The Pennsylvania State University The Graduate School Department of Electrical Engineering ENERGY HARVESTING USING AC MACHINES WITH HIGH EFFECTIVE POLE COUNT A Dissertation in Electrical Engineering by Richard Theodore Geiger 2010 Richard Theodore Geiger Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2010 ii The dissertation of Richard Theodore Geiger was reviewed and approved* by the following: Heath Hofmann Associate Professor, Electrical Engineering Dissertation Advisor Chair of Committee George A. Lesieutre Professor and Head, Aerospace Engineering Mary Frecker Professor, Mechanical & Nuclear Engineering John Mitchell Professor, Electrical Engineering Jim Breakall Professor, Electrical Engineering W. Kenneth Jenkins Professor, Electrical Engineering Head of the Department of Electrical Engineering *Signatures are on file in the Graduate School iii ABSTRACT In this thesis, ways to improve the power conversion of rotating generators at low rotor speeds in energy harvesting applications were investigated. One method is to increase the pole count, which increases the generator back-emf without also increasing the I2R losses, thereby increasing both torque density and conversion efficiency. One machine topology that has a high effective pole count is a hybrid “stepper” machine. However, the large self inductance of these machines decreases their power factor and hence the maximum power that can be delivered to a load. This effect can be cancelled by the addition of capacitors in series with the stepper windings. A circuit was designed and implemented to automatically vary the series capacitance over the entire speed range investigated. The addition of the series capacitors improved the power output of the stepper machine by up to 700%. At low rotor speeds, with the addition of series capacitance, the power output of the hybrid “stepper” was more than 200% that of a similarly sized PMDC brushed motor. Finally, in this thesis a hybrid lumped parameter / finite element model was used to investigate the impact of number, shape and size of the rotor and stator teeth on machine performance. A typical off-the-shelf hybrid stepper machine has significant cogging torque by design. This cogging torque is a major problem in most small energy harvesting applications. In this thesis it was shown that the cogging and ripple torque can be dramatically reduced. These findings confirm that high-pole-count topologies, and iv specifically the hybrid stepper configuration, are an attractive choice for energy harvesting applications. v TABLE OF CONTENTS LIST OF FIGURES ..................................................................................................... viii LIST OF TABLES ....................................................................................................... xii ACKNOWLEDGEMENTS ......................................................................................... xiii Chapter 1 INTRODUCTION ....................................................................................... 1 Energy Harvesting ................................................................................................ 1 Applications for Energy Harvesting ..................................................................... 2 Performance Metric for Energy Harvesting ......................................................... 5 Contribution .......................................................................................................... 13 Thesis Overview ................................................................................................... 14 Chapter 2 REVIEW OF ELECTROMAGNETIC FIELD THEORY.......................... 17 Maxwell Equations ............................................................................................... 17 Magnetic Circuits and Fields ................................................................................ 18 Magnetic Circuit Analogy .................................................................................... 20 Soft Magnetic Materials ....................................................................................... 22 Permanent Magnets .............................................................................................. 25 Faraday‟s Law, Terminal Voltage, and Inductance .............................................. 27 Electromagnetic Energy, Co-energy, and Torque ................................................ 28 Permeance ............................................................................................................. 33 Chapter 3 THE NEED FOR HIGH POLE COUNT .................................................... 35 Electrical Power of a Synchronous Generator ...................................................... 35 Torque as Function of Machine Parameters ......................................................... 37 Efficiency of a Synchronous Generator ................................................................ 38 Increasing the Electrical Power from a Synchronous Generator .......................... 39 Possible High Pole Count Machine Topologies ................................................... 41 Hybrid Stepper Machine ....................................................................................... 44 Construction .................................................................................................. 44 Teeth .............................................................................................................. 45 Field Windings in the Stator .......................................................................... 47 Flux Paths ...................................................................................................... 47 Maximum Power Point of the Hybrid Stepper ..................................................... 49 Effective Bandwidth of Series Capacitance ......................................................... 52 Effects of Magnetic Saturation ............................................................................. 52 Specific Power Indicator ....................................................................................... 53 Chapter 4 MODEL DEVELOPMENT ........................................................................ 54 vi Method of Analysis ............................................................................................... 54 Determine Equivalent Magnetic Circuit Model of 2 Phase HSM ........................ 57 Developing the Expression for Flux in Each Pole ................................................ 60 Description of 2D FEA Model Used .................................................................... 62 Finite Element Software ....................................................................................... 65 Comparison of FEA to Experimental Results of Baseline Machine .................... 67 Chapter 5 DESIGN OF VARIABLE CAPACITOR CIRCUIT .................................. 69 Design ................................................................................................................... 69 Circuit Implementation ......................................................................................... 72 Capacitor Array ............................................................................................. 74 Switches ......................................................................................................... 75 Switch Drive Control ..................................................................................... 75 Diode Rectifier .............................................................................................. 76 Chapter 6 EXPERIMENTAL RESULTS .................................................................... 77 Test Setup ............................................................................................................. 78 Test Results ........................................................................................................... 80 Back-emf, Series Capacitance, and Load Resistance .................................... 80 Comparison of Measurements to Linear Model (no AC/DC rectification) ... 81 Optimal Load Resistance ............................................................................... 83 Power with Discrete Series Capacitance ....................................................... 84 Comparison: Stepper and Brushed PMDC .................................................... 87 Comparisons: NEMA 8, 11 and 23 size steppers. ......................................... 88 Number of Pole Pairs ..................................................................................... 89 Power versus Average Torque ....................................................................... 90 Cogging Torque ............................................................................................. 91 Results with Auto-switching Capacitor Circuit ............................................. 91 Chapter 7 EXPERIMENTAL RESULTS .................................................................... 95 Comparison of Slotted Teeth Model to a Cosine Distribution of Permeance ...... 98 Number of Pole Pairs (Nr) .................................................................................... 100 Tooth width to pitch ratio, t/p ............................................................................... 109 Tooth Height to Pitch Ratio, d/p ........................................................................... 112 Stator Tooth