Abstract Transformer Design for Dual Active Bridge
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ABSTRACT TRANSFORMER DESIGN FOR DUAL ACTIVE BRIDGE CONVERTER by Egor Iuravin Power transformers have a long history which takes root in 19th century when Michael Faraday introduced the definition of the electromagnetic induction. In the beginning of the 1960s, there was a tendency to increase the frequency of switch mode power supplies. This thesis provides the detailed summary of operating principles, design, simulation and experimental analysis of high frequency power transformers. The focus of this research is to find an optimal transform solution for the DAB converter operating at a power level of 2 kW. Furthermore, the investigation will be carried out to estimate and measure the contact loss of a transformer. TRANSFORMER DESIGN FOR DUAL ACTIVE BRIDGE CONVERTER A Thesis Submitted to the Faculty of Miami University in partial fulfillment of the requirements for the degree of Master of Science in Computational Science and Engineering by Egor Iuravin Miami University Oxford, Ohio 2018 Advisor: Dr. Mark J. Scott Reader: Dr. Haiwei Cai Reader: Dr. Dmitriy Garmatyuk ©2018 Egor Iuravin This Thesis titled TRANSFORMER DESIGN FOR DUAL ACTIVE BRIDGE CONVERTER by Egor Iuravin has been approved for publication by College of Engineering and Computing and Department of Electrical and Computer Engineering ____________________________________________________ Dr. Mark J Scott ______________________________________________________ Dr. Haiwei Cai _______________________________________________________ Dr. Dmitriy Garmatyuk Table of Contents 1. Introduction ...........................................................................................................................2 1.1 The history of the transformers .......................................................................................................2 1.2 Dual Active Bridge Converter .........................................................................................................3 1.3 Thesis objectives ................................................................................................................................5 1.4 List of the chapters ...........................................................................................................................5 2. Transformer basics ................................................................................................................7 2.1 Transformer operation .....................................................................................................................7 2.1.1 Ideal Transformer ........................................................................................................................9 2.1.2 Real Transformer .........................................................................................................................9 2.2 High-frequency transformers overview ........................................................................................10 2.3 Magnetic Core types and Materials ..............................................................................................13 2.3.1 Saturation ...................................................................................................................................13 2.3.2 Magnetic Core Materials ...........................................................................................................14 2.3.3 Ferrite Core Shapes ...................................................................................................................16 2.4 Winding Types ................................................................................................................................17 2.4.1 Litz Wire ....................................................................................................................................17 2.4.2 Printed circuit board ..................................................................................................................18 2.4.3 Copper sheet. .............................................................................................................................19 2.5 High-frequency transformers design ............................................................................................19 3. Magnetizing inductance and parasitic components .........................................................26 3.1 Leakage and magnetizing inductance ...........................................................................................26 3.1.1 Leakage inductance determination ............................................................................................28 3.1.2 How to change the leakage inductance in the transformer ........................................................29 3.1.3 Magnetizing inductance determination......................................................................................29 3.1.4 How to change the magnetizing inductance ..............................................................................30 3.2 Winding Capacitance .....................................................................................................................31 3.2.1 Determination of the winding capacitance ................................................................................32 3.2.2 How to change the winding-to-winding capacitance .................................................................33 3.3 Contact Resistance ..........................................................................................................................33 4. Transformer loss ..................................................................................................................35 4.1 Winding loss ....................................................................................................................................35 4.1.1 Determination of the winding resistance ...................................................................................39 4.2 Core loss ...........................................................................................................................................40 4.2.1 Modified Steinmetz equation (MSE). ........................................................................................41 4.2.2 Generalized Steinmetz equation (GSE) .....................................................................................41 4.2.3 Improved GSE method (IGSE)..................................................................................................42 4.2.4 Natural Steinmetz equation (NSE) ............................................................................................42 4.2.5 Waveform coefficient Steinmetz equation (WCSE) ..................................................................42 4.2.6 Determination of the core loss ...................................................................................................44 5. Simulation and Experimental Results ...............................................................................45 5.1 Transformers Design ......................................................................................................................45 5.2 Simulation ........................................................................................................................................47 5.3 Experimental results .......................................................................................................................49 5.4 Comparison and Cost .....................................................................................................................53 6. Conclusion and future work ...............................................................................................55 Appendix ......................................................................................................................................60 iii List of Tables Table I. Characteristic of the main magnetic core materials .........................................................15 Table II. Initial data of the power transformers .............................................................................45 Table III. transformer’s cores data ................................................................................................46 Table IV. Loss coefficients ...........................................................................................................48 Table V. Comparison of the results ...............................................................................................52 Table VI. Comparison of the Transformer’s cost ..........................................................................53 iv List of Figures Figure 1.1: Faraday's ring transformer [4] .......................................................................................2 Figure 1.2: Voltage waveforms of the dual active bridge converter ...............................................4 Figure 1.3: Dual active bridge converter. ........................................................................................5 Figure 2.1: The electric diagram of the transformer. .......................................................................8 Figure 2.2: The ideal transformer circuit. ........................................................................................9 Figure 2.3: The real transformer equivalent circuit. ........................................................................9 Figure 2.4: The model of the planar transformer. .........................................................................11