University of Texas at Tyler Scholar Works at UT Tyler Electrical Engineering Theses Electrical Engineering Spring 5-8-2012 Four-Coil Wireless Power Transfer Using Resonant Inductive Coupling Sravan Annam Follow this and additional works at: https://scholarworks.uttyler.edu/ee_grad Part of the Electrical and Computer Engineering Commons Recommended Citation Annam, Sravan, "Four-Coil Wireless Power Transfer Using Resonant Inductive Coupling" (2012). Electrical Engineering Theses. Paper 19. http://hdl.handle.net/10950/87 This Thesis is brought to you for free and open access by the Electrical Engineering at Scholar Works at UT Tyler. It has been accepted for inclusion in Electrical Engineering Theses by an authorized administrator of Scholar Works at UT Tyler. For more information, please contact [email protected]. FOUR-COIL WIRELESS POWER TRANSFER USING RESONANT INDUCTIVE COUPLING by SRAVAN GOUD ANNAM A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering Department of Electrical Engineering David M. Beams, Ph.D, PE, Committee Chair College of Engineering and Computer Science The University of Texas at Tyler May 2012 Acknowledgements I appreciate my advisor Dr. David M. Beams for his continuous teaching, guidance, support and patience throughout my thesis work. His vast knowledge and valuable suggestions were very helpful in achieving my target. I thank my committee members Dr. Hassan El-Kishky and Dr. Hector A. Ochoa for their valuable time and reviews. I thank Dr. Mukul Shirvaikar for his continuous support from the beginning of my master’s course. I am grateful to each and every professor and friends for their teachings and guidance. I thank my family members for their love and encouragement. Finally I thank the almighty god for this wonderful life. Table of Contents List of Figure……………………………………………………………………………………...iii List of Tables……………………………………………………………………………………...vi Abstract…………………………………………………………………………………………...vii Chapter One: Introduction……………………………………………………………………….1 1.1 Organization of thesis……………………………………………………………….2 Chapter Two: Background……………………………………………………….……………...3 2.1 Early developments in wireless power transfer………………………………………...3 2.2 Methods for wireless power transfer ................................................................................ 5 2.3 Developments in wireless power transfer (WPT): ......................................................... 6 2.4 Review of prior research in WPT: .................................................................................... 8 Chapter Three: Development and experimental validation of a coupled-resonant model for wireless power transfer……..………………………………………………………… 11 3.1 Model development……………………………………………………………………...11 3.2 Matlab ® simulation program for analysis of four-coil WPT networks..…………..13 3.3 Experimental validation of the four-coil WPT matlab model…...…………………..15 3.3.1 Experimental setup…………………………………………………………………17 3.3.2 Validation with D23 = 25.4mm………...…………………………………………..18 3.3.3 Experimental results with D23 =38.1mm………………………………………….22 3.3.4 Experimental results with D23 = 50.8mm….……………………………………...24 3.4 Summary…………………………………………………………………………...26 Chapter Four : Calculation of mutual inductance from magnetic vector potential for WPT applications………………………………………………………………………………27 4.1 Calculation of mutual inductance from the magnetic vector potential……………...28 i 4.2 Numerical methods for calculation of mutual inductance from the magnetic vector potential .………………………………………………………………………………………30 4.3 Computation of self-inductance with the method of magnetic vector potential…...31 4.4 Empirical tests of numerical computation of self and mutual inductances………..32 4.4.1 Experimental coil descriptions and comparison of measured and calculated self-inductances……………………………………………………………………...…….33 4.4.2 Measured and calculated mutual inductances between a pair of coils…………………………………………………………………………………………34 4.5 Application to inductors backed by ferrite……..……………………………………...37 4.5.1 Experiment in simulating inductance of a coil in proximity to two ferrite sheets 38 4.6 Summary………………………………………………………………………….............42 Chapter Five: Design of WPT systems by reflected impedances in loosely-coupled inductors………………………………………………………………………………….42 5.1 WPT system model: ......................................................................................................... 42 5.2 Reflected impedance in mutually-coupled inductors with RC termination .............. 44 5.3 Reflected impedance in mutually-coupled inductors with resistive termination: .... 49 5.4 Application of reflected impedances to the analysis of a four-coil WPT system: ... 51 5.5 Application of reflected impedances to the design of a four-coil WPT system: ...... 54 5.6 Validation of the design methodology using impedance transformation .................. 58 5.6.1 Experimental method of design validation ...................... ………………………..59 5.6.2 Summary of experimental results ........... ………………………………………….61 5.6.3 Discussion ............................................................................................. ……………..64 5.7 Summary ............................................................................................................................ 66 Chapter Six: Conclusions and future work………...…………………………………………69 6.1 Conclusions ....................................................................................................................... 67 6.2 Future work ....................................................................................................................... 67 References………...……………………………………………………………………………..68 ii List of Figures Figure 2.1: Tesla’s wireless energy apparatus as depicted in US patent 645,576………...3 Figure 2.2: Tesla’s Wardenclyffe Tower………..…………………………………………….4 Figure 2.3: Launch port (inductive charger for iPad2)...................................................................6 Figure 2.4: Samsung wireless charging hub for 3D glasses………………………………………7 Figure 3.1: Overall schematic of the four-coil wireless power transfer (WPT) system ………...11 Figure 3.2: Graphical user interface for WPT Model…………………………………………....14 Figure 3.3: Definition of initial radius and horizontal pitch of a single-layer spiral coil ……….16 Figure 3.4: Coil geometry of model-validation experiments…………………………………….17 Figure 3.5: Experimental apparatus for tests to validate Matlab WPT simulation program…………………………………………………………………………………………..18 Figure 3.6: Simulated and measured input current I1 vs. frequency.…………………………….20 Figure 3.7: Simulated and measured voltage across L2 vs. frequency….………………………..20 Figure3.8: Voltage across L3 vs. frequency……………………………………………............…21 Figure 3.9: Voltage across RL vs. frequency ……………………….……………………………21 Figure 3.10: Simulated and measured input current I1 vs. frequency…………...……………….22 Figure 3.11: Voltage across L2 vs. frequency …………………………………………………...23 Figure 3.12: Voltage across L3 vs. frequency………………………………………………...….23 Figure 3.13: Voltage across RL vs. frequency……………………………………………...…….24 Figure 3.14: Simulated and measured input current I1 vs. frequency…………………………....24 Figure 3.15: Voltage across L2 vs. frequency …………………………….……………………..25 Figure 3.16: Voltage across L3 vs. frequency …….………………….………………………….25 Figure 3.17: Voltage across RL vs. frequency………………...………………………………….26 Figure 4.1: Basic four-coil WPT system…………………………………………………………27 Figure 4.2: Geometry for computation of flux linkages and mutual inductance between closed paths L1 and L2………………………………………………………………………………...…28 Figure 4.3: Geometry for computation of magnetic vector potential and mutual inductance…...29 Figure 4.4: Geometry for numerical estimation of magnetic vector potential and mutual iii inductance………………………………………………………………………………………..30 Figure 4.5: Example of interleaved inductors for applying the magnetic-vector potential method to calculation of self-inductance of a spiral coil…………………………………………………32 Figure 4.6: GUI of the solenoid creator………………………………………………………….33 Figure 4.7: GUI of Matlab mutual inductance calculator .............................................................36 Figure 4.8: Inductors LA and LB positioned above a sheet of high-permeability ferrite material……………………………………………………………………………………37 Figure 4.9: Solenoid coils mounted coaxially ……………..…………………………………38 Figure 4.10: Simulated and measured results for mutual inductance between two solenoid coils vs. height over a ferrite sheet………………………………………………………………...…..38 Figure 4.11: Geometry for experiments for determining the inductance of a spiral-wound coil between ferrite sheets……………………………………………………………………...……..40 Figure 4.12: Measured and simulated inductance of a spiral-wound coil between ferrite sheets……………………………………………………………………………………………..41 Figure 5.1: Coupled-inductor model for resonant wireless power-transfer system……………. 43 Figure 5.2: Coupled inductors with RC termination with voltage source excitation……………46 Figure 5.3: Equivalence of mutually-coupled inductors with RC termination and a single coil with reflected resistance Rref and reactance Xref …………………...…………………………….47 Figure 5.4: Resistive and reactive components of the input impedance at the terminals of La for values specified and for kab = 0.2 …………………………………………………..……………48 Figure 5.5: Resistive and reactive components of the input impedance at the terminals of La for values specified and for kab = 0.4 …………...……...……………………………………………49 Figure 5.6: Resistive and reactive components