A soft switch back to back bi directional DC DC converter and the FPGA based digital control design

A SOFT-SWITCHING BACK-TO-BACK BI-DIRECTIONAL DC-DC CONVERTER AND THE FPGA BASED DIGITAL CONTROL DESIGN XU XINYU A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2008 Acknowledgements First and foremost, I would like to thank my supervisors, Prof. Ashwin M. Khambadkone, and Prof. Ramesh Oruganti, for their constantly guidance, encouragement, and thought-provoking discussions throughout the course of the research. I sincerely appreciate their valuable advice and help. I am grateful to National University of Singapore for supporting this research project through the research grant R-263-000-154-112 Universal Power Electronic Cell. In addition, I would like to thank the laboratory officers for their logistics support and assistances rendered. In no order of merit, they are Mr. Teo Thiam Teck (Centre for Power Electronics), Mr. Woo Ying Chee and Mr. Mukaya Chandra (Electrical Machines & Drives Laboratory) and Mr. Abdul Jalil Bin Din (PCB Fabrication Facility). I also thank the National University of Singapore for providing me with the scholarship support and excellent research facilities. I would like to thank my friends, Anshuman Triphthi, Kanakasabai Viswanathan, Singh Ravinder Pal, Kong Xin, Deng Heng, Yin Bo, Chen Yu, Cao Xiao, Toh Meng Leong, Lim Ban Thian, and Lim Joo Peng Barry for their concerned help. I thank the National Semiconductor, Texas Instrument, EPCOS AG, and Ferroxcube for their support in providing samples for testing. Finally, I would like to thank my dearest family: my parents, my wife Yanyan, my brother Xiaofeng and my sister-in-law Huifen, and my cute niece Wenwen. I dedicate this thesis to them. Without their love, confidence and support, I will not be able to finish the work. Summary In this thesis, a soft switching back-to-back bi-directional DC-DC converter is proposed, and an FPGA based digital control design for it is developed. The bi-directional DC-DC converter is able to handle the power flow in both directions, either from the high voltage side to the low voltage side (step-down mode), or from the low voltage side to the high voltage side (step-up mode). Hence it can be used to transfer power between two networks which have different voltages or different functions. Compared to the bi-directional topologies which have been reported in the reference, the proposed bi-directional topology has no input inductor in the circuit. It always functions as a minimal phase system in both the step-down and step-up mode operations. There is no RHP (right-half-plane) zero in the system model. This makes the converter model simple and reduces the difficulty of designing the close loop control. The converter is also able to reduce the switching power loss by realizing the zero voltage switching (ZVS) for all switches in the circuit. The simple structure, small component count and the ZVS transition means low cost, high efficiency and high power density of the converter. Compared to the analog system, the digital control system has the following advantages: low power dissipation, short design cycle and low design effort, and ease of designing complicated control structure. Hence a digital controller is proposed in the thesis. A Xilinx Spartan-3 FPGA (field programmable gate array) is selected as the hardware platform to implement the digital system. In this thesis, the practical implementation of the digital controller is investigated. The main focus is trying to reduce the requirements on the digital platform, such as lowering the power consumption. During the implementation process of the digital controller, the dynamic range of the voltage error is restricted, which helps to reduce the word length of the controller. The proposed bi-directional converter is operated with fixed duty ratio and phase shift control. Through analysis, a simple fist-order system is obtained for the converter. Using a digital PI controller, the close loop system achieves a satisfactory dynamic performance in both step-down and step-up mode operations. A 100 W prototype converter is built, and a maximum efficiency of 92.3% is measured in the experiment. The back-to-back bi-directional converter is developed based on a soft switching asymmetrical PWM half-bridge (APHB) DC-DC converter. Analysis and control design for the APHB converter is carried out first, which provides a foundation for the proposed bi-directional converter design. The APHB converter is one of the complementary driven PWM converter topology, which presents an inherent ZVS capability. Compared to conventional soft switching resonant converters, the APHB converter has the following advantages: low voltage/current stress level, low conduction loss, and constant frequency PWM control. In this thesis, the ZVS transition process in the APHB converter is analyzed. The influence of transformer leakage inductance and the interlock delay time between complementary gate signals on the ZVS transition is investigated. Based on the analysis, we calculated the bounds for the two circuit parameters, that ensures the successful ZVS transition. Although the APHB converter is a good soft switching topology, it has an unwieldy transfer function for control design. The converter is a fourth-order system. There is a double pole and double zero in the transfer function, which produces a notch in the bode diagram. This complicated structure, especially the notch makes the control design quite challenging. It is difficult to achieve a satisfactory phase margin and bandwidth for the close loop system. In this thesis, a design method for simplifying the control structure is presented, which solves the notch problem and facilitates the control design. i Contents List of Figures iv List of Tables Introduction 1.1 Bi-directional DC-DC Converters . . . . . . . . . . . 1.1.1 Digital Control Design . . . . . . . . . . . . . 1.2 Soft Switching Technique and the APHB Converter . 1.3 Control Analysis and Design of the APHB converter . 1.4 Contributions of the Thesis . . . . . . . . . . . . . . 1.5 Thesis Layout . . . . . . . . . . . . . . . . . . . . . . viii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 12 13 15 Background and Problem Definition 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Bi-directional Converters . . . . . . . . . . . . . . . . . 2.3 Digital Control Design . . . . . . . . . . . . . . . . . . 2.4 Asymmetrical PWM Half Bridge DC-DC Converter . . 2.4.1 Modification of the APHB converter . . . . . . 2.4.2 Soft Switching Analysis of the APHB Converter 2.4.3 Control Scheme of the APHB Converter . . . . 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 18 19 25 32 38 41 43 47 The APHB Converter: Foundation of the Back-to-Back Bi-directional DC-DC Converter, Part I: Analysis of the Circuit Topology and Soft Switching Transition 49 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2 Asymmetrical PWM Half-bridge Topology . . . . . . . . . . . . . . . 51 3.3 Principle of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.4 Converter Design Considerations . . . . . . . . . . . . . . . . . . . . 58 3.4.1 Revised Output Voltage . . . . . . . . . . . . . . . . . . . . . 58 ii 3.5 3.6 3.4.2 Considerations to ensure ZVS Transition . . . . . . . . 3.4.3 Gate Signal Generator and PCB Layout Considerations Experimental Results and Analysis . . . . . . . . . . . . . . . 3.5.1 Experimental Results . . . . . . . . . . . . . . . . . . . 3.5.2 Power Loss Analysis . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 69 70 70 72 76 The APHB Converter: Foundation of the Back-to-Back Bi-directional DC-DC Converter, Part II: FPGA based Digital Control Design 79 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.2 Model Derivation of the APHB Converter . . . . . . . . . . . . . . . 83 4.3 Consideration on the Input Capacitance . . . . . . . . . . . . . . . . 90 4.4 Voltage Feed-forward Loop Design . . . . . . . . . . . . . . . . . . . . 92 4.5 Influence of Non-ideal Capacitors to the System Transfer Function . . 95 4.6 Analog Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.6.1 Hardware Implementation . . . . . . . . . . . . . . . . . . . . 106 4.7 Digital Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.8 Digital Control Implementation . . . . . . . . . . . . . . . . . . . . . 111 4.8.1 Selection of the Analog to Digital Converter (ADC) . . . . . . 111 4.8.2 Digital PWM Design . . . . . . . . . . . . . . . . . . . . . . . 113 4.8.3 Choice of the Controller Resolution . . . . . . . . . . . . . . . 114 4.8.4 Dynamic Range of the Voltage Error Ve . . . . . . . . . . . . . 121 4.8.5 Design of the Controller Filter Structure . . . . . . . . . . . . 129 4.9 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 4.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 The Soft-Switching Back-to-Back Bi-directional DC-DC Converter 137 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 5.2 Step-down Mode Operation . . . . . . . . . . . . . . . . . . . . . . . 139 5.2.1 Principle of Operation . . . . . . . . . . . . . . . . . . . . . . 139 5.2.2 Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . 145 5.2.3 Input and Output Capacitance Selection . . . . . . . . . . . . 148 5.2.4 ZVS Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 5.2.5 Bounds Calculation for the Transformer Leakage Inductance . 151 5.2.6 Possible ZVS Range . . . . . . . . . . . . . . . . . . . . . . . 154 5.2.7 Bounds Calculation for the Interlock Delay Time . . . . . . . 155 5.2.8 Large Signal Average Model and Small Signal Model Derivation 156 5.2.9 Digital Controller Design . . . . . . . . . . . . . . . . . . . . . 159 5.3 Step-up Mode Operation . . . . . . . . . . . . . . . . . . . . . . . . . 162 5.3.1 Principle of Operation . . . . . . . . . . . . . . . . . . . . . . 162 5.3.2 Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . 167 5.3.3 Input and Output Capacitance Selection . . . . . . . . . . . . 170 iii 5.4 5.5 5.6 5.7 5.3.4 ZVS Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.5 Bounds Calculation for the Transformer Leakage Inductance . 5.3.6 Possible ZVS Range . . . . . . . . . . . . . . . . . . . . . . . 5.3.7 Bounds Calculation for the Interlock Delay Time . . . . . . . 5.3.8 Large Signal Average Model and Small Signal Model Derivation 5.3.9 Digital Controller Design . . . . . . . . . . . . . . . . . . . . . Digital Controller Implementation . . . . . . . . . . . . . . . . . . . . Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . Power Loss Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.1 Gate Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.2 Power Loss Analysis for Low Load Condition . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 173 175 175 176 178 178 182 187 190 191 194 Conclusions And Future Work 195 6.1 Scope of Future Research . . . . . . . . . . . . . . . . . . . . . . . . . 197 Bibliography 200 A List of Publications 210 B Photos of the Experimental Prototype Converter 212 iv List of Figures 1.1 1.2 1.3 1.4 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 Application of the bi-directional converter: dual-voltage electric systems in automobiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . Application of the bi-directional converter: the Fuel Cell and the energy storage system . . . . . . . . . . . . . . . . . . . . . . . . . . . . The soft-switching back-to-back bi-directional converter . . . . . . . . The asymmetrical PWM half bridge (APHB) DC-DC converter . . . Bi-directional converter transfers power from 42 V system to 14 V system Bi-directional converter in the standby status . . . . . . . . . . . . . Bi-directional converter transfers power from 42 V system to 14 V system Bi-directional converter transfers power from 14 V system to 42 V system The ZVS bi-directional C´ uk converter [1] . . . . . . . . . . . . . . . . Bi-directional DC-DC converter proposed by Jain et al. [2] . . . . . . Phase-shift bi-directional DC-DC converter [3] . . . . . . . . . . . . . The dual half bridge bi-directional DC-DC converter proposed by Peng et al. [4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The soft-switching back-to-back bi-directional converter . . . . . . . . Block diagram of the digital controlled system . . . . . . . . . . . . . Binary expression of the duty ratio command D(k) . . . . . . . . . . General switching characteristics . . . . . . . . . . . . . . . . . . . . (a) Parallel-loaded resonant converter, (b) series-loaded resonant converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) ZVS resonant-switch converter, (b) ZCS resonant-switch converter The asymmetrical PWM half bridge DC-DC converter . . . . . . . . The APHB converter with half wave rectifier . . . . . . . . . . . . . . The voltage transfer ratio of the ideal APHB converter . . . . . . . . The modified asymmetrical PWM half bridge DC-DC converter . . . The APHB converter with the asymmetrical transformer turns ratios The output inductor current ripple ∆iL vs. the duty ratio D . . . . . 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Conferences: • Xinyu Xu, Ashwin M Khambadkone, Ramesh Oruganti, ”A Soft-Switched Backto-Back Bi-directional DC-DC Converter with the FPGA based Digital Control for Automotive Applications”, Proceedings of the 33th Annual Conference of the IEEE Industrial Electronics Society (IECON 2007), Nov 2007. • Xinyu Xu, Ashwin M Khambadkone, Ramesh Oruganti, ”An Asymmetrical 211 Half Bridge Flyback Converter with Zero-Voltage and Zero-Current Switching”, Proceedings of the 30th Annual Conference of the IEEE Industrial Electronics Society (IECON 2004), Nov 2004, page 767-772. • Xinyu Xu, Ashwin M Khambadkone, Ramesh Oruganti, ”Close Loop Control of an Asymmetrical Half Bridge DC-DC Converter Considering Parasitics Effect”, Proceedings of the 35th IEEE Power Electronics Specialists Conference (PESC 2004), June 2004, page 1642-1647. • Xinyu Xu, Ashwin M Khambadkone, Ramesh Oruganti, ”Analysis and Design of an Optimized Asymmetrical Half-Bridge DC-DC Converter”, Proceedings of the 5th international conference on power electronics and drive systems (PEDS 2003), Nov 2003, page 120-125. • Ashwin M Khambadkone, Ramesh Oruganti, Jiang Yonghong, Xinyu Xu, ”Power Electronic Systems Using Versatile Power Electronic Cell: UPEC”, Proceedings of the 33rd IEEE Power Electronics Specialists Conference (PESC 2002), Jun 2002, page 620-625. 212 Appendix B Photos of the Experimental Prototype Converter 213 Figure B.1: 3.3 V APHB Converter 214 Figure B.2: 14 V APHB Converter 215 Figure B.3: Analog control board 216 Figure B.4: Xilinx Spartan-3 FPGA 217 Figure B.5: ADC board 218 Figure B.6: Back-to-back bi-directional DC-DC Converter [...]... this thesis is the analysis and design of a soft switching bi- directional DC- DC converter, including the circuit design and the FPGA based digital control design 1.1 Bi- directional DC- DC Converters The bi- directional DC- DC converter can act as the energy linkage between different networks which have different voltages and functions For example, the bi- 5 directional converter is very appropriate for the. .. based on the APHB converter The objectives of the chapter are 17 listed as follows: • Analysis of the operation principle of the bi- directional converter • Analysis of the ZVS transition as well as the circuit parameters The possible ZVS range of the load variation is also calculated • Derivation of the large signal average model and the small signal model for the bi- directional converter Based on the derived... bi- directional converter transfers power from the fuel cell to the battery or ultra-capacitor, and the energy is stored there On the other hand, if the AC load like a traction motor can regenerate power, the bi- directional converter can also store this part of energy to the battery or ultra-capacitor • During the load transient conditions, since the dynamic response of the fuel cell may not be fast enough to. .. Application of the bi- directional converter: dual-voltage electric systems in automobiles The bi- directional DC- DC converters can also be applied in the fuel cell application and the battery or ultra-capacitor based energy storage system [7], [8], as shown in Fig 1.2 The bi- directional converter is able to provide the following two functions • When the system operates in the storage mode, the bi- directional. .. solves the notch problem in the control structure and facilitates the control design 1.5 Thesis Layout Chapter 1 presents a brief introduction of this thesis The soft switching technology and an asymmetrical PWM half bridge DC- DC converter is introduced Based on them, a soft switching back- to -back bi- directional DC- DC converter is proposed Chapter 2 reviews the development of the bi- directional converters,... of the digital platform, e.g., FPGA, has attracted lots of interest from the researchers, as it is reprogramable, has high execution speed, and also its cost is low This makes it very suitable to implement and test the digital controller during the design period Once the digital control design is verified on the FPGA platform, it can be easily translated into the synthesis with standard ASICs (application... examine and review the development of the bi- directional converter In order to achieve the bi- directional function based on the soft switching APHB converter, the background of the APHB converter is investigated The remaining problems in the APHB converter and the bi- directional converter which have not been solved in the past research is discussed 19 2.2 Bi- directional Converters In this thesis, the. .. calculated, that ensures the successful ZVS transition Chapter 4 analyzes the system model of the APHB converter Based on it, a digital control design is presented The objectives of this chapter are listed as follows: • The input capacitance value is selected carefully, which can solve the notch problem in the bode diagram and facilitate the control design • FPGA based digital control design for the APHB converter. .. decreased to zero The zero voltage switching is thus achieved It can be seen from Fig 1.4 that the parasitic capacitance of the switch and the leakage inductance of the transformer form the resonant network, and achieve the ZVS There is no need to insert additional components to produce the resonance An important advantage of the APHB converter is that the resonant condition only exists during the small... optimum because its analysis is not easy and it poses difficulties in the design of the output filter 11 To overcome the above drawbacks, the asymmetrical PWM half bridge (APHB) DCDC converter is proposed as an alternative solution by Imbertson and Mohan [12], Oruganti [14], as shown in Fig 1.4 In this thesis, the APHB topology is the base circuit The back- to -back bi- directional converter is developed based . from the fuel cell to the battery or ultra-capacitor, and the energy is stored there. On the other hand, if the AC load like a traction motor can regenerate power, the bi- directional converter can. design and the FPGA based digital control design. 1.1 Bi- directional DC- DC Converters The bi- directional DC- DC converter can act as the energy linkage between dif- ferent networks which have different. power converters, such as the DC- DC, AC -DC, DC- AC converters. The main focus of this thesis is the analysis and design of a soft switching bi- directional DC- DC converter, including the circuit design