POWER DECOUPLING METHODS FOR REDUCED CAPACITANCE
SWITCHED RELUCTANCE MOTOR DRIVE
by
Fan Yi
APPROVED BY SUPERVISORY COMMITTEE:
______Dr. Babak Fahimi, Chair
______Dr. Mehrdad Nourani
______Dr. Dinesh K. Bhatia
______Dr. Bilal Akin
Copyright 2017
Fan Yi
All Rights Reserved
To my family
POWER DECOUPLING METHODS FOR REDUCED CAPACITANCE
SWITCHED RELUCTANCE MOTOR DRIVE
by
FAN YI, BS
DISSERTATION
Presented to the Faculty of
The University of Texas at Dallas
in Partial Fulfillment
of the Requirements
for the Degree of
DOCTOR OF PHILOSOPHY IN
ELECTRICAL ENGINEERING
THE UNIVERSITY OF TEXAS AT DALLAS
August 2017
ACKNOWLEDGMENTS
I would like to take this opportunity to thank all the people who have supported and helped me during my graduate study.
I am extremely grateful to my advisor and the founding director of the Renewable Energy and
Vehicular Technology (REVT) Laboratory, Dr. Babak Fahimi, who has always been supportive and guided me through my Ph.D. study. His illuminating and insightful view of power electronics and motor drives makes every discussion with him a wonderful and valuable learning experience.
Dr. Fahimi also has provided numerous opportunities for me to obtain skills, gain experience, and meet with people from industry and academia. I am greatly honored to have him as my Ph.D. advisor.
I would like to thank my committee members, Dr. Akin, Dr. Nourani and Dr. Bhatia, without whose valuable comments and suggestions I would not have completed my dissertation.
My appreciation also goes to my friends and colleagues, especially Wen Cai and Zhuangyao Tang.
I feel lucky to have their support both in research and life.
Finally, I would like to show my gratitude to my parents, Jijun Yi and Wenhui Lei, for their endless and unconditional love.
June 2017
v
POWER DECOUPLING METHODS FOR REDUCED CAPACITANCE
SWITCHED RELUCTANCE MOTOR DRIVE
Fan Yi, PhD The University of Texas at Dallas, 2017
ABSTRACT
Supervising Professor: Dr. Babak Fahimi
Limited fossil fuel resources and environmental concerns are driving industries towards more energy efficient and environment friendly solutions. Players in the automotive industry are producing increasing amount of hybrid electric vehicles and full electric vehicles. Thus, the electric drive system, as an integral part of electric vehicles, is receiving substantial attention from both the industry and academia. Many commercially successful electric vehicles utilize permanent magnet synchronous motor (PMSM) in the electric drive system due to its high torque and power density, and high efficiency. However, in recent years, the uncertainty of the pricing of rare earth materials leads to extensive investigation of rare earth material-free electric machines. Among them, switch reluctance motor (SRM), featuring simple and rugged structure, low cost, and high reliability is a serious contender for electric vehicle applications.
Due to its operation principle, the power of a SRM inherently greatly fluctuates in both motoring and generating modes of operation. This characteristic requires high capacitance in the SRM drive system, which causes increase in volume and decrease in reliability, thus preventing the adaptation of SRMs in electric vehicles, despite their advantages over other competing types of machines.
vi
Hence, a thorough investigation and methods of mitigation are important to encourage further adoption of SRMs in the automotive industry.
In this dissertation, operation principle and energy conversion process in SRMs are introduced first to facilitate understanding of the high capacitance requirement in SRM drive systems. A topology that can greatly reduce such requirement is introduced, with its operation principle and control strategy analyzed. Methods to improve the control of the topology and to allow generating mode with SRMs are proposed. Furthermore, a generalized method of reducing capacitance requirement of SRM drive systems is developed. Based on the generalized method, a better topology is then proposed. The operation principle and control strategy of this topology are also discussed. Comprehensive simulations and experiments are conducted to validate the proposed methods, and the results are included in this dissertation.
vii
TABLE OF CONTENTS
ACKNOWLEDGMENTS ...... v
ABSTRACT ...... vi
LIST OF FIGURES ...... xi
LIST OF TABLES ...... xiv
CHAPTER 1 INTRODUCTION ...... 1 1.1 Background Information ...... 1 1.1.1 History of SRM ...... 1 1.1.2 Operation Principle of SRM ...... 3 1.1.3 Energy Conversion in SRM ...... 8 1.1.4 Design and Control of Conventional SRM Drives...... 14 1.2 Literature Review of Capacitance Reduction for Power Converters ...... 18 1.3 Research Motivation and Objectives ...... 21
CHAPTER 2 POWER DECOUPLING WITH THE INTEGRATED MULTI-PORT CONVERTER...... 23 2.1 Introduction to the IMPC ...... 23 2.2 Mode Analysis and Modeling ...... 27 2.2.1 Mode Analysis...... 27 2.2.2 Modeling of the Drive System ...... 35 2.2.3 Current Ripple Coupling Relationship ...... 43 2.3 Control Strategy ...... 47 2.3.1 Control Strategy Description ...... 47 2.3.2 Repetitive Control ...... 49 2.3.3 Repetitive Controller Design ...... 51 2.4 Simulation and Experimental Results ...... 52 2.4.1 Simulation Results...... 53 2.4.2 Experimental Results...... 57 2.5 Summary ...... 63
viii
CHAPTER 3 GENERALIZED POWER DECOUPLING AND THE QUASI-Z-SOURCE INTEGRATED MULTI-PORT CONVERTER ...... 65 3.1 Generalized Power Decoupling Concept for SRM Drives ...... 66 3.2 Introduction to the Z-Source Family Converters ...... 68 3.3 The Quasi-Z-Source Integrated Multi-Port Converter for SRM Drive ...... 71 3.3.1 Topology Derivation of the ZIMPC ...... 72 3.3.2 Capacitance Requirement Using the ZIMPC for SRM Drive ...... 75 3.4 Control Strategy ...... 77 3.4.1 Mode Analysis...... 77 3.4.2 Generalized Modeling ...... 82 3.4.3 Multi-Objective Control Method ...... 88 3.5 Simulation and Experimental Results ...... 90 3.5.1 Simulation Results...... 90 3.5.2 Experimental Results...... 95 3.6 Summary ...... 104
CHAPTER 4 PRACTICAL CONSIDERATIONS ...... 106 4.1 Generating Mode of Operation ...... 106 4.1.1 SRM Drive System in Generating Operation ...... 107 4.1.2 Generating Operation of the IMPC Topology...... 107 4.1.3 Generating Operation of the ZIMPC topology ...... 116 4.2 Efficiency Analysis ...... 118 4.3 Volume Analysis ...... 125 4.4 Summary ...... 128
CHAPTER 5 CONCLUSION AND FUTURE DEVELOPMENT ...... 129 5.1 Conclusion ...... 129 5.2 Future Development...... 130
APPENDIX ...... 132
REFERENCES ...... 133
ix
BIOGRAPHICAL SKETCH ...... 138
CURRICULULM VITAE
x
LIST OF FIGURES
1.1 SRM in electric vehicle applications (courtesy Nidec SR Drives) ...... 2
1.2 Configuration of PHEV and BEV...... 3
1.3 Geometry and simulated flux path of a 6/4 SRM ...... 4
1.4 Single-phase basic machine with flux path ...... 5
1.5 Phase inductance versus rotor position of the single-phase machine ...... 5
1.6 Electromagnetic torque direction of the single-phase machine ...... 6
1.7 Inductance profile and example excitation profiles for motoring and generating modes of operation of a three-phase SRM ...... 7
1.8 Flux versus current plot with energy relationship...... 8
1.9 Energy conversion in motoring mode ...... 9
1.10 Power of SRM, source versus time plot and capacitor voltage versus time ...... 11
1.11 Power transfer in a SRM drive system ...... 11
1.12 Energy conversion in generating mode...... 12
1.13 A 100 kW SRM drive ...... 14
1.14 ASHB topology for SRM drive ...... 15
1.15 Hysteresis control of phase current ...... 16
1.16 Topologies with reduce number of cables ...... 17
2.1 Derivation of the IMPC topology ...... 25
2.2 Four modes of the IMPC topology ...... 30
2.3 Important waveforms of the IMPC topology ...... 30
2.4 Alternative configuration of the IMPC topology ...... 34
xi
2.5 Simplified IMPC topology for modeling ...... 36
2.6 Bode plots for the transfer functions from the two disturbances to dc source current ...... 45
2.7 General one-degree-of-freedom feedback control system model ...... 46
2.8 Control diagram for the SRM drive using the IMPC topology ...... 47
2.9 Conventional and modified structures of the plug-in repetitive controller ...... 50
2.10 Frequency Response of the repetitive controller ...... 51
2.11 Simulation waveforms of the IMPC topology ...... 55
2.12 Simulation waveforms of the input current without and with repetitive control ...... 56
2.13 Experimental setup...... 58
2.14 Experimental waveforms for comparison between ASHB and IMPC topologies ...... 60
2.15 Experimental waveforms and FFT analysis results ...... 61
2.16 On-the-fly insertion of the repetitive controller ...... 63
3.1 ASHB topology with high capacitance requirement ...... 67
3.2 Generalized power decoupling topology with multiple ports for reducing capacitance requirement ...... 67
3.3 Two Z-source inverters ...... 70
3.4 Derivation of the ZIMPC topology ...... 73
3.5 Important waveforms of the ZIMPC topology ...... 78
3.6 Five modes of the ZIMPC topology ...... 80
3.7 The simplified ZIMPC topology for modeling and control design ...... 83
3.8 The control diagram for the proposed topology ...... 88
3.9 Simulation waveforms in steady state...... 93
3.10 Simulation waveforms of speed control with increased load torque ...... 94
xii
3.11 Photo of the test setup ...... 96
3.12 Experimental switching waveforms ...... 97
3.13 Waveform showing the capacitor voltage and current of the two phases ...... 98
3.14 Experimental waveforms and FFT analysis results ...... 100
3.15 Experimental waveforms of sudden increase of speed ...... 102
3.16 Experimental waveforms of speed control with increased load torque ...... 103
3.17 Experimental efficiency test results ...... 104
4.1 Simulation waveforms of generating mode using the IMPC topology in steady state ....110
4.2 Dynamic simulation waveforms of generating mode with speed control ...... 111
4.3 Experimental setup...... 113
4.4 Experimental results of generating mode using the IMPC topology ...... 115
4.5 Experimental results of seamless transition from motoring mode to generating mode using the IMPC topology ...... 116
4.6 Simulation waveforms of generating mode using the ZIMPC topology ...... 118
4.7 The derivation of an alternative configuration of the IMPC topology ...... 119
4.8 Current distribution in the boost unit of the IMPC topology ...... 121
4.9 Efficiency comparison of different topologies ...... 122
A.1 Cross-section and 3D view of the 2-phase SRM ...... 132
xiii
LIST OF TABLES
2.1 Parameters of the Motor Drives in the Experiments ...... 53
3.1 Comparasion between the ZIMPC and the ASHB Topologies ...... 75
3.2 Parameters of the Simulation Models ...... 91
3.3 Parameters of the ZIMPC-Based Motor Drive ...... 95
A.1 Parameters of the Switched Reluctance Motor ...... 132
xiv
CHAPTER 1
INTRODUCTION
In this chapter, background information of Switched Reluctance Motor (SRM), its typical driving circuit and control strategy is provided first to show the reason for high capacitance requirement in SRM drives. Subsequently, the literature review of relevant research work aiming at reducing capacitance requirement of SRM drives is presented. Lastly, the research motivation and objectives are introduced.
1.1 Background Information
1.1.1 History of SRM
Switched Reluctance Motor (SRM) is a type of electric machine that generates reluctance torque only, which means that the torque generation is solely dependent on the variation of magnetic reluctance. Developed shortly after the discovery of electromagnetism in 1820s-1830s and the invention of the first electromagnet by William Sturgeon in 1824, SRM is considered one of the earliest-invented electric machines. Notable early prototypes of electric motor employing the switched reluctance principle include those invented by W. H. Taylor and Robert Davidson around
1838 to 1940 [1].
Although a series of improvements were made to the early SRM prototypes, interests mostly shifted to dc machines and ac machines since lack of reliable current commutation method caused poor performance of SRMs. However, thanks to the invention and development of power semiconductor devices and digital control, SRM drive systems are again being considered for a
1
variety of applications. Also, advancement in computer technology allows for comprehensive performance analysis and design optimization, leading to better exploitation of SRM’s advantages.
The main advantages of SRM are summarized as follows.
• Simple and rugged rotor structure.
• Wide speed range and constant power speed region.
• No need for permanent magnets.
• Can easily achieve regeneration and generates no torque when not excited.
• High fault tolerant capability due to multi-phase configuration.
(a) (b)
Figure 1.1. SRM in electric vehicle applications (courtesy Nidec SR Drives [3])
Nowadays, thanks to its advantages over other types of electric machines, SRM becomes a serious contender in pumps and compressors, appliances, conveyors, electric propulsion, and other applications.
Especially, SRMs find their applications in various types of electrical vehicles (EVs) including full-electric vehicles and hybrid electric vehicles [2]. Two examples of electric vehicles utilizing
SRM are shown in Figure 1.1 [3]. Figure 1.1a shows a hybrid electric bus, and Figure 1.1b shows
2
an electric all-terrain vehicle. The structures of a plug-in hybrid electric vehicle (PHEV) and a full- electric vehicle or battery electric vehicle (BEV) are shown in Figure 1.2, where the electric motor can be SRM. Here, the power source for the SRM will be the onboard battery pack.
PHEV BEV
Electric Electric ICE Motor Motor
Inverter Inverter
Gas Tank
Figure 1.2. Configuration of PHEV and BEV
1.1.2 Operation Principle of SRM
Often categorize as variable reluctance machine, SRM utilizes no Lorentz force while rely on the variation of magnetic reluctance to produce torque. To illustrate the operation principle of SRMs, a typical 3-phase SRM with 6 stator poles and 4 rotor poles (6/4 pole configuration) is simulated with ANSYS Maxwell. As illustrated in Figure 1.3, both the stator and the rotor are constructed with ferromagnetic material and have high saliency. Two stator poles in opposite position (180 mechanical degrees apart) form a pole pair and are configured as one phase. The inductance of the phases changes significantly as the rotor poles move to different position relative to stator phases.
There are concentrated coils on the stator poles only (red parts) and no coil on the rotor poles.
3
Figure 1.3 shows the magnetic flux lines when only phase A is energized. In the state depicted in this figure, a torque in the clockwise direction is applied to the rotor, since by rotating clockwise, the rotor and stator will form a flux path with less reluctance than its current position.
Figure 1.3. Geometry and simulated flux path of a 6/4 SRM
The main flux path in Figure 1.3 can be simplified as a single-phase basic machine with stator winding shown in Figure 1.4, which has 2 stator poles and 2 rotor poles (2/2 pole configuration).
Since the single-phase machine has two rotor poles, it has two electrical cycle per mechanical cycle. For this machine, if saturation is neglected, the inductance variation of the stator winding versus rotor position is plotted for one electrical cycle in Figure 1.5.
4
Figure 1.4. Single-phase basic machine with flux path Inductance
Unaligned Aligned Rotor Angle
Figure 1.5. Phase inductance versus rotor position of the single-phase machine
With the single-phase basic machine, the basic principle of operation of the SRM can be explained. In each electrical cycle, there are two equilibrium points: the aligned position and the unaligned position. For the aligned position, the reluctance reaches the minimum value, and any movement of the rotor will cause an increase in reluctance. For the unaligned position, the reluctance reaches the maximum value, and any movement will cause a decrease in reluctance. In
5
any position between the equilibrium points, if the stator phase is energized, the rotor will tend to move to the position where minimum reluctance is obtained, which is the aligned position. Thus, in the position depicted in Figure 1.4, when there is enough current in the winding shown, there will be attracting force on the rotor, and torque is generated in the clockwise direction.
Figure 1.6. Electromagnetic torque direction of the single-phase machine
It is worth noticing that even if the direction of the current in the stator winding is reversed, the same torque will be generated for this position. In addition, if the rotor moves past the aligned position, as shown in Figure 1.6, if there is still current in the stator winding, torque in clockwise direction will be generated and thus, for typical application where only torque in one direction is desired, the stator winding will be energized up to half of each electrical cycle only. Then, it becomes obvious that to properly drive a SRM, the rotor position must be known. The information of the rotor position is usually obtained using a position sensor such as encoder attached to the
6
shaft of the machine, while position sensor-less techniques are also developed to eliminate the position sensor to improve reliability and reduce cost of SRM drive systems.
The single-phase SRM can then be expanded to SRMS with more stator poles and rotor poles.
As explained above, one stator phase can generate torque in up to half of each electrical cycle only.
Thus, to produce continuous torque with less torque ripple, SRMs are usually configured to have multiple stator poles and multiple rotor poles. One example is the 6/4 pole configuration shown before. The inductance profile and example excitation profiles of this SRM is shown in Figure 1.7, assuming rotor angle increases from left to right on the horizontal axis. The red boxes indicate an example excitation profile for motoring mode and the green boxes indicate an example excitation profile for generating mode. This SRM will be able to produce torque with less ripple. Other commonly-used configurations include the 3-phase 12/8, 4-phase 8/6, etc. [4].
Phase A Drive A Drive A
Phase B
Drive B Drive B Inductance Phase C Drive C Drive C
Rotor Angle
Figure 1.7. Inductance profile and example excitation profiles for motoring and generating modes of operation of a three-phase SRM
7
As mentioned above, the SRM can be also used to generate negative torque by simply changing the excitation angles of the machine. In this way, SRM can work as a generator. In this operation mode, the field is still established by the stator current, as will be explained later.
1.1.3 Energy Conversion in SRM
To understand the capacitance requirement in SRM drive systems, it is necessary that one examine the energy conversion in SRM. Like many other types of motors, if losses are ignored, the electrical energy delivered into SRM will be converted to mechanical energy and delivered to the load, or stored in the machine as magnetic energy. This energy conversion can be analyzed with the co-energy theory.
Ψ (V·s) B Ψa θa Em
E c A Ψu θu dΨ
O i (A)
Figure 1.8. Flux versus current plot with energy relationship
Firstly, the energy in one machine phase is analyzed. The energy can be analyzed using the flux linkage versus phase current curve for each phase, where the horizontal axis is the phase current and the vertical axis is the flux linkage. The graph is shown in Figure 1.8. In this figure, the flux linkage curve has three parts: OA, AB and BO. This partitioning is because both the phase current
8
and the phase inductance are changing. The OA part correspond to positions closer to the unaligned position where inductance is low and phase current is rising. The AB part correspond to when the current is held at a constant value. And the BO part correspond to the positions closer to the aligned position where inductance is high and phase current is falling.
Ψ (V·s) B Ψa θa Em
E c A Ψu θu
O i (A)
Figure 1.9. Energy conversion in motoring mode
In motoring mode, the excitation starts at the unaligned position, and ends at the aligned position. Thus, when the machine is operating in the motoring mode, the flux linkage curve will be travelled counter-clockwise, that is, O-A-B-O, as shown in Figure 1.9. In one take a very small time step and thus a small change of the flux linkage, then the amount of energy transferred to the machine in this instance can be represented using the area enclosed by the straight line representing the starting flux linkage, the flux linkage curve, the vertical axis and the straight line representing the ending flux linkage, as shown in Figure 1.9.
It is then clear that before the starting point of part BO, energy is transferred to the machine while for part BO, energy is transferred from the machine. Conversely, for part BO, since the flux
9
linkage is decreasing, so the energy is transferred from the machine. The total OABCO area represents the energy transferred to the machine, which includes area OABO which represents magnetic energy that mostly converted to mechanical energy and area OBCO which represents magnetic energy that mostly transferred back from the machine. Energy of the OABO area is called coenergy which is converted to mechanical work, while the energy of OBCO is the energy store in the magnetic field of the machine phase, and transferred back from the machine, which does not convert to mechanical work. The magnetic energy can be calculated with Equation 1.1.
u E i, d mag a (1.1) a
When the machine is operating in non-saturated mode, Equation 1.1 can be simplified as:
u 11 E i, d a i22 L i (1.2) mag a22i a a a
From the above analysis, one can tell that during one commutation cycle of a phase, the power to the machine varies greatly and even reverses direction if there is no overlap between phase. This observation also justifies the high saturation effect in the phases as can be seen by the shape of curve BO, since if the machine does not operate in the saturation region, a large amount of energy transferred to the machine will be transferred back from the machine. Thus, to improve torque density and efficiency of the SRM drive system, the machine is always designed to be excited into the saturation region.
Considering that the operation of a SRM needs continuous commutation of all the phases, the power to it can be plotted as shown in Figure 1.10. The shape of the valley is also related to the overlap between the excitation positions of phases. Less overlap will result in worse condition
10
since total negative energy will increase. However, less or even no overlap is sometimes the optimal excitation pattern considering maximum-torque-per-ampere control [5].
P PSRM
PSource
t
VCap
t
Figure 1.10. Power of SRM, source versus time plot and capacitor voltage versus time
Then, if one would like the dc source to only provide constant power while all the ripple power be provided by capacitors, the relationship can be illustrated as shown in Figure 1.11.
Capacitors
Pdiff
Dc PSource Circuit PSRM SRM source
Figure 1.11. Power transfer in a SRM drive system
The Pdiff in this figure is mainly caused by two factors: existence of Emag and the change of mechanical power.
11
Ψ (V·s) B Ψa θa Em
E c A Ψu θu
O i (A)
Figure 1.12. Energy conversion in generating mode
In generating mode, the excitation starts at the aligned position, and ends at the unaligned position, though exact angles may change depending on the control target. Thus, in this mode, the flux linkage curve will be travelled clockwise, that is, O-B-A-O, as shown in Figure 1.12.
Following the analysis for the motoring mode, one can tell that the converter has to provide significant amount of magnetic energy to the machine before energy will be generated by the machine. Also, the generation power will decrease as the rotor moves towards the unaligned position. Again, combining all the phases together to get the power generation curve, it is clear that in the generating mode, the output power of a SRM varies greatly. It is worth noting that when in generating mode, it is often that the SRM phase current is not held at a constant value but rather left uncontrolled once excited, which will result in the absence of flat part AB. This is to achieve maximum power generation while partially sacrificing torque controllability. However, the analysis still holds under this condition.
12
The capacitance requirement can be approximated by the energy storage required resulted from the power ripple in a cycle and voltage ripple limit on the dc link capacitors. Also, it can be assumed that the dc source is providing constant power since it is the design goal. Then, the capacitors will need to store the energy which equals the integration of the power when it is higher than the average power over time in a cycle, where the time of a cycle is related to the speed of the rotor. This relationship is shown in Equation 1.3.
11 P CV22 CV C,max C,min PP avg 22 (1.3)
VVVC C,max C,min
Usually, VC is required to be less than 5% of VC, avg when the dc-link capacitors are directly connected to the dc source to limit the dc current ripple. Then, the minimum capacitance can be determined by the energy storage requirement and the voltage ripple requirement.
EE Cmin 222 2 2 (1.4) (VC,min v dc ) V C,min 2 V C,min v dc v dc
This equation also reveals that to reduce the capacitance requirement, one can increase the nominal voltage and/or increase the voltage ripple.
The above analysis for both motoring and generating operation modes reveals that SRMs operating in both modes will cause greatly varying power seen by the converter or driver. If the driver relays only on passive absorption of capacitors in parallel to the dc source, the total capacitance must be very large due to the low voltage ripple requirement by the dc source. In
Figure 1.13, a 100 kW SRM drive is shown. The capacitors take up about half of the total volume, while the other half mainly includes the power devices and the heat sink. In addition, since the frequency of the power ripple changes greatly as the machine speed changes, passive filter cannot
13
be easily designed to filter out the ripple. Thus, active compensation should be utilized to cancel the input current ripple seen by the dc source.
Switches
Capacitors
Heatsink
Figure 1.13. A 100 kW SRM drive
1.1.4 Design and Control of Conventional SRM Drives
With the basic principle of operation explained, the topologies for SRM drives and their control can be introduced.
The control parameters required for a SRM drive include the turn-on angle, the turn-off angle and current.
Usually, phases of a SRM are not directly connected, and each phase is driven independently using one asymmetrical H-bridge (ASHB). The fact that each phase only require current in one direction justifies the use of asymmetrical H bridges. Then, the number of asymmetrical H bridges used in the driving circuit of SRM will be that same as the number of stator phases, which enables the independent control of current in each phase. A capacitance is need in parallel to the dc source
14
to provide ripple power for the motor. The complete ASHB topology for driving a SRM is shown in Figure 1.14.
Phase a Phase b Phase c
Zl
D2 D4 D6 S1 S3 S5
Vin C
D1 S2 D3 S4 D5 S6
SRM
Figure 1.14. ASHB topology for SRM drive
The phase current regulation in this topology is achieved by turning on and off both switches at the same time. Current sensors are put on all the phases so that for each phase the current can be measured. Hysteresis control is usually employed to regulate the current. To better illustrate the current control, only one phase is depicted in Figure 1.15, where the gate signal is shown along
with the phase current waveform. When the phase current decreases to the lower band at time t1
and t3 , both switches will be turned on and kept on until the phase current increase to the upper
band, such as at time t2 , when both switches will be turner off and kept off until the phase current falls to the lower band again.
15
In the ASHB topology, each phase of the SRM is connected to one asymmetrical H bridge, as the name implies. Practically, to reduce the torque ripple of the machine, it is very typical for a
SRM to have more than 3 phases. For a n-phase SRM, there has to be n asymmetrical H bridges and 2 n cables. Increased number of power devices and cable will lead to increase in manufacturing and maintenance cost. As a result, several other topologies have been proposed to drive the machine will fewer power devices and cables. Some of these topologies are shown in Figure 1.16, including the Miller topology and the C-dump topology [6].
Zl
S1 D2 BEMF
Vin C + - iph D1 S2
(a)
on off
g1 & g2
Upper bond iph Lower bond
t1 t2 t3
(b)
Figure 1.15. Hysteresis control of phase current
16
S0 D1 D2 D3
C Vdc D0 S3 S4 S5
SRM
(a) Miller topology
S0 D1 D2 D3
C Vdc D0 S1 S2 S3
L
SRM
(b) C-dump topology
Figure 1.16. Topologies with reduce number of cables
17
1.2 Literature Review of Capacitance Reduction for Power Converters
For other commonly-used electric machine such as three-phase permanent motors and induction motors, in steady state, the total magnetic energy stored in the machine does not change significantly, and the torque ripple is usually smaller than that of SRMs. Thus, almost no ripple power will propagate to the dc source, as the magnetic energy exchange mostly happens between the three phases. But for the SRM, during the period of current commutation of phases, there exists significant energy transfer between the converter and the SRM, which contains much magnetic energy that does not contribute to the output kinetic energy of the machine. The output kinetic power of the SRM in motoring mode, or the input kinetic power in generating mode, also fluctuates as the torque varies. This leads to large power ripple in the dc source if the energy storage element in the converter does not absorb enough power ripple. Thus, in a SRM driver, large capacitance is usually necessary.
The large capacitance requirement is also applicable to many single-phase system, which also suffers from large power ripple in the ac port. When the power ripple is not desirable at the dc source, large capacitance is also needed at the dc port to keep low current ripple from affecting the dc source. Such kinds of dc sources may include photovoltaic panels, fuel cells, battery packs, etc.
Due to the high volume of film capacitors and the short lifetime of electrolytic capacitors [7], many researches have been launched in adopting passive or active approaches to cancel the undesirable power ripple in power converters without using large capacitance. In single-phase systems for renewable energy generations and fuel cell applications, most of the power ripple is concentrated at a certain frequency (100 or 120 Hz), which is twice the ac side frequency (50 or 60 Hz), which simplifies ripple compensation. Liu and Lai analyzed the current ripple generation and propagation
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in fuel cell power generation system, and proposed a dual-loop control method to reduce the current ripple in the fuel cell without modifications to the circuit topology, in [8]. Also for single- phase grid-connected fuel cell power generation applications, authors of [9] proposed to add a center tap to the transformer primary winding and connect a LC branch to it. By modifying the modulation sequence, the power ripple can be provided by the small capacitance in the LC branch.
Wai and Lin proposed to use an extra full bridge unit with a small capacitance to the dc bus to inject the ripple current, so that instead of using large electrolytic capacitors, smaller capacitance can meet the requirement for renewable energy generation applications [10]. Furthermore, in [11], they showed that coupled inductors can be added into several topologies such as bi-directional H- bridge inverter topology and bi-directional DC-DC topologies for actively injecting current ripples into the dc bus with small capacitance. Several new topologies and improved control methods are proposed for inverters and rectifiers with power decoupling capability to mitigate the power ripple in literatures such as [12, 13] for microgrid applications. For instance, [14] proposed a virtual capacitor-based control strategy for better restraining the power ripple in the small capacitance. In
[15], previous methods are summarized and the idea of using three-port converters with tipple port to achieve power decoupling and thus minimize the capacitance of sing-phase inverters and rectifiers is proposed.
Compared with applications investigated in the above literatures, power ripple in SRM drive system is different in several ways, which requires different solutions. First, the frequency of the power ripple in SRM drive systems varies with the motor speed, thus limiting the usage of the presented solutions in SRM drives. Second, in SRM drives, power ripple caused by current commutation and torque variation is nonlinear because of the high nonlinearity presented in the
19
SRM, which contains harmonics distributed in different frequencies instead of mainly concentrated on a certain frequency. Wide-spectrum harmonic requires different control methods to compensate. Third, the power ripple frequency can be much higher than double-utility frequency because of wide speed range of the SRM, which features high-speed operation. Hence, it is desirable to investigate solutions for power ripple control specifically for SRM drive systems.
There are mainly three ways to reduce the capacitance requirement in SRM drive systems, namely modifying the machine topology, the excitation profile, and utilizing new driving circuit topologies. Several literatures proposed to change the SRM design to reduce the power ripple generation. A specific current profile is proposed for SRMs to reduce the input current pulsation in [16], but this method is only applicable to pseudo-sinusoidal SRMs rather than regular SRMs.
An additional auxiliary winding is also proposed in [17] to buffer the ripple power, but the additional winding will affect the optimal design for performance and cost of existing SRMs.
Similarly, sinusoidal bipolar excitation with no current commutation is proposed for regular three- phase SRMs in [18] to reduce the power ripple on the SRM side. However, the optimal torque generation will be affected and the maximum-torque-per-amperage cannot be realized. Direct dc- link voltage control was realized by modifying the current commutation in phase in [19, 20], so that a smaller dc-link capacitance can be used without significant negative effects on machine performance. However, this research is not focused on the power ripple issue of the dc source so the effects on it is not investigated. Similarly, W. Suppharangsan proposed an alternative current control technique and current profile in place of the conventional hysteresis current control and trapezoidal current profile for dc-link capacitor minimization in [21]. However, the current stress for switches and diodes would increase and the efficiency will be adversely impacted. McDonald,
20
et al. proposed to use the magnetically biased inductor made with the soft magnetic composite material as the inductor in the passive LC filter to accommodate for the variable frequency of the current ripple in [22], but the design of the inductor is rather difficult and the target machine and its operation conditions have to be taken into consideration. In [23], split dc-link capacitors technology is presented to reduce the dc-link capacitance requirement of two-phase SRMs under the precondition of balanced energy consumption between two capacitors.
1.3 Research Motivation and Objectives
In EVs, the dc source would often consist of Lithium-ion (Li-ion) battery packs because of its high power and energy density. Such large ripple current required by SRM would cause several problems: (1) excessive temperature rise occurs in the battery pack which leads to bigger cooling system and even thermal management requirement, (2) capacity fading resulted from the excessive temperature rise [24], and (3) pulse charging and pulse discharging is reported to be detrimental to Li-ion batteries’ performance [25]. The latter affects the accuracy of battery monitoring and management [26], which might further run to battery’s safety issue [27]. As a result, the cost and size of the battery pack and thermal management usually form a major part of the overall system.
Conventionally, large electrolytic capacitors are used to restrain this undesirable ripple power, however, the theoretical lifetime of electrolytic capacitances is much shorter than the lifetime of semiconductors and other passive components [28, 29].
A comprehensive review of previous efforts to reduce the high capacitance requirement of SRM drive reveals that further investigation on this topic is needed to provide better topologies and control strategies.
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Moreover, SRM allows for bi-directional power conversion, which means that it can operate in both motoring and generating modes. The latter is vital for EV applications since it enables regenerative braking. This can help to extend the driving range of vehicles by harvesting and converting kinetic energy to electric energy and charging the batteries during the braking. Similar to the large ripple in the power drawn by the SRM during motoring operation mode, the generating operation mode also generate power with large ripple. Therefore, it is important to study the converter and control strategy performance in generating operation mode, and develop a flexible power flow control method that can achieve seamless transition between the two operation modes.
To summarize, the research objectives include:
• Investigate the derivation of topologies for reduced capacitance SRM drive. Develop
topologies according to the transient power unit-based generalized topology for reduced
capacitance SRM drive; Modeling and theoretical analysis of derived topologies;
Extending of the concept or the topologies for other drive applications.
• Develop control strategies suitable for the derived topologies and target applications and
analyze the performance of control strategies using the models of derived topologies.
Further investigate on the control strategy to improve drive system efficiency according to
the characteristics of the drive topologies and the SRM.
• Investigate the practical considerations of adopting proposed topologies and control
method: Bidirectional operation capability of proposed topologies; Efficiency and volume
of drives using proposed topologies.
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CHAPTER 2
POWER DECOUPLING WITH THE INTEGRATED MULTI-PORT CONVERTER
In this chapter, a new topology that can achieve reduced capacitance requirement in SRM drives called integrated multiport power converter (IMPC) will be analyzed in detail. This topology has been proved to be able to reduce the capacitance requirement in SRM drive, but further investigation is needed. Starting with mode analysis of the topology, a detailed model of the topology with SRM is provided, based on which advanced control strategy is discussed to further improve the performance of the SRM drive system. This chapter contains the reprints of two previously published papers1 co-authored by the author of this dissertation. The author would like to acknowledge the co-author Wen Cai for his contribution to the work.
2.1 Introduction to the IMPC
A new integrated multiport power converter (IMPC) has been proposed and analyzed for SRM drives in [30]. The capacitance requirement and the operation principle with control strategy of
IMPC is explained, proving that this topology can successfully reduce the capacitance requirement in SRM drives while maintaining very low dc source current ripple. It also has the additional advantages of reduced number of power devices and less bulky wire harness. These advantages
1 © 2015 IEEE. Reprinted, with permission, from Fan Yi, Wen Cai, Modeling, Control, and Seamless Transition of the Bidirectional Battery-Driven Switched Reluctance Motor/Generator Drive Based on Integrated Multiport Power Converter for Electric Vehicle Applications, IEEE Transactions on Power Electronics, December 2015. © 2015 IEEE. Reprinted, with permission, from Fan Yi, Wen Cai, Repetitive control-based current ripple reduction method with a multi-port power converter for SRM drive, IEEE Transportation Electrification Conference and Expo (ITEC), June 2015.
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make it a potential candidate for EV applications with battery packs. However, the topology is not analyzed in detail to show it effects on the performance of the SRM when used in place of conventional topologies such as the ASHB topology. In addition, the model provided cannot be easily used for controller analysis and design. Thus, further discussion is needed to fully utilize the topology.
To facilitate further discussion on this topology, it is shown in Figure 2.1. Also, it derivation with the so-called switch-multiplexing technique is also depicted in Figure 2.1, with details presented in [30].
However, for the topology to be successfully applied for EV applications, the whole drive system including the SRM should be studied. Better control strategy for the current loop for high speed operation is important. Especially, bi-directional power transfer must be realized with the
IMPC topology to achieve regenerative braking in EVs. This chapter develops the model of the overall system incorporating SRM and IMPC. Both motoring and regenerating modes can be described using this model. Subsequently, a new control method is proposed to achieve battery current ripple reduction and phase current control. An extra repetitive control branch is added in order to further improve the performance of the current control loop, especially at high speed operation when the bandwidth of the PI controller is insufficient. In addition, based on a unified model for both motoring and regenerating modes, the proposed control scheme can achieve seamless transition between the two modes, which helps to restrain the overcurrent and improve the system reliability. Experimental results are presented to validate the feasibility and performance of the proposed control method.
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Boost Unit Phase a Phase b Phase c
L C D0 S1 D2 S3 D4 S5 D6
V1
S0 D1 S2 D3 S4 D5 S6
SRM
(a) ASHB topology with additional boost unit
Multiplexed leg
S1 D1 D2 D3
C L
S2 S3 S4 S5 V1
SRM
(b) IMPC topology with a multiplexed leg
Figure 2.1. Derivation of the IMPC topology
Compared to converters utilizing the ASHB topology, the presented IMPC has several advantages [30]. These advantages include:
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• Both the average voltage and the ripple voltage of the capacitors can be large, since the
capacitors are separated from the dc source, which allows for reduction of the capacitance
requirement as much as possible.
• The current through the dc source is filtered by an inductor, thus no large electrolytic
capacitor in parallel with the dc source is necessary. Moreover, the requirement for the dc
source voltage is relaxed and can be lower than what the SRM needs (i.e. it doesn’t act as
dc link).
• The dc link voltage and the excitation voltage is flexible. By increasing the excitation
voltage, the time for de-energizing phases decreases so that conduction angle could be
increased and larger average torque could be obtained. The speed range is widened which
is especially appealing for high speed applications.
• Only five switches, three diodes, one inductor and one small capacitance are needed in the
IMPC in a three-phase SRM drive which means lower cost and higher power density in the
motor drive. If the SRM contains n phases, n+1 legs are necessary so that n+2 switches and
n diodes are needed in total.
• Only n+1 wires are required to drive an n-phase SRM, which means less bulky wire harness.
In addition, like the ASHB, the IMPC can handle bi-directional power transfer between the SRM and the dc source. This is usually a battery pack or fuel cell in vehicular applications.
Even though the current ripple and capacitance reduction function provided by IMPC have been verified, it mainly focuses on the motoring mode of operation. The generating mode hasn’t been discussed using IMPC. In addition, a simple control method is employed to control the converter, which limits its performance. Because dc source current, output current as well as dc capacitor
26
voltage have to be controlled, a multi-loop control method is necessary. Unfortunately, the coupling relationship between different loops has not been estimated yet. This relationship will generate disturbance for all the control loops and worsen its ripple reduction capability.
When employing the IMPC topology instead of ASHB for battery-driven SRMs in motoring or generating mode, there are several control objectives for the system. The battery current and the phase current for SRM should be both always controlled. Also, the capacitor voltage has to be limited within a certain range according to the requirement of the SRM and the voltage rating of the capacitors and power devices. With these requirements, the control strategy becomes more complicated. Furthermore, voltage ripple on dc capacitor cannot be ignored if the battery current is controlled at a constant value because the ripple power required by the SRM should be compensated by the dc capacitors and thus the ripple will be significant. This voltage ripple can also complicate the controller design. To properly design the controller, mode analysis of the
IMPC, along with modeling and analysis of the drive and SRM are needed.
2.2 Mode Analysis and Modeling
2.2.1 Mode Analysis
The mode analysis is important for the understanding of the operation and effective control of the converter and the machine. Since the switch-multiplexing technique is utilized to share same power devices for multiple purposes so that the total number of power devices can be reduced, the boost operation of the boost unit and the machine excitation operation will affect each other. This interaction will lead to very different behavior than when the two converters are simply cascaded into two stages, and will impact the performance as well as the efficiency. Assuming that all the
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switches are operating at the same switching frequency, the following mode analysis is performed to reveal the effects.
For the sake of simplicity, only the operation of one phase will be considered in this analysis.
The simultaneous operation of two phases will be similar. Based on the state of the three switches considered, namely the two switches in the boost unit and the one switch of the phase leg, there are totally four modes. The two switches in the boost unit work in complementary mode with dead band. The four modes for the motoring mode of operation are shown in Figure 2.2. A graph of
illustrative waveforms of the inductor current iL , machine phase current iph and capacitor voltage
vC are shown along with the states of switches S1 and S3 in Figure 2.3. In this figure, the duty
cycles of the two switches are labeled with d1 and d3 .
S1 D1 D2 D3
C L
S2 S3 S4 S5 V1
SRM
(a)
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S1 D1 D2 D3
C
L V1 S2 S3 S4 S5
SRM
(b)
S1 D1 D2 D3
C L
S2 S3 S4 S5 V1
SRM
(c)
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S1 D1 D2 D3
C L
S2 S3 S4 S5 V1
SRM
(d)
Figure 2.2. Four modes of the IMPC topology
Mode 1 2 3 4
g1 d1
g3 d3
iL
iph
vC
t0 t1 t2 t3 t4 t5 t6
Figure 2.3. Important waveforms of the IMPC topology
With Figure 2.3, the four modes are analyzed in detail as follows.
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One switching period of the converter is from t0 to t 4 . Signal g1 and g3 represent the gate
signal for S1 and S3 respectively. S1 and S2 always operate in complementary mode with dead band.
Mode 1: This mode starts at and ends at t1 . In mode 1, both S1 and S3 are off. For the machine phase, this is the de-energizing mode. The phase current will decrease due to the back-
EMF and the capacitor voltage. The magnetic energy stored in the machine will be transferred into the capacitors in the converter. At the same time, the inductor current is rising since it is connected in series with the dc source.
Mode 2: At time , is turned on and S2 is turned off, while is kept off. In mode 2, the machine will be in the freewheeling state, and the capacitors will be charged by the inductor
current. The inductor is being discharged by the voltage vvC dc , and the machine phase is being de-energized by the back-EMF. It is worth noticing that in this mode, because of the switch- multiplexing, two current loops are sharing the same switch , and the current flow directions are different. Thus, since most of the time the phase current of the machine is higher than the
inductor current, the actual current flowing through is iiph L .
Mode 3: At time t 2 , S1 is kept on and S2 is kept off, while S3 is turned on. This is the energizing mode for the machine phase. The phase current rises because of the high capacitor voltage. The current in the inductor keeps decreasing as the same as in mode 2, and the capacitors are being charged with the inductor current, causing the voltage to continue to increase. As seen
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in the previous mode, the switch-multiplexing again causes reduced current flowing through the
switch S1 .
Mode 4: While S3 is kept on, S1 is turned off and S2 is turned on at time t3 . This is another freewheeling mode for the machine, during which the phase current decreases due to the back-
EMF. The inductor current iL will start to increase because of the dc source voltage. Similarly, since the inductor current and the phase current have different directions, the current flowing
through S2 is iiph L . The capacitor voltage does not change in this mode since there is not current flowing through it.
From the above mode analysis, a few important characteristics of the IMPC can be observed and will be useful in later discussions about this topology. They are summarized as follows.
1. The steady-state capacitor voltage is still determined by the duty cycle of switches and , with the average capacitor voltage governed by Equation 2.1.
1 vvC in (2.1) d1
2. The effective exciting voltage applied to the machine phase that magnetizes the phase is
determined by the overlap duty cycle of switches and , which is the overlap of d1 and d3 ,
thus the time between t 2 and . The maximum effective exciting voltage is obtained when
is completely covered by . This gives the maximum value equals to vin . Thus, it is not affected by the average capacitor voltage, unlike the topology before applying switch-multiplexing, which
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has a cascaded boost stage and ASHB stage and can increase the exciting voltage applied to the machine. The average effective exciting voltage can be expressed as in Equation 2.2.
1 ve v in d1 v in (2.2) d1
3. The effective voltage that de-energizes the machine phase is related to the boost duty cycle
instead. This voltage is determined by the time when both S1 and S3 are off. As a result, the maximum de-energizing voltage is obtained when is always off in a period, and can be expressed as in Equation 2.3.
1 vde v in v in (2.3) d1
4. The performance of the machine can benefit from an adjustable voltage applied to it. Since it is desired that the current ripple from the dc source is very small, it is not possible to adjust the capacitor voltage at high frequency. Also, the dc source voltage is fixed. However, point 2 and 3 shows that although there is a maximum possible value for the energizing and de-energizing voltage, they are adjustable by adjusting the length of d3 and its relative position to d1. The freewheeling modes can be utilized to lower the current ripple in the SRM phases, thus lowering the torque ripple. Also, one can increase the average capacitor voltage when high speed operation starts.
5. It is possible to have a different configuration of the IMPC topology with the boost unit, which is shown in Figure 2.4. This topology has the positive end of the dc source and the capacitor connected together. Thus, it will have a fixed effective de-energizing voltage which equals to the
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dc source voltage, while have an effective energizing voltage that is related to the boost ratio. This variant can be of interest for certain SRM designs.
7. The above analysis only focuses on the operation of one phase. When two phases are operating at the same time, one can notice that it is not possible to simultaneously apply energizing and de- energizing voltage to two phases. This phenomenon is observed and studied for single-bus star- connected (Miller) topology. Previous solutions proposed for the Miller topology are also applicable to the proposed IMPC topology, such as in [6].
8. It is also possible and under certain conditions desirable to have different switching frequencies for the two switches in the boost unit and the switches in the phase legs. To have a smaller inductor size, a high switching frequency is desired for the boost unit, while having a lower switching frequency for other switches leads to lower switching losses.
S0 D1 D2 D3 V1
L C S0’ S1 S2 S3
SRM
Figure 2.4. Alternative configuration of the IMPC topology
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2.2.2 Modeling of the Drive System
To study the drive system, a model incorporating both the IMPC and SRM is needed. First, the models of the SRM and the IMPC are analyzed separately. The stator pole number of the SRM is
denoted by n. The current through each phase is ik , k 1, n , and the current through the inductor
is iL . The bridge connected to the dc source is multiplexed, so there is only a single stage. It is desirable to establish a model of the entire system including both the IMPC and the motor windings. For the sake of simplicity, the mutual inductances between different phases are ignored, and speed of the motor is assumed to be constant considering that the time constant of the electrical circuit is much smaller than that of the mechanical system. Based on the average model of the converter with SRM’s phase currents taken into account, Equation 2.4 can be derived.
diL L vin 1 d v C R L i L dt (2.4) dv nn C C11 d iL i k d k i k dt kk11
Where d is the duty cycle of switch S2 ; d1 to dk are the duty cycles of switches connected to
phases 1 through k, respectively; iL is the inductor current, i1 to ik are phase currents of phases
1 through k, respectively; RL is the resistance of the inductor; vC is the voltage of the capacitor.
It is assumed that the current in each phase is continuous when the phase is energized. It is
n n assumed that the current through the SRM phases is Id1 (equals ik ) and Id 2 (equals 1 dikk k 1 k1
), the simplified model of IMPC is shown in Figure 2.5.
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Similarly, SRM can be modeled using electromagnetic equations. Considering that the flux linkage of a phase is related to both the position of the rotor and the current flowing through the phase, the equation for each phase of the SRM is expressed as in Equation 2.5.
dk k di k k d k di k Lik , vk R k i k R k i k R k i k L k, i i k (2.5) dt ik dt k dt dt k
Also, the phase excitation voltage of the converter can be expressed as Equation 2.6.
vk11 d v C d k v C d k d v C (2.6)
The electromechanical equations for SRM can be written as Equation 2.7 using a simplified model introduced in [31].
d v Ri dt d 1 (2.7) TTeL dt J d dt
Where is the flux, is the mechanical speed, Te is the electromagnetic torque, TL is the load torque and J is the total moment of inertia. The calculation of the parameters in generating mode and motoring mode are analyzed in sequence.
S1
L C
S2 V1 I1
Figure 2.5. Simplified IMPC topology for modeling
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1) Magnetic flux linkage
The expression for is shown in Equation 2.8. Since L is related to and i, the derivative of is expressed in terms of θ and L.
d dL dL di L ,() i i i L i (2.8) dt d di dt
Considering that L is a periodic function of rotor position, θ can be expressed in form of truncated Fourier series as shown in Equation 2.9. For the sake of simplicity, only the first three orders are considered, as shown in Equation 2.10.
L, i Ln i cos nN r n (2.9) n0
LiALiALi, 0 1 cos Nrr 1 ALi 2 cos 2 N 2 (2.10)
The coefficients AL0 i , AL0 i , AL0 i are expressed using the inductance at unaligned
position ( Lu ), that at aligned position ( La ) and the inductance at the midway from the aligned
position to the unaligned position ( Lm ).
11 AL0 La L u L m 22 1 AL1 Lau L (2.11) 2 11 AL2 La L u L m 22
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Since saturation effect is negligible at unaligned position, Lu can be assumed constant.
However, La and Lm are highly affected by phase currents because of magnetic saturation. They can be approximated using polynomial functions given by Equation 2.12.
k n Lan i a i n0 k (2.12) n Lmn i b i n0
The inductance at unaligned position and aligned position stay the same for motoring mode and generating mode. If hysteresis effect is ignored, the midway inductance for the two modes should be the same as well. Otherwise, the midway inductance can be replaced with another coefficient:
k n Lm_1 m i b n i (2.13) n0
Based on Equation 2.8 to Equation 2.13, Equation 2.14 is obtained:
dL 1 1 1 L i BLa BL u BL m BL a BL ucos N r di 2 2 2 11 BLa BL u BL m cos 2 N r (2.14) 22 dL Nr BLa BL usin N r BL a BL u 2 BL m sin 2 N r d 2
Where the coefficients are calculated as:
k n BLan i n1 a i n0 k (2.15) n BLmn i n1 b i n0
And the coefficient BLu is fixed as Lu . The derivative of in Equation 2.8 can be re-written as:
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d Nr i La L usin N r L a L u 2 L m sin 2 N r dt 2 11 BLa BL u BL m 22 (2.16)
BLa BL u cos N r 1 di BLa BL u BL m cos 2 N r 2 dt
2) Electromagnetic torque
From the coenergy relations, the electromagnetic torque can be developed as a closed form solution based on the phase current and the inductance at each position.
Nr 2 Te i CL a CL usin N r ( CL a CL u 2 CL m )sin 2 N r (2.17) 4
In Equation 2.17, the coefficients are:
k 2 n CLan i a i n0 n 2 k (2.18) 2 n CLmn i b i n0 n 2
While the coefficient CLu equals Lu . For motoring mode, the phase current exists in the range
[0°, 180°] for . Under this condition, Te is positive. For generating mode, phase current is applied
in the range of [180°, 360°] for . Therefore, Te becomes negative. No matter SRM operates in motoring mode or generating mode, Equation 2.17 is valid. Moreover, all the coefficients ( ,
CLm andCLa ) should be the same for motoring mode and generating mode, which means that the equivalent model doesn’t change during mode transition and a generalized control solution can be designed to cover both modes and the transition.
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Combining Equation 2.14 to Equation 2.17, one can get the state space equations of the SRM drive system, which is shown in Equation 2.19.
di LL v 1 d v R i dt in C L L dv n Cc 1 d i d d i dt L k k k1 N 2ddvRi r iLL sin N LLL 2 sin 2 N kCkk kau r aum r dik 2 dt 11 BLa BL u BL m BL a BL ucos N r BL a BL u BL m cos 2 N r 22 d dt d 1 N r 2 i CLa CL usin N r CL a CLu 2 CL m sin 2 N r T L dt J 4
(2.19)
Where kn[1, ] .
Since the inductance of each phase depends on both the rotor position and the current, it is time- variant and non-linear. It is preferred to linearize it around a steady-state operation point. By linearization, the system performance can be analyzed, and then the corresponding controller design can be completed. However, since the magnetic saturation of SRM will affect the operation point, it is necessary to verify the closed-loop stability using the large-signal model after inserting the controller.
Considering that the rate of variation in rotor speed is much smaller than that of voltage and current, speed can be assumed to be constant (i.e., d dt is fixed). Re-writing Equation 2.19, the equivalent model is shown in form of state-space equations as Equation 2.20.
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x Ax Bu (2.20) y Cx
T x [ vc , i L , i12 , i ,... i n ] T Where u [ vin , d , d12 , d ,... d n ] , T y [ iLn , i1 ,..., i ]
1 D DD DD 01 ... n CCC 1 D R L 0 ... 0 LL A 2DD 2RNN , 1 1 r 0 ... 0 MM ...... 0 ... 0 2DD 2RNN n nr 0 ... 0 MM
n II kL I L 0kn1 1 ... CCC 1 V C 0 ... 0 LL B 22VV , 0CC 0 0 MM 22VV 0CC 0 0 MM 22VV 0CC 0 0 MM
0 0 0 ... 0 0 1 0 ... 0 C 0 0 1 ... 0 , ...... 0 0 0 ... 1
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11 M BLa BL u BL m BL a BL ucos N r BL a BL u BL m cos 2 N r 22 . NLLNLLLN a usin r a u 2 m sin 2 r
Where D represents the duty cycle of the lower switch in the common leg and D1 to Dn are the duty cycles for the lower switches in the other legs which correspond to each stator phase of SRM.
Even though speed variation is slow, the coefficients in Equation 2.20 are changing following
. One can simplify the equations according to the specific operational condition of SRM. For instance, during most of the time, there is only one motor phase working and the others are in idle mode. Hence, the number of the state-space equations in Equation 2.23 can be limited at 3.
Meanwhile, if one uses hysteresis control method to keep the SRM phase current constant, the effect caused by the dc bus voltage can be ignored. Then the SRM phase current can be considered as disturbance for the inductor current control and the dc bus voltage control.
The phase inductance is assumed to be constant and the derivative of phase inductance with respect to position θ is also assumed to be constant. At certain position, these two parameters can be obtained with Equation 2.10 and expressed as Equation 2.21. Variables are perturbed as shown in Equation 2.21.
iLLL I i vCCC V v (2.21) ik I k i k
L, iLALiALi cos N ALi cos 2 N k k0 1 r 1 2 r 2 Li, (2.22) k KNALi sin N 2 NALi sin 2 N r1 r 1 r 2 r 2
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For SRM, only one phase is energized during most of the time. Hence, if only the current flowing through one phase is considered, the small signal model can be derived as shown in Equation 2.23.
diL L 1 D vC V c d R L i L dt dvC C1 DiIdDDiIddk L L k k k ( k ), [1, n ] (2.23) dt
dik Lk Vdd c k DDvRiKi k C k k k dt
There are three output variables and two input variables in this model. However, the control loops for each of the three variables will have separate bandwidths. The phase current control loop should be designed to have the highest bandwidth while the dc capacitor voltage control loop has the lowest bandwidth. As a result, the model can be analyzed as separate single-input-single-output
subsystems. Taking the Laplace transform of Equation 2.23, the relationship between iL , ik and
duty cycles d, dk can be derived as shown in Equation 2.24.
Js i s d s (2.24) L Ts
2 CsVC DDVDDVk C k C J s IkL I 11D Lk s R k K L k s R k K D 22 (2.25) Cs Ls RL 1 D D D k Ls R L Ts 11D Lkk s R K D
2.2.3 Current Ripple Coupling Relationship
Since that the input current, the output current and the dc capacitor voltage should be controlled, the overall system is multiple input & multiple output (MIMO). The coupling relationship has to
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be addressed especially between the input current and output current. The experimental results will indicate the effect caused by coupling relationship. According to the simplified model in Figure
2.5, the state-space equations in Equation 2.26 can be derived.
di LL v i R 1 d v dt in L L C (2.26) dv CC 1 d i I I dt L d12 d
Subsequently, the transfer functions from the different disturbance sources, i.e., Id1 and Id 2 , to the current ripple in the inductor are derived. The dependence of disturbance upon the system can be analyzed using the transfer functions.
i s 1 D2 GsL d1 2 2 Isd1 LCs R Cs 1 D L (2.27) is 1 D Gs L d 2 Is 2 2 d 2 LCs RL Cs 1 D
The main frequency of the current ripple is determined by the structure of the SRM, namely the number of phases and the number of rotor poles for a regular SRM, the phase excitation scheme and the rotor speed. If all stator phases are excited using the same turn-on and turn-off angles and the same current magnitude, the main frequency can be obtained as Equation 2.28.
fm N n phase n pole, rotor (2.28)
Where N is the mechanical speed of the shaft and is measured in revolutions per second. However, if the phases are excited differently, a lower frequency component will be significant:
fm N n pole, rotor (2.29)
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The values of the circuit elements and the configuration of the SRM used in the experiments and the calculation of transfer functions are listed in Table 2.1 in the experimental results section.
Assuming that the SRM analyzed here operates in the speed range of 1000 rpm to 2000 rpm.
The steady-state duty cycle of the upper switch is set at 0.5, which means that the voltage of the capacitor is controlled at twice the voltage of the battery theoretically. Then the parameters in
Table 2.1 can be inserted into the transfer functions Equation 2.27 and Equation 2.28 to obtain their Bode plots. The Bode plots of the above transfer functions are shown in Figure 2.6.
Figure 2.6. Bode plots for the transfer functions from the two disturbances to dc source current
The above transfer functions and the corresponding Bode plots show a very high gain from the disturbance to the input current at the frequency range corresponding to the assumed speed range
of the SRM. Specifically, the gain is about 3.3 dB for transfer function Gd1 and 9.3 dB for transfer
function Gd 2 at 200 Hz, which is the main frequency component caused by the large disturbing currents when the motor is running at a speed of 1000 rpm. Ignoring the measurement errors, the
45
current control loop can be modeled using the general one-degree-of-freedom feedback control
system model shown in Figure 2.7, where K is the controller, G is the plant and Gsd () is the transfer
function from disturbance to the output of the system that can be Gd1 or Gd 2 in the previous
Equation 2.27 and Equation 2.28.
Figure 2.7. General one-degree-of-freedom feedback control system model
The error sensitivity function of the output to disturbance can be expressed as Equation 2.29.
1 Srd I KG G (2.29)
From the state-space Equations 2.26 the transfer function for the plant G can be derived as:
iLC s 1 D I V Cs Gs 2 (2.30) D s LCs RL Cs 1 D
In Equation 2.30, it is shown that Gd can be very large at a frequency range of disturbance d.
Due to its limited gain at higher frequency, using a simple PI controller as K in Figure 2.7 cannot
ensure a small value of Sr to suppress the output error at that frequency range. This reveals that the input current from the dc source is impacted by the current fluctuation incurred by the SRM, and that a simple PI controller will not be able to successfully eliminate this effect. A properly designed plug-in repetitive controller will be designed and inserted into K to provide enough gain
46
at the frequencies where the input current is disturbed to negate this impact.
2.3 Control Strategy
2.3.1 Control Strategy Description
Capacitor voltage Inductor current control loop control loop vcap_ref iL_ref d PWM PI PI 1 + + + generator - Repetitive + - controller vcap iL
ω Adaptive f0, θ0 controller g1 & g2
- g g ωref iref I iph_ref 3 ~ 5 + PI ph_ref Hysteresis IMPC, SRM generator controller and sensors Speed control loop iph Sensed values Control system vcap, iL, iph, ω
Figure 2.8. Control diagram for the SRM drive using the IMPC topology
The proposed control method has been shown in Figure 2.8. There are two control branches, one is IMPC control including dc capacitor voltage and battery current, and the second one is SRM control with speed, torque and phase currents. In IMPC control branch, the average dc capacitor voltage is sampled and regulated at a constant value. The output of this control loop is the battery current reference. With the detected battery current, the duty cycle of the first leg is regulated to make the battery current track the reference. In the inner loop, repetitive controller is inserted in series with PI controller to reduce the low-frequency ripple which cannot be restrained using PI controller alone. On the other hand, in SRM control branch, the speed or torque is expected to be
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regulated. The output of this control loop is the reference for phase currents. Subsequently the phase current is regulated using a hysteresis controller and the dynamic performance is guaranteed.
In Figure 2.8, g1 and g2 are the PWM signals for S1 and S2 , respectively. Meanwhile, g5 , g4
and g5 are the signals for S3 , S4 and S5 .
There is a phase current generation unit I ph_ ref generator in Figure 2.7. This unit is to transfer
the peak current command iref to phase current in each winding. is the electrical rotor angel which changes from 0° to 360ᵒ. When the current command is positive, the phase current command
equals iref when the rotor goes from unaligned position to aligned position. When the rotor passes the aligned position, the phase current reference drops to 0. Under this condition, the motor works in motoring mode. Otherwise, when the current command is negative, the phase current keeps 0 before the rotor goes through aligned position. After that, the current becomes the absolute value of the current reference. This is the generating mode of operation. An example excitation profile is shown in Figure 1.7.
From the proposed control method, it can also be seen that the bandwidth of dc capacitor voltage control loop is less than battery current control bandwidth because the battery current control is considered as an inner loop. This would make the DC capacitor to provide the low-frequency power ripple and restrain the current ripple of the battery. Another advantage is that the energy difference during dynamic response time would also be compensated by the dc capacitor instead of battery. It could remove the overcharging or discharging condition and expand the battery lifetime.
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2.3.2 Repetitive Control
In the control scheme proposed earlier, it is required that the inner current loop must have a higher bandwidth than that of the voltage loop, which provides relatively high dynamics in order to eliminate the impact of the disturbances and track the reference to maintain capacitor voltage.
Although this linear control method is able to stabilize the system and largely reduce the inductor current ripple from the source, its limited dynamic performance prevents it from further reducing the ripple to a desired level, especially when the motor is running at high speed. Considering that the disturbances are repeated under certain frequency related to the rotor speed, and that the speed changes much slower than current, it is proposed to use repetitive controller to increase the control bandwidth and further reduce the current ripple.
Repetitive control is a well-known technique used to reject periodic disturbances or to track periodic reference signals. Repetitive control follows the internal model principle which states that if the closed-loop controller can internally generate the reference signal and/or the disturbance, it can then track the reference or reject the disturbance without steady-state error. Initially proposed by Shinji Hara, et al. in [32] for servo systems, it has been successfully applied to various applications including power electronics circuits and motor drive systems. The authors of [32] also examined the stability of repetitive controller and proposed to use low-pass filter to ensure the stability, which is vital for the successful implementation of repetitive controllers. Many literatures have reported use of repetitive control in PWM inverters to reduce total harmonic distortion [33].
Also, it is applied to the control of motors in hard disk drives to achieve high performance in rejecting disturbances of the control of read/write head position [34]. In [35], it is applied in the control of robotic arms to reduce the tracking error when periodic reference input is given. For
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applications requiring tracking periodic reference or rejecting periodic disturbance, repetitive control has shown easy implementation as well as superior performance.
A typical structure repetitive controller is shown in Figure 2.9a. The repetitive controller structure employed is shown in Figure 2.9b. The major difference is that in conventional repetitive controllers, the period of the reference signal or the disturbance is usually fixed and known.
Examples include the grid frequency. However, in adjustably speed drive system, one cannot assume constant speed, since the speed can be influenced by the drive or by the load. Thus, the disturbance caused by a SRM is more precisely related to the rotor position. To accommodate the changing speed, the conventional fixed-time delay block is replaced with a delay based on rotor position. Instead of delaying the input with a fixed time, the position-based delay block always delays the input signal by a certain mechanical angle which is determine by the stator/rotor configuration and excitation pattern.
+ i Adjustable Low-pass e + Gain delay filter θ Plug-in Repetitive controller
(a) Conventional structure
+ i Low-pass e + Delay Gain filter Plug-in Repetitive controller
(b) Modified structure to accommodate adjustable speed drive
Figure 2.9. Conventional and modified structures of the plug-in repetitive controller
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2.3.3 Repetitive Controller Design
The frequency response of the repetitive controller used in this system is shown in Figure 2.10. It can be seen that in the fundamental frequency and its harmonics, though the low-pass filter suppresses the gain of the repetitive controller, it still has very high gains. Thus, a good steady- state performance of the proposed control method can be expected. However, since the frequency of the phase current would vary following the rotor speed, another adaptive controller is inserted into the control method as in Figure 2.8. This adaptive controller outputs the fundamental frequency of the repetitive controller and compensates for the phase shift caused by sampling, conversion, and control delay.
(a) Without any filters
(b) With moving average filter
Figure 2.10. Frequency Response of the repetitive controller
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In the repetitive controller, a low-pass filter is needed to ensure the stability of the control system. Since the filtered results are not needed instantly and will be fed into the control loop in the next period, it is possible to implement zero-phase low-pass filters, which are non-causal in repetitive controllers. A simple finite impulse response moving average low-pass filter as expressed in Equation 2.31 is used in this paper, because it is easy to design and implement in digital microcontrollers.
1 nq yxni (2.31) 2n +1 i n q
Inserting the low-pass filter into the repetitive controller, the new transfer function can be expressed as Equation 2.32, where q(s) is the transfer function of the low-pass filter.
1 K (2.32) r 1 q ( s ) esf/
There are also other possible choices for low-pass filters which can bring advantages to the performance of the repetitive controller. More discussions on the design of the low-pass filter can be found in the literatures [36, 37].
2.4 Simulation and Experimental Results
The feasibility and the control performance with conventional control methods using IMPC have been verified with simulation and experiments. In this section, comparison of steady-state and dynamic performance between these two topologies at generating mode of operation is developed with emphasis on dc port and the dc bus capacitor voltage. The detailed parameters of the IMPC and ASHB are all listed in Table 2.1. The switching frequency is selected to be 20 kHz in consideration of the power rating of the SRM and the dc bus voltage. After that, two test-beds
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based on the IMPC and the ASHB are built and used to drive the same 2-phase SRM experimentally. The corresponding experimental results will be displayed to compare their performance.
Table 2.1. Parameters of the Motor Drives in the Experiments
Asymmetrical H-bridge converter (ASHB) Parameter Value Input voltage 280 V Switches STGIPS30C60 Dc bus capacitor 660 µF Integrated multiport power converter (IMPC) Parameter Value Input voltage 110.0 V to 128.0 V Dc bus voltage 280 V Switches STGIPS30C60 Switching frequency 20 kHz Inductor 540 µH, 24 mΩ Dc bus voltage 250 V to 350 V Dc bus capacitor 220 µF
2.4.1 Simulation Results
Simulation model based on IMPC with three-phase symmetrical SRM is built in
MATLAB/Simulink in order to verify the feasibility of IMPC in motoring mode since Figure 2.11 shows the steady-state waveforms at generating mode including the flux (Figure 2.11a), the torque
(Figure 2.11b), the battery current (Figure 2.11c) and the capacitor voltage (Figure 2.11d). Even
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though the torque ripple (Figure 2.11b) is large which needs large power ripple through the converter, the battery current is controlled at a constant value (2 A) with small ripple (0.18 A peak- to-peak) in Figure 2.11c. The power ripple is compensated by the dc capacitor which leads to 40
V peak-to-peak voltage ripple as shown in Figure 2.11d.
1) Motoring Mode of Operation
Both the conventional ASHB SRM drive system and the IMPC SRM drive system with conventional control method and the proposed control method are simulated using
MATLAB/Simulink. Moving average filter is designed and utilized in the repetitive controller.
The parameters used in the simulation models are listed in Table 2.1.
(a)
(b)
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(c)
(d)
(e)
Figure 2.11. Simulation waveforms of the IMPC topology
2) Repetitive Control
In this simulation, the speed of the SRM is regulated at 1000 RPM, this is achieved by regulating the reference phase currents using a PI controller for the speed control loop. All phases are excited using the same fixed turn-on and turn-off angles and the same reference current.
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(a)
(b)
(c)
Figure 2.12. Simulation waveforms of the input current without and with repetitive control
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From Equation 2.29 it can be told that the largest frequency content is 200 Hz. This is verified in the simulation using the conventional ASHB. The current waveform clearly indicates a large current ripple of 200 Hz.
The simulation results from different topologies and controllers are shown in Figure 2.12a and
Figure 2.12b. The frequency components of different input current results are analyzed with fast
Fourier transform (FFT). The results of this analysis are plotted in Figure 2.12c.
In Figure 2.11c, one can notice that there are peaks at f0 , which is 200 Hz and its multiples
such as 2 f0 (400 Hz), 3 f0 (600 Hz) and 4 f0 (800 Hz). When the proposed controller is implemented using moving average filter, the 200 Hz component is reduced to 0.15 % of the dc component, while its multiples are greatly reduced as well.
2.4.2 Experimental Results
The experiments are conducted with a special two-phase SRM which has bidirectional startup capability [38]. The SRM employs a shifted two-stack structure with eight stator poles and eight rotor poles on each stack. The coils on the stator of each stack are connected in series to form one phase, and the two stacks are shifted with respect to each other to allow reliable startup and smooth operation. The cross section, including rotor and stator of the SRM used in the experiments is shown in the appendix. A detailed analysis of the motor structure can be found in [38]. Each phase winding has one end connected to the common multiplexed leg with two switches, and the other end connected to phase legs consisted of one diode and one switch. A brushed dc machine with terminals connected to a resistor bank is used as the load for the SRM. The rotor position of the
SRM is detected with an encoder connected at another end of the dc machine.
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The converters are built with intelligent molded power module STGIPS30C60 from
STMicroelectronics. The maximum IGBT collector-emitter voltage is 600 V and the maximum continuous collector current is 30 A. The switching frequency is 20 kHz. The prototype is shown in Figure 2.13. Major parameters are listed in Table 2.1. Three cases are compared with experimental waveforms: ASHB with PI controllers, IMPC with PI controllers and IMPC with proposed control method. All these three control methods are implemented digitally using microcontroller unit TMS320F28335 by Texas Instruments.
Figure 2.13. Experimental setup
In the experiments, the average dc capacitor voltage is controlled at 280 V. When the input current from the dc source is controlled, large voltage ripple on the dc capacitors can be observed because the stored energy in the capacitors are used to compensate the power difference between the motor and the batteries during current commutation periods. However, it is worth pointing out that the capacitance cannot be too small even if the input current can be perfectly controlled, because enough capacitance is necessary to provide sufficient energy without excessive voltage
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drop during startup and to keep the dc bus voltage in a reasonable range. In the prototype, the total capacitance is selected at 220 µF. This is to keep the total voltage ripple less than 70 V to ensure two things: first, the lowest voltage is high enough so as not to impact the performance of the SRM drive, and second, the highest voltage is limited so that the voltage stress of capacitor and switches are limited within safe range.
For the motoring mode of operation, a brushed dc machine with resistor bank is coupled to the
SRM as the load. The SRM is driven by the battery through the converter (ASHB or IMPC), hence the energy is transferred from battery to SRM. SRM converts the electric energy to mechanical energy with positive torque. The dc machine converts mechanical energy to electric energy and dissipates it with the resistor bank load.
Using the conventional ASHB as the drive, current waveforms of the two motor phases and input current waveform are shown in Figure 2.14a. The two phases of the stator are driven alternatively according to the rotor position. For this converter, three 220 µF electrolytic capacitors are connected in parallel in the dc bus and at the input source. Even though large capacitors are used, the input current from the battery still has large ripple and the peak-to-peak value is 13.8 A.
Furthermore, the current becomes negative when the dc bus capacitor doesn’t absorb enough energy during the de-energizing period of a stator phase. The proposed IMPC with conventional control method is tested under motoring mode of operation and the corresponding waveforms are shown in Figure 2.14b.
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(a)
(b)
(c)
Figure 2.14. Experimental waveforms for comparison between ASHB and IMPC topologies
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(a)
(b)
(c)
Figure 2.15. Experimental waveforms and FFT analysis results
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The output current waveform is almost the same. However, the important difference is observed at the input port. The input current and the dc bus voltage are shown in Figure 2.14b (CH2) and
Figure 2.14b (CH1), respectively. The frequency distributions of the input currents are shown in
Figure 2.14c, which clearly shows 85 % reduction of fundamental frequency component and more than 66 % ripple reduction for other frequencies. There is a low-frequency voltage ripple on dc bus, however, the ripple of the input current is reduced significantly. The waveforms reveal that the peak-to-peak current is less than 2.8 A which is only 20 % of the input current when asymmetrical H-bridge converter is used.
Figure 2.15a shows the steady-state waveform with reduced capacitors from 660 µF to 220 µF.
Comparing such waveform with Figure 2.14b, it can be seen that the input current is almost the same, but the voltage ripple at dc capacitor is enlarged which can be estimated with theoretical analysis. After that, the proposed control method is implemented at the same test-bed. The corresponding waveforms are shown in Figure 2.15b. It can be found that the current spike has been removed and the peak-peak value is 0.8 A (5.7 % of the input current when compared to
ASHB). The detailed frequency distribution is listed in Figure 2.15c which reveals the significant current ripple reduction by using the presented control method.
The waveforms in Figure 2.14 and Figure 2.15 suggest that the proposed topology can act as the drive for SRM instead of the conventional ASHB topology and the control method is suitable for the proposed topology.
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Figure 2.16. On-the-fly insertion of the repetitive controller
Figure 2.16 shows the comparative results with/out repetitive controller. Without repetitive controller, the battery current contains 3.6 A peak-to-peak current ripple. After inserting repetitive controller, the peak-to-peak current ripple is decreased to 0.9 A. But the capacitor voltage ripple
(peak-to-peak) is increased from 46.2 V to 68.8 V because more power ripple is compensated by the capacitor instead of the battery.
2.5 Summary
In this chapter, a unified model covering motoring mode and generating mode for SRM drives with the IMPC topology is developed and a generalized control method based on the system model is presented. To further reduce the current ripple during high speed operation, repetitive control is introduced and adopted. The topology with the control method can significantly restrain the low- frequency ripple current of the dc source, has bidirectional power transfer ability, and features reduce power devices count and cable number, which makes it suitable for EV applications.
Seamless transition between generating mode and motoring mode is also possible. The validity
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and stability of the proposed control method with IMPC is verified with simulation and experimental results.
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CHAPTER 3
GENERALIZED POWER DECOUPLING AND THE QUASI-Z-SOURCE
INTEGRATED MULTI-PORT CONVERTER
In the previous chapter, it is seen that the IMPC topology is effective in reducing capacitance requirement, switch numbers and cable numbers. However, the topology has certain limitations and disadvantages as has been revealed. It is then desirable to generalized the idea behind the
IMPC topology and consider additional power decoupling topologies. In this chapter, a generalized power decoupling concept for SRM drive is established from the IMPC topology to facilitate deriving new topologies, and the quasi-Z-source integrated multi-port converter (ZIMPC) is derived from this concept. Then, detailed mode analysis, modeling and control strategy are presented for the proposed ZIMPC topology. Both motoring and generating modes of operation can be realized using this topology. Simulation results show that this topology is effective in reducing the capacitance requirement while overcoming some limitations of the IMPC topology.
In the end, the topology is verified with experimental results. This chapter contains the reprint of a previously published paper2 co-authored by the author of this dissertation. The author would like to acknowledge the co-author Wen Cai for his contribution to the work.
2 © 2016 IEEE. Reprinted, with permission, from Fan Yi, Wen Cai, A Quasi-Z-Source Integrated Multiport Power Converter as Switched Reluctance Motor Drives for Capacitance Reduction and Wide-Speed-Range Operation, IEEE Transactions on Power Electronics, January 2016.
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3.1 Generalized Power Decoupling Concept for SRM Drives
As demonstrated previously, to reduce capacitance requirement in a SRM drive system, one can increase the voltage of the capacitors and/or increase the voltage ripple of the capacitors. However, it is also necessary to maintain low voltage ripple on the input capacitors to avoid high input current from dc source. Having the dc source connected in parallel with the dc-link capacitors means that the converter has no control over the power flow of the dc source and that of the capacitors. Then, if the converter can control the power flow, it can then decouple the power of the dc source, the capacitors and the power of the SRM, so that the dc power source provides only the average power while the capacitors provide the ripple power, during any operating modes of the machine.
In Chapter 2, it has been shown that the boost unit in the IMPC topology has the above- mentioned power decoupling capability, thus reducing the capacitance requirement in the converter. However, a few drawbacks have also been discussed in Chapter 2. Especially, the boost unit in IMPC makes the voltage stress of the capacitor and semiconductors much higher than that in ASHB if high demagnetizing voltage is necessary. This worsens the system efficiency and the performance at high speed (Higher dc voltage is preferred because of faster current commutation process, but it is limited by the voltage rating of the capacitors and power devices.). As a result, it is desirable to derive other topologies that can provide the same power decoupling functionality while overcoming these drawbacks.
According to previous discussion, to derive more power decoupling topologies, the derivation of the IMPC topology can be generalized, as shown in Figure 3.1 and Figure 3.2.
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Large capacitance
Dc Bus . . .
source
-
-
-
Phase a Phaseb Phaseb + Phasea + Phase+ c SRM Phase c
Figure 3.1. ASHB topology with high capacitance requirement
Small capacitance
Dc port
Ripple P
Dc Bus . . .
source PAverage PSRM Dcport Transient Power Unit
Phase a + Phase a - Phase b - Phase b + SRM Phase c + Phase c - ......
Figure 3.2. Generalized power decoupling topology with multiple ports for reducing capacitance requirement
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Figure 3.1 shows the conventional ASHB topology for SRM drives. Each half bridges are shown. Then, the generalized topology is derived and shown in Figure 3.2. In this generalized topology, the boost unit is replaced with a transient power decoupling unit with ports for connections with a dc source, capacitors and motor phases respectively. The power decoupling unit is responsible for controlling the power flow so that the dc source provides the average power and minimized ripple power, and the capacitors provide most of the ripple power. Thus, the required capacitance is greatly reduced. From this generalized topology, it is possible to derive other topologies that can achieve the same functionality by choosing other appropriate power decoupling units and adopting similar control structure. Also, to allow the SRM to operate in both motoring and generating modes, the chosen unit must support bidirectional power transfer between all three ports. To compensate for the increased power device count caused by the additional transient power unit, this generalized topology also depicts the shared leg between all phases as a result of applying the switch multiplexing technique. Though similar to what can be seen in a
Miller topology, this shared leg can be further multiplexed with the power devices required in the transient power unit.
Members in the Z-source converter family have the potential because of their intrinsic multi- port structure of having two capacitors. The ability to boost the dc link voltage higher than the input dc voltage is also a desirable feature for motor drive systems. To select an appropriate topology from the Z-source family, the members are examined.
3.2 Introduction to the Z-Source Family Converters
The first Z-source inverter (ZSI) [39] was proposed in 2002 by F. Z. Peng. ZSI has the ability of boosting the dc link voltage, thus by combining the boost dc-dc stage and the inverter stage for
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electric propulsion systems, it can achieve better efficiency. Right after that, a series of semi-Z- source/quasi-Z-source/trans-Z-source inverters have been presented and studied in [40-43].
Especially, four quasi-Z-source inverters [43] were proposed in 2008 by J. Anderson and F. Z.
Peng to overcome the major drawbacks of the voltage-fed and current-fed Z-source inverters, such as discontinuous input current and high voltage and current stress. In 2013, the Γ-Z-source inverter series are proposed with higher operation gain in [40]. Z-source inverters have been utilized in various applications because of their special impedance characteristic [44, 45]. The bidirectional operation of quasi-Z-source inverter for electric vehicle applications has been studied in [46] by
Guo. With the extra Z-source unit, Z-source family inverters can achieve voltage boost and thus increase the dc link voltage range, which makes them suitable for EV applications. In addition, dead time is not necessary in unidirectional Z-source family inverters, which helps with circuit protection and harmonic reduction.
The voltage-fed quasi-Z-source inverter with continuous input current has been proposed for single-phase photovoltaic (PV) inverter applications in [47] and [48], which also requires low current ripple from the dc source, which is the PV panel in this case. The authors of [48] developed a comprehensive model of the single-phase quasi-Z-source inverter, and provided hardware design guidelines. Especially, due to the characteristics of the voltage-fed quasi-Z-source inverter with continuous input current, it has been considered for double-grid-frequency current ripple suppression for reduced-capacitance single phase PV inverter applications [49]. In this work, because of the fixed frequency of the grid, a proportional resonant controller is used in the current control loop to suppress the double-grid-frequency current ripple. Coupled inductor has been
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reported to be used for the two inductors in the quasi-Z-source unit by Feng Guo, et al. in [46] to minimized the size and weight of the magnetic components.
L2
C1 C2
Vin
L1
Ac Load (Grid, Motor …)
(a) The original Z-source inverter
C1
L1
L2
Vin
C2
Ac Load (Grid, Motor …)
(b) Voltage-fed quasi-Z-source inverter with continuous input current
Figure 3.3. Two Z-source inverters
Since the proposed topology is based on the voltage-fed quasi-Z-source inverter with continuous input current, the steady-state average inductor current and capacitor voltage relationship in this topology will be useful in later discussion. The governing equations for it are shown as follows.
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D VV C1 12 D in 1 D VV (3.1) C2 12 D in P IILL12 Vin
In Equation 3.1, D is the shoot-through duty cycle. The equivalent dc link voltage will be the total voltage of the two capacitances, which equals:
1 VV (3.2) dc12 D in
3.3 The Quasi-Z-Source Integrated Multi-Port Converter for SRM Drive
Since the capacitors in the quasi-Z-source unit are inherently separated from the dc source, they can also be used to compensate power ripple caused by current commutation in SRMs, thereby smoothing the current from the dc source.
By replacing the boost unit with the quasi-Z-source unit, the voltage stress of the capacitors and semiconductor power devices can be dramatically reduced. Compared with existing motor drives or capacitance reduction solutions for SRMs, the presented quasi-Z-source integrated multiport converter (ZIMPC) has three major advantages: first, the capacitance required in this topology can be greatly reduced, with their voltage rating decreased as well. This can contribute to size and cost reduction of the drive; second, it is possible to control the input current at virtually a constant value so that the dc source would not be affected by the large current ripple. Such current ripple is undesirable for dc source, especially battery packs used in electric vehicles; third, this topology can be easily adopted for various types of SRMs directly, including SRMs with arbitrary phase number, or the recently-proposed double-stator SRM, because it has no special requirements for
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motor structure and can be easily expanded to increase phase number. Advanced power flow control for ZIMPC with repetitive control is introduced which can reduce the impact of input current harmonics with varying frequency. In addition, with ZIMPC, it is possible to maintain low capacitor voltages at low speed to reduce power losses, while boost the capacitor voltages and the equivalent phase exciting voltage at high speed to ensure enough torque generation and thus widens the constant power speed range.
3.3.1 Topology Derivation of the ZIMPC
Adding a quasi-Z-source unit in front of ASHB, the topology based on quasi-Z-source unit and
ASHB is shown in Figure 3.4. Since the asymmetrical leg cannot achieve shoot-through mode, an extra shoot-through les is necessary. Therefore, it needs eight switches and six diodes for a three-phase SRM. Subsequently, switch multiplexing technique is employed here to reduce switch number to simplify the topology. In order to illustrate the idea of switch multiplexing, an extra leg instead of a single switch is shown in Figure 3.4. (a).
Switch multiplexing is an effective technique to simplify topologies for multiport systems and may achieve better efficiency, depending on the operating conditions. It is to share some of the power devices of two or more topologies so as to decrease the number of switches and to simplify the overall topology. It is worth pointing out that switch multiplexing is generally accompanied with a modified modulation strategy different than the ones adopted for the topologies before multiplexing. By multiplexing switches, the shoot-through leg and one leg from each phase can be combined into one leg. Based on this method, the quasi-Z-source integrated multiport converter is derived as shown in Figure 3.4.
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Shoot-through Phase a Phase b Phase c leg Quasi-Z-source unit
C1
D1 D3 D5 S7 S1 S3 S5 L1 L2
Vin S9
C2
S2 D2 S4 D4 S6 D6 S8
SRM
(a) The ASHB topology with quasi-Z-source unit
Multiplexed leg Quasi-Z-source unit
C1
D1 D2 D3 S1 L1 L2
Vin S6
C2
S2 S3 S4 S5
SRM
(b) The ZIMPC topology
Figure 3.4. Derivation of the ZIMPC topology
Compared with the conventional topologies introduced in Chapter 1, the presented ZIMPC has advantages listed below:
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• The capacitor is separated from the dc source. Hence the dc source voltage would not be
affected by the capacitor voltage.
• Both the average voltage and the ripple voltage of the capacitor can be large which will
decrease the capacitance value as much as possible.
• The current through the dc source is filtered by an inductor, thus no electrolytic capacitor
is necessary any more in parallel with the input dc source. Moreover, the requirement on
dc source voltage is relaxed, and it can be lower than what the SRM needs since it does not
act as dc link. This is important for electric propulsion drive applications.
• The equivalent dc link voltage is flexible without needing an extra boost stage. By
increasing the dc link voltage, the time for energizing and de-energizing of each phase
decreases so that conduction angle can be better controlled and larger average torque could
be obtained. The constant power speed range(CPSR) is widened, which is especially
appealing for automotive and high-speed application.
• There are six switches, three diodes, two inductors and two capacitors in ZIMPC for three-
phase SRM which can achieve cost reduction and enhance the power density of the motor
drive. Furthermore, if the SRM has n phases, n+1 legs would be necessary so that n+3
switches and n diodes are required.
• The wire harness connecting to the SRM is less bulky since only n+1 cables are required
for an n-phase motor.
The comparison between the proposed ZIMPC and conventional ASHB topologies has been summarized in Table 3.1. The comparison is performed for three-phase SRM drives using the two topologies. In addition, for comparison of size, cost, efficiency and stresses, same motor excitation
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voltage is assumed. For comparison of CPSR, the same input dc voltage to the converters is assumed. Size and cost reduction is achieved mainly by decreasing the usage of electrolytic capacitor. Voltage stress of semiconductors and capacitors increases because of boosted voltage.
Current stress will increase for the switch in the quasi-Z-source unit and the two switches in the common leg only if overlap between various phases is large. Higher total efficiency is guaranteed because of the decreased semiconductor count by employing switch multiplexing.
Table 3.1. Comparasion between the ZIMPC and the ASHB Topologies
Input current Topology Size Cost Efficiency ripple ZIMPC Small Low High Low ASHB Large High High High Semiconductor Semiconductor Capacitor Topology voltage stress current stress voltage stress CPSR ZIMPC High High High Large ASHB Medium Medium Medium Medium
3.3.2 Capacitance Requirement Using the ZIMPC for SRM Drive
Regardless of the placement of the capacitors, most of the transient power is desired to be processed by those capacitors instead of the dc source. The relation between the capacitor voltage, the transient energy and the capacitor has been written in Equation 1.4. For ZIMPC, the two capacitors in the quasi-Z-source unit can be used to compensate for the power ripple. Since the voltage ripple in the two capacitors are always the same, the relationship between the capacitor voltage, the transient energy and the capacitance can be re-written as:
2 Et v C C1 C 2 2 v C C 1 v C 1 C 2 v C 2 (3.3)
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For the quasi-Z-source unit, the average voltage of C1 equals the sum of input voltage and the
average voltage of C2 . If they have the same capacitance ( CCC12), Equation 3.3 can be simplified as:
1 i2 CE t (3.4) 22vC v C v C2 v in
Comparing Equation 1.4 and Equation 3.4, it can be seen that vc 2 v c2 v in v in since vvc2 in
. Also, vc is no longer required to be less than 5 % of input voltage since the two capacitors are not in parallel with the dc source. Therefore, with the two capacitors in quasi-Z-source unit, the required capacitance can be decreased significantly. For example, if the input voltage is 200 V and the energy ripple is 10 J, ASHB needs 10 mF 200 V capacitance. If ZIMPC is utilized, the voltage
of C2 is set at 300 V with 80 V voltage ripple, one 260 µF 400 V and one 260 µF 200 V capacitors can be used instead. This case study reveals that 90 % of capacitance reduction is possible by using
ZIMPC in place of ASHB. In practical system, the voltage ripple is further limited by the maximum and minimum allowed voltage. Moreover, the capacitor size can be decreased further if one uses
high-capacitance value for C1 and low-capacitance value for C2 , since the voltage rating for C1
is lower than that of C2 (for example, 100 µF 400 V and 650 µF 200 V). It is worth noticing that decreasing capacitor values will increase the voltage ripple across the dc-link. This may limit the speed range of the SRM drive and as such careful selection of the capacitor values for the targeted speed range is necessary.
The above theoretical analysis provides an estimation for minimized capacitance required in Z- source unit to compensate for the power ripple. However, parameters design of Z-source unit
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would influence the stability of the overall system. More detailed calculation about capacitors and inductors in Z-source unit can be found in [48].
3.4 Control Strategy
Even though it is possible to achieve power ripple compensation by replacing ASHB with ZIMPC, a proper control strategy should be employed. Firstly, the ripple of the input current must be
restrained. Secondly, the voltage of the capacitors ( vC1 and vC 2 ) need to be regulated within a certain range considering capacitor voltage rating and SRM performance. Thus, multi-objective power flow control is necessary when using ZIMPC. In this section, the operational modes of
ZIMPC are analyzed. Then, the equivalent model of the overall system with ZIMPC and SRM is developed. After that, an advanced multi-objective control method is presented with current ripple reduction for dc source and speed/torque control for SRM.
3.4.1 Mode Analysis
The modulation sequence and important waveforms have been shown in Figure 3.5 and Figure
3.6. Shoot-through is employed in the common leg connected to all three phases of the SRM. For
the quasi-Z-source unit, S6 is turned off in shoot-through mode and is turned back on in non- shoot-through mode. The modulation of the remaining part is the same as in IMPC which has been discussed in Chapter 2.
Based on the modulation sequence shown above, there are five modes for each phase. The waveforms for other phases are similar and can be analyzed using the same principle. The modes are listed below:
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1 2 3 4 5 d g1 s d0 g2
g3 d1 g6
iL1 iL2 ipa v1 v2
t0 t1 t2 t3 t4 t5 t6 t7 t8
Figure 3.5. Important waveforms of the ZIMPC topology
C1 S1 D1 D2 D3
L1 S6 L2
C2 S2 S3 S4 S5 Phase a- Phase a+ Phase b- Phase b+ SRM Phase c- Phase c+
(a)
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C1 S1 D1 D2 D3
L1 S6 L2
C2 S2 S3 S4 S5 Phase a- Phase a+ Phase b- Phase b+ SRM Phase c- Phase c+
(b)
C1 S1 D1 D2 D3
L1 S6 L2
C2 S2 S3 S4 S5 Phase a- Phase a+ Phase b- Phase b+ SRM Phase c- Phase c+
(c)
C1 S1 D1 D2 D3
L1 S6 L2
C2 S2 S3 S4 S5 Phase a- Phase a+ Phase b- Phase b+ SRM Phase c- Phase c+
(d)
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C1 S1 D1 D2 D3
L1 S6 L2
C2 S2 S3 S4 S5 Phase a- Phase b- Phase a+ SRM Phase b+ Phase c- Phase c+
(e)
Figure 3.6. Five modes of the ZIMPC topology
Mode 1: S1 and S6 are turned on, S2 and S3 are turned off. The voltage drops across the two
inductors are negative ( vvin C2 and vC1 ). Two inductors are being de-energized. The capacitors are being charged and their voltages increase. Meanwhile, zero voltage is applied to the phase winding and the phase current, in the motoring mode, decreases because of the negative
back electromotive force (BEMF, vbemf ) as shown in Figure 3.6a.
Mode 2: S1 , S3 and S6 are turned on, S2 is turned off. The current of two inductors continue to decrease. The voltage of two capacitors decreases by the virtue of a negative current.
Meanwhile, the phase current increases because the phase voltage changes from 0 to vvCC12 ,
and the voltage of the phase inductance becomes vC12 v C v bemf . Figure 3.6b shows the corresponding equivalent circuit.
Mode 3: As shown in Figure 3.6c, S1 , S2 and S3 are turned on, and S6 is turned off. The
voltage drops between two inductors are vvin C1 and vC 2 , respectively ( vin v C12 v C if ripples
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are ignored). Thus, the inductor current increases and the capacitors are being discharged in this mode. Meanwhile, zero voltage is applied to the phase winding by the circuit and the phase current decreases because of a negative BEMF. This is also the shoot-through mode for the quasi-Z-source unit.
Mode 4: In this mode (Figure 3.6d), S2 , S3 and S6 are turned on, S1 is turned off. This mode is similar to Mode 1; both are freewheeling mode for the SRM. Both inductors are being discharged and the voltage of the two capacitors increases. In addition, zero voltage is applied to the phase
winding by the circuit, and the phase winding of SRM is being de-energized with vbemf , causing the phase current to decrease.
Mode 5: S2 and S6 are turned on, S1 and S3 are turned off as Figure 3.6e shows. The two inductors are being discharged. The voltages of the two capacitors are decreasing with current
iiph in . The phase voltage applied by the drive circuit changes from 0 to vvin C1 , and
voltage drop across the phase inductance is vbemf v in v C1 , hence the phase current decreases.
Based on the mode analysis above, it can be seen that the phase can be energized with the
average voltage drop as shown in Equation 3.5. In Equation 3.5, vC 2 is the voltage of the capacitor
C2 , ds is the shoot-through duty cycle, d0 is the duty cycle of Sk2 and 1 dk is the duty cycle
of Sk2 . From Equation 3.5, the maximum excitation voltage is vin1 d s / 1 2 d s . By
regulating the duty cycle , the exciting voltage can be higher than the input voltage vin , as shown in Equation 3.5.
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1 ds vpk v c2 d 0 d k v in d 0 d k (3.5) 12 ds
3.4.2 Generalized Modeling
There are two parts to be modelled: the proposed ZIMPC and the SRM. The stator pole number of
SRM is denoted by n. It is desirable to establish a generalized model of the entire system including the ZIMPC and the SRM. For the sake of simplicity, the mutual inductances between different phases of SRM are ignored.
Based on the average model of ZIMPC with SRM’s phase currents taken into account, Equation
3.6 can be derived.
di LL1 v 1 d v d v R i 1dt in s C 1 s C 2 L 1 L 1 di LL2 v 1 d v v R i 2C 2 s C 1 C 2 L 2 L 2 dt n (3.6) dvC1 C111 diidisLesL 2 2 di sL 2 ddidi 0 kpk 0 L 2 dt k1 dv n C 2 C211 diidisLesL 2 2 di sL 2 ddidi 0 kpk 0 L 2 dt k 1
Where 1 ds is the duty cycle of switch S6 , d0 is the duty cycle of switch S1 , and d1 to dk
are the duty cycles of switches connected to phases 1 through k, respectively. iL1 , iL2 , RL1 and RL2
are the currents through the inductors L1 and L2 , and their equivalent series resistances, vC1 , vC 2
are the voltages of the capacitors C1 and C2 . Besides, i1 to ik are phase currents of phases 1 through k, respectively. It is assumed that the current in each phase is continuous when the phase
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is energized. The total current from quasi-Z-source unit to SRM phases is represented with ie (
n ie d0 d k i pk ). The simplified model of ZIMPC is shown in Figure 3.7. k1
C1 ie
L1 S6 L2 S12
vin C2
Figure 3.7. The simplified ZIMPC topology for modeling and control design
Similarly, SRM can be modeled using electromechanical equations. Considering that the flux linkage of a phase is related to both the position of the rotor and the current flowing through the phase, the voltage equation for each phase of the SRM is expressed as in Equation 3.7.
dk k di k k d k di k Lik , vk R k i k R k i k R k i k L k, i i k (3.7) dt ik dt k dt dt k
Also, the phase excitation voltage of the converter can be expressed as Equation 3.8.
vk d0 v C 2 d k v C 2 d 0 d k v C 2 (3.8)
To model the SRM, the electromechanical equations are needed. These will include the
equations for the magnetic flux linkage , rotor speed , electromagnetic torque Te , which has been derived in Chapter 2, and are repeated here.
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d v Ri dt d 1 (3.9) TTeL dt J d dt
Where,
d Nr 11 iLL a usin N r LLL a u 2 m sin 2 N r BLBLBL a u m dt 2 2 2 , 1 di BLa BL ucos N r BL a BL u BL m cos 2 N r 2 dt
Nr 2 Te i CL a CL usin N r ( CL a CL u 2 CL m )sin 2 N r . 4
Combining the model of ZIMPC and that of SRM described in Equation 3.6 and 3.9, the generalized state-space equations of the overall system is obtained as in Equation 3.10.
di LL1 v 1 d v d v R i 1dt in s C 1 s C 2 L 1 L 1 di LL2 v 1 d v v R i 2dt C 2 s C 1 C 2 L 2 L 2 n dvC1 C11 diidis L 2 e s L 2 1 dis L 2 ddid 0 k pk 0i L 2 dt k1 n dvC 2 C211 diidis L 2 e s L 2 di s L 2 ddidi 0 k pk 0 L 2 dt k1 (3.10) N r 2dk d0 v c R k ikk iN di 2 k dt M d dt d NTrL2 iCLCLk a usin N r CLCL a u 2 CL m sin 2 N r dt4 J J
Where,
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11 M BLa BL u BL m BL a BL ucos N r BL a BL u BL m cos 2 N r 22
NLLNLLLN a usin r a u 2 m sin 2 r . kn1,
Like the model developed for the IMPC topology, the model in Equation 3.10 also applies to both motoring mode and generating mode. Again, a generalized control solution can potentially cover the two modes as well as the transition between the two modes.
As seen in Equation 3.10, the inductance of each phase depends on both the rotor position and the current, thus it is time-variant and non-linear. It is preferred to linearize it around a steady-state operating point. By linearization, the system performance can be analyzed and the controller design can be performed.
Since the rate of variation in rotor speed is much smaller than that of voltage and current, speed can be assumed to be a constant. Re-writing Equation 3.10, the equivalent model is shown in form of state-space equations as Equation 3.11.
x Ax Bu (3.11) y Cx
Where,
T x [ vC1 , v C 2 , i L 1 , i L 2 , i 1 , i 2 ,... i n ] T u [ vin , d01 , d s , d ,... d n ] , T y [ iL1 , i L 2 , i 1 ,..., i n ]
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1DDDDDD 0 0 0Sn0 0 1 ... 0 CCC 1 1 1 1DDDDDD 0 0 0Sn0 0 1 ... 0 CCC 2 2 2
1DDSSRL1 0 0 ... 0 LLL 1 1 1 A 1 DDR , SS L2 0 0 ... 0 LLL2 2 2 2DD 2RNN 10 1 r 0 ...... 0 MM ...... 2DDn 0 2RNN nr 0 0 0 ... 0 MM
n II kL2 III 0kn1 L21 ... CCCC1 1 1 1 n II kL2 III 0kn1 L21 ... CCCC 2 2 2 2 1 VV 0 CC12 0 ... 0 B LL , 11 VV 0 0CC12 0 ... 0 L 1 22VV 0CC22 0 ... 0 MM ...... 22VV 0CC22 0 0 0 MM
0 0 0 ... 0 0 0 0 ... 0 C 0 0 1 ... 0 . ...... 0 0 0 ... 1
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Where DS represents the duty cycle of the shoot-through time, D0 is the duty cycle of the upper
switch ( S1 ) of the common leg, and D1 to Dn are the duty cycles for the lower switches in the other legs which correspond to each stator phase of SRM. Even though speed variation is slow, the coefficients in Equation 3.11 are changing with respect to . One can simplify the equations based on the specific operational conditions of SRM. The SRM phase current can be considered
as disturbance for the inductor current control iL1 and the capacitor voltage control vC 2 .
The phase inductance is assumed to be constant and the derivative of phase inductance with respect to position is also assumed to be constant. At certain position, these two parameters can be obtained using Equation 1.14 and expressed as Equation 3.12.
L, iLALiALi cos N ALi cos 2 N k k0 1 r 1 2 r 2 Li, (3.12) k KNALi sin N 2 NALi sin 2 N r1 r 1 r 2 r 2
To consider the worst-case scenario, only one phase of the SRM is excited at each instant.
Hence, if only the current flowing through one phase is considered, the small signal model can be derived as shown in Equation 3.13.
di LL1 v 1 d v d v R i dt in S C1 S C 2 L 1 L 1 diL2 L vCSCCLL2 1 d v 1 v 2 R 2 i 2 dt n dvC1 C111 diidiS L 2 e S L 2 di S L 2 ddidi 0 k pk 0 L 2 (3.13) dt k1 n dvC 2 C211 diidiS L 2 e S L 2 di S L 2 ddidi 0 k pk 0 L 2 dt k1 di Lpk V d d D D v R i K i kdt C20 k k 02C k pk pk
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Taking the Laplace transform of Equation 3.13, the relationship between iL1 and duty cycles ds can be derived as shown in Equation 3.14.
Js i s d s (3.14) LS1 Ts
Where,
2 CsV DDVDDV J s C I I 00k C k c 11DkL L s R K L s R K D 00k k k k . 22 Cs Ls RL 1 D00 D D k Ls R L Ts 11D00 Lkk s R K D
3.4.3 Multi-Objective Control Method
The proposed multi-objective power flow control method has been illustrated in Figure 3.8.
Capacitor voltage Inductor current control control loop loop vc2_ref iL1_ref d PWM Co1 Co2 0 + generator +- +- Repetitive + vc2 iL1 controller
ω Adaptive f0 , θ0 d1 controller gs , g1 & g2
- Modified iref I iph_ref + Co3 ph_ref hysteresis ZIMPC, SRM ωref generator controller g3 ~ g5 and sensors Speed control loop iph Sensed values v , i , i , ω Control system c2 L ph
Figure 3.8. The control diagram for the proposed topology
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There are two control branches, one is ZIMPC control including capacitor voltage and input current, and the second one is SRM control with speed/torque and phase current. In ZIMPC control
branch, the average voltage of capacitor C2 is detected and regulated at a constant value. The
voltage command is decided based on the requirement of speed (higher capacitor voltage for C2 is needed for high speed operation of SRM). The output of the capacitor voltage control loop is the input current reference. With the detected input current iL1, the duty cycle of the shoot-through
time ( dS ) is regulated to make the input current track the reference. In this inner loop, a repetitive
controller is inserted in series with controller ( Co1 ) to reduce the low-frequency ripple which cannot be restrained using conventional controller alone. On the other hand, in SRM control branch, the speed or torque is expected to be regulated. The output of this control loop is the reference for phase currents. Subsequently the phase current is regulated using a hysteresis controller with a
satisfactory dynamic performance. In Figure 3.8, g1 and g2 are the PWM signals for S1 and S2 ,
respectively, gS is the PWM signal for S6 . Meanwhile, g3 , g4 and g5 are the signals for S3 , S4
and S5 .
There is a modified hysteresis controller in Figure 3.8 which is different from the hysteresis
controller used in ASHB. This block outputs the signals for S3 , S4 and S5 . When the phase
current is lower than the referred minimum value, switches ( S3 , S4 and S5 ) are on; when it is higher than the reference, switches are off. Otherwise, their state keeps unchanged. The hysteresis
block also outputs the duty cycle for S1 in Figure 3.8. As written in Equation 3.5, the rising slope of phase current is decided by the voltage difference between the midpoint voltage of the first leg and that of the other legs. In order to shorten the rise time, the average voltage of the midpoint of
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the first leg should be regulated to a relative high value. During other times, this voltage is desired to be kept low so as to keep the phase current ripple limited. In consideration of the fact that the middle voltage is calculated using Equation 3.15, the rising slope can be adjusted by regulating
d0 . The duty cycle can be controlled according to the requirements of current profiles to optimized the performance.
1ds d0 d pk vvmid in (3.15) 12 ds
The proposed ZIMPC and its power flow control method as SRM drives have been described.
It is worth pointing out that ZIMPC also allows the SRM to work as a generator. Similar to the
control of the IMPC introduced in Chapter 2, the I ph_ ref generator block controls the current
excitation profile. For motoring operation, the phase current command equals iref when the rotor goes from unaligned position to aligned position. When the rotor passes the aligned position, the phase current reference changes to 0. For generating operation, the phase current keeps 0 before
the rotor reaches aligned position. Then, the phase current command becomes iref . The rest of the control system remains the same, and the capacitor voltage as well as the source current can still be regulated.
3.5 Simulation and Experimental Results
3.5.1 Simulation Results
To validate the proposed ZIMPC topology and the control strategy, a simulation model is built with MATLAB/Simulink. The detailed hardware parameters of the ZIMPC have been listed in
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Table 3.2. A symmetrical three-phase SRM model is used in the simulation. In consideration of that the power rating of SRM is less than 2 kW and the phase voltage is less than 400 V, a switching frequency of 20 kHz is chosen. In terms of the quasi-Z-source unit, the inductors can be designed using the switching frequency and desired current ripple through the input source. Meanwhile, the capacitors are selected according to the capacitance calculation introduced previously and theoretical analysis in [48].
Table 3.2. Parameters of the Simulation Models
ZIMPC Parameter Value
DC Voltage Source (V1) 350V DC
Capacitor (C1) 300 µF
Capacitor Voltage ( vc1 ) 100 V DC, 60 V AC
Capacitor (C2) 220 µF
Capacitor Voltage ( vc2 ) 450 V DC, 60 V AC
Inductor (L1) 2 mH, 10 mΩ
Inductor (L2) 2 mH, 10 mΩ
Switching frequency (fs) 20 kHz Switched Reluctance Motor Parameter Value Stator pole number 6 Rotor pole number 4 Inertia momentum 0.05 kg·m2 Friction coefficient 0.02 N·m·s
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The corresponding control method is implemented based on the designed power flow as introduced. Figure 3.9 shows the steady-state waveforms including the flux (Figure 3.9a), the three-phase current (Figure 3.9b) and the torque (Figure 3.9c) which demonstrate the topology can transfer power from the input source to the SRM. From Figure 3.9c, it can be seen that there is
large torque ripple ( Te 18 N m). On the other hand, the input current ( iL1 ) and the capacitor
voltage ( vC 2 ) are shown in Figure 3.9d and Figure 3.9e, respectively. The input current is about 3
A with less than 0.6 A ripple. The required power ripple caused by current commutation is compensated by the two capacitors in quasi-Z-source unit, which lead to 22 V peak-to-peak voltage
ripple on C2 .
(a)
(b)
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(c)
(d)
(e)
Figure 3.9. Simulation waveforms in steady state
The dynamic performance of ZIMPC with symmetrical SRM is also tested. At first, the speed is controlled at 900 rpm. The peak value of phase current is 35 A. At t=0.7 s, the load torque changes from 5 N·m to 15 N·m. It can be seen that the capacitor voltage decreases to compensate the power mismatch in Figure 3.10a. After about 350 ms, the capacitor average voltage is regulated back to 450 V. The voltage overshoot is limited at less than 17%. The capacitor voltage ripple
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(peak-to-peak) is enlarged from 22 V to 50 V because larger power ripple is necessary for current commutation. Figure 3.10b shows the input current. It goes up from 3 A to 6 A smoothly without overshoot. Meanwhile, the phase currents increase from 35 A to 62 A as shown in Figure 3.10c.
(a)
(b)
(c)
Figure 3.10. Simulation waveforms of speed control with increased load torque
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The waveforms in Figure 3.9 and Figure 3.10 reveal that the proposed topology can act as the drive for SRM instead of the conventional ASHB topology and the control method proposed is suitable for the proposed topology.
3.5.2 Experimental Results
Two prototypes based on the conventional ASHB topology and the proposed ZIMPC have been built to compare their performances. The same 2-stack 2-phase SRM used in the experiments of
Chapter 2 is used again to test the feasibility of ZIMPC and to show its advantages. Also, the dc alternator is coupled with the SRM and a power resistor bank is connected to the output of dc alternator, which acts as load.
Table 3.3. Parameters of the ZIMPC-Based Motor Drive
Z-source Integrated multiport converter (ZIMPC) Parameter Value Input voltage 40 V to 100 V Switching frequency 20 kHz
Inductor (L1) 1 mH, 14 mΩ
Inductor (L2) 1 mH, 14 mΩ
Capacitor (C1) 220 µF
Capacitor (C2) 220 µF
Capacitor voltage ( vc1 ) 40 V to 90 V
Capacitor voltage ( vc2 ) 70 V to150 V
Considering the voltage and current rating, MOSFET IPL65R130C7 from Infineon is used as the power switches and RFUS20NS6STL from Rohm semiconductor is used as the power diodes.
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While it is desirable to choose low capacitance, too low of a capacitor value will hinder the performance of ZIMPC because of low excitation voltage resulted from high voltage ripple. For the prototype used in the experiments, the capacitor values are selected to keep the voltage ripple less than 50 V to ensure that (1) the lowest possible voltage is high enough so as not to impact the performance of the SRM drive; and (2) to limit the voltage stress of capacitor and semiconductors.
For the control part, the designed power flow control scheme is implemented using ARM-based microprocessor XMC4400 from Infineon. Similar to the simulation, the switching frequency is selected at 20 kHz. The corresponding sampling and control period is set at 50 µs. The detailed hardware parameters of the prototypes are listed in Table 3.3. The picture of the prototype is show in Figure 3.11. The corresponding experimental results are displayed to compare their performances.
Figure 3.11. Photo of the test setup
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1) Switching waveforms
(a)
(b)
Figure 3.12. Experimental switching waveforms
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The switching waveform is shown in Figure 3.12 to illustrate the operation of the quasi-Z-source unit. Figure 3.12a shows the waveforms of input current and voltage along with the voltage across the H bridge, while Figure 3.12b shows the waveforms of the current and voltage of one phase along with the voltage across the H bridge. The shoot-through event can be observed in the H bridge voltage in Figure 3.12a and Figure 3.12b.
2) Steady-state waveforms
When using ZIMPC converter as SRM drive, the current waveform of the two stator phases currents are shown in Figure 3.13. The two phases of the stator are driven alternatively according
to the rotor position. In addition, the capacitor average voltage ( vC 2 ) is controlled at 75 V.
Figure 3.13. Waveform showing the capacitor voltage and current of the two phases
Figure 3.14 shows the experimental comparison of ASHB and ZIMPC. When using ASHB, an
1100 µF electrolytic capacitor is used to remove the current ripple caused by current commutation.
Figure 3.14a shows the corresponding waveform. The peak-to-peak input current ripple is 13.8 A.
During the period of second phase de-energizing, the input current becomes minimum (-3.9 A).
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(a)
CH1: Phase a current CH2: Capacitor voltage
CH3: Input current
CH1:5A/div; CH2:50V/div; CH3:5A/div; Time:20ms/div
(b)
CH3: Capacitor voltage CH1: Phase a current
CH2: Input current
CH1:5A/div; CH2:2A/div; CH3:50V/div; Time:20ms/div
(c)
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(d)
Figure 3.14. Experimental waveforms and FFT analysis results
Instead of ASHB, ZIMPC is used to drive the same SRM. In this ZIMPC, only two 220 µF capacitors are used in the quasi-Z-source unit. Figure 3.14b shows the experimental result using
ZIMPC with fixed shoot-through period. Compared with Figure 3.14a, the input current is kept almost positive and the peak-to-peak ripple is 8.0 A. Moreover, the capacitor voltage contains 30
V ripple. After that, the control method presented is employed and the waveform is in Figure 3.14c.
The input current peak-to-peak ripple is controlled within 0.6 A. Meanwhile, the capacitor voltage ripple is enlarged to 45 V to compensate the low-frequency power ripple. The frequency distribution of the input current in these three cases is shown in Figure 3.14d.
The above experimental results reveal that the proposed ZIMPC can reduce more than 60 % of the capacitance requirement with less switches and diodes. By controlling the input current with shoot-through time, the input current can also be optimized with 90 % low-frequency ripple reduction.
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3) Dynamic waveforms
The dynamic tests are also done with ZIMPC to verify the validity of the power flow control method. Figure 3.15 shows the dynamic waveform of capacitor voltage and input current regulation in experiment. At the beginning, the phase currents are maintained at 5 A, the input
current is controlled at 1.95 A. The capacitor voltage ( vC 2 ) is about 75 V with 37 V ripple. After that, the phase currents are increased to 8.5 A. The capacitor voltage drops to 63 V to provide the power mismatch. Meanwhile, the input current goes up because of the voltage drop. After about 1 s dynamic response time, the average capacitor voltage goes up back to 75 V, while the voltage ripple increases to 50 V. The input current is controlled at 2.6 A. The voltage overshoot is limited at less than 15 %.
Figure 3.16 shows the dynamic waveform in experiment. The speed command is 500 rpm and the capacitor voltage ( ) command is 80 V. At the beginning, the speed is controlled at 500 rpm with phase currents of around 5 A, the capacitor voltage ( ) is controlled at 80 V with 30 V ripple, and the input current is controlled at 1.4 A. At -1.5 s, the resistance connected to the dc alternator is decreased so that the load is increased. The speed drops to around 380 rpm, while the phase currents command goes up because of the speed drop, causing the capacitor voltage to drop and the input current to increase. After about 2.5 s dynamic response time, the speed goes up back to 500 rpm, the average capacitor voltage ( ) is maintained at 80 V, while the voltage ripple increases to 40 V and the input current increases to 2.2 A.
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(a)
(b)
(c)
(d)
Figure 3.15. Experimental waveforms of sudden increase of speed
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(a)
(b)
(c)
(d)
Figure 3.16. Experimental waveforms of speed control with increased load torque
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4) Efficiency
The efficiency of the prototype is tested in experiments and shown in Figure 3.17. The maximum efficiency is around 93.5%. It is shown that the converter can achieve efficiencies of higher than
90% when the output power is higher than 150 W.
Figure 3.17. Experimental efficiency test results
3.6 Summary
In this chapter, the IMPC topology discusses in the previous chapter is analyzed to derive the generalized power decoupling topology for SRM drives. A quasi-Z-source integrated multiport converter (ZIMPC) is then derived from the generalized topology to overcome some of the disadvantages of the IMPC topology. The ZIMPC topology can achieve capacitance reduction and wide-speed-range operation of SRM. The requirement for capacitance to provide the power ripple can be reduced significantly. This can prolong the converter’s lifetime and increase its power density. The current ripple through the dc source is reduced by controlling the shoot-through duty
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cycle of the quasi-Z-source unit. In addition, performance during high-speed operation can be improved with higher equivalent exciting voltage permitted by the quasi-Z-source unit, enabling a wider CPSR. The proposed drive system is modeled and corresponding control method is proposed. The validity and performance of the proposed ZIMPC is verified by the simulation and experimental results. Comparative results reveal that the capacitor can compensate for 90% of periodical transient power ripple with only 40% capacitance as compared to ASHB for SRM drives.
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CHAPTER 4
PRACTICAL CONSIDERATIONS
It has been demonstrated that the proposed topologies and control strategy can substantially reduce the capacitance requirement while maintaining little current ripple from the dc source. However, for the successful adoption of the proposed methods for EV applications, several practical considerations have to be made.
Firstly, the regenerative braking ability is vital for motor drive in EV applications. As has been analyzed, as long as the power decoupling unit supports bidirectional power transfer between any two ports, the derived topologies can achieve generating mode of operation, and thus support regenerative braking. The proposed IMPC and ZIMPC topologies are both derived with power decoupling units with such ability, and thus are theoretically able to operate in generation mode.
Secondly, the efficiency has to be compared since it directly impact the range. The switch multiplexing technique merges the transient power unit and the machine driving legs, which can potentially reduce the power losses comparing to the two-stage topologies, and even the ASHB topology, even though current in some power devices is increased. Thus, closer examination is needed for the comparison of efficiency of the proposed topologies and existing topologies.
4.1 Generating Mode of Operation
In this chapter, the model developed earlier will be utilized to show that the topologies can handle generating mode of operation of SRMs, and that seamless transition is possible between motoring and generating modes. Then, simulation and experimental results are presented to validate the analysis.
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4.1.1 SRM Drive System in Generating Operation
Analysis in Chapter 1 shows that any SRM can be used for generation by simply changing the excitation angle, and that the current flow direction does not need to change when the machine enters generating mode from motoring mode. In this mode, the phases of the SRM will be excited after the rotor poles move past the aligned position. This facilitates the design of SRM driving circuit supporting both motoring and generating modes of operation.
Although it is possible that under generating mode, the SRM can be controlled in a similar manner to when it operates in motoring mode, phase current may become uncontrolled when the speed is high [50]. After the power circuit excites the machine phase, due to the high back-EMF, the phase current may keep increasing when negative voltage is applied to it. This is the well- known single pulse current mode of switched reluctance generator. In this mode, the control can be done by changing firing angle instead of adjusting reference current [51]. Study of this kind of operation has also been done for the Miller topology, which is applicable to the proposed IMPC and ZIMPC topologies. However, since torque control is usually desired for regenerative braking in EVs, the following discussion will only focus on generation with current-controlled mode.
4.1.2 Generating Operation of the IMPC Topology3
Since the boost unit in the IMPC topology is implemented with two switches, it can inherently support generating mode of operation. In generating mode, the excitation angles are changed to
3 © 2015 IEEE. Reprinted, with permission, from Fan Yi, Wen Cai, Modeling, Control, and Seamless Transition of the Bidirectional Battery-Driven Switched Reluctance Motor/Generator Drive Based on Integrated Multiport Power Converter for Electric Vehicle Applications, IEEE Transactions on Power Electronics, December 2015.
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produce negative torque, while the average capacitor voltage control loop still maintains the same average voltage to the reference value, but generates negative dc source current reference value, since the energy from the machine will raise the capacitor voltage.
From the electromagnetic torque equation described in Equation 2.17, it can be seen that the model developed is able to cover both motoring mode and generating mode of operation. By exciting the phases when the rotor is approaching the aligned position from the unaligned position, the torque would be positive which means that SRM works at motoring mode. Conversely, when the phase is excited when the rotor moves from the aligned position to the unaligned position, the electromagnetic torque would be negative.
The speed/torque control loop in Figure 2.7 shows that when the speed or torque is too high, the current reference would decrease or even become negative. The corresponding electromagnetic torque would decrease from positive to negative smoothly. During this transition period, SRM switches from motoring mode to generating mode without excessive overshoot. At the same time, the generated electrical energy will be transferred into the dc capacitors and cause capacitor voltage to increase. To keep the capacitor average voltage constant, the inductor current will also be regulated to a negative value by current control loop in the control scheme. Thus, eventually the energy generated by the machine is transferred into the dc source, such as the battery pack on an electrical vehicle. This function benefits EVs, because the energy is desirable to be absorbed by the battery instead of wasted while braking or decelerating. With regenerative braking, the efficiency of the overall system can be improved and the range can be increased. Conversely, to increase the speed SRM, the capacitor voltage will decrease because of more electromagnetic
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torque being generated. Consequently, the dc source current increases to boost the dc capacitor average voltage.
1) Simulation Results
To validate the generating mode of operation with the IMPC topology, simulation is conducted using Simulink. Figure 4.1a shows that the flux of each phase reaches the high value very fast due to excitation by the driver, and then decreases as the rotor moves to unaligned position while converting kinetic energy to electric energy, and then quickly decreases to zero. Negative electromagnetic torque is generated. The battery current is controlled at a constant value (2 A) with small ripple (0.18 A peak-to-peak) in Figure 4.1c. The power ripple is compensated by the dc capacitors, which leads to 40 V peak-to-peak voltage ripple as shown in Figure 4.1d.
Figure 4.2 indicates the dynamic performance under test. At first, the speed is controlled at 1000 rpm as shown in Figure 4.2a. When t=0.1 s, the load torque changes from -4.5 N·m to -6 N·m. It can be seen that the speed of the SRM goes up after this step change in torque. However, 100ms later, it goes back to 1000rpm again. Figure 4.2b and Figure 4.2c show the three-phase current waveforms during this dynamic process. As shown in Figure 4.2d, at the beginning of the transient process, the dc capacitor is charged by SRM, and then the voltage is regulated back to 280 V. Both the phase current and battery current increase smoothly with less than 11 % overshoot and 250 ms dynamic response time.
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(a)
(b)
(c)
(d)
Figure 4.1. Simulation waveforms of generating mode using the IMPC topology in steady state
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(a)
(b)
(c)
(d)
Figure 4.2. Dynamic simulation waveforms of generating mode with speed control
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2) Experimental Results
To allow the SRM drive to operate in both motoring and generating modes, ten 12 V automotive lead-acid batteries are connected in series as the dc source, so that the dc source can both provide and absorb energy. A brushed dc machine is mechanically coupled to the SRM to act as the load or prime mover. The dc machine is driven by a dc power supply through a dc circuit breaker, and is connected in parallel with a resistor bank as the load. The polarity of the connection between the dc machine and the dc power supply is configured in the way that the machine will rotate in reverse to the direction of the SRM in motoring mode. The resistor bank will not influence the operation of the system when the breaker is on, and will act as the load when the breaker is off.
The configuration is illustrated in Figure 4.3, with the blue arrows indicating the possible directions of power flow.
This configuration allows for both motoring and generating modes of operation since both machines are connected with electric load/source, thus it also allows for the transition between the two modes. In the following experiments, the transiting is triggered by manually operating the breaker. The controller can easily determine the correct operating mode thanks to the reversed rotating directions.
The generating mode of operation of SRM is tested with the dc machine driven by dc power supply (Switch in Figure 4.3a is on). When the dc machine is connected to dc power supply and resistor load, it provides positive mechanical torque. At this time, SRM acts as load and it absorbs energy from the alternator. Meanwhile, IMPC is used to transfer energy from SRM to the battery pack.
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SRM Dc machine
SRM Driver
Breaker Resistor bank Dc power Battery supply
(a)
(b)
Figure 4.3. Experimental setup
Figure 4.4a shows the current through the battery when using the IMPC structure without proposed control method. The low-frequency ripple is too large to be ignored. Even though the average current is 3.99 A, the peak-to-peak value is 8.20 A. On the contrary, if using IMPC as well as the proposed control method, the battery current would be constant (3.84 A) with only a small
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ripple which is displayed in Figure 4.4b. The peak-to-peak ripple is limited in only 0.86 A.
Moreover, from the frequency distribution in Figure 4.4c, the ripple at f0 is 0.24 A which is only
6 % of that without proposed control method (4.05 A). In addition, all the other low-frequency ripples are decreased by at least 50 %.
(a)
(b)
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4.5 3.99 4.05 4 3.84 3.5 3 2.5 2 1.5 Amplidute (A) Amplidute 1 0.24 0.42 0.330.24 0.5 0.12 0.030.06 0 0 1 2 3 4 f0 (Hz) IMPC w/o Control IMPC w/ Control
(c)
Figure 4.4. Experimental results of generating mode using the IMPC topology
3) Seamless Transition
The dynamic performance of the presented control method is also tested with seamless transition capability. The experimental waveform is shown in Figure 4.5. At the beginning, switch in Figure
4.3a is off and SRM works in motoring mode. When switch is turned on and the power supply is connected to dc alternator, SRM drive switches from motoring mode to generating mode of operation automatically. It can be seen that the dynamic time is 2.1 s and there is no overshoot of battery current during the dynamic process. In addition, there is 9% overshoot in dc capacitor voltage which doesn’t exceed capacitor voltage rating. It is worth pointing out that during the transition, even though the speed changes a lot, and the rotation direction is reversed, the repetitive controller is always in effect. The only intervention is that the stored values are cleared when the rotation direction changes. During other time, the repetitive controller adjusts the delay according to the speed of the machine, and the stability and effectiveness are shown.
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Figure 4.5. Experimental results of seamless transition from motoring mode to generating mode using the IMPC topology
In short, the above simulation and experimental results reveal that the proposed control method can keep the battery current ripple less than 6 % of the average current and achieve seamless transition with no overshoot in battery current and 9 % overshoot in DC capacitor voltage. This demonstrates the feasibility and superiority of the proposed control method.
4.1.3 Generating Operation of the ZIMPC topology
In Chapter 3, it has been shown that the diode in the original quasi-Z-source unit is replaced with a switch to implement the ZIMPC topology. This replacement is necessary even for normal operation of the topology in motoring mode of operation, as shown in the mode analysis. Also, by doing this, generating mode of operation is allowed for the SRM since the switch is necessary for bidirectional power transfer capacity of quasi-Z-source unit.
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Again, to operate the SRM in generating mode with the ZIMPC topology, one only needs to change the excitation angle and use the same outer voltage control loop, and the negative reference value for the current control loop will be automatically generated by the outer loop.
The generating mode of operation of the ZIMPC topology is verified in simulations. The results are shown in Figure 4.6.
(a)
(b)
(c)
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(d)
(e)
Figure 4.6. Simulation waveforms of generating mode using the ZIMPC topology
4.2 Efficiency Analysis
Although both topologies feature reduced number of power devices, one has to carefully examine the operating conditions to compare the efficiency of the proposed topologies with the conventional ASHB topology and other existing topologies, since the voltage and current stresses of some power devices have changed because of switch multiplexing.
To compare the efficiency, the conduction losses and the switching losses must be analyzed.
The analysis assumes that constant current in phases for both topologies. If the speed of the SRM is no very high and current commutation time is much less than the constant current period, the losses during the constant current period form the major part of total losses. This part of losses is analyzed in this chapter.
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Boost Unit Phase a Phase b Phase c
L C D0 S1 D2 S3 D4 S5 D6
V1
S0 D1 S2 D3 S4 D5 S6
SRM
(a)
Multiplexed leg
D1 S2 S3 S4
C L
S1 D2 D3 D4 V1
SRM
(b)
Figure 4.7. The derivation of an alternative configuration of the IMPC topology
First, conduction losses are analyzed. Since the machine phase currents are assumed to be same in both topologies, the conduction losses in the phase leg of the IMPC can be assumed to be the same as the conduction losses in one of the two legs of the ASHB topology. For the ASHB
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topology, conduction losses in the two legs connected to the same machine phase are the same.
Some of the existing topologies, which aim to reduce the total number of power devices and cables, may suffer from increased conduction losses due to less devices. One example is the previously mentioned C-dump topology. In this topology, part of the stored magnetic energy in the SRM is transferred to the additional C-dump capacitor, and the energy is then transferred back to the dc source capacitor. This current from the C-dump capacitor can add up with the phase current and cause increased conduction losses in the shared switch, and the additional inductor also needs to stand high current.
For the IMPC topology, in the multiplexed leg, the load current can be greatly less than the phase current since the input dc current also provides part of the phase current. Thus, the current flowing through the power devices in the multiplexed leg is the difference between the phase current and the input dc current. One may notice that in the derivation of the IMPC topology shown before, another way of switch multiplexing is possible. This leads to an important observation that when employing the switch multiplexing technique, merging different set of switches can cause significant difference in the current and thus the efficiency.
For example, one may choose to multiplex the switch and diode of the boost unit with another phase leg in each phase, as shown in Figure 4.7a. In this way, one can use a diode instead of a switch in the multiplexed leg, as shown in Figure 4.7b. However, this is not preferred for two reasons. First, this configuration will not allow the SRM to operate in generating mode, since it is not able to transfer energy from the capacitor to the dc source. However, generating mode of operation is necessary for electric vehicle applications. Second, this configuration will cause
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increased current stress in the multiplexed. This is because before switch multiplexing, the current flow direction through the multiplexed devices are all the same, thus, after multiplexing, the current stress will be the sum of the current in each multiplexed leg. This increased current stress will lead to the choice of more expensive devices and lower efficiency.
On the other hand, when there is overlap between the constant current periods of two phases, the current in the multiplexed leg will be twice the phase current minus the input dc current, which will increase the conduction losses in the leg.
Regarding switching losses, both topologies employs hard switching. The switching losses of single turn-on and turn-off mainly depend on the load current and the voltage being switched.
Although the voltage stress increases for the power devices in the IMPC topology, it is again worth noticing that because of the switch multiplexing, the current flowing through the multiplexed leg can be greatly reduced under many operation conditions. This may also lead to reduced switching losses in the IMPC topology under certain operation conditions.
S1 D1 D2 D3
C L IS
IL S2 S3 S4 S5 V1
Iph
SRM
Figure 4.8. Current distribution in the boost unit of the IMPC topology
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Another factor that determines the total switching losses is the number of switching times. For the ASHB topology, all switches are controlled with hysteresis current controller, while in the
IMPC topology, all phase legs are controlled with hysteresis current controller while the multiplexed leg is controlled at constant switching frequency. For the IMPC topology, the volt- second balance must be met for the input inductor, which means that the terminal voltage across the machine phase will be the same as the input dc voltage during magnetization. When the average capacitor voltage is controlled at twice the input dc source voltage, again according to the volt- second balance principle, the demagnetization voltage will also be the same as the input dc voltage.
Thus, the number of switching times for the power devices in the ASHB topology should be the same as that of the power devices under hysteresis current control of the IMPC topology. As for the multiplexed leg, it is assumed that the number of switching times during the constant current time is the same as other legs, then, for the simplicity of analysis, all switches can be seen as being operated at the same switching frequency. Then, the switching losses are estimated with single turn-on and turn-off losses without considering the hysteresis behavior.
Total Losses (W)
ASHB
IMPC
ZIMPC
0 200 400 600 Switching Conduction, IGBT Conduction, diode
Figure 4.9. Efficiency comparison of different topologies
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With the above analysis, total losses of the two topologies need to be compared for different operation conditions. Here, a 10 kW SRM drive is assumed to compare the losses. The devices selected are IGBT IGW100N60H3 and diode IDW50E60, both from Infineon, working at 20 kHz.
The losses are determined using datasheet parameters, mainly the switching energy and voltage drop across devices. The dc source voltage is 200 V for both topologies, so the average input current is 50 A, and the phase current is 100 A. The results are plotted in Figure 4.9. Under this operation condition, the conduction losses dominate. As a result, even though the voltage stress is increased, the IMPC has lower total losses, which is around 90.3 % of the total losses of the ASHB topology. However, this may not be the case if the average power is low, which happens if the coenergy is low and the magnetic energy not converted to mechanical energy is high, such as the non-saturated operation of SRM. It is then clear that as the input dc current increases relatively to the phase current, the IMPC topology becomes more favorable than the ASHB topology in terms of efficiency. Since the input dc current represents the average “active” power transferred to the machine, it means the IMPC topology is particularly preferred for heavy load condition.
Similarly, for the ZIMPC topology, the shoot-through current is in reverse direction with the phase current in the shoot-through freewheeling mode, and thus reducing the current stress of one switch in the shoot-through leg to less than the phase current in this mode. The difference is in that the reduction only happens during the shoot-through period, and during other time the current is still the phase current. For the switch in the quasi-Z-source unit, the losses during each mode differ.
Referring to Figure 2.3, during the mode 2, the current is the difference between the phase current and twice the input current; while there is no current in it during the shoot-through period (mode
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3). In these two modes, the conduction losses are very small. However, during freewheeling modes
1 and 4, the device current is twice the input current, while in mode 5 the current will be the sum of the input current and the phase current. In these three modes, the conduction losses are increased, causing higher total losses in the ZIMPC topology comparing to the ASHB topology when excitation voltage is only required to be equal to the input dc voltage. However, in practical designs, the voltage stress in this device is lower, thus employing a high current low voltage device will give better efficiency due to optimized conduction losses. Also, if excitation voltage higher than the input dc voltage is desired, an extra boost stage must be added before the ASHB topology, while the ZIMPC topology can inherently boost the voltage. Under such situation, the overall efficiency of the two-stage converter will drop significantly.
In addition, it is possible to further reduce the switching losses in the IMPC topology. Thanks to the boost unit, the average capacitor voltage is adjustable, and lowering it can lead to reduction of switching losses for single turn-on and turn-off, as well as decreased number of switching times of the power devices under hysteresis control, since the demagnetization voltage is lowered. Since lower average capacitor voltage will prolong the current commutation process when the machine phase is being turned off, one should find a balance between reduce switching losses and performance under different operation conditions of the SRM.
For the ZIMPC topology, the voltage stress across the switches is not necessarily twice the input dc voltage to provide demagnetizing voltage equal to the dc source voltage, as required for the
IMPC topology, and the magnetizing voltage is not fixed to the same as the input voltage. Instead, the capacitor voltage and the input current are controlled with the shoot-through duty cycle, while the magnetizing voltage and the demagnetizing voltage are controlled with the duty cycle of the
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two switches of the common leg. The additional degree of freedom brings the ability of dynamically adjusting the voltage applied to the machine without affecting the capacitor voltage and input current. This will lead to reduced switching losses when high excitation voltage is needed, and thus can benefit high speed operation of the machine.
4.3 Volume Analysis
Aside from the microcontroller and the power devices, the size of the motor driver is mainly determined by the size of the heat sink and the passive components including the inductors and the capacitors. It is worth noting that the volume of the cable assembly is also largely reduced. Here, the comparison in size will be analyzed mainly with passive component volume. The proposed
IMPC topology and the ZIMPC topology bring the benefit of greatly reduced total capacitance and thus greatly reduced total volume of capacitors. However, the addition of inductor will result in additional volume. In the proposed topologies, the inductors introduced are dc inductors with small current ripple, so the size is mainly determined by the dc current rating and inductance.
For both topologies, the dc current rating of the inductor connected to the dc voltage source can be easily calculated using the maximum output power of the converter and the dc source voltage.
The input current ripple requirement will determine the inductance of the inductors. Since a small capacitor can be used in parallel to the dc source to absorb only the switching frequency current ripple, the input current ripple is set at 20 %. Assume that the dc source voltage is 250 V, and the input power is 50 kW, which is typical for HEVs.
If the ASHB topology is used, the capacitance requirement is estimated with the energy storage requirement in a period. Using simulation, the capacitors are determined to be required to store 80
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J of energy temporarily. The capacitance can be calculated with Equation 1.4. The total volume of capacitors is estimated to be 10.2 L.
The inductance used for the IMPC topology can be determined using Equation 4.1.
d 1 LVin in (4.1) fIsw in
A typical duty cycle of 50 % is assumed. The inductance is calculated to be 156 H. The volume of such an inductor is estimated to be 1.9 L.
The capacitance is estimated to be reduced by 70 %, and the volume is then 3.1 L. The total volume of the capacitors and the inductor is 5.0 L, which is only about half the total volume required for the ASHB topology.
Although the ZIMPC requires two inductors, previous analysis shows that to generate the same exciting voltage for magnetizing and demagnetizing, this topology needs less input voltage, and the duty cycle can be smaller. Also, the other inductor in this topology does not need to be as large as the input inductor, since its value will not influence the input current ripple if designed properly.
For example, if an input voltage of v is chosen of the IMPC topology, one can choose 2/3 v as the input voltage for the ZIMPC topology and use a shoot-through duty cycle of 0.25.
The input inductance used for the ZIMPC topology can be determined using Equation 4.2.
11 d d LinV in (4.2) 12 d fIsw in
In this calculation, a typical shoot-through duty cycle of 20 % is assumed. Since the ZIMPC does not require as high dc link voltage as the IMPC, the shoot-through duty cycle is much smaller and thus the inductance can be much smaller, assuming same input dc voltage. The inductance is
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calculated to be 83 H. If the same inductance is used for both two inductors, the total volume can be estimated to be the roughly the same as the previously calculated 156 H inductor for the IMPC topology.
If additional reduction in the inductor volume is desired, for both topologies, one can choose to increase the switching frequency of the power decoupling unit thus increasing the switching frequency seen by the inductor. Replacing only the switches in the power decoupling unit by silicon carbide switches will help to maintain high efficiency while the switching frequency is increased.
Furthermore, for the ZIMPC topology, there are two ways the inductor volume can be significantly reduced. Firstly, since the two inductors can be replaced by a single coupled inductor with only one core, much smaller inductance can be used than the inductance required in the IMPC topology [46]. Also, since the flux from the two windings can partially cancel, the coupled inductor can have less volume. Secondly, if one of the diodes of the phase legs is replaced by a switch, then the shoot-through duty cycle can be distributed to that leg. This will result in a doubled switching frequency seen by the inductors.
In addition, since capacitors in the ZIMPC topology are under less voltage stress, the total volume can be smaller than that of the IMPC topology.
In conclusion, the IMPC topology can greatly reduce the total passive element volume, and the
ZIMPC topology can achieve further reduction in the volume comparing to the IMPC topology.
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4.4 Summary
In this chapter, practical considerations when utilizing the proposed methods have been discussed.
First, the generating mode of operation of SRM using the proposed power decoupling topologies has analyzed and validated. It is shown that if the transient power unit can support bidirectional power transfer between all ports, it will be able to support motoring and generating modes of SRM while achieving capacitance reduction. Second, it is shown that the total volume of passive elements can be reduced in the proposed topologies because of the reduced capacitance, even if extra inductors are needed. Third, it is shown that the efficiency of the drives can be improved by using the proposed method, if operation conditions are carefully considered.
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CHAPTER 5
CONCLUSION AND FUTURE DEVELOPMENT
5.1 Conclusion
SRM is becoming a serious contender for EV applications. Because of phase current commutation and the non-linearity of SRM, there is a large pulsation in the power flow between the machine and the driver. A simple way to constrain this undesirable ripple power in the converter and prevent it from being seen by the battery pack is to use large capacitance in parallel with the dc source, which absorbs the ripple power. However, the use of large electrolytic capacitors will greatly add to the cost and size of the SRM drive systems. In addition, electrolytic capacitors are known to have much shorter lifetime and higher failure rate. Thus, methods to reduce the capacitance required in SRM drive systems are investigated to improve their power density and reliability.
They key contributions of this dissertation are listed as follows.
• A unified model covering motoring mode and generating mode for SRM drives using the
IMPC topology is developed and a generalized high-bandwidth control method with
seamless transition ability is presented. With the topology and control strategy, the
capacitance requirement in SRM drives can be greatly relaxed. The validity and stability is
verified using simulation and experimental results.
• The generalized power decoupling topology that can achieve capacitance reduction is
derived from the IMPC topology. Based on the generalized topology, more SRM driver
topologies with reduced capacitance requirement can be developed. Different derived
topologies may feature certain advantages because of the transient power unit selected.
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• A quasi-Z-source integrated multiport converter (ZIMPC) is derived from the generalized
power decoupling topology. Analysis, modeling and control design are discussed for this
topology. Thanks to the quasi-Z-source unit, this topology features the advantages of lower
voltage stress and adjustable excitation voltage with larger range, comparing to the IMPC
topology.
• Practical considerations of adopting the proposed method for EV applications are discussed,
including the generating mode of operation and mode transition of the proposed topologies,
the power density and efficiency comparison of different topologies. Simulation and/or
experimental results are presented.
5.2 Future Development
• With the proposed topologies and control strategy, adjustable excitation voltage during
operation is enabled. Especially, for the ZIMPC topology, magnetizing voltage and
demagnetizing voltage can be adjusted without affecting the dc link voltage, thanks to its
additional degree of freedom. Properly adjusting the voltage applied to the SRM phases
during different operating modes and different stages of current commutation can lead to
additional benefits, such as better dynamic response, increased efficiency, and reduced
acoustic noise.
• More topologies can be derived from the generalized power-decoupling topology by
inserting different transient power units. Further investigations of more possible topologies
are desired to discover candidates with lower cost, higher efficiency, and better power
density. Isolated topologies are also possible if isolated transient power units are used.
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Isolated topologies are desirable for direct solar panel-driven drive systems, which can be useful in remote areas without convenient access to electric power. In such systems, large capacitance is usually needed to ensure that dc current is taken from solar panels, and the proposed method can potentially solve the problem.
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APPENDIX
DETAILS ON THE SRM USED IN EXPERIMENTS
Table A.1. Parameters of the Switched Reluctance Motor Switched Reluctance Motor (SRM) Parameter Value Rated speed 1500 rpm Rated power 1.2 kW Rated phase current 14 A Non-saturation inductance 9 mH (unaligned) / 31 mH (aligned) Saturation inductance (at 15.4 A) 9 mH (unaligned) / 23 mH (aligned)
Figure A.1. Cross-section and 3D view of the 2-phase SRM4
4 © 2016 IEEE. From L. Gu, W. Wang, B. Fahimi, A. Clark, and J. Hearron, "Magnetic Design of Two-Phase Switched Reluctance Motor with Bidirectional Startup Capability," IEEE Transactions on Industry Applications, vol. 52, no. 3, pp. 2148-2155, 2016.
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BIOGRAPHICAL SKETCH
Fan Yi was born in Jinan, China. He received his Bachelor of Science degree in Electrical
Engineering from Shandong University, Jinan, China in 2013. He started his Ph.D. study at The
University of Texas at Dallas in August 2013. During the Ph.D. study, he was working as a research assistant in the Renewable Energy and Vehicular Technology Laboratory at The
University of Texas at Dallas. His research interests include analysis, design, and control of power converters for motor drive and renewable energy applications.
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CURRICULULM VITAE
Fan Yi
Address: 800 West Campbell Road, EC33, Richardson, Texas 75080 Email: [email protected]
EDUCATION HISTORY
• Doctor of Philosophy, Electrical Engineering, The University of Texas at Dallas,
Richardson, TX, August 2017
• Bachelor of Science, Electrical Engineering and Automation, Shandong University, Jinan,
China, June 2013
WORK EXPERIENCE
• Research Assistant, The University of Texas at Dallas, August 2013 to August 2017
• Motor Control Intern, ABB Inc. US Corporate Research Center, September 2016 to
December 2016
PUBLICATIONS
• Fan Yi, Wen Cai “A Quasi-Z-source Integrated Multiport Power Converter as Switched
Reluctance Motor Drives for Capacitance Reduction and Wide-Speed-Range Operation,” in
IEEE Transactions on Power Electronics, vol. 31, no. 11, pp. 7661-7676, Nov. 2016.
• Fan Yi, Wen Cai “Modeling, Control and Seamless Transition of Bi-directional Battery-
Driven SRM/Generator Drive based on IMPC for EV Applications,” in IEEE Transactions on
Power Electronics, vol. 31, no. 10, pp. 7099-7111, Oct. 2016.
• Wen Cai, Fan Yi, Cosoroaba, E.; Fahimi, B., "Stability Optimization Method Based on Virtual
Resistor and Nonunity Voltage Feedback Loop for Cascaded DC–DC Converters," in IEEE
Transactions on Industry Applications, vol.51, no.6, pp.4575-4583, 2015.
• Dingyi He, Wen Cai and Fan Yi, "A power decoupling method with small capacitance
requirement based on single-phase quasi-Z-source inverter for DC microgrid
applications," 2016 IEEE Applied Power Electronics Conference and Exposition (APEC),
Long Beach, CA, 2016, pp. 2599-2606.
• Wen Cai, Fan Yi “Topology simplification method based on switch multiplexing technique to
deliver DC–DC–AC converters for microgrid applications,” in IEEE Energy Conversion
Congress and Exposition (ECCE), pp.6667-6674, 20-24 Sept. 2015.
• Fan Yi, Wen Cai “Repetitive Control–Based Current Ripple Reduction Method with a Multi–
Port Power Converter for SRM Drive,” in IEEE Transportation Electrification Conference &
Expo (ITEC), pp.1-6, 14-17 June 2015.
HONORS AND AWARDS
• First class scholarship of Shandong University, 2010.
• Nari-Relays scholarship, 2010.
• Second class scholarship of Shandong University, 2011.
• Outstanding winner of Mathematical Contest in Modeling, 2013.
• Louis Beecherl, Jr. Graduate Fellowship, The University of Texas at Dallas, 2016.
LANGUAGES
• Mandarin Chinese
• English
PROFESSIONAL MEMBERSHIPS
• Student Member, IEEE