Steady-State Analysis of PWM Z-Bridge Source DC-DC Converter A thesis submitted in the partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering By Lokesh Kathi B.Tech., Koneru Lakshmaiah University, Guntur, India, 2013 2015 Wright State University WRIGHT STATE UNIVERSITY GRADUATE SCHOOL January 5, 2016 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY Lokesh Kathi ENTITLED Steady-State Analysis of PWM Z- Bridge Source DC-DC Converter BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in Electrical Engineering. ‘ Marian K. Kazimierczuk, Ph.D. Thesis Director Brian Rigling, Ph.D. Chair Department of Electrical Engineering College of Engineering and Computer Science Committee on Final Examination Marian K. Kazimierczuk, Ph.D. Yan Zhuang, Ph.D. Lavern Alan Starman, Ph.D. Robert E. W. Fyffe, Ph.D. Vice President for Research and Dean of the Graduate School Abstract Lokesh, Kathi. M.S.E.E., Department of Electrical Engineering, Wright State Uni- versity, 2015. Steady-state analysis of pulse-width modulated (pwm) z-bridge source dc-dc converter. A pwm z-bridge source dc-dc converter has a potential to play a prominent role in renewable energy applications, as it provides boosted and regulated output voltage and also behaves as an intermediate buffer between the source and the load. A complete circuit analysis of the z-bridge source converter is needed to understand the operation of this converter. Steady-state analysis of pulse-width modulated (pwm) z-bridge source dc-dc converter operating in continuous conduction mode (ccm) is given. Expressions describing waveforms of voltages across and currents through the all components of the pwm z-bridge source dc-dc converter to operate in steady- state condition are derived. The output-to-input voltage conversion ratio for ideal (lossless) and non-ideal (lossy) conditions are derived. Expressions for the minimum z-network inductance, the minimum filter inductance, and the minimum z-network capacitor are derived to operate converter in ccm. To determine the total power loss in pwm z-bridge source dc-dc converter, power loss expressions for each and every component and the overall efficiency of the pwm z-bridge source dc-dc converter are determined. Using power loss expressions, the efficiency analysis graphs are plotted using matlab to obtain the suitable operating region for the pwm z-bridge source dc-dc converter in terms of duty cycle, output current, and input voltage. An example of pwm z-bridge source dc-dc converter is considered and steady-state analysis is performed in saber. The simulation reults of designed pwm z-bridge source dc-dc converter are used to validate the theoretical results.Plant characteristics of pwm z-bridge source dc-dc converter are performed and the results are reported. iii Contents 1 Introduction 2 1.1 Switching-Mode Voltage Regulators . ... 2 1.2ThesisObjectives .............................. 3 1.3ThesisOutline................................ 3 2 Overview of Z-Source Inverters 5 2.1OriginofZ-SourceNetwork . 5 2.2Z-SourceInverters.............................. 6 2.3 PWM Z-Source DC-DC Converter with a Simplified Circuit Representation ............................... 11 2.4 Transfiguration of PWM Z-Source DC-DC Converter circuit to a Circuit of Simplified Bridge Network Representation . 12 3 Steady-State Analysis of PWM Z-Bridge Source DC-DC Converter in CCM 14 3.1 Circuit description of a PWM Z-Bridge Source Converter . ..... 14 3.2Assumptions................................. 14 3.3 Shoot-Through State (Time Interval 0 <t ≤ DT ) ............ 16 3.4 Non Shoot-Through State (Time Interval DT <t ≤ T ) ......... 19 3.5 DC Voltage Transfer Function (MV DC ).................. 25 4 Derivations of Expressions for Passive Components 27 4.1 Minimum Inductance of Z-Network Inductor to Operate in CCM.... 27 4.2 Minimum Inductance of Filter Inductor to Operate in CCM . ..... 29 iv 4.3 Minimum Capacitance Values for Z-Network and Filter Capacitors in CCM..................................... 31 4.3.1 Minimum Capacitance of Z-Network Capacitor in CCM at Shoot-Through State (0 <t ≤ DT )................. 31 4.3.2 Minimum Capacitance of Z-Network Capacitor in CCM at Non Shoot-Through State (DT <t ≤ T )................. 33 4.4 Design Example and Simulation Results . 34 4.5 Efficiency, Power Losses, and DC Voltage Conversion Factor of Z-BridgeSourceDC-DCConverter . 39 5 Plant Characteristics of PWM Z-Bridge Source DC-DC Converter in CCM 44 5.1 PWM Z-Bridge Source DC-DC Converter with Varying Duty Cycle . 44 5.2 PWM Z-Bridge Source DC-DC Converter With Varying Load Resistance 46 5.3 PWM Z-Bridge Source DC-DC Converter With Varying Input Voltage . 49 6 Conclusion 52 6.1Summary .................................. 52 6.2FutureWork................................. 53 6.3ThesisContributions ............................ 53 7 Bibliography 55 v List of Figures 2.1 Circuit of a x-shaped z-source network. 5 2.2 Circuit of a z-source bridge network. 6 2.3 Circuit of Wheatstone bridge network. 7 2.4 Circuit of the basic framework of a z-source converter/inverter for all types of power conversions. (a) Circuit with the z-source x-shaped network. (b) Circuit with the z-source bridge network. 8 2.5 Circuit of multi-level inverter with z-source bridge network at shoot-through state. (a) Circuit, when the switch is on. (b) Equivalent circuit, when the switch is on. 9 2.6 Circuit of multi-level inverter with the z-source bridge network at non-shoot-through state.. (a) Circuit, when the switch is off. (b) Equivalent circuit, when the switch is off. 11 2.7 Circuit of the pwm dc-dc converter with z-source x-shaped network. 12 2.8 Simplified circuit representation of pwm z-bridge source dc-dc converter. 12 3.1 Circuit of a pwm z-bridge source dc-dc converter. 14 3.2 Circuit of the pwm z-bridge source dc-dc converter with identical z-network inductors and capacitors. 16 vi 3.3 Circuit of the pwm z-bridge source dc-dc converter, when switch is on and diode is off. 16 3.4 pwm z-bridge source dc-dc converter at shoot-through state. (a) Equivalent circuit with Kirchoff current loops, when the switch is on and diode is off. (b) Equivalent circuit with the filter circuit replaced with dc current source iLf . (c) Equivalent circuit with the two z-network inductor L and capacitor C network are replaced with two ac current sources iL 18 3.5 Circuit of the pwm z-bridge source dc-dc converter, when the switch is off & the diode is on. 20 3.6 Simplified circuit of the pwm z-bridge source dc-dc converter with Kirchoff voltage loops, when the switch is off and the diode is on. 20 3.7 Equivalent circuit of the pwm z-bridge source dc-dc converter with the filter circuit is replaced with a dc current source, when the switch is off and the diode is on. 21 3.8 Circuit of the pwm z-bridge source dc-dc converter with Kirchoff current loops, when the switch is off and the diode is on. 21 3.9 Voltage waveforms of the z-bridge source dc-dc converter in ccm. 23 3.10 Current waveforms of the z-bridge source dc-dc converter in ccm. 24 4.1 ccm/dcm boundary of pwm z-bridge source dc-dc converter for normalized load current with respect to z-network inductance as a function of duty cycle. 28 vii 4.2 ccm/dcm boundary of pwm z-bridge source dc-dc converter for normalized load resistance with respect to z-network inductance as a function of duty cycle. 28 4.3 ccm/dcm boundary of pwm z-bridge source dc-dc converter for normalized load current with respect to filter inductance as a function of duty cycle. 30 4.4 ccm/dcm boundary of pwm z-bridge source dc-dc converter for normalized load resistance with respect to filter inductance as a function of duty cycle. 30 4.5 ccm/dcm boundary of pwm z-bridge source dc-dc converter for normalized filter inductance with respect to z-network inductance as a function of duty cycle. 31 4.6 Variation in efficiency η as a function of output current IO of z-bridge source dc-dc converter 35 4.7 Power and output voltage waveforms of pwm z-bridge source dc-dc converter in ccm. 38 4.8 Current waveforms of z-network inductor and filter inductor of pwm z-bridge source dc-dc converter in ccm. 38 4.9 Variation in efficiency η as a function of input voltage VI of pwm z-bridge source dc-dc converter. 41 4.10 Variation in efficiency η as a function of load resistance RL of z-bridge source dc-dc converter. 41 viii 4.11 Variation in efficiency η as a function of to duty cycle D of z-bridge source dc-dc converter. 42 4.12 Variation in dc voltage conversion factor MV DC as a function of duty cycle D of z-bridge source dc-dc converter. 42 4.13 Variation in duty cycle D as a function of output current IO of z-bridge source dc-dc converter. 43 4.14 Variation in efficiency η as a function of output current IO of z-bridge source dc-dc converter. 43 5.1 Circuit of the pwm z-bridge source dc-dc converter circuit with the varying duty cycle. 44 5.2 Gate-source voltage, output voltage, and power waveforms of the pwm z-bridge source dc-dc converter with the varying duty cycle. 45 5.3 Z-network capacitor voltage and output voltage waveforms of the pwm z-bridge source dc-dc converter with the varying duty cycle.