Design, Analysis, Implementation and Operation of a Brushless Doubly Fed Reluctance Motor Drive

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2018-06-04 Design, Analysis, Implementation and Operation of a Brushless Doubly Fed Reluctance Motor Drive

Rebeiro, Ronald Shourav

Rebeiro, R. S. (2018). Design, Analysis, Implementation and Operation of a Brushless Doubly Fed Reluctance Motor Drive (Unpublished doctoral thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/31965 http://hdl.handle.net/1880/106730 doctoral thesis

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Design, Analysis, Implementation and Operation of a Brushless Doubly Fed Reluctance Motor

Drive

Ronald Shourav Rebeiro

A THESIS

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE

DEGREE OF DOCTOR OF PHILOSOPHY

GRADUATE PROGRAM IN ELECTRICAL AND COMPUTER ENGINEERING

CALGARY, ALBERTA

JUNE, 2018

The permanent magnet synchronous motor (PMSM) is a popular choice for variable speed

drive (VSD) applications. However, concerns regarding the low availability and price volatility of

rare earth permanent magnet materials are encouraging researchers to reduce or even remove the

permanent magnets from electrical machines without significantly compromising their

performance. The Brushless Doubly Fed Reluctance Machine (BDFRM) can be a promising

prospect with its unique advantageous features over other conventional machines. The BDFRM

has two stator windings and a reluctance type rotor. It does not consist of brushes, rotor circuits or magnets. This makes the BDFRM an attractive prospect of a controllable, low cost, low maintenance machine which can be even more robust and versatile than the PMSM. If such a machine is commercially realized, it will be highly suitable to operate in locations of limited accessibility or harsh climate. With proper control technique being utilized, it can be an attractive replacement for two important electrical applications: wind power system and electric vehicle.

The concept of Brushless Doubly Fed Machine (BDFM) was first introduced more than a century ago. Much of the published literature has analyzed existing designs, rather than focusing on the design process and effective operation of possible commercial machines.

This work describes the complete evaluation of a ducted rotor BDFRM design process through time-stepped finite element analysis (FEA), a prototype machine built based on the design, and two-converters based operation of the BDFRM drive in three different operating modes. In this regard, theoretical aspects and control approach are also discussed and explained. Another objective of this work is to investigate the two-converters based frequency sharing operation

(Mode-3) of the prototype BDFRM drive. In this case, the total applied frequency is split between the two stator windings with a specific ratio. Thus, the frequency dependent core loss can be

ii reduced. Besides, this approach can provide additional degrees of freedom for control, extend the constant torque region, and increase the machine power density.

iii Acknowledgements

First and foremost, I’d like to thank the University of Calgary and my supervisor Dr.

Andrew M. Knight for guiding me all the way in my research. The completion of this research work would not have been possible without the continuous support, careful supervision, and encouragement from Dr. Knight. I started my research at the University of Alberta before I transferred my program to the University of Calgary. Therefore, the University of Alberta deserves my acknowledgment as well. I thank the Final Exam Committee members and the ECE

Department administration personnel for their valuable suggestions and assistance during my exam. I acknowledge the ample support of Tech Support personnel (Garwin Hancock, Rob

Thomson, and others) while I was developing the drive facility and running the tests at the machine lab.

My special gratitude goes to my parents (Denis Rebeiro & Elizabeth Rebeiro) who were the prime source of my inspiration. Similarly, I acknowledge the inspiration and teaching from all my teachers from my early years who had faith in my abilities (particularly Dr. Mohammad Ali

Choudhury, Dr. Md. Abdul Matin, Dr. Nasir Uddin, and Dr. Tapan K. Chakraborty). During the last few years, my wife Jackline played a major role in this journey with her constant support and care. I also acknowledge the moral support from my sisters and their families, my well-wishing elders, relatives, and friends. My classmates and colleagues also made my journey easier by cheering me up and holding thoughtful conversations. Finally, I’d like to thank the Almighty on this occasion for all the good things in my life.

iv Table of Contents

Abstract ...... ii Acknowledgements ...... iv Table of Contents ...... v List of Tables ...... vii List of Figures and Illustrations ...... viii List of Symbols, Abbreviations and Nomenclature ...... xii

CHAPTER 1: INTRODUCTION ...... 1 1.1 Introduction ...... 1 1.2 History of BDFRM ...... 3 1.3 Research Motivation ...... 4 1.4 Thesis Contribution ...... 9 1.5 Thesis Organization ...... 10

CHAPTER 2: THEORY OF BDFRM ...... 12 2.1 Basic Operation Principle of BDFRM ...... 12 2.2 Previous Relevant Research on BDFRM...... 13 2.3 Operation Principle of a Ducted Rotor BDFRM ...... 18 2.4 Control Strategy of BDFRM ...... 22 2.5 BDFRM Operation with Appropriate Frequency Division ...... 26

CHAPTER 3: DESIGN OF BDFRM, SIMULATION RESULTS AND DATA ANALYSIS ...... 28 3.1 Choice of Number of Rotor Poles...... 28 3.2 Proposed BDFRM Design ...... 30 3.2.1 Evolution of the Proposed Design in JMAG ...... 35 3.2.2 Windings Configuration of the Proposed Design ...... 40 3.3 Simulation & Data Analysis: Synchronous BDFRM Operation ...... 41 3.4 Simulation & Data Analysis: Two-Converters Based Operation ...... 46 3.5 Advantages of Two-Converters Based Operation ...... 51 3.6 Compensation for End Winding Leakage Inductance Effect ...... 53 3.7 Structural Analysis and Final Design for Machine Manufacturing Process ...... 55 3.8 Calculation of Machine Inductance from Simulation ...... 58

CHAPTER 4: PROTOTYPE MOTOR AND TEST FACILITY ...... 60 4.1 Stator and Rotor Laminations Design ...... 60 4.2 Design of the Rotor Core ...... 64 4.3 Stator Windings Arrangement ...... 65 4.4 Assembly of the Machine ...... 68 4.5 Motor Drive Implementation ...... 70 4.6 Control Strategy of Two-Converters Based Operation ...... 73

CHAPTER 5: EXPERIMENTAL TESTING ...... 77 5.1 Measurement of Actual Machine Inductances ...... 77 5.2 Operating Mode-1: Synchronous BDFRM Operation ...... 80

v 5.2.1 Synchronous Operation with Variable Field Currents ...... 81 5.2.2 Synchronous Operation at Variable Speed Levels ...... 84 5.3 Operating Mode-2: Conventional BDFRM Operation ...... 85 5.4 Operating Mode-3: Frequency Sharing Operation with Two Variable Frequencies92 5.5 Discussion ...... 97

CHAPTER 6: CONCLUSION ...... 99 6.1 Summary ...... 99 6.2 Possible Future Work ...... 100

REFERENCES ...... 101

vi List of Tables

Table 3-1: Initial Design Specifications ...... 31

Table 3-2: Parameters Initially Chosen by Designer for the design in Table 3-1 ...... 31

Table 3-3: Modified Design Specifications Considering 0.8 mm Air-gap Length...... 33

Table 3-4: Calculated Parameters for the Modified Design in Table 3-3 ...... 33

Table 3-5: Data Table of Output Torque (Synchronous Operation) ...... 42

Table 3-6: Data Table of Winding-1 Flux Linkage (Synchronous Operation) ...... 42

Table 3-7: Data Table of Winding-2 Flux Linkage (Synchronous Operation) ...... 43

Table 3-8: Data for Torque & Power Responses (Synchronous Operation) ...... 45

Table 3-9: Data for Torque & Power Responses (Case: f 1 = 80%, f 2 = 20%) ...... 47

Table 3-10: Data for Torque & Power Responses (Case: f 1 = 70%, f 2 = 30%) ...... 47

Table 3-11: Data for Torque & Power Responses (Case: f 1 = 64%, f 2 = 36%) ...... 48

Table 3-12: Calculated End Winding Leakage Inductance (EWLI) values with Corresponding Speeds and Applied Currents for Initially Run JMAG Cases...... 54

Table 3-13: Desired Operating Points of the Proposed BDFRM after EWLI Compensation...... 54

Table 3-14: Inductance values (Case: 8-pole winding excited, 4-pole winding open) ...... 58

Table 3-15: Inductance values (Case: 4-pole winding excited, 8-pole winding open) ...... 58

Table 4-1: Windings Arrangement on the BDFRM Stator ...... 66

Table 5-1: Calculated test and simulation inductances with 4-pole winding open circuit ...... 79

Table 5-2: Calculated test and simulation inductances with 8-pole winding open circuit ...... 79

vii List of Figures and Illustrations

Figure 1-1: General classification of electric motors...... 2

Figure 2-1: Conceptual diagram of BDFRM...... 12

Figure 2-2: Schematic diagram of the synchronous dual-winding reluctance generator system with a loaded 3-phase diode rectifier considered in [8], [9]...... 14

Figure 2-3: (a) composite 3-phase stator winding structure (distributed over 36 semi-closed stator slots), (b) salient rotor structure, and (c) control winding DC connection of the synchronous dual-winding reluctance generator system considered in [8], [9]...... 15

Figure 2-4: Illustration of linearized ideal segmented rotor structure [59]...... 19

Figure 3-1: Idealized air-gap flux density functions [59] for cases: (a) p1 = 6, p2 = 2, pr = 4; (b) p1 = 8, p2 = 4, pr = 6; (c) p1 = 6, p2 = 4, pr = 5...... 29

Figure 3-2: Cross-sectional views of some predecessor designs: (a) Design 1, (b) Design 2, (c) Design 3...... 36

Figure 3-3: Magnetic flux density line plots of the corresponding predecessor designs: (a) Design 1, (b) Design 2, (c) Design 3...... 37

Figure 3-4: A cross-sectional view of the final simulation version of the proposed design...... 38

Figure 3-5: Magnetic flux density contour & line plot of the final simulation version of the proposed design...... 38

Figure 3-6: 8-pole and 4-pole windings configuration of the BDFRM...... 39

Figure 3-7: Contour plot of simulated torque data of the proposed design...... 43

Figure 3-8: Contour plot of simulated winding-1 flux linkage data of the proposed design...... 44

Figure 3-9: Contour plot of simulated winding-2 flux linkage data of the proposed design...... 44

Figure 3-10: Predicted Torque and Power responses for Synchronous BDFRM Operation (winding-1: 100% applied frequency, winding-2: 0% applied frequency)...... 45

Figure 3-11: Predicted Torque and Power responses for two-converters based BDFRM Operation (winding-1: 80% applied frequency, winding-2: 20% applied frequency)...... 48

Figure 3-12: Predicted Torque and Power responses for two-converters based BDFRM Operation (winding-1: 70% applied frequency, winding-2: 30% applied frequency)...... 49

Figure 3-13: Predicted Torque and Power responses for two converter BDFRM Operation (winding-1: 64% applied frequency, winding-2: 36% applied frequency)...... 49

viii Figure 3-14: Comparison of torque predicted from flux lookup table with time-stepped FEA simulation...... 50

Figure 3-15: Predicted torque responses for all the case studies...... 52

Figure 3-16: Predicted power responses for all the case studies...... 52

Figure 3-17: Desired operating points plot of the proposed drive after EWLI compensation. .... 55

Figure 3-18: Displacement contour plot from structural analysis of the final manufacture version of proposed BDFRM design (displacement is 100 times scaled)...... 57

Figure 3-19: Global Stress (in the radial plane) contour plot from structural analysis of the final manufacture version of proposed BDFRM design...... 57

Figure 4-1: The cross-sectional view of a stator lamination drawn in AutoCAD...... 61

Figure 4-2: The cross-sectional view of a single rotor segment drawn in AutoCAD...... 61

Figure 4-3: The cross-sectional view of the complete rotor drawn in AutoCAD...... 62

Figure 4-4: The actual stack of stator laminations...... 63

Figure 4-5: An actual single rotor segment lamination...... 63

Figure 4-6: The cross-sectional view of the rotor core with stator-rotor drawn in AutoCAD. .... 64

Figure 4-7: Top view of the wound stator core...... 67

Figure 4-8: Side view of the wound stator core with end winding connections and welded part clearly visible...... 67

Figure 4-9: Different parts of machine assembly designed in SolidWorks software [Courtesy: Machine Shop, Schulich School of Engineering, University of Calgary]...... 68

Figure 4-10: Hexagonal shaped rotor core with rotor segment laminations attached...... 69

Figure 4-11: Side view of the BDFRM assembly before the casing is closed...... 69

Figure 4-12: BDFRM coupled with the load PMSM mounted on the steel base...... 70

Figure 4-13: Implemented BDFRM drive setup in the lab...... 71

Figure 4-14: Schematic diagram of the implemented closed-loop motor drive...... 72

Figure 4-15: Block diagram of the control strategy of the BDFRM drive...... 74

Figure 5-1: Test setup to measure actual BDFRM inductances...... 78

ix Figure 5-2: Power Analyzer screenshot at 600 rpm synchronous speed with 3.7 A field current (3 N-m)...... 81

Figure 5-3: Power Analyzer screenshot at 600 rpm synchronous speed with 4.5 A field current (5 N-m)...... 82

Figure 5-4: Power Analyzer screenshot at 600 rpm synchronous speed with 5.4 A field current (5 N-m)...... 82

Figure 5-5: Experimental load points (synchronous operation) of the actual BDFRM on top of the contour plot of previously simulated torque data of the proposed BDFRM design. .. 83

Figure 5-6: Torque and output power responses in synchronous speed operation (Mode-1)...... 84

Figure 5-7: Power Analyzer Screenshot at 400 rpm speed and 4 N-m load torque (f 1 = 60 Hz, f2 = -20 Hz)...... 86

Figure 5-8: Power Analyzer Screenshot at 500 rpm speed and 4 N-m load torque (f 1 = 60Hz, f2 = -10Hz)...... 87

Figure 5-9: Power Analyzer Screenshot at 600 rpm speed and 4 N-m load torque (f 1 = 60Hz, f2 = 0Hz)...... 87

Figure 5-10: Power Analyzer Screenshot at 700 rpm speed and 4 N-m load torque (f 1 = 60Hz, f2 = 10Hz)...... 88

Figure 5-11: Power Analyzer Screenshot at 800 rpm speed and 4 N-m load torque (f 1 = 60Hz, f2 = 20Hz)...... 88

Figure 5-12: Power Analyzer Screenshot at 900 rpm speed and 4 N-m load torque (f 1 = 100Hz, f 2 = -10Hz)...... 89

Figure 5-13: Power Analyzer Screenshot at 1000 rpm speed and 4 N-m load torque (f 1 = 100Hz, f 2 = 0Hz)...... 89

Figure 5-14: Power Analyzer Screenshot at 1100 rpm speed and 4 N-m load torque (f 1 = 100Hz, f 2 = 10Hz)...... 90

Figure 5-15: Power Analyzer Screenshot at 1200 rpm speed and 4 N-m load torque (f 1 = 100Hz, f 2 = 20Hz)...... 90

Figure 5-16: Torque and output power responses of the BDFRM drive (operating mode-2): 600 rpm speed is considered as the synchronous speed (f 1 = 60 Hz; f 2 is variable)...... 91

Figure 5-17: Torque and output power responses of the BDFRM drive (operating mode-2): 1000 rpm speed is considered as the synchronous speed (f 1 = 100 Hz; f 2 is variable)...... 91

Figure 5-18: Power Analyzer screenshot of the BDFRM frequency sharing test (operating mode-3) at 600 rpm speed and 5 N-m load torque (f 1 = 42Hz, f 2 = 18Hz)...... 94 x Figure 5-19: Power Analyzer screenshot of the BDFRM frequency sharing test (operating mode-3) at 700 rpm speed and 5 N-m load torque (f 1 = 49Hz, f 2 = 21Hz)...... 94

Figure 5-20: Power Analyzer screenshot of the BDFRM frequency sharing test (operating mode-3) at 800 rpm speed and 5 N-m load torque (f 1 = 56Hz, f 2 = 24Hz)...... 95

Figure 5-21: Power Analyzer screenshot of the BDFRM frequency sharing test (operating mode-3) at 900 rpm speed and 5 N-m load torque (f 1 = 63Hz, f 2 = 27Hz)...... 95

Figure 5-22: Power Analyzer screenshot of the BDFRM frequency sharing test (operating mode-3) at 1000 rpm speed and 5 N-m load torque (f 1 = 70Hz, f 2 = 30Hz)...... 96

Figure 5-23: Power Analyzer screenshot of the BDFRM frequency sharing test (operating mode-3) at 1100 rpm speed and 5 N-m load torque (f 1 = 77Hz, f 2 = 33Hz)...... 96

Figure 5-24: Torque and output power responses of the BDFRM drive in frequency sharing operation (operating mode-3)...... 97

xi List of Symbols, Abbreviations and Nomenclature

Symbol Definition p1 1st winding pole numbers p2 2nd winding pole numbers pr Rotor pole numbers ω1 1st winding supply (electrical) angular frequency (rad/s) ω2 2nd winding supply (electrical) angular frequency (rad/s) ωm Rotor mechanical speed in rad/s M mmf harmonic function Peak mmf harmonic function Permeability of free space (4 π×10 7 H/m) 0 g Air-gap length B( θm1 ) Air-gap flux density function at θm1 point β(θm1 ) Normalized air-gap flux density function at θm1 point Resulting peak flux density harmonic in winding i due to specific electric loading in winding j Cij Coupling factor Specific electric loading (rms) N Number of turns per phase ̅ ph kw1 Fundamental winding factor r Air-gap radius Iph 1st winding rated phase current (rms) ksat Saturation factor l Machine stack length Eij Induced voltage in winding i due to specific electric loading in winding j 1st winding 3-phase voltages 2nd winding 3-phase voltages 1st winding 3-phase currents 2nd winding 3-phase currents 1st winding 3-phase flux linkages 2nd winding 3-phase flux linkages

R1 1st winding resistance

R2 2nd winding resistance

θr Rotor electrical angle (rad)

θm Rotor mechanical angle (rad)

L1m 1st winding magnetizing inductance

L2m 2nd winding magnetizing inductance Peak mutual inductance

L1l 1st winding leakage inductance

xii L2l 2nd winding leakage inductance θ Angular position of dq -axes rotating reference frame ω Angular frequency of dq -axes rotating reference frame K Reference frame transformation matrix 1st winding dq -axes flux linkages 2nd winding dq -axes flux linkages 1st winding peak (balanced) phase voltage 2nd winding peak (balanced) phase voltage 1st winding peak (balanced) phase current 2nd winding peak (balanced) phase current θ10 Phase of 1st winding phase-a current w.r.t. arbitrary rotating reference frame of angular frequency ω θ20 Phase of 2nd winding phase-a current w.r.t. arbitrary rotating reference frame of angular frequency ω 1st winding dq -axes currents in the arbitrary rotating reference frame of angular frequency ω1 2nd winding dq -axes currents in the arbitrary rotating reference frame of angular frequency ω1 1st winding dq -axes currents in the arbitrary rotating reference frame of angular frequency ω2 2nd winding dq -axes currents in the arbitrary rotating reference frame of angular frequency ω2 1st winding dq -axes flux linkages in the arbitrary rotating reference frame of angular frequency ω1 2nd winding dq -axes flux linkages in the arbitrary rotating reference frame of angular frequency ω1 1st winding dq -axes flux linkages in the arbitrary rotating reference frame of angular frequency ω2 2nd winding dq -axes flux linkages in the arbitrary rotating reference frame of angular frequency ω2 τ Torque output f1 1st winding supply frequency (Hz) f2 2nd winding supply frequency (Hz) rout Stator outside radius

B1-pk 1st winding peak flux density

B2-pk 2nd winding peak flux density J Pre-defined specific electric loading

Jratio Specific electric loading ratio

xiii J1 1st winding specific electric loading

J2 2nd winding specific electric loading

τd Torque density

τd-airgap Air-gap volume torque density

L11 1st winding self-inductance

L22 2nd winding self-inductance

L12 Mutual inductance between the windings woh End winding overhang Rated maximum for any phase-to-neutral peak voltage

VDC DC bus voltage of the power converters used Modulation index for the applied Space Vector Pulse m Width Modulation (SVPWM)

ωe Total supply (electrical) angular frequency (rad/s)

ω8e 8-pole winding (electrical) angular frequency (rad/s)

θe Total electrical angle (rad)

θ8e Electrical angle contribution from the 8-pole winding (rad)

θ4e Electrical angle contribution from the 4-pole winding (rad) x Ratio of the 8-pole winding frequency to the total applied frequency of the BDFRM drive

xiv

CHAPTER 1: INTRODUCTION

1.1 Introduction

The invention and consequent improvement of different electric motors is one of the most significant success points of modern science history. Electric motors are a critical and integral part in almost all aspects of science and technology. Electric motors act as the workhorses for almost every industry like manufacturing, paper mills, petroleum industry, plastic industry, automotive industry, mining and drilling companies, automation etc. They consume more than half of all electrical energy produced.

Michael Faraday demonstrated the conversion of electrical energy into mechanical energy by electromagnetic means for the first time in 1821 [1]. In his experiment, he showed that a free- hanging wire, dipped into a pool of mercury, rotated around a permanent magnet when a current was passed through the wire. There were some demonstration devices too around that time, but they were unsuitable for practical applications due to their primitive construction. The first commutator-type DC motor capable of taking significant loads was invented by scientist William

Sturgeon in 1832 which was then followed by DC motor built and patented by American inventor couple Emily and Thomas Davenport in 1837 [1]. But these motors had the critical drawback of the high cost of zinc electrodes required in the primary battery, and therefore they were commercially unsuccessful.

The first practical AC motor (initial brushless induction motor) was invented and demonstrated by Italian scientist Galileo Ferraris [2]. This invention of the induction motor is a breakthrough in electric motor history as AC motors are more robust, efficient and effective than previously introduced DC motors. Electric motors are mainly classified as DC and AC types. The general classification is shown in Fig. 1-1.

Figure 1-1: General classification of electric motors.

The brushless doubly-fed reluctance machine (BDFRM) belongs to a group of interesting machines which include the classic cascaded induction machine, the traditional doubly fed slip ring induction machine, and the brushless doubly-fed induction machine (BDFIM) [3-5].

The BDFRM has two sets of stator windings that are wound to have different numbers of magnetic poles. Traditionally the first winding of the machine is known as the primary winding

referring to the fact that it is connected to the grid supply. The second winding is called the

secondary winding and traditionally is inverter-fed in a modern BDFRM drive system. But in this

work, the two windings will be fed separately from two power converters. Control of power flow

between the windings and the rotor shaft occurs through the rotor design, which modulates the

magnetic coupling between the stator windings. The presence of the variable reluctance path for

the flux in the machine essentially modulates the stator mmf waveforms, resulting in the formation

of corresponding flux density harmonics, which can link the opposite winding.

Since its initial development some 40 years ago, the BDFRM has been mostly ignored

because of the performance limitations imposed by the critical reluctance rotor design. However,

improvements of reluctance rotors have resulted in renewed interest in the BDFRM. This together

with the promise of higher efficiency and simpler control compared to the BDFIM suggests that

further investigation of the BDFRM is justified. Various design aspects and the proposed two

power converter based real-time operation of BDFRM are explored and investigated in this work.

1.2 History of BDFRM

The conceptual basis of brushless doubly-fed machines is more than a century old [3, 4] and numerous papers have been published to address the analysis of prototype machines, e.g. [6-

29]. These works highlight the potential capabilities of BDFRM, but the majority of the published literature analyze existing designs, rather than giving clues regarding commercially viable

BDFRM designs.

More recently various control methods have been developed for BDFRM such as scalar control [30, 31], voltage & flux vector-oriented control [32, 33], direct torque & flux control (DTC)

[34, 35], reactive power control [36, 37], direct power control (DPC) [38], and non-linear multiple- input multiple-output (MIMO) control using Lyapunov’s theory [39, 40]. Some of these works are solely theoretical with analytical concept [30, 31] or numerical simulation studies [39, 40]. In some research works, stator frame-based control algorithms have been proposed and supported with experimental results. The algorithms are developed for both type of drive systems: with shaft- 3

position sensor [31, 35, 36, 38] and without sensor [34, 37]. However, in these works, experimental

results for only unloaded variable speed machines are shown. Besides, methods in [31], [34] are

sensitive to machine parameters uncertainty which limits the optimum performance.

Since the last decade, BDFRM has been investigated as a prospective replacement of

doubly-fed induction generator (DFIG) for wind power applications [30, 41-46]. One primary

objective of these works is to overcome the reliability issues and high operational cost of

conventional DFIGs [47-53] while ensuring the same economic advantage of fractionally rated

power electronics equipment. As explained in some of the works [30, 39, 40, 43], for a typical

variable speed ratio of 2:1 in wind turbines and similar drive systems, the reduction in power

converter rating relative to the machine itself can be as much as 75%. Some other works also have

focused on the prospective advantage of BDFRM over DFIG regarding better fault ride-through

capability without a crowbar circuitry due to larger leakage inductances and consequently lower

fault currents [54-56].

1.3 Research Motivation

Quick & precise speed & torque response, robustness, and quick speed recovery from any disturbance are some main concerns for variable speed drive applications. In comparison with other common conventional machines, BDFRM holds an edge with some advantageous features.

Among the commercially used electric motors, the separately excited DC motor requires the simplest control strategy because of the decoupled nature of its field and armature quantities. But the DC motor has critical disadvantages such as low torque density, low power-weight ratio, limited speed range of operation, power loss in field circuit, lack of robustness, need for frequent maintenance, high cost due to brushes & commutators. Induction motors are very popular and widely used in various industrial applications because of certain advantages over DC motors like 4

low cost, robustness and low maintenance requirement. But induction motors have some inherent

limitations that researchers cannot ignore when performance is the top priority rather than cost.

The induction motor always has to operate at a lagging power factor and lower than synchronous

speed. Besides, real-time implementation of induction motor drive requires sophisticated modeling

and estimation of machine parameters.

The disadvantages of the DC motor and the induction motor encouraged further extensive research on synchronous motors in VSD applications. The synchronous motor’s control algorithm is less complex because it rotates at synchronous speed and thereby eliminates slip power loss. But again, conventional synchronous motors have some disadvantages like the additional external DC power supply requirement and presence of slip rings & brushes at the rotor side. The permanent magnet synchronous motor (PMSM) provided a very good solution in this case by eliminating the extra power supply, slip rings, brushes and power loss due to excitation. The PMSM can yield higher torque density and operate at a higher efficiency level than the induction motor. Extensive research and experimentation have already been performed on PMSM drives by numerous researchers and engineers in the last few decades. In this regard, the prospect of BDFRM has often been overlooked.

However, concerns regarding the low availability and higher cost of rare earth permanent magnet materials over the course of the coming years are encouraging research efforts to reduce or even eliminate the permanent magnets from electric machines without compromising too much performance like torque density and efficiency. For both surface mounted and interior permanent magnet machines, some magnets that are located in the rotor can be replaced by DC field coils to reduce the cost [57]. But, since the DC field windings are located inside the rotor, slip rings and brushes are still required. Besides, potential demagnetization of the permanent magnets caused by

DC field coil generated heat must be carefully mitigated during the design process. To overcome

these issues, the BDFRM and other machines like the DC-excited switched flux machine, hybrid

doubly salient machine, and hybrid switched flux machine have been proposed and developed.

The BDFRM has some uncommon characteristics that allow them to operate both as a synchronous

machine and as an induction machine, depending on the control approach applied. They do not

consist of brushes, slip rings, rotor circuits or magnets. This combination creates an attractive

prospect of a controllable, low cost, low maintenance machine which will be even more robust and

versatile than the PMSM [6, 10, 11, 16, 21]. It is a common criticism against BDFRM that

prototypes proposed earlier yielded relatively low efficiency, power factor, and torque density

when compared to commercial machines [17], or sometimes conceded excessive eddy current loss

in case of axially laminated structure [20]. However, some recent works have been reported

regarding meticulous designs of BDFRM which can enable it to operate within a wide sub-

synchronous and super- synchronous speed range with high efficiency and torque density at a

commercial level [19, 58-60].

If such a machine is commercially realized, it will be highly suitable to operate in locations where accessibility is limited, such as offshore or in harsh climates. If proper control technique is established and utilized, BDFRM can be a very attractive prospect for two important electrical applications: wind turbine system and electric vehicle. These two perspectives are discussed in the next two paragraphs.

Doubly-fed induction generator (DFIG) is the most commonly used machine in wind

power systems. This is primarily due to the fact that the power electronic converter has to handle

only a fraction of the generator’s rated power. This means that a smaller size power converter with

reduced power loss and cost can be selected. But DFIG has some certain inherent disadvantages

owing to its structure and a complex control method employing two back-to-back voltage source

converters (rotor-side and grid-side). In case of DFIG, the stator winding is directly connected to

the grid and the rotor winding is connected to the rotor-side converter via slip rings and brushes.

So a certain drawback of the DFIG is the need for slip rings which results in higher operating and

maintenance costs [61]. Along with the back-to-back converters, DFIG also requires additional

power electronic circuits and components such as a crowbar to establish the over-current protection

of the rotor-side converter during power system disturbances. So, the illusion of significantly lower

costs of DFIG system’s power electronics seems to be misleading when all the necessary

components of the fault ride-through capable DFIG system are taken into consideration. Now,

BDFRM has the potential to be a better equivalent of DFIG machine because it does not require

brushes & slip rings which results in low maintenance cost and no rotor power loss at all. BDFRM

can also operate with a much simpler control method and better fault ride-through capability as

mentioned in the previous section. Besides, the BDFRM can run at higher rated speeds than

commonly used DFIGs. The prototype BDRFM with 6 rotor magnetic poles built in this research

work can run at 1000 rpm rated speed. In comparison, the DFIG is considered as a medium speed

drive with rated speed in the range of 300 to 650 rpm [46, 53, 55].

Contrary to popular belief, the history of use of electric motors in vehicles is actually quite old. The first hybrid vehicle system, which was a combination of a special steam engine, a separately excited DC generator, and eight electric motors, was implemented by J. J. Heilmann in

1893-94 for Ouest Railway in France [62]. Those early hybrid vehicles were known as "petrol- electric vehicles". But vehicles incorporating electric motors did not really flourish significantly in the last century as it was expected initially due to high fixed cost and various technical issues.

However, recently plug-in hybrid vehicles and electric vehicles are promoted worldwide as a way

of curbing consumption of fossil fuels and reducing greenhouse gases emission. Electrical vehicle technology is considered as a mean of sustainable transport and one of the tools of green energy or renewable energy. In Canada, many utility companies and research centres have initiatives in this area, with the objective to assess the impact of the wide-scale deployment of these vehicles on the electric grid [63]. There is substantial interest on the part of multinational automobile manufacturers to supply vehicles to the local market, and on the part of equipment manufacturers to develop specialized components for this market. The recent trend in the automotive industry is to focus research efforts on DC machines [64, 65], induction motor drives [66, 67], PMSM drives

[68-71] and brushless DC (BLDC) motor drives [72-78]. Additionally, research on switched reluctance motor (SRM) drives [79-81] is quite promising and some researchers are also proposing unconventional axial flux machines [82-84]. However, a possible application of BDFRM or similar machines in this technology has been overlooked so far. Some of the research works actually discuss the detailed comparisons of performance and efficiency among the conventional motor drives used in hybrid or electric vehicles [85-91].

PMSMs are the most popular motor technology for hybrid vehicle applications and used in hybrid cars like Toyota Prius, Honda Insight etc. But magnets cost aside, PMSMs are also not very efficient at extended speed range due to the flux weakening which requires high d-axis current. In comparison, a BDFRM can run beyond rated speed without flux weakening method. Like the case of PMSM, flux weakening method is also required to run the IM at higher than base speed. But this approach results in higher breakdown torque which leads to a shorter constant-power speed range and oversizing of the IM. SRM has certain advantages like simple construction, low mass production cost, fault tolerance, high power density etc. However, SRMs are not widely being used in hybrid vehicles as they come with significant drawbacks like high acoustic noise, high

electromagnetic interference (EMI) noise, torque ripple, complex converter topology requirement

etc. Therefore, to further improve the performance of hybrid vehicles, BDFRM can be employed

in place of conventional machines with its comparative advantages of low cost and robustness.

Unlike synchronous reluctance machines, there is not much-published information about

the appropriate design of radially laminated rotors for a BDFRM. Therefore, inspired by recent

improved BDFRM designs [58-60], this topic has been chosen for research to explore the BDFRM

design aspects through FEA simulation & analysis with an aim to implementing a commercially

viable prototype BDFRM drive system.

1.4 Thesis Contribution

This thesis presents the step-by-step process of building a ducted rotor BDFRM from first principles and through detailed magnetic analysis. Then the thesis explores the operation of this machine through the implementation and testing of the corresponding BDFRM drive in three different operating modes. Thus, the complete evaluation of a ducted rotor BDFRM design process is covered in this thesis.

This research work investigates the two power-converters based operation of the BDFRM.

Unlike all the previous works on BDFRM, the two stator windings are fed separately from two separate power converters. This arrangement can enable the operation of the BDFRM in wide speed range comprised of sub-synchronous, synchronous and super-synchronous regions depending on the supply frequencies applied to the windings. Higher speed beyond rated speed can be achieved without employing flux weakening technique. Steady-state speed-torque responses are investigated at different operating points.

With the proper control technique being utilized, BDFRM has the potential to be an attractive prospect for two important applications: a) electric vehicles, b) wind turbine systems. In 9

case of electric vehicles, BDFRM can be used in place of conventionally used PMSM with its

comparative advantages of low cost and robustness. Two-converters based operation also provides

an additional degree of freedom in this kind of operation. In a split battery configuration, power

can be transferred from one winding circuit to the other for battery charging purpose (operating

mode-2). When both battery units are charged up, both windings can contribute to yield more

torque (operating mode-3). In case of wind turbine systems, BDFRM can be a better alternative

for popularly used doubly fed induction generator (DFIG). The BDFRM has some advantages over

the DFIG because of its much simpler control method and lack of brushes & slip rings. Therefore,

the BDFRM can be used as a robust and low maintenance wind turbine generator.

1.5 Thesis Organization

Two power-converters based operation approach provides additional degrees of freedom for control, can extend the constant torque region and increase the power density of the machine.

But before the machine building and real-time operation, careful design and analysis of the proposed BDFRM are required to comprehend the commercial feasibility issues. Besides, suitable operating points of the machine and the appropriate ratio of the total applied frequency sharing between the two windings are to be calculated carefully. These are important steps to follow before exploring the machine’s response over a wide speed range while ensuring that the peak voltage of either winding does not exceed the rated maximum value. This thesis is organized into several chapters to cover and explain all these areas of this research work.

The first chapter introduces the topic of BDFRM to the reader and explains the motivation behind this research work in depth. This chapter also outlines the contribution of this thesis. The second chapter will start with the basic operation and theory of BDFRM which is deduced by previous researchers. In the latter part of this chapter, additional mathematical and theoretical 10

findings of this research work are also included. The background theory and equations will form the basis of the proposed design of the machine which is elaborated in Chapter 3. This chapter explains specific design aspects of the proposed BDFRM. Then Chapter 3 focuses on finding appropriate operating points of the machine for two power-converters based operation by carrying out time-stepped finite element analysis (FEA) simulations. The development of the proposed

BDFRM design and corresponding FEA simulations are carried out using a commercial package

JMAG Designer. Chapter 4 describes the proposed machine building, winding and drive system development steps. This chapter also discusses the control strategy of two power-converters based operation of the BDFRM drive system. Chapter 5 presents the experimental results of various two power-converters based operation tests to support the FEA simulations. Finally, Chapter 6 concludes the research work by discussing the summary and possible future work on this topic.

CHAPTER 2: THEORY OF BDFRM

This chapter discusses the basic operation and theory of Brushless Doubly Fed Reluctance

Machine (BDFRM) which is outlined by past research works. After the initial discussion about operation principle and control theory, mathematical and theoretical findings regarding frequency division between two converters are also included.

2.1 Basic Operation Principle of BDFRM

The BDFRM has two sets of three-phase stator windings that are wound to have different

numbers of magnetic poles, and a reluctance rotor having half the total number of stator poles. A

schematic block diagram of the connections of a BDFRM is presented in Fig. 2-1. Traditionally

the first winding of the machine is known as the ‘power winding’ referring to the fact that it is

connected to the grid supply. The second winding is called the ‘control winding’ and traditionally

is inverter-fed in a modern BDFRM drive system. But in this work, the two windings will be fed

separately from two power converters and therefore they are denoted as ‘winding 1’ and ‘winding

2’ respectively in Fig. 2-1.

Figure 2-1: Conceptual diagram of BDFRM.

Control of power flow between the windings and the rotor shaft occurs through careful

design of the rotor. As the two windings have different numbers of pole pairs, ideally there should

be no coupling between them if the machine has a round rotor. So rotor saliency is the key to the

satisfactory operation of the BDFRM. The presence of the variable reluctance path for the flux in

the machine essentially modulates the stator mmf waveforms, resulting in the formation of

corresponding flux density harmonics, which can link the opposite winding. Coupling between the

stator windings occurs under the following constraints [14]:

, (1) = = , . (2) = ± = ± where p1, p2, and pr are the first winding, second winding and rotor pole numbers respectively; ω1,

ω2 are the first winding and second winding electrical angular supply frequencies, and ωm is the rotor mechanical speed in rad/s. Analysis of the second case in (2) was shown to not provide the desired coupling for some pole combinations [60] and may result in designs that are not realistic for manufacturing the machine. This work will focus on the designs that meet the criteria described in the first case in (1).

2.2 Previous Relevant Research on BDFRM

In [8] and [9], performance characteristics of a synchronous dual-winding reluctance generator are investigated by Ojo and Wu while feeding an impedance load and a rectifier load.

This is a particularly interesting case regarding the motivation for this very research work and thus is elaborated hereby. As the control winding is fed with a DC source, the frequency of the generated voltage is directly proportional to the rotor speed. When the rotor speed is regulated unlike the case of wind turbines, the load voltage frequency is constant irrespective of load, in

which case a rectifier-inverter system (power converter) is not required as in the case of induction generator to obtain a regulated voltage and frequency supply. In these cases, the load voltage is regulated by careful selection of the excitation capacitors and regulation of the control winding excitation current. In [8], the modeling and analysis of the synchronous dual-winding reluctance generator with a DC control winding excitation is presented which is an interesting choice because their investigated machine is essentially the machine of interest for the proposed research work of this thesis, i.e. , BDFRM. Furthermore, the authors have suggested that the model equations derived in [8] can be applied to investigate the transient and steady-state performance of the doubly-fed synchronous reluctance motor fed from a variable or constant frequency supply. The operation strategy and few relevant equations derived in [8] for the synchronous dual-winding reluctance generator are briefly discussed below.

Fig. 2-2 shows the schematic diagram of the machine considered in [8] operating as a generator feeding a three-phase rectifier load via its power winding. The composite stator winding structure, salient rotor structure, and control winding connection are also shown in Fig. 2-3. The two stator windings have pole pair numbers of p and q respectively for the power winding (A-B-

C) and control winding (a-b-c) while the rotor has a salient structure with rp pole pairs.

Figure 2-2: Schematic diagram of the synchronous dual-winding reluctance generator system with a loaded 3-phase diode rectifier considered in [8], [9].

(a)

(b) (c)

The two stator windings combine to a single unit with three parallel paths per phase where the windings from power terminals (A-B-C) has one pole pair (p = 1) , and from control terminals

(a-b-c) it has three pole pairs (q = 1). The control winding, as shown in Fig. 2-3 (c), is connected

to a DC voltage source. With the power winding connected to a balanced three-phase voltage

source having a frequency of p, the voltage equations of the control winding are expressed as, (3) = (4) = 15

(5) = where n is the neutral point of the control winding, Rs is the per-phase control winding resistance.

The flux linkages of the control winding are also given as,

(6) = (7) = (8) = where Laa , L bb , L cc are the self-inductances of the control winding phases carrying currents Ias , I bs ,

Ics respectively; Lab , L bc , L ca are the mutual inductances between the control winding phases. The mutual inductances between the control and power winding phases are given by Lij where i = a, b, c and j = A, B, C . IAp , I Bp , I Cp are the currents flowing in the power winding phases. The inductances are given by the following expressions [16],

= = =

= = = − /2

= = = (9) = = = − /2

where, , , = = , β = 2 π/3, k = 0, 1, 2 (10) = cos ( − ) where, , = () sin ( ) k = 0 for = = k = 1 for , = = k = 2 for , = = 16

. = ( ) The electrical and mechanical rotor angular positions are θr and θrm respectively and the rotor pole pitch is defined as α. Np and Ns are the effective numbers of series connected

turns/pole/phase for the power and control windings respectively. The minimum air-gap length is

g, R is the rotor radius, and the effective machine length is l. The per-phase leakage inductances

of the power and control windings are Llp and Lls respectively.

The phase ‘A’ voltage of the balanced three-phase power winding is also given as,

(11) = where Rp is the per-phase power winding resistance and the corresponding flux linkage λAp is given as below,

(12) = The self-inductance of phase ‘A’ power winding is designated as LAA . Similarly, phase ‘B’

and ‘C’ voltage equations can also be written. Then complex d-q transformation and harmonic

balance techniques have been applied to the voltage equations to make them time-invariant. The

resulting time-invariant equations are as follows,

(13) = (14) = (15) ∗ = ( ) [ ] where Te is the electromagnetic torque and, , . = = In [8], additional model equations are also derived incorporating per-phase shunt capacitors

(C p, C q) connected across the power and control winding terminals, load resistance and inductance

(R o, L o), rectifier filter capacitance and inductance (C d, L d) to determine the performance characteristics of the generator. However, the model was not used to investigate the performance of a dual-winding synchronous motor. Besides, no suggestion was provided as to how the motor can possibly be operated beyond synchronous speed as only one power converter was used in these works [8], [9].

Some of these unanswered questions will be addressed and explored in this work for the case of a ducted rotor BDFRM. The reason for the choice of a ducted rotor machine for this work is explained at the beginning of the next section.

2.3 Operation Principle of a Ducted Rotor BDFRM

While the simple salient rotor structure is useful for understanding the BDFRM operation principle, this type of rotor structure exhibits inferior performance compared to that obtained with ducted rotor design [92, 93]. For ducted rotor design, the air flux barriers weaken the rotor structure which may lead to deformation due to centrifugal forces during higher speed operation or increase manufacturing difficulty since the lamination may be less rigid than a traditional lamination. In

[59], structural FEA using JMAG has been carried out on a number of variations to find out the optimized ducted rotor design which can prevent structural deformation at high-speed rotation and at the same time keeps a nice balance of uniform flux density, saturation & torque ripple. Like the examples of [59, 60], a similar ducted rotor pattern is followed in this work which will be discussed later in detail in Chapter 3. The theoretical approach from those works [59, 60] is reviewed hereby in this section.

It is noteworthy that the term ‘rotor pole number’ in case of literature associated with

BDFRM is a misnomer as it is not consistent with the conventional definition of the term. In this

case of ducted rotor type BDFRM, ‘rotor pole number’ can also be an odd number which actually

implies an odd number of rotor segments is used. If an odd number of rotor segments are used,

there will still be an even number of magnetic poles in the air-gap at any instant. To remain

consistent with the existing terminology used in this field, the term ‘rotor pole number’ is used in

this work to be synonymous with the ‘number of periodic rotor segments’.

Now for the ducted rotor design in consideration with infinitely permeable steel, according

to Fig. 2-4, the flux entering the rotor at a given point θm1 in the air-gap must be equal to the flux exiting the rotor at a known point θm2 . The angular positions in the air-gap are related in the

following manner,

θm2 = θm1 + λr - 2α. (16)

and, α = mod( θm1 - θm0 , λr) (17) where rotor segment angular period and θm0 is the initial mechanical position of the rotor = d-axis. Angles θmx , λr, α are defined in mechanical radians.

Let’s consider an mmf harmonic given by the form,

(18) = cos

Figure 2-4: Illustration of linearized ideal segmented rotor structure [59].

Assuming the ideal case of infinitely permeable steel as an initial design step, the

magnitude of the air-gap flux density at a given position can be written as a normalized function

relative to the peak magnitude that would be obtained with a round rotor of air-gap length g. The normalized function can be defined as,

(19) () ( ) = It is possible to calculate the air-gap flux density by using Ampere’s circuital law and the summation of two mmf functions at the angles defined in (16). Therefore,

(20) () = [() − ()] (21) ()() () = The normalized air-gap flux density can also be written in terms of θm1 and θm2 as,

(22) () = cos − cos The peak of a flux density harmonic of space order i, produced as a result of the modulation of an mmf harmonic of space order j by the rotor structure, can be defined in terms of a coupling factor Cij by using the normalized flux density function,

(23) = where, , (24) = , (25) = () cos . (26) = () sin A solution of the integrals in (25), (26) can be carried out numerically because of modulo function required in (17).

Traditional electrical machine design equations are employed along with (23) in order to

develop an initial design [24, 59, 60]. To start with, the rms specific electric loading of a winding ̅ j can be defined in terms of the number of turns per phase Nph , fundamental winding factor kw1 ,

air-gap radius r, and rms phase current Iphj as,

. (27) ̅ = Assuming series connected coils, the peak mmf is given by,

. (28) = √2 ̅ Applying (23) with a saturation factor ksat , the resulting air-gap flux density harmonic i is

given by,

. (29) = = √2 ̅ Here, ksat accounts for all mmf drops in the iron of the machine, i.e., the difference between saturated steel and theoretical infinitely permeable steel. The rms magnitude of a voltage induced in a stator winding with pole number pi by the flux density harmonic in (29) can be calculated as,

. (30) = (2) √ A relationship between the induced voltage in winding i and the forcing specific electric loading j can be obtained by substituting (29) in (30) as mentioned below,

. (31) = (4 ) ̅ At maximum torque per ampere, the magnitudes of the first winding voltage components can be given by,

, (32) = sin () . (33) = 21cos ( )

Substitution of (27) in (31) enables one to obtain theoretical expressions for self and

coupling inductances.

2.4 Control Strategy of BDFRM

In a previously published conference paper [94] written by the author of this thesis, a general control strategy based on torque-current relation has been discussed and supported by mathematical equations. The discussion from that paper [94] is reviewed hereby in this section.

The a-b-c three-phase voltage equations of the two sets of stator windings of the BDFRM can be written as,

(34) = (35) = where suffix ‘1’ and ‘2’ are used to denote the first and the second winding respectively. The numbers of poles of the two stator windings and the rotor design have to be chosen in a manner that in an ideal case the self-inductance of each winding is independent of rotor position and only the coupling between windings depends on rotor position. The rotor electrical angle θr is defined in terms of number of rotor poles pr and rotor mechanical angle θm as in,

(36) = In this case, the flux linkage equations for the windings can be written as,

− − 2 2 − − = 2 2 − − 2 2

2 2 cos( ) cos − 3 cos 3 (37) 2 2 cos − 3 cos 3 cos( ) cos 2 cos() cos − 2 3 22 3

2 2 cos( ) cos − 3 cos 3 2 2 = cos − 3 cos 3 cos( ) 2 2 cos 3 cos( ) cos − 3 − − + 2 2 (38) − − 2 2 − − 2 2 where L1m , L 2m , are the first winding magnetizing inductance, second winding magnetizing inductance and peak mutual inductance respectively. L1l, L 2l are the first and second winding

leakage inductance respectively [58]. Eqns. (37) and (38) can be further simplified by referring to

an arbitrary q- and d- axes reference frame of rotating frequency at position: (39) = As both windings are wound on the stator, a single reference frame transformation matrix

K can be used to refer both the stator circuits to the new reference frame [96].

cos() cos(− 2 ) cos( 2 ) (40) 3 3 = sin() sin(− 2 ) sin( 2 ) 3 3 1 1 1 Using (40) to transform2 (37) & (38)2 to an arbitrary reference2 frame and neglecting zero- axis terms gives,

0 sin cos (41) 0 sin − cos = cos sin 0 sin − cos 0 with , , , and [58]. = = = = (2 − ) As an initial condition, let’s consider the physical arrangement of the windings in a way such that the a-axis of each winding is co-incident with reference axis (angle θ=0 ) and the first

winding phase-a has zero offset at time t=0 . Besides, both sets of winding voltages are assumed

to be balanced cosine functions with angular frequencies ω1 and ω2 [58]:

(42) = cos () , = cos ( ) Assuming lagging current flow in each winding,

(43) = cos ( − ) , = cos ( − ) where θ10 and θ20 are the relative phase of the currents with respect to the arbitrary reference frame

at t=0 [58]. The q-d axes currents in the arbitrary rotating reference frame can be written as [58],

(44) = [ ( − ) − − ( − ) − ] (45) = [ ( − ) − − ( − ) − ] Now, in order to simplify the flux linkage equations of (41), let’s consider two different

arbitrary rotating reference frames of angular frequencies ω1 and ω2 for the first and the second

winding respectively. Based on this assumption, eqns. (44) and (45) give:

(46) = cos( ) (47) = −sin( ) (48) = cos ( − ) ( − ) (49) = −sin ( − ) ( − ) (50) = cos ( − ) ( − ) (51) = −sin ( − ) ( − ) (52) = cos( ) (53) = −sin( ) where prefix ‘1’ and ‘2’ are used to denote the first (angular frequency ω1) and the second (angular

frequency ω2) reference frames respectively.

Now, by substituting (46) to (53) in (41) and setting , it can be = ( ) shown that,

(54) = cos ( ) cos( − − ) (55) = −sin ( ) sin( − − ) (56) = cos (∆ − ) cos (−∆ − ) (57) = sin (∆ − ) − sin (−∆ − ) (58) = cos (∆ − ) cos (−∆ − ) (59) = −sin (∆ − ) sin (−∆ − ) (60) = cos ( − − ) cos ( ) (61) = sin ( − − ) − sin ( ) where It can be observed from (54) to (61) that the q-d axes flux linkages of the ∆ = − . two windings are DC quantities in their respective reference frames whereas they become AC variables in their opposite reference frames.

The torque of the machine can be calculated by using standard reference frame theory and by simplifying the inductance matrix given in (41) if the reference frame is chosen in a manner that [14, 16]: = 2 (62) = − ( ) (63) = ( − ). It can be implied from (63) that the torque output of the machine is directly proportional to

rotor pole number, peak variation of mutual windings between windings, and peak currents in both

the windings which will be supported with FEA simulation results and data in the next chapter.

Inspection of (63) along with (54), (55) and (60), (61) indicates that if θ10 and θ20 are zero, torque is maximized given that the rotor initial angle is 90 degrees. In that case, the self and mutual fluxes are orthogonal in both windings. This operating condition provides a simple framework on which to base FEA investigations of performance.

2.5 BDFRM Operation with Appropriate Frequency Division

Let’s recall the relationship between the induced voltage in winding i and forcing specific electric loading j as expressed in (31). Now, by replacing the common coefficients in (31) with a constant A, we can write,

(64) = Assuming similar rms specific electric loading and fundamental winding factor for the two windings, we may write the four equations for induced voltages in the two windings from (64) as:

(65) = (66) = (67) = (68) = To utilize the maximum limit of induced voltage capacity in both windings, one has to ensure during operation that,

(69) = = However, in BDFRM theory we know that,

(70) = (71) = 26

By combining the above terms in (69), (70), (71), we can deduce:

(72) = Substituting p1=8, p2=4 and the numerical values of the coupling factors from an initially

proposed design, it can be concluded from (72) that,

. (73) 35 = 65 Eqn. (73) gives the relation between the applied frequencies of the two windings based on the initial design and analysis which will be discussed in detail in the next chapter. The initial frequency ratio is a prediction which can be later adjusted according to the results of FEA simulations. It should also be noted that this mathematical analysis neglects the voltage induced across leakage inductance [95].

CHAPTER 3: DESIGN OF BDFRM, SIMULATION RESULTS AND DATA ANALYSIS

This chapter proposes an optimum design of Brushless Doubly Fed Reluctance Machine

(BDFRM). At first, the proposed design is chosen from a few initial trial designs which have been

outlined in JMAG software on the basis of BDFRM operation principle equations explained in

Chapter 2. Then specific simulations have been run on it to obtain detailed characteristics data.

After the simulation, thorough analysis and calculation have been carried out to predict the

dynamic performance of the machine in different modes of operation. In the next step, static

structural analysis simulation has been carried out on the proposed design in order to determine its

sustainability at higher speed operation. Based on the static analysis, further modifications have

been introduced in the final design in order to enhance its feasibility. The design steps, simulations and data analysis in this whole process will now be discussed in detail in the following sections of this chapter.

3.1 Choice of Number of Rotor Poles

Recall the BDFRM operation theory from the previous chapter. In [59], to understand the performance of a ducted rotor, the idealized air-gap flux density waveforms produced by the windings (defined as ‘grid’ and ‘secondary’ in that paper) are plotted and observed for three different design cases which are: (a) p1 = 6, p 2 = 2, p r = 4; (b) p1 = 8, p 2 = 4, p r = 6; (c) p1 = 6, p 2

= 4, p r = 5 . The initial rotor position is arbitrarily set to 15 mechanical degrees so that the q-axis coincides with phase a-axis. The exact shape of the ideal flux density waveform depends on the angle between the stator currents and the rotor position. All three cases are shown in Fig. 3-1.

It can be observed from the cases in Fig. 3-1 that the flux density in each segment is symmetric about the centre of the segment where the air-gap mmf is zero and the flux density from one segment to the next one is discontinuous. Case ‘a’ stator windings’ flux density waveforms

(a)

(b)

(c) Figure 3-1: Idealized air-gap flux density functions [59] for cases: (a) p1 = 6, p2 = 2, pr = 4; (b) p1 = 8, p2 = 4, pr = 6; (c) p1 = 6, p2 = 4, pr = 5.

exhibits negative periodicity over 180° mechanically whereas case ‘b’ exhibits positive

periodicity. Consequently, the radial projection of reluctance force is balanced throughout the

circumference of the machine. But unlike cases ‘a’ and ‘b’, case ‘c’ does not exhibit any symmetry

which considers an odd number of rotor poles. Therefore, an unbalanced magnetic pull is expected

in this case due to unbalanced radial forces. This observation and information are considered in

choosing the number of rotor poles in the proposed design.

In [60], self-coupling and mutual coupling factors for different valid combination of pole

numbers are calculated to wisely decide on the desired number of first and second winding poles.

As in that work, based on the coupling factors and also the observation of idealized flux density

functions discussed just above, p1 and p2 are chosen to be 8, 4 respectively so as to avoid unbalanced magnetic pull and unwanted coupling between stator windings. Therefore, pr is found out to be 6 according to (1) in the proposed design.

3.2 Proposed BDFRM Design

Initial calculations for the design dimensions have been carried out with the careful choice of suitable pole combinations for the stator windings, desired rotor speed and understanding of

(16) to (31) as mentioned in Chapter 2. The initial design condition should be the synchronous speed obtained when the second winding is fed from a DC supply. At this speed, the desired power rating for the first winding can be calculated, which, along with the desired terminal voltage, can be used to calculate the first winding current. The aforementioned equations allow the required first winding self-induced voltage component to be calculated in terms of air-gap length and stator bore. The only step which is different from typical machine design is that of the second winding current and turns calculation. In this work, the second winding rated current is chosen to be equal

to the first winding rated current in order to simplify the winding design and provide a reasonable

second winding induced voltage.

To investigate torque and speed responses, a tentative initial design has been chalked out to meet the requirements presented in Table 3-1. The practical reasons behind choosing these initial design specifications should be explained hereby. Considering optimum amplitude modulation

Table 3-1: Initial Design Specifications 1st winding phase Voltage 100 V (rms)

1st winding Frequency 100 Hz

Output Power 1000 W

1st winding Power Factor 0.8 lagging

Specific Electric Loading 32000 A/m (rms)

1st winding rated Current 4.2 A (rms)

Synchronous Speed 1000 rpm

Output Torque 9.55 N-m

Table 3-2: Parameters Initially Chosen by Designer for the design in Table 3-1

p1 8

p2 4

pr 6

Saturation Factor 0.6

Air-gap radius (r) 70 mm

Air-gap length (g) 0.5 mm

Number of stator slots 24

Number of rotor ducts 12

stator tooth : slot width ratio 3 : 2

stator yoke : tooth ratio 2 : 1

index 1.15 for power converters employing space vector pulse width modulation (SVPWM) switching, and 120 V (rms) output of supply phase-to-neutral, 104.35 V (rms) can be expected at the phase-to-neutral points of the machine. This number is rounded to 100 V (rms) for the choice of first winding phase voltage. The available load machine (a previously built permanent magnet synchronous machine) in the lab was designed for 1000 rpm rated speed. Therefore, to be compatible with the load machine’s rated speed, 1000 rpm is chosen as the synchronous speed of the BDFRM design. Obviously, the motor with a 6-pole reluctance rotor will run at 1000 rpm speed when the first winding will be supplied 100 Hz frequency and the second winding will be fed DC current from the converters.

Applying the design approach mentioned at the beginning of this section, the designer is required to make some informed choices about a number of variables in order to attain a reasonable design. The parameters chosen for the initial design in Table 3-1 are presented in Table 3-2. Stator winding pole numbers have been chosen to satisfy the requirements of a 6-pole rotor required for

1000 rpm synchronous speed at 100 Hz first winding frequency. Air-gap diameter is chosen to minimize the rotor volume while maintaining the surface linear speed to an acceptable value (7.33 m/s). Air-gap length is adjusted to achieve a peak air-gap flux density close to 1.0 T with the expectation of between 1.5 T and 2.0 T in the stator teeth. The numbers of stator slots and rotor ducts are chosen based on the design pattern and investigation presented in [59]. ‘Stator tooth: Slot width’ and ‘Stator yoke: tooth’ ratios are chosen to achieve acceptable values of flux density in the stator laminations based on the peak air-gap flux density.

Now, the choice of air-gap length ( g) is critical in defining the overall characteristics of the machine. The initially chosen value of 0.5 mm has been later understood to be too small and inconvenient to implement in a prototype machine. Therefore, a more realistic air-gap length of

Table 3-3: Modified Design Specifications Considering 0.8 mm Air-gap Length 1st winding phase Voltage 63 V (rms)

1st winding Frequency 100 Hz

Output Power 630 W

1st winding Power Factor 0.8 lagging

Specific Electric Loading (J) 32000 A/m (rms)

1st winding rated Current (I ph ) 4.2 A (rms)

Synchronous Speed 1000 rpm

Output Torque (τ) 6 N-m

Air-gap length (g) 0.8 mm

Table 3-4: Calculated Parameters for the Modified Design in Table 3-3 Stack length (l) 37 mm

Stator Outside Radius (rout ) 110 mm

1st winding peak flux density (B1-pk ) 0.38 T

2nd winding peak flux density (B 2-pk ) 0.27 T

1st winding Specific Electric Loading (J 1) 16220 A/m

2nd winding Specific Electric Loading (J 2) 15780 A/m

No. of 1st and 2nd winding Turns/Phase 72 each

Torque Density (τd) 1.3415 N-m/l

Air-gap volume torque density (τd-airgap ) 10.47 N-m/l

1st winding Self-Inductance (L 11 ) 14.71 mH

Mutual Inductance between the windings (L 12) 19.47 mH

2nd winding Self-Inductance (L 22 ) 26.67 mH

1st winding phase Resistance (R1) 2.77

2nd winding phase Resistance (R 2) 4.05

0.8 mm is chosen in the final design. This choice changes the initial specifications of the machine

mentioned in Table 3-1. The new specifications for the modified design are presented in Table 3-

3. All other parameters (except air-gap length) presented in Table 3-2 are kept the same in the final

design.

Calculated parameters for the final design are presented in Table 3-4. It can be observed that the proposed BDFRM design has a much larger air-gap diameter than stack length. The proposed design also indicates that the machine is capable to exert a reasonable torque density.

Some important relations that are used to calculate the parameters of Table 3-4 are mentioned hereby in this section.

Specific electric loading ratio (Jratio ) can be calculated from power factor angle θ, pole numbers, and coupling factors.

(1) = . Respective specific electric loading of the two windings can be calculated from the following

relations,

, . (2) = / = where J is the pre-defined specific electric loading (32000 A/m). Now, the stack length l can be

calculated from the following relation,

(3) = . . where V1 are I1 are the 1st winding rated rms voltage and current.

Self and mutual inductance values can be calculated from the following equation,

(4) = . . . .

The peak flux density values of the two windings can be calculated from the following

three relations,

, (5) √() = . . , (6) = √( ) . (7) = √( ) Stator outside radius ( rout ) can be calculated from air-gap radius ( r), tooth-slot width ratio,

tooth-yoke length ratio by using geometrical relations. Torque density (τd) and air-gap volume

torque density (τd-airgap ) can be calculated from the following two relations,

, (8) × = () (9) = where woh is the end winding overhang.

3.2.1 Evolution of the Proposed Design in JMAG

After sorting out the various design variables, the proposed design is outlined in JMAG and basic simulations are run to test the response of the tentative design. Emphasis has been given to the responses of output torque and magnetic flux density distribution. Naturally, to improve the proposed design, several similar designs have been outlined and simulated, and the simulation findings have been used to further modify the initially proposed design for the sake of the machine’s better performance. Some of the predecessors of the final version of the proposed design are presented in Fig. 3-2 and their corresponding magnetic flux density line plots are presented in

Fig. 3-3.

(a)

(b)

(c)

Figure 3-2: Cross-sectional views of some predecessor designs: (a) Design 1, (b) Design 2, (c) Design 3. 36

(a)

(b)

(c) Figure 3-3: Magnetic flux density line plots of the corresponding predecessor designs: (a) Design 1, (b) Design 2, (c) Design 3.

Figure 3-4: A cross-sectional view of the final simulation version of the proposed design.

Figure 3-5: Magnetic flux density contour & line plot of the final simulation version of the proposed design.

In Fig. 3-2, the rotor segments are highlighted with blue color. The stator core and the stator slots are highlighted with green and maroon colors respectively. It can be observed from Figs. 3-

2 & 3-3 that ‘Design 1’ rotor segments have the largest iron surface. However, it does not really yield the largest output torque because of the flux leakage that occurs mostly between segments through the narrow joints between segments. The torque output also has a significant noise content.

Figure 3-6: 8-pole and 4-pole windings configuration of the BDFRM.

‘Design 2’ is the next improved design which removes a large amount of iron from the inner or the lower part of the rotor segments and thus prevents flux leakage to some extent.

However, it still undergoes significant flux leakage within each segment through the small joints between rotor ducts. Then the proposed design has been further improved by introducing ‘Design

3’ which looks similar to ‘Design 2’ but does away with the duct joints present in its two predecessors. Besides, ‘Design 3’ limits the number of rotor ducts to 2 for each segment. Finally, to make the machine more robust and efficient in terms of magnetic flux distribution, the lower parts of the rotor segments in ‘Design 3’ have been further trimmed and thereby the final simulation version of the proposed design has been reached. The final simulation version of the proposed design and its corresponding magnetic flux density line plots are presented in Figs. 3-4 and 3-5 respectively.

3.2.2 Windings Configuration of the Proposed Design

Two 3-phase fully pitched windings are wound on the stator with 72 turns/phase for each of them. The windings configuration is presented in detail in Fig. 3-6. The shorter solid arrows are used to draw the 8-pole winding and the longer dotted arrows are used to draw the 4-pole winding.

The colors red, green, and blue are used to specify the phases a, b, and c respectively. As observed from Fig. 3.6, the 8-pole 3-phase winding is placed at the openings of the stator slots (closer to the rotor segments). And the 4-pole 3-phase winding is placed at the bottom sections of the stator slots considering the future machine building process with long end winding connections of the 4-pole winding. The building and the winding processes of the prototype machine will be discussed in detail in the next chapter.

3.3 Simulation & Data Analysis: Synchronous BDFRM Operation

In this case study, synchronous operation of BDFRM is investigated by first appropriately

simulating the proposed design in JMAG software, and then performing calculations & analysis

on the collected data. In this arrangement, the first winding is connected to a power converter

providing variable frequency power supply while the second winding is always connected to a DC

supply. In this setup, this machine is actually analogous to a conventional synchronous motor

where the second winding acts as the field control circuit whereas the first winding acts as the

power winding.

Commercial FEA package JMAG Designer is used to carry out the specific simulation tests. In order to obtain different characteristic responses like induced voltage, flux linkage, inductance and torque of the machine, a number of JMAG study cases have been simulated on the proposed BDFRM design by applying sufficient number of different amplitude current inputs ( I1 and I2) in the two windings with a specific combination of frequencies (80Hz for I1 and 20Hz for

I2). Based on the output data of those simulations, respective data tables of output torque and the

two windings flux linkages have been calculated which are presented in Tables 3-5, 3-6 and 3-7

respectively. Contour maps of torque, winding-1 flux linkage, and winding-2 flux linkage are

plotted in Figs. 3-7, 3-8, 3-9 respectively.

It is noteworthy in Fig. 3-7 that the predicted torque is proportional to the product of the

peak currents in both the windings as predicted by (63) in Chapter 2. The total flux linking

winding-1, in Fig. 3-8 can be seen to be a function of both winding currents. However, Fig. 3-9

clearly indicates that the winding-2 flux linkage is more strongly dependent on self-inductance.

The low influence of winding-1 current on winding-2 flux linkage is due to the fact that the flux

linkages contributions are orthogonal and winding-2 has the lower pole number.

Table 3-5: Data Table of Output Torque (Synchronous Operation)

Torque (N-m) Torque (N-m) Torque (N-m) Torque (N-m) Torque (N-m) Torque (N-m) I1-peak (A) (at I2-peak =1A) (at I2-peak =2A) (at I2-peak =3A) (at I2-peak =4A) (at I2-peak =5A) (at I2-peak =6A)

1 0.179 0.379 0.583 0.781 0.967 1.14

2 0.372 0.763 1.164 1.555 1.927 2.275

3 0.571 1.154 1.742 2.321 2.876 3.401

4 0.773 1.546 2.317 3.077 3.813 4.514

5 0.972 1.934 2.885 3.822 4.736 5.61

6 1.163 2.311 3.443 4.557 5.644 6.686

Table 3-6: Data Table of Winding-1 Flux Linkage (Synchronous Operation)

Flux Linkage-1 Flux Linkage-1 Flux Linkage-1 Flux Linkage-1 Flux Linkage-1 Flux Linkage-1 I1-peak (Wb-turn) (Wb-turn) (Wb-turn) (Wb-turn) (Wb-turn) (Wb-turn) (A) (at I2-peak =1A) (at I2-peak =2A) (at I2-peak =3A) (at I2-peak =4A) (at I2-peak =5A) (at I2-peak =6A)

1 0.03 0.046 0.066 0.087 0.107 0.127

2 0.052 0.061 0.075 0.092 0.11 0.128

3 0.077 0.081 0.09 0.103 0.117 0.133

4 0.103 0.104 0.109 0.118 0.129 0.142

5 0.128 0.127 0.129 0.135 0.143 0.153

6 0.152 0.15 0.15 0.153 0.159 0.167

Table 3-7: Data Table of Winding-2 Flux Linkage (Synchronous Operation)

Flux Linkage-2 Flux Linkage-2 Flux Linkage-2 Flux Linkage-2 Flux Linkage-2 Flux Linkage-2 I1-peak (Wb-turn) (Wb-turn) (Wb-turn) (Wb-turn) (Wb-turn) (Wb-turn) (A) (at I2-peak =1A) (at I2-peak =2A) (at I2-peak =3A) (at I2-peak =4A) (at I2-peak =5A) (at I2-peak =6A)

1 0.053 0.106 0.159 0.21 0.259 0.304

2 0.071 0.107 0.158 0.208 0.256 0.301

3 0.098 0.113 0.159 0.207 0.254 0.299

4 0.123 0.123 0.163 0.208 0.253 0.298

5 0.145 0.146 0.17 0.21 0.253 0.297

6 0.162 0.165 0.178 0.215 0.255 0.297

Torque (N-m) 5 6-7

5-6

4 4-5 3-4

2-3 3 1-2 Winding 2 Current (A) Current 2 Winding 0-1 2

1 1 2 3 4 5 6 Winding 1 Current (A)

Figure 3-7: Contour plot of simulated torque data of the proposed design.

Figure 3-8: Contour plot of simulated winding-1 flux linkage data of the proposed design.

Figure 3-9: Contour plot of simulated winding-2 flux linkage data of the proposed design.

Table 3-8: Data for Torque & Power Responses (Synchronous Operation)

Speed Max Torque I1-peak I2-peak V1-phase-peak V2-phase-peak Power f1 (Hz) f2 (Hz) (rpm) (N-m) (A) (A) (V) (V) (W)

1354 6.686 6 6 142 0 135.4 0 948 1476 5.61 5 6 142 0 147.6 0 867 1581 4.736 5 5 142 0 158.1 0 784 1756 3.813 4 5 142 0 175.6 0 701 1924 3.077 4 4 142 0 192.4 0 620 2200 2.321 3 4 142 0 220 0 535 2504 1.742 3 3 142 0 250.4 0 457 3017 1.164 2 3 142 0 301.7 0 368 3725 0.763 2 2 142 0 372.5 0 298 4959 0.379 1 2 142 0 495.9 0 197

10 1000 Max Torque (N-m) 9 900

8 Power (W) 800 7 700

6 600

5 500

4 400 (W) Power Torque (N-m) Torque 3 300

2 200

1 100

0 0 0 1000 2000 3000 4000 5000

Speed (rpm)

Figure 3-10: Predicted Torque and Power responses for Synchronous BDFRM Operation (winding-1: 100% applied frequency, winding-2: 0% applied frequency).

When the values of the winding resistances are known, Fig. 3.7 gives information about

the appropriate currents in the windings so as to increase the torque output with minimum copper

loss. The data from Figs. 3-7, 3-8, 3-9 are used to predict the maximum torque capability speed

curve with the terminal voltage of winding-1 equal to the rated maximum. These data tables are

prepared considering the initial parameters mentioned in Tables 3-1 and 3-2. Therefore, the rated

maximum for phase-to-neutral peak voltage is set to be 142 V here with some safety margin which

can be calculated from the converter equation below (considering a 250 V DC-link):

(10) = . The torque and power curves for synchronous operation are plotted in Fig. 3-10 and the corresponding data points are presented in Table 3-8. A speed range of 0 to 5000 rpm is chosen to illustrate all the case studies. For this case study involving the synchronous operation, winding-2 is always connected to DC supply. Therefore, the frequency contribution of winding-1 is 100% and has the range of 0 to 500 Hz as observed from Fig. 3-10.

3.4 Simulation & Data Analysis: Two-Converters Based Operation

In this case study, two power converter operation of BDFRM is investigated as both the

windings are simulated with AC supplies. The aim of this investigation is to understand how the

capability of the design may be expanded by use of an AC converter in the second, or control

winding, rather than a DC current controller. Three different combinations of applied current

frequency sets have been used to investigate this operation. In the first JMAG study of two

converter operation, frequency contribution of winding-1 and winding-2 are chosen to be 80% and

20% respectively. In the second JMAG study, the respective frequency contributions are 70% and

30%. The third study is a particularly interesting case where frequency contributions of 64% and

Table 3-9: Data for Torque & Power Responses (Case: f 1 = 80%, f 2 = 20%)

Speed Max Torque I1-peak I2-peak V1-phase-peak V2-phase-peak Power f1 (Hz) f2 (Hz) (rpm) (N-m) (A) (A) (V) (V) (W)

1692 6.686 6 6 142 63.12 135.38 33.85 1185

1845 5.61 5 6 142 68.78 147.59 36.90 1084

1976 4.736 5 5 142 62.91 158.06 39.52 980

2195 3.813 4 5 142 69.76 175.61 43.90 876

2405 3.077 4 4 142 62.72 192.38 48.09 775

2750 2.321 3 4 142 71.44 219.98 55.00 668

3130.5 1.742 3 3 142 62.64 250.44 62.61 571

3771.5 1.164 2 3 142 74.79 301.73 75.43 460

4656 0.763 2 2 142 62.81 372.46 93.11 372

Table 3-10: Data for Torque & Power Responses (Case: f 1 = 70%, f 2 = 30%)

Speed Max Torque I1-peak I2-peak V1-phase-peak V2-phase-peak Power f1 (Hz) f2 (Hz) (rpm) (N-m) (A) (A) (V) (V) (W)

1934 6.686 6 6 142 108.21 135.38 58.02 13543

2108 5.61 5 6 142 117.90 147.59 63.25 1239

2258 4.736 5 5 142 107.84 158.06 67.74 1120

2509 3.813 4 5 142 119.59 175.61 75.26 1002

2748 3.077 4 4 142 107.51 192.38 82.45 886

3143 2.321 3 4 142 122.47 219.98 94.28 764

3578 1.742 3 3 142 107.39 250.44 107.33 653

4310 1.164 2 3 142 128.21 301.73 129.31 525

5321 0.763 2 2 142 107.67 372.46 159.63 425

Table 3-11: Data for Torque & Power Responses (Case: f 1 = 64%, f 2 = 36%)

Speed Max Torque I1-peak I2-peak V1-phase-peak V2-phase-peak Power f1 (Hz) f2 (Hz) (rpm) (N-m) (A) (A) (V) (V) (W)

2125 6.686 6 6 142.6 142.7 136 76.5 1488

2470 4.736 5 5 142 141.6 158.08 88.92 1225

3005 3.077 4 4 142 141.1 192.32 108.18 968

3910 1.742 3 3 141.9 140.8 250.24 140.76 713

5820 0.763 2 2 142 141.3 372.48 209.52 465

13 1300 12 1200 11 1100 10 Max Torque (N-m) 1000 9 900 8 Power (W) 800 7 700 6 600

5 500 (W) Power Torque (N-m) Torque 4 400 3 300 2 200 1 100 0 0 0 1000 2000 3000 4000 5000 Speed (rpm)

Figure 3-11: Predicted Torque and Power responses for two-converters based BDFRM Operation (winding-1: 80% applied frequency, winding-2: 20% applied frequency).

15 1500 14 1400 13 Max Torque (N-m) 1300 12 1200 11 Power (W) 1100 10 1000 9 900 8 800 7 700 6 600 Power (W) Power Torque (N-m) Torque 5 500 4 400 3 300 2 200 1 100 0 0 0 1000 2000 3000 4000 5000 Speed (rpm)

Figure 3-12: Predicted Torque and Power responses for two-converters based BDFRM Operation (winding-1: 70% applied frequency, winding-2: 30% applied frequency).

15 1500 14 Max Torque (N-m) 1400 13 1300 12 Power (W) 1200 11 1100 10 1000 9 900 8 800 7 700 6 600 Power (W) Power Torque (N-m) Torque 5 500 4 400 3 300 2 200 1 100 0 0 0 1000 2000 3000 4000 5000 Speed (rpm)

Figure 3-13: Predicted Torque and Power responses for two converter BDFRM Operation (winding-1: 64% applied frequency, winding-2: 36% applied frequency). 49

Figure 3-14: Comparison of torque predicted from flux lookup table with time-stepped FEA simulation.

36% have been calculated & found out to result in the most effective two converter BDFRM operation according to the overall simulation data. Similarly, like synchronous operation, in all these three new case studies, the previously calculated torque and flux linkages data (from Tables

3-5, 3-6, 3-7) have been utilized for further calculation and prediction. These new sets of data of predicted torque and output power responses are presented in Tables 3-9, 3-10, 3-11. Using a constraint that neither winding terminal voltage may exceed the rated maximum voltage, these sets of data are used to predict the maximum torque capabilities for the three cases. The resulting torque and power capability plots are presented in Figs. 3-11, 3-12, 3-13. It is clear that allowing winding-

2 to operate at variable AC frequency significantly enhances the capability of the design.

The frequency ratio of 64%-36% used in the final case corresponds to the operating condition where the terminal voltages of both the windings are at the maximum operating limit

(142 V), with both windings operating with identical currents. This operating condition is demonstrated in Table 3-11. At this moment, the reader may recall from (73) in Chapter 2 that the

deduced frequency ratio for the two windings for two converter operation has been 65%-35%.

Therefore, the simulated and predicted response of the machine has been found out to be very close

to the initial theoretical benchmark. To justify the predicted torque response in the final case study,

the calculated data points are compared with re-simulated time-stepped FEA of these points. This

comparison plot is presented in Fig. 3-14.

3.5 Advantages of Two-Converters Based Operation

From the observation of torque and corresponding power responses of the two converter operation

case studies (Figs. 3-11, 3-12, 3-13), it can be implied that the two-converters based operation of

BDFRM has certain advantages over conventional synchronous operation (Fig. 3-10). The

predicted torque and power responses for all the case studies are plotted simultaneously in Figs.

3-15 and 3-16 respectively.

Fig. 3-15 demonstrates that all three of the two converter operation cases significantly extend the operating speed range of the machine in the constant torque region. In comparison with conventional synchronous BDFRM operation, the 64%-36% frequency ratio case extends the constant torque operating speed range by 57%. This obviously corresponds to a 57% increase in the power output for the same physical machine as demonstrated in Fig. 3-16. Therefore, the two- converters based operation can increase the power density of the machine. It will also reduce machine core loss because of the shared frequencies between the two windings. Conversely, considering the peak speed for the original design power, in Fig. 3-16, the speed at which the designed power can be obtained is extended to almost 2.3 times the original speed with a DC current in winding-2.

Figure 3-15: Predicted torque responses for all the case studies.

Figure 3-16: Predicted power responses for all the case studies.

3.6 Compensation for End Winding Leakage Inductance Effect

Since two windings are wound in the confined space of stator slots, it is obvious that the actual machine will have significantly long end winding connections. The phenomenon of ‘end winding leakage inductance’ (EWLI) and its possible effect on the machine voltage are also considered in this work. The magnetic field produced by the coils’ ends represents a leakage magnetic field and the corresponding inductance is defined as EWLI. Calculation of this inductance as accurate as possible is very important because it influences the ratio of self & mutual inductances and thereby the total winding voltage.

In this work, JMAG Express is used to approximate the EWLI values for the windings.

The calculated EWLI values with the corresponding initially simulated speed cases are presented in Table 3-12. The end winding leakage inductance values are included as circuit parameters prior to the simulations of the five different speed cases. Based on the output of these simulations, respective data tables of winding flux linkage and output torque have been calculated. The database is then used to predict the maximum torque capability speed curve with the terminal voltages of each winding operating close to the maximum limit 142 V (considering 250 V DC-link voltage converters), and with both windings operating at identical currents. These calculated operating points are presented in Table 3-13. The frequency sharing combination for the two windings is found to be 64.5%-35.5% in this case study. Speed, torque and output power at the desired operating points of the machine are plotted in Fig. 3-17.

Table 3-12: Calculated End Winding Leakage Inductance (EWLI) values with Corresponding Speeds and Applied Currents for Initially Run JMAG Cases.

1st winding 2nd winding Speed I1-peak I2-peak 1st winding 2nd winding f1 (Hz) f2 (Hz) total Leakage total Leakage (rpm) (A) (A) EWLI (mH) EWLI (mH) Reactance ( Ω) Reactance ( Ω)

3270 6 6 212.5 114.5 7.063 2.644 3.678 2.557

3800 5 5 247 133 8.231 2.652 4.516 2.702

4590 4 4 298.3 160.7 9.88 2.635 5.742 2.844

5940 3 3 386.1 207.9 12.64 2.605 7.596 2.908

8750 2 2 568.7 306.3 18.34 2.566 10.99 2.856

Table 3-13: Desired Operating Points of the Proposed BDFRM after EWLI Compensation.

Speed Max Torque I1-peak I2-peak V1-phase-peak V2-phase-peak Power f1 (Hz) f2 (Hz) (rpm) (N-m) (A) (A) (V) (V) (W)

600 6.381 6 6 27.18 27.11 38.70 21.30 401

1000 6.381 6 6 45.30 45.18 64.50 35.50 668

1500 6.381 6 6 67.96 67.78 96.75 53.25 1002

2000 6.381 6 6 90.61 90.37 129.00 71.00 1336

3130 6.381 6 6 141.80 141.43 201.89 111.12 2091

3655 4.573 5 5 141.98 141.46 235.75 129.75 1750

4445 2.901 4 4 141.88 140.42 286.70 157.80 1350

5800 1.682 3 3 141.93 139.91 374.10 205.90 1022

Power (W) Max Torque (N-m)

7 2100

6 1800

5 1500

4 1200

3 900 Power (W) Power Torque (N-m) Torque

2 600

1 300

0 0 0 1000 2000 3000 4000 5000 6000

Speed (rpm)

Figure 3-17: Desired operating points plot of the proposed drive after EWLI compensation.

3.7 Structural Analysis and Final Design for Machine Manufacturing Process

The initial design of the BDFRM has been modified on the basis of the analysis of previously simulated FEA electromagnetic and torque data in order to develop the proposed design. A cross-sectional view of the initially proposed machine is already presented in Fig. 3-4 where the rotor centre part of the machine is yet to be suggested. However, the implemented machine is to be operated at relatively high speed. Now the air flux barriers of the design in Fig.

3-4 naturally weaken the radially laminated rotor structure which leads to deformation of the structure due to centrifugal forces applied during high-speed operation. They can also increase manufacturing difficulties as the laminations may be less rigid than conventional ones. Therefore, static structural analysis of the proposed design has been carried out to investigate the design’s

sustainability. Based on this structural analysis data, minor but very important modifications are

introduced in the proposed design in Fig. 3-4. Thus the final manufacture version of the proposed

design is obtained. This version of the design can be sent to the manufacturing company to build

the machine stator and rotor laminations. Regarding structural analysis, ‘displacement’ and ‘global

stress’ contour plots data are presented for the final manufacture version design in Figs. 3-18 and

3-19 respectively. For both these figures, the actual deformation displacement is scaled by a factor

of 100 for better visibility, and the color map changes from purple (no deformation) to red

(maximum deformation).

In this work, M-19 Steel is the material chosen to construct the stator and rotor of the machine in

JMAG simulations. Fig. 3-18 shows the maximum displacement in a rotor segment found to be

only 0.0034mm. The maximum stress on the rotor is also well below the set safety margin of

minimum sustainable value for commercial steels. According to Fig. 3-19, maximum global stress

in the radial plane is 20.6779 MPa. In comparison, the acceptable global stress value for

commercial steels lies approximately between 100 and 230 GPa. To obtain these results in the final

manufacture version of the design, two important modifications are introduced to the proposed

simulation design in order to improve the stress response of the machine:

1) Fillets are introduced at both the corners between the two ducts of the rotor segments,

2) Narrow bridges or joints are placed at the middle points between two ducts of the same

rotor segment.

It is noticeable from Fig. 3-18 that the maximum displacement occurs near the edges and joints of the rotor ducts. The maximum stress also occurs near the joints between the rotor ducts and at the bridges.

Figure 3-18: Displacement contour plot from structural analysis of the final manufacture version of proposed BDFRM design (displacement is 100 times scaled).

Figure 3-19: Global Stress (in the radial plane) contour plot from structural analysis of the final manufacture version of proposed BDFRM design. 57

3.8 Calculation of Machine Inductance from Simulation

Mutual inductance is a very important parameter for BDFRM since its output torque is directly proportional to the mutual magnetic coupling between the two stator windings. A BDFRM unit with higher mutual inductance will yield higher torque output. Therefore, mutual inductances

Table 3-14: Inductance values (Case: 8-pole winding excited, 4-pole winding open)

V1-phase-peak (V) V2-phase-peak (V) I1-peak (A) L88 (H) L48 (H) (at I2 = 0) (at I2 = 0)

0.606 9.42 4.24 0.041 0.019

1.167 18.27 8.31 0.042 0.019

1.581 24.83 11.32 0.042 0.019

2.104 33.1 15.15 0.042 0.019

2.535 39.74 18.31 0.042 0.019

2.922 45.46 21.1 0.041 0.019

Table 3-15: Inductance values (Case: 4-pole winding excited, 8-pole winding open)

V1-phase-peak (V) V2-phase-peak (V) I2-peak (A) L84 (H) L44 (H) Coupling Ratio (at I1 = 0) (at I1 = 0)

0.696 4.89 21.75 0.019 0.083 0.32

1.269 9.08 39.95 0.019 0.084 0.32

1.571 11.23 49.4 0.019 0.083 0.32

1.848 13.16 57.81 0.019 0.083 0.32

2.124 15.09 65.93 0.01885 0.082 0.33

2.310 16.36 71.22 0.019 0.082 0.33

of the final manufacture version design have been calculated from some additional JMAG

simulation data. Self-inductance of both windings have also been calculated to compare with

mutual inductances.

To calculate the inductance values of the machine, at first several study cases have been simulated in JMAG Designer where one of the windings is kept open and the other winding is excited with an AC supply. In the process, respective data of induced voltage, applied current have been collected, and inductance values have been calculated by using the following basic formula:

(11) = ωλ = The calculated self and mutual inductance values are presented in Tables 3-14 & 3-15 along with their respective current and induced voltage values. It is noticeable from these two tables that the two sets of mutual inductance values (L48 and L84) have been found almost identical.

CHAPTER 4: PROTOTYPE MOTOR AND TEST FACILITY

This chapter provides details about the steps of the real machine building process such as lamination design and manufacturing, winding of the stator, and assembly of all the machine parts.

Next, the control strategy of the two-converters based operation of this motor drive system incorporating the assembled Brushless Doubly Fed Reluctance Machine (BDFRM) is discussed.

4.1 Stator and Rotor Laminations Design

The final design (in JMAG Designer) proposed in Chapter 3 must be delivered in an acceptable format for an external manufacturer company Proto Laminations Inc. [97]. Therefore, the stator and the rotor parts of the final design have been drawn using AutoCAD software. The

AutoCAD version of the stator is shown in Fig. 4-1. The stack length ( l) is 37 mm. If each lamination is 0.3556 mm (or 0.014 inches) thick, total (approximately) 104 stator laminations have to be attached and welded together to prepare the 37 mm stator stack.

The rotor stack assembly is similar to the stator as the stack length (l) is the same (37 mm).

However, the rotor is comprised of 6 identical small segments which are required to be placed on to the grooves along the circumference of a specially designed hexagon shaped shaft core. So total

104×6 = 624 rotor laminations are required to prepare the complete 37 mm rotor stack. The special design of the shaft core is presented in the next section. The air-gap (g) between rotor and stator is

0.8 mm. The cross-sectional view of a single rotor segment lamination is shown in Fig. 4-2. The

AutoCAD version of the complete rotor with 6 segments is shown in Fig. 4-3. These AutoCAD designs of stator and rotor laminations have been sent to the manufacturer company.

Figure 4-1: The cross-sectional view of a stator lamination drawn in AutoCAD.

Figure 4-2: The cross-sectional view of a single rotor segment drawn in AutoCAD. 61

Figure 4-3: The cross-sectional view of the complete rotor drawn in AutoCAD.

Based on the AutoCAD designs, stator and rotor laminations are laser cut and delivered by the manufacturer company. Close-up pictures of stator and rotor segment laminations are presented in Figs. 4-4 and 4-5 respectively.

Figure 4-4: The actual stack of stator laminations.

Figure 4-5: An actual single rotor segment lamination.

Figure 4-6: The cross-sectional view of the rotor core with stator-rotor drawn in AutoCAD.

4.2 Design of the Rotor Core

The final design of Chapter 3 prepared with JMAG Designer does not account for the implementation issue of holding the rotor segments with the shaft of the machine. Therefore, this issue is addressed at this point to ensure the appropriate assembly of the machine parts in the machine shop of the University of Calgary. Due to the absence of rotor segment joints in the final

BDFRM design, a specially designed hexagonal shaped rotor core is required to be built which

can hold all the individual rotor segments in its six grooves along its circumference. The design of

the rotor core with the stator-rotor drawn in AutoCAD is presented in Fig. 4-6.

4.3 Stator Windings Arrangement

After receiving the laminations, the stator is wound with two sets of three-phase single layer fully-pitched windings in an external electrical shop. Obviously, one of the windings is an 8- pole concentrated winding and the other one is a 4-pole concentrated winding. The windings specifications are as follows,

a) Turns per coil: 72,

b) Slot/pole/phase (8-pole winding): 1,

c) Slot/pole/phase (4-pole winding): 2,

d) Conductor size: AWG 20.

The windings arrangement sequence with respect to phase A, B, C connections is presented in

Table 4-1.

The top and side views of the wound stator core are presented in Figs. 4-7 and 4-8

respectively. One of the concerns regarding the construction of a prototype BDFRM is the end

winding formation with two sets of windings with different pole numbers as they must be wound

on the same stator slots. As can be seen in Figs. 4-7 and 4-8, the 4-pole winding is set at the bottom of the slots with the 8-pole winding closer to the rotor. There is no particular difficulty in the winding assembly as can be seen in Fig. 4-8. However, the end winding projection from the stator is probably longer than what may be achieved in mass production. It can be seen that the overall volume including the end windings is more than double the active lamination volume.

Table 4-1: Windings Arrangement on the BDFRM Stator Stator Slot 4-pole Winding 8-pole Winding Serial No. 1 A-Go C-Go 2 A-Go B-Return 3 C-Return A-Go 4 C-Return C-Return 5 B-Go B-Go 6 B-Go A-Return 7 A-Return C-Go 8 A-Return B-Return 9 C-Go A-Go 10 C-Go C-Return 11 B-Return B-Go 12 B-Return A-Return 13 A-Go C-Go 14 A-Go B-Return 15 C-Return A-Go 16 C-Return C-Return 17 B-Go B-Go 18 B-Go A-Return 19 A-Return C-Go 20 A-Return B-Return 21 C-Go A-Go 22 C-Go C-Return 23 B-Return B-Go 24 B-Return A-Return

Figure 4-7: Top view of the wound stator core.

Figure 4-8: Side view of the wound stator core with end winding connections and welded part clearly visible. 67

4.4 Assembly of the Machine

The next step of the machine building process is to meticulously assemble the different parts of the machine: the wound stator, rotor segments, rotor support, rotor holding discs, shaft, bearings, and casing. This step has been carried out in the machine shop of the University of

Calgary and the corresponding SolidWorks design is shown in Fig. 4-9. The additional parts like rotor support, shaft, rotor holding discs, and casing have been built in the machine shop. Fig. 4-10 shows the actual hexagonal shaped non-magnetic steel rotor support built in the machine shop with rotor segment laminations attached to its grooves. This figure clearly shows the large hole at the centre of the rotor support to accommodate the shaft, and also six smaller holes made in it for cooling purpose. The assembled BDFRM is then mounted on an existing steel base frame. Fig. 4-

11 shows the side view of the mounted BDFRM just before the final assembly. The rotor holding disc is clearly visible in this figure.

Figure 4-9: Different parts of machine assembly designed in SolidWorks software [Courtesy: Machine Shop, Schulich School of Engineering, University of Calgary]. 68

Magnetic steel rotor lamination

Non-magnetic steel Non-magnetic steel support rotor support Figure 4-10: Hexagonal shaped rotor core with rotor segment laminations attached.

Figure 4-11: Side view of the BDFRM assembly before the casing is closed. 69

Load PMSM Torque Transducer

Couplers BDFRM Connection box Thermocouple Steel Base

Figure 4-12: BDFRM coupled with the load PMSM mounted on the steel base.

On the steel base, the BDFRM is coupled with the existing 1 kW permanent magnet

synchronous machine (PMSM) which is used as the load machine. The coupled machines on the

steel base are shown in Fig. 4-12 where the torque transducer and the couplers are also visible.

4.5 Motor Drive Implementation

The proposed two power converter based closed-loop motor drive system incorporating

BDFRM has been implemented by using the PwrCon system from Denkinetic Pty Ltd. [98] which is a Digital Signal Processor (DSP) based system and uses a Texas Instruments TMS320F28335 microcontroller. The PwrCon system and TMS320F28335 microcontroller are programmed in

C++ language. TMS320F28335 is actually a 32-bit floating point microcontroller with operating

PC -2 PC -1

Power Analyzer

Variac Converter -3

DSP -2 DSP -1

Converter -2 Converter-1

Load PMSM BDFRM Figure 4-13: Implemented BDFRM drive setup in the lab.

frequency up to150 MHz. It is equipped with 6-channel Direct Memory Access (DMA) Controller

(for ADC, ePWM etc.), maximum 18 PWM outputs, up to 88 shared General-Purpose Input/output

(GPIO) pins, and 12-bit 16-channel ADC module. Besides, it has 256K×16 Flash and 34K×16

SARAM on-chip memory [99].

The complete implemented motor drive setup in the lab is pictured in Fig. 4-13. In this motor drive, Space Vector Pulse Width Modulation (SVPWM) control and signal interfacing are carried out by the PwrCon DSP system whereas the stator windings of the BDFRM are fed from

Figure 4-14: Schematic diagram of the implemented closed-loop motor drive.

two separate 750 V (DC max), 20 KW, IGBT based newer version Semikron Semiteach three-

phase rectifier-inverter systems with 4400 F capacitance DC link. The microcontroller receives actual motor (BDFRM) speed signal and line current inputs from an encoder and LEM current sensors respectively via PwrCon system peripheral boards. The PwrCon system also gives the provision to display signal waveforms in oscilloscope via its D/A channels. As mentioned earlier, the existing 1 kW PMSM is used as the load machine in this motor drive; the load current (and consequently the load torque) in PMSM is controlled by a separate set of PwrCon DSP system, power converter, encoder, torque transducer and LEM current sensors. The two PwrCon systems for BDFRM and load machines are identical. However, the power converter used to supply load torque is a 350 V (DC max)), 10 KW, IGBT based older version Semikron three-phase rectifier- inverter system with 3000 F capacitance DC link.

In this closed-loop BDFRM drive with PMSM load system, 3 power converters and 2

PwrCon systems are operated to simultaneously control speed (BDFRM) and torque (PMSM). In

summary, PC-1 interfaces with DSP-1, which controls both converters connected to the BDFRM

test machine; PC-2 interfaces with DSP-2, which controls the converter connected to the load

machine (PMSM). PC-2 is used to set the load torque conditions; PC-1 controls the speed and

operating mode of the BDFRM.

The schematic diagram of the closed-loop motor drive is shown in Fig. 4-14. In this figure,

‘E’ and ‘T’ denote optical incremental encoder and torque transducer respectively which are both mounted on the coupled rotors of the machines. The two stator windings of the BDFRM are supplied from power converters 1 & 2 via variac or autotransformer. The generated emf at the load

PMSM terminals is fed to 3rd power converter whose DC link is interconnected with those ones of the other two converters. Therefore, in this setup, essentially the 1st and 2nd power converters are used as three-phase rectifier-inverters, whereas the 3rd power converter is used only as a three- phase controlled rectifier. As briefly mentioned earlier, the TMS320F28335 microcontroller receives the real-time speed and torque signals from ‘E’ & ‘T’ respectively, and current signals from LEM current sensors. Two control loops (speed and torque) are employed and eventually, the microcontrollers generate 3 different sets of PWM gating signals for the 3 power converters to control both speed and torque simultaneously.

4.6 Control Strategy of Two-Converters Based Operation

Field-oriented control (FOC) technique [100] is applied in two loops to operate this

BDFRM drive. The structural block diagram of the FOC scheme is shown in Fig. 4-15. The diagram has two almost identical halves; the top half is showing the control blocks for the 8-pole winding and the bottom half is associated with the 4-pole winding.

The three-phase currents for both windings iabc8 and iabc4 are measured by the two sets of

current sensors, and these measurements are fed to the respective Clarke transformation module. 73

Figure 4-15: Block diagram of the control strategy of the BDFRM drive.

The outputs of these projections are the stationary two-axes current components iαβ 8 and iαβ 4. These

current components are the inputs for the Park transformation modules which yield iqd8 and iqd4 currents in the respective d-q rotating reference frames. These d-q axes actual current components are subsequently compared with the corresponding flux component references ( and ) and ∗ ∗ torque component references ( and ). For the case of 8-pole winding, torque component ∗ ∗ reference is the output of the speed PI controller. The current errors are fed as the inputs to the ∗ four current PI controllers. The outputs of the current controllers are vqd8 and vqd4 which are applied to the inverse Park transformation modules. The outputs of these Park transformation modules are vαβ 8 and vαβ 4 which are the components of the stator vector voltage in the ( α, β) stationary orthogonal reference frame. These are the inputs for the SVPWM modules. The SVPWM modules generate the gating signals to drive the two power converters which supply power to the two windings of the BDFRM.

It is noteworthy that the electrical angle calculations ( θ8e and θ4e ) are essential for all the

Park transformations which is shown at the centre of the diagram. These electrical angles can be

calculated from the real-time mechanical angle and speed ( θm and ωm) variables which are obtained from the encoder. The calculation method will vary slightly depending on the control mode applied in the operation. This will be further discussed in detail in Chapter 5.

It is also clear from (1) in Chapter 2 that the BDFRM operation with two power converters provides an infinite range of supply frequency combinations for any given speed. If the second winding is supplied at DC, all power is supplied from winding-1 whereas winding-2 is purely for field control; if both the windings have positive frequency, both converters contribute power; if the windings have a combination of positive and negative frequency, power can be circulated between the converters. This type of two-converters based operation of the BDFRM has not been

investigated by other researchers so far. Therefore, the work to investigate how well the machine functions in this supply configuration is entirely new. This specific part of the research work is an original contribution and this work should be able to result in an understanding of how well this type of motor will work relative to other types of machine.

CHAPTER 5: EXPERIMENTAL TESTING

This chapter presents the experimental test results of the BDFRM drive. Before testing the drive in different speed regions, self and mutual inductances of the two windings have been measured by running the motor in open circuit setup. Then the BDFRM drive is tested in sub- synchronous, synchronous and super-synchronous speed levels with different inputs of load torque. These experimental tests have been carried out in three different operating modes: a) synchronous BDFRM operation, b) conventional BDFRM operation, c) two variable winding frequencies from two AC power-converters based operation. The corresponding test results have been discussed accordingly.

5.1 Measurement of Actual Machine Inductances

The self and mutual inductances of the actual machine (BDFRM) have been measured even before the implementation of the BDFRM drive setup. This test setup is shown in Fig. 5-1. For inductance measurement, open circuit tests have been carried out on the two windings of the

BDFRM. In this regard, one of the winding is excited from a variac and the other winding is kept open. The same test is repeated with the windings connections reversed. For both cases, input current and both windings voltages are measured using an oscilloscope and a multi-meter. From these collected data, corresponding self-inductances ( L88 , L 44 ) and mutual inductances ( L48 , L 84 ) of the real machine are calculated.

The first open circuit test (excited 8-pole winding with open 4-pole winding) data and corresponding measured inductance values are mentioned in Table 5-1. In the same table, measured inductance values from the experiment are also compared with respective values from same condition FEA simulation. Similarly, for the second open circuit test (excited 4-pole winding

with open 8-pole winding), measured and simulated inductance values are obtained and presented

in Table 5-2. All the voltages mentioned in these two tables are phase-to-neutral quantities.

It can be observed from Tables 5-1 and 5-2 that there is less than 10% difference between the simulated and measured self-inductance values. But mutual inductance values obtained from tests are larger than those from simulations. This increase in mutual inductance may be attributed to some undesired direct coupling at 60 Hz from an unknown source which is not influenced by rotor modulation. To investigate this issue, the machine can be run as a load at half rated speed and the induced voltages can be examined. However, the mutual inductance values in the tables are much smaller compared to the self-inductance values. The low comparative mutual inductance also provides some explanation about the reduction of output torque in the following test results.

Variac

Oscilloscope Multimeter BDFRM

Load -box

Figure 5-1: Test setup to measure actual BDFRM inductances.

Table 5-1: Calculated test and simulation inductances with 4-pole winding open circuit

Test Data Simulation Data (V) (A) L88 (H) (V) L48 (H) (A) L88 (H) (V) L48 (H) 9.42 0.58 0.043 6.78 0.031 0.61 0.041 4.24 0.019

18.27 1.2 0.04 14.15 0.031 1.17 0.042 8.31 0.019

24.83 1.67 0.039 19.52 0.031 1.58 0.042 11.32 0.019

33.1 2.23 0.039 23.6 0.028 2.1 0.042 15.15 0.019

39.74 2.69 0.039 28.87 0.029 2.54 0.042 18.31 0.019

45.46 3.11 0.039 33.53 0.029 2.92 0.041 21.1 0.019

Table 5-2: Calculated test and simulation inductances with 8-pole winding open circuit

Test Data Simulation Data (V) (A) L44 (H) (V) L84 (H) (A) L44 (H) (V) L84 (H) 21.75 0.68 0.085 6.98 0.027 0.7 0.083 4.89 0.019

39.95 1.26 0.084 12.91 0.027 1.27 0.084 9.08 0.019

49.4 1.58 0.083 16.31 0.028 1.57 0.083 11.23 0.019

57.81 1.85 0.083 19.15 0.027 1.85 0.083 13.16 0.019

65.93 2.12 0.082 21.93 0.027 2.12 0.082 15.09 0.019

71.22 2.38 0.079 23.49 0.026 2.31 0.082 16.36 0.019

As part of the testing procedure, the BDFRM is also run in a short circuit connection setup.

In this regard, one of the winding is excited from the variac while the other winding is connected

to the balanced 3-phase load-box shown in Fig. 5-1. The motor has been observed to run at a low

speed with low excitation voltage. In this case, the operated BDFRM is analogous to a wound rotor

induction motor.

5.2 Operating Mode-1: Synchronous BDFRM Operation

In all the operating modes of BDFRM tests, the two stator windings are connected to two separate power converters. In case of Operating Mode-1, one winding is supplied with a fixed DC current and the other winding is supplied with variable frequency to adjust the speed. To enable the synchronous operation of this BDFRM in Operating Mode-1, the total command frequency is applied on the 8-pole winding and only DC command current ( ) is applied on the d-axis of the ∗ 4-pole winding. Thus, in this operation, the 4-pole winding acts as the field circuit of a

conventional synchronous motor, whereas 8-pole winding is analogous to the armature winding.

The second converter acts as a DC supply since it supplies only DC current to the 4-pole winding.

Let us recall the “Operation Mode Control” block of Fig. 4-15 in Chapter 4 to review the control

strategy of this synchronous BDFRM operation. The associated field oriented control (FOC)

technique has already been discussed in Chapter 4 which is common for all three operating modes.

The only difference among the operating modes is the way how the electrical angles ( θ8e and θ4e ) are calculated in “Operation Mode Control” block from the encoder output variables ( ωm and θm).

For Operating Mode-1, the electrical angle contribution from the 8-pole winding ( θ8e) and the total electrical angle ( θe) can be calculated from the following relations,

ωe = pr.ωm (1)

ω8e = ωe (2) 80

θ8e = ∫ω8e dt (3)

θe = pr.θm (4)

Finally, the electrical angle contribution from the 4-pole winding ( θ4e) is calculated from the other

two electrical angles in the following manner,

θ4e = θe - θ8e (5)

5.2.1 Synchronous Operation with Variable Field Currents

In this test, the BDFRM drive is operated as a synchronous machine at a fixed speed of 600

rpm with 60 Hz total frequency. The objective of this test is to allow output torque evaluation at

defined field currents and for comparison with simulation data from Chapter 3. The BDFRM is

operated with three different values of (4-pole) control winding DC currents: 3.7 A, 4.5 A, 5.4 A.

Figure 5-2: Power Analyzer screenshot at 600 rpm synchronous speed with 3.7 A field current (3 N-m).

Figure 5-3: Power Analyzer screenshot at 600 rpm synchronous speed with 4.5 A field current (5 N-m).

Figure 5-4: Power Analyzer screenshot at 600 rpm synchronous speed with 5.4 A field current (5 N-m). 82

Figure 5-5: Experimental load points (synchronous operation) of the actual BDFRM on top of the contour plot of previously simulated torque data of the proposed BDFRM design.

The 8-pole winding is operated using closed loop PI current control to maintain a steady state speed of 600 rpm as the load torque is adjusted from the load PMSM. Screenshots from the

Power Analyzer showing machine three-phase voltage, current and power at three different field currents and their respective highest load torque are provided in Figs. 5-2, 5-3, and 5-4. Fig. 5-2 clearly shows that the motor does not exert enough torque and generate enough power like the other two cases since the field current (3.7A) has not been sufficient enough to drive the desired

load torque. The recorded output torque at each operating point is plotted on top of the contour map of the simulated torque data in Fig. 5-5. The combined contour and point torque-currents map shows good agreement between experimental test data and numerical simulation data from Chapter

3 (Fig. 3-7). The case with 4.5 A field current is the most efficient since it yields almost the same amount of output power as in the case with the highest field current (5.4 A).

5.2.2 Synchronous Operation at Variable Speed Levels

The synchronous operation of the BDFRM described in the previous section is also performed at different higher speed levels with a fixed field current to yield optimum torque output.

The objective of this test is to observe the machine responses with synchronous speed operation at various speed levels. The BDFRM torque and output power responses have been plotted in Fig. 5-

6 which fairly resembles the simulates response of the proposed design in Chapter 3 (Fig. 3-10).

Torque & Power Responses of Synchronous BDFRM Operation 6 600

5 500

4 400

3 300 Torque (N-m) Torque

2 Torque (N-m) 200 (W) Power Output

Output Power (W) 1 100

0 0 0 300 600 900 1200 1500 Speed (rpm)

Figure 5-6: Torque and output power responses in synchronous speed operation (Mode-1).

5.3 Operating Mode-2: Conventional BDFRM Operation

In this operating mode, frequency sharing operation of the BDFRM can be investigated by applying two frequencies in the two windings in a specific way. In case of Operating Mode-2, one winding is supplied with a fixed AC frequency and the other winding is supplied with variable frequency to adjust the speed. To enable the conventional operation of this BDFRM in Operating

Mode-2, the 8-pole winding is kept at a fixed frequency and the 4-pole winding frequency is varied to adjust the actual speed of the motor in accordance with the command speed. As described in

Chapter 4, the two PwrCon DSP systems of the BDFRM drive are controlled and monitored using

Code Composer Studio (CCS). The command speed contribution from the 8-pole winding ( ) ∗ is set as a constant from the CCS panel. Electrical angle θ8e is calculated in the following manner,

θ8e = ∫ dt (6) ∗ The electrical angle contribution from the 4-pole winding ( θ4e) can be calculated from the

following relations,

θe = ∫pr.ωm dt (7)

θ4e = θe - θ8e (8)

In this operation mode, the BDFRM drive has been run with load in a wide speed range and two sets of data are recorded. In the first set of tests, the 8-pole winding supply frequency f1 is kept fixed at 60 Hz whereas the 4-pole winding frequency f2 is varied to operate the motor at different speed levels of 400, 500, 600, 700 and 800 rpm. For example, when 800 rpm is asked as the command speed ( ) for the drive, θ4e is adjusted in the manner such that f2 reaches to the ∗ value of 20 Hz which is added on to the value to the fixed f1 (60 Hz) to yield the total required frequency of 80 Hz. Similarly, when the command speed is 400 rpm, f2 reaches to the value of -20

Hz which then opposes the fixed f1 (60 Hz) to yield the total required frequency of 40 Hz. Thus,

the motor can be run in both super-synchronous and sub-synchronous regions using this frequency

sharing control method. For the case of 600 rpm command speed, mathematically f2 becomes zero which allows only DC current in the 4-pole winding and enables the synchronous operation.

In the second set of tests, the 8-pole winding supply frequency f1 is kept constant at 100

Hz whereas the 2nd winding frequency f2 is varied to operate at speed levels of 800, 900, 1000,

1100 and 1200 rpm. Sample screenshots from the Power Analyzer showing machine three-phase

voltage, current and power at different speed points and 4 N-m load torque are shown in the Figs.

from 5-7 to 5-15.

In each case, the frequency contributions from the two stator windings ( f1 and f2) can be

observed from the right-hand side columns of the screenshots under the label names ‘Freq(I1)’ and

Figure 5-7: Power Analyzer Screenshot at 400 rpm speed and 4 N-m load torque (f 1 = 60 Hz, f 2 = -20 Hz). 86

Figure 5-8: Power Analyzer Screenshot at 500 rpm speed and 4 N-m load torque (f 1 = 60Hz, f 2 = -10Hz).

Figure 5-9: Power Analyzer Screenshot at 600 rpm speed and 4 N-m load torque (f 1 = 60Hz, f 2 = 0Hz). 87

Figure 5-10: Power Analyzer Screenshot at 700 rpm speed and 4 N-m load torque (f 1 = 60Hz, f 2 = 10Hz).

Figure 5-11: Power Analyzer Screenshot at 800 rpm speed and 4 N-m load torque (f 1 = 60Hz, f 2 = 20Hz). 88

Figure 5-12: Power Analyzer Screenshot at 900 rpm speed and 4 N-m load torque (f 1 = 100Hz, f 2 = -10Hz).

Figure 5-13: Power Analyzer Screenshot at 1000 rpm speed and 4 N-m load torque (f 1 = 100Hz, f 2 = 0Hz). 89

Figure 5-14: Power Analyzer Screenshot at 1100 rpm speed and 4 N-m load torque (f 1 = 100Hz, f 2 = 10Hz).

Figure 5-15: Power Analyzer Screenshot at 1200 rpm speed and 4 N-m load torque (f 1 = 100Hz, f 2 = 20Hz).

Torque & Power Responses: Synchronous Speed 600 rpm 500

400 4

300 3

200 Torque (N-m) Torque 2

Torque (N-m) (W) Power Output

1 100 Output Power (W)

0 0 400 500 600 700 800 Speed (rpm)

Figure 5-16: Torque and output power responses of the BDFRM drive (operating mode-2): 600 rpm speed is considered as the synchronous speed (f 1 = 60 Hz; f 2 is variable).

Torque & Power Responses: Synchronous Speed 1000 rpm 700

5 600

4 500

400 3

300 2 Torque (N-m) Torque (N-m) Torque

200 (W) Power Output Output Power (W) 1 100

0 0 800 900 1000 1100 1200 Speed (rpm) Figure 5-17: Torque and output power responses of the BDFRM drive (operating mode-2): 1000 rpm speed is considered as the synchronous speed (f1 = 100 Hz; f 2 is variable). 91

‘Freq(I3)’ respectively. For example, in Fig. 5-7, f1 and f2 are 60Hz and 20Hz respectively. But they oppose each other and therefore the net frequency driving the motor is 40 Hz which yields

400 rpm speed for this BDFRM (sub-synchronous operation). On the contrary, in Fig. 5-11, the two applied frequencies are adding up to drive the motor at 800 rpm speed with 80 Hz total applied frequency (super-synchronous operation). Similar traits can be observed in the other Power

Analyzer screenshots. The only exceptional cases are shown in Figs. 5-9 and 5-13 where the

BDFRM is run in synchronous mode. The combined torque and output power responses of the two sets of experiments are plotted in Figs. 5-16 and 5-17.

Figs. 5-16 and 5-17 imply that the implemented BDFRM drive exhibits similar satisfactory torque responses when it is run at 600 or 1000 rpm as the synchronous speed with constant first winding applied frequency and variable second winding applied frequency. These figures also demonstrate better torque response of this mode compared to operating mode-1 since the torque outputs at different speed levels remain close to the base output at 600 or 1000 rpm.

In an electric vehicle with split battery configuration, this operating mode can add a very interesting degree of freedom. Applying a negative frequency on a winding allows power circulation from one winding to the other which can be used to charge up a depleted battery unit.

5.4 Operating Mode-3: Frequency Sharing Operation with Two Variable Frequencies

In case of Operating Mode-3, both windings are supplied with variable frequencies from the two converters. The frequency sharing ratio for the two windings can be set in the code by defining a control variable x. The electrical angle contribution from the 8-pole winding ( θ8e) and

the total electrical angle ( θe) can be calculated from the following relations,

ωe = pr.ωm (9)

ω8e = x. ωe (10)

θ8e = ∫ω8e dt (11)

θe = pr.θm (12)

In (10), x defines the ratio of the 8-pole winding frequency to the total applied frequency of the

BDFRM drive. Let’s recall from Chapter 2 that the numerical value of x would be 0.65 or 65% for the ideal case of two-converters based frequency sharing operation. The electrical angle contribution from the 4-pole winding ( θ4e) is calculated from the other two electrical angles in the following manner,

θ4e = θe - θ8e (13)

In this operating mode, the BDFRM drive has been run with 5 N-m full load at speed levels

600, 700, 800, 900, 1000 and 1100 rpm. Frequency ratio 70% - 30% is applied in the two BDFRM windings for optimum real-time operation. The sample screenshots from the Power Analyzer capturing BDFRM three-phase voltage, current, and power at each speed are shown in the Figs. from 5-18 to 5-23. The frequency contributions from the two stator windings ( f1 and f2) are recorded in the right-hand side columns of the screenshots under the label names ‘Freq(I1)’ and

‘Freq(I3)’ respectively.

The corresponding BDFRM drive torque and output power responses in frequency sharing operation are plotted in Fig. 5-24. Compared to the other operating modes, this mode shows the best torque response since the output torque remains the same at varying speed levels. When both battery units are fully charged in a split battery configured electric vehicle, both windings can contribute to yield more torque by utilizing this operating mode.

Figure 5-18: Power Analyzer screenshot of the BDFRM frequency sharing test (operating mode-3) at 600 rpm speed and 5 N-m load torque (f 1 = 42Hz, f 2 = 18Hz).

Figure 5-19: Power Analyzer screenshot of the BDFRM frequency sharing test (operating mode-3) at 700 rpm speed and 5 N-m load torque (f 1 = 49Hz, f 2 = 21Hz).

Figure 5-20: Power Analyzer screenshot of the BDFRM frequency sharing test (operating mode-3) at 800 rpm speed and 5 N-m load torque (f 1 = 56Hz, f 2 = 24Hz).

Figure 5-21: Power Analyzer screenshot of the BDFRM frequency sharing test (operating mode-3) at 900 rpm speed and 5 N-m load torque (f 1 = 63Hz, f 2 = 27Hz).

Figure 5-22: Power Analyzer screenshot of the BDFRM frequency sharing test (operating mode-3) at 1000 rpm speed and 5 N-m load torque (f 1 = 70Hz, f 2 = 30Hz).

Figure 5-23: Power Analyzer screenshot of the BDFRM frequency sharing test (operating mode-3) at 1100 rpm speed and 5 N-m load torque (f 1 = 77Hz, f 2 = 33Hz).

Torque & Power Responses: Frequency Sharing Operation 600

5 500

4 400

3 300

Torque (N-m) Torque 2

200 (W) Power Output

Torque (N-m) 1 100 Output Power (W)

0 0 600 700 800 900 1000 1100 Speed (rpm)

Figure 5-24: Torque and output power responses of the BDFRM drive in frequency sharing operation (operating mode-3).

5.5 Discussion

The BDFRM drive has been tested at different speed and load points by employing three different operating modes. In each operating mode, two power-converters based operation of the built BDFRM has been demonstrated. In case of synchronous BDFRM operation with variable field currents (Mode-1), the torque-current responses from the test results fairly match the simulated response from Chapter 3.

In the operating modes 2 and 3, frequency sharing operation is investigated. It can be deduced from the comparison of Fig. 5-6 and Figs. 5-16, 5-17, 5-24 that the frequency sharing operation enables the BDFRM to yield smoother torque response and higher power outputs at sub- synchronous and super-synchronous speed regions. Thus, frequency sharing operation increases the power density of the BDFRM drive in comparison with synchronous BDFRM operation.

Operating mode-3 demonstrates the best torque response. However, operating mode-2 can provide

an advantageous way of charging a depleted battery unit in a split battery configured electric

vehicle.

However, hereby it is noteworthy that certain simulated load points like 6 N-m and very high-speed points have not been possible to reach due to the electrical constraints of the built machine. Resistance values of the 8-pole and 4-pole windings used in the initial simulations are

1.22 and 2.44 respectively. These values have been re-evaluated later based on the

optimization of the initially proposed design. However, the measured resistances of the built

machine have been found out to be 2.8 and 6 respectively. The additional resistance of the

two windings have resulted in higher copper losses, and more importantly, they have also left less

‘space’ for the winding voltages (back EMF) to be bound within the rated maximum boundary.

This means that the back EMFs of the two windings in real-time experiments exceed the maximum

limit with less command speed or less applied load torque operating points than those cases of

numerical simulations presented in Chapter 3. To mitigate this practical issue in a future possible

work, careful considerations must be made regarding the choice of the windings conductor size

and the electrical quality of the chosen wire.

The smaller mutual inductance compared to the large self-inductance values also has its

influence on torque output. The low comparative mutual inductance leads to weaker magnetic

coupling and therefore lower output torque. Smaller air-gap can be realized in a commercial

machine to increase mutual inductance and thereby improve mutual coupling. This will also

increase the machine torque density.

CHAPTER 6: CONCLUSION

6.1 Summary

The original contribution of this thesis is the complete evaluation of a ducted rotor BDFRM design process through magnetic analysis, corresponding prototype machine building, and two- converters based operation of the prototype BDFRM drive in three different operating modes.

This research work explores the practical design factors and analysis of the Brushless

Doubly Fed Reluctance Machine (BDFRM) with the aim of implementation of a commercially feasible prototype with acceptable performance. Basic operation theory of the ducted rotor

BDFRM is discussed, and a simple control approach to maximize the capability of a given design is presented. A novel two-converters based operation theory with frequency sharing between the two windings is introduced, and corresponding FEA simulations are analyzed. Based on the FEA analysis and static structural analysis, the final design of the machine is presented for investigation.

Subsequently, the prototype BDFRM is built and assembled based on the final design. The

BDFRM drive system is then implemented using a Texas Instruments DSP. The BDFRM design and the actual motor drive implementation steps are discussed in detail.

The implemented BDFRM drive is operated with two power converters and tested at different speed and load conditions applying field-oriented control approach. The control algorithm with three different operating modes has been explained in detail in this work. Different operating points are investigated in sub-synchronous, synchronous and super-synchronous speed regions. Predicted simulation torque data is matched with actual machine data when the motor is run in the synchronous mode with variable field currents (operating mode-1). Frequency sharing two-converters based operations have been investigated in two different operating modes. In operating mode-2, the BDFRM drive exhibits satisfactory torque responses when it is run at 600

rpm or 1000 rpm as the synchronous speed. In these cases, the first winding applied frequency is kept constant (60 Hz or 100 Hz) and the second winding applied frequency is varied. In operating mode-3, it has been possible to successfully split the total applied frequency between the two stator windings with any specific ratio. Besides, this mode of frequency sharing operation yields constant torque response over a variable speed range.

6.2 Possible Future Work

Due to practical limitations, the physical and electrical characteristics of the windings of the built machine could not be emulated from the proposed design. The windings resistance values of the actual machine have been found out to be significantly larger than the proposed design values. This leads to additional copper loss and results in lower efficiency. In this work, the focus was not given to observe and study the efficiency pattern of the drive in wide speed range. This aspect of the drive performance can be covered in a possible future work to find ways to improve the efficiency of the operation.

Additionally, a sophisticated cooling system can be added to the BDFRM drive to ensure safer operation, particularly at higher load operating points. Another possible way to improve the efficiency is to increase the output torque and power by reducing the air-gap length of the machine.

Thus, the power density of the machine will be improved too. However, one must also consider the issues of overall cost and implementation feasibility regarding the precise calibration and correction process for maintaining a very small air-gap length.

Current waveforms from test results show some ripple of higher frequency. This can come from a higher flux density harmonic of significant magnitude. In a future work, Fourier analysis can be used to identify the harmonics order. Based on the analysis, short-pitched 4-pole winding

(instead of fully-pitched) can be considered during machine building to reduce the current ripple. 100

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