DESIGN AND CONTROL OF A HIGH-EFFICIENCY DOUBLY-FED BRUSHLESS MACHINE FOR POWER GENERATION APPLICATIONS DISSERTATION

Transcription

1 DESIGN AND CONTROL OF A HIGH-EFFICIENCY DOUBLY-FED BRUSHLESS MACHINE FOR POWER GENERATION APPLICATIONS DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Bo Guan, M.S. Graduate Program in Electrical and Computer Engineering The Ohio State University 014 Dissertation Committee: Dr. Longya Xu, Advisor Dr. Jin Wang Dr. Mahesh Illindala

2 Copyright by Bo Guan 014

3 Abstract Due to its similar terminal characteristics like a wound-rotor Doubly-Fed Induction Machine (DFIM) and rugged rotor structure without brushes and slip rings, the Doubly-Fed Brushless Machine (DFBM) has attracted much attention for years, especially in the applications of variable-speed constant-frequency power generation and in adjustable speed drive system. However, the theory and modeling of DFBM still have not been sufficiently developed. Suffering from inherent deficiencies such as low mutual coupling between two windings, difficulties in rotor structure design and non-optimized control, the DFBM made an impression of low torque density and lower energy efficiency. The research objectives of this dissertation are to: (1) give a systematic and quantitative analysis of the mechanism, modeling and control of DFBM; and () design and build a highefficiency DFBM based doubly-fed power generation system. Firstly, a detailed nonlinear analysis of DFBM by using the Finite Element Analysis (FEA) method is given. The mechanism of electromechanical energy conversion of the DFBM is investigated through the analysis of internal magnetic flux distribution, and of terminal characteristics of winding flux linkage and induced speed voltage (Back-EMF). The proposed harmonic decomposition method is utilized for the quantitative analysis of the asymmetric, nonsinusoidal and pulsating air-gap flux density, and assists in the evaluation of the modulation capability of the DFBM. Secondly, the mathematic models of DFBM in both dynamic and steady state conditions are systematically examined. The results of the study confirm the previous findings by the FEA and contribute to a quantitative analysis of the mathematic model of DFBM. The deduced dynamic ii

4 and steady state equivalent circuits suggest that the DFBM has the same form and similar expression of mathematical model as those of a conventional DFIM. After the modeling of DFBM, the basic concept of field orientation control of torque and flux (and decouple control of active and reactive power) is introduced and analyzed in the steady state conditions. Then, the dynamic responses of the field orientation are discussed with the highlights of transient characteristics and expression of the flux linkage and torque. The implementation of the field orientation is also investigated. Finally, the latest investigation of optimal design and advanced control results of DFBM are presented. The challenges of designing a high-efficiency DFBM system are discussed in detail with the identified solutions of the optimal design and control. Using design principles assisted by FEA, an original design of a 00kW radially-laminated reluctance DFBM system is achieved, capable of,000 N.m in the speed range of 400-1,00 rpm, with a frame size comparable to that of a brush-type DFIM. The designed machine is built and tested in both a steady state and in dynamic conditions, and the experimental results are suitably agreed with the design objectives. The most successful results include the DFBM power delivery with more than 5% overload capability and energy efficiency higher than 90%, occupying 75% of the designed torque-speed regime. The theoretical and experimental results represent breakthroughs in doubly-fed brushless technology. The feasibility of DFBM technology for practical application is fully established. iii

5 Dedicated to my family and people that I love. iv

6 Acknowledgments I would like to express deepest gratitude to my advisor, Dr. Longya Xu, who has been consistently providing academic guidance, funding support, opportunities and encouragement throughout my graduate study. His profound knowledge, creative way of thinking and perspective of future have inspired me to explore in the academic world, keep thinking and put thoughts into practice. His guidance not only helps me in the graduate study but also will deeply and positively influence me a whole life. I also want to thank Dr. Jin Wang, Dr. Donald Kasten, Dr. Steven Sebo and Dr. Mahesh S. Illinda for helping me understand the essence of the power electronics and power systems. I would like to give my thanks to Dr. Vadim Utkin for his education of the control theory. Additionally, I would like to thank Dr. Hao Huang and Dr. Abbas Mohamed from GE Aviation for providing attractive research projects, financial support, and also the opportunity for me to gain high-level industry experience in USA. My special thanks go to Dr. Yifan Zhao, Dr. Li Zhen and Dr. Xingyi Xu from Kinway Tech. Inc. and Dr. Yi Ruan from Shanghai University for initially bringing me into the area of power electronics and motor drives. I would like to thank my senior fellows Dr. Jiangang Hu, Dr. Yuan Zhang, Dr. Wenzhe Lu and Dr. Song Chi for their help to my study and life in Columbus. I also want to thank my junior group members Dr. Kaichien Tsai and Dr. Zhendong Zhang for the team works on many fantastic projects, and spending days and nights together. I have to give thanks to Yazan Alsmadi for his contribution to my work especially when I was out of the campus. I also want to thanks my other v

7 junior graduate students Dr. Ernesto Inoa, Mr. Yu Liu, Mr. Haiwei Cai, Mr. Dakai Hu, Dr. Ke Zhou, Mr. Cong Li, Mr. Feng Guo and Mr. Mark Scott for their friendship and support. I have to give special thanks to Hui Li and Zifei Dai for their friendship and support. Finally, I would like to thank my parents Yunya Guan and Weirong Guan, and my girl friend Anqi Zhang, for their endless love and consistent efforts to support me. I am truly grateful for having such a happy and supportive family. vi

8 Vita July 003 B.S. Electrical Engineering, Shanghai University, Shanghai, China October 004 September 006..Research and Development Engineer, Kinway Technologies, Inc., Shanghai, China March 006 M.S. Electrical Engineering, Shanghai University, Shanghai, China March 007 February Project Research Associate, GE Aviation, Dayton, Ohio September 006 present Graduate Research Associate, The Ohio State University, Columbus, Ohio Publications B. Guan and L. Xu, A Novel Adaptive Algorithm for Rotor-Flux and Slip Estimation of Field- Oriented Induction Machine Drives, in IEEE Energy Conversion Congress and Exposition, (ECCE) 009, pp.1547,155, Sept. 0-4, 009. B. Guan, Y. Zhao and Y. Ruan, Torque Ripple Minimization in Interior PM Machines using FEM and Multiple Reference Frames, in 1 st IEEE Conference on Industrial Electronics and Application, Singapore, May 4-6, 006. H. Cai, B. Guan and L. Xu, Low Cost PM Assisted Synchronous Reluctance Machine for Electrical Vehicles, in IEEE Transactions on Industry Electronics, vol.61, no.10, pp , Oct vii

9 L. Xu, E. Inoa., Y. Liu and B. Guan, A New High-Frequency Injection Method for Sensorless Control of Doubly-Fed Induction Machines, in IEEE Transactions on Industry Applications, vol.48, no.5, pp , Sept. - Oct. 01 L. Xu, B. Guan and J. Hu, A Robust Sensorless Control Algorithm for Induction Generator Operating in Deep Flux Weakening Region, in Conf. Rec. of IEEE IAS Annual Meeting 008, pp.1-8, Oct. 5-9, 008. L. Xu, B. Guan, H. Liu, L. Gao and K. Tsai, Design and Control of a High-efficiency Doubly- Fed Brushless Machine for Wind Power Generator Application, in IEEE Energy Conversion Congress and Exposition (ECCE) 010, pp , Sept. 1-16, 010. H. Cai, B. Guan and L. Xu, Optimal Design of Synchronous Reluctance Machine a Feasible Solution to Eliminating Rare Earth Permanent Magnets for Vehicle Traction Applications, in The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 33 Iss: 5, 014 Z. Zhang, L. Xu, Y. Zhang and B. Guan, Novel Rotor-side Control Scheme for Doubly- Fed Induction Generator to Ride through Grid Faults, in IEEE Energy Conversion Congress and Exposition (ECCE) 010, pp , Sept. 1-16, 010. L. Xu, E. Inoa., Y. Liu and B. Guan, A New High-Frequency Injection Method for Sensorless Control of Doubly-Fed Induction Machines, in IEEE Energy Conversion Congress and Exposition (ECCE) 011, pp , Sept. 17-, 011. L. Gao, B. Guan, Y. Zhou and L. Xu, Model Reference Adaptive System Observer Based Sensorless Control of Doubly-Fed Induction Machine, in IEEE International Conference on Electrical Machines and Systems (ICEMS) 010, pp , Oct , 010. H. Cai, B. Guan, L. Xu and W. Choi, Optimal Design of Synchronous Reluctance Machine A Feasible Solution to Eliminating Rare Earth Permanent Magnets for Vehicle Traction Applications, in Ninth International Conference on Ecological Vehicles and Renewable Energies (EVER) 01, March -4, 01 Fields of Study Major Field: Electrical and Computer Engineering viii

10 Table of Contents Abstract... ii Dedication.... iv Acknowledgments... v Vita... vii List of Tables... xii List of Figures... xiii Chapter 1: Introduction History of Doubly-Fed Brushless Machines DFBM Structure and System Configuration Dissertation Overview... 7 Chapter : Analysis of DFBM by Finite Element Analysis (FEA) Method DFBM Geometry and Winding Structure Air-gap Flux Density Distribution Winding Flux Linkage and Back-EMF Comparison of 4/6 and 4/8 Pole Combination Conclusions Chapter 3: Modeling and Equivalent Circuit of DFBM Dynamic Equations of DFBM in a Stationary a,b,c Reference Frame Voltage Equations of DFBM... 5 ix

11 3.1. Inductances of DFBM Complex Variable Model of DFBM Equations of DFBM in a Rotating d-q Reference Frame Operational Equivalent Circuits of DFBM Power and Torque Equations Conclusions Chapter 4: Field Orientation Control of DFBM for Doubly-Fed Power Generation Applications Steady State Field Orientation Control of DFBM Steady State Operation of DFBM in the Stator Flux Reference Active and Reactive Power Control Dynamic Field Orientation Control of DFBM Conclusions Chapter 5: Design, Construction and Experimental Study of the Prototype DFBM System Energy Efficiency of a DFBM Torque Density of a DFBM Sizing of the Prototype DFBM Segmental Rotor Design of the Prototype DFBM Performance Prediction of the Prototype DFBM by the FEA Method Experimental Results of the Prototype DFBM Steady State Testing of the Prototype DFBM x

12 5.6. Dynamic Testing of the Prototype DFBM Conclusions Chapter 6: Conclusions and Future Work Conclusions Future Work Bibliography xi

13 List of Tables Table 1 Comparison of Effective Air-Gap Flux Density and Rotor Modulation Capability between the 4/6 and 4/8 Pole Combination Table Specifications and Main Dimensions of the Prototype DFBM xii

14 List of Figures Figure 1.1 Two Induction Machines in Cascade Connection... Figure 1. Rotor Structures of the DFBM... 5 Figure 1.3 Main Configuration of a DFBM system... 5 Figure.1 DFBM Stator and Rotor Assembly (4/6 Pole Combination) Figure. Dual Stator Windings of the DFBM (4/6 Pole Combination) Figure.3 Discretized Field Model of the DFBM (Mesh Plot in FEA) Figure.4 Cross Section Flux Distribution with DC Excitation of 4-Pole Winding Figure.5 Air-Gap Flux Density with DC Excitation of 4-Pole Winding (4/6 Pole Combination) Figure.6 Details of Cross Section Flux Distribution and Air-Gap Flux Density with 4-Pole MMF Excitation Figure.7 Distribution of the Magnetic Poles with the 4-Pole MMF Excitation (Case I) Figure.8 Distribution of the Magnetic Poles with the 4-Pole MMF Excitation (Case II) Figure.9 Harmonics of Air-Gap Flux Density with 4-Pole MMF Excitation (4/6 Pole Combination)... 0 Figure.10 Effective Harmonics of Air-Gap Flux Density with 4-Pole MMF Excitation... 0 Figure.11 Actual Waveform vs. Effective Harmonics of Air-Gap Flux Density with 4-Pole MMF Excitation... 1 Figure.1 Cross Section Flux Distribution with DC Excitation of 6-Pole Winding... Figure.13 Air-Gap Flux Density with DC Excitation of 6-Pole Winding (4/6 Pole Combination)... 3 xiii

15 Figure.14 Harmonics of Air-Gap Flux Density with 6-Pole MMF Excitation (4/6 Pole Combination)... 4 Figure.15 Self Flux Linkage of 4-Pole Winding Versus Rotor Positions with DC Excitation. 6 Figure.16 Self Flux Linkage of 6-Pole Winding Versus Rotor Positions with DC Excitation. 7 Figure.17 Self Flux Linkage of 4-Pole Winding at 0 rpm with AC, 40Hz Excitation... 8 Figure.18 Self Flux Linkage of 4-Pole Winding at 1,00 rpm with AC, 40Hz Excitation... 8 Figure.19 Self Flux Linkage of 4-Pole Winding at -1,00 rpm with AC, 40Hz Excitation... 9 Figure.0 Mutual Flux Linkage of 4-Pole Winding with DC Excitation of 6-Pole Winding Figure.1 Back-EMF of 4-Pole Winding with DC Excitation of 6-Pole Winding at 1,00 rpm... 3 Figure. Mutual Flux Linkage of 6-Pole Winding with DC Excitation of 4-Pole Winding Figure.3 Mutual Flux Linkage of 4-Pole Winding with AC, -60Hz Excitation of 6-Pole Winding Figure.4 Back-EMF of 4-Pole Winding with AC, -60Hz Excitation of 6-Pole Winding Figure.5 Mutual Flux Linkage of 6-Pole Winding with AC, 40Hz Excitation of 4-Pole Winding Figure.6 Cross Section Flux Distribution with DC Excitation of 4-Pole Winding (4/8 Pole Combination)... 4 Figure.7 Air-Gap Flux Density with DC Excitation of 4-Pole Winding (4/8 Pole Combination) Figure.8 Harmonics of Air-Gap Flux Density with 4-Pole MMF Excitation (4/8 Pole Combination) Figure.9 Harmonics of Air-Gap Flux Density with 8-Pole MMF Excitation (4/8 Pole Combination) xiv

16 Figure.30 Mutual Flux Linkage of 8-Pole Winding with AC, 40Hz Excitation of 4-Pole Winding Figure.31 Mutual Flux Linkage of 4-Pole Winding with AC, 80Hz Excitation of 8-Pole Winding Figure 3.1 Magnetic Axes of a DFBM... 5 Figure 3. d-q Axes and - Axes Relative to Magnetic Axes of a DFBM Figure 3.3 Complex Vector Equivalent Circuit of a DFBM in the d-q Reference Frame Figure 3.4 Scalar Form Equivalent Circuits of a DFBM in the d-q Reference Frame Figure 3.5 Operational Complex Vector Equivalent Circuit of the Dynamic Model of a DFBM64 Figure 3.6 Positive Sequence Steady State Equivalent Circuit of a DFBM Figure 3.7 Negative Sequence Steady State Equivalent Circuit of a DFBM Figure 4.1 General Steady State Equivalent Circuit of a DFBM (per phase) with Referral Ratio a Figure 4. Steady State Equivalent Circuit of a DFBM (per phase) without Leakage Inductance on the Side of Stator Figure 4.3 Steady State Equivalent Circuit of a DFBM in the Stator Flux Reference When Magnetizing Current is Supplied Only by Stator Winding Figure 4.4 Phasor Diagram of a DFBM in the Stator Flux Reference When Magnetizing Current is Supplied Only by Stator Winding Figure 4.5 Steady State Equivalent Circuit of a DFBM in the Stator Flux Reference When Magnetizing Current is Supplied Only by Stator Winding Figure 4.6 Phasor Diagram of a DFBM in the Stator Flux Reference When Magnetizing Current is Supplied Only by Stator Winding xv

17 Figure 4.7 Steady State Equivalent Circuit of a DFBM in the Stator Flux Reference When Magnetizing Current is Supplied by Both Stator Windings 1 and... 8 Figure 4.8 Phasor Diagrams of a DFBM in the Stator Flux Reference When Magnetizing Current is Supplied by Both Stator Windings 1 and Figure 4.9 Active Power Balance of a Brushless Doubly-Fed Power Generation System Figure 4.10 Phasor Diagram of a DFBM in d-q Axes Stator Flux Reference Figure 4.11 Dynamic Torque Diagram of a DFBM Represented by Oriented Flux and q-axis Current Stator Flux Reference Figure 4.1 Dynamic Torque Diagram of a DFBM Represented by Currents Stator Flux Reference... 9 Figure 4.13 Control Block Diagram for Field Orientation Control of a DFBM Figure 5.1 Stator Lamination of the Prototype DFBM Figure 5. Rotor Cross-sectional View of the Prototype DFBM Figure 5.3 Lamination for Rotor Segments Figure 5.4 Asymmetrical Rotor Magnetic Structure of the Prototype DFBM in a No-Load Condition Figure 5.5 Magnetizing Curve of the Prototype DFBM by the FEA Figure 5.6 Torque Capability of the Prototype DFBM with Rated Currents by the FEA Figure 5.7 Magnitude of Air-Gap Flux Density Distribution of the Prototype DFBM by the FEA Figure 5.8 Stator, Rotor and Total Assembly of the Prototype DFBM Figure 5.9 Main Circuit Configuration of the Developed Converter Module Figure 5.10 Photos of the Experimental Testing Setup Figure 5.11 v-i Waveforms in the No-Load Condition of the Prototype DFBM xvi

18 Figure 5.1 Measured Magnetizing Curve of the Prototype DFBM Figure 5.13 Measured Iron Losses in the No-Load Conditions of the Prototype DFBM Figure Pole Stator Winding Current and Grid Voltage Waveforms in Steady State Loaded Conditions Figure 5.15 Grid/ 6-Pole Winding Current Voltage Waveforms in Steady State Loaded Conditions Figure 5.16 Efficiency Contours in Loaded Conditions Based on Measurements Figure 5.17 Voltages and Current Waveforms of the Grid-Side Converter during the Process of its Grid-Friendly Integration Figure 5.18 Grid, Induced 6-Pole Winding Voltages and 4-Pole Winding Current Waveforms of the Prototype DFBM System before Stator-Side Grid Integration Figure 5.19 Grid, Induced 6-Pole Winding Voltages and4-pole Winding Current Waveforms of the Prototype DFBM System during the Process of Stator-Side Grid-Friendly Integration Figure 5.0 Dynamic Performance of the Prototype DFBM System Active Power Control Figure 5.1 Dynamic Performance of the Prototype DFBM System Reactive Power Control. 1 Figure 5. Continuous Full Load Operation of the Prototype DFBM in a Wide Speed Range xvii

19 Chapter 1: Introduction 1.1 History of Doubly-Fed Brushless Machines Doubly-Fed Brushless Machines (DFBMs) have attracted attention in recent years in the application of variable-speed constant-frequency generating and adjustable speed drive systems [1-9]. With the advances of power electronics technologies, a DFBM appears very attractive because of its rugged structure (absence of slip rings and brushes), decent compatibility with a power converter, and flexible operational modes for various application needs. In particular, a DFBM resembles the terminal characteristics of a wound-rotor Doubly-Fed Induction Machine (DFIM), which has made DFBM a very competitive candidate in applications where doubly-fed operational modes are preferred but slip rings and brushes are not allowed. The basic concept of DFBM can be traced back nearly 100 years and has experienced three major development waves. In the very early and first wave, around the s, Hunt and Creedy researched the concept of the self-cascaded induction motor. Stemming from the cascaded induction machine, the self-cascaded induction motor essentially is two wound induction motors in a special arrangement. Mechanically, the two induction motors share a common shaft and, at the same time, the two sets of rotor windings are electrically self-cascaded [1, ]. As a result, the overall system was left with two sets of terminals for the two sets of stator windings. Since the two sets of rotor windings are self-cascaded, no brushes and slip rings are needed, as shown in Figure

20 Stator winding1 Common shaft Stator winding V ABC DFIM1 DFIM V abc Connected rotor windings Figure 1.1 Two Induction Machines in Cascade Connection High starting torque and speed regulation were obtained with certain success. With the help of power electronics control, this early version of DFBM, with minor variations, still finds application today [3]. Fifty years later was the second wave (around the 1970s). Broadway, Thomas, Kusko, Somuah, and others conducted further research and published their in-depth understanding in self-cascaded induction motor [4-8]. It was proposed to merge the two sets of stator windings by a dual-tapped stator windings wound into a common stator core. Also, it was proposed to design a special rotor common to the dual-tapped stator windings. In this way, the early version of DFBM evolved from the self-cascaded induction motor with a common shaft, to a single electric machine in a common stator house. However, in terms of modeling and analysis of the machine, all researchers during that period still treated the machine as two separate machines but built into a single frame. Along the way, creative ideas sprouted: of particular mention is Broadway s rotor in two styles, the nested cage rotor and the salient reluctance rotor that could be equally effective for the single-frame self-cascaded induction motor [4-5]. With somewhat complicated derivations, Broadway gave steady-state equations and an equivalent circuit for the self-cascaded machine, and named it Brushless Stator-Controlled Synchronous- Induction Machines [6-7]. At the beginning of the 1980s one attempt was made by Heyne and El-Antably to prototype Broadway s version of DFBM [9]. This prototype is perhaps the firstever detailed experimental investigation, which, to a certain degree, verified the basic principles

21 but did not produce meaningful torque density and energy efficiency for practical applications. In addition, control principles were developed and algorithms implemented. The renewed interest in DFBM in the 1990s, regarded as the third wave with much strength, was driven by the rapid advances in modern power electronics, which, supposedly, took full advantage of possible potentials of the DFBMs in variable-speed drives and variable-speed constant-frequency generators. Many papers have been published continuing the discussions of the DFBM principles, modeling, operational characteristics, and possible advanced control methods and applications [10-3]. The most important development in this stage is that researchers have formally established the identity of DFBM as a special machine, instead of treating it as two machines in self-cascade, that is, a combination of two induction machines built on a common shaft or single stator house [3-3]. Their research established that, regardless of rotor types, the DFBM terminal characteristics resemble those of a wound-rotor DFIM. Detailed field analysis of DFBM further verified that the two sets of stator windings in a DFBM resemble the mutual coupling characteristics of the stator and rotor windings in a conventional wound-rotor DFIM. However, from the structure robustness point of view, the attractiveness of the DFBM machine is evident the machine can be operated as a conventional DFIM but eliminate all the headaches associated with brushes and slip rings, from high costs of building and maintaining the machine to the serious reliability issues. Attracted by the features of brushless and doubly-fed operation modes, several prototype DFBMs were built. Unfortunately, the experiment results did not show great promise, with efficiency only about 75% and inability to reach the designed full power [3-34]. Nevertheless, the research results during the last twenty years did reveal clearly a series of fundamental issues and challenges with respect to the design and control of a DFBM. Compared to its counterpart with brushes/slip-rings, the issues of DFBM to the researchers are serious, including: a) What are the rules for DFBM optimal electromagnetic design to maximize torque 3

22 and power density? b) What are the suitable control algorithms for a DFBM system? c) How can the energy efficiency be substantially improved? d) What are the ultimate limits on design and control of such a machine? Evidently, these challenges are of practical significance and demanding application. Without innovative breakthroughs to the issues, the dreamed DFBM technology would remain as a dream on academic papers. 1. DFBM Structure and System Configuration The rotor structures of the DFBM (shown in Figure 1.), are categorized into two major types: nested-loop cage rotor and reluctance rotor [3, 33]. Compared to the cage rotor structure, the reluctance rotor with flux barriers produces stronger mutual coupling characteristics of the two stator windings, resulting in higher torque capability and efficiency [7-9]. The axiallylaminated reluctance rotor has been well investigated in the literature so that its pros and cons are quite clear [35, 36]. To further reduce the eddy current losses of the rotor, a radially-laminated reluctance rotor recently has been chosen in many research studies for applications in which high efficiency is required [37, 38]. In this thesis, the study has concentrated on the design and control of a radially-laminated reluctance rotor based DFBM with the aim of high efficiency performance in doubly-fed power generation applications. A typical radially-laminated reluctance DFBM based variable speed drive (or power generation) system as shown in Figure 1.3 consists of three main components: a DFBM, a backto-back converter and an associated controller [39-4]. The DFBM is a controlled electric machine, meaning that for its practical applications, it is necessary to mate the DFBM with a bidirectional power flow converter. 4

23 (a) Nested-Loop Cage Rotor (b) Salient Pole Rotor without Flux Barrier (c) Axially-Laminated Reluctance Rotor with Flux Barrier (d) Radially-Laminated Reluctance Rotor with Flux Barrier Figure 1. Rotor Structures of the DFBM 3-phase Power Grid q Stator Winding p Stator Winding 1 Converter DFBM Mechanical Feedback Controller Electrical Feedback Figure 1.3 Main Configuration of a DFBM system 5

24 As shown, the stator of a DFBM has two sets of 3-phase sinusoidally distributed windings. One set of windings, the primary, is fed with variable voltages at variable frequencies from a converter, which is also connected to the power grid. The other set of windings, the secondary, is directly connected to the power grid. When both sets of stator windings are fed from a set of 3- phase symmetric currents, two rotating MMFs are produced along the DFBM air-gap. Since the two sets of windings differ in pole numbers, one of p and another q, and the excitation currents are of different frequencies, one of 1 and another, the rotating MMFs differ from each other. According to electric machine fundamentals, under normal conditions, the two stator MMFs have no useful interaction for electromechanical energy conversion, except for torque and force oscillations. However, in the structure as described, with the magnetic modulation of the rotor, the two MMFs do have useful interaction for electromechanical energy conversion [41, 49]. The rotor of the DFBM can be built in one of the two styles: the rotor with nested cages of p r circuits, or rotor with reluctance segments of p r pieces where: (1.1) Eq. (1.1) indicates that p r, the number of rotor nested cage circuits or reluctance segments, is constrained by the pole numbers of the two sets of stator windings. Eq. (1.1) simply states that among the three numbers (p r, p and q) we can independently choose two (two degrees of freedom) and the third is determined by the equation. The operation of the DFBM relies on the interaction of the two stator MMFs through modulation action of the rotor. When one set of symmetrical sine-wave currents of frequency 1 are flowing in the primary windings, threephases of back EMFs will be induced with a frequency of in the secondary windings and vice versa. The two electrical frequencies, 1 and, in the primary and secondary are related to the rotor mechanical speed rm by 6

25 (1.) Electromechanical energy conversion will occur in the DFBM if Eq. (1.) is satisfied. Eq. (1.) clearly shows that, among the three speeds ( 1, and rm ), we can independently control two (two degrees of freedom) and the third is determined by the equation. In motor operation for speed control, a predetermined rotor speed rm is achievable if 1 and are controlled. As in generator operation, variable-speed constant-frequency generation is achievable by the DFBM if 1 or rm are predetermined, with controlled conforming to Eq. (1.). Depending on the sequence and value of the controlled frequency, a DFBM can operate in different modes [40, 41]. In particular, in the doubly-fed mode with =0, the DFBM operates as a synchronous machine. On the other hand, with 0 (positive sequence) or <0 (negative sequence), a DFBM can operate as an induction machine below or above synchronous speed. In terms of power flow, regardless at the sub-, super-, or synchronous rotor speed, a DFBM always can be operated as a motor or generator. For the above arguments, it is more reasonable just to name this machine doubly-fed brushless machine or DFBM, rather than to call it doubly fed brushless cage induction or reluctance machine, as in the past literature. The machine is not called a cage or reluctance machine because it is substantially different from both conventional cage induction and synchronous reluctance machines in the traditional and classical sense of cage or reluctance machines. 1.3 Dissertation Overview This dissertation presents the latest investigation of modeling, optimal design and advanced control of a radially-laminated reluctance DFBM with an original design of 00kW/1,00rpm for 7

26 high-efficiency and high-reliability doubly-fed power generation applications. The dissertation is organized as follows. Chapter presents the detailed nonlinear analysis of a DFBM by using the Finite Element Analysis (FEA) method. Through the investigation of the air-gap flux distribution, winding flux linkage and back-emf, the magic and mechanism of DFBM have been studied. Based on the information in Chapter, Chapter 3 examines the dynamic and steady state modeling (equations and equivalent circuits) of the DFBM in both stationary (a,b,c) and rotating (d-q) reference frames. The concept of the complex vector is used to represent the machine equations. Chapter 4 studies the principles of field orientation control of the DFBM. Firstly, the basic concept of decoupling control of torque and flux (or active and reactive power) is introduced and analyzed in the steady state conditions. Next, the dynamic response characteristics and implementation of the field orientation are discussed. In Chapter 5, the challenges of designing a high-efficiency DFBM and system are highlighted. Following the challenge description are the identified solutions to the optimal design. Using Finite Element Analysis (FEA), the thesis presents the original design of DFBM and system in a power rating of 00kW for a speed range of 400-1,00rpm. The designed machine is built and tested in the laboratory and both of the steady-state and dynamic experimental results are presented and analyzed. Chapter 6 concludes the research of the dissertation and renders an outline for possible future works. 8

27 Chapter : Analysis of DFBM by Finite Element Analysis (FEA) Method This chapter presents the detailed nonlinear analysis of DFBM by using the Finite Element Analysis (FEA) method. The results are considered accurate because the complicated geometry of the DFBM and nonlinearity of the materials are taken into full account [7]. Through the investigations of the internal magnetic field analysis of flux distribution, terminal characteristics of winding flux linkage and back-emf, the magic and mechanism of DFBM are studied. Lastly, a comparison study of two cases of pole number combinations is presented to show various advantages and disadvantages of different pole number combinations with an odd number and even number of rotor segments..1 DFBM Geometry and Winding Structure Firstly, a DFBM with 4/6 pole combination in the stator winding and five rotor segments is chosen as the prototype for the following analysis. The cross-section of the DFBM is shown in Figure.1. The dual 4-pole and 6-pole three-phase sinusoidally distributed stator windings are illustrated in Figure.. As shown in Figure.3, to achieve an accurate computation of FEA, the cross-section are well discretized especially for the area of air-gap where the Magnetomotive Force (MMF) drop is dominant in the whole magnetic path. 9

28 Figure.1 DFBM Stator and Rotor Assembly (4/6 Pole Combination) (a) 4-pole Stator Winding (b) 6-pole Stator Winding Figure. Dual Stator Windings of the DFBM (4/6 Pole Combination) 10

29 Figure.3 Discretized Field Model of the DFBM (Mesh Plot in FEA). Air-gap Flux Density Distribution For electrical machines, the total flux of the core is indeed dependent on the sum of the air-gap flux and leakage flux [54]. As known, the torque capability, induced speed voltage, core and teeth saturation of an electrical machine are closely related to the air-gap flux density. Therefore, the air-gap flux density is chosen as a key parameter to investigate the main magnetic flux characteristics of the DFBM. Since the core flux density is the spatial integral of the air-gap flux density, if the core flux density is sinusoidal, then the air-gap flux density also should be co-sinusoidal with the same fundamental frequency as that of the core flux density [54]. Compared to conventional AC machines, the pole number of the two windings and the number of rotor segment are different for the DFBM. It is interesting to determine the unique characteristics of the flux distribution and particular air-gap flux pattern. As indicated in Eq. (1.), when the p pole and q pole windings are doubly excited by two sets of three-phase sinusoidal currents with different frequencies of ω 1 and ω, two sinusoidally 11

30 distributed MMFs are created with frequencies of and. The combined MMF will interact with the rotor permeance in conditions of p+q (could be an odd number) pieces of rotor segments and rotor speed of, and essentially produce a complicated and inexplicit air-gap flux distribution [8]. For an electrical machine, the flux pattern is dependent solely on the relative position between the MMF and rotor permeance, no matter what the frequency of the applied current excitation is, and no matter whether the rotor is rotating or not. Therefore, to simplify the analysis of flux distribution and air-gap flux density, the DFBM is singly excited by a three-phase DC current [7]. In Figure.4, when the 4-pole winding is excited by a three-phase DC current, the flux distribution and air-gap flux density are plotted at six different rotor positions spatially spanning 7 degrees. Since the rotor has five pieces of rotor segment, the air-gap flux pattern should be repetitive for every 7 degrees in space. Note that, although a 4-pole sinusoidally distributed MMF is produced in the stator winding, a non-sinusoidal and even asymmetric flux distribution is created by the effect of the rotor permeance of five pieces of rotor segment. The asymmetric magnetic field will produce an unbalanced magnetic pull, resulting in noises and vibrations [49, 50]. Some interesting observations are listed as follows: When the 4-pole MMF is applied in the stator, with the rotor permeance, the flux distribution is unlike the conventional 4-pole electrical machine with four symmetric curls of flux line. Due to the effect of the magnetic barrier in the rotor structure, the flux follows the path provided by the laminations, resulting in curls of flux line over each segment. The entire flux distribution over the cross section of this machine is asymmetric. For instance, in Figure.4 (a), the flux density over segments 1and 4 are obviously higher than those of segments, 3 and 5. Furthermore, each curl of flux line over each segment also is not exactly symmetric 1

31 about its axis. As shown in Figure.5, the characteristic of this asymmetric flux distribution spanning each segment is more clearly present by the air-gap flux density. A special feature is in one of the five segments (e.g., Segment #3 in Figure.4 (a) and Segment #4 in Figure.4 (c)) over which there are more than one curl of flux line. Meanwhile, the flux pattern and corresponding air-gap flux density are extremely different from those of the other four segments. For this segment, as shown in Figure..6, the waveform of the airgap flux density is even more asymmetric and full of harmonics, and its magnitude is much lower than the others. It means that the magnetic capability of 1/5 (0%) of the iron lamination has not been fully utilized, and potentially resulting in degraded torque capability and efficiency to some extent. To describe the magnetic flux characteristics of the DFBM more straightforwardly, the distribution of the magnetic polarities over the cross section of the machine is pointed out. Figure.7 illustrates the distribution of the magnetic poles with the 4-pole MMF excitation. Unlike the conventional 4-pole machine with the normal flux pattern: N-S - S-N - N-S - S- N, the flux pattern of the DFBM is N-S - S-N - N-S - S-N - S-N. It seems that one more pair of S-N is created, since there are five pieces of rotor segments with special flux barrier design. As shown in Figure.8, the distribution of the magnetic polarities becomes N-S - S-N - N-S - N-S-N - S-N at some of the rotor positions. In previous literature, due to the asymmetric, non-sinusoidal and pulsating features of the airgap flux density, it was difficult to perform some quantitative analysis and find an effective method to evaluate the characteristics of the air-gap flux density. In this study, the harmonic decomposition method has been utilized. Since there are two sinusoidally distributed MMFs with frequencies of and when the DFBM are doubly excited by two sets of three-phase sinusoidal currents, not only the fundamental component but also the corresponding 13

32 effective harmonics of the flux need to be taken into account. If the Fast Fourier Transform (FFT) algorithm is applied to the waveform of the air-gap flux density in Figure.4, the amplitude of the harmonic components across the frequency spectrum are achieved and shown in Figure.9, where the nd harmonic component indicates the 4-pole magnetic flux distribution, and the 3 rd harmonic component represents the 6-pole magnetic flux distribution. It is noted that, although only a 4-pole sinusoidally distributed MMF is produced in the stator winding, both the 4-pole and 6-pole flux distributions are dominantly created along the air-gap by the effect of the rotor permeance. The magnitude of the 6-pole air-gap flux density (B 6 ) is 96.1% of that of the 4-pole air-gap flux density (B 4 ). The equation of could be used to represent the mutual coupling between the 4 and 6-pole windings in terms of flux density. As can be shown in Figures.10 and.11, the main characteristics of the air-gap flux density are clearly demonstrated by the combination of the 4- and 6-pole air-gap flux densities. This special function of the rotor structure could be interpreted as the modulation capability of modulating the 4-pole MMF into the 6-pole flux along the air-gap. If this 6-pole flux (generated by the rotor modulation) interacts with the 6-pole MMF (generated by the current excitation in the 6-pole stator winding), the electromagnetic torque is possibly created. Therefore, the effective harmonic component of the air-gap flux density is the 6-pole flux by the rotor modulation when the 4-pole MMF is applied, and vice versa. To achieve higher torque, the higher mutual coupled flux density resulting from the rotor modulation is desired. The design of the rotor structure of the DFBM has been extensively studied by researchers to enhance the modulation function. The modulation ability of the rotor is a key feature affecting the torque capability of this machine and could be represented by the amplitude of the effective harmonic component of the air-gap flux density. 14

33 # #3 #1 #4 #5 (a) θr (b) θr = 1 # #3 #4 #1 #5 (c) θr = 4 (d) θr = 36 (e) θr = 48 (f) θr = 60 Figure.4 Cross Section Flux Distribution with DC Excitation of 4-Pole Winding 15

34 Air-Gap Flux Density (T) Air-Gap Flux Density (T) Air-Gap Flux Density (T) Air-Gap Flux Density (T) Air-Gap Flux Density (T) Air-Gap Flux Density (T) θ r = θ r = θ r = θ r = θ r = θ r = Locations in Air-Gap (Degree) Figure.5 Air-Gap Flux Density with DC Excitation of 4-Pole Winding (4/6 Pole Combination) 16

35 Air-Gap Flux Density (T) Locations in Air-Gap (Degree) θ r = Figure.6 Details of Cross Section Flux Distribution and Air-Gap Flux Density with 4-Pole MMF Excitation 17

36 Air-Gap Flux Density (T) N S S N S N N S N S N S S N N S S N S N θ r = Locations in Air-Gap (Degree) Figure.7 Distribution of the Magnetic Poles with the 4-Pole MMF Excitation (Case I) 18

37 Air-Gap Flux Density (T) N N S S S N N S N S N N S S N N S N S N S N θ r = Locations in Air-Gap (Degree) Figure.8 Distribution of the Magnetic Poles with the 4-Pole MMF Excitation (Case II) 19

38 Air-Gap Flux Density (T) Amplitude of Air-Gap Flux Density (T) Harmonic Order Figure.9 Harmonics of Air-Gap Flux Density with 4-Pole MMF Excitation (4/6 Pole Combination) Pole Air-Gap Flux Density 6 Pole Air-Gap Flux Density Total Air-Gap Flux Density Locations in Air-Gap (Degree) Figure.10 Effective Harmonics of Air-Gap Flux Density with 4-Pole MMF Excitation 0

39 Air-Gap Flux Density (T) 1.5 S S N N S N S S N N Effective Air-Gap Flux Density Actual Air-Gap Flux Density Locations in Air-Gap (Degree) Figure.11 Actual Waveform vs. Effective Harmonics of Air-Gap Flux Density with 4-Pole MMF Excitation Figures.1 and.13 show the similar characteristics of the flux distribution and air-gap flux density at six different rotor positions spatially spanning 7 degrees, while the 6-pole winding is singly excited by a set of three-phase DC current. The harmonics of air-gap flux density under the excitation of 6-pole MMF are illustrated in Figure.14, where the 4-pole air-gap flux is generated by the rotor modulation and treated as the effective flux component. The magnitude of the 4-pole air-gap flux density (B 4 ) is 6.4% of that of the 6-pole air-gap flux density (B 6 ). 1

40 # #3 #1 #4 #5 (a) θr (b) θr = 1 # #1 #3 #4 #5 (c) θr = 4 (d) θr = 36 (e) θr = 48 (f) θr = 60 Figure.1 Cross Section Flux Distribution with DC Excitation of 6-Pole Winding

41 Air-Gap Flux Density (T) Air-Gap Flux Density (T) Air-Gap Flux Density (T) Air-Gap Flux Density (T) Air-Gap Flux Density (T) Air-Gap Flux Density (T) θ r = θ r = θ r = θ r = θ r = Locations in Air-Gap (Degree) θ r = Figure.13 Air-Gap Flux Density with DC Excitation of 6-Pole Winding (4/6 Pole Combination) 3

42 Amplitude of Air-Gap Flux Density (T) E Harmonic Order Figure.14 Harmonics of Air-Gap Flux Density with 6-Pole MMF Excitation (4/6 Pole Combination).3 Winding Flux Linkage and Back-EMF To verify the electromechanical energy conversion of an electrical machine or an electromechanical system, in general, the winding flux linkage and induced voltage due to the movement of the rotor are investigated. If the stator winding flux linkage varies as the rotor is rotating, a voltage will be induced according to Faraday s Law, and will be referred to as the speed voltage or Back-EMF. Simultaneously, if a current is injected into the stator winding as well, the electrical power is generated depending on the phase angle between the induced voltage and current, thus the electromechanical energy conversion is accomplished [51]. For either a field winding or a permanent magnet synchronous machine, if the rotor flux linking the stator winding changes due to the rotation of the rotor, then a speed voltage is induced. An induction machine has a similar mechanism of electromechanical energy conversion. Under 4

43 normal conditions of an induction machine, a rotor current is induced by the slip between the rotor speed and rotating field for a squirrel cage rotor, while a current is intentionally injected into the rotor winding for a wound-rotor DFIM [51]. Therefore, a rotor flux resulting from its current links the stator winding and varies according to the rotation of the rotor; thus, a speed voltage is produced. In a reluctance machine, although there is no effective current in the rotor, a speed voltage is also induced and proves the electromechanical energy conversion. When the stator current enters into the armature winding, the corresponding MMF is established along the air-gap and produces flux linking of the rotor side. The paths of the resulting flux are different in terms of permeance according to the different positions of the reluctance type rotor [51]. As a result, the stator flux linkage changes due to the movement of the rotor and then a speed voltage is induced in the stator. In this chapter, the mechanism of electromechanical energy conversion of the DFBM is investigated by the analysis of the winding flux linkage and induced speed voltage (Back-EMF). As known, there are two sets of three-phase windings with different pole numbers in the stator of DFBM. Two types of winding flux linkage are particularly defined as follows [7]: Self flux linkage: the flux linked by one phase of the windings when this set of three-phase windings with the same pole number is excited by a three-phase sinusoidal current. Mutual flux linkage: the flux linked by one phase of the windings when the other set of threephase windings with a different pole number is excited by a three-phase sinusoidal current. (a) Self Flux Linkage Flux linkage is a property of a winding (two-terminal element), which is not only related to flux distribution but also to winding distribution. The defined self flux linkage could be explained as the flux weighted by one phase of the windings in a set of same pole number, when an air-gap flux is created by this set of three-phase windings excited by a three-phase sinusoidal 5

44 Self Flux Linkage (T) Y1 [Wb] current. Thus, the self flux linkage is a lumped description or terminal characteristic of the magnetic flux in an electrical machine from a single phase point of view [7]. There are two ways to evaluate the characteristics of the self flux linkage, by a DC or AC current excitation alternatively. In Figure.15, the three-phase self flux linkages of the 4-pole winding versus the rotor positions are plotted, when the 4-pole winding is singly excited by a three-phase DC current. As shown, the self flux linkage is mainly a DC quantity with small AC pulsations. For the DC component, it could be explained as the self flux linkages are independent of rotor positions, and there are mainly no flux linkage variations and so as no induced speed voltages. On the other hand, the small AC pulsation of flux linkage will cause a small AC speed voltage. However, the DC current excitation and AC induced speed voltage will not produce average electromagnetic power and torque. The similar results of the self flux linkages of the 6-pole winding with DC excitations are shown in Figure XY Plot Curve Info 150kwdc FluxLinkage(PhaseA_4) Setup1 : Transient FluxLinkage(PhaseB_4) Setup1 : Transient FluxLinkage(PhaseC_4) Setup1 : Transient Time [ms] Rotor Position (Degree) Figure.15 Self Flux Linkage of 4-Pole Winding Versus Rotor Positions with DC Excitation 6

45 Self Flux Linkage (Wb) Y1 [Wb] Curve Info FluxLinkage(PhaseA_6) Setup1 : Transient FluxLinkage(PhaseB_6) Setup1 : Transient FluxLinkage(PhaseC_6) Setup1 : Transient Time [ms] Rotor Position (Degree) Figure.16 Self Flux Linkage of 6-Pole Winding Versus Rotor Positions with DC Excitation As shown in Figures.17,.18 and.19, when the 4-pole winding is singly excited by a 40Hz three-phase AC current, the corresponding self flux linkages are also sinusoidal in 40Hz and have a 10 degree phase angle difference in each phase. By comparing the characteristics at 0 rpm, 1,00 rpm and -1,00rpm, it has been proven that the fundamental components of the self flux linkage in the three speeds are the same in terms of magnitude and phase angle. The self flux linkage with AC current excitation is not related to the rotor speed and position, if the effect of the slight harmonic components is neglected. The harmonic induced speed voltage interacting with the fundamental current will not deliver average real power but energy oscillation. Similar characteristics may be achieved in the conditions of the 6-pole winding with AC excitation. 7

46 Self Flux Linkage (Wb) Y1 [Wb] Self Flux Linkage (Wb) Y1 [Wb] XY Plot 3 Curve Info FluxLinkage(PhaseA_4) Setup1 : Transient FluxLinkage(PhaseB_4) Setup1 : Transient FluxLinkage(PhaseC_4) Setup1 : Transient Time [ms] Time (ms) Figure.17 Self Flux Linkage of 4-Pole Winding at 0 rpm with AC, 40Hz Excitation Curve Info FluxLinkage(PhaseA_4) Setup1 : Transient FluxLinkage(PhaseB_4) Setup1 : Transient FluxLinkage(PhaseC_4) Setup1 : Transient Time [ms] Time (ms) Figure.18 Self Flux Linkage of 4-Pole Winding at 1,00 rpm with AC, 40Hz Excitation 8

47 Self Flux Linkage (Wb) Y1 [Wb] XY Plot 3 Curve Info FluxLinkage(PhaseA_4) Setup1 : Transient FluxLinkage(PhaseB_4) Setup1 : Transient FluxLinkage(PhaseC_4) Setup1 : Transient Time [ms] Time (ms) Figure.19 Self Flux Linkage of 4-Pole Winding at -1,00 rpm with AC, 40Hz Excitation Through the investigation of the characteristics in both DC and AC current excitations, the fundamental component of the defined self flux linkage is verified to be not a function of rotor position and speed, and so cannot produce the speed voltage which is necessary for the electromechanical energy conversion. It is concluded that the singly excited DFBM is certainly in a no-load condition without average power production. (b) Mutual Flux Linkage The mutual flux linkage is defined as the flux linked by one phase of the windings when the other set of three-phase windings with a different pole number is excited by a three-phase sinusoidal current. The defined mutual flux linkage could be explained as the flux weighted by one phase of the windings in a set of same pole number, when an air-gap flux is created by the other set of three-phase windings with a different pole number excited by a three-phase sinusoidal current [7, 8]. By intuitional thinking, the mutual flux linkage should be substantially different 9

48 with the self flux linkage due to the different pole numbers and pole pitches of these two windings and the special structure of the rotor. There are also two methods to evaluate the characteristics of the mutual flux linkage, by a DC or AC current excitation alternatively. In Figure.0, the defined three-phase mutual flux linkages of the 4-pole winding versus the rotor positions at two rotor speeds of 1,00 rpm and -1,00 rpm are plotted, when the 6-pole winding is singly excited by a three-phase DC current. As shown, the mutual flux linkage is mainly a sinusoidal AC quantity with high frequency harmonics. For the fundamental component of the waveforms, it should be noted that, unlike the self flux linkage, the mutual flux linkages are definitely related to the rotor positions. These fundamental flux linkage variations will produce induced Back-EMF in the 4-pole windings (shown in Figure.1) which are needed for electromechanical energy conversion. If a three-phase sinusoidal current with the same frequency as that of the induced speed voltage is injected into the 4-pole winding, an average electromagnetic power and torque could be produced. The mechanism of the electromechanical energy conversion of DFBM could be explained as: when the stator current enters the 6-pole winding, the corresponding MMF is created along the air-gap, producing flux which links both the rotor side and the 4-pole winding. The paths of the resulting flux are different in terms of permeance, according to the different positions of the reluctance type rotor [7]. Moreover, the rotor related flux variation could only be weighted by the 4-pole winding instead of the excited 6-pole winding. As a result, the defined mutual flux linkage of the 4-pole winding varies due to the movement of rotor and then a speed voltage is induced. In other words, the mutual coupling between the two windings is implemented by the effect of the designed reluctance type rotor. 30

49 Mutual Flux Linkage (Wb) Y1 [Wb] Mutual Flux Linkage (Wb) Y1 [Wb] Curve Info FluxLinkage(PhaseA_4) Setup1 : Transient FluxLinkage(PhaseB_4) Setup1 : Transient FluxLinkage(PhaseC_4) Setup1 : Transient Time [ms] Time (ms) (a) Rotor Speed at 1,00 rpm Curve Info FluxLinkage(PhaseA_4) Setup1 : Transient FluxLinkage(PhaseB_4) Setup1 : Transient FluxLinkage(PhaseC_4) Setup1 : Transient Time [ms] Time (ms) (b) Rotor Speed at -1,00 rpm Figure.0 Mutual Flux Linkage of 4-Pole Winding with DC Excitation of 6-Pole Winding 31

50 Back-EMF (kv) Y1 [kv] Curve Info InducedVoltage(PhaseA_4) Setup1 : Transient InducedVoltage(PhaseB_4) Setup1 : Transient InducedVoltage(PhaseC_4) Setup1 : Transient Time [ms] Time (ms) Figure.1 Back-EMF of 4-Pole Winding with DC Excitation of 6-Pole Winding at 1,00 rpm On the other hand, although the flux distribution along the air-gap is asymmetrical, nonsinusoidal and full of harmonics, it is observed that the defined mutual flux linkage is quite sinusoidal while the MMF, winding and rotor are of different pole numbers. It proves the fact that the flux linkage is related not only to flux distribution but also to the winding distribution. As observed, the frequency relation among the 4-pole, 6-pole windings and rotor speed is following the constraint indicated in Eq. (1.). Similar results of the mutual flux linkages of the 6-pole winding with DC excitations in the 4- pole winding are shown in Figure.. 3

51 Mutual Flux Linkage (Wb) Y1 [Wb] Mutual Flux Linkage (Wb) Y1 [Wb] XY Plot 1 Curve Info FluxLinkage(PhaseA_6) Setup1 : Transient FluxLinkage(PhaseB_6) Setup1 : Transient FluxLinkage(PhaseC_6) Setup1 : Transient Time [ms] Time (ms) (a) Rotor Speed at 1,00 rpm Curve Info FluxLinkage(PhaseA_6) Setup1 : Transient FluxLinkage(PhaseB_6) Setup1 : Transient FluxLinkage(PhaseC_6) Setup1 : Transient Time [ms] Time (ms) (b) Rotor Speed at -1,00 rpm Figure. Mutual Flux Linkage of 6-Pole Winding with DC Excitation of 4-Pole Winding 33

52 As shown in Figure.3, when the 6-pole winding is singly excited by a 60Hz three-phase AC current, the corresponding mutual flux linkages of the 4-pole winding are also mainly sinusoidal AC waveforms and have a 10 degree phase angle difference in each phase. By comparing with the characteristics at 0 rpm, 1,00 rpm and -1,00 rpm, it has been validated that the mutual flux linkage is a function of the rotor position. The magnitudes of the fundamental component of the mutual flux linkages in the three speeds are the same, due to the same current excitation. However, the frequencies of the waveforms are different, while the frequency relation among the 4-pole, 6-pole windings and rotor speed is also following the constraint in Eq. (1.). Similar characteristics could be observed in Figure.5 under the conditions of the 6-pole winding with AC excitation in the 4-pole winding. It is noted that the mutual flux linkage varies in a sinusoidal (with harmonics) profile with respect to the rotor position. Therefore, as shown in Figure.4, the induced Back-EMF will be mainly sinusoidal as the rotor is rotating. The induced speed voltage interacting with the fundamental current will deliver average torque as real power. The rotor position related mutual flux linkage proves the effective mutual coupling of the two windings with different pole numbers through the modulation function of the designed rotor. It should be noted that, in many cases, the three-phase mutual flux linkages of one set of windings are not identical in terms of profile by each phase, which is unlike conventional AC electrical machines. The reasons are listed as follows: The number of the rotor segment is odd. The pole numbers and pole pitches of the two sets of windings are different. There exists unbalanced air-gap flux distribution. However, Figures.3 (b) and.5 (b) show the cases of the mutual flux linkages with the three-phase balanced waveforms and same profile, when the frequencies of the 4-pole winding, 6- pole winding and rotor are 40Hz, -60Hz, and 0Hz respectively. It is interesting to note that the 34

53 Mutual Flux Linkage (Wb) Y1 [Wb] three-phase mutual flux linkages in one set of winding have the same profile with a 10 degree phase angle difference in each phase, when the frequencies are following the equation: (.1) With the constraints of both Eqs. (1.) and (.1), the generated flux will be felt and weighted evenly by each phase of windings in one set with the same pole number, and therefore create three-phase balanced flux linkage. This is an important hint to control this machine in an optimal way with three-phase balanced flux linkages, and so as balanced voltages and currents. The specific control method of this type of electrical machine will be discussed in details in the later chapter Curve Info FluxLinkage(PhaseA_4) Setup1 : Transient FluxLinkage(PhaseB_4) Setup1 : Transient FluxLinkage(PhaseC_4) Setup1 : Transient Time [ms] Time (ms) (a) Rotor Speed at 0 rpm continued Figure.3 Mutual Flux Linkage of 4-Pole Winding with AC, -60Hz Excitation of 6-Pole Winding 35

54 Mutual Flux Linkage (Wb) Y1 [Wb] Mutual Flux Linkage (Wb) Y1 [Wb] Figure.3 continued Curve Info FluxLinkage(PhaseA_4) Setup1 : Transient FluxLinkage(PhaseB_4) Setup1 : Transient FluxLinkage(PhaseC_4) Setup1 : Transient Time [ms] Time (ms) (b) Rotor Speed at 1,00 rpm XY Plot 3 Curve Info FluxLinkage(PhaseA_4) Setup1 : Transient FluxLinkage(PhaseB_4) Setup1 : Transient FluxLinkage(PhaseC_4) Setup1 : Transient Time [ms] Time (ms) (c) Rotor Speed at -1,00 rpm 36

55 Back-EMF (V) Y1 [V] Back-EMF (V) Y1 [V] XY Plot 4 Curve Info InducedVoltage(PhaseA_4) Setup1 : Transient InducedVoltage(PhaseB_4) Setup1 : Transient InducedVoltage(PhaseC_4) Setup1 : Transient Time [ms] Time (ms) (a) Rotor Speed at 0 rpm XY Plot 4 Curve Info InducedVoltage(PhaseA_4) Setup1 : Transient InducedVoltage(PhaseB_4) Setup1 : Transient InducedVoltage(PhaseC_4) Setup1 : Transient Time [ms] Time (ms) (b) Rotor Speed at 1,00 rpm continued Figure.4 Back-EMF of 4-Pole Winding with AC, -60Hz Excitation of 6-Pole Winding 37

56 Mutual Flux Linkage (Wb) Y1 [Wb] Back-EMF (kv) Y1 [kv] Figure.4 continued Curve Info InducedVoltage(PhaseA_4) Setup1 : Transient InducedVoltage(PhaseB_4) Setup1 : Transient InducedVoltage(PhaseC_4) Setup1 : Transient Time [ms] (c) Rotor Speed at -1,00 rpm Time (ms) XY Plot Curve Info FluxLinkage(PhaseA_6) Setup1 : Transient FluxLinkage(PhaseB_6) Setup1 : Transient FluxLinkage(PhaseC_6) Setup1 : Transient Time [ms] Time (ms) (a) Rotor Speed at 0 rpm 38 continued Figure.5 Mutual Flux Linkage of 6-Pole Winding with AC, 40Hz Excitation of 4-Pole Winding

57 Mutual Flux Linkage (Wb) Y1 [Wb] Mutual Flux Linkage (Wb) Y1 [Wb] Figure.5 continued Curve Info FluxLinkage(PhaseA_6) Setup1 : Transient FluxLinkage(PhaseB_6) Setup1 : Transient FluxLinkage(PhaseC_6) Setup1 : Transient Time [ms] Time (ms) (b) Rotor Speed at 1,00 rpm Curve Info FluxLinkage(PhaseA_6) Setup1 : Transient FluxLinkage(PhaseB_6) Setup1 : Transient FluxLinkage(PhaseC_6) Setup1 : Transient Time [ms] Time (ms) (c) Rotor Speed at -1,00 rpm 39

58 By means of the FEA of the flux linkages and induced voltages in various excitations, the mechanism of the electromechanical energy conversion of DFBM is investigated. The important conclusions could be summarized as follows: As DFBM is singly excited in one set of winding with the same pole number, only the defined self flux linkage will be produced in this winding and not related to the rotor position. In this condition, there is no directly mutual coupling between the singly excited winding and rotor. Therefore, the singly excited DFBM is certainly in a no-load condition without average torque delivery. Through the modulation effect of the designed reluctance type rotor, these two windings of different pole numbers are mutual coupled. Thus, the electromechanical energy conversion is feasible when the two windings are properly and doubly excited. The corresponding flux linkages and induced voltages are primarily in a sinusoidal profile with harmonics, if a sinusoidal current is injected into the winding. The frequency relation among the two windings and rotor speed is always following the constraint in Eq. (1.). Unlike the conventional AC machine, in many cases, the three-phase mutual flux linkages of one set of windings are not identical in terms of profile by each phase. It is also identified that, with the constraint of Eq. (.1), the flux could be evenly weighted by each phase of winding in one set, consequently producing a three-phase balanced flux linkage with the exactly same profile. The frequency relation in Eq. (.1) could be implemented to control this machine and so as to achieve three-phase balanced performances. 40

59 .4 Comparison of 4/6 and 4/8 Pole Combination According to the FEA results of the DFBM with the 4/6-pole combination, the asymmetric magnetic flux distribution due to the rotor peameance of the five pieces of rotor segment is an issue resulting in unbalanced magnetic pull, noise, vibration and also a three-phase unbalanced flux linkage. To avoid these undesirable characteristics of the asymmetric magnetic flux distribution, another pole combination of the 4/8 with the 6 rotor segments is chosen for further investigation. The DFBM of the 4/8 pole combination consists of the same stator core, air-gap length and 4- pole winding distribution as those of the 4/6-pole combination version. Obviously, there is a set of 8-pole, three-phase windings in the stator of the machine with the 4/8 pole combination. The major distinction between these two machines is the number of rotor segments, since the 4/8 pole combination will have six (an even number) rotor segments in contrast to the case of five (an odd number) rotor segments for the 4/6-pole combination. To assess the flux distribution of the 4/8 pole combination, the 4-pole winding is also excited by a three-phase current, which is the same case as the 4/6-pole combination. From the information shown in Figure.6, it is apparent that the flux follows the path of the iron lamination, and results in six curls of flux line over the cross section. Interestingly, unlike the results of the 4/6-pole combination, the entire flux distribution is centro-symmetric about the center of the circle through the effect of the rotor permeance of the six pieces of rotor segments. Therefore, the serious issues of unbalanced magnetic pull, noise and vibration are avoided for the 4/8 pole combination with six rotor segments. 41

60 #3 # #4 #1 #5 #6 Figure.6 Cross Section Flux Distribution with DC Excitation of 4-Pole Winding (4/8 Pole Combination) As can be seen from Figure.7, the air-gap flux density also clearly indicates the characteristic of this centro-symmetric flux distribution, although the waveform is non-sinusoidal and full of harmonics. Furthermore, special findings are in two of the six segments (e.g., Segment # and 5 in Figure.8) in which the magnitudes of the air-gap flux density are much lower than the other four segments. These results indicate that the magnetic capability of /6 (33.3%) of the iron lamination has not been fully utilized. It is important to note that, compared to the 4/6-pole combination, the utilization of the magnetic core for the 4/8 pole arrangement is less effective, and possibly results in degraded torque capability and efficiency. 4

61 Air-Gap Flux Density (T) Locations in Air-Gap (Degree) θ r = Figure.7 Air-Gap Flux Density with DC Excitation of 4-Pole Winding (4/8 Pole Combination) For the purpose of quantitative analysis, the FFT algorithm is also applied to the waveform of the air-gap flux density in Figure.7. The results, as shown in Figures.8 and.9, indicate that the 4-pole and 8-pole flux components are dominantly generated through the 4-pole or 6-pole MMF excitation and modulation effect of the rotor permeance. The comparisons of the effective air-gap flux density and rotor modulation capabilities between the 4/6 and 4/8 pole combination are highlighted in Table 1. The data of this comparative study indicate that the 4/6-pole combination motor has higher air-gap flux density no matter which stator winding is excited. Another important finding is that the mutual coupling between the 4- and 6-pole windings in terms of flux density is more effective than that of the 4/8 pole combination. Therefore, this study confirms that the rotor modulation capability of the 4/6 pole combination is stronger than that of the 4/8 pole combination; as a result, higher torque production and efficiency are expected for the 4/6-pole combination. 43

62 Amplitude of Air-Gap Flux Density (T) Amplitude of Air-Gap Flux Density (T) Harmonic Order Figure.8 Harmonics of Air-Gap Flux Density with 4-Pole MMF Excitation (4/8 Pole Combination) Harmonic Order Figure.9 Harmonics of Air-Gap Flux Density with 8-Pole MMF Excitation (4/8 Pole Combination) 44

63 4/6 Pole Combination 4-Pole Flux Density (B 4, T) 6-Pole Flux Density (B 6, T) Mutual Coupling (%) 4-Pole MMF Excitation: B 6 /B 4 = 96.1% 6-Pole MMF Excitation: B 4 /B 6 = 6.4% 4/8 Pole Combination 4-Pole Flux Density (B 4, T) 8-Pole Flux Density (B 8, T) Mutual Coupling (%) 4-Pole MMF Excitation: B 8 /B 4 = 93.5% 8-Pole MMF Excitation: B 4 /B 8 = 5.1% Table 1 Comparison of Effective Air-Gap Flux Density and Rotor Modulation Capability between the 4/6 and 4/8 Pole Combination As discussed, for the 4/6-pole combination, mutual flux linkage is three-phase unbalanced in many cases, mainly due to the effect of the rotor structure having an odd number of pieces of segments. The corresponding mutual flux linkage of the 4/8 pole combination under the conditions of various current excitations and speeds are calculated by the FEA and exhibited in Figures.30 and.31. From the graphs, interestingly, it can be seen that the three-phase mutual flux linkages of one set of winding are exactly identical in terms of profile with a 10 degree phase angle difference in each phase, despite their different winding excitations and rotor speeds. It indicates that the generated flux could always be felt and weighted evenly by each phase of the windings in one set with the same pole number, and thus creates a three-phase balanced flux linkage. This is a significant difference of electric magnetic characteristic between the 4/6 and 4/8 pole combination, which could be mainly interpreted by the parity of the number of the rotor segment. The results of this study show that the rotor permeance with an even number of segments will produce a centro-symmetric flux (density) distribution and accordingly three-phase balanced flux linkages, while the even number pieces of rotor segments could create asymmetric flux distribution, resulting in unbalanced three-phase flux linkages. The three-phase balanced 45

64 Mutual Flux Linkage (Wb) Mutual Flux Linkage (Wb) flux linkage property (winding terminal characteristic) of the machine makes it more suitable for grid-tied and smooth torque required applications Time (ms) (a) Rotor Speed at 0 rpm Phase A Phase B Phase C Phase A Phase B Phase C Time (ms) (b) Rotor Speed at 1,00 rpm Figure.30 Mutual Flux Linkage of 8-Pole Winding with AC, 40Hz Excitation of 4-Pole Winding 46

65 Mutual Flux Linkage (Wb) Mutual Flux Linkage (Wb) Phase A Phase B Phase C Time (ms) (a) Rotor Speed at 0 rpm Phase A Phase B Phase C Time (ms) (b) Rotor Speed at 1,00 rpm Figure.31 Mutual Flux Linkage of 4-Pole Winding with AC, 80Hz Excitation of 8-Pole Winding 47

66 Taken together, the findings of this comparative study between the 4/6 and 4/8 pole combination could be extended to represent the different features between the odd number and even number of rotor segments. The following conclusions can be drawn from the present study: When an even number of rotor segments is used, the flux distribution is centro-symmetric about the center of the circle without the issues of the unbalanced magnetic pull, noise and vibration due to the asymmetric flux distribution existing in the rotor structure with an even number of segments. As the difference between the pole numbers of the two sets of windings becomes smaller, the higher is the air-gap flux density and the more effective rotor modulation capability is achieved. In other words, when (e.g., the 4/6 pole combination), the torque capability is potentially optimized. However, at the same time, the number of rotor segments is odd with the issue of unbalanced flux distribution. The flux linkage as a winding terminal characteristic is also affected by the pole combination. Evidence shows that the flux linkage is three-phase balanced when the number of rotor segments is even, whereas the three-phase mutual flux linkages of one set of windings are not always identical in terms of profile. For the pole combination selection, to achieve higher torque production and higher efficiency of the motor, an odd number of rotor segments with the smallest difference between the pole numbers of the two windings is the best choice. On the other hand, an even number of rotor segments could be considered for the grid-tied and smooth torque output applications where the three-phase balanced terminal characteristics and magnetic properties are important. 48

67 .5 Conclusions In this chapter, magnetic field analysis of flux distribution, terminal characteristics of winding flux linkage and back-emf are examined by using the FEA to illustrate the characteristics of the DFBM. These findings are summarized as follows: The main magnetic field characteristic of the DFBM is its non-sinusoidal and even asymmetric flux distribution by the effect of the rotor permeance of rotor segments. In this study, the harmonic decomposition method has been utilized for the quantitative analysis of the asymmetric, non-sinusoidal and pulsating air-gap flux density, and aids in the evaluation of the modulation capability of the DFBM. The mechanism of electromechanical energy conversion of the DFBM is investigated by the analysis of the winding flux linkage and induced speed voltage (Back-EMF). By means of both DC and AC current excitations alternatively, the characteristics of the defined self- and mutualflux linkages are evaluated. Although the flux distribution along the air-gap is asymmetrical, non-sinusoidal and full of harmonics, it is observed that the defined mutual flux linkage is rotor position dependent and quite sinusoidal while the MMF, winding and rotor are of different pole numbers. Compared to conventional AC machines, in many cases, the three-phase mutual flux linkages of one set of windings are not identical in terms of profile by each phase. It is also identified that, with the constraint of Eq. (.1), the flux could be evenly weighted by each phase of winding in one set, consequently producing a three-phase balanced flux linkage with the exactly same profile. Through the comparative study between the 4/6 and 4/8 pole combination, it is concluded that, to achieve high torque production and high efficiency of the motor, an odd number of rotor segments with the smallest difference between the pole numbers of the two windings is the best choice. On the other hand, an even number of rotor segments could be considered for the grid- 49

68 tied and smooth torque output applications when the three-phase balanced terminal characteristics and magnetic properties are important. 50

69 Chapter 3: Modeling and Equivalent Circuit of DFBM After the investigation of the mechanism of the DFBM by using the FEA method in the previous chapter, Chapter 3 examines the mathematic models of the DFBM in both dynamic and steady state conditions. Following the logic of analysis of electrical machines proposed by Lipo and Krause [48, 5, 53], the dynamic model of the DFBM is first developed in the stationary a,b,c reference frame. The complex vector approach is used to express the machine s equation in a more compact form [48]. Then, to eliminate the coupling among the two stator windings and rotor with different frequencies and positions, the mathematic equations are transformed to a common rotating d-q reference frame. Based on the machine s equations, the corresponding equivalent circuits are developed to give a clear illustration of the DFBM. 3.1 Dynamic Equations of DFBM in a Stationary a,b,c Reference Frame For a DFBM, there are two separate three-phase windings placed in the stator with different pole numbers and without direct electromagnetic coupling between each other. The rotor permeance plays a dominant role in the indirect interaction or mutual coupling of the two stator windings. The corresponding winding configuration and magnetic axes of a DFBM are conceptually shown in Figure

70 b1-axis b-axis i b v b1 i b1 v a a-axis v b i a θ r v a1 i a1 a1-axis i c1 c1-axis v c1 v c i c1 c-axis Figure 3.1 Magnetic Axes of a DFBM Voltage Equations of DFBM The stator voltage equations of a DFBM could be expressed as [48]: v r i (3.1) v r i (3.) where the vectors are defined as v v v v i i i i (3.3) v v v v i i i i (3.4) The flux linkages are functions of inductance and current [48]: (3.5) 5

71 (3.6) where i i (3.7) i i (3.8) i i (3.9) i i i (3.10) 3.1. Inductances of DFBM Applying the winding function theory, the mutual inductance between any two windings i and j of the DFBM could be expressed as [4, 9, 5 and 53]: θ r c θ i i (3.11) where p i and p j are the pole pair numbers of the windings i and j, p r is the number of the rotor segments which is also called the rotor pole number here. The represents the angle difference between phases in winding j. 53

72 Inductances of one stator winding By setting p r = p i +p j, p i p j, i = j= 1 and = 0, then the self inductances of the stator winding 1 are obtained: r (3.1) The subscript m here denotes the effective magnetizing inductance. The leakage inductance is added to express the total self inductances of the stator winding 1: r r (3.13) r By denoting the magnetizing inductance of the stator winding 1 as: r (3.14) then the total self inductance of the stator winding 1could be written as: By setting =, the mutual inductances between the phases a 1, b 1 and c 1 in stator winding 1 are obtained: (3.15) r (3.16) As a result, the flux linkage of stator winding 1 due to the three-phase current i is expressed: 54

73 i i (3.17) Similarly, the flux linkage of stator winding due to the three-phase current i is: i i (3.18) where is the leakage inductance of the stator winding. Inductances between two stator windings By setting p r = p i +p j, p i p j, i = 1, j=, and = 0 in Eq. (3.11), then the mutual inductances between the stator winding 1 and are obtained: r θ θ (3.19) By setting =, the mutual inductances between the phases a 1 and b, phase b 1 and c, phase c 1 and a, are obtained: θ r θ (3.0) 55

74 By setting =, the mutual inductances between the phases a 1 and c, phase b 1 and a, phase c 1 and b, are obtained: θ r θ (3.1) As a result, the mutual flux linkage of stator winding 1 due to the three-phase current i is expressed as: i θ θ θ θ θ θ θ θ θ i (3.)) Similarly, the mutual flux linkage of stator winding due to the three-phase current i is expressed as: i θ θ θ (3.3) θ θ θ i θ θ θ Through the calculations of the inductances based on the principle of winding function, it is concluded that the self inductances and mutual inductances between the phases in the same set of stator winding are constants, while the mutual inductances between the two windings are sinusoidal functions of the rotor position. The results of this study confirm the previous findings by the Finite Element Analysis of the flux linkage and contribute a quantitative analysis of the math model of the DFBM. 56

75 3. Complex Variable Model of DFBM To express the machine equations in a more compact form, the complex vector approach is utilized [48]. Defining a (3.4) and complex variable a a (3.5) where the symbol f could represent any of the three-phase variables like voltage, current, flux linkage, etc. v r i (3.6) where v v av a v (3.7) i i ai a i (3.8) a a (3.9) From Eq. (3.17): a a i i (3.30) From Eq. (3.): i a a a a a a a a i (3.31) a a a a where θ θ. 57

76 i (3.3) So the total flux linkage of stator winding 1 in complex variable form is i i (3.33) Similarly, the total flux linkage of stator winding in complex variable form is i i (3.34) The turns ration transformation has been done by referring the stator winding to winding 1 as utilized for a transformer and defining the variables [48]: v v (3.35) i i (3.36) (3.37) r r (3.38) (3.39) Denoting the effective magnetizing inductance r (3.40) The voltage equations could be written as: v r i i i (3.41) v r i i i (3.4) or 58

77 v r i i i i (3.43) v r i i i i (3.44) where θ. 3.3 Equations of DFBM in a Rotating d-q Reference Frame As known, the theory of reference frame has been widely used for electrical machine analysis, where the time-varying and position-varying parameters and variables become constants [48, 55 and 56]. A rotating d-q reference frame is defined and illustrated in Figure 3., where θ is the angle by which the q-axis leads phase a of the stator winding 1. For a DFBM, the d-q axes could be arbitrary, but normally are set to rotate with the same frequency as one set of the stator windings. b1-axis b-axis β-axis d-axis a-axis q-axis θ θ r α-axis a1-axis c1-axis c-axis Figure 3. d-q Axes and - Axes Relative to Magnetic Axes of a DFBM 59

78 The equations express the transformation of variables from the stationary a,b,c to the rotating d-q reference frame [48]. θ θ θ (3.45) θ θ θ (3.46) (3.47) So the transformation matrix is: θ θ θ θ θ θ (3.48) Due to the winding (wye or delta) connection of DFBM, the zero sequence component is neglected here. a a (3.49) Similarly, a a (3.50) The voltage equations in a rotating d-q reference frame could be written as: v r i i i i i (3.51) v r i i i i i (3.5) where θ. 60

79 The d-q equations in complex variable form could be rewritten as: v r i i i i (3.53) v r i i i i (3.54) and where the flux linkages are: i i i i i (3.55) i i i i i (3.56) So the complex vector equivalent circuit of a DFBM is shown in Figure 3.3: r m + 3 m r + v 1 1 i 1 i m r + v - - Figure 3.3 Complex Vector Equivalent Circuit of a DFBM in the d-q Reference Frame Eqs. (3.51) and (3.5) could also be transformed to be in scalar form as: v r i (3.57) v r i (3.58) where i i i i i (3.59) i i i i i (3.60) For the stator winding : 61

80 v r i (3.61) v r i (3.6) where i i i i i (3.63) i i i i i (3.64) The real variable d-q voltage equations in a matrix form could be rewritten as: v v v v r r r r i i i i (3.65) The d-q equivalent circuit of a DFBM in scalar form is in exactly the same form as the complex vector equivalent circuit shown in Figure

81 r m + 3 m r + v 1 1 i 1 i m r + v - - r m + 3 m r + v 1 1 i 1 i m r + v - - Figure 3.4 Scalar Form Equivalent Circuits of a DFBM in the d-q Reference Frame 3.4 Operational Equivalent Circuits of DFBM By combining Eqs. (3.53) and (3.54) with Eqs. (3.55) and (3.56), the voltage equations of the stator winding 1 and in complex variable form could be reconstructed and expressed as: v r i i i r i i i i (3.66) v r i i i r i i (3.67) i i To obtain a more straightforward expression, the voltage equation of the stator winding is multiplied by the operator [48]. Then, v r i i i i (3.68) 63

82 As shown in Figure 3.5, the resultant equivalent circuit is a clear and operational explanation of the dynamic model of a DFBM [48]. r m m + r + + r + v 1 i 1 i m + + v + r Figure 3.5 Operational Complex Vector Equivalent Circuit of the Dynamic Model of a DFBM The analysis of the steady state operation is convenient and effective for understanding the basic characteristics and performance of the electrical machine. Generally, the steady state characteristics are represented by using equivalent circuits and phasor diagrams. These constraints of steady state operation are normally summarized as [57]: Three-phase sinusoidal voltage excitations which result in three-phase sinusoidal currents in two sets of stator windings Constant rotor speed operation No saturation effect in the iron core Constant resistances and inductances except for variable mutual inductances due to rotor motion For a general three-phase voltage excitation, v c (3.69) v c (3.70) v c (3.71) 64

83 the voltage could be expressed as the sum of two complex exponentials by using the Euler relation [48]: v (3.7) Denote the peak values of the voltages as v v v (3.73) then the voltages could be written as [48]: v (3.74) v (3.75) v (3.76) The defined voltage in complex variable form in Eq. (3.7) becomes v v av a v By defining the positive sequence voltage a a a a (3.77) a a (3.78) and the negative sequence voltage a a (3.79) then the voltage in complex variable form is rewritten as v (3.80) For a balanced three-phase voltage, the negative sequence component equals zero and so 65

84 v (3.81) where is the peak value of the phase voltage. The voltage equations in a rotating d-q reference frame could be written as [48]: v v (3.8) To obtain the steady state equivalent circuit of a DFBM, the complex vector voltage equations in Eq. (3. 66) and (3.68), and the corresponding dynamic equivalent circuit shown in Figure 3.5 could be utilized. If the model is referred to the stator winding 1, then (3.83) For the positive sequence which is an exponential function of, the operators (3.84) and (3.85) Then, the positive sequence steady state equivalent circuit of a DFBM is achieved and shown in Figure 3.6. r r m m + 1 I 1 I 1 m Figure 3.6 Positive Sequence Steady State Equivalent Circuit of a DFBM Similarly, for the negative sequence that is an exponential function of, the operators 66

85 (3.86) and (3.87) Then, the negative sequence steady state equivalent circuit of a DFBM is obtained and shown in Figure 3.7. r m m r I I 1 1 m + - Figure 3.7 Negative Sequence Steady State Equivalent Circuit of a DFBM Taken together, these results of both dynamic and steady state equivalent circuits suggest that the DFBM has the same form and similar expression of a mathematical model as those of a conventional DFIM. For a DFBM, the magnitude of the defined is 50% of the magnetizing inductance of a conventional DFIM with the same stator winding design, stator iron shape, air-gap dimension and stack length. However, it does not mean that the magnetizing inductance of a DFBM is only half that of the DFIM. The reason is that these mathematical results of DFBM are all based on the assumption of the inverse gap function as [9, 53 and 54]: θ c θ (3.88) which is approximately derived by utilizing a rotor of a conventional salient pole machine. As mentioned previously, various researches are being done - such as special electromagnetic and 67

86 structure design of rotor, pole combination choosing, etc. - in order to improve the mutual coupling between the two windings and to enlarge the magnetizing inductance of a DFBM. The leakage inductances of a DFBM could be redefined as and for two stator windings which are definitely larger than those of the stator and rotor windings of a DFIM. As indicated, for a DFBM based power generation system, the leakage inductance of one stator winding could be effective to smoothing out the harmonics of the current from the inverter, while the leakage inductance of the other winding becomes part of an LC or LCL filter tied to the grid. Thus, the leakage inductances of a DFBM are useful to enhance the performance and reduce the cost of the extra inductance based filter in doubly-fed power generation applications. 3.5 Power and Torque Equations The electrical power flowing into the two windings of the DFBM is the sum of products of the voltages and currents [48]: v i v i v i v i v i v i v i v i (3.89) The power equation in a rotating d-q reference frame could be written as [48]: v i v i v i v i (3.90) which could also be expressed in a scalar form v i v i v i v i (3.91) By use of Eqs. (3.66) and (3.67), Eq. (3.90) is expressed as 68

87 r i i i i r i i (3.9) i i which could be reorganized as r i r i i i i i i i i (3.93) i i i where the first term r i r i is the copper loss due to winding resistance; the second term i i i i represents the change rate of the magnetic energy of the leakage and mutual inductances of the DFBM; Thus only the third term is related to the electromechanical power [48]: i i i i i i (3.94) Through a process of mathematical derivation, the electromechanical power is developed as Im i i i i i i (3.95) Then, the electromagnetic torque of the DFBM could be expressed as Im i i i i i i (3.96) Note that the flux linkage of stator 1 is 69

88 i i (3.97) Then the electromagnetic torque can be expressed by the flux linkage and current of stator 1( and i ) as Im i i i Im i (3.98) Similarly, the electromagnetic torque can be expressed by the flux linkage and current of stator ( and i ) as Im i (3.99) Denote the air-gap flux linkage as i i (3.100) The electromagnetic torque could also be represented by the air-gap flux linkage and current of stator 1 or ( and i ori ) as Im i Im i (3.101) Considering the torque control of the DFBM, the electromagnetic torque is reasonably derived from the interaction of flux linkage of one stator winding and current of the other winding [48]. By inserting the following stator current equations into Eq. (5.85) i i (3.10) i i (3.103) the corresponding torque expressions become 70

89 Im i (3.104) Im i 3.6 Conclusions By means of the FEA of the electromagnetic field, the mechanism of a DFBM was addressed in the previous chapter. In this chapter, mathematic models of DFBM are systematically examined. Based on the principle of winding function, the inductances in the stationary a,b,c reference frame are calculated. In this investigation, it is shown that the self inductances and mutual inductances between the phases in one set of stator winding are constants, while the mutual inductances between the two windings are sinusoidal functions of the rotor position. The results of this study confirm previous findings by the FEA of the flux linkage and contribute a quantitative analysis of the mathematic model of the DFBM. The equations of the DFBM in the rotating d-q reference frame are deduced and expressed in a complex vector form. The analysis of both dynamic and steady state equivalent circuits suggest that the DFBM has the same form and similar expression of mathematical model as those of a conventional DFIM. For a doubly-fed power generation application, the comparatively larger leakage inductances of stator winding of a DFBM are useful in smoothing out the harmonics of the current and could be treated as part of an inductance based filter. 71

90 Chapter 4: Field Orientation Control of DFBM for Doubly-Fed Power Generation Applications In this chapter, similar to the analysis of the conventional DFIM [41-48], the principles of field orientation control of a DFBM especially for doubly-fed power generation applications are investigated. First, the basic concept of decoupling control of torque and flux (or active and reactive power) has been introduced and analyzed in the steady state conditions. The dynamic response characteristics and implementation of the field orientation are then discussed. 4.1 Steady State Field Orientation Control of DFBM As known, the basic principle of the field orientation control is to control the electromagnetic field flux and armature MMF (torque) independently [48]. Usually, the flux and MMF are perpendicularly oriented. Denote stator inductances: (4.1) (4.) By introducing a referral ratio a, the general dynamic model of a DFBM in complex form could be transformed as [48]: i v r i i a a r i a i a i i a (4.3) and 7

91 av a r i a a i a r i a a a i a (4.4) a i i a or av a r i a a a i a (4.5) a i i a If a, the dynamic equations of a DFBM become the expressions shown in Eqs. (3.66), (3.67) and (3.68). Therefore, the general voltage equations (per phase) in steady state conditions (only the positive sequence is considered) could be represented as [48]: r I a I a I I a (4.6) a a r I a a a I a a I I a (4.7) The general equivalent circuit of a DFBM in steady state conditions is shown in Figure 4.1. a r r 1 1 a m a a m + 1 I 1 a m I a + ae + a Figure 4.1 General Steady State Equivalent Circuit of a DFBM (per phase) with Referral Ratio a 73

92 Clearly, by setting a, the conventional equivalent circuit previously shown in Figure 3.6 has been achieved. From the equivalent circuit, the torque could be represented by using the air-gap power r I I E I (4.8) where E is the induced voltage due to the flux of stator winding, and is the angle between the phasors of E and I. Similar to a synchronous machine, the torque control of the DFBM could be achieved through the independent control of the induced voltage E and stator current I, where I is related to the air-gap flux. To further simplify the torque control of a DFBM to be like a DC machine, the turns referral ratio a is set as [48]: a (4.9) Then, the leakage inductance on the side of stator becomes zero. The corresponding equivalent circuit is observed in Figure 4.. r m m r I 1 1 m I m + m E - + m - Figure 4. Steady State Equivalent Circuit of a DFBM (per phase) without Leakage Inductance on the Side of Stator 74

93 It is important to note that the voltage across the magnetizing reactance equals the induced voltage E. It means that the magnetizing current is directly in charge of the flux of stator winding rather than the defined air-gap (mutual) flux. Thus, it could be called stator flux orientation [48] Steady State Operation of DFBM in the Stator Flux Reference There are three cases to explain the basic principles of the steady state operation of a DFBM in the stator flux reference. Case I: when the magnetizing current is supplied only by stator winding 1 In the Case I, the current of stator winding 1 I could be straightforwardly divided into the magnetizing component I and torque component I, where the I goes into the magnetizing reactance and I into the induced voltage E due to the stator flux. So the equivalent circuit could be redrawn and shown in Figure 4.3. r m m r I 1 1 m I 1M I 1 = m I + m E - + m - Figure 4.3 Steady State Equivalent Circuit of a DFBM in the Stator Flux Reference When Magnetizing Current is Supplied Only by Stator Winding 1 75

94 From the equivalent circuit, the magnetizing current I is calculated by I E E (4.10) As known, the induced voltage is defined as the derivative of flux linkage with respect to time. In other words, the induced voltage is the time rate change of flux linkage. So the induced voltage E due to the flux of stator winding is E (4.11) Substituting the induced voltage equation Eq. (6.11) into Eq. (6.10), yields the stator flux linkage I (4.1) Therefore, the flux linkage of stator winding could be directly controlled by the magnetizing current component I of stator winding 1. In the stator flux reference, when all the magnetizing current is provided by the stator winding 1, the power factor angle between the phasors E and I is zero. As a result, the torque is expressed as E I E I I I I (4.13) where I I. As indicated in Eqs. (4.1) and (4.13), the flux of stator winding and torque of a DFBM could be respectively controlled by the magnetizing and torque component of current of the stator winding 1 in the defined stator flux reference, when the magnetizing current is only provided by the stator winding 1. 76

95 The phasor diagram of a DFBM in the case I based on the equivalent circuit of Figure 4.3 is shown in Figure 4.4. It is interesting to note, if the stator winding is short circuit, the equivalent circuit of DFBM becomes the same form as that of an induction machine. 1 r 1 I m I 1 I m I 1 m m E I 1M I 1 = m I 1M Figure 4.4 Phasor Diagram of a DFBM in the Stator Flux Reference When Magnetizing Current is Supplied Only by Stator Winding 1 Case II: when the magnetizing current is supplied only by stator winding ( ) In the Case II, the current of stator winding 1 I goes through only the induced voltage E. The flux linkage of stator winding is solely produced by the magnetizing current in stator winding. The current of stator winding, I, has been divided into a magnetizing component I and a torque component I. As shown in Figure 4.5 (a), the equivalent circuit is redrawn with The voltage equation becomes I I (4.14) 77

96 r I I I (4.15) r I I E Then, the induced voltage is represented as a voltage source in Figure 4.5 (b) without magnetizing reactance in the circuit. As known, the induced voltage is provided by the flux of stator winding, only due to the magnetizing excitation in stator winding, and is proportional to the sum of the rotor electrical speed (electrical radians per second) and the electrical angular frequency of stator winding. E I (4.16) Since there is no magnetizing current from the stator winding 1, the phasor angle between E and I is zero, so. Therefore, the torque is E I I (4.17) Another interpretation of a DFBM is obtained by using a synchronous model in Figure 4.5 (c), where the voltage is deduced as r I I I r I I I I r I I I I (4.18) r I I I r I I Here the current of stator winding, I, is similar to the field current of a synchronous machine, where I is the Back-EMF in this machine. 78

97 The phasor diagram of a DFBM in the case II, based on the equivalent circuit of Figure 4.5, is shown in Figure 4.6. As indicated, when, the terminal power factor of stator winding 1 is always lagging. r m m r I = I 1 1 m I M I m + m E - + m - (a) Induction Machine-Type Equivalent Circuit r m I 1 m E = 1 m (b) Equivalent Circuit without Magnetizing Reactance r I 1 b = 1 m I (c) Synchronous Machine-Type Equivalent Circuit Figure 4.5 Steady State Equivalent Circuit of a DFBM in the Stator Flux Reference When Magnetizing Current is Supplied Only by Stator Winding 79

98 r 1 I m I 1 I I 1 m E I m I M m m r I = m I M Figure 4.6 Phasor Diagram of a DFBM in the Stator Flux Reference When Magnetizing Current is Supplied Only by Stator Winding In the study of this case, the equivalent circuit of DFBM is found to be very similar to a wound-rotor synchronous machine. Compared to the DC field current excitation of a conventional AC synchronous machine, the magnetizing current of a DFBM could be an AC variable. Case III: when the magnetizing current is supplied by both stator windings 1 and ( ) In the Case III, both of stator windings1 and provide magnetizing currents for the flux of stator winding. Therefore, I I I I (4.19) The corresponding induction machine-type equivalent circuit is shown in Figure 4.7 (a), where the voltage equation is 80

99 r I I I I r I I (4.0) r I I E Similarly, the voltage equation in a synchronous machine model is deduced r I I I I r I I I (4.1) r I I E I The resultant synchronous machine-type equivalent circuit is presented in Figure 4.7 (b). Comparing Case III to Cases I and II, the power factor angle between the phasors E and I could be no longer zero, and. The phasor diagram of a DFBM in Case III ( ) is shown in Figure 4.8. Through the vector control of the current of stator winding 1, the terminal power factor of the stator windings could be intentionally regulated to be unity, lagging or leading. The torque is calculated from the real power in the circuit E I I (4.) 81

100 r m m r I 1 1 m I M I m m E m - (a) Induction Machine-Type Equivalent Circuit r I 1 b = 1 m I = m m E 1 I 1 (b) Synchronous Machine-Type Equivalent Circuit Figure 4.7 Steady State Equivalent Circuit of a DFBM in the Stator Flux Reference When Magnetizing Current is Supplied by Both Stator Windings 1 and 8

101 I m 1 r 1 I m I 1 I m I M I 1 m m r m E I = m I 1 + m I (a) I Lagging, and I Leading I m I 1 1 r 1 I m I 1 m E I m I M m m r I = m I 1 + m I (b) I Leading, and I Leading continued Figure 4.8 Phasor Diagrams of a DFBM in the Stator Flux Reference When Magnetizing Current is Supplied by Both Stator Windings 1 and 83

102 Figure 4.8 continued I m m m r I r 1 I 1 1 I M I m m E m 1 1 I 1 I 1 = m I 1 + m I (c) I Lagging, and I Lagging 4.1. Active and Reactive Power Control In a doubly-fed power generation system as shown in Figure 1.3, if the mechanical loss in the shaft is neglected, then mechanical power equals the electromagnetic power: (4.3) where and are the electromagnetic powers of stator windings 1 and, respectively. From Eq. (4.), the total electromagnetic power is expressed as: I (4.4) and for each stator windings I (4.5) I (4.6) The total active power generated from the machine to the grid is 84

103 (4.7) where and are the active powers generated from stator windings 1 and to the grid, respectively. (4.8) (4.9) where and are the losses within the two windings, which are normally neglected for convenient analysis. Taken together, it is concluded that the torque and active powers in these two windings could be effectively controlled in the stator flux -oriented reference through the vector control of the current of stator winding 1. The active power flow of a brushless doubly-fed power generation system at different speed conditions is illustrated in Figure M c h 3-phase Power Grid Stator Winding Stator Winding 1 Converter 1 M c h DFBM (a) Sub-synchronous Speed ( ) continued Figure 4.9 Active Power Balance of a Brushless Doubly-Fed Power Generation System 85

104 Figure 4.9 continued 1 1 M c h 3-phase Power Grid Stator Winding Stator Winding 1 Converter M c h DFBM (b) Synchronous Speed ( ) M c h 3-phase Power Grid Stator Winding Stator Winding 1 Converter 1 M c h DFBM (c) Super-synchronous Speed ( ) 86

105 For the reactive power, since the stator winding 1 is connected to the back-to-back converter not directly tied to the grid, the reactive power from the generator in steady state operation is defined as the reactive power in the stator winding : Im I Im I I (4.30) Since the reactive power is aimed to be controlled by the current of stator winding 1, the reactive power is expressed by using the following equations: I I (4.31) and I I (4.3) Therefore, I I I (4.33) 4. Dynamic Field Orientation Control of DFBM For a high performance motor drive or generation system, the dynamic response characteristics are important [48]. The decoupling control of torque and flux of a DFBM in steady state operations is investigated in Section 4.1, based on complex vector equivalent circuits. In this section, with the same basic concepts of the steady state field orientation control, concerns about the dynamics are discussed and analyzed in the rotating d-q reference frame. The control strategy of the designed DFBM is developed based on the features of a doubly-fed generation system illustrated in Figure 1.3. One set of the stator windings is constantly connected 87

106 to the power grid with a fixed voltage of constant frequency, and the other to a converter of variable voltage and frequency, adapted to the rotor speed. Instructed by the torque equations in the previous analysis, we can improve current utilization of the DFBM by locking the phase angle of the two sets of stator current to a special angle, to realize the so-called vector control principle; that is, the phase angle of the current in the two sets of stator windings needs to be maintained at an optimal value for maximum torque production [41 and 49]. The dynamic model of a DFBM in the arbitrary rotating d-q reference frame at the speed of is [41]: v r i (4.34) v r i (4.35) v r i (4.36) v r i (4.37) i i (4.38) i i (4.39) i i (4.40) i i (4.41) i i (4.4) As described in the previous chapter, to implement the decouple control of the torque and flux, field orientation along the second winding field flux is utilized. It can be realized by selecting the second winding flux as the reference frame and orienting the d axis to. As a result, is achieved with the following important relations [41 and 49]: 88

107 v r i (4.43) v r i (4.44) i i (4.45) i i (4.46) i (4.47) Similar to the expression of the (stator flux ) field orientation in the steady state, the phasor diagram of a DFBM in the d-q axes is shown in Figure i m 1 1 r 1 i 1 v 1 i m i 1 ( 1 rm ) v r i = 0 q-axis = i + m i 1 d-axis Figure 4.10 Phasor Diagram of a DFBM in d-q Axes Stator Flux Reference The major difference between the steady state and dynamic behaviors concerns the oriented flux. Using Eq. (4.45), the current i could be expressed by and i i i (4.48) and be inserted into Eq. (4.43) yielding 89

108 r v r i (4.49) Therefore, the oriented stator flux becomes r v r r i (4.50) v i As indicated in Eq. (4.50), in a transient state, the oriented flux linkage is the output of a first order transfer function (with a time constant ) of two inputs of the current i and voltage v. It means that there is a lag in the response of the flux to the corresponding magnetizing current and voltage [48]. Combining the information of the flux linkage from Eq. (4.50) and torque expression from Eq. (4.47) in the stator flux reference, the torque diagram in terms of the oriented flux linkage in stator winding and q-axis current of stator winding 1 has been illustrated in Figure i 1 m 1 + r + v r r 3 m r i 1 Figure 4.11 Dynamic Torque Diagram of a DFBM Represented by Oriented Flux and q-axis Current Stator Flux Reference 90

109 Alternatively, in the same reference frame, the torque could be represented in totality by currents instead of flux and current. Inserting the flux linkage expression of Eq. (4.40) into the voltage Eq. (4.43) to suppress the oriented flux, the d-axis current of stator winding is obtained. i v i (4.51) The investigation of current i has shown that In the steady state, i is the current only due to the voltage v across the resistance r i v r (4.5) In the dynamic state, as shown in Eq. (4.51), changes in current i and voltage v will additionally create induced current i and result in a transient in the torque production. As a result, the torque is calculated by i i i i v i i i (4.53) The corresponding torque diagram in terms of the current in stator windings 1 and is illustrated in Figure 4.1. To implement the field orientation control, the spatial phase angle and magnitude of the oriented stator flux must be investigated. Through the so-called Clark transformation in Eq. (4.54), the voltage components v v and current components i i in the stationary - reference are obtained [41]. (4.54) 91

110 i 1 v m m r 1 + r 1 r 1 + r - i m i i + 3 m r i 1 Figure 4.1 Dynamic Torque Diagram of a DFBM Represented by Currents Stator Flux Reference The corresponding magnitude and phase angle of the stator flux could be calculated by using the voltage and current components in the stationary - reference [41]: v r i (4.55) v r i (4.56) Therefore: (4.57) θ a (4.58) In the practical applications, the pure integrator is replaced by a designed low-pass filter to avoid the DC bias issue of an integral due to the initial values and noises of the input signals. As mentioned, in a DFBM based doubly-fed generation system, the stator winding is directly connected to the grid with the mostly constant magnitude and frequency of the terminal voltage. 9

111 Therefore, the corresponding flux linkage is approximately unchanged and can be derived from Eqs. (4.55) and (4.56). Consequently, as indicated in Eq. (4.47), in the (stator flux ) field orientation reference frame, the instantaneous torque control could be implemented by controlling the q axis current component of the stator winding 1: i. If the voltage drops of the winding resistance are neglected, active and reactive power at the terminal of the stator winding can be derived as [41]: i (4.59) v i v i i i (4.60) The less obvious control strategy for the DFBM is that the two sets of stator windings are of different pole-pitch and excited with currents of different frequencies, implying that the same space angle in the DFBM air-gap means different electrical angles to the two sets of stator windings [41 and 49]. The angle equivalence transformation, however, can be obtained by integrating both sides of Eq. (1.), resulting in θ θ θ (4.61) Evidently, Eq. (4.61) plays a key role to translate the three different phase angles into a uniform scale and then field orientation or the vector control principle is applied to the DFBM. According to Eq. (4.59), if the current component, i, which is in phase with respect to the induced speed voltage is controlled, the torque production and real power of the DFBM is proportionally controlled. On the other hand, if the current component i orthogonal to the induced speed voltage, due to the mutual flux linkage variation is controlled, the reactive power and, thus, the terminal power factor will be proportionally controlled according to Eq. (4.60) [41 and 49]. The control block diagram for the field-orientation control of the DFBM is shown in 93

112 Figure It is not surprising that this DFBM, like its brush-type counterpart, can be conveniently used to achieve decoupled control of active and reactive power, a very useful feature for variable-speed constant-frequency in wind turbine generator applications, in which the active power often needs to be controlled, due to the wind speed, reactive power and reactive power demands from the utility grids [41 and 49]. A B C Q * + - P * + ω rm * PI i d * PI PI ω rm S sw i d1 * + - i q1 * + - PI PI v d1 * v q1 * θ, θ rm i d1 i q1 e j(θ +p r θ rm ) e -j(θ +p r θ rm ) v α1 * v β1 * Φ/3Φ i α1 i β1 Grid Side Converter v a1 * v b1 * v c1 * SVPWM 3Φ/Φ v dc i a1 i b1 - θ rm, ω rm + θ Flux linkage Observer Encoder DFBM P Q P&Q Caculation v d v q i d i q θ e -jθ e -jθ v α v β i α i β 3Φ/Φ 3Φ/Φ v a v b i a i b Cal. v ab v bc Grid Figure 4.13 Control Block Diagram for Field Orientation Control of a DFBM 4.3 Conclusions In this chapter, the principles of field orientation control of a DFBM, especially for doublyfed power generation applications, are investigated. 94

113 Based on the analysis of steady state operation of the DFBM in the field orientation control, in the three types of cases, the equivalent circuit of a DFBM could be transformed into the same form as an induction machine, a wound-rotor synchronous machine, or a conventional DFIM, respectively. Through the proper vector control of the current of one stator winding, the active and reactive power could be independently controlled, while the terminal power factor of the stator windings could be intentionally regulated to be unity, lagging or leading. With the same basic concepts of the steady state field orientation control, concerns about the dynamics are discussed and analyzed in the rotating d-q reference frame. The major difference between the steady state and dynamic behaviors concerns the oriented flux. The transient characteristics and expression of the flux linkage and torque are discussed. Finally, the implementation of the field orientation of a DFBM is investigated. 95

114 Chapter 5: Design, Construction and Experimental Study of the Prototype DFBM System To achieve a design of a DFBM with high efficiency, many factors need to be considered. In this chapter, the challenges of designing a high-efficiency DFBM system are highlighted. Following the challenge description are the identified solutions to the optimal design. Using Finite Element Analysis (FEA), the thesis presents the original design of a DFBM and system in a power rating of 00kW for a speed range of 400-1,00 rpm. The designed machine is built and tested in the laboratory and both of the steady state and dynamic experimental results are presented and analyzed [49]. 5.1 Energy Efficiency of a DFBM To maximize energy efficiency of a DFBM is equivalent to minimizing various losses, mainly the iron and copper losses for the machine operated in various load conditions [49]. First, considerations of minimizing copper losses immediately exclude the selection of a rotor with nested cage circuits for the DFBM design. This is because for the DFBM with the nested cage rotor, the modulation function of the rotor is obtained at the costs of currents in the nested cages, inherently causing significant conduction losses. If choosing the current-free reluctance rotor, there will be no rotor copper losses while achieving the goal of modulating the two stator MMFs. While minimizing copper losses favors a current-free reluctance rotor, there are still choices among the various reluctance structures: simple saliency, radially-laminated reluctant segments, axially-laminated and others. As discussed before, the simple salient rotor is easily eliminated for 96

115 its poor modulation capability. If turning to the axially-laminated rotor for greater modulation capability, the eddy current losses become unacceptable. It is logical that a radially-laminated rotor in segments is chosen over the axially-laminated rotor, if equal or stronger modulation capability is achievable. The design of a radially-laminated segmental rotor to achieve large modulation capability and minimized eddy-current losses seems the only hopeful solution to a high efficiency DFBM. A detailed design approach of a radially-laminated rotor is discussed in the next section [49]. 5. Torque Density of a DFBM In the previous publication, it was made clear by both the linear and non-linear models that for a DFBM, when one set of stator windings is excited, back EMFs will be induced in the other set of stator windings of different pole numbers, due to mechanical rotation of the rotor [33]. The induced EMFs under the influence of a moving rotor are the keys for a DFBM to accomplish electromechanical energy conversion because the induced voltage is termed induced speed voltage. Assuming that a set of currents with the same frequency as that of the induced speed voltage are injected into the second set of stator windings, then the electromechanical power and electromagnetic torque occur. The general form of the torque production in DFBM is: E I E I I I (5.1) I where the E 1 and E, are the induced back EMFs, the speed voltages associated with the variations of the mutual flux linkages; I 1 and I are the phase currents; is the angle between the induced speed voltage and the current; and m1 and m are the mutual flux linkages under the 97

116 given currents. Note that in the torque derivation, the relation m1 / m =I 1 /I is used and the frequency constraint given in Eq. (1.) is observed [49]. Examining Eq. (5.1), the torque production is related to the DFBM magnetic structure. Note that in the equation, the currents, I 1 and I, and phase angle are externally controlled variables and only the mutual flux linkages, m1 and m are linked to the DFBM parameter (mutual inductance) or its magnetic structure. According to the electric machine fundamentals, the mutual inductance of any electric machine between two windings is proportional to the winding turn numbers and the magnetic permeance of the magnetic flux paths. If the DFBM stator windings and iron laminations are of a traditional design as those in any traditional machine, we are left with choices only in the DFBM rotor design. It is important to note that the function of the DFBM rotor is to modulate one MMF (for example a 6-pole MMF) to create the largest possible number of flux lines in another pole number (for example, the 4-pole flux lines). It is clear that the larger the rotor modulation capability, the better the rotor design and the mutual inductance between two sets of stator windings [49]. Previous investigations on rotor styles indicate that the rotor style has strong effects on the rotor modulation capabilities. For the rotor with nested cage circuit, the modulation effects are medium but rotor currents in the cage circuits are necessary and, hence, conduction losses are inevitable. On the other hand, for the current-free reluctance segmental rotor, the modulation capabilities are diverse, depending on the reluctance structures. Three types of current-free reluctance rotors were investigated in detail, including simple salient reluctance rotor, axiallylaminated reluctance rotor and radially-laminated reluctance segmental rotors [7]. It is discovered that the simple salient rotor, through robust and low cost, has a poor modulation capability and has parasitic pole numbers in addition to the intent segmental number p r. Therefore, the simple salient pole rotor is of little use in DFBM design. The axially-laminated rotor showed very strong 98

117 magnetic modulation, creating the largest mutual coupling between the two stator windings. One major concern with the axially-laminated rotor, however, is its inability to block eddy-current circulation in the planes vertical to the magnetic flux lines that continuously and radically change due to the rotor s magnetic modulation. The resultant eddy currents can cause serious problems for the DFBM: a) heavy eddy current losses; and b) distorted flux line distribution pushed by the large eddy currents. Based on the above considerations, innovative approaches are needed to design the rotor that achieves both strong rotor modulation capability and is immune to eddy current losses [49]. In addition to the rotor style selection and lamination design, it is also found that the combination of the DFBM pole numbers are of great influence to the rotor modulation and, thus, to the mutual coupling of the two stator windings. In [7], three cases of pole number combinations are investigated using the same stator frame and lamination structures: a) p=1, q= and p r =3; b) p=1, q=3 and p r =4; and c) p=, q=3 and p r =5. With finite element analysis for the conditions of the same currents, the torque production for the 4/6-pole combination (p r =5) is 40-50% more than what is achieved in the other two cases. Returning to the study posted in Chapter.4, it is known that the mutual coupling between the 4 and 6-pole windings in terms of flux density is more effective than that of the 4/8 pole combination. Therefore, the investigation confirms that the rotor modulation capability of the 4/6-pole combination is stronger than that of the 4/8 combination, resulting in higher torque production. To achieve a motor design with high efficiency performance, the 4/6-pole combination is chosen for the prototype motor design and construction [49]. The strong impact of the DFBM pole number combination on DEBRM is obvious. The results of torque capability investigation are consistent with those from the investigation of the induced speed voltages and the effective air-gap flux density of the DFBM. 99

118 5.3 Sizing of the Prototype DFBM The sizing of the 00kW/1,00rpm DFBM begins with a comparable and conventional wound-rotor DFIM. Since the DFBM to be designed relies on the rotor modulation to create mutual coupling between the two sets of stator windings with different pole numbers, the frame size has been purposely enlarged by 5%, compared to that of the conventional doubly fed induction machine, to take its inherent lower mutual coupling into consideration. By trial-anderror, the DFBM machine s main dimensions are determined as listed in Table, together with the DFBM specifications. Power (kw): 00 Rated rpm: 1,00 Stator OD (mm): 740 V line (volts, rms): 380 Power Grid Hz: 50 Stator ID (mm): 501 I 1 (amps, rms): st Winding: 3-, 4-pole Rotor OD (mm): I (amps, rms): 15.5 nd Winding: 3-, 6-pole Rotor ID (mm): 00 Power Factor: variable Rotor Segmts: 5 Length (mm): 600 Cooling: water Insulation Class: F Air-Gap (mm) 0.8 Table Specifications and Main Dimensions of the Prototype DFBM As summarized in the table, the DFBM is designed with two sets of stator windings, one for the 6-pole and another for the 4-pole. The synchronous speed of the designed DFBM is set at 600 rpm and, in order to deliver the rated power of 00kW, the DFBM needs to run at a super synchronous speed of 1,00rpm. In operation, the second stator winding of the 6-pole will be connected to the power grid of 50Hz while the primary stator winding of the 4-pole will be controlled by a bi-directional converter, consisting of two inverters in back-to-back connection. The stator lamination of the prototype DFBM is shown in Figure

119 Figure 5.1 Stator Lamination of the Prototype DFBM 5.4 Segmental Rotor Design of the Prototype DFBM The emphasis of the DFBM design is placed in its current-free rotor since it significantly affects its power density and energy efficiency. As indicated in Figure 5., the rotor is designed with five laminated rotor segments while each segment is formed by a stack of radial laminations with a proper pressure. A single sheet of rotor lamination for one rotor segment is shown in Figure 5.3. The designed laminations in the radial direction serves dual purposes: a) to force the magnetic flux lines travelling along the five paths imposed by the designed magnetic paths; and b) to minimize the eddy-current losses by orienting the lamination parallel to the magnetic flux lines. 101

120 The ratio of air space to the width of the magnetic path is carefully maintained at :3, so that when the full load currents apply, the iron materials do not saturate to guarantee strong modulation capabilities of the rotor. It is noticeable that the rotor design ensures that the entire rotor body is non-electrical and nonmagnetically conductive except for the magnetic paths designed on purpose. This is because any magnetic and electrical short circuits are not allowed, so as not to misguide the flux lines and degrade the DFBM power density, and therefore reduce the energy efficiency. Also evident is that, if any heat generation caused by losses on the rotor is excessive, the heat dissipation becomes formidable. Precautions have been taken in the rotor design to minimize all possible losses. Additionally, non-electrical and non magnetic conductive epoxy bonding materials are chosen to hold all laminated segments together for rotor mechanical integrity and proper heat dissipation. Figure 5. Rotor Cross-sectional View of the Prototype DFBM 10

121 Figure 5.3 Lamination for Rotor Segments 5.5 Performance Prediction of the Prototype DFBM by the FEA Method As the final step in the design, finite element analysis has been utilized to verify three design objectives: a) mutual coupling and induced back EMFs; b) torque production under various controlled conditions; and c) magnetic field distribution and magnetic loading under no-load and loaded conditions. As shown in Figure 5.4, the magnetic field of the prototype DFBM in a noload condition is asymmetrical, and calculation of the entire magnetic field for the DFBM is needed. Obviously, the simulation result of the magnetic flux distribution agrees with the previous investigation in Chapter. For the first objective verification, only one of the two sets of stator windings is excited with a three-phase sinusoidal current; the induced back EMF voltages are computed for another set of the stator windings based on the winding flux linkage variations as the rotor positions change. This calculation is repeated at many current levels all the way to close iron core saturation. All calculation results of induced voltages are summarized in the magnetizing curves shown in Figure 5.5. The results show that the two sets of stator windings do emulate the functions of the stator and rotor windings, respectively, in a conventional doubly fed induction machine; that is, when one set of windings is excited, an induced speed voltage occurs in another set of windings. In 103

122 Induced Voltage (V) Voltage/V addition, the relationship among the three frequencies constrained by Eq. (1.) is fully verified. Figure 5.4 Asymmetrical Rotor Magnetic Structure of the Prototype DFBM in a No-Load Condition rpm Excitation Current/A Current (A) Figure 5.5 Magnetizing Curve of the Prototype DFBM by the FEA For the second design objective verification, finite element analysis is used to calculate torque production of the designed DFBM. In the calculation, both sets of the stator windings are excited with the frequencies conforming to Eq. (1.). At the same time the relative phase angles 104

123 Torque (N.m) Torqur/Nm between the two stator current vectors are changed as a parameter of the torque production computation. The torque computation by finite element analysis is directly based on the magnetic flux density and field intensity on each element. The results are considered accurate because the complicated geometry of the DFBM and nonlinearity of the materials are taken into full account. The torque production of the DFBM as a function of the phase angle between the currents in the two sets of stator windings is shown in Figure 5.6 for the rated current levels listed in Table. The results clearly show that the rated torque is fully achievable and the designed DFBM power capability is verified. Another result we can derive at the rated power level is the copper losses for the proportional amount of torque. For the rated torque condition (1,600 N.m), the copper losses of both stator windings are summed to be about 3kW, less than % of the rated output power Phase Angle Angle/ of Currents (Degree) Figure 5.6 Torque Capability of the Prototype DFBM with Rated Currents by the FEA For the third objective verification, finite element analysis is used to plot the magnetic field distributions for typical no-load and loaded conditions. It is our experience that difficulties in predicting iron core losses are substantial since both the magnetic field distributions in space and variations in time of the DFBM are not sinusoidal as compared to those in a conventional AC 105

124 Magnitude of Air-Gap Flux Density (T) Mag_B [tesla] machine. We have investigated the typical locations across all iron core areas to identify magnetic saturation points and magnetic field variation patterns. The most important observation is the asymmetrical distribution of air-gap flux density as shown in Figure 5.7. In the figure, the five segments conduct magnetic flux in different amounts and an asymmetrical magnetic distribution forms. The asymmetrical magnetic distribution implies an unbalanced pulling force in the radial direction and non-uniformed torque force distribution along the DFBM air-gap. The finite element field plot suggests special attention: unbalanced radial forces have to be investigated by experimental testing of the designed DFBM XY Plot 1 Curve Info Mag_B Setup1 : Transient Time='0s' Distance [meter] Rotor Position (Degree) Figure 5.7 Magnitude of Air-Gap Flux Density Distribution of the Prototype DFBM by the FEA 5.6 Experimental Results of the Prototype DFBM The designed 00kW/1,00rpm DFBM was built and tested in the laboratory. Photos of the DFBM stator, rotor and total assembly are shown in Figure 5.8. As observed, the stator terminals 106

125 are doubled because of the dual stator windings, while the rotor is current-free with no windings, brushes, and slip rings. The stator cooling is achieved by the water jacket built into the stator frame and the rotor cooling is greatly simplified, solely relying on natural ventilation. The simple rotor cooling method is made possible because of greatly reduced losses and heat generation: no copper losses and only about half of the total iron losses. A high performance water cooled 150kW back-to-back converter has been designed and built to drive the DFBM. Figure 5.9 shows the main circuit configuration of the developed converter module. The specification is as follows: Input Voltage: 380 ~ 560 Vac Output Voltage: 0 ~ 560 Vac DC-bus Voltage: 800 Vdc Rated output current: 50 A Max output current: 300A Converter efficiency: 98.84% (rated power) Water cool flow rate: 1.5 GPM Heatsink temp. rise: deg. (rated power) Switching device (IGBT) rating: 100V, 300 A Switching frequency: 5 ~ 10 khz The overall experimental testing setup is shown in Figure 5.10 and all important system components are labeled. 107

126 a) Stator b) Rotor c) Assembled DFBM Figure 5.8 Stator, Rotor and Total Assembly of the Prototype DFBM 108

127 Converter Module for PWM Rectifier Converter Module for PWM inverter 3-Phase D/Y Transformer DFBM Dynamic Braking Figure 5.9 Main Circuit Configuration of the Developed Converter Module (a) 00kW Dynamometer Testing Bed Figure 5.10 Photos of the Experimental Testing Setup continued 109

128 Figure 5.10 continued (b) 150kW Back-to-Back Converter (c) DSP Based Control System (d) 3-, 690V/300A LCL Filter 110

129 5.6.1 Steady State Testing of the Prototype DFBM The steady state testing of the DFBM focuses on five major aspects: i) no-load induced voltages, ii) iron losses, iii) grid connection with doubly fed control modes, iv) torque-power capabilities, and v) energy efficiency over the designed speed-torque region. For the steady state experimental testing concerning i), the purpose is to experimentally verify the magnetizing characteristics of the designed DFBM. The test results are shown in Figure 5.11 (a) for the two stator winding voltages, and (b) excitation current in one and induced voltage in another set of stator windings. (a) Yellow Trace: Line to Line Voltage of Stator Winding 1 v Blue Trace: Line to Line Voltage of Stator Winding v = 405V(peak) = 8V (peak) (b) Purple Trace: Line to Line Voltage of Stator Winding v = 44V(peak) Green Trace: Phase Current of Stator Winding 1 i = 55.A (peak) Figure 5.11 v-i Waveforms in the No-Load Condition of the Prototype DFBM 111

130 Induced Voltage (V) Also, the measured magnetizing curve of the DFBM is shown in Figure 5.1. As indicated in the figures, the induced voltages are in good sine waveforms and the induced speed voltage levels, as a function of excitation current, in very good agreement with what were predicted by the design and finite element analysis. The results clearly confirm that the design principles and calculation approaches used here are reliable, and the designed DFBM itself is capable of meeting the design expectations Excitation Current (A) Figure 5.1 Measured Magnetizing Curve of the Prototype DFBM For the experimental testing concerning iron losses in ii), first the DFBM is driven by the dynamometer to the synchronous speed of 600 rpm without exciting any stator windings, and input power to the shaft measured. Then, maintaining the same speed as in the first step, one set of stator windings are excited with a controllable current over a predetermined range, corresponding to the specified induced voltage range. For this voltage range, both input power and induced voltages are recorded. Based on the difference of input power in the first and second steps, we obtain the iron losses as a function of operation voltages. Figure 5.13 shows, corresponding to the operation voltage range, the iron losses of the DFBM in a range from several 11

131 Iron Losses (W) hundred watts to as high as kW, depending on the operation voltages Operating Voltage (V) Figure 5.13 Measured Iron Losses in the No-Load Conditions of the Prototype DFBM For the steady state experimental testing concerning iii), the grid connection characteristics and control algorithms, the 6-pole stator windings of the DFBM are fed directly from the power grid and the 4-pole to the controlled power converter. The recorded steady state current and grid voltage waveforms of both the 4-pole and 6-pole winding are shown in Figures 5.14 and 5.15, respectively. As demonstrated by the waveforms, the currents in those two windings are well sinusoidally controlled, even though there are substantial harmonics existing in the grid voltages. Moreover, the DFBM can continuously achieve decoupled reactive and active power through the vector control of current components, i and i, via the converter for lagging, leading, and unity power factor operations. As featured by any doubly-fed machines, the controlled active power through the back-to-back converter set is only a fraction of the total rating of the system, resulting in a low-cost DFBM drive system. 113

132 Time (10.0ms/div) Green Trace: Grid/6-Pole Stator Winding Voltage (50V/div) Yellow Trace: DC-bus Voltage of Converter (100V/div) Purple Trace: 4-Pole Stator Winding Phase Current (100A/div) Figure Pole Stator Winding Current and Grid Voltage Waveforms in Steady State Loaded Conditions 114

133 (a) Lagging Power Factor (b) Leading Power Factor (c) Unity Power Factor (d) 50% Loaded Condition Purple Traces: Grid/ 6-Pole Stator Winding Phase Current (50A/div) Yellow Trace: Grid/ 6-Pole Stator Winding Voltage (50V/div) Figure 5.15 Grid/ 6-Pole Winding Current Voltage Waveforms in Steady State Loaded Conditions For the steady state experimental testing concerning iv) and v), the power capabilities and energy efficiency, the DFBM is loaded with active power on the two stator windings, and input and output power recorded for efficiency evaluation. The power capability testing is conducted in the neighborhood of five levels of torque (400, 800, 1,00, 1,600, and,000 N.m), combined with four levels of speed (400, 600, 900, and 1,00 rpm). In this way, the total tested sample points are twenty. At each operating point, the energy efficiency is examined. As indicated by 115

134 the results, the designed DFBM machine is fully capable of rated power (00kW) and can be 5% above the rated power (50kW). The energy efficiency of the DFBM is plotted in Figure 5.16 by the equal-efficiency contours. Clearly shown by the contour plot, for the tested torque-speed (power) region, 75% of operating points in the regime have efficiencies higher than 90%, 50% operating points higher than 9%, and 35% operating points higher than 94%, including the rated and over-rated power operating points. The torque and power capability of the designed DFBM is very satisfactory and energy efficiency is record-breakingly high in the electric machine family of similar ratings %-98.00% Speed (rpm) %-96.00% 9.00%-94.00% 90.00%-9.00% 88.00%-90.00% Torque (NM) 86.00%-88.00% Figure 5.16 Efficiency Contours in Loaded Conditions Based on Measurements Acoustic noise and vibration have been found to be a problem for the DFBM built. At a fixed rotor speed, the noise and vibration intensities are proportional to the voltage levels applied to the DFBM stator windings, instead of load levels. The relationship between the noise intensity and voltage levels can be attributed to the magnetic flux levels in the DFBM field. This is a direct indication that the asymmetrical magnetic field distribution might be responsible for the acoustic noises and mechanical vibrations. Furthermore, it can be derived that, if the magnetic flux 116

135 distribution of the field can be improved to symmetric around the rotating structures, the noise and vibration problems may be alleviated Dynamic Testing of the Prototype DFBM The dynamic testing of the DFBM system and its grid integration in both the grid-side and stator-side converter focuses on these major aspects: i) grid-friendly integration of the grid-side converter, ii) grid-friendly integration of the stator-side converter, iii) active and reactive power control, and iv) a full load operation in variable speeds. For the dynamic experimental testing concerning i), the grid-friendly integration of the gridside converter, an algorithm of grid voltage-oriented vector control, is utilized to realize the gridfriendly integration and the regulation of the DC bus voltage of the Back-to-Back converter. As shown in Figure 5.17, through the proper control, there is no inrush current flowing from the gridside converter to the grid once the power circuit starts to operate as a PWM rectifier, and so implements the smooth grid-friendly integration. The DC bus voltage of the converter could be well regulated by the control of the active power current component of the grid-side converter. For the dynamic experimental testing concerning ii), the grid-friendly integration of the stator-side converter, the stator flux oriented vector control discussed in the previous chapter remains the key principle of this technology. It is known that the grid voltage waveforms are sampled by the voltage sensors and fed back to the real time controller. Firstly, based on the information of grid and the principle of the proposed field orientation control, by means of regulation of the reactive power current component i, the induced 6-pole stator voltage could be controlled with the same magnitude, frequency and in phase to the grid voltage, regardless of the rotor speed (as indicated in Figure 5.18). After this, as can be seen in Figure 5.19, the grid 117

136 integration of the stator winding is expected to be friendly without any unacceptable current or voltage transients to the grid. Time (0.0ms/div) Yellow Trace: DC-bus Voltage of Converter (100V/div) Purple Trace: Grid-Side Converter Voltage (50V/div) Blue Trace: Grid Voltage (50V/div) Green Trace: Grid-Side Converter Current (100A/div) Figure 5.17 Voltages and Current Waveforms of the Grid-Side Converter during the Process of its Grid-Friendly Integration 118

137 Time (10.0ms/div) Purple Trace: Induced 6-Pole Winding Voltage before Grid Integration (50V/div) Blue Trace: Grid Voltage (50V/div) Yellow Trace: DC-bus Voltage of Converter (00V/div) Green Trace: 4-Pole Stator Winding Phase Current (100A/div) Figure 5.18 Grid, Induced 6-Pole Winding Voltages and 4-Pole Winding Current Waveforms of the Prototype DFBM System before Stator-Side Grid Integration 119

138 Time (40.0ms/div) Yellow Trace: DC-bus Voltage of Converter (100V/div) Blue Trace: 6-Pole Stator Winding/ Grid Voltage (50V/div) Green Trace: 6-Pole Stator Winding Phase Current (100A/div) Purple Trace: 4-Pole Stator Winding Phase Current (00A/div) Figure 5.19 Grid, Induced 6-Pole Winding Voltages and4-pole Winding Current Waveforms of the Prototype DFBM System during the Process of Stator-Side Grid-Friendly Integration For the dynamic experimental testing concerning iii), it is known that the active and reactive power control is equivalent to the vector control of the current components, i and i, respectively. The dynamic responding of the active power generation during the process of the 35kW load on and off is shown in Figure 5.0. The generated active power follows the command well with acceptable transients in the controlled phase current of the 4-pole winding and also the DC bus voltage of the converter. Similarly, the experimental results of the dynamic reactive power control under the step on and off commands are shown in Figure 5.1, where the reactive power and corresponding current components are effectively regulated to follow the commands. 10

139 As observed, during the transient of reactive power, there is no influence to the DC bus voltage of the converter. Time (100.0ms/div) Yellow Trace: DC-bus Voltage of Converter (100V/div) Blue Trace: Active Power Command (50kW/div) Green Trace: Active Power Response (50kW/div) Purple Trace: 4-Pole Stator Winding Phase Current (100A/div) Figure 5.0 Dynamic Performance of the Prototype DFBM System Active Power Control 11

140 Time (100.0ms/div) Time (40.0ms/div) Yellow Trace: DC-bus Voltage of Converter (100V/div) Blue Trace: Reactive Power Command (50kVA/div) Green Trace: Reactive Power Response (50kVA/div) Purple Trace: 4-Pole Stator Winding Phase Current (100A/div) Figure 5.1 Dynamic Performance of the Prototype DFBM System Reactive Power Control 1

141 For the dynamic experimental testing concerning iv), the full load operation in variable speeds, as shown in Figure 5., the prototype DFBM generation system is stably and continuously operated with constant torque speeding up from 00 rpm to 1,000 rpm and also down from 1,000 rpm to 00 rpm. As can be seen, due to the constant torque and grid connection, the active power and current of the 6-pole stator winding is remaining constant under variable speed operations. On the other hand, for the converter controlled 4-pole stator winding, the active power depends upon the rotor speed and is proportional to its changeable electrical frequency. Time (1.0s/div) (a) Rotor Speed from 00 rpm to 1,000 rpm Yellow Trace: DC-bus Voltage of Converter (50V/div) Green Trace: 6-Pole Stator Winding Phase Current (00A/div) Purple Trace: 4-Pole Stator Winding Phase Current (00A/div) continued Figure 5. Continuous Full Load Operation of the Prototype DFBM in a Wide Speed Range 13

142 Figure 5. continued Time (1.0s/div) (b) Rotor Speed from 1,000 rpm to 00 rpm 5.7 Conclusions This chapter presents the latest investigation of optimal design and advanced control results of the DFBM. The challenges of designing a high-efficiency DFBM and system are discussed in detail and the effective solutions to the optimal design and control are identified. Using design principles assisted by the FEA, an original design of a 00kW radially-laminated reluctance DFBM system is achieved, capable of,000 N.m in the speed range of 400-1,00 rpm with a frame size comparable to that of a brush type doubly fed induction machine. The designed machine is built and tested in both the steady state and dynamic conditions, and the experimental results are in excellent agreement with the design objectives. The most successful results include the DFBM power capability of more than 5% over the rated value and energy efficiency higher than 90%, occupying 75% of the designed torque-speed regime. 14 These theoretical and