution to both direct and quadrature axis excitation. A stator current controller is ultimately implemented in the drive. This controller utilises a technique similar to that used in the field regulated reluctance machine [27]. Phase windings are designated as supplying either direct or quadrature axis current depending on their positi relative to the rotor. In the drive control the work of Law et. al. is effectively extended to larger phase number machine with a wye connected stator. Importantly the stator connection significantly reduces the power electronic requirement for the drive and its associated cost. Performance measures are made on the drive to demonstrate its characteristics. 1.4 Thesis Outline The remainder of this thesis is organized as follows: Chapter 2 develops a magnetic circuit model for the SynRM. This model is based on a lumped element analysis of the motor's magnetic circuit and includes allowance for saturation in the machine's iron. The key stator and rotor dimensions relevant to the design process are identified. An iterative algorithm is determined which optimizes these parameters.

32 Introduction Chapter 3 presents the construction details for the 5.kW nine-phase SynRM designed and built as part of this project. The results of magnetization and torque tests, carried out on t machine, are given. They are compared with the theoretical values determined during the design process. Chapter 4 defines the stator inductance matrix for the nine-phase SynRM and consequentiy develops the generalized d-q equations. These results can be readily extended to any 'n' phase machine. Chapter 5 outlines two field-oriented control strategies for the nine-phase SynRM drive. The first strategy is based on a simple designation of the stator phase windings as supplying direct or quadrature excitation. The second is based on the generalized d-q equations and theory developed in Chapter 4. Simulation results that predict the motor's dynamic performance are presented. Chapter 6 addresses the hardware implementation issues associated with the nine-phase inverter and DSP controller. The practical hardware setup is described. Chapter 7 details the software implementation issues in the drive system as well as presenting the performance results from it. These results are compared with the simulation predictions in Chapter 5. Chapter 8 is a summary of the relevant conclusions and possible extensions that can be drawn from the work presented in this thesis.

33 Magnetic Circuit Modelling and Design Optimization of the SynRM 18 CHAPTER 2 Magnetic Circuit Modelling and Design Optimization of the SynRM 2.1 Introduction This chapter develops a magnetic circuit model for the SynRM. The model predicts the air-gap flux density distribution and torque output from the machine. It is applied in a design optimization algorithm and criteria are determined to achieve optimal SynRM performance. Section 2.2 outlines the rationale behind the design strategy. It has been previously noted t the torque per rms ampere of the SynRM can be increased, with the addition of a third harmonic component to the spatial MMF waveform [22]. This argument is carried to its logical conclusion by assuming an ideal "rectangular" stator current distribution. The rotor salienc the SynRM naturally produces a "rectangular" air-gap flux density distribution and it follows that the optimal torque per rms ampere ratio will be obtained with a rectangular stator curre distribution. Additionally, it is proposed to consider the entire magnetic circuit of the SynRM (stator and rotor) when optimizing its design. Existing work has focused largely on determining the L d optimal rotor dimensions only, in order to maximize the saliency ratio, [4, 27, 41, 53]. L Q Saliency ratio is chosen because of its relationship to the torque and power factor produced the machine. This approach is flawed as both rotor and stator dimensions can affect the motor's performance. By focusing solely on the rotor dimensions the best result possible is only to optimize the rotor dimensions for a given stator and winding configuration. Further, achieve a practical machine design, overall dimensions and thermal issues need to also be

34 Magnetic Circuit Modelling and Design Optimization of the SynRM 19 considered. With this view, saliency ratio is replaced by continuous torque / mass as the optimization criteria. The basis of the magnetic circuit model is the existing work carried out by Ciufo [9, 1]. He uses a lumped element model that includes the majority of SynRM dimensions to determine expressions for motor inductances and flux densities. Ciufo's work is described in Section 2.3 and extended to include saturation effects in Section 2.4. Saturation effects are critical in design optimization, as rated conditions should bring the SynRM to its saturation limit. Section 2.5 describes the optimization algorithm. Not all of the machine dimensions are independent. Some sections of the machine carry the same magnetic flux as others. For example, the stator teeth and rotor iron both carry direct axis flux. Specifying one dimension automatically sets the requirement for the other. Thus, the various machine dimensions are classified as either independent or dependent. The key independent dimensions are identified and an optimization algorithm determined for these. The remaining machine dimensions are calculated from the key dimensions. Section 2.6 presents the results of optimization over a range of motor sizes (1 - lookw). Sensitivity of SynRM performance to the key dimensions is also considered. Conclusions are drawn with regard to optimal SynRM design. 2.2 Design Strategy With the renewed interest in the SynRM, several researchers have considered aspects of the design optimization problem. A large portion of work has focused on analysis and comparison of rotor structures [8, 48, 52, 53]. While this work highlights the potential of the axially laminated SynRM it stops short of providing optimal machine dimensions. Where effort has focused on machine dimensions it has been limited to rotor dimensions in sinusoidally excited machines [4, 41]. The approach has been to maximize the saliency ratio, -j-, or alternatively

35 Magnetic Circuit Modelling and Design Optimization of the SynRM 2 the "torque index", L d - L q, using combinations of finite element analysis, lumped element modelling and other analytical techniques. Some recent research has moved on to consider non-sinusoidally excited machines [22, 27, 57]. However, design considerations here have been limited to the stator winding configuration only. The implications of non-sinusoidal excitation on the machine dimensions have yet to be explored. A key focus of this work is to consider the implications of non-sinusoidal stator excitatio the optimal dimensions of the SynRM. Significantly, the approach to SynRM design optimization presented is unique in three aspects: 1. It assumes non-sinusoidal stator excitation. 2. It considers all dimensions of the SynRM, both on the stator and rotor. 3. It seeks to optimize the torque / mass ratio for the entire machine rather than the saliency ratio. The SynRM does not naturally produce sinusoidal flux waves in the air-gap. The rotor salien of the SynRM produces a "rectangular" air-gap flux density distribution. If a rectangular s current distribution interacts with this flux the SynRM generates its optimal torque. Furth the machine will exhibit lower copper losses in comparison to a similarly rated sinusoidal current machine. These ideas are supported by recent work showing that the addition of a th harmonic component to the MMF distribution can raise the torque per rms ampere of the machine [22, 56]. This idea is carried to its logical conclusion by assuming that the motor indeed excited by an ideal, rectangular stator current distribution. In practical terms, th will be approximated by designing machines with non-sinusoidally distributed stator winding consisting of more than three phases. To ensure optimal SynRM designs are obtained, as opposed to optimal designs for a given stator, all rotor and stator dimensions are included in the design model. Existing work on SynRM design optimization has focused on one or two key rotor dimensions. Stator dimensions have been largely ignored with prototype rotors designed and built to fit existi

36 Magnetic Circuit Modelling and Design Optimization of the SynRM 21 induction machine stators, complete with their existing stator winding. The difficulty here is that rotor dimensions are inherently linked to stator dimensions. By fixing the stator dimensions, you automatically fix some rotor dimensions. As an example, it is expected that the iron in the rotor should be matched to the iron in the stator teeth. This is necessary as sections of the motor carry similar magnetic flux. Indeed any given rotor or stator dimension can limit the machine's performance if not chosen correctly. To avoid this pitfall the entire magnetic circuit of the motor will be considered as a whole. The most accurate analytical method to account for all the stator and rotor dimensions is tha finite element analysis. The disadvantage of this approach is that it is computationally expensive and time consuming. Further, this type of analysis does not necessarily provide insight into what are the key performance limits and relationships. For these reasons it was decided to use an analytical approach based on a lumped element approximation to the SynRM magnetic circuit. Finite element analysis will be used only to validate the final results. Any optimization requires a goal or performance measure. The goal proposed is to produce the largest continuous torque / mass ratio for a given frame size. (Mass is defined as the sum of rotor and stator iron making up the magnetic circuit plus the stator windings. It does not include the motor frame or shaft.) Traditionally, the performance measure has been either saliency ratio or torque index. These values have been used because they determine the machine's power factor and torque output, respectively. They will not be used in this instanc for two reasons. First, they only reflect the fundamental component of torque and neglect any contribution from higher harmonics expected in a square current machine. Further, to focus solely on torque or power factor performance neglects other important elements in a practical machine design. Most significantly machine size and thermal issues must be considered. The torque / mass goal obviously addresses the size issue. Thermal issues will be considered internal to the design optimization, as they will pose limits on some dimensions.

37 Magnetic Circuit Modelling and Design Optimization of the SynRM Magnetic Circuit Model The requirement for the design optimization is an analytical model that is based on the machin dimensions and includes allowance for saturation. Several researchers have attempted to find analytical expressions for SynRM torque and fluxes, given the machine dimensions [4, 16, 39, 4]. A common difficulty has been obtaining an accurate representation of quadrature axis flux. Ciufo offers a significant contribution with this respect [9, 1]. He recognizes two potential paths for quadrature axis flux. The traditionally acknowledged path is that transv to the rotor laminations. Another path can be shown to exist where quadrature axis flux passes from the rotor to the stator and back again. This "zigzag" flux has been observed by other researchers using finite element analysis [4, 17, 41] but has not been previously accounted fo in any analytical modelling. In overview, Ciufo initially determines an expression for quadrature axis reluctance based on the two flux paths. The expression is obtained from a lumped element approximation to the machine's magnetic circuit. The elements themselves are detenruned from the relevant rotor and stator dimensions. Ciufo proceeds to calculate both the air-gap flux density distribution and quadrature axis flux. However, his analysis contains no consideration for the effects of magnetic saturation in the machine iron. The requirement that the design model include such allowance remains. A motor at rated conditions would be expected to be operating with at least some portion of its iron at the saturation limit. Section 2.4 will extend Ciufo's model to i saturation effects thus forming a suitable basis for the design model. Before proceeding with this analysis the original work will be considered in more detail. Ciufo considers a "snapshot" of the SynRM with its rotor in a random position. The "frozen" machine's magnetic circuit can be modeled as a network of reluctances associated with the a gaps and the non-magnetic laminations in the rotor. The machine iron is assumed to have zero magnetic reluctance.

38 Magnetic Circuit Modelling and Design Optimization of the SynRM 23 Figure 2.1(a) shows a typical section from a two-pole SynRM. The section is taken towards the centre of the rotor away from the pole edges. The shaded and non-shaded areas do not represent the magnetic and non-magnetic laminations. Instead, the shaded sections represent portions of the rotor that allow quadrature axis flux to pass from one side of the stator to th other. The non-shaded sections represent portions of the rotor located over stator slot opening that do not facilitate flux being passed from one side of the stator to the other. Thus, both t traditional and zigzag quadrature axis flux paths can be recognized. (a) straight q-axis flux path (b) A _<: zigzag flux path X.) ;) B Air-gap reluctance of zigzag flux path 1 B Represents reluctance of steel / fibre laminations between A&B Figure 2.1 Equivalent magnetic circuit model. Figure 2.1(b) illustrates how the lumped element approximation to the quadrature axis channel is constructed. In particular, the circuit between nodes A and B is developed. The nonmagnetic portions of the circuit are represented by reluctances. These reluctances are determined from the motor dimensions. Once calculated, they can be combined to obtain a value for the quadrature axis reluctance per metre, R q, given by [9]; gekojrl Rq Mo(8 e Ni t l.6r s L s +.5/T 2 R 2 L s t rl ) (2.1) where, g e = effective air-gap length (m) N s i, = number of stator slots t H = ratio of fibre : fibre plus iron in the rotor

39 Magnetic Circuit Modelling and Design Optimization of the SynRM 24 juo = permeability of free space (4TC X 1" 7 H/m) R s = stator inner radius (m) L s = stator length (m) This equation is derived fully in Appendix G. Having established the equivalent quadrature axis reluctance the SynRM flux distributions can be calculated. The method used is to consider various MMF loops as well as continuity of flux in the different regions of the machine. One further simplifying assumption is made. The stator teeth and slots are "smeared" into a continuous entity. Thus, an ideal stator current distribution is obtained with no stator slot effects. Ciufo does this analysis and shows that the resulting expressions accurately predict the average fluxes in the SynRM [1]. Figure 2.2 shows a typical profile of the air-gap flux density distribution obtained using Ciuf model. In this instance, a two-pole machine is assumed with typical levels of direct and quadrature axis excitation. The distribution can be thought of as an average flux density produced by the direct axis excitation. Or in other words, the air-gap flux density distribution with slotting effects removed. At either end of the pole face the flux density rises or falls due to the flow of quadrature axis flux. Quadrature axis flux is concentrated here as this path offers lower magnetic reluctance than through the relatively large air-gap at the pole edges. 1.2-, 1 - /""""".8 H ^ ,,, Angular displacement (rad) Figure 2.2 Typical air-gap flux density distribution in a two-pole SynRM

40 Magnetic Circuit Modelling and Design Optimization of the SynRM Saturation Effects For Ciufo's work to be utilized in a design model, allowance needs to be made for saturation effects. Figure 2.3 shows a simplified representation of a two-pole SynRM. The rotor is assumed to have a constant width equal to the average direct axis length, L^. The value for L& can be calculated given the specific rotor dimensions in the corresponding real machine. Figure 2.3 Simplified magnetic circuit of SynRM. Quadrature axis flux is confined to a channel through the centre of the rotor. This channel has reluctance / metre, R q given by equation (2.1). The remaining portions of the rotor only carry flux along the direct axis. Further simplifying assumptions made are; 1. The stator has no teeth or slots. Stator currents are assumed to be distributed in a thin veneer along the inside surface of the stator. The current distribution is described by J s ().

41 Magnetic Circuit Modelling and Design Optimization of the SynRM No quadrature axis flux, <P n, passes from the rotor pole edges. 3. The rotor, H,(G), and stator, H s (), magnetic field intensities are functions o angular position only. Differential equations that describe the air-gap flux density distribution, B g () quadrature axis flux, <j) q (), are initially formed. They are derived by consid 1 and 3 and continuity of flux in areas 2 and 4 of Figure 2.3. Loop 1 passes fro the rotor, parallel to the laminations, crossing the air-gap to the stator. It th incremental portion of the stator, just inside its surface, before crossing the a The loop is completed at the middle of the rotor where it passes transverse to t laminations to reach its starting point. Summing the MMF's around this loop gives ^H r ()-^-B g ()-H s ()R sl d + J s ()R st d 2 Mo +-^B g ( + d)+^h r ( + d) + q ()R st dr q =O Mo ^ L^dif r (^) + g^dg (g) _ + + = 2 d }io d Area 2 is a small portion of the rotor that spans its width. Summing the fluxes gives; B g {n - )L r R r d - B g ()L r R r d + <t> q () - q ( + d) = ^-^ = RL[B g <n-&)- B g ()] (2.3) 8 g d Loop 3 is a path through the entire rotor cross section, across the air-gaps and just inside its inner surface. Summing the MMF's gives; lj()rd= ~\H s ()Rd + ^-[B g (7T-9) + B g ()] e Vo + ^[H r (7i-) + H r ()] (2.4)

42 Magnetic Circuit Modelling and Design Optimization of the SynRM 27 Area 4 is a small portion of the stator that spans the width of the yoke. Summing the fluxes into this region gives; B g ()R st d + B s () = B s ( + d) BA) = YdB s() R d (2.5) The following boundary condition is required; v2y (-A = v ^ j (2.6) Symmetry of the system requires; B() = B(TT + ) (2.7) Equations (2.2) to (2.7) can be solved numerically to obtain the air-gap flux density distribution across the rotor pole face and the quadrature axis flux over the width of the rotor. The numerical technique used to solve the system of differential equations is presented in A D. To determine this solution a simple approximation is made to the B-H characteristic for t motor iron. Figure 2.4 shows the B-H curve assumed. The iron has infinite permeability un its flux density reaches its saturation level of 1.7T. Past this point the iron flux den only marginally at 5uo H/m. B i k. 1.7T slope = 5uo 4 ^ w H -1.7T ^ r Figure 2.4 B-H characteristic assumed for iron.

43 Magnetic Circuit Modelling and Design Optimization of the SynRM 28 Figure 2.5 shows a typical air-gap flux density distribution obtained when square current excitation is applied to the stator. A two-pole machine under similar conditions to those in Figure 2.2 is assumed. Figure 2.5(a) and 2.5(b) show in isolation the direct and quadrature ax contributions to air-gap flux density distributions respectively. Significantly, when the components are combined in Figure 2.5(c), the peak where quadrature axis flux previously added to direct axis flux is removed. This corresponds to the point where the rotor and stator iron is first driven into saturation. (a) 6 n ] ( (b) e to r ~ «-2 -/" / / Q.15-, OS oj J. 15 I y. u 2 Angular displacement (jad) Angular displacement (rad) (c) 1 -, p r n i i U I I Angular displacement (rad) Figure 2.5 Air-gap flux density distributions with iron saturation effects with (a) direct axis excitation, (b) quadrature axis excitation, (c) combined direct and quadrature axis excitat

44 Magnetic Circuit Modelling and Design Optimization of the SynRM Optimization Algorithm To proceed from the SynRM magnetic model to a design optimization algorithm requires further simplification to the magnetic model. A piecewise linear approximation is applied to the air-gap flux density distribution predicted by the magnetic model. The approximation assumes that the direct axis excitation sets up an average flux density across the pole face. rated conditions this flux density should place the rotor iron at its saturation limit. All quadrature axis flux is assumed to flow through the final stator tooth located at the end of t rotor pole face. Figure 2.6 shows the approximation as applied to a typical model air-gap flux density distribution. Having established this simple approximation, the torque produced by the machine can be calculated as the cross product of flux density and current. 1 -, p /T~ Angular displacement (rad) Figure 2.6 Piecewise linear approximation to the air-gap flux density distribution The goal of the design optimization process is to produce the largest torque / unit mass. (Mas is defined as the sum of the rotor and stator iron that makes up the magnetic circuit plus the copper that makes the stator windings. It does not include the motor frame or shaft). To this end, the machine iron should be fully utilized at rated conditions. Considering this latter requirement, it becomes apparent that some dimensions are independent and can be freely

45 Magnetic Circuit Modelling and Design Optimization of the SynRM 3 adjusted to optimize the performance parameter. Other dimensions are dependent on the key variables and require no optimization Key Independent Dimensions The key independent dimensions in the SynRM are rotor pole pitch ( P ), rotor radius (R r ) rotor iron : iron + fibre ratio (r ), air-gap (g), maximum stator winding current densit (J max ) and stator slot opening (5). These are the values that will be determined in the optimization algorithm. There are other dimensions that could be classified as independent. These are not included in the optimization process as they are better selected on the basis of practic limitations in either the machine construction or stator phase windings. Specifically, these dimensions are; ROTOR IRON LAMINATION THICKNESS (T L ) Thinner rotor laminations lead to smaller effective air-gaps as flux-fringing effects ar reduced. Further benefits of thin rotor laminations are that the increased number of laminations per pole decreases quadrature axis inductance [53], reduces torque ripple an possibly reduces losses caused by pulsating fluxes [3, 4]. A practical limit exists to h thin laminations can be made. As thickness is reduced the number of laminations required increases as does constructional difficulty. A sensible lower limit to laminati thickness is.3 to.5mm. It has been suggested that using standard lamination material available in this size range, may contribute to reducing SynRM manufacturing cost [8]. NUMBER OF ROTOR POLE PAIRS (o) A two-pole SynRM is conceptually simple, yields high saliency, but is difficult to construct. The major problem is that the rotor structure leaves no space for the rotor shaft. Four or six pole motors are preferred [8]. Generally, four-pole machines are more common as they are easier to manufacture when compared to a six-pole machine.

46 Magnetic Circuit Modelling and Design Optimization of the SynRM 31 NUMBER OF STATOR SLOTS (N.) The number of stator slots depends largely on the stator winding. Factors that will influence the number of slots include the number of stator phases, the number of poles and whether the winding is distributed or concentrated. Commonly used values in AC motors are 36 and 48. STATOR TOOTH TIP THICKNESS (X) Figure 2.7 shows an enlarged view of a stator tooth. The tips of the tooth are assumed to be triangular. The base of the triangle corresponds to the tooth tip thickness (X). It is chosen to be approximately half of the triangle height (H). This was considered a good compromise between providing sufficient mechanical strength to the tooth tip while limiting the path for stator leakage fluxes. X =.5H Figure 2.7 Stator tooth tip detail Dependent Dimensions Considering the requirement to fully utilize the machine iron at rated conditions, it becomes apparent that some dimensions in the SynRM are dependent on others. These dependent dimensions are;

47 Magnetic Circuit Modelling and Design Optimization of the SynRM 32 STATOR TOOTH TO SLOT WIDTH RATIO (WT/W S ) In the absence of leakage fluxes, the ratio of the stator tooth width to stator slot width should be equal to the ratio of rotor iron to fibre. The stator teeth, over the rotor pole face, carry the same direct axis magnetic flux as the rotor iron. Ideally, the stator tooth and rotor iron should saturate at the same operating point, otherwise one section of iron will not be fully utilized. If allowance is made for leakage fluxes then the tooth width is be raised marginally as only the teeth carry this additional component of flux. STATOR SLOT DEPTH (D) Stator slot depth is set given the stator current density and rotor pole pitch. Slot depth i set to allow sufficient excitation in the stator winding over the rotor pole edges to fully flux the rotor iron in the direct axis. Once slot depth is set, an effective direct axis excitation, J d (A/m), is obtained. The quadrature axis excitation, J q, is set to the same value. This provides the maximum continuous torque without exceeding the winding current density rating. STATOR YOKE DEPTH (Y) The stator yoke depth is set to allow sufficient return path for the direct axis flux. Ideally, the stator yoke over the pole sides, the rotor and stator tooth iron over the pole face will reach saturation at the same operating point. MOTOR AXIAL LENGTH (D The rotor and stator stack lengths are set to the same value. The length is restricted by the allowable temperature rise in the winding. The thermal model of the motor assumes the stator winding generates heat through resistive losses. The heat is primarily dissipated, via natural convection, from the exposed area of the windings at the ends of the stator according to the equation,

48 Magnetic Circuit Modelling and Design Optimization of the SynRM 33 Q = ha(t 1 -T 2 ) (2.8) where, Q = heat flow (W) h - heat transfer coefficient (W m" 2 K" 1 ) A = exposed surface area of winding (m 2 ) Ti = winding temperature (K) T 2 = ambient temperature (K) The heat transfer coefficient was approximated using measurements from a similarly sized induction motor stator. The value for acceptable rise in the stator winding's temperature above ambient was chosen to be 4 C based on the wire insulation characteristic. In the optimization, a longer motor produces more torque. However, increasing the length of the machine also increases the winding length along with the associated conduction losses. As there is a limit to how much heat can be dissipated from the ends of the winding an equilibrium position must be found that maintains the winding temperature within acceptable limits. This thermal limit effectively sets the continuous rating of the machine Optimization Algorithm Figure 2-8 shows in block diagram form the algorithm used to optimize the SynRM design. This process optimizes the design for a given rotor radius. It consecutively considers each key independent dimension finding its optimal value in isolation. The algorithm repetitively cycles through all the key dimensions until the performance in (torque / unit mass) converges to a maximum value. While optimizing each key dimension a subroutine is called that sets the dependent dimensions to appropriate values. The optimization process was repeated using different initial values. In each case the process yielded the same solution providing confidence that a global and not local maximum was being found. The entire algorithm is simple enough to be implemented in any spreadsheet environment that supports macro routines.

49 Magnetic Circuit Modelling and Design Optimization of the SynRM 34 f Start ) (start) " Select rotor radius Adjust variable being optimized II i ' Optimize pole pitch Set slot depth to flux direct axis } ' Optimize steel to fibre ratio Set J J d 1 ' Optimize airgap Set yoke depth to carry d-axis flux } ' Optimize current density Set rotor length to satisfy thermal cond. 1 ' Optimize slot opening Compute torque / mass 1./Has T/m^^ ^\conve rged?./ Finish J (^Return J Figure 2.8 Block diagram of optimization algorithm. 2.6 Optimization Results and Analysis Four-pole SynRMs were designed for a range of machine sizes (1 - lookw). Figure 2.9 shows the optimum values of the key independent motor dimensions as the machine size was varied. Of particular note are the values obtained for rotor pole pitch and steel : steel + fibre ratio. Results indicate advantages associated with large rotor pole pitches (approaching 18 electrical

50 Magnetic Circuit Modelling and Design Optimization of the SynRM 35 degrees) and steel : steel + fibre ratios between These results differ to other published values which have indicated smaller pole pitches (12 electrical degree) and larger steel: steel + fibre ratios (.6 to.7) to be desirable [4,41,53]. Power' vs 'Rotor Radius' Pole Pitch' vs 'Rotor Radius' Rotor Radius (mm) Rotor Radius (mm) 14 'steel: steel +fibre'vs Rotor Radius' 'Current Density' vs Rotor Radius'.475 -i Rotor Radius (mm) 14 a 7 s 6 ^ Q Rotor Radius (mm) 14 'Airgap' vs Rotor Radius' 'Slot Opening' vs Rotor Radius'.4 f ' 3 I- - 2 " 3 o.i - o Rotor Radius (mm) Rotor Radius (mm) Figure 2.9 Optimum motor dimensions as machine size is varied. The difference lies in the stator current distributions assumed for the optimization. In a threephase machine sinusoidal current distributions are present and the edge regions of large pole faces are not fully utilized. Under these conditions it is necessary to put more iron in the rotor to maximize the direct axis flux in the useful central region of the pole face. By lifting the restriction of sinusoidal currents it has been possible to utilize the whole pole face creating better utilization of the machine iron.

51 Magnetic Circuit Modelling and Design Optimization of the SynRM 36 Also of note is the optimal air-gap, which is relatively small. For the 5kW motor, discussed in Chapter 3, the optimal air-gap was determined to be.3mm. This is approximately half of that typically encountered in a similarly sized induction motor. In an induction motor the rotor heats up due to the currents present in it. As a consequence, allowance for temperature rise made in the choice of bearings. Given this restriction on the bearing type a lower limit on t possible air-gap is set in the induction motor design. Significantly, the SynRM rotor carries current and is subject to no internal heating. Thus, the smaller air-gaps proposed are achiev Of course, other mechanical factors such as tolerances for cost effective manufacturing and unbalanced magnetic pull due to rotor eccentricities would also need to be considered if the motor were to progress beyond the experimental prototype stage. In a broader sense, the "shape" of the stators designed was encouragingly similar to those of comparable induction machines. Generally a SynRM of similar rating to an induction machine is only marginally smaller than the induction machine. However, the SynRM is significantly lighter due to the reduced iron content in the rotor. The rotors themselves have similar diameters and lengths. Ratios such as slot depth to yoke depth also remain in proportion. In Chapter 3 a 5kW machine design is described in detail. For that particular design the sensitivity of performance relative to the key dimensions was considered. Figure 2.1 shows graphs of the variation in torque / mass as the individual independent dimensions were varied Noting the scales, the most critical design parameters are pole pitch and steel : steel + fib ratio. The accuracy of the other dimensions has less significant effect on the machine performance. In particular the stator slot opening (not shown here) had very small effect on SynRM performance as predicted by the design model.

52 Magnetic Circuit Modelling and Design Optimization of the SynRM ^ Z i 21 a 1.5- a I '" **.5 - Rotor pole pitch (rad) , -a 2 « z I 2 ' 85 a 2.8- " f ,3 f Steel: steel + fibre ] -a Z95 " i 2 ' 9 " S * J «"5 - f 2-7_ H '.2 ' ' ' Air-gap (mm) 1.4 ' ~ CO o 2-9" " *" / \ f ^ Current density (A/mm^) Figure 2.1 Sensitivity of Machine Performance to Design Parameters 2.7 Summary A magnetic circuit model has been developed for the SynRM. This model takes into account all key stator and rotor dimensions and includes allowance for saturation in the magnetic circuit. It predicts the average flux densities in the machine and hence the torque output. The model could be further simplified by applying a piecewise linear approximation to it under the condition of rated operation. This allows for a very simple rated torque calculation based on the motor dimensions. The actual process of designing a machine initially involves examining the relationships between the various dimensions. The key independent design variables were determined to be rotor pole pitch, rotor radius, rotor steel: steel + fibre ratio, air-gap, stator current dens stator slot opening. Other dimensions can be shown to depend on these or on thermal requirements. Of the design variables the most critical are rotor pole pitch and steel : steel fibre ratio.

53 Magnetic Circuit Modelling and Design Optimization of the SynRM 38 It has been shown that larger pole pitches (approaching 18 electrical degrees) and steel: steel + fibre ratios slightly smaller than.5 produce the optimal motor performance. These values are contrary to other published results. The difference is due to the assumed stator current excitation. Square current excitation has been assumed in this instance because of the greater torque per rms ampere achievable through it.

54 The 5kW Synchronous Reluctance Motor 39 CHAPTER 3 The 5kW Synchronous Reluctance Motor 3.1 Introduction A prototype 5kW SynRM was built based on the design optimization specifications. This allowed for experimental verification of the design model and a means for validating fieldoriented control techniques at a later stage. Figure 3.1 shows a photograph of the constructed machine. This chapter outlines the construction methods and performance results of static tests carried out on the experimental machine. Figure 3.1 Prototype 5kW SynRM. Section 3.2 deals with the motor construction. The "ideal" optimized design is initially presented. Practical constraints in constructing a one off prototype forced some compromises in the design dimensions. The construction methods along with the necessary modifications are

55 The 5kW Synchronous Reluctance Motor 4 presented. The most significant compromise in construction was due to the small stator slot openings originally specified. The impact of these and solutions to the problems that aro be considered. Section 3.3 presents and analyses the results of tests made on the experimental machine. Design model predictions for the machine's torque and winding inductance values are compared with those predicted by finite element analysis and more importantly, the actual measured values. Only static performance results are presented in this section, dynamic performance results are contained in Chapter kW SynRM Construction A four-pole, 5kW SynRM was designed based on the design optimization algorithm. It achieved a nominal torque / mass ratio of 2.98 Nm/kg which promised significant improvemen over that of a conventional induction motor. Typically, in this size range, induction moto have torque / mass ratios in the range of 1.2 to 1.8 Nm/kg. Table 3.1 summarizes the key dimensions of the motor. Appendix A contains detailed mechanical drawings for the motor. Rotor Stator Pole Pitch 1.44 rad Slots 36 Steelrsteel +fibreratio.45 Outer Diameter 168mm Radius 64mm Slot depth 22mm Length 5mm Yoke depth 2mm Lamination thickness.35mm Length 5mm Slot opening.6mm General Tooth tip thickness 1.5mm Poles 4 Air-gap.3mm Current 1.8A Phases 9 Voltage 415V Current density 4.8A/mm 2 Speed 75rpm Table 3.1 Key 5kW SynRM dimensions

56 The 5kW Synchronous Reluctance Motor 41 STATOR CONSTRUCTION The SynRM stator dimensions are similarly proportioned to those of a standard induction machine. Notably, the outer diameter and length of the stator are of the same magnitude as would be expected in a comparably sized induction machine. Further ratios such as the slot depths to yoke depth are typical of an induction machine design and a realistic current d was obtained. The stator laminations were constructed from.5mm Ly-Core 23. Ly-Core 23 is a standard electrical steel lamination material with a maximum core loss of 2.3W/kg at 5Hz. Figure 3 is a photograph of a single stator lamination prior to assembly. The full mechanical deta the lamination are shown on drawings Al and A2 of Appendix A. Figure 3.2 5kW SynRM stator lamination The laminations were laser cut. Laser cutting was preferred over punching as it allowed the stator teeth to be made with a curved face. This ensured that the machine air-gap would be more uniform. Laser cutting also allowed the stator to be skewed.

57 The 5kW Synchronous Reluctance Motor 42 The stator was skewed one tooth pitch over its length. A common problem observed in SynRMs is that of cogging torque. This arises where the stator teeth magnetically "lock" i the rotor laminations. Physically this can lead to torque pulsations in the motor shaft or extreme cases a motor that is difficult to start. Skewing the stator prevents the stator rotor laminations aligning exactly. An additional benefit of this arrangement may be a reduction in the flux pulsations in the rotor laminations leading to lower rotor eddy curr losses. The very small slot openings (.6mm) created some problems in the laser cutting process. Normally it is possible to obtain a clean edge when laser cutting by blowing high-pressure nitrogen gas onto the cut. However, this process does trap heat in the cut area. The fine around the stator tooth tips meant that nitrogen gas could not be used without causing hea damage. Consequently the laminations were cut but with burring occurring along the edges. This burring had to be removed manually and the laminations did not stack as compactly as originally hoped. The laminations were secured together by four bolts distributed evenly around the edge of stator. These points also doubled as a means of securing the stator to the motor base as c seen in Figure 3.1. STATOR WINDING The design model assumed an ideal rectangular stator current distribution. The stator was wound with a nine-phase concentrated winding to approximate this ideal. The physical configuration of the winding is as shown in drawing A4 of Appendix A. Consultation with motor rewinders suggested a good "rule of thumb" was that 7% of the available slot area could be filled with current carrying copper. The remainder of the sl is lost due to the gaps formed when bundling the conductors. The design model generated th slot dimensions based on this rule. Given the stator current distribution, the slot depth

58 The 5kW Synchronous Reluctance Motor 43 increased until 7% of the slot area multiplied by the stator current density gave the current required over one slot pitch. To determine the size of the wire and number of turns in the stator winding several factors to be considered. These include the width of the slot opening, the maximum voltage available at the inverter output, the currents required and the speed at which the motor is required t produce rated torque. The maximum number of turns in the winding is set by the maximum inverter output voltage and the speed the motor is required to operate at. It is necessary that the output voltage r greater than the speed voltage generated in the winding so that the stator currents can be controlled. In this instance, this relationship can be quantified as follows. Each phase of stator winding consists of four coils connected in series. Assuming negligible resistance th voltage across the entire winding is approximated by, v-a 1 - dt -AN^ (3.1) dt where, y/= flux linkage of one coil (Wb) N = number of turns / coil <p= flux in one coil (Wb) Flux linking the coil will vary as the rotor moves. Assuming that the air-gap flux density distribution is a rectangular block over the rotor pole face the voltage equation can be mo to, d(j) da ~ANB g LRcv (32) v~an da dt

59 The 5kW Synchronous Reluctance Motor 44 where, a = rotor position (rad) B g = air-gap flux density (T) L = motor axial length (m) R = air-gap radius (m) co= rotor speed (rad/s) The motor's rated speed is 15rpm while fully fluxed (B g =.85T). Substituting into Equation (3.2) with the speed voltage term limited to 6% of the inverter dc link voltage (587V) shows that the maximum number of turns in each coil is 26. The size of the wire is found by dividing the total cross sectional area of copper required slot by the number of turns. This calculation gives a diameter of.5mm. Mother "rule of thumb" is that the maximum wire diameter that can be installed into a slot is half the slot opening. In the 5kW SynRM the slot openings are.6mm wide. It was proposed to use four.25mm wires in parallel to obtain the equivalent cross-sectional area of one.5mm wire. Two problems occurred with this approach. First, the wire insulation thickness becomes significant compared to the copper thickness in small diameter wire. Second, the large numb of turns of parallel strands are more difficult to stack in the slot. Both of these factors reduce the percentage of slot area that can be filled with copper. Hence, it was necessary reduce the number of turns in the stator coils. The final winding configuration used four coils of.25mm diameter wire in parallel. Each c had 17 turns. This meant that only 55% of the available slot area is filled with copper. T operating the machine at rated torque will involve exceeding the current rating of the stat winding. This is only possible for short time periods. However, it will still allow experim verification of the machine's predicted performance. In hindsight, there is a strong argume for making the slot openings larger in future machines. This sacrifices only a small fracti the machine performance but yields a much more practical machine to construct.

60 The 5kW Synchronous Reluctance Motor 45 ROTOR CONSTRUCTION Figure 3.3 is a photograph of the 5.kW SynRM rotor. A full mechanical schematic is shown on drawing A5 of Appendix A. The rotor was constructed on a stainless steel shaft. The rotor laminations were built fr.48mm sheet steel. Plastic film is used as spacing between the rotor laminations to mai the steel: steel + fibre ratio at the designed value of.45. The steel laminations were than those specified in the design model (.35mm). This was due to availability of materi will only marginally increase the effective air-gap in the final machine. The rotor laminations are secured in position by stainless steel screws inserted radiall the centre of the laminations. The entire structure is bonded in epoxy resin for addition strength. Figure kW SynRM rotor

61 The 5kW Synchronous Reluctance Motor Results and Analysis The design model predicted that the prototype SynRM would produce a torque of 36Nm at rated current. At a speed of 15rpm this corresponds to a power of 5.65kW. FINITE ELEMENT ANALYSIS Prior to construction, finite element analysis was performed on the design to validate the m predictions. In particular, the air-gap flux density distribution and machine torque were measured. These values were of interest as they are also generated in the design model calculations. For the purpose of the finite element analysis it was assumed that the stator slots over the pole edges carried rated direct axis current. Similarly, slots over the rotor pole face carr rated quadrature axis current. Figure 3.4 shows the graphs of air-gap flux density, over the rotor pole face, as predicted by the finite element analysis and the design model. The flux density distribution generated in the finite element analysis contains variations due to sta effects. In contrast, the design model prediction represents an average air-gap flux density value. To enable the two graphs to be compared a moving average was applied to the finite element analysis results. This moving average operates over one stator tooth pitch. The resu is represented by the third curve in Figure 3.4. The shape of the averaged finite element re show similar levels of air-gap flux density to those predicted by the design model. The port of the air-gap where flux density reduces due to quadrature flux is wider in the finite elem analysis but the reduction is not as large. This last observation is not unexpected as the approximation made as part of the design model was that all quadrature axis flux flows throu the final stator tooth at the edge of the rotor pole face. Using finite element analysis the SynRM torque was determined to be 35Nm. With the stator excitation unchanged the rotor was moved over one stator tooth pitch to see how the torque output would vary. The motivation for this test was to observe any potential problem with

62 The 5kW Synchronous Reluctance Motor 47 cogging torque. This problem has been previously noted in other experimental machines [4, 41]. Figure 3.5 shows the variation in torque as the rotor was moved. In this figure, torque be seen to vary by less than 3%, which was considered to be quite acceptable. For this test n effort was made to modify the stator currents to reduce the torque variation. It may be possi to reduce the variations further by appropriately adjusting the phase currents with rotor po if so desired. Finite Element model l/\ e ^ A K '5 v f A / ' 'r i If * $ - ^ AJGL /-l-/j^ /I /.4 n i u Design model / f\ ^1... u 1 I ' Angular displacement (degrees) f 5 Figure 3.4 Air-gap flux density distribution in 5kW SynRM. Figure 3.5 Variation of SynRM torque with rotor position.

63 The 5kW Synchronous Reluctance Motor 48 On the basis of thefiniteelement analysis results the machine was constructed with confidence in its potential for achieving the design goals. Static tests were performed machine. These tests involved measuring the winding characteristics of the m STATOR WINDING MEASUREMENTS Figure 3.6 shows the model used to represent a single phase winding on the S winding resistance was measured to be 27.4Q. This resistance is relatively l poor packing factor achieved in the stator winding due to the problems assoc small slot opening. Stator leakage inductance was found by measuring the win with the rotor removed. The value was detennined to be.18h. Rs L s o VV rv " v " > AQ..18H Re p> LM ") ' ' R s Stator winding resistance Ls R c LM Stator leakage inductance Core loss resistance Magnetizing inductance Figure 3.6 Phase winding model The core loss resistance and magnetizing inductance were found by applying a the winding. As the stator winding resistance and leakage inductance are kno model components could be detennined from terminal voltage and current measu loss resistance was measured to be 117& when the direct axis was aligned wi coil. The direct axis inductance is a function of current because of iron sa Figure 3.7 shows the direct axis magnetizing inductance versus rms phase cur measured from the prototype machine.

64 The 5kW Synchronous Reluctance Motor n g u Current (Amps rms) Figure 3.7 Direct axis magnetizing inductance. Similarly, core loss resistance was measured to be 27&Q, when the quadrature axis was align with the axis of a coil. Figure 3.8 shows the quadrature axis magnetizing inductance versus phase current curve measured from the prototype machine..2 n g.12 - I Current (Amps rms) 1.5 Figure 3.8 Quadrature axis magnetizing inductance. Figure 3.9 shows the magnetizing inductance of one phase winding versus rotor position. The unsaturated saliency ratio is 7. If leakage reactance is included the saliency ratio become 4. This is smaller than that reported for other sinusoidal rnachines but is not surprising

65 The 5kW Synchronous Reluctance Motor 5 design criteria was not to optimise this ratio. Specifically, the contribution of harmonic components of current compensate for the reduced saliency ratio. Figure 3.1 shows the mutual inductance between two coils on the stator again plotted as rotor position is varied. Observe that the inductances do not vary sinusoidally. This is because of the rotor saliency a concentrated stator winding. These results will be used to establish the validity of the inductance matrix calculations in Chapter 4. Figure 3.9 Magnetizing inductance of one phase versus rotor position Figure 3.1 Mutual inductance between two stator phase windings versus rotor position.

66 The 5kW Synchronous Reluctance Motor Summary A 5kW four-pole nine-phase SynRM was designed and built. Some compromises were necessary in the construction. Most significantly the small slot openings led to difficulty manufacturing the stator laminations and consequently winding the stator. In Chapter 3 it was noted that the overall machine performance was not very sensitive to slot opening. In hindsight, this dimension could have been increased without significantly affecting the result As the design was compromised the prototype is unable to sustain 5kW-power output continuously. However, it was possible to confirm this rating using finite-element analysis an short duration load tests (results presented in Chapter 7). The final measurements taken were of the winding characteristics. These will be required when implementing controllers at a later stage. Additionally the results verify inductance versus position calculations presented in Chapter 4.

67 Generalized Equations for a Nine Phase SynRM 52 CHAPTER 4 Generalized Equations for a Nine Phase SynRM 4.1 Introduction A nine-phase four-pole experimental SynRM has been designed and built. To model and control the motor's performance requires the determination of appropriate voltage and to relationships. This chapter derives these equations specifically for the nine-phase SynR method used can be readily extended to any "n" phase SynRM. The generalized d-q equations for the three-phase SynRM are well known. By convention the direct (d) axis lies along the low reluctance flux path, parallel to the rotor lamination quadrature (q) axis lies along the high reluctance flux path, transverse to the rotor lam Thus, the conventional d-q voltage and torque equations are [41], Vd=L d^ + RJ d -CL q i q (4.1) dt v q =L q^ + RJ q +CL d i d (A.2) T = ^p(l d -L q )i d i q (4.3) The aim of this chapter is to develop the analogous equations for the nine-phase machine. will allow the SynRM to be modeled and simulated and appropriate control strategies developed. Chapter 5 will specifically consider methods of implementing field-oriented control.

68 Generalized Equations for a Nine Phase SynRM 53 The generalized d-q equations have been previously found for the five-phase machine [57]. The key to this derivation is appropriately defining the stator inductance matrix. It is neces to include sufficient harmonic components in the stator frame to be able to deduce a transformation, to the d-q harmonic reference frame, that is both useful and invertible. The traditional approach to this problem is to use approximations to the stator winding distributio and air-gap length as functions of angular displacement around the stator. These are then combined to produce an expression for inductance. However, this approach becomes increasingly tedious, as higher harmonics are included in the analysis. Section 4.2 presents an alternative method for deriving the stator inductance matrix. A generalized expression is determined for the mutual inductance between two concentrated coils, positioned arbitrarily on the stator. The approach used is to make an approximation to the airgap flux density distribution and hence calculate the flux linkages. The mutual inductance expression obtained is then used to determine the elements of the stator inductance matrix give the specific dimensions of the nine-phase machine. Sections 4.3 and 4.4 derive the generalized voltage and torque equations for the nine-phase SynRM, respectively. An orthogonal transformation is deduced for the stator inductance matrix. The transformation is applied to the standard stator voltage and torque equations. This transforms the equations from the stator reference frame to the synchronous reference frame. In the synchronous reference frame the direct and quadrature harmonic components of current and voltage are effectively isolated. This offers potential advantages for the simulation and cont of the drive to be explored in Chapter The Stator Inductance Matrix The stator inductance matrix, L s (cc), describes the relationship between the stator phase currents, i, and the stator flux linkages, X s, in the SynRM such that,

69 Generalized Equations for a Nine Phase SynRM 54 A s =L s (a)i_ s (4.4) The stator inductance matrix elements are a function of rotor position, a, due to the rotor saliency. Figure 3.1 showed that the mutual inductance between two phase windings on the experimental machine varied as a non-sinusoidal function of rotor position. A general expression describing this variation with rotor position for two arbitrary coils on the stat the SynRM can be obtained. This expression can then be used to determine the individual inductance matrix elements for the nine-phase machine given its relevant dimensions. Traditionally, approximations are made to the stator winding distribution and air-gap length functions of angular displacement around the stator. These expressions are then used to determine the inductance values including the necessary harmonic components [3, 33, 57]. This approach becomes increasingly cumbersome when higher order harmonics are included in the analysis. An alternative approach based on first approximating the air-gap flux density distribution is presented here. OA' Figure 4.1 Generalized coils on SynRM stator Figure 4.1 shows the general case of two fully pitched concentrated coils on the stator of pole SynRM. The axes of the cods are separated by /? radians. The rotor has a pole pitch of

70 Generalized Equations for a Nine Phase SynRM 55 radians and is at an angle of a radians to the axis of coil A. The air-gap flux density can be approximated if the rotor position and dimensions are known. (a) (b) a> n-6 9. a B e Bd S B -nn. a 71/ /2 Q Figure 4.2 Air-gap flux density distribution If current is passed through coil A then a magnetic flux is set up in the machine. Figure 4. shows two approximations to the air-gap flux density distribution, around the periphery of

71 Generalized Equations for a Nine Phase SynRM 56 rotor. The distribution in Figure 4.2(a) is typical when coil A is positioned over the edges of the rotor pole. The situation is similar to that represented in Figure 4.1 and is described n-9 p mathematically by the condition a < in a two-pole machine. The full rotor crosssection is available to carry direct axis flux. This flux is large because of the low reluctanc the path. It is denoted as producing air-gap flux density B d in the figure. In contrast, flux crossing the larger air-gap at the rotor pole edges travels over a high reluctance path. Consequently, the flux and the resultant flux density are much smaller. This flux is termed quadrature axis flux and the flux density due to it is labeled B q. Figure 4.2(b) shows a second situation where coil A is positioned over the rotor pole face. Mathematically this corresponds to the condition a > in a two-pole machine. In this instance, only a reduced portion of the rotor cross-section actually links the two sides of coi and is available to carry the direct axis flux. The remainder of the rotor pole face and edges present a high reluctance path to magnetic flux and as such only carry the smaller quadrature axis flux. The air-gap flux density distributions shown represent an approximation to the actual distributions. The validity of the approximations will be demonstrated by comparing the calculated inductance values to those measured in Chapter 3. The error introduced by the approximation is analogous to that obtained when the air-gap is approximated as a rectangular function as has been done by other researchers [3, 33, 57]. In the interest of simplifying the mathematical analysis, it is advantageous to consider each o these air-gap flux density distributions as the sum of a direct axis component and a quadrature axis component. Implicit in this decomposition is the assumption that there is no saturation in the machine iron. Figure 4.3 shows a typical decomposition. Both cases shown in Figure 4.2 can be decomposed in this way. Note that what is designated solely as direct axis flux in Figur

72 Generalized Equations for a Nine Phase SynRM is shown to be a combination of direct and quadrature flux in Figure 4.3. In decomposing either case the quadrature axis component is identical. Only the shape of the direct axis component changes dependent on the rotor position. / B d B B d - B -F- 1_ J~» / ^ + zf * -R Figure 4.3 Decomposition of air-gapfluxdensity distribution The direct and quadrature axis air-gap flux density distributions can now be individually decomposed into their Fourier series components. There are two expressions for the direct a flux density distribution depending on the rotor position. Quadrature axis flux density distribution is independent of rotor position. r n^ BAff)J^zM ± sin V 2 J cos(n(t9 - a)) case (a) ft n=x(odd) n (4.5) B-l A(B d -B a ),A (-1) 2 cos(ncr),, n.\. Bd(^ = JLJ. _ ^ I i / -cos(n(-a)) case(b) n n=x{odd) n (4.6) ft n=l{odd) n n-x (4.7) The flux linking coil B, due to the current in coil A, can be calculated by integrating the air-gap flux density distribution between the two sides of coil B. Hence,

73 Generalized Equations for a Nine Phase SynRM 58 r' Wa.=N \B g (e)l r Rd6 {48) T* where, L r = Rotor length (m) R = Air-gap radius (m) N = Number of turns / coil The mutual inductance values between the coils are now calculated by simply divid linkage by current to get; n-x (n\ p (-1) 2 sin S(B d -B Q )L r RN ^ { 2, M«w(aO= : ^ r^ -cos(n(a+fi)) case (a) (4.9) ni a n=\{odd) n S(B d -B q )L r RN ~ cos( na ) M a^d(d)= " _, ^cos(n(cr+^)) case(b) (4.1) ft l a n=x(odd) n SB q L r RN - cos(n^) M ab - q (a)= q Y^- (4.11) ftl a n=\(odd) K where, i a = Phase A current (A) Figure 4.4 shows graphs of the theoretical self-inductance of phase winding 'a' a inductance between phase winding 'a' and 'e' of the experimental machine. These g formed by using appropriate combinations of equations (4.9) to (4.11). Calculated and maximum inductances are used. They are the theoretical equivalent to the meas in Figures 3.9 and 3.1. To allow comparison, the measured data points have been Figure 4.4. A close correlation can be observed between the measured and theoreti

74 Generalized Equations for a Nine Phase SynRM 59 (a) Self Inductance vs Rotor Position 6 12 Rotor position (degrees) 18 (b) Mutual Inductance vs Rotor Position Rotor position (degrees) Figure 4.4 Theoretical and measured (a) self inductance for phase 'a' and (b) mutual inductance between phase 'a' and 'e' for the experimental SynRM. The impact of the transition from case (a), direct axis excitation to case (b) excitation is minimal. In the self-inductance curve the effect is to reduce the upper peak of the triangular waveform. For the mutual inductance curve the effect is barely noticeable. One of the key characteristics of the designed SynRM is that it has a large rotor pole pitch that approaches n radians (electrical). In these circumstances it is reasonable to approximate the mutual

75 Generalized Equations for a Nine Phase SynRM 6 inductance verses rotor position curve with the triangular wave, obtained using case (b) direct axis excitation, alone, hi effect we are assuming the rotor pole pitch is n radians (electr Under the assumption that the rotor pole pitch approaches n radians electrical the direct a quadrature axis inductance expressions can be combined to give a tidy expression for the mutual inductance between two coils on the stator of a SynRM. 8(B d -B a )L r RN - cos(na)cos(n(a+j3)) 8B q L r RN ^ cos(nfi) M ab (a)= f l_ 1 + 2_ ZT~ n ft^-a n=\(odd) m a n=l(odd) =± ^ "Wto^4g, tv ± map. (4,2) ft n=x(odd) n ft n=l(odd) where! Ld =MS^L (4.B) n n = phase inductance when d-axis aligned with phase axis 9 B q L r R7jN (414) = phase inductance when q-axis aligned with phase axis This expression can now be used to form the stator inductance matrix given the nine-phase SynRM dimensions. Consideration must be given to how many spatial harmonic components from the mutual inductance expression (4.12) should be included in each element of the inductance matrix. The stator inductance matrix is formed with a view to performing a non singular d-q transformation upon it. This goal sets the imnimum number of harmonics requi An analogy can be drawn to the more familiar three-phase machine where there are two independent phase currents. A three-phase d-q transformation is based on resolution along two quadrature components of the fundamental flux wave. The transformation for a nine-pha

76 Generalized Equations for a Nine Phase SynRM 61 machine involves eight independent currents. There are not enough degrees of freedom for them to be associated with the fundamental flux wave alone. To be able to deduce a transformation which is useful and invertible one needs a model of machine incorporating space flux harmonics up to and including the seventh harmonic (odd only). This provides eight degrees of freedom in the transformed variables. Since the sta star connected with no neutral there are only eight independent variables in the origina and eight degrees of freedom will suffice. Thus the (i,j)'th element of the inductance m L s (a), for a machine with p pole pairs, is given by; M«)=A- i cos(m r )/?,) n=l(odd) n + L^ _ cos(m2a + +,--2)^) ) (^s) n=l(odd) K A where ' L^ = ( L d + L q ) (4.16) JL A L diff =-j( L d-l q ) (4.17) P = ^ ~ h (4-18) P 9 = Angle between adjacent phase axes (radians). The inductance matrix is symmetrical and a transformation matrix, T(a), can be found such the orthogonal transformation T(or) L s (a) T T (a) yields a diagonal matrix. The transformat matrix is,

77 Generalized Equations for a Nine Phase SynRM 62 ^il' "cw sw cm sij C5(a) Sij a$ 57(4 1.V2 C(a+&5) S(<rt^ C3(a-^ 53(a+&^ C5(a+8^ 55(a+8t^ C7(a+&5) S7(a+&$ 1 C(ar-2$ S{a-2$i da-lfy 53(a-24 C5(a-2t^ S5(a-2c5) C7(a-2c5) S7(a-2^ 1 C(a+6$ S(a+6^ C3(a+di5 S3(a-^ C5(a-^ S5(a+65) a{a-^sj Sl{a+6$ 1 C[a-4S) S{a-4% C{a-A$) S3{a-4^ Cia-A$ S^a-Ad) C7(a-4$j Sl{a-A$ 1 C(a+4Sj S(a+4$ C3(a+4J( S3(a+45) C5(a-H^ 55(a+4^ Cj{a+4$) Sl[a+4$ 1 C(a-6^ S(a-G5j C3(a-65S S3(a-6^ C5(a-6^ S5(a-ci$) a(a-6^ S7(a-6^ 1 C(a+2^ S{a+2Sj C^eHQSj Sip+ty Cia+ty S5(a+25) Cl[aY2$ Sl(a+2$ 1 V~2 C(c-&f S(a-&5) C3(a-&j) S3(a-&5) C5(a-g^ S5(a-84 C7(a-&$ S7(a-&^ 1 (4.19) where, a = pa S = * 9 S, C denote sine and cosine functions respectively. The transformed matrix, L^ = T(a) L s (or) T T (a), has diagonal elements that are constan independent of rotor position. All other elements in the transformed inductance matr zero. The diagonal elements are representative of the fundamental, third, fifth and s spatial harmonic, direct and quadrature components of stator inductance. They are not exact values in a physical sense but a scaled representation produced by the transfo elements are, = ^-L L di L * - ^ L -J--L d5 25K 2 L %-L 95 25^2 9 d L d 3 " ^ ^ - ^ Ld1 L. 'ql " A9TT 2 d 36 A9n 2 q

78 Generalized Equations for a Nine Phase SynRM Voltage Equation The stator voltage equation for any machine is;. d. (4.2) where in the case of a nine-phase machine, v s = stator phase voltage vector = <x v b v t y i s = stator phase current vector = (*«h hf A s = stator flux linkage vector = (A a A b... Af r s = stator winding resistance The stator flux linkage term in equation (4.2) can be replaced by the product of the stator inductance matrix, L s («r), and the stator current vector, i s. Applying the product rule to this term yields an alternative form of the voltage equation expressed in variables that can be measured at a motors terminals. dt da where, da m- dt = rotor speed (rad/s)

79 Generalized Equations for a Nine Phase SynRM 64 The difficulty in applying equation (4.21) directly is that the terms in the inductance matrix depend upon rotor position. The orthogonal transformation of Section 4.2 eliininated dependence in the transformed inductance matrix. The same transformation can be appli the terms of equation (4.21) to yield the d-q voltage equations. Thus, T(flr)v, = r s T(a)i s + T(a)L s (a)^- + T(a)^^-aji s dt da Simplifying, v d9 = rj(a)i s +T(a)L s (a)t\a)t(a)^ + T(a)^^T\a)cM(a)i s «.-r,u + L^ + {lx-)^r<»-lj.^r<»^ (4,2, where, = T(a)v, v^ = transformed d - q voltage vector = (v, v v d3 v?3 v d5 v q5 v dl v ql? i dq = transformed d - q current vector = T(af)i, = (fdx l QX l d3 *,3 ^5 ^5 '<" \l ) The bracketed terms in equation (4.22) can be evaluated given the specific inductan (4.15) and transformation matrix (4.19) for the motor. In the case of the four-pole

80 Generalized Equations for a Nine Phase SynRM 65 experimental machine these matrix identities have been evaluated to obtain identities (4.23) and (4.24). The L^term is as previously defined in equation (4.17). 18 W is* 6L W 1 6L diff da "W 3-6JW 2-6^ 23i Z6L m and, dljd) da T*(o» = -1 1 (4.24) Substituting the matrix identities (4.23) and (4.24) into equation (4.22) yields the d-q voltage equations in component form (4.25 to 4.32). Note that the stator winding of the experimental SynRM is star connected with no neutral. As such there are only eight independent stator phase currents and no zero sequence component. Only eight transformed variables are required to describe the system. Equations (4.25 to 4.32) represent the same information as equation (4.21). However, they are significantly easier to work with because of the reduced couplings between the windings. Also the inductance terms are constant and do not vary with rotor position. Essentially the experimental machine has been represented by a simpler set of

81 Generalized Equations for a Nine Phase SynRM 66 equations without sacrificing any generality. Equations (4.25) and (4.26) when compared to the standard d-q voltage equations for a three phase machine, (4.1) and (4.2), contain factor of two in the speed voltage term. This is due to the machine being analysed poles. Vw, = r s i dl +L dl -^- + 2L,fljL (4.25) dt v 'qx = ~ r±, 'JV +L,-? ' ^gx L -, 2L,M "^dx""dx A, (4.26) v d3 = Va +L <*-^- + 6 V*.73 (4 ' 27) v q i=rj q3 +L q^-6l d3 ax d3 (4.28) v d5 = rj d5 +L d5^ + lol q5 COi q5 (4.29) v q s=r s i q5+ L q5^-1l d5 COi d5 (4-3) Vdi=r s i dl+ L dl^ + lal ql i ql (4-31) ^=rj q^l ql^-lal d7 ai dl (4-32)

82 T e = 2 (^i ~ L qx)idxi q x + 6 ( L d3 ~ L q3 )i d3 i q3 (4.34) Generalized Equations for a Nine Phase SynRM Torque Equation To complete the generalized description of the SynRM a torque equation is required. Assurnin that the SynRM can be modeled as a linear magnetic system its co-energy, W co, will be equal t the stored magnetic energy; 1 T W co=-isl s (a)i s (4.33) The electrical torque can be found from the rate of change of the system co-energy with respect to rotor position; T = dw - da i's constant 1. T dh (a). = i 1 2' s da - s = ±?X(a)T(a)^^-T T (a)t(a)i s 2 da = \l dq \rw ^TV)k The bracketed term is identical to one that arose in deriving the voltage equations. It has been previously evaluated to obtain result (4.23), which can now be substituted to yield the d-q torque equation (4.34). +1(^5 - L q5 )i d5 i q5 + 14(Iy 7 - L ql )i dl i ql Note that the torque equation indicates that the fundamental, third,fifth and seventh harmonic components of current all contribute to torque production within the SynRM. If the higher harmonic components of current are absent the form of the torque equation reduces to the 3 familiar three-phase result without the scaling factor, which is a product of the 2 transformation used.

83 Generalized Equations for a Nine Phase SynRM Summary The generalized d-q voltage and torque equations have been derived for the nine-phase SynRM. These were obtained by applying an orthogonal transformation to the standard stator voltage and torque equations. The transformed equations are significantly more useful than the equivalent stator reference frame equations. This is because the transformation effectively removes the couplings between the stator phase windings. The transformed motor voltages and currents correspond to the combined direct and quadrature components of these variables. Further, the transformed inductance values are constant, independent of rotor position. The simplified mathematical description of the machine opens the door to the possibility of simulating motor performance as well as the design and implementation of appropriate control strategies. This forms the focus of the next chapter.

84 Field-Oriented Control of the SynRM 69 CHAPTER 5 Field-Oriented Control of the SynRM 5.1 Introduction This chapter considers two methods of implementing field-oriented control in the nine-phase synchronous reluctance drive. Field-oriented control involves separately controlling the direct and quadrature axis excitations in the motor. Different control strategies can be used to achie such goals as maximum torque, maximum rate of change of torque and maximum power factor from the drive [2]. In this instance, the methods are discussed from the point of view of implementing a "constant current in the inductive axis" type controller. Direct axis excitation is maintained at a constant value to ensure that the machine remains fully fluxed. Quadrature axis excitation is varied to control the motor's torque. The control methods presented are essentially means to control the direct and quadrature currents in the SynRM. Section 5.2 describes what is termed the "stator current controller". If the SynRM rotor position is known, then a current reference can be generated for each of the stator phase windings. The portions of the stator winding over the rotor pole sides are designated as supplying the direct axis excitation. The remainder of the stator winding is designated as supplying quadrature axis excitation. Thus, a current reference is generated. Law et. al. used similar strategy for defining the current references in their field regulated reluctance machi [5, 27, 28]. The important difference being that the individual phase windings were isolated in the field regulated machine. Each phase was supplied by a separate full bridge inverter. In thi thesis, the windings are star connected. The motor is supplied from a nine-phase voltage source inverter eliminating half of the power switches required in the comparable field regulated machine. Current is controlled by switching the individual phases to the positive or negative inverter bus depending on the phase current's relationship to its reference.

85 Field-Oriented Control of the SynRM 7 Section 5.3 explains what is termed the "transformed frame vector controller". In this instance control is performed in the transformed rotor current space, which is generated by applying the d-q transformation of Chapter 4 to the stator currents. This method recognizes that the entire stator winding contributes to both direct and quadrature axis excitation rather than the simple designation used in the stator current controller. The current reference is generated in the transformed current space and the optimal voltage vector is selected and applied periodically to control the position of the current vector. Both strategies are described and simulation results presented to highlight their relative merits Section 5.4 summarizes the key characteristics of the two controllers. The stator current controller was implemented in the experimental drive system. Practical performance measurements for this controller are recorded in Chapter 7 to provide validation of the simulation results. 5.2 Stator Current Controller The stator current controller designates portions of the stator winding as supplying either direc or quadrature axis excitation in the SynRM. This assignment is based on the individual phase winding's position relative to the rotor. Once a phase winding is assigned as supplying either direct or quadrature axis excitation its current need only be controlled to the appropriate value STATOR CURRENT REFERENCE The idea of splitting the stator into sections, supplying either the direct or quadrature axis excitation, was introduced in Chapter 2 with application to the design model. There the effect of stator slotting was ignored. Effectively the stator teeth and slots were assumed to be "smeared" together so that a continuous current distribution could be obtained around the stator periphery. In the design model, the area of the stator over the rotor pole sides carries the current that supplies direct axis excitation. The area of the stator, over the rotor pole face, carries quadrature axis current.

86 Field-Oriented Control of the SynRM 71 In a real machine the continuous current distribution of the design model has to be approximated by the stator winding. Logically the phase windings over the rotor pole sides carry direct axis current while the phase windings over the pole face carry quadrature axis current. Thus, the stator phase current reference values can be generated given knowledge of the rotor's position and its dimensions. On initial inspection the exercise of generating the stator current reference appears trivial, however, two practical constraints arise with respect to the stator slot effects and the winding configuration. In a real machine current is not continuously distributed but is concentrated in the stato slots. Step changes in the stator current distribution can only be made at a slot opening. As the rotor moves, individual phase windings at either edge of the rotor pole face must make a transition from supplying purely direct axis excitation to purely quadrature axis excitation or vice versa. 7.5 Rotor movement > Rotor Stator 1 IA,REF L ' t "Tv-L!»! t j ; 6 IB,REF i < H! Figure 5.1 Compensation for slot effects in the stator current reference

87 Field-Oriented Control of the SynRM 72 Figure 5.1 shows how the current references for two adjacent phase windings are compensated for the stator slot effects. Actual dimensions from the 5kW machine are used. The rotor is assumed to be moving to the right where is the angle between the phase A winding and the rotor quadrature axis. While the rotor pole side is over the phase A slot opening this winding supplies the direct axis excitation. Similarly, phase B winding supplies direct axis excitation when the pole side is over its slot opening. Ther is a transition period where the pole side is entirely over the tooth between the phase A and phase B winding. In this instance both phase A and B are effectively supplying the direct axis excitation. Phase A current reference is ramped from the direct axis value to the quadrature axis value over this interval. Similarly, the phase B current reference is ramped but in the reverse direction. The stator phase winding is star connected. Consequently, the individual phase currents must sum to zero. To aid in achieving this requirement adjacent phase windings on the stator have their connection polarities reversed. Given the 5kW machine dimensions, typically one phase supplies the direct axis excitation, while the other eight phases supply quadrature excitation. The eight quadrature current phases will conveniently sum to zero. A fraction of the current reference from the ninth phase, that supplies direct a excitation, must be subtracted from each of the other eight phases so that all nine phase currents sum to zero. Figure 5.2 illustrates the modification made to the stator current reference values. A situation is assumed where the phase A winding is supplying the entire direct axis excitation. Phases B to I are positioned over the rotor pole face and carry quadrature ax current. Adjacent phases have their connection polarities reversed so that their currents go in opposite directions. The reversed connections ensure that the quadrature phase currents still physically pass in the same direction through their respective slots. The first graph plots the individual phase currents in the ideal situation where direct axis

88 Field-Oriented Control of the SynRM 73 current and quadrature axis current are independent. These currents do not sum to zero. In the second scenario, an offset equal to one eighth of the direct axis current is subtracted from each quadrature phase. Thus, the sum of the currents is now zero. A B C D tf G H I T3 ID IQ 'I 1 I I "- II II -IQ ID IQ T 8 -lo Figure 5.2 Phase current adjustments for star connected stator. IREF Figure 5.3 Typical phase current reference versus rotor position.

89 Field-Oriented Control of the SynRM 74 Figure 5.3 shows a typical current reference for one stator phase of the 5kW machine. The current reference is plotted against rotor position. Compensation for both stator slotting effects and the stator winding connection are included in the current reference INVERTER SWITCHING STRATEGY The inverter is switched at a fixed frequency. During each control cycle, the switching pattern is generated by comparing each phase current reference with the corresponding phase current feedback. If the reference is higher than the feedback value then the respective phase winding is switched to the positive inverter bus. Conversely, if the reference is lower than the feedback value then the phase is switched to the negative inverter bus. Clearly, one advantage of the stator current controller is the simplicity the switching algorithm STATOR CURRENT CONTROLLER SIMULATION To verify the stator current controller's performance it was initially simulated in MATLAB / Simulink. Figure 5.4 shows a block diagram of the simulated system Appendix F contains the full set of simulation source files. The simulation can be divided into two logical components. The controller represents the actual control algorithm, as would be implemented in a DSP type device. The drive models the inverter / motor hardware. Considering the drive model in more detail, it can be seen that the actual modelling of motor is done in the transformed rotor current plane. The input to the drive model is th inverter-switching pattern, generated by the controller. This is is converted to a volta vector, initially in the stator current plane, which is then rotated to form the equival vector in the rotor plane. The voltage equations (4.25 to 4.32) are used to determine th change in the rotor plane current vector. Instantaneous torque is determined using the rotor plane torque equation (4.24). Torque is integrated to obtain rotor speed and once

90 Field-Oriented Control of the SynRM 75 again to obtain rotor position. Thus all electrical and mechanical characteristics of the motor are represented. Position eed«f Speedy T CONTROLLER S' DRIVE A. Is.»b Position CONTROLLER DETAIL SpeedVd Speeds, O- Generate stator current reference Determine inverter switching Zero order hold -ols,b Position Q Position DRIVE DETAIL \co(t)dt Speed Calculate position S' O- ^ v s V, f(y r,co) Wr) Torque \t(t)dt -*Q Speed Calculate stator voltage vector Calculate rotor voltage vector Calculate current vector Calculate torque Calculate speed --o Is,m Calculate stator currents Figure 5.4 Stator current controller simulation block diagram

91 Field-Oriented Control of the SynRM 76 The controller regulates the direct axis component of current to afixedvalue appropriate for fluxing the machine. A PI speed controller generates the quadrature axis compone of the current reference. These references, combined with rotor position, are used t generate the individual stator phase current references as previously described. The inverter legs are switched to the positive or negative inverter bus depending on the relationship between phase current reference and feedback. Thus the inverter switchi configuration is generated. A zero-order hold is included to duplicate the controlle fixed frequency operation. "Cm (Oref o «* i k h G, 7> + l ' \J r 1 (Of/b Speed controller Current / torque controller Figure 5.5 Speed controller including approximation to torque control loop Figure 5.5 shows an approximation to the stator current controller. The model has been reduced to a speed controller cascaded with a current / torque controller. The torqu controller is approximated by a first order lag element. Figure 5.6 shows the step response of the torque controller as simulated. The gain of the torque loop is given the ratio of motor torque to quadrature axis current when the direct axis is fully _ 12 (Nm)._._ /A G = = 12 Nm/A KA) The time constant will be approximated by the L/R ratio of the quadrature axis circuit. L g _.15(H) = 5.5rns ' R 27.4()

92 Field-Oriented Control of the SynRM 77 Figure 5.6 Step response of torque controller The speed controller parameters, G m and T m, are chosen in accordance with the "symmetrical optimum" as is normal practice with transfer functions containing a double integration [35]. In this case for the unloaded SynRM it was determined that Go, =.2 (As/rad) and T w =.35 seconds. This resulted in an optimally damped speed loop 5.3 Transformed Frame Vector Controller Vector control in the transformed rotor current plane offers potential improvements over the stator current controller. The stator current controller designates portions of the stator wind as contributing solely to direct or quadrature axis excitation. In reality, linkages between the stator phase windings mean that all sections of the stator winding contribute to both direct and quadrature axis excitation. The stator controller only identifies the dominant contribution of each phase and neglects any secondary effects. Transforming the stator phase currents into the rotor current plane isolates the individual harmonic components of direct and quadrature excitation. A controller based in the rotor current plane has the advantage of being able to control these components directly. This should lead to more accurate torque control and better dynamic torque performance from the drive.

93 Field-Oriented Control of the SynRM TRANSFORMED FRAME CURRENT REFERENCE The current reference for the transformed frame vector controller is formed as an approximation to the ideal stator current distribution in the design model. The design model assumed a rectangular current distribution located in a thin veneer along the stator's inner surface. The stator current controller generated its reference by approximating the shape of the current distribution, making the necessary allowances fo stator slot effects and the connection of the winding. For the transformed frame vector controller the current reference is generated as the harmonic components of the ideal current distribution. These components are found from the Fourier series decomposition of the ideal. Figure 5.7 shows the current reference vectors for the transformed frame vector controller thus formed. Effectively, the reference becomes a set of stationary vectors in the rotor current plane whose lengths have a simple proportional relationship to what was designated direct and quadrature axis current in the design model..61 IQ Q.28 I D.31 IQ.27 I D >D.26 I D >D.16 IQ 4.24 I D >D Fundamental Plane,rd 3 Harmonic Plane 5 th Harmonic Plane 7 th Harmonic Plane Figure 5.7 SynRM current reference in transformed rotor current plane The current reference is restricted to containing harmonic components up to and including the seventh harmonic only. This is to ensure that the current reference vect retain a simple proportional relationship to direct and quadrature components of

94 Field-Oriented Control of the SynRM 79 excitation. Further, the eight-dimensional reference vector matches the degrees of freedom inherent in a nine-phase star-connected motor. Interestingly, higher harmonic components can be included in the reference as is the case in the stator current controller. This is not done by adding extra dimensions to the current vector reference because of the Umited number of degrees of freedom available. Instead, the existing vectors require variable components to be added to them to account for higher order harmonic components. The implication is that the simple proportional relationship between the current vectors and the direct and quadrature axis excitation is lost and the generation of the current reference becomes a complex task. This idea has not been pursued as the additional contribution to torque of higher harmonic components reduces with the order of harmonic as can be seen in the d-q harmonic torque equation (4.34). In the torque equation, the third harmonic component potentially contributes an additional 33% of the maximum fundamental torque to the output. The seventh harmonic contribution drops to 14% of the maximum fundamental torque. Higher harmonics if included would contribute less again. It was felt that the benefit of adding the higher harmonics did not warrant the additional controller complexity. Once the current reference is generated, the transformed frame vector controller must ensure that the transforms of the actual currents map to the reference vectors. During each control cycle the optimal inverter switching configuration (or voltage vector), must be selected and applied VOLTAGE VECTOR SELECTION Selecting the optimal inverter switching configuration, during each control cycle, is significantly more difficult in a nine-phase drive than a conventional three-phase drive. In a three-phase drive motor currents are represented as a two-dimensional current vector. The controller chooses from 2 3 = 8 two-dimensional voltage vectors (where 7 are

95 Field-Oriented Control of the SynRM 8 distinct) to control the position of the current vector and hence the machine. By extension, to implement vector control in a nine-phase machine leads to attempting to control an eight-dimensional current vector by choosing from 2 9 = 512 (511 distinct) eight-dimensional voltage vectors. The selection of the voltage vector is further complicated by the different inductances seen in the direct and quadrature axes as well as the different harmonic planes. This point is best demonstrated by first considering the voltage vector selection process in three-phase induction motor drive. In an induction machine the direct and quadrature inductances are equal. A vector controller selects the voltage vector that will control t motor currents closest to the desired current vector. The selection is carried out in the voltage plane by calculating the ideal voltage vector, v^ai, and comparing it to the possible voltage vectors, v inv (s) (where s denotes the inverter-switching configuration). Thus, the optimal voltage vector is found by minimizing the error, v^is) - v^a/. This process works because the error in the current plane is proportional to the error in the voltage plane. Performing the comparison in the voltage plane reduces the number of calculations necessary. For the nine-phase SynRM drive, where there are different inductances along the direct and quadrature axes (and indeed in the different harmonic planes), an alternative approach is required. The method in the three-phase induction motor drive, of minimizing v inv (s) - vu** applies equal weight to direct and quadrature axis voltage components. However, when the corresponding events in the current plane are considered, it can be seen that equal voltage errors in the direct and quadrature axes w produce different current errors because of the unequal inductances. Consequently, when minimizing the voltage error the individual components need to be scaled relative to the associated inductances to ensure the best result is achieved in the current plane. The scaling function for the voltage error is;

96 Field-Oriented Control of the SynRM 81 r a 1 L 9-2- (Vmv W ~ V ideal Y = ( V inv (- " Videal ) X 9 L a 25-^- L d 25 (5.1) 49 _L L d 49 It is possible to greatly reduce the number of voltage vectors necessary to choose from by using symmetries in the voltage planes. Figure 5.8 shows the d-q harmonic components of the available voltage vectors in the nine-phase drive. These are generated by applying the transformation of Chapter 4 to the stator voltages generated given all possible inverter-switching configurations. In the fundamental plane it can be observed that the pattern of voltage vectors repeats itself every 2. The problem of selecting the optimal voltage vector in this plane can be reduced to selecting the optimal voltage vector in a 2 sector.

97 Field-Oriented Control of the SynRM 82 Fundamental Plane 3rd Hannonic Plane «"*»/ 2- '' 11» To % <?i&# Oi** * *,,*»% % < J 3- Direct axis 5 th Harmonic Plane 7th Hannonic Plane 1 I r- S-4 a &, * * * *;W«J< Tf*» < % *»*«? #» < 5";.. a **>v St * * * * * «&f5 «*** V* *. V*t -4 J Direct axis Figure 5.8 Voltage vectors from a nine-phase inverter Figure 5.9 shows the voltage vectors from the to 2 sector of the fundamental plane and the associated vectors in the higher harmonic planes. Should a vector be required from outside this range then it is rotated in steps of 2 until it falls within thi For example, finding the vector that best approximates VZ68, in the fundamental plan would correspond to finding the vector closest to VZ8. When rotating the voltage vector in the fundamental plane by 9 the corresponding vector in the third harmonic plane must be rotated by 39. Similarly, the vector in the fifth harmonic plane shou rotated by 59 and so forth.

98 Field-Oriented Control of the SynRM 83 Fundamental Plane 3rd Harmonic Plane»» * - «>-«- a -4 I -1 fl) 1 2 Direct axis 5th Harmonic Plane 7th Harmonic Plane 3i 2.5- a, r a " X ' 2 3 i 1. i » J » 1J Direct axis Direct axis Figure 5.9 Voltage vectors from - 2 sector of fundamental plane. Having determined the optimal voltage vector in the to 2 sector it must be converted back to the appropriate sector and switching configuration. Due to the symmetry of the machine there is a logical relationship between the switching configuration for a vector in one 2 sector and the corresponding vector in an adjacent sector. If the inverter switching state is represented as a 9-bit binary number moving from one 2 sector to th next in a clockwise direction involves inverting each bit and shifting them one place to the left. The most significant bit loops around into the least significant bit position. Figure 5.1 illustrates this concept.

99 Field-Oriented Control of the SynRM 84 Plane axis Fundament!.,. 4 2 VZ3 (Switching configuration 111). ***"* V./1 (Switching configuration ) D - axis Figure 5.1 Voltage vector relationship to inverter switching configuration. The method of dividing into 2 segments reduces the comparison requirement from 512 to 52 vectors. The disadvantage of this approach is that it limits the choice of vectors in the higher harmonic planes. The optimal region in the fundamental plane is considered but the corresponding components in the higher harmonic planes may not be in the desired locations. The impact of this restricted choice will be demonstrated in the simulation results TRANSFORMED FRAME VECTOR CONTROLLER SIMULATION The transformed frame vector controller was also simulated in MATLAB / Simulink. Figure 5.11 shows a block diagram of the simulated system. Appendix F contains the full set of simulation source files. As expected, the drive model is identical to that used to simulate the stator current controller. The controller model represents the actual control algorithm as would be implemented in a DSP type device. The controller consists of a cascaded speed and current loop. The speed controller is a PI controller that generates the quadrature current reference to vary torque. The direct current reference is held constant to maintain machine flux. A set of reference vectors, in the rotor current plane, are generated as multiples of the nominal direct and quadrature

100 Field-Oriented Control of the SynRM 85 excitation levels. The d-q harmonic voltage equations (4.25 to 4.32) are used to determine the ideal voltage that is required to maintain the current reference. This voltage vector is rotated into the stator voltage plane, compared with the available voltage vectors and the inverter switching configuration detennined. Position Spee<W Speedm, CONTROLLER i ' S' DRIVE A I Idq.Ph CONTROLLER DETAIL Position Q Speed rc f (y Speedm, O- Lj,rt Speed controller /(' >' ) Generate rotor current reference /(/*.*» V r, d J 1 - Calculate ideal rotor voltage Calculate stator voltage Zero order hold f(y,m) Select inverter switching dq.cb Figure 5.11 Transformed frame vector controller simulation block diagram Three strategies for the voltage vector selection were simulated. These were; 1. Comparing the ideal vector with all 512 possible vectors and selecting the closest vector. The errors in each harmonic plane are weighted equally. 2. Comparing the ideal vector with all 512 possible vectors but with scaling to allow fo different inductances in different axes and harmonic planes. The errors in each harmonic plane are weighted according to equation (5.1).

101 Field-Oriented Control of the SynRM Comparing the ideal vector only with vectors from the corresponding 2 sector in the fundamental plane. Voltage scaling was still employed with this method. The errors in each harmonic plane are weighted according to equation (5.1). Figure 5.12 shows a comparison of the step responses in the current components for the three voltage vector selection strategies. The rotor was simulated as being locked and inverter DC bus set to 2V. Direct axis excitation is set to 2A at seconds. Quadrat axis excitation is stepped from to IA at.5 seconds. The controller updated the voltage vector selection at a 5kHz frequency. In each case the d-q harmonic components are recorded and graphed separately. Further, Figure 5.13 shows the corresponding changes in torque when the step change is made in quadrature axis current. 23 i Oi I -i Oi - / Time (s) ~ liliiwiilii.iililjkjilliiljil P W I i -If::- T i."f-!.l!i! 'hi rf'i'silm W^i,^i.i L..^i 1.W 1.1' '.2 1 Jo.25.3 i» *ii iaiti»»iimjirt«-1 Timefs) Tlme(s) Figure 5.12a Step response of d-q current components (Case I)

102 Field-Oriented Control of the SynRM 87 2-i 1J * 1 OJJ.6 1JJ- IA j / / ' 1.S.1.15 Tax if).2 r.25 J 12 1 < j3 S Oi 3 A 2 ** -2- Ik L lllklk k fl lb ill i HiiiSl ^3 J Time (s) l-i 3 i -.5 cr -3 o.tts8 t"rvtp Time (s) Figure 5.12b Step response of d-q current components (Case IT) < f -3 i Time(s) tty^uiMiiyVlUi I,.1.. if hpi!i '.'.- '";if V" m T ". n^'n'^fpt Tune(s) Figure 5.12c Step response of d-q current components (Case IH)

103 Field-Oriented Control of the SynRM Figure 5.13 Response of torque to step change in currents

104 Field-Oriented Control of the SynRM 89 The following conclusions can be drawn from the simulation results; 1. In the steady state, the Case I controller (simple comparison of the ideal voltage vector with all possible vectors, without scaling) gives good current regulation. However, during changes in current loss of control is evident. Noticeably the third, fifth and seventh harmonic components of direct axis current go negative on initial excitation. Similarly, considerable overshoot can be seen in the corresponding quadrature components. The torque response appears quite good. Most noticeably, the response is faster, contains no overshoot and maintains low ripple. However, this is somewhat misleading. The simulation torque calculation assumes constant inductances. The presence of current transients gives the appearance of fast torque response where saturation effects would limit the available torque in the real machine. 2. The introduction of voltage scaling in Case II improves the steady state regulation of the higher harmonic current components and slightly reduces it in the case of the fundamental component. This is to be expected as the scaling reduces the controller's sensitivity to errors in the higher inductance axes. Transient performance is improved markedly with no negative excursions in the direct axis currents and reduced overshoot in the quadrature components. The torque response remains quite good with noticeably less ripple than observed in Case I. 3. Case HI demonstrates the effect of reducing the voltage vector selection to vectors in a 2 sector in the fundamental plane. The steady state and transient current regulation nearly matches that of the Case II controller. The most noticeable difference is a slight increase in ripple, which is also reflected in the steady state torque regulation. Indications are that this would be an acceptable method of voltage vector selection. The reduced number of calculations necessary to use this method makes it the most practical scheme to implement.

105 Field-Oriented Control of the SynRM 9 Comparing the torque response of the transformed frame vector controllers (Figure 5.13) to that of the stator current controller (Figure 5.6) shows that the vector controller offers both improved torque regulation and faster step response. This improvement was as expected from a vector type controller. One problem, which has been previously alluded to, is the time necessary to carry out the calculations to implement vector control. This practical constraint will be examined further in Chapter Summary Two methods of implementing field-oriented control in the nine-phase SynRM have been presented and simulated. The stator current controller generates stator phase current references based on rotor positio A simple hysteresis switching strategy is used to control the phase currents. The main advantage of this approach is its simplicity to implement. Running the inverter with a relativ modest control cycle frequency of 5kHz achieved quite acceptable current regulation. The transformed frame vector controller offers improved performance over the stator current controller. By controlling the isolated d-q harmonic components of current better current regulation and faster transient performance are achieved. This is demonstrated in simulations conducted with the identical control cycle frequency as the simulated stator current controlle The limitation of the transformed frame vector controller is the time necessary for the background calculations.

106 The Nine Phase Inverter and DSP Controller 91 CHAPTER 6 The Nine Phase Inverter and DSP Controller 6.1 Introduction This chapter describes the inverter and DSP controller used in the project. Figure 6.1 shows a block diagram of the system hardware. Logically, it can be divided into three main sections. These are the inverter power circuit, the DSP controller and the controller interface circuit. Appendix B contains the complete electrical circuit diagrams for the hardware and a full parts list. Figure 6.2 is a photograph of the assembled inverter power and controller interface circuits. r INVERTER POWER CIRCUIT 3 Phase Supply DC Link Power Supply Dynamic Brake Circuit Inverter / v Motor Encoder CONTROLLER INTERFACE CIRCUIT Gate Drive Circuit Current Sensing Circuit Shaft Encoder Interface DSP CONTROLLER Figure 6.1 Block diagram of the inverter and controller circuit.

107 The Nine Phase Inverter and DSP Controller 92 Figure 6.2 Inverter hardware 6.2 Inverter Power Circuit The power circuit is that of a typical voltage source inverter. Electrical circuit diagr B2, of Appendix B, show the circuit detail. Figure 6.1 further divides the power circuit three logical components. These are the DC link power supply, the dynamic brake circuit the inverter proper. DC LINK POWER SUPPLY The DC link power supply is an uncontrolled AC to DC converter. Figure 6.3 divides the power supply into its components. It consists of a three-phase bridge rectifier and DC l filter. The rectifier is nominally rated for 12V / 3A. The DC link filter consists of a 34.4m inductor and a looouf electrolytic capacitor (a combination of four electrolytic capacit used to achieve the desired voltage rating). During initial power up a 1Q resistor is

108 The Nine Phase Inverter and DSP Controller 93 temporarily placed in series with the capacitor to limit inrush current as the capacitor is first charged. This resistor is bypassed by an external relay after.5 seconds. Three phase -415V5Hz Variable supply Bridge Filter Rectifier Figure 6.3 DC link power supply Dependent upon the AC supply voltage, the DC link power supply is capable of supplying up to 3A DC, at a voltage up to 56V DC, with minimum ripple. This represents an oversized system in terms of its current rating but allows for maximum flexibility with regard to futu work. DYNAMIC BRAKE CIRCUIT A diode rectifier is used in the DC link power supply. This means that energy cannot be transferred from the DC bus back into the AC mains. During braking, the kinetic energy of th motor is transferred to the DC bus via the anti-parallel diodes in the inverter proper. The dynamic brake circuit provides the means to dissipate this energy and better regulate volta the DC bus. The dynamic brake circuit consists of a 94Q resistor and IGBT switch connected in series across the DC bus. Energy transfer back into the DC link from the motor causes the bus voltage to rise. The dynamic brake circuit detects this voltage rise and switches the resist across the DC bus, dissipating the energy.

109 The Nine Phase Inverter and DSP Controller 94 The electrical circuit diagram for the dynamic brake control is on drawing B3 of Appendix B. The voltage level, which the dynamic brake circuit operates at, is adjustable to a value appropriate to the circuit's input voltage. INVERTER CIRCUIT Figure 6.4 shows a schematic diagram of one phase of the inverter proper. A pair of IGBTs switch the output phase connection to either the positive or negative DC bus. Each of the IGBTs has an anti-parallel power diode across its collector - emitter terrninals. The diod provides a path for load currents during IGBT switching. +VBUS O v 'BUS Figure 6.4 Circuit diagram for one phase of inverter The power devices used are insulated gate bipolar transistors (IGBTs) and power diodes. IGBTs were chosen because of their ability to switch high currents and voltages quickly. Additional benefits were a relatively simple gate drive circuit and a square safe operating which would not require snubber circuitry. The IGBTs and power diodes are nominally rated for 12V / 8 A. To achieve maximum torque the motor requires phase currents of 2A pea ic. Again this represents an oversized system in t of current rating but allows maximum flexibility with regard to future work. Thermal considerations normally form an important part of a power circuit design. In this instance we are operating the power devices at the lower end of their rated operating range

110 The Nine Phase Inverter and DSP Controller 95 As a consequence no detailed thermal design was done other than taking the usual precautions of mounting the devices on appropriately sized heatsink. More rigorous thermal calculatio and design would be required if the circuit was to be operated at its maximum electrical 6.3 DSP Controller The controller software was implemented on an Innovative Integration ADC64 Digital Signal Processor (DSP) board. This card mounts directly to the PCI bus internal to a computer. F the computer, source code can be downloaded to the ADC64 via the PCI bus. The ADC64 connects to the outside world via a 1 way SCSI-2 connector. The salient features of thi board are indicated in an excerpt from the device data sheet in Appendix E. With respect this project the key features are now summarized. PROCESSOR The ADC64 board contains a Texas Instruments TMS32C32 6MHz DSP chip. This device is capable of performing 32-bit floating-point arithmetic, which again gives maximum flexibi when implementing control algorithms. The Texas Instruments processor itself was preferre because of its ready availability and good documentation. ANALOGUE I/O The board has 64 analogue inputs. (These are achieved by using 8 independent channels eac connected through an 8-1 multiplexer.). The individual Analog to Digital Converters (ADCs have 16-bit resolution with a maximum sampling frequency of 2kHz. The voltage range of each input can be user selected to a maximum of ±1V. This maximum value was chosen to limit the impact of any noise in the analog feedback signals. In addition, the board contains two 16 bit analogue outputs. These were not necessary to implement the drive system, however, were invaluable when it came to real time monitoring internal control software variables during commissioning.

111 The Nine Phase Inverter and DSP Controller 96 DIGITAL I/O The ADC64 has provision for 16 bits of TTL compatible digital I/O. The hardware setup of ADC64 board restricts the way in which these 16 bits can be configured. They must be configured as, all outputs, all inputs or a combination of 8 inputs and 8 outputs. This re had further impact on the interface circuitry, where a combination of 9 outputs and some inputs were ideally required. The method used to overcome this problem is detailed in the following section. INTERRUPTS The TMS32C32 has 16 prioritized interrupts from various sources including software, external pins and internal timers. Interrupts were used in two circumstances. The control cycle time is fixed by using a timer interrupt to initiate the main control l method ensures a constant cycle time, which is necessary in implementing control algorithm It is preferred over trying to estimate the timing of a piece of code that runs continuou latter approach is subject to errors where the code executes over multiple paths affectin cycle time. An additional external interrupt pin is used in the shaft encoder interface circuitry. Th TMS32C32 has four external interrupt pins. The default ADC64 configuration uses all of these interrupts for reading and writing from the PCI bus, A/D status and interrupting th from the host computer. As the control code operates on a fixed cycle time the interrupt A/D status could be reconfigured for use in the shaft encoder interface circuitry. This c is detailed further in the following section. COUNTERS The ADC64 has six 16-bit timer/counters independent of the DSP processor chip. Five of the can be configured for triggering A/D conversions. Most notably one counter is pinned out t

112 The Nine Phase Inverter and DSP Controller 97 the board's external interface for counting external events up to rates of 1MHz. This counter is utilized in the shaft encoder interface to count pulses from the shaft encoder. SOFTWARE Software can be written for the DSP processor in C or Assembler. The standard Texas Instruments assembler / linker is used in preparing executable code. The actual control code is written in C. A listing of the code can be found in Appendix C. The actual code operation is detailed in Chapter Controller Interface Circuit Interfacing the DSP controller to the power circuit involved correctly matching the D electrical requirements to those of the external hardware. Inherent in this process w with the issue of voltage isolation between the two systems. GATE DRIVE CIRCUIT Figure 6.5 shows an overview of the entire gate drive circuit. It can be divided into logical blocks being the gate drive decoder, blanking time circuitry and the gate dri DSP CONTROLLER Gatel Gate 2 Gate 3 Select 1 Select 2 Switch A Switch B etc. Switch A + Switch A etc. Gate Drive Decoder Blanking Time Circuitry Gate Drive Circuitry Figure 6.5 Block diagram of gate drive interface circuit.

113 The Nine Phase Inverter and DSP Controller 98 The DSP controller has a total of 16 digital I/O points. These can be configured as 16 inputs, 16 outputs or a combination of 8 inputs and 8 outputs. To input data from the shaft encoder required the use of at least one digital input. Therefore, the number of digital outputs was restricted to eight, which was insufficient to drive the nine phases of the inverter directly. The problem is overcome by multiplexing the nine gate drive signals onto only three gate drive outputs. The gate drive decoder block decodes these three gate and two address signals to reproduce the original nine gate drive signals. The electrical circuit diagram for the gate dr decoder is on drawing B6 of Appendix B. In the power circuit the output phase connection is always switched to either the positive or negative DC bus. During a transition state, care must be taken to ensure that both the IGBTs in one phase are not turned on simultaneously, thus avoiding "shoot through" currents and potential device damage. This is achieved by turning one IGBT off and waiting for a short time period (termed blanking time) before turning the other IGBT on. The blanking time is physically achieved using a combination of RC timing circuit and Schmitt trigger. The blanking time is set to 5ps. Drawing B5 of Appendix B contains the full electrical circuit diagram of the blanking time circuit. The gate drive proper provides electrical isolation between the driving logic and the inverter power circuit. It also provides amplification of the logic signal to a level appropriate for driving IGBTs. Voltage isolation is achieved by using a 74OL61 opto-coupler on the logic signal. Amplification requires a separate supply fed through a transformer, again for isolatio purposes. The output, IGBT switching signal, is a ±15V signal with a series 15Q resistance. This resistance serves to slow the turn-off time of the IGBT preventing latchup. A full electrical circuit diagram for the gate drive circuit is shown in drawing B4 of Appendix B.

114 The Nine Phase Inverter and DSP Controller 99 CURRENT SENSING The electrical circuit diagram of the current sensing circuit can be found on drawing B8 of Appendix B. In summary, phase currents are measured using LEM LTA5P/SP1 current transducers. These are Hall effect devices capable of measuring instantaneous currents up t 5A. Other features of the device are its wide frequency range (DC to 1kHz) and large voltage isolation rating (3kV at 5Hz). As the motor currents are not to exceed 2A peak the ph windings are looped five times through the sensors. This allows a greater portion of the cu transducers operating range to be utilized. The current transducer has both a voltage output (scaled loomv/amp) and current output (scaled 1mA/Amp). The current output was used with a 5Q. burden resistor to give a scaled current signal of 4A = 1V. The DSP controller has 8 ADCs that can each be multiplexed to 8 different inputs to give a total of 64 analog inputs. For speed, only 8 phases are read to avoid the need for multiple The ninth phase current is determined because all phase currents must sum to zero. Finally, the ADCs perform a 16-bit conversion and are scaled to accept a ±1V input. As a consequence, internal to the DSP, current signals are scaled such that 4A = SHAFT ENCODER INTERFACE The rotor position is measured using a Hewlett-Packard three channel optical encoder. Two channels, A and B, generate 1 pulse per revolution signals in quadrature. Rotor position be determined by suinming pulses while direction is given by the phase relationship between the signals. Figure 6.6 demonstrates the phase relationship between channels A and B for forward and reverse rotation. The third channel, I, gives one index pulse per revolution wh is useful for synchronization.

115 The Nine Phase Inverter and DSP Controller 1 Forward rotation Reverse rotation mfim nn B Figure 6.6 Shaft encoder outputs. The hardware for the shaft encoder interface circuit is shown in drawing B9 of Appendix B. Figure 6.7 summarizes in block diagram form the circuit's key functions. The three optical encoder outputs are first fed to a buffer / filter circuit. The filter removes any high frequ noise in the signals. Count A B Buffer/ Filter D > Q i Up / Down Synch Figure 6.7 Block diagram of shaft encoder interface circuit. Channel A is used to clock a counter on the ADC64 DSP board. The counter is set to continuously count down. The control software adds / subtracts the change in the counter over one control cycle to an accumulative position variable. A D flip-flop is used to examine the phase relationship between channel A and channel B signals. The output from the flip-flop provides indication of forward or reverse operation.

116 The Nine Phase Inverter and DSP Controller 11 Finally, the synchronization pulse initiates an edge triggered interrupt on the ADC64 processor board. This interrupt resets the position counter to the value corresponding to the location of the synchronization pulse.

117 The SynRM Drive Software and Performance 12 CHAPTER 7 The SynRM Drive Software and Performanc 7.1 Introduction This chapter describes the software implementation of the stator current controller of Chapter 5 with the hardware described in Chapter 6. Performance results for the completed drive are then presented. Section 7.2 describes the control software developed to implement the stator current controlle from a block diagram perspective. The full source code is contained in Appendix C for additional reference. The feasibility of implementing the transformed frame vector controller in the existing hardware is also considered. This analysis highlights potential means for implementing the more advanced controller in the future. Section 7.3 presents the performance results for the drive. Specifically, the drive's current regulation, speed response and torque response are all demonstrated. These results are compared with those predicted from the design model in Chapter 2 and the dynamic simulations of Chapter 5. Appropriate conclusions are then drawn. 7.2 Control Software The software implementing the stator current controller on the ADC64 DSP development board will be described here. The full source code (in C programming language) is contained in Appendix C. Initially, preference was to implement the transformed frame vector controller because of its superior performance. Unfortunately this was not possible given current technical constraints and the limits of the existing hardware. Before proceeding with a description of the stator current controller software the practical constraints preventing

118 The SynRM Drive Software and Performance 13 implementation of the transformed frame vector controller will be briefly discussed. This also serves to highlight means for future implementation of the more sophisticated controller TRANSFORMED FRAME VECTOR CONTROLLER In Chapter 5 it was demonstrated through simulation that the transformed frame vector controller offered significant performance advantages over that of the stator current controller. Figure 7.1 shows a simplified block diagram of the key controller functions necessary to implement the transformed frame vector controller. For comparable operation to the simulation (which had a 5kHz control cycle) the key functions need to be completed within 2u.s. 1 Read stator currents Transform currents into rotor plane Calculate the ideal voltage vector Select the best voltage vector Set inverter switching configuration tv Figure 7.1 Key control functions necessary to implement the transformed frame vector controller. The viability of the transformed frame vector controller can be determined by estimating the processor time necessary to perform the functions shown in Figure 7.1. READ STATOR CURRENTS Reading the stator phase currents requires eight analog-to-digital conversions (the nint phase current is dependent on the other eight and can be calculated). The ADC64 is equipped to read up to eight analog inputs simultaneously with a maximum lops conversion time [24]. The outputs from the A/D converters are memory mapped to the TMS32C32 processor. Thus, reading the stator currents will take a maximum of IOJIS assuming negligible time to calculate the ninth phase current.

119 The SynRM Drive Software and Performance 14 TRANSFORM CURRENTS To transform the currents from the stator reference frame to the rotor d-q reference requires multiplying the 9x1 stator phase current vector by the 9x9 transformation matrix, T(a). For the TMS32C32 processor a single floating point operation requires one clock cycle or 33ns [55]. Additionally, the elements in the transformation matri contain sine and cosine functions. Each sine / cosine function call typically takes to complete. Thus, an approximate figure for the calculation time required for the transform operation is calculated as; [81 (multiplications) + 81 (additions)] x 33ns + 81(sin/cos) x 2.2u.s = 184u.s CALCULATE IDEAL VOLTAGE VECTOR The ideal voltage vector is calculated using the d-q voltage equations in component (4.25 to 4.32). There are eight components in the voltage vector and each component calculation requires six multiplications and three additions. Thus, the total time necessary to perform the calculation is; 8 x ^(multiplications) + 3(additions)] x 33ns = 2.4p,s SELECT VOLTAGE VECTOR To select the best voltage vector requires the computation of the distance between e potential vector and the ideal. Further, the individual voltage components need to b scaled to account for the different inductances seen in the machine axes. Thus, each vector evaluation requires fifteen additions and sixteen multiplications. If all the possible vectors are considered the calculation stage of the selection process will 512 x [15(additions) + ^(multiplications)] x 33ns = 525u.s Restricting the selection area to a 2 segment in the fundamental plane reduces the number of vectors to be considered to 52. The calculation time in this case would be

120 The SynRM Drive Software and Performance x [15(additions) + ^(multiplications)] x 33ns = 53u.s The values calculated must be sorted to select the optimal vector. The time required to perform the sorting function can be estimated as one clock cycle for each voltage vector considered. Thus, the voltage vector selection process will require 525u.s x 33ns = 542p.s if all vectors are considered and 53 jis + 52 X 33ns = 55p,s if only a restricted segment is considered. SET INVERTER SWITCHING CONFIGURATION The digital outputs of the ADC64 are capable of switching at 7ns [24]. As nine outputs are required, and the ADC64 controller only caters for eight, external multiplexing is needed. The speed that these signals can be multiplexed becomes the limiting factor. With the present hardware the gate signals are sent as three sets of three with a 1u.s interval between each set. Thus, a period of 2u.s is required to set the inverter switc configuration. The total time necessary to perform the cycle by cycle calculations to implement the transformed frame vector controller in the existing hardware is, lops + 184u.s + 2.4u.s + 525ns + 2u.s = 741u.s Section presented simulation results for the transformed frame vector controller with a 5kHz control cycle. Clearly the software based equivalent cannot be implemented on the hardware assembled for this project. The main problem areas are the current transformation and the voltage vector selection portions of the code. One solution is to run the controller at a slower control frequency. Figure 7.2 shows the simulated torque response for a controller operating at 1kHz (1ms control period). Comparing this result with those in Figure 5.3 it can be seen that the stator current controller at 5kHz regul

121 The SynRM Drive Software and Performance 16 torque better than the transformed frame vector controller at 1kHz. For this reason the transformed frame controller was not implemented in hardware. Figure 7.2 Step torque response of transformed frame vector controller at 1kHz As a footnote, it may be possible to implement the transformed frame vector controller a higher control frequencies by, (a) Modifying the hardware. One potential way of reducing the time necessary for the current transformation is to do the transformation in hardware external to the DSP controller. By using a FPGA (field-programmable gate array) or PLD (programmable logic device) type device and employing look-up tables for the sine / cosine functions it should be possible to obtain the transformed currents at faster speeds. This idea has already been successfully demonstrated in a three-phase controller using discrete logic components [6]. (b) Reducing the voltage vectors considered when selecting the optimal value. The voltage vector selection problem can be reduced by restricting selection to a 2 segment in the fundamental plane as described in Chapter 5. This requires considerably less calculation time and has been shown to sacrifice little in terms of performance. Unfortunately time and financial restrictions have prevented these options being fully explored at this stage.

122 The SynRM Drive Software and Performance STATOR CURRENT CONTROLLER The stator current controller requires substantially less background computation than t transformed frame vector controller does. As such it is easier to implement at higher control frequencies in the DSP controller. Figure 7.3 shows a block diagram of the stat current controller software. The corresponding sections of code are similarly labeled i the source code listing in Appendix C. The functionality of the main blocks will now be briefly considered. INITIALIZATION The initialization block defines the hardware and software configuration of the DSP controller. Specifically, variables are defined and initialized, the DSP peripherals an interrupts are configured and all gate drive outputs are set to logic low. ALIGN POSITION FEEDBACK The stator current controller requires accurate knowledge of rotor position to function Rotor position is tracked by counting pulses from a 1 pulse / revolution shaft encod The pulse count is aligned to rotor position by monitoring a synchronization pulse (occurs once per revolution) from the encoder that triggers an external interrupt on th DSP. The software waits for two synchronization pulses prior to starting. The rotor shaft has to be rotated manually to obtain these synchronization pulses. Messages written to the terminal advise of the program status during the alignment operation. INITIALIZE TIMER INTERRUPT To ensure the code operates at a fixed control cycle a timer interrupt is used. It is s frequency of 5kHz. Execution of each cycle of the main control loop only proceeds upon receipt of this interrupt.

123 The SynRM Drive Software and Performance Initialize timer interrupt NO Read speed reference Read position / speed PI speed controller Calculate stator current reference Read phase currents Switch gate states Figure 7.3 Stator current controller software block diagram

124 The SynRM Drive Software and Performance 19 RECEIVE TIMER INTERRUPT The software holds itself at this point until the timer interrupt is received. At the executing the main software loop the control returns to this point and waits for the ne interrupt to occur. READ SPEED REFERENCE The speed reference is read once per control cycle. The ADC64 can read eight analog inputs simultaneously. These are all required to read the eight phase currents. As a consequence the speed reference must be read separately. The value is multiplexed with one of the phase current inputs. A 3p,s delay is introduced after the speed reference i read and the channel multiplexed to ensure the system has time to settle before reading the phase current value later in the code. The external speed reference is a ±1V signal. The analog to digital conversion process inverts this so that 1V = This reference is divided by 16 so that +1V = -25 (which will be shown to correspond to -615rpm). READ POSITION / SPEED One of the ADC64 peripheral counters is configured to continuously count down. It is clocked by pulses from the shaft encoder. The change in this counter over each control cycle is added or subtracted to a cumulative position variable depending on the motors direction of rotation. A digital input generated from the shaft encoder interface circ used to indicate forward or reverse direction. There are two variables in software. Variable "position" counts from to 1 corresponding to one revolution of the motor. Variable "modpos" counts from to 18 corresponding to rotor rotation in mechanical degrees.

125 The SynRM Drive Software and Performance 11 Speed is represented by the change in the cumulative position variable. The speed value is updated every 1 control cycles (2ms). As such its value is scaled so that 2 = 6rpm. PI SPEED CONTROLLER The quadrature current reference is generated by a PI speed controller. The controlle includes limits on the integrator storage variable to prevent wind-up as well as a l the controller's output. The latter acts as additional protection against exceeding inverter and motor ratings. The selection of the proportional and integral gain components is discussed in Section When the speed feedback is small the speed controller is operated as a purely proportional controller to ensure stable operatio CALCULATE STATOR CURRENT REFERENCE The nominal direct axis reference is set to a fixed value to flux the SynRM. Once the rotor position is known and the quadrature reference set the stator phase current references can be generated. This is done by calling function "curr_ref'. The functio has defined in it the typical phase current reference shape (Figure 5.3). It picks th appropriate point off the curve as the reference value for each phase current. READ PHASE CURRENTS The phase current analog to digital converters are triggered and read once every con cycle. The analog signals are converted to 16-bit binary values and stored in memory locations ADC to ADC3. Individual phase values are obtained by isolating the appropriate 16-bits from the memory locations. The ninth phase current is obtained as the inverted sum of the other eight. The phase current variables are scaled so that I The effect of the analog to digital converters sign change is negated in hardwa by wiring the current transducers backwards.

126 The SynRM Drive Software and Performance 111 SWITCH GATE STATES The inverter switching configuration required for each phase is found by comparing the phase current to the reference. The total inverter-switching configuration is stored in lowest nine bits of variable "gate_state". These bits are written three at a time to the output because of the limited number of outputs available. A IOJLXS delay is inserted between each write to allow time for the external multiplexer circuitry to switch. The control software was written to operate at 5kHz to match that simulated in Chapter 5 The actual time that is required for the code to execute one cycle is 14ps. This is sufficiently small to avoid exceeding the control cycle period of 2us. There remains some scope for the control cycle frequency to be increased if desired, which would lead to better current regulation. The time that elapses between reading the currents and establishing the output switching configuration is approximately 3u.s. The majority of this time (2u.s) is required to multiplex the gate drive signals. The time could be significantly reduced by using a DSP controller with sufficient digital outputs to drive the nine-phases without multiplexin However, 3p,s remains small with respect to the entire control cycle and is considered acceptable. 7.3 Performance Results This section presents the results of performance tests and measurements made on the com drive. In particular, results will be presented from a magnetization test as well as cu regulation, speed response and torque output measurements. These results will be compar with those predicted from the design model and simulations. MAGNETIZATION TEST The machine was run with no load at a fixed speed. The nominal level of direct axis exc (I D ) was varied and one phase's voltage and current waveforms monitored. By observing th

127 The SynRM Drive Software and Performance 112 change in the voltage waveform it is possible to detect the start of magnetic saturation within the machine. Figure 7.4 shows typical current and voltage waveforms recorded during the magnetization test. In this instance, Figure 7.4(a) shows one phase current waveform with the motor operating at 2rpm. The nominal level of direct axis excitation is IA. There is minimal quadrature axis excitation as the machine is being operated unloaded. Figure 7.4(b) shows the voltage waveform measured on the corresponding phase winding. The voltage waveform was obtained by applying a moving average to the PWM waveform measured at the motor terminals. While the phase winding is supplying quadrature excitation, the change in flux linking the coil produces an average voltage in the winding. Imposed on the average voltage is an oscillation produced by the changing current reference as the rotor moves. It is the relationship between the average voltage and the nominal direct axis excitation that of particular interest. Figure 7.4(c) shows the voltage waveform again with a moving average applied over one tooth pitch. This allows the average voltage in a phase winding, while it is supplying quadrature excitation, to be discerned more clearly. In this instance the direct axis excitation of IA at a speed of 2rpm is producing an average voltage of approximately 35V. Figure 7.5 summarizes the measurements made of the average phase voltage as direct axis excitation is varied. The measurements were obtained with the machine operating at a speed of 35rpm. There is a linear relationship between voltage and current until the iron starts to saturate. Saturation occurs at approximately 1.7A direct axis current. This compares with the expected value of 1.6A predicted in the design model (Section 3.2). The measured value is marginally higher because the design model prediction is based on a linear approximation to the iron B-H characteristic as opposed to the actual characteristic.

128 The SynRM Drive Software and Performance 113 (a) (b) (c).45 time (s) Figure 7.4 Typical current and voltage waveforms recorded during magnetization test (I D = 1 A, co = 2rpm)

129 The SynRM Drive Software and Performance 114 > 8- <u Ml 75 - B O 7 > <u Xi a direct axis current (A) Figure 7.5 Magnetization test results (co = 35rpm) CURRENT REGULATION Figure 7.6 shows the phase current waveforms recorded with the machine operating at var speeds. The inverter DC bus voltage was held at a constant value of 25V for each measurement. The direct axis excitation is set to the rated value of 1.7A. Quadrature e is set by the speed loop to the value necessary to maintain the speed of the unloaded mo The direct and quadrature components of current can be clearly recognized along with the adjustments made for stator slotting and winding connection.

130 The SynRM Drive Software and Performance 115 (a) (b) (c) Figure 7.6 Phase current waveforms (a) co = 8rpm, (b) co = 2rpm and (c) co = 345rpm (inverter bus voltage = 25V)

131 The SynRM Drive Software and Performance 116 Figure 7.7 Phase current waveform detail versus position for (a) co = 8rpm, (b) co - 2rpm and (c) co = 345rpm (inverter bus voltage = 25V)

132 The SynRM Drive Software and Performance 117 As the rotor speed increases, the current waveforms begin to diverge from the shape of the ideal reference. Figure 7.7 shows an enlarged portion of each of the waveforms presented in Figure 7.6. To allow comparison, the sections of the waveforms corresponding to direct axis excitation have been shown plotted against rotor position. Clearly, as speed increases the siz of the direct axis current block reduces suggesting an upper speed limit. Beyond a point reduced direct axis excitation will lower the flux in the machine and reduce the available torque. This relationship will be examined further in discussion on the torque measurements. SPEED RESPONSE The motor was operated with a known moment of inertia (its own rotor and shaft). The drive's response to step changes in the speed reference were recorded and compared with those from the dynamic simulations in Chapter 5. Figure 7.8 shows the speed and quadrature current values recorded in response to a step change in speed reference from 1 rpm to 24 rpm at time zero. The speed and quadrature current values were obtained by writing the appropriate variables in the controller to the digital-to-analog converter. A small amount of overshoot w oscillation can be observed in the measured values. Contributing to the oscillation was an electrical noise problem noted in the shaft encoder feedback path. Random noise spikes caused additional pulses to be counted affecting the position and speed feedback values. Figure 7.8 also shows the simulated speed and quadrature current values in response to the same step change in speed reference. The rise time of the speed variable in the simulation matches that obtained in the experimental system. Further, the simulated quadrature current pulse is of the same order of magnitude as that measured. One notable difference between the simulated and experimental systems is the steady state quadrature current value. The simulation does not include mechanical losses, such as friction, so the steady state quadratur current is shown to be zero amps.

133 The SynRM Drive Software and Performance 118 (a) 3 -i * \ a e- a measured - simulated time (s).3.4 (b) Figure 7.8 Measured and simulated speed and quadrature current values in response to a step change in speed reference from loorpm to 24rpm. The performance of the drive while reversing was also measured. Figure 7.9 shows the measured and simulated speed and quadrature current values. In this instance the speed reference is changed from +15 rpm to -15 rpm at time zero. Again the time constant of the speed response and magnitude of quadrature current pulse can be seen as matching in the two systems.

134 The SynRM Drive Software and Performance 119 (a) S Br. -.2 measured simulated time (s) (b).2 -s/ 1 < cr -.2 J ^ ^ measured simulated time (s) Figure 7.9 Measured and simulated speed and quadrature current values in response to a step change in speed reference from +15rpm to -15rpm. TORQUE MEASUREMENT The SynRM was coupled to a DC machine to perform torque measurements. The DC was used to set the system speed. With the machines operating at a constant speed the quadrature current set point for the SynRM was adjusted. The actual shaft torque output from the machine could be measured using a torque transducer mounted at the coupling between the machines. Various torque measurements under different conditions were made and will now be presented.

135 The SynRM Drive Software and Performance 12 Figure 7.1 shows the torque versus quadrature current measurements made with the motor turning at very low speed «5rpm). For this test and subsequent torque tests, the direct axis excitation was set to the rated value of 1.8A. This result approximates the locked rotor torqu obtainable from the machine. Notice that the torque varies linearly with quadrature axis curre until saturation effects become evident at the extremes of the graph. Included on the graph is the "ideal" linear torque versus quadrature current curve for a 5kW four-pole SynRM. The measured and ideal curves align quite well except for the end points. The maximum torque available was measured to be 27.6Nm compared to the rated value of 31.8Nm. This value is low for a combination of reasons. Primarily, the original design calculations and finite eleme analysis results were based on a machine with straight slots. The experimental machine had skewed slots to reduce cogging torque. However, skewing also reduces the available torque from the machine. Adding to the reduction in available torque are the effects of the design compromises made during construction. Most significantly, the amount of iron that was placed in the rotor was lower than hoped due to the practical difficulties associated with stacking t multiple laminations. Consequently the effective air-gap flux density is reduced in the experimental machine lowering torque output. Figure 7.1 Torque versus quadrature current with SynRM at very low speed (< 5rpm)

136 The SynRM Drive Software and Performance 121 The next series of tests were performed with the motor operating at higher speeds and the inverter dc link voltage adjusted to different levels. This allowed the dynamic torque performance of the SynRM to be measured. In addition, the relationship between the dc link voltage and the effective maximum speed could be examined. Figure 7.11 shows three graphs. Each graph records the measured torque versus quadrature current results obtained at differe speeds. The first graph is for the case where V^ = 2V DC. The second and third graphs are for V LINK = 4V and 56V respectively. 4- (b) ' 1 " 2 i n J ) T) J Iq(A) 2rpm /Iflfl m m 6rpm Vlink = 4V

137 The SynRM Drive Software and Performance 122 (c) Figure 7.11 Torque versus quadrature current for SynRM with (a) VUNK = 2V, (b) V L INK = 4V and (c) V LIN K = 56. For a given inverter DC link voltage, a linear relationship is maintained between the SynRM torque output and the quadrature current reference. This matches the low speed characteristic shown in Figure 7.1. As speed is increased a point is reached where the maximum torque begins to reduce. Examination of the phase current waveform at this point shows that the controller is unable to maintain the level of direct axis excitation. Figure 7.12 demonstrates this last point by showing two phase current waveforms recorded in the SynRM under different conditions. In Figure 7.12 (a) the direct axis current reference is to 1.8A and quadrature axis current reference is set to IA. Both portions of the current waveform are clearly recognizable. In Figure 7.12 (b) the direct axis current reference is aga set to 1.8A while the quadrature axis current reference is raised to 1.5A. The section of the current waveform that supplies direct axis excitation fails to reach 1.8A. The controller is no longer able to control the direct axis portion of the waveform to the desired level. Physically the speed voltage term in that phase winding has increased and there is insufficient inverter voltage to drive direct axis excitation to the level required. Consequently, the machine flux

138 The SynRM Drive Software and Performance 123 falls along with the output torque as can be seen in Figure 7.11 at higher quadrature reference values. current (a) (b) Figure 7.12 SynRM phase current (a) Id = 1.8A, L, = IA and (b) Id = 1.8A, L. = 1.5A. Figure 7.11 (c) shows that the drive in its present form is unable to produce rated torque at 15rpm. This problem could be overcome by reducing the number of turns on the stator phase winding.

139 Conclusions 124 CHAPTER 8 Conclusions The broad motivation for this thesis was to investigate and develop the potential of the fieldoriented SynRM drive. This drive offers potential benefits such as greater torque density, higher efficiency and simpler control algorithms compared to the commonly used induction machine drive. In particular, the project has focused on axially laminated SynRMs with rectangular stator current excitation. Where the majority of existing works on axially laminated SynRM design assume sinusoidal stator excitation the approach here was to presuppose a "rectangular" stator current distributi The rotor saliency of the SynRM naturally produces a rectangular air-gap flux density distribution. Assuming rectangular stator currents leads to machine designs with a greater output torque per rms ampere. However, the choice to use a rectangular stator current distribution changes what are the traditionally recognized optimal machine dimensions. Further, to produce the current distributions one requires a concentrated, multiphase stator winding. This necessitates the development of new techniques for field-oriented type current control. With regard to the machine design an analytical model, based on a lumped-element approximation to the machine's magnetic circuit, has been developed for the motor. The model takes into account all of the motor dimensions and includes allowance for magnetic saturation in the machine iron. Applying the model to the design process yielded machines featuring large rotor pole pitches (approaching 18 electrical degrees) and rotor iron : iron +fibre ratios slightly smaller than.5. These values are noted as different to those generally accepted for sinusoidally excited machines (pole pitches * 12 electrical degrees, iron : iron + fibre «.6.7). The reason for the difference is that the rectangular stator current distribution allows

140 Conclusions 125 full rotor pole face to be utilized to carry machine magnetic flux. Sinusoidally excited machines concentrate the flux in a narrower band and hence exhibit narrower poles with more rotor iron. Apart from the rotor pole pitch and iron to fibre ratio, the remaining optimized SynRM dimensions are similarly proportioned to those of comparably sized induction machines. The one notable exception is the air-gap width. In induction machines, the rotor carries significa currents and is subject to heating. As this heat is conducted along the rotor shaft allowance must be made for it in the tolerance of the bearings chosen. This mechanical allowance effectively sets the lower limit on the air-gap width in induction machines. The SynRM rotor carries no current and is not subject to the same heating. Finer tolerance bearings can be chosen and smaller air-gaps are achievable. This argument of course assumes other mechanical issues such as maintaining necessary tolerances for cost effective manufacturing and allowing for unbalanced magnetic pull due to rotor eccentricities can be resolved in a commercial product. The air-gaps suggested by the design model are generally half of those found in comparably sized induction machines. A 5kW four-pole nine-phase experimental SynRM was constructed based on the design model. Finite element analysis and experimental measurements confirmed the performance of the prototype machine matched the design expectations. To control the experimental machine required the development of appropriate field-oriented control techniques for the multiphase environment. Initially, generalized d-q voltage and torq equations were derived for the machine. These are significantly more useful than the equivalent stator reference frame equations because the transformation effectively removes the coupling between the stator phase windings. Further, the transformed inductances are constant, independent of rotor position. The generalized equations allowed the motor's performance to be easily simulated and suggested potential control strategies.

141 Conclusions 126 Two methods of implementingfield-orientedcontrol in the nine-phase SynRM were presented. The first was termed the "stator current controller". Stator phase windings are designated as supplying purely direct or quadrature axis excitation depending on their position relative to rotor pole face. Thus, a set of phase current references is generated and a simple hysteresis switching strategy can be implemented in an inverter to control the phase currents to these values. This control strategy was implemented in the experimental drive. Experimental measurements of the drive's performance were obtained validating the predictions from the simulated drive. The second controller was termed the "transformed frame vector controller". The controller operates on the transformed current variables. By controlling the isolated d-q harmonic components of current better current regulation and faster transient performance were achieved in simulation. This controller was not implemented in the experimental drive. The computational requirement prevented its implementation in the hardware assembled for this project. However, means are suggested for implementing the higher performance controller in the future. In summary, the following points can be made with regard to the experimental drives advantages / disadvantages and areas needing further research; (a) The experimental drive demonstrated a high torque density albeit at low speeds. It has been noted that the speed range could be extended with a more appropriately configured stator winding. Another alternative is to increase the voltage rating of the inverter, although this would come at a significant cost penalty. (b) The multiphase structure offers redundancy, which is advantageous in applications where the drive must run continuously. (c) The efficiency of the drive configuration has not been resolved. The initial prototype is compromised by its stator-winding configuration. This contains long end windings and

142 Conclusions 127 requires a high current density to achieve rated torque. Ideally a second prototype should be constructed, using the knowledge obtained with regard to practical machine design requirements, to allow a more realistic evaluation of the drives efficiency. Included in this investigation should be consideration of the iron losses in the axially laminated rotor structure. (d) The current controller implemented is quite simple but effective. To achieve higher performance more complicated control strategies are required. The computational requirement here is prohibitive with existing technology. Further investigation is necessary into ways in which this problem may be overcome. (e) The axially laminated rotor structure requires further investigation from a mechanical viewpoint. In particular questions to be considered include mechanical integrity at high speed along with methods for economical manufacture given the unusual rotor structure and the tighter tolerances necessary to support a small air-gap. (f) Another issue is the cost of the inverter. The experimental drive requires three times the number of power electronic switches compared to a standard three-phase drive. Clearly this is more expensive but perhaps not by as much as the three to one ratio suggests. It must be remembered that the current rating of the individual switches is reduced in the multiphase case, lowering their cost. Further, over time the cost of semiconductor devices continues to reduce relative to the cost of the machine itself. If efficiency gains are realised then drive life cycle costing may even justify the higher initial capital cost.

143 References 128 REFERENCES [1] RE Betz, "Control of Synchronous Reluctance Machines", Proceedings of IEEE-IAS Annual Meeting, Detroit, pages , September [2] RE Betz, "Theoretical Aspects of Control of Synchronous Reluctance Machines", IEE Proceedings - B, Volume 139, Number 4, pages , July [3] I Boldea and SA Nasar, "Emerging Electric Machines with Axially Laminated Anistropic Rotors: A Review", Electric Machines and Power Systems, Volume 19, pages , [4] I Boldea, ZX Fu and SA Nasar, "Performance Evaluation of Axially - Laminated Anistropic (ALA) Rotor Reluctance Synchronous Motors", IEEE Transactions on Industry Applications, Volume 3, Number 4, pages , July / August [5] TJ Busch, JD Law and TA Lipo, "Magnetic Circuit Modelling of the Field Regulated Reluctance Machine Part II: Saturation Modelling and Results", IEEE Transactions on Energy Conversion, Volume 11, Number 1, pages 56-61,1996. [6] BJ Chalmers and AS Mulki, "New Reluctance Motors With Unlaminated Rotors", Proceedings IEE, Volume 117, Number 12; pages , 197. [7] BJ Chalmers and AS Mulki, "Design and Performance of Reluctance Motors with Unlaminated Structures", IEEE Transactions on Power Apparatus and Systems, Volume 91, pages ,1972. [8] BJ Chalmers and L Musaba, "Design and Field-Weakening Performance of a Synchronous Reluctance Motor with Axially Laminated Rotor", Proceedings of IEEE IAS Annual Meeting, pages , October [9] PP Ciufo, D Piatt and BSP Perera, "Magnetic Circuit Modelling of a Synchronous Reluctance Motor", Australian Universities Power Engineering Conference 1994, Adelaide, Volume 1, pages [1] PP Ciufo, D Piatt and BSP Perera, "Magnetic Circuit of a Synchronous Reluctance Motor", Electric Machines and Power Systems, Volume 27, Number 3, pages , [11] AJO Cruickshank, RW Menzies and AF Anderson, "Axially Laminated Anistropic Rotors for Reluctance Motors", Proceedings of IEE, Volume 113, Number 12, pages , 1966.

144 References i 129 [12] AJO Cruickshank, AF Anderson and RW Menzies, "Theory and Performance of Reluctance Motors with Axially Laminated Anistropic Rotors", Proceedings of IEE, Volume 118, Number 7, pages ,1971. [13] W Fong, "Change-Speed Reluctance Motors", "Proceedings IEE, Volume 114, Number6, pages ,1967. [14] W Fong and JSC Htsui, "A New Type of Reluctance Motor", Proceedings IEE, Volume 117, Number 3, pages ,197. [15] A Fratta, A Vagati and F Villata, "Control of a Reluctance Synchronous Motor for Spindle Applications", IPEC Japan 199. [16] A Fratta, GP Troglia, A Vagati and F Villata, "Evaluation of Torque Ripple in High Performance Synchronous Reluctance Machines", Proceedings of IEEE Industry Applications Society Annual Meeting, Volume 1, pages ,1993. [17] CL Gu, LR Li, KR Shao and YQ Xiang, "Anistropic Finite Element Computation of High Density Axially-Laminated Rotor Reluctance Machine", IEEE Transactions on Magnetics, Volume 3, Number 5, pages , September [18] MR Harris and TJE Miller, "Comparison of Design and Performance Parameters in Switched Reluctance and Induction Motors", Fourth International Conference on Electrical Machines and Drives, pages 33-37, [19] VB Honsinger, 'The Inductance L d and L q of Reluctance Machines", IEEE Transactions on Power Apparatus and Systems, Volume 9, pages , [2] VB Honsinger, "Steady-State Performance of Reluctance Machines", IEEE Transactions on Power Apparatus an Systems, Volume 9, pages , [21] VB Honsinger, "Inherently Stable Reluctance Motors Having Improved Performance", IEEE Transactions on Power Apparatus and Systems, Volume 91, pages , [22] JS Hsu (Htsui), SP Liou and HH Woodson, "Peaked-MMF Smooth-Torque Reluctance Motors", IEEE Transactions on Energy Conversion, Volume 5, Number 1, pages 14-19, March 199. [23] JS Hsu (Htsui), SP Liou and HH Woodson, "Comparison of the Nature of Torque Production in Reluctance and Induction Motors", IEEE Transactions on Energy Conversion, Volume 5, Number 2, pages 34-39,199. [24] Innovative Integration "ADC64 Hardware Manual" First Edition 1994.

145 References 13 [25] MJ Kamper and AF Volschenk, "Effect of Rotor Dimensions and Cross Magnetisation on L d and L q Inductances of Reluctance Synchronous Machines with Cageless Flux Barrier Rotor", IEE Proceedings - Part B, Volume 141, Number 4, pages ,1994. [26] J.K. Kostko, "Polyphase Reaction Synchronous Motor", Journal of ATF.R Volume 42, pages ,1923. [27] JD Law, A Chertok and TA Lipo, "Design and Performance of Field Regulated Reluctance Machine", IEEE Transactions on Industry Applications, Volume 3, Number 5, pages , September / October [28] JD Law, TJ Busch and TA Lipo, "Magnetic Circuit Modelling of the Field Regulated Reluctance Machine Part I: Model Development", IEEE Transactions on Energy Conversion, Volume 11, Number 1, pages 49-55, [29] PJ Lawrenson and LA Agu, "A New Unexcited Synchronous Machine", Proceedings IEE, Volume 11, Number 7, pagel275,1963. [3] PJ Lawrenson and LA Agu, "Theory and Performance of Polyphase Reluctance Machines" Proceedings IEE, Volume 111, Number 8, pages , August [31] PJ Lawrenson and LA Agu, 'Low Inertia Reluctance Machines", Proceedings IEE, Volume 111, Number 12, pages , December [32] PJ Lawrenson, 'Two-Speed Operation of Salient-Pole Reluctance Machines", Proceedings IEE, Volume 112, Number 12, pages , [33] PJ Lawrenson and SK Gupta, "Developments in the Performance and Theory of Segmental-Rotor Reluctance Motors" Proceedings IEE, Volume 114 Number 5, pages , May [34] PJ Lawrenson and SR Bowes, "Stability of Reluctance Machines", IEE Proceedings, Volumell8, pages , [35] W Leonhard, "Control of Electrical Drives", Springer - Verlag, Heidelberg, [36] SP Liou, HH Woodson and JS Hsu, "Steady-State Performance of Reluctance Motors Under Combined Fundamental and Third-Harmonic Excitation Part I: Theoretical Analysis", IEEE Transactions on Energy Conversion, Volume 7, Number 1, pages ,1992. [37] TA Lipo and PC Krause, "Stability Analysis of a Reluctance Synchronous Machine", IEEE Transactions on Power Apparatus and Systems, Volume 86, pages , [38] TA Lipo, "Novel Reluctance Machine Concepts for Variable Speed Drives", 6 Meditteranean Electrotechnical Conference Proceedings, Volume 1, pages 34-43,1991.

146 References 131 [39] X Luo, A El-Antably and TA Lipo, "Multiple Coupled Circuit Modeling of Synchronous Reluctance Machines", Proceedings of IEEE Industry Applications Society Annual Meeting, Volume 1, pages ,1994. [4] I Marongiu and A Vagati, "Improved Modelling of a Distributed Anistropy Synchronous Reluctance Machine", Proceedings of IEEE Industry Applications Society Annual Meeting, pages ,1991. [41] T Matsuo and TA Lipo, "Rotor Design Optimization of Synchronous Reluctance Machine", IEEE Transactions on Energy Conversion, Volume 9, Number 2, pages ,1994. [42] RW Menzies, 'Theory and Operation of Reluctance Motors with Magnetically Anistropic Rotors I - Analysis", IEEE Transactions on Power Apparatus and Systems, Volume 91, pages 35-41, [43] RW Menzies, RM Mathur and HW Lee, 'Theory and Operation of Reluctance Motors with Magnetically Anistropic Rotors II - Synchronous Performance", IEEE Transactions on Power Apparatus and Systems, Volume 91, pages 42-45, [44] TJE Miller, A Hutton, C Cossar and DA Staton, "Design of a Synchronous Reluctance Motor Drive", IEEE Transactions on Industry Applications, Volume 27, Number 4, pages , [45] TJE Miller, "Brushless Permanent-Magnet and Reluctance Motor Drives", Oxford University Press, [46] AL Mohamadein, YHA Rahim and AS Al-Khalaf, "Steady-state performance of selfexcited reluctance generators", IEE Proceedings, Part B, Volume 137, Number 5, pages ,199. [47] EL Owen, "Evolution of Induction Motors - the Ever Shrinking Motor", IEEE Industry Applications Magazine, Volume 3, Number 1, pages 16-18, January / February [48] D, Piatt, "Reluctance Motor with Strong Rotor Anistropy", IEEE Transactions on Industry Applications, Volume 28, Number 3, pages ,1992. [49] H Ramamoorty and PJ Rao, "Optimisation of Polyphase Segmented Rotor Reluctance Motor Design: A Nonlinear Programming Approach", IEEE Transactions on Power Apparatus and Systems, Volume 98, pages ,1979. [5] SC Rao, "Dynamic Performance of Reluctance Motors with Magnetically Anistropic Rotors", IEEE Transactions on Power Apparatus and Systems, Volume 95, pages ,1976.

147 References 132 [51] PE Scheihing, M Rosenberg, M Olszewski, C Cockrill and J Oliver, "United States Industrial Motor Driven Systems Market Assessment: Charting a Roadmap to Energy Savings for Industry", US Department of Energy, Motor Challenge Program, [52] DA Staton, TJE Miller and SE Wood, "Optimisation of the Synchronous Reluctance Motor Geometry", Fifth International Conference on Electric Machines and Drives 1991, pages [53] DA Staton, TJE Miller and SE Wood, "Maximizing the Saliency Ratio of the Synchronous Reluctance Motor", IEE Proceedings-B, Volume 14, Number 4, pages , July [54] C Studer, A Keyhani, T Sebastion and SK Murphy, "Study of Cogging Torque in Permanent Magnet Machines", IEEE Industry Applications Society 32 nd Annual Meeting, Volume 1, pages 42-49,1997. [55] Texas instruments 'TMS32C3X User's Guide", Literature number SPRU31E, July [56] HA Toliyat, L Xu and TA Lipo, "A Five Phase Reluctance Motor with High Specific Torque" IEEE Transactions on Industry Applications, Volume 28, Number 3, pages , May/June [57] HA Toliyat, M M Rahimian and TA Lipo, "dq Modelling of a Five Phase Synchronous Reluctance Machine Including Third Harmonic of Air-Gap MMF' Conference Record of the 1991 IEEE Industry Applications Society Annual Meeting Volume 1 pages [58] HA Toliyat, MM Rahimian and TA Lipo, "Analysis and Modelling of Five Phase Converters for Adjustable Speed Drive Applications", Proceedings of Fifth European Conference on Power Electronics and Applications, Volume 5, pages , [59] L Xu and J Yao, "A Compensated Vector Control Scheme of a Synchronous Reluctance Motor Including Saturation and Iron Losses", IEEE Transactions on Industry Applications, Volume 28, Number 6, pages , November / December 1992.

148 133 Publications of Work Performed as Part of This Thesis [6] CE Coates and D Piatt, "Field-Oriented Control of a Synchronous Reluctance Motor", Proceedings of Australian Universities Power Engineering Conference 1994, Adelaide. [61] CE Coates, D Piatt and VJ Gosbell, "Generalised Equations for a Nine Phase Synchronous Reluctance Motor", Proceedings of Australian Universities Power Engineering Conference 1996, Melbourne, Volume 1, pages [62] CE Coates, D Piatt and BSP Perera, "Design Optimisation of an Axially Laminated Synchronous Reluctance Motor" Proceedings of the IEEE Industry Applications Society Annual Meeting 1997, Volume 1, pages [63] CE Coates, D Piatt and VJ Gosbell, "Control and Performance of a Nine-Phase Synchronous Reluctance Drive" Proceedings of Australian Universities Power Engineering Conference 2, Brisbane, pages [64] CE Coates, D Piatt and VJ Gosbell, "Performance Evaluation of a Nine-Phase Synchronous Reluctance Drive", Accepted for inclusion at the IEEE Industry Appications Society Annual Meeting 21, Chicago.

149 APPENDIX A APPENDIX A 5kW SynRM Schematics A1 5kW SynRM Stator lamination A2 A3 A4 A5 5kW SynRM Stator Tooth Detail 5kW SynRM Rotor Cross Section 5kW SynRM Stator Winding Details 5kW SynRM Rotor

150 FILLETS R5 Z Notes: 1. All dimensions are in millimetres. 2. Laminations are to be either.35 or.5mm Lycore 23 or similar material. 3. A is the angle between the axis of the tabs and one slot. 4. If.35 mm material is used 17 laminations are required for one stator (this includes spares). For the skewed stator angle A increments by.69 degrees between successive laminations. 5. If.5mm material is used 12 laminations are required for one stator (this includes spares). For the skewed stator angle A increments by.99 degrees between successive laminations. 5kW SynRM Stator Lamination DRAWN: CEC DATE: 4/12/95 SCALE: 1:2

151 Notes: 1. All dimensions are in millimetres. 2. Teeth have parallel sides. 3. Tooth faces are to be (or at least approximate) arcs of radius 64.29mm. 4. Slot bottoms are to be arcs of radius 87.46mm. Tnis requirement is less critical than that for the tooth faces. 5kW SynRM Stator Tooth Detai DRAWN: CEC DATE: 4/12/95 SCALE: 2:1

152

153 Notes: 1. The stator has a 9 phase concentrated winding. 2. One phase winding consists of four coils (numbered 1 to 4 in diagram) connected in series. 3. Each of the four coils consists of four identical coils in parallel. Each of these has 17 turns of.25 mm diameter wire. 5kW SynRM Winding Details DRAWN: CEC DATE: 7/2/97 SCALE: 1:2 Al

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155 APPENDIX B Inverter Schematics B1 Power Circuit Diagram (1 of 2) B2 Power Circuit Diagram (2 of 2) B3 Dynamic Brake Control Circuit B4 Gate Drive Circuit B5 DSP Interface - DSP Cable (1 of 5) B6 DSP Interface - Gate Decoder I (2 of 5) B7 DSP Interface - Gate Decoder II (3 of 5) B8 DSP Interface - Current Feedback (4 of 5) B9 DSP Interface - Shaft Encoder (5 of 5) BIO Inverter Gate Drive Board Layout B11 Inverter Gate Drive Board PCB Artwork B12 Inverter Parts List

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165 AO ^engi ' N u '-p rs JU 1 nr "H r A d'l Ag+ r*n TLP n- M =>erigi A =engi AO Ag+ ->engi AO ^engt AO d'l Ag+ -QOtoin 31WS J3 Baa fura) 231 AO AO d'l Ag+ AO ^engi A d'l Ag.

166

167 Designation B12 - INVERTER PARTS LIST Description Quantity Dwg B1 (Inverter - Power Circuit Diagram - sht 1/2) DB1 L1 EC1 - EC4 PR1 PR2 - PR3 Tdb CB1 M T 3 Phase Rectifier 12V/3A Semikron SKD31/12 Rectifier Heat Sink 1.56 C/W Inductor 34.4mH Capacitor (electrolytic) 1uF 4VDC Capacitor mounting clips 51 mm dia. Resistor 1R2W Resistor 47R 3W IGBT 12V/8AGT8Q11 IGBT Heatsink Circuit Breaker 24V AC 2A Main Relay Timer Relay Dwg B2 (Inverter - Power Circuit Diagram - sht 2/2) Ta-Ti Da-Di IGBT 12V/8AGT8Q11 IGBT Heatsink Power Diode 12V / 8A Diode Heatsink Dwg B3 (Inverter - Dynamic Brake Control Circuit) IC1 P1 R1 R2 R3, R4 R5, R6 R7 R8 TL71 Op Amp Potentiometer 1k 1 turns Resistor 1M.6W Resistor 1k.6W Resistor 1k.6W Resistor 18k.6W Resistor 1M.6W Resistor 15R.6W Dwg B4 (Inverter - Gate Drive Circuit) BR1 C1.C2 FET1 FET2 IC1 IC2 R1 -R3.R1, R11 R4 R5.R9 R6 R7, R8 Z1 -Z4 Z5.Z6 Transformer 24V to -15V,-15V 6VA W4 bridge rectifier 4V 1.5A Capacitor 33uF 25V IRF952 - Power MOSFET 1V 6A IRF51 - Power MOSFET 1V 5.6A 74OL61 - high speed optocoupler LF357N - BiFET high speed op amp Resistor 1k.25W Resistor 1R.25W Resistor 1k.25W Resistor 15R.25W Resistor 33R.5W 15V.4WZener Diode 15V5WZener Diode Terminals - 2 way Terminals - 3 way

168 Designation B12 - INVERTER PARTS LIST Description Quantity Dwg B5 (Inverter - DSP Interface - DSP Cable - sht 1/5) Klippon 34 way interface module Ribbon cable 34 way 34 way IDC female socket connector SCSI2 1 way male connector Dwg B6 (Inverter - DSP Interface - Gate Decoder I - sht 2/5) 74HC139A Dual 1-of-4 Decoder / Demultiplexer MC1413B Dual Type D Flip-Flop Resistor 1k.6W Capacitor 1nF Dwg B7 (Inverter - DSP Interface - Gate Decoder II - sht 3/5) C1.C2 D1.D2 IC1 R1.R2 Capacitor 47pF Diode Hex Schmitt Trigger 416 Resistor 22k.6W Dwg B8 (Inverter - DSP Interface - Current Feedback - sht 4/5) CTa - CTi Ra-Ri Current Transducer Resistor 5R.6W 9 9 Dwg B9 (Inverter - DSP Interface - Shaft Encoder - sht 5/5) 416 Hex Inverter MC1413B Dual Type D Flip-Flop Resistor 5k6.6W Capacitor 1 nf

169 APPENDK C C-l APPENDIX C Control Program Listing

170 APPENDDC C C-2 /********************** ******************************************** * * STACUR Stator Current Controller Program Version 2 15 / 2 / 2 * This program implements the stator current controller on * * the ADC64 DSP board. An extended description of code can * * be found in Chapter 7. * * * ******************************************************************/ #include ftinclude #define #define #define #define void void int "periph.h" "stdio.h" timer_int sync_int P I timer_int() sync_int(); curr_ref(); l c_int9 c_int3 5 1 II Declare global variables // Set to type volatile so interrupt routines can access them. volatile int timer_int_flag; //flag to indicate.2ms interval volatile int sync_int_flag; //flag to indicate sync pulse volatile int position; //rotor position (-999) void main() { /************************************************ * * * INITIALIZATION * * * ************************************************/ // Declare local variabl es int count_old; //Counter value from previous cycle int count_new; //Counter value from current cycle int iaref, iafb //Phase A current reference / feedback int ibref, ibfb //Phase B current reference / feedback int icref, icfb //Phase C current reference / feedback int idref, idfb //Phase D current reference / feedback int ieref, iefb //Phase E current reference / feedback int ifref, iffb //Phase F current reference / feedback int igref, igfb //Phase G current reference / feedback int ihref, ihfb //Phase H current reference / feedback int iiref, iifb //Phase I current reference / feedback int id, iq; //Direct / quadrature components of current int modpos; //Rotor position (degrees electrical) 1 int sampleo; //Temporary storage analog inputs & 3 int samplel; //Temporary storage analog inputs 2 & 5 int sample2; //Temporary storage analog inputs 4 & 7 int sample3; //Temporary //Inverter switching storage analog config. inputs (9 bit 6 & binary) int gate_state; //Speed reference int spdref;

171 APPENDIX C C-3 int int int int int int int spderr; speed; posold; n; prop ; integral; intold; //Speed error //Speed feedback //Old position value for speed f/b calc. //Loop counter //PI controller prop. comp. of output //PI controller integral comp. of output //PI controller integrator memory // Configure ADC64 board MHZ = 6; *DIO_CONFIG = 1; *PIT1_D = xb4, *PIT1_C = Oxff; //set clock speed //d-d7 outputs, d8-dl5 inputs //set timer/counter 1 chan 2 to mode 2 //load timer/counter 1 chan 2 to *PIT1_C = Oxff; enable_monitor(); enable_clock(); enable_interrupts() // Oxffff (LSB first) // Initialise variables timer_int_flag =; sync_int_flag =; count_old = Oxffff; speed =; n = ; intold =; id = 8; // Initialise // Initialise // Initialize // Initialize // Initialize // Initialize // Set direct timer interrupt flag sync pulse interrupt flag count_old speed feedback loop counter integrator memory axis current reference // Initialise external interrupt install_int_vector(sync_int,3); enable_interrupt(2); //put sync_int isr at address 3 //sets IE register bit 2 // Initialise analog inputs MADC); *(ADC1); *(ADC2); *(ADC3) *(INT_MASK) = x f; set_gain(,) set_gain(l,) set_gain(2,) set_gain(3,) set_gain(4,) set_gain(5,) set_gain(6,) set_gain(7,) trigger(,); timer(,5) set_mux(,) set_mux(l,) set_mux(2,) set_mux(3,) set_mux(4,) set_mux(5,) set_mux(6,) set_mux(7,l) trigger(,1); trigger(,2) trigger(,3! // Turn all phases off gate_state = x; *DIO = (gate_state x18) & x7; us (1); *DIO = ((gate_state» 3) x18) & OxOOOf; us(1); *DIO = ((gate_state» 6) x18) & x17;

172 APPENDLK C C-4,************************************************ * * * ALIGN POSITION FEEDBACK * * * ************************************************/ printf("\n\n Waiting to align position feedback"); // Wait until rotor position calibrated do { } while (sync_int_flag == ); sync_int_flag = ; do { } while (sync_int_flag == ) ; posold =75; // Initialize position memory for speed calc. printf("\n\n Ready"); /************************************************ * * INITIALIZE TIMER INTERRUPT * * ************************************************/ timer(6,5); //set on chip timer to 5kHz install_int_vector(timer_int,9); //put timer_xnt isr at add. 9 enable_interrupt(8); //sets IE register bit 8 // Main loop do { /************************************************ * RECEIVE TIMER INTERRUPT? 1***********************************************/ // Cycle at 5kHz do { } while (timer_int_flag ==);,************************************************ ' * * * READ SPEED REFERENCE. * 1***********************************************/ sample3 = *ADC3; sample3 = *ADC3; spdref = (sample3» 16); spdref = spdref/16; set_mux(7,); us (3); *ADC3=;

173 /************************************************ * * * READ POSITION / SPEED * * * *************************************************; //Read rotor position *PIT1_D = x8; count_new = *PITl_C; count_new = ((*PIT1_C «8) + count_new) & Oxffff; if (count_new <= countold) { if ((*DIO & x1) == x1) { position = position - count_old + count_new; } else { position = position + count_old - count_new; } } else { if ((*DIO & x1) == x1) { position = position - count_old - Oxffff + count_new; } else { position = position + count_old + Oxffff - count_new; } } if (position > 999) position = position - 999; if (position < ) position = position + 999; modpos = (position * 36. / 1.); modpos = modpos % 18; n = n + 1; if (n=1) { speed = position - posold; if (speed < -15) speed = speed + 1; if (speed > 15) speed = speed - 1; posold = position; n = ; }

174 APPENDIX C C-6 /********************************************* * ** * * * PI SPEED CONTROLLER * * * ************************************************, // Speed controller spderr = spdref - speed; prop = spderr * P; integral = intold + I * spderr; intold = integral; if (intold > 8) intold = 8; if (intold < -8) intold = -8; iq = prop + integral; if (iq > 8) iq = 8; if (iq < -8) iq = -8; /************************************************ * * * CALCULATE STATOR CURRENT REFERENCE * * * ************************************************/ // Calculate the phase current references (scaled IA = 8192) iaref = curr_ref(modpos, id, iq) ; ibref = curr_ref(modpos + 1, id, iq); icref = curr_ref(modpos + 2, id, iq) ; idref = curr_ref(modpos + 12, id, iq) ; ieref = curr_ref(modpos + 4, id, iq); ifref = curr_ref(modpos + 14, id, iq) ; igref = curr_ref(modpos + 6, id, iq) ; ihref = curr_ref(modpos + 16, id, iq) ; iiref = curr_ref(modpos + 8, id, iq) ;,************************************************ * * * READ PHASE CURRENTS * * * ************************************************/ // Read phase currents (scaled IA = 8192) sampleo = *ADC; sampleo = *ADC; samplel = *ADC1; samplel = *ADC1, sample2 = *ADC2; sample2 = *ADC2, sample3 = *ADC3; sample3 = *ADC3, set_mux(7,1); iafb = (sampleo «16)» 16; ibfb = (sampleo» 16); icfb = (samplel «16)» 16; idfb = (samplel» 16) ; iefb = (sample2 «16)» 16; iffb = (sample2» 16); igfb = (sample3 «16)» 16; ihfb = (sample3» 16) ; iifb = -(iafb + ibfb + icfb + idfb + iefb + iffb + igfb + ihfb);

175 APPENDIX C C-7 /***************************************^ * * SWITCH GATE STATES ******* * * * * ******************** **************************** II Switch outputs gate_state = x; if (iafb < iaref) gate_state if (ibfb < ibref) gate_state if (icfb < icref) gate_state if (idfb < idref) gate_state if (iefb < ieref) gate_state if (iffb < ifref) gate_state if (igfb < igref) gate_state if (ihfb < ihref) gate_state if (iifb < iiref) gate_state = = = = = = = = x1; gate_state gate_state gate_state gate_state gate_state gate_state gate_state gate_state x2 x4 x8 x1 x2 x4 x8 x1 *DIO = (gate_state x18) us(1); & x7; *DIO = ((gate_state» us(1); 3) x18) & OxOOOf; *DIO = ((gate_state» 6) x18) & x17; timer_int_flag = ; } while (1); curr_ref(offset,id,iq) int offset; int id; int iq; { // Define local int ref; // Make offset modulo 18 offset = offset % 18; // if if if if if if if if if // Rotor position relative to phase winding // Direct axis current reference (IA = 8192) // Quadrature axis current reference (IA = 8192) function variables // Phase current reference (IA = 8192) Calculate phase current reference (offset <= 4) ref = id; ((offset > 4) & (offset <= 6)) ref = interp(offset,4,6,id,iq+id/8) ; ((offset > 6) & (offset <= 14)) ref = iq+id/8; ((offset > 14) & (offset <= 16)) ref = interp(offset,14,16,iq+id/8,iq-id/8) ; ((offset > 16) & ((offset > 24) & id/8,iq+id/8); ((offset > 26) & ((offset > 34) & (offset <= 24)) ref = iq-id/8; (offset <= 26)) ref = interp(offset,24,26,iq- (offset <= 34)) ref = iq+id/8; (offset <= 36)) ref = interp(offset,34,36,iq+id/8,iq-id/8) ; ((offset > 36) & (offset <= 44)) ref = iq-id/8;

176 APPENDIX C C-8 } if if if if if if if if if if if if if if if if if if if if if if if if if if if if ((offset > 44) & (offset <= 46)) ref = id/8,iq+id/8); (offset > 46) & (offset <= 54)) ref = (offset > 54) & (offset <= 56)) ref = interp(offset,54,56,iq+id/8,iq-id/8) (offset > 56) & (offset > 64) & id/8,iq+id/8); (offset > 66) & (offset > 74) & (offset <= (offset <= 64)) 66)) (offset <= 94)) (offset <= 96)) ref ref interp(offset,44, 46, iqiq+id/8; iq-id/8; interp(offset,64,66,iq- (offset <= 74)) ref iq+id/8; (offset <= 76)) ref mterp (off set, 74, 76, iq+id/8, iq-id/8) l (offset > 76) & (offset <= 84)) ref = (offset > 84) & (offset <= 86)) ref = id/8,-id); (offset > 86) & (offset > 94) & iq-id/8); (offset > 96) & (offset <= (offset > 14) & (offset <= iq-id/8,-iq+id/8); (offset > 16) & (offset <= 114 (offset > 114) & (offset <= 116 iq+id/8,-iq-id/8); (offset > 116) & (offset <= 124 (offset > 124) & (offset <= 126 iq-id/8,-iq+id/8); (offset > 126) & (offset <= 134 (offset > 134) & (offset <= 136 iq+id/8,-iq-id/8); (offset > 136) & (offset <= 144 (offset > 144) & (offset iq-id/8,-iq+id/8); (offset > 146) & (offset 14) (offset > 154) & (offset <= 156 iq+id/8,-iq-id/8); (offset > 156) & (offset <= 164 (offset > 164) & (offset <= 166 iq-id/8, -iq+id/8),- (offset > 166) & (offset <= (offset > 174) & (offset <= iq+id/8,id); ((offset > 176) & (offset <= ref = ref = ref = ) ref ref ref ref ref ref ref ref ref ref ref ref ref ref ref 18)) ref = id; // Return phase current reference from function return ref; iq-id/8; interp(offset,84,86,iq- -id; interp(offset,94,96,-id, = -iq-id/8; = interp(offset,14,16, = -iq+id/8; = interp(offset,114,116, = -iq-id/8; = interp(offset,124,126, = -iq+id/8; = interp(offset,134,136,- = -iq-id/8; = interp(offset,144,146, = -iq+id/8; = interp(offset,154,156, = -iq-id/8; = interp(offset,164,166, - = -iq+id/8; = interp(offset,174,176,- interp(x,xl,x2,yl,y2) int x,xl,x2,yl,y2; { int ans,- ans = ( (y2 - yl) * x + (yl * x2 - xl y2; / (x2 - xl); return ans;

177 APPENDIX C void timer_int(void) { timer_int_flag = 1; } void sync_int(void) { sync_int_flag = 1; position = 75; }

178 APPENDED D-l APPENDIX D Numerical Solution to SynRM Model Differential Equations The air-gap flux density distribution, B g (), and quadrature axis flux, ^), ar by equations (2.2) to (2.7), derived in chapter 2. These equations are repeated convenience; L da <Mr() + 8e_ Sll-RH () + RJ() + ()RR = (D-l) 2 d9 Mo d d(b iff) r l -^ = RL[B g in-)- B g ()\ (D-2) ]j()rd= ]H s ()Rd + -^[B g (7T-) + B g ()] e Mo + i*-[ff,(>r-) + ff,()] (D-3) gk R d <t> q fy=w Z Y') = * v-5) B g (-) = B g (7t-9) (D-6) The flux density in the rotor iron, BJ), is related to the air-gap flux densi B r () = t r xb g () (D-7) where, t r = ratio of iron : iron + fibre in the rotor

179 APPENDDCD D-2 The iron is assumed to have a B-H characteristic as shown in Figure 2.4. This characteristic is described mathematically by; H = (B + 1.7) 5M (B-1.7) 5A 5< <B<1J B>\.1 (D-8) In our instance, the rotor iron is in saturation if B^) > (t r x 1.7). When the iron is in saturation substituting equation (D-7) into (D-8) and differentiating gives; dh r () = 1 db g () d 5/y r d (D-9) - The system of equations can be solved over the rotor pole arc given by < <. Numerical methods were used to solve the differential equations. A st chosen to be; x = B g () B s () q (-) B g (-9) BA-9) (D-1) Effectively, a solution is determined by starting at both ends of the pole face and iterating towards the centre. This approach was required as the state derivative equations assume knowledge of both B g () and B g (-).

180 APPENDIX D D-3 The state derivative equations are; &(9) = RL[BA-)-B()\ B' g () = \ R B' s () = -B Y g () -M-{j() + ^q()r q } 8e l -^^{j()^q(9)r q } WgJr+k da <&' (-) = -RL[B g () - B g (-)] B: (-) = t^{j(-)+^ql :-9)R q } 8e lom t r R J( _^) +?( _^j logjr+l^ -R B' s (-9) = -irb g {-) Y B g ()<t r x\.l B()>t r x\.l B g ()<t r xl.l B g ()>t r x\.l (D-ll) (D-12) (D-13) (D-14) (D-15) (D-16) Equation (D-5) gives the initial value for both quadrature flux variables to be Substituting = -?- into equation (D-3) determines the relationship between B \ 5 '-, to be; (d f and B. f-q\ \ *- J ( Yl = f B r K V * ) (D-17) Symmetry requires B s v 2 v = -B, f- \ V 2 J

181 APPENDIX D D-4 Assuming values for both the air-gap and stator yoke flux densities at = - - forms the 2 initial conditions for the state vector. Thus, the initial state vector becomes; x, = (D-18) The values for Kj and K2 can be found by iterating until the air-gap and stator yoke flux densities, found by approaching from either side of the pole face, match at the centre rotor pole face. The solution was determined using MATLAB. The routines used are included below for reference. ymam.m % Outer loop that is used to solve calculation of machine % flux densities when both direct and qaudrature axis % excitation are present. Uses matlabs optimisation routine % in cascaded loops. % Subroutines: ymainsub, ydesol, yde, yexc % Define global variables global Jd Jq BgO theta sv BsO bgb m; % Request user defined variables Jd = input('enter direct axis excitation (A/m) [4] if isempty(jd) Jd = 4; end '); Jq = input('enter quadrature axis excitation (A/m) [-2] '); if isempty(jq) Jq = -2; end

182 APPENDDCD D-5 % Initial approximation to air gap and yolk flux density % at -thetap/2 BsO = -1.76; bgb =.2; opt = fzero('ymainsub',bso); % Form state and angle matrices State(l:m,1:3) = sv(l:m, 1:3) ; state(m+1:2*m-l,1:3) = flipud(sv(l:m-l, 4:6) ) ; angle (l:m / l) = thetad :m, 1) ; angle(m+l:2*m-l,l) = -flipud (thetad :m-l,l) ) ; % Plot solution subplot(3,1,1) plot(angle,state(:,1) ) subplot(3,1,2) plot(angle,state(:,2)) subplot(3,1,3) plot(angle,state(:,3)) ymainsub.m function y2 = ymainsub(bso) global bsb bst BsOa bgb sv m; BsOa = BsO; BgO = bgb; bgb = fzero('ydesol',bgo); y2 = sv(m,3)-sv(m,6); ydesol.m % This function solves the DE that describes the _ SynRM i % it has both direct and quadrature axis excitation % Saturation is allowed for. function error = ydesol(bgo) % Define global variables global theta sv BsOa uo Jd Rs thetap ge W Tnml m; Bsat = 1.7;

183 APPENDKD D-6 % Solve DE for given initial state thetao = -thetap/2; thetaf = ; Bgb = BgO; % Determine the starting vector values for the ODE. if BsOa > -Bsat if Bgb>Tnml*Bsat Bgt = uo*(jd*rs*(pi/2-thetap)-w*(bgb/tnml-1.7)/(1* u)/ge-bgb; if Bgt>Tnml*Bsat Bgt = 1*u*Tnml*(Jd*Rs*(pi/2-thetap)+1.7*W/(5*u)) /(1*ge*Tnml+W)-Bgb; end elseif Bgb<-Tnml*Bsat Bgt = uo*(jd*rs*(pi/2-thetap)-w*(bgb/tnml+1.7)/(1*u)) /ge-bgb; if Bgt>Tnml*Bsat Bgt = 1*u*Tnml*Jd*Rs*(pi/2-thetap)/(1*ge*Tnml+W)- Bgb; end else Bgt = uo*jd*rs*(pi/2-thetap)/ge-bgb; if Bgt>Tnml*Bsat Bgt = 1*u*Tnml*(Jd*Rs*<pi/2-thetap)+(.17*W-ge*Bgb) /uo)/(1*ge*tnml+w); end end else if Bgb>Tnml*Bsat Bgt = u*((jd+(bsa+1.7)/(5*u))*rs*(pi/2-thetap)-w*( Bgb / Tnml -1.7) /(1*u))/ge-Bgb; if Bgt>Tnml*Bsat Bgt = lo*uo*tnml*((jd+(bsoa+1.7)/(5*uo))*rs*(pi/2- thetap )+1.7*W/(5*uO))/(1*ge*Tnml+W)-Bgb; end

184 APPENDDCD D-7 elseif Bgb<-Tnml*Bsat Bgt = u*((jd+(bsa+1.7)/(5*u))*rs*(pi/2-thetap)-w* (Bgb /Tnml+1.7)/(1*u))/ge-Bgb; if Bgt>Tnml*Bsat Bgt = 1*u*Tnml*(Jd+(Bsa+1.7)/(5*u))*Rs*(pi/2- thetap )/(1*ge*Tnml+W)-Bgb; end else Bgt = uo*(jd+(bsa+l.7)/(5*uo))*rs*(pi/2-thetap)/ge- Bgb; if Bgt>Tnml*Bsat Bgt = 1*uO*Tnml*((Jd+(BsOa+1.7)/(5*uQ))*Rs*(pi/2- thetap)+(.17*w-ge*bgb)/uo)/(1*ge*tnml+w); end end end svo = [ Bgb BsOa Bgt -BsOa]'; tspan = [thetao thetaf]; [theta,sv] = ode45('yde',tspan,svo); % Test boundary condition (ie. error at midpoint in airgap % flux density distribution) m = size(theta,1); error = sv(m, 2) -sv(m, 5),- yde.m % This function defines the state derivative vector defining % the DE that describes the SynRM when it has both direct and % quadrature axis excitation. Saturation is allowed for. function svdot=yde(theta,sv) % define global variables global Rr Lr uo Rs Req ge Y Tnml W; Bsat = 1.7; svdot = zeros(6,l); svdot(l)= Rr*Lr*(sv(5)-sv(2));

185 APPENDDCD D-8 if sv(3) < -Bsat if abs(sv(2)) > Bsat*Tnml svdot(2)= -1*uO*Rs*Tnml*(yexc(theta)+sv(l) * Req+(sv(3)+1.7) /(5*u)) /(1*ge*Tnml+W); else svdot(2)= -uo*rs*(yexc(theta)+sv(l)*req+(sv(3) +1.7)/(5*u))/ge; end else if abs(sv(2)) > Bsat*Tnml svdot(2)= -1*uO*Rs*Tnml*(yexc(theta)+sv(l) *Req) /(1*ge*Tnml+W); else svdot(2)= -uo*rs*(yexc(theta)+sv(l)*req)/ge; end end svdot(3)= Rs*sv(2)/Y; svdot(4)= -Rr*Lr*(sv(2)-sv(5)); if sv(6) > Bsat if abs(sv(5)) > Bsat*Tnml svdot(5)= 1*uO*Rs*Tnml*(yexc(-theta)+sv(4)*Req-(sv(6)- 1.7)/(5*u))/(1*ge*Tnml+W); S S S vdot(5)= uo*rs*(yexc(-theta)+sv(4)*req-(sv(6) - 1.7)/(5*u))/ge; end else if abs(sv(5)) > Bsat*Tnml 1*uO*Rs*Tnml*(yexc( svdot(5)= theta)+sv(4)*req)/(1*ge*tnml+w) ; S S vdot(5)= uo*rs*(yexc(-theta)+sv(4)*req)/ge; end end svdot(6)= -Rs*sv(5)/Y;

186 APPENDDCD D-9 yexcm % Define the excitation current on the stator. function yl=yexc(theta) global Jq; % Block current case. yl = Jq;

187 APPENDIX E Device Data Sheets ADC64 DSP Board Technical Specification GT8Q11 BY329 IGBT 12V / 8A Power Diode 12V / 8A

188 Sixty-four channel A/D, 32-bit floating-point DSP and PC! bus interface Features: " 6 MHz TMS32C32 Processor Ei g ht Multiplexed 2 kh; A/D Input-, Two D/A Outputs,.,,.,;,:. / Applications: Sonar - '' i'~- Vibration monitonns ta logging Mm -»; *" ^y^l.wft^fpw^mmmiwmm ^St^iHSHi 'i* *'.' ;'m.l K-:>mkAXff!m m vm &wi2mm ^is ^"^^jtyrbs^gb hm-mt&wms&mm SHAai^m^mFiB^^n j- IHfiHEHi^S "rr IIHmBa HUJBft K** :* - ip jpm]w_*gl j^; BaSs Overview The ADC64 heralds a new era in PC-based data acquisition. Bringing together for the first time a low-cost, high-performance DSP core, a dazzling array of analog and digital I/O with screaming fast 132 Mbyte/sec PCI bus performance, the ADC64 is THE value platform for next-generation, intelligent data acquisition system designs. Example Application The analog output chain consists of two independent instrumentationgrade 16-bit D/A converters. Writes to specific memory-mapped locations latch data into the selected D/A output roister. Subsequent conversion-triggering of any D/A pair, either via a DSP software command or an external TTL trigger, will update the analog outputs within a conversion period (< 5 us). The on-chip timers are augmented by six external channels via two on-board 82C54s. These timers may be used for pulse stream generation or multichannel timing. More commonly, they are used to multi-rate analog acquisition applications. A simple high-speed memory-mapped 1 6-bit latch is available to support general-purpose digital I/O. Direction is jumper-configurable in banks of eight bits. The port may be software or externally clocked at rates to 5 MHz and each bit on the port is capable of sourcing or sinking 32 ma. Fig. 1 - TheADC64j eight, independent analog input channels are ideal for data logging applications, aid as this vibration monitoring system. Expansion The ADC64 is compatible with the full range of 3XBUS cards for I/O expansion including analog I/O Industry Pack modules via the 3XPACK and SCSI devices via SCSI3X. ftecessor Core TheADC64 features the high-performance Texas Instruments TMS32C32 32-bit floating-point DSP capable of up to 6 MFLOPS/3 MIPS. On-chip peripherals include two flexible 32-bit counter/timers, two prioritized D M A controllers, a bidirectional sync serial port, 2 Kbytes of dual-access SRAM and a prioritized interrupt controller. Memory on the ADC64 may be expanded to include up to 512 Kbytes of zero wait-state SRAM. On-board Peripherals Hie analog input chain has eight 16-bit, instrumentation-grade A/D converters addressable as pairs by the DSP via four memory mapped locations. Each A/D features an analog input that is simultaneously sampled upon receipt of a DSP software command or an external TTL trigger. Each of the native analog inputs is routed through a differential instrumentation amplifier into a six-pole (12 db/decade) anti-alias filter. The anti-alias filter circuit has a set of matched resistors to control the filter roll off frequency. Though configured for the maximum Nyquist frequency of 1 khz by default, custom cutoff frequencies may be special ordered. Host PC Interface The ADC64 is a half-size card that plugs into a standard 3 2-bit PCI bus slot. The PCI bus interface supports bus mastering, directed by the DSP, capable of bursts of 132 Mbytes/sec and sustained transfers of 2 Mbytes/sec on most host platforms. This provides superior connectivity with transfer rates well above competing C32 offerings featuring awkward, register-based interfaces suitable only for object code downloading. Multiple cards may be installed in systems with full driver support under Windows 95 and NT. Hardware Option! a Options (any combination) ;', 6 MHz/3 MFLOPS S.E. or Differen!'al Analog I/O options Breakout Moduie Peripherals SCS!3X 3XPACK Fig. 2 The ADC64 may be equipped with a variety ol options and add-on peripherals to meet performance and cost goals in OEM applications. tel (818) fax (818) » A. Innovative jot Integration

189 I x > c Cl k a I Development Tools The ADC64 is may be programmed in C or Assembler using the tools available in the Development Package. Components within this package fully support development of custom DSP applications. The Windows device driver and DLL provided in the Zuma Toolset support host PC application development in Visual C or Basic, Borland C/Builder/ Delphi and any other environment capable of linking to a standard Windows DLL. Numerous target and host example programs are provided as well as support applets for graphic terminal emulation, object file downloading, etc. Alternately, the board is compatible with a number of third-party packages including LabView, Hypersignal RIDE and DASYLab for users seeking a turnkey data acquisition and analysis solution. Additionally, the revolutionary Ventura library is available for the ADC64 to provide full bandwidth access to the extensive hardware complement of the ADC64 without any DSP programming. O E M Configurations The ADC64 can be configured tofit your specific requirements and provide an optimal mix of performance, cost and features. Contact Innovative Integration with your specific O E M requirements. Software Options I Development Took Ventura Tl C/Assembler Code Hammer *f-* Zuma Toolset Fig. 3 - Custom software for the ADC64 may be generated using the cross development tools. Alternatively; a variety of turnkey applications are available. Ordering information All ADC64 boards include: TMS32C32 processor, 128 K W w«lt-st«te SRAM, cither four or eight 2 khz A/Dj each with programmable gain (x 1,2,4,8), six-pole anti-alias filter with jumperable on/off selection; two independent D/A channels each with smoothing filter; one sync serial port; three 16-bit timers; two 3 2-bit timers with bus mastering PCI host interface with FIFOs; 16-bit digital I/O ADC6*. Board Options Basic board 82- Basic ADC64 board: 4 MHz processor; lour channels muxed 8:1 single-ended Altemalm ADC64 board configurations 82-1 ADC64 with 6 MHz processor; eight channels muxed 8:1 single-ended 82-7 ADC64 with 6 MHz processor; four channels muxed 4:1 differential 82-5 ADC64 with 6 MHz processor; four channels muxed 8:1 single-ended 82-6 ADC64 with 6 MHz processor; eight channels muxed 4:1 differential Peripherals SCSI 3X SCSI-2 adapter Screw-terminal breakout module & cable for high-density 1-pin analog I/O connector XPACK Documentation 511 ADC64MDC64 hardware manual 512 ADC64/cADC64 software manual 521 Texas Instruments TMS32C3x User's Guide 522 Code Composer software manual 5238 Digital Signal Processing with C and the TMS32C3 textbook with diskette by Chaussing (details 'C3x signal processing techniques) A Innovative * & Integration te! (818) Software and Support 532 Zuma Toolset for ADC64/cADC Ventura DLL (or ADC64MDC64 Hardware-assisted C/Assembler Source Level Debuggers Code Hammer with MPSD hardware/code Composer software - for any "C3xbased board Code Hammer with MPSD hardware only - for any'c3x-based board 543 Code Composer software - lor any 'C3x or 'C4x-based board; Development Package 92- Development Package for ADC64. Indudesall of the following: 541 Texas Instruments floating-point C compilation system for'c3x/''c4x 82-1 ADC64 with 6 MHz processor; eight channels muxed 8:1 singleended Screw-temvoal breakout module and cable for high-density 1-pin analog I/O connector ADC64/cADC64 hardware manual ADC64/cADC64 software manual Texas Instruments TMS32C3x User's Guide Zuma Toolset for ADC64/cADC64 Code Hammer with MPSD hardware/code Composer software - for any C3x-based board

190 ADC64 Technical Specifications Pnxesor Men»ry Flash Memory FIFO Memory Debug Port Host PC Interface FIFO Memory : Disltal I/O j Timers/Counters Serial Ports Power Requirements Connectors Physicals Compatible Add-on Cards Development Languages Turnkey Software Packages C/Assy Source Debugger Software Libraries Texas Instruments TMS32C32 32-bitfloating-point DSP Smized instruction set (or DSP -drip resources: 512 x 32 memory,- eight accunulators; hardware muh»ger, barrel shifter; two DMA controllers; serial port; two 32-bit timers,- 16 prioritized interrupts; 64-word instruction cache DSP speed = 4 or 6 MHz Zero wait-state; 1 28 K x 32 4 Mbit (512 K byte) on-board reprogrammable I/O mapped on DSP XDS-51 compatible MPSD port for emulation and scan path testing; Supports C/Assembly source level debugging with Code Hammer PCI 32-bit; consumes 64 I/O locations, one interrupt Auto-mappable into PC I/O space by PCI BIOS Supports bidirectional interrupt driven operation - one PC interrupt Multiple cards supported 16 bits TTL input or output, 64 ma sink/ 32 ma source Two 32-bit timers in DSP clocked at DSP speed/4. Six 1 6-bit timers using independent 1 MHz timebase One on DSP chip. On-chip: up to 15 Mbaud; 8, 16 or 3 2 formats; synchronous serial interrupt support + 5 V 1.1 A, ma, +12 V 3 ma On-board 5W DC-DC converter with Timing Sources short protection for clean analog power, 1 W total power consumption SCSI-2 1-pin female for analog and digital I/O; DIN 9 6 female for DSP expansion; 2-pin card-tocard synchronizing connectors, I D O 2 male for MPSD debugger port. IDC1 4 for serial port D/A Converter Half-size PCI card; 7.6 in. long x 4.2 in. high; max component height.75 in. Resolution Temp range: -7 C Output Range SCSI3X SCSI-2 interface; 3XPACK Industry feck adapter C or Assembler using Tl cross-development tools. Peripheral libraries and Windows drivers via Zuma Toolset Block-diagram DSP design: Hypersigna! Windows, DSPower, DASYUb and LoggerPCI Code Hammer Ventura, Zuma Toolset A/D Converter 8 Channels Resolution Update Rate Settling Time Analog Dev,ces, AD976. Each converter hasind. hltenng. Interrupt off conv. complete. Each A/D muxed either 4:1 differential or 8:1 single-ended 16-bit 2 khz 5 us (no 1 V step settling Analog Input Range S/H Ratio +/-1 V, V, -1 Y -5 V, +/-5 V 88 db THD.9 db Dynamic Range 9 db Cain Error +/-5% Differential +3/-2LSB Linearity Error Bipolar Zero Error Trimmable Aperture Delay 4 ns Aperture Jitter Meets AC specs Programmable Gain PGA26: 1,2,4,8 Input Impedance 1 Mohm 11 3 PF Filter Characteristics 6-pole filter, with user-specifiable roll off -3 db at 1 khz Filter may be disabled (Rev H and up) Software sdect from one of six 16-bit counter/tim or DSP memory mapped access or external TTL source MUX Characteristics DG48 for 8:1 single-ended inputs; DG49 for 4:1 differential inputs Switch time: 3 ns System Scan Rate 64 channels: 25 khz; 32 channels: 5 khz; 8 channels: 2 khz Slew Rate Settling Time Update Rate S/N Ratio THD.9% max Bipolar Zero Error able Differential Non-Linearity +/-1 LSB max D/A Glitch Impulse Impulse 15 V-ns Temp Range -7 C Filtering Interface to DSP Conversion Timing Sources Two channels two Burr-Brown DAC 712. Each D/ A channel has independent filtering 16-bit -5 V, +/-5V,+ 1 V 15 V/ us 1 3 us (no 2 V step,- 2.5 us LSB step settling to.8% 2 khz.63% max Output smoothing filter - single pole filter, 2 khz rolloff (custom with cap/resistor change) Memory-mapped Software select from one of six 1 6-bit counter/timer sources or DSP memory-mapped access or external TTL source Fig. 4 - ADC64 with 'C3S DSP, 64 channels I/O,! channels D/A and PCI bus. jot tel (818) fax (818) A\ Innovative Jk^k Integration