Power Converters, Drives and Controls for Sustainable Operations 9781119791911

Citation preview

Power Converters, Drives and Controls for Sustainable Operations

Scrivener Publishing 100 Cummings Center, Suite 541J Beverly, MA 01915-6106 Publishers at Scrivener Martin Scrivener ([email protected]) Phillip Carmical ([email protected])

Power Converters, Drives and Controls for Sustainable Operations

Edited by

S. Ganesh Kumar Marco Rivera Abarca and

S. K. Patnaik

This edition first published 2023 by John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA and Scrivener Publishing LLC, 100 Cummings Center, Suite 541J, Beverly, MA 01915, USA © 2023 Scrivener Publishing LLC For more information about Scrivener publications please visit www.scrivenerpublishing.com. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions. Wiley Global Headquarters 111 River Street, Hoboken, NJ 07030, USA For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com. Limit of Liability/Disclaimer of Warranty While the publisher and authors have used their best efforts in preparing this work, they make no rep­ resentations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchant-­ ability or fitness for a particular purpose. No warranty may be created or extended by sales representa­ tives, written sales materials, or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further informa­ tion does not mean that the publisher and authors endorse the information or services the organiza­ tion, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Library of Congress Cataloging-in-Publication Data ISBN 9781119791911 Front cover images supplied by WikiMedia Commons Cover design by Russell Richardson Set in size of 11pt and Minion Pro by Manila Typesetting Company, Makati, Philippines Printed in the USA 10 9 8 7 6 5 4 3 2 1

Contents Preface xxi

Part I: Power Converter Topologies for Sustainable Applications

1

1 DC-DC Power Converter Topologies for Sustainable Applications 3 Nandish B. M., Pushparajesh V. and Marulasiddappa H. B. 1.1 Introduction 4 1.2 Classifications of DC-DC Converters 4 1.2.1 Classification of Linear Mode DC-DC Converters 5 1.2.1.1 Series Regulators 5 6 1.2.1.2 Parallel Regulators 1.2.2 Classification of Hard Switching DC-DC Converter 6 1.2.2.1 List of Isolated DC-DC Topologies 6 1.2.2.2 Classification of Non-Isolated DC-DC Converters 10 16 1.2.3 Classification of Soft Switching DC-DC Converter 1.2.3.1 Zero Current Switching (ZCS) 16 1.2.3.2 Zero Voltage Switching (ZVS) 16 1.3 Applications of DC-DC Converters in Real World 16 1.4 Conclusion 18 References 18 2 DC-DC Converters for Fuel Cell Power Sources M. Venkatesh Naik, Paulson Samuel and Srinivasan Pradabane 2.1 DC-DC Boost Converter in Fuel Cell (FC) Applications 2.2 DC-DC Buck Converter 2.3 DC-DC Buck-Boost Converter 2.4 DC-DC Cuk-Converter

21 22 26 27 29 v

vi  Contents 2.5 DC-DC Sepic Converter 2.6 Multi-Phase and Multi-Device Techniques for Ripple Current Reduction 2.6.1 Multi-Device Boost Converter 2.6.2 Multi-Phase Interleaved Boost Converter 2.6.3 Multi-Device Multi-Phase Interleaved Boost Converter 2.7 The Proposed High Gain Multi-Device Multi-Phase Interleaved Boost Converter 2.7.1 Operating Principle of HGMDMPIBC 2.8 Non-Inverting Buck-Boost Converters for Low Voltage FC Applications 2.8.1 Single Switch Non-Inverting Buck-Boost Converter 2.8.2 Interleaved Buck-Boost Converter 2.9 Proposed Multi-Device Buck-Boost Converter for Low Voltage FC Applications 2.10 The Proposed Multi-Device Multi-Phase Interleaved Buck-Boost Converter for Low Voltage FC Applications 2.11 Converter Configurations for Integrating FC with 400 V Grid Voltages 2.11.1 Series Configuration 2.11.2 DC-Distributed Configuration 2.12 Conclusions References

30 32 33 35 37 42 44 48 49 52 57 59 62 62 64 65 66

3 High Gain DC-DC Converters for Photovoltaic Applications 71 M. Prabhakar and B. Sri Revathi 71 3.1 Introduction 3.1.1 Role of DC-DC Converter in Renewable 72 Energy System 3.1.2 Classical Boost Converter (CBC) 75 3.2 Gain Extension Mechanisms 77 3.2.1 Voltage-Lift Capacitor (Clift) 77 3.2.2 Coupled Inductor (CI) 78 3.2.3 Voltage Multiplier Cells (VMC) 79 3.3 Synthesis of High Gain DC-DC Converters 80 3.3.1 Concept of Interleaving 80 3.3.2 Interleaving Mechanism with Coupled Inductors (CIs) 83 3.3.3 VMCs at Secondary Side of CIs 84 3.4 Development of High Gain DC-DC Converters (HGCs) 84

Contents  vii 3.4.1 HGC with 3 CIs, Clift, and VMC 3.4.1.1 Design Details of HGC-1 3.4.1.2 Experimental Results of Prototype HGC-1 and Discussion 3.4.2 3-Phase Interleaved HGC with 1 CI, Clift, and VMC 3.4.3 Modular HGC with 3 CIs, Clift, and 3 VMCs 3.4.4 Compact HGC Based on Multi-Winding CI, Clift, and VMC 3.4.4.1 Voltage Stress on Devices 3.4.4.2 Current Stress on Devices 3.5 Operating Capabilities of the Proposed HGCs – A Comparison 3.5.1 Electrical Characteristics 3.5.1.1 Ideal Voltage Gain 3.5.1.2 Loss Distribution Profile 3.5.2 Stress on Switches 3.5.2.1 Peak Voltage Stress 3.5.2.2 Peak Current Stress 3.5.3 Structural Parameters 3.5.3.1 Coefficient of Coupling (k) 3.5.3.2 Component Count (CC) and Component Utilisation Ratio (CUR) 3.6 Salient Features of the Presented High Gain Converters 3.7 Summary and Outlook References

85 90 95 101 104 107 109 109 111 111 111 113 115 116 117 117 117 118 119 120 122

4 Design of DC-DC Converters for Electric Vehicle Wireless 127 Charging Energy Storage System T. Kripalakshmi and T. Deepa 128 4.1 Introduction 130 4.2 Isolated Converters 4.2.1 Bridge Type 130 4.2.2 Z-Source Type 131 4.2.3 Sinusoidal Amplitude High Voltage Bus Converter (SAHVC) 131 133 4.2.4 Multiport Converter 4.3 Non-Isolated Converter 133 4.3.1 Conventional Converters 133 4.3.2 Interleaved Converter 134 4.3.3 Multi-Device Interleaved 135

viii  Contents 4.4 Design of DC-DC Converter with Integration of ICPT and Battery Implementation with Digital Control Loop 136 4.4.1 Design of DC-DC for BEV with the Integration of ICPT 136 4.4.2 Digital Control with Sliding Mode Control Approach 139 4.5 Design of Converter with Hybrid Energy Storage System and Bidirectional Converter 143 145 4.6 Conclusion References 145 5 Performance Analysis of Series Load Resonant (SLR) DC–DC Converter A. Mitra, S. Bhowmik, A. Halder, S. Karmakar and T. Paul 5.1 Introduction 5.2 Theoretical Background 5.3 Simulation Results 5.4 Conclusion References

149 149 151 155 157 158

6 Review on Different Methodologies of DC-AC Converter 159 Pushparajesh V., Marulasiddappa H. B. and Nandish B. M. 6.1 Introduction 160 162 6.2 Different Multilevel Inverter Topologies 6.2.1 Diode Clamped MLI (DCMLI) 162 6.2.2 Flying Capacitor MLI 164 6.2.3 Cascaded H-Bridge MLI 165 6.2.4 New Hybrid Cascaded MLI 167 6.2.4.1 Stepped Wave Modulation Topology (SWMT) 167 6.2.4.2 Fourier Series of Proposed Waveform 168 6.2.4.3 Proposed Topology (New Hybrid MLI) 169 6.3 Comparison between Various MLI 172 6.4 Conclusion 173 References 173 7 Grid Connected Inverter for Solar Photovoltaic Power Generation K.K. Saravanan and M. Durairasan 7.1 Single Phase Seven Level Inverter Fed Grid Connected PV System 7.1.1 Seven Level Inverter Topology 7.1.2 PWM Technique for Seven Level Inverter

175 176 176 177

Contents  ix 7.1.3 Modelling and Simulation Analysis of Seven Level Inverter 180 181 7.2 Simlink Model of Nine Level H-Bridge Inverter 7.3 Three Phase Fifteen Level Inverter Fed Grid Connected System 182 7.3.1 Modified System of Fifteen Level Inverter 182 7.3.2 Modelling of Cascaded H-Bridge Fifteen 183 Level Inverter 7.3.3 Evaluation of THD 184 7.4 Fesability Analysis of Photovoltaic System 185 in Grid Connected Inverter 7.4.1 Modified PV-DVR System 185 187 7.4.1.1 Dynamic Voltage Restorer (DVR) Mode 7.4.1.2 Uninterruptable Power Supply (UPS) Mode 187 7.4.1.3 Energy Conservation Mode 187 7.4.1.4 Idle Mode 187 7.4.2 Photovoltaic DC-DC Converter 188 191 7.4.3 Maximum Power Point Tracking of PV System 7.4.4 Methods of Maximum Power Point Tracking 192 7.4.4.1 Perturb and Observe Method 192 7.4.4.2 Incremental Conductance Method 193 7.4.4.3 Current Sweep Method 193 194 7.4.4.4 Constant Voltage Method 7.4.5 Comparison of MPPT Methods 194 7.4.6 Operating Principle of P&O MPPT 195 7.4.7 Simulation Results of PV-DVR System 195 197 7.4.8 Grid Connected System Using PV Syst Tool 7.4.8.1 PV System Simulation Result Analysis 199 199 7.5 Conclusion 7.6 Future Scope of Work 200 References 200 8 A Novel Fusion Switching Pattern Generation Algorithm for “N-Level” Switching Angle Algorithm Based Trinary Cascaded Hybrid Multi-Level Inverter Joseph Anthony Prathap and T.S. Anandhi 8.1 Introduction 8.2 Trinary Cascaded Hybrid MLI Circuitry 8.3 Switching Angle Algorithm 8.3.1 Equal Phase Switching Angle Algorithm (EP-SAA)

203 204 206 208 209

x  Contents 8.3.2 Half Equal Phase Switching Angle Algorithm (HEP-SAA) 209 8.3.3 Feed Forward Switching Angle Algorithm (FF-SAA) 209 8.3.4 Half Height Switching Angle Algorithm (HH-SAA) 209 8.4 9-Level Trinary Cascaded Hybrid Multi-Level Inverter 210 8.4.1 SAA for 9-Level TCHMLI 210 8.4.2 Generation of Switching Function 215 for the 9-Level Trinary Cascaded Hybrid MLI 8.4.3 Generation of DPWM for the 9-Level Trinary 215 Cascaded Hybrid MLI 8.4.4 Simulation Results of 9-Level Trinary Cascaded Hybrid MLI 216 222 8.5 27-Level Trinary Cascaded Hybrid MLI 8.5.1 SAA for 27-Level TCHMLI 223 8.5.2 Generation of Switching Function for the 27-Level 225 Trinary Cascaded Hybrid MLI 8.5.3 Generation of DPWM for the 27-Level Trinary 231 Cascaded Hybrid MLI 8.5.4 Simulation Results of 27-Level Trinary Cascaded 231 Hybrid MLI 8.6 81-Level Trinary Cascaded Hybrid MLI 240 8.6.1 SAA for 81-Level Trinary Cascaded Hybrid MLI 240 8.6.2 Generation of Switching Function for the 81-Level Trinary Cascaded Hybrid MLI 248 8.6.3 Generation of DPWM for 81-Level Trinary Cascaded Hybrid MLI 265 8.6.4 Flow Diagram of 81-Level Trinary Cascaded 266 Hybrid MLI 8.6.5 5 Roles of Design Resolution in Trinary Cascaded 266 Hybrid MLI 8.6.6 Simulation Results of 81-Level Trinary Cascaded 268 Hybrid MLI 8.7 FPGA Experimental Validation with Specification 279 8.8 Hardware Results and Discussion 279 8.9 Conclusion 280 References 290 9 An Inspection on Multilevel Inverters Based on Sustainable Applications L. Vijayaraja, R. Dhanasekar and S. Ganesh Kumar 9.1 Introduction

293 293

Contents  xi 9.2 Multilevel Inverters in Sustainable Applications 9.3 Development of Multilevel Inverter 9.3.1 Diode-Clamped 9.3.2 Flying Capacitor 9.3.3 Cascaded H-Bridge MLI 9.4 Symmetric MLI 9.5 Asymmetric MLI 9.6 An Examination on Current MLI’s 9.7 Summary Acknowledgement References

Part II: Electric Machines and Drives for Sustainable Applications 10 Technical Study of Electric Vehicle Charging Infrastructure and Standards R. Seyezhai and S. Harika 10.1 Introduction 10.2 Background 10.3 Review of EV Charging Infrastructure 10.4 Review of DC-DC Converters for EVCs 10.5 Standards for EV and EVSE 10.5.1 Description of EV Connector 10.6 Charging Stations in India 10.7 Conclusion References 11 Implementation of Model Predictive Control for Reduced Torque Ripple in Orthopaedic Surgical Drilling Applications with Permanent Magnet Synchronous Machine Ramya L. N. and Sivaprakasam A. 11.1 Introduction 11.2 Role of Motor in Orthopaedic Drilling Applications 11.2.1 BLDC Motors 11.2.2 Permanent Magnet Synchronous Motors 11.2.2.1 PMSM Machine Equations 11.2.3 Control Methods of PMSM 11.3 Model Predictive Control 11.3.1 Structure of MPC 11.3.2 Cost Function 11.4 Predictive Control Techniques for PMSM

294 299 299 300 301 301 305 307 311 311 311

315 317 317 318 320 323 327 330 331 332 332

337 338 341 341 341 342 343 347 348 349 350

xii  Contents 11.4.1 Conventional Model Predictive Torque Control (MPC) 11.4.2 Proposed MPC Technique 11.5 Implementation and Results 11.5.1 Comparative Study of Steady State Performance of Proposed MPC and Conventional MPC under Loaded Condition 11.5.2 Steady State Performance at 50% Rated Speed 11.5.3 Steady State Performance at 100% Rated Speed 11.5.4 Real-Time Simulation Result Analysis with OPAL-RT Lab 11.5.4.1 Steady-State Response 11.5.4.2 Start-Up Response 11.6 Implementation Analysis 11.7 Conclusion References

350 352 354 355 356 357 357 358 359 359 362 362

12 High Precision Drives for Piezoelectric Actuators 367 Based Motion Control Microsystems D. V. Sabarianand and P. Karthikeyan 12.1 Introduction 368 12.2 Driving Methods of PEA 369 12.3 Driver Circuits for Driving PEA in High Voltage Applications 369 12.4 Different Types of Power Supply Used for Driving the Piezo Driver 377 12.5 Different Types of Voltage Regulator Used for Driving 380 the Piezo Driver 385 12.6 Conclusions References 386 13 Design and Analysis of 31-Level Asymmetrical 391 Multilevel Inverter Topology for R, RL, & Motor Load E. Duraimurugan, R. S. Jeevitha, S. Dillirani, L. Vijayaraja and S. Ganesh Kumar 13.1 Introduction 391 13.2 Incorporation of Multilevel Inverters in Various Applications 392 13.3 Modeling of 31-Level Asymmetric Inverter 394 13.3.1 Mathematical Modeling of 31-Level Inverter 395 13.3.2 Modes of Operation 396 13.3.3 Switching Principle of 31-Level Inverter 398

Contents  xiii 13.4 Simulation Circuit and Result Discussions 13.4.1 Block Diagram for Pulse Generation 13.4.2 Simulation of 31-Level Inverter with R Load 13.4.3 Simulation of 31-Level Inverter with RL Load 13.4.4 Simulation of 31-Level Inverter Fed with 1φ Induction Motor 13.5 Conclusion Acknowledgement References 14 Permanent Magnet Assisted Synchronous Reluctance Motor: Analysis and Design with Rare Earth Free Hybrid Magnets P. Ramesh, D. Pradhap and N. C. Lenin 14.1 Introduction 14.2 Literature Survey 14.3 Construction and Torque Equation 14.4 Design Specifications and Machine Topologies 14.5 No-Load Characteristics 14.6 Performance at Various Operating Regions 14.7 Conclusion Acknowledgment References 15 Design of Bidirectional DC – DC Converters and Controllers for Hybrid Energy Sources in Electric Vehicles R. Chandrasekaran, M. Satish Kumar Reddy, K. Selvajyothi and B. Raja 15.1 Introduction 15.2 Need For Hybrid Energy Management Systems in EV 15.3 Hybrid Energy Storage System (HESS) 15.3.1 Passive Parallel HESS 15.3.2 Parallel Converter HESS 15.4 Bidirectional DC-DC Converters (BDC) 15.5 Specifications of DC-DC Converters 15.6 Control Strategy 15.7 Results and Discussion 15.8 Conclusions References 16 Design of Rare Earth Magnet Free Traction Motor Akhila K. and K. Selvajyothi 16.1 Introduction 16.2 Comparison Among Traction Motor Choices

400 400 400 402 405 407 407 407 411 411 413 415 417 421 424 429 433 433 437 437 439 440 441 441 442 446 447 449 459 460 463 464 468

xiv  Contents 16.3 Motor Peak Power Calculation Based on Vehicle Dynamics 16.4 Operating Principle of SynRM & Basic Terminologies 16.5 SynRM Design Concepts: Effect of Design Parameters on Performance 16.6 Analytical Design of SynRM 16.6.1 Stator & Winding Design 16.6.2 Rotor Design 16.6.2.1 Determining Barrier End Angle, αm 16.6.2.2 Determining Segment Width, Si 16.6.2.3 Determining Barrier Width, W1i 16.7 Electromagnetic Analysis –Results & Discussion 16.8 Investigation on Impact of Different Parameters 16.8.1 Torque-Speed Curve 16.9 Summary 16.10 Future Work References 17 Implementation of Automatic Unmanned Battery Charging System for Electric Cars Shefali Jagwani 17.1 Introduction 17.2 Proposed System 17.3 MATLAB Simulation 17.3.1 Mathematical Modelling 17.3.2 Simulation and Analysis of Battery Discharging at EV Charging Station 17.4 Conclusion References 18 Improved Dual Output DC-DC Converter for Electric Vehicle Charging Application R. Latha 18.1 Introduction 18.2 Proposed Dual Output Quadratic Boost Converter 18.2.1 Solar PV System 18.2.1.1 Mathematical Modeling of PV System 18.2.2 Switching Methodology 18.2.2.1 Topology of Proposed Converter 18.2.3 Estimation of Parameters of Proposed SIDO Converter 18.2.3.1 Design Example

473 475 482 486 486 490 491 491 493 496 500 506 510 513 513 517 518 521 523 523 526 529 529 533 534 537 537 537 538 539 543 544

Contents  xv 18.3 Simulation of the Proposed Converter 18.4 Experimental Results 18.5 Conclusion References 19 DFIG Based Wind Energy Conversion Using Direct Matrix Converter Vineet Dahiya Chapter-I Introduction 19.1 Introduction to Matrix Converters 19.2 Introduction to Control and Modulation Techniques in Matrix Convertor 19.3 Introduction to Predictive Control Techniques Chapter-II Concept and System Description: Doubly Fed Induction Generator (DFIG) in Wind Energy Conversion System Chapter-III Modeling and Simulation of DFIG in MATLAB Chapter-IV The Matrix Converter and Predictive Control Technique 19.4 Topologies of Matrix Converters and Use of Predictive Control 19.5 Conclusion 19.6 Scope for Future Work References

Part III: Trends in Control Methods for Sustainable Applications 20 Microgrid: Recent Trends and Control S. Monesha and S. Ganesh Kumar 20.1 Introduction 20.2 MG Concept 20.2.1 Different Structures of MG 20.2.1.1 AC MG 20.2.1.2 DC MG 20.2.1.3 Hybrid AC/DC MG 20.2.1.4 Urban DC MG 20.2.1.5 Ceiling DC MG 20.3 MG Control Layer 20.4 Functional Requirements of MG Management

545 545 550 551 553 554 554 558 559 562 562 562 571 571 574 574 583 588 589 590

595 597 598 599 600 600 601 602 602 602 603 604

xvi  Contents 604 20.4.1 Forecast 20.4.2 Real-Time Optimization 604 20.4.3 Data Analysis and Communication 604 20.4.4 Human Machine Interface 605 20.5 Energy Management Schemes 605 20.5.1 Communication-Based Energy Management 605 20.5.2 The Communication-Less Energy Management System 608 611 20.6 Overview of MG Control 20.6.1 Power Flow Control by Current Regulation 611 20.6.2 Power Flow Control by Voltage Regulation 612 20.6.3 Agent-Based Control 613 20.6.4 Multi-Agent System (MAS) Based Distributed Control 613 20.6.5 PQ Control 614 20.6.6 VSI Control 614 20.6.7 Central Control 614 615 20.6.8 Master/Slave Control 20.6.9 Distributed Control 615 20.6.10 Droop Control 616 20.6.11 Control Design Based on Transfer Function 616 20.6.12 Direct Lyapunov Control (DLC) 617 617 20.6.13 Passivity Based Control (PBC) 20.6.14 Model Predictive Control (MPC) 618 20.7 IEEE and IEC Standards 621 20.8 Challenges of MG Controls 623 624 20.8.1 Future Trends Acknowledgement 624 References 624 21 Control Techniques in Sustainable Applications 631 R. Dhanasekar, L. Vijayaraja and S. Ganesh Kumar 21.1 Introduction 632 21.2 Sliding Mode Control Techniques in Sustainable Applications 634 644 21.3 Passivity-Based Control in Sustainable Applications 21.4 Model Predictive Control in Sustainable Applications 650 655 21.5 Conclusion Acknowledgement 655 References 655

Contents  xvii 22 Optimization Techniques for Minimizing Power Loss in Radial Distribution Systems by Placing Wind and Solar Systems 659 S. Angalaeswari, D. Subbulekshmi and T. Deepa I. Introduction 660 22.1 Distribution Systems 660 22.2 Radial Distribution Network 661 22.3 Power Loss Minimization 662 22.4 Optimization Techniques 664 22.5 MATLAB Tools for Optimization Techniques 670 674 22.6 Conclusion References 675 Appendix 679 23 Passivity Based Control for DC-DC Converters 681 Arathy Rajeev V.K. and Ganesh Kumar S. 681 23.1 Introduction 23.2 Passivity Based Control 683 23.3 Control Law Generation Using ESDI, ESEDPOF, ETEDPOF 686 23.3.1 Energy Shaping and Damping Injection (ESDI) 686 23.3.2 Exact Tracking Error Dynamics Passive Output 687 Feedback (ETEDPOF) 23.3.3 Exact Static Error Dynamics Passive Output Feedback 692 23.4 Control Law Generation Using ETEDPOF 692 Method for DC Drives 23.4.1 Buck Converter Fed DC Motor 692 697 23.4.2 Boost Converter Fed DC Motor 23.4.3 Luo Converter Fed DC Motor 701 23.5 Sensitivity Analysis 706 23.5.1 Sensitivity Analysis of Buck Converter 707 23.5.2 Sensitivity Analysis of Boost Converter 709 23.5.3 Sensitivity Analysis of a Luo Converter 710 23.6 Reference Profile Generation 713 23.6.1 Boost Converter Fed DC Motor 713 23.6.2 Luo Converter Fed DC Motor 715 23.7 Load Torque Estimation 719 23.7.1 Reduced-Order Observer for Load Torque Estimation 719 720 23.7.2 SROO Approach for Load Torque Estimation

xviii  Contents 23.7.3 Load Torque Estimation Using Online Algebraic Approach 721 23.7.4 Sensorless Online Algebraic Approach (SAA) for Load Torque Estimation 723 23.8 Applications of PBC 724 23.9 Conclusion 726 References 728 24 Modeling, Analysis, and Design of a Fuzzy Logic Controller for Sustainable System Using MATLAB T. Deepa, D. Subbulekshmi and S. Angalaeswari 24.1 Introduction 24.2 Modeling of MIMO System 24.3 Analysis of MIMO System Using MATLAB 24.4 Optimization Techniques for PID Parameter 24.4.1 Controller Design 24.4.1.1 PID Controller Design 24.4.2 Optimization of PID Controller Parameter 24.5 Fuzzy Logic Controller Using MATLAB/Simulink 24.6 Conclusion References

731 732 734 734 742 742 742 743 744 745 746

25 Development of Backstepping Controller for Buck Converter 749 R. Sureshkumar and S. Ganesh Kumar 25.1 Introduction 749 25.2 Buck Converter With R-Load 751 25.2.1 Mathematical Model 752 752 25.2.2 Buck Converter with PMDC Motor 753 25.2.3 Mathematical Model 25.3 Controller Design 754 25.3.1 Basic Block Diagram for PI/Backstepping Controller 754 754 25.3.2 Conventional PI Controller Design 25.3.3 Backstepping Controller Design 756 25.3.4 Backstepping Control Algorithm 757 25.3.5 Controller Design for Buck Converter 757 with R-Load 766 25.4 Simulation Results 25.5 Hardware Details 768

Contents  xix 25.5.1 Buck Converter Specifications 25.5.2 Advanced Regulating Pulse Width Modulator 25.5.3 Principles of Operation 25.6 Hardware Results 25.7 Conclusion References 26 Analysing Control Algorithms for Controlling the Speed of BLDC Motors Using Green IoT V. Evelyn Brindha and X. Anitha Mary 26.1 Introduction 26.2 Working of BLDC Motor 26.3 Speed Control of Motor 26.4 Speed Control of BLDC Motor with FPGA 26.5 Advancements in Green IoT for BLDC Motors 26.6 Conclusion References

771 773 774 775 777 778 779 779 780 781 786 786 787 787

Index 789

Preface With an increasing demand for power production, along with demand for power conversion and motor control in electric vehicles (EVs), there is a great demand for power converters and related technologies. Similarly, a related field, “drives and controls,” is gaining prominence due to the increasing use of linear motors, actuators, robots, pneumatics and hydraulic cylinders. Such a rapid growth is in compliance with sustainable development goals (SDGs) and Industry 4.0. Considering the above facts, we, the editors, deemed it necessary to put together this much needed book, Power Converters, Drives and Controls for Sustainable Operations. This book has been aptly divided into three parts. As in any conversion process, the efficiency of power conversion is the most important issue. Part I of the book is on switched-mode converters and deals with the need for power converters, their topologies, principles of operation, their steady-state performance, and applications. Conventional topologies like buck, boost, buck-boost converters, inverters, multilevel inverters and derived topologies (such as high gain, bridge converters, and resonant converters) are covered in Part I with features and their applications in fuel cells, photovoltaic (PV) and EVs. Switching inverters have been gaining in popularity over linear inverters, due to their inherent higher efficiency. Over the past decade, a variety of strategies to switch the inverter switches have been evolved for various applications. Hence, in this part, concepts of switched-mode inverters, pulse width modulated switching schemes for inverters, three-phase 15-level gridconnected inverters, harmonic elimination techniques, and current controlled inverters are also discussed. Part II of the book is concerned with electrical machines and converters used for EV applications. Standards for EV, charging infrastructure, and wireless charging methodologies are addressed. Machines such as permanent magnet synchronous motors, induction motors, permanent magnet-assisted synchronous reluctance motors, synchronous reluctance motors and doubly-fed induction generators are considered for analysis. xxi

xxii  Preface Further, converters such as DC-DC converters, 31-level asymmetrical multilevel inverters, single input dual output converters and matrix converters used for EV applications are discussed here. The last part deals with the dynamic model of switched-mode converters. In any DC-DC converter, it is imperative to control the output voltage as desired. Such a control may be achieved in a variety of ways. While several types of control strategies are being evolved, the popular method of control is through the duty cycle of the switch at a constant switching frequency. This part of the book briefly reviews the conventional control theory and builds on the same to develop advanced techniques in the closed-loop control of switch mode power converters (SMPC), such as sliding mode control, passivity-based control, model predictive control (MPC), fuzzy logic control (FLC), and backstepping control. We, the editors acknowledge the help received from the research scholars Mr. R. Dhanasekar and Mr. L. Vijayaraja, Sri Sairam Institute of Technology, Chennai, India and Dr. S. Sanjeevi, Professor (Retired), Department of Geology, Anna University, Chennai, India. We, the editors hope that this book will be useful for the readers who are working in power electronics and sustainable applications. Editors Dr. S. Ganesh Kumar Assistant Professor (Selection Grade), Department of Electrical and Electronics Engineering, Deputy Director, Centre for Academic Courses, Anna University, Chennai, India Email: [email protected] Dr. Marco Rivera Abarca Full Professor, Department of Electrical Engineering, Universidad de Talca, Chile Email: [email protected] Dr. S.K. Patnaik Professor, Department of Electrical and Electronics Engineering, Anna University, Chennai, India Former Director, All India Council for Technical Education (AICTE), New Delhi, India Email: [email protected]

Part I POWER CONVERTER TOPOLOGIES FOR SUSTAINABLE APPLICATIONS

1 DC-DC Power Converter Topologies for Sustainable Applications Nandish B. M.1, Pushparajesh V.2* and Marulasiddappa H. B.1 Department of Electrical and Electronics, Jain Institute of Technology, VTU, Karnataka, India 2 Department of Electrical and Electronics, FET, Jain Deemed to be University, Karnataka, India 1

Abstract

A sustainable development of modern power equipment needs a power variable converter. Small scale electrical appliances/motors need modern power converters for better efficiency. As the world is moving fast with electrification bypassing the use of fossil powers in every aspect, for example electric vehicles. Power switching converters brings lots of applications for every converter with different power rating. In this chapter, DC-DC converter topologies are discussed in detail about classification and applications of different DC-DC converter. As the DC-DC converters are basically designed for power flow control from DC power source to another DC source or device. These are static power converters with wide applications in modern era like hospitals for medical equipment’s, micro and mini grids with Vehicle to Grid (V2G) technology and Railways. Application of various DC-DC converts are discussed in detail for linear mode, hard switching and soft switching DC-DC converter. Keywords:  Static power converter, micro grid, power switching converter

*Corresponding author: [email protected] S. Ganesh Kumar, Marco Rivera Abarca and S. K. Patnaik (eds.) Power Converters, Drives and Controls for Sustainable Operations, (3–20) © 2023 Scrivener Publishing LLC

3

4  DC-DC Converters for Sustainable Applications

1.1 Introduction New emerging technologies in electric vehicles, computers, smart phones, and tablets are concentrating on the development of efficient battery chargers. This has become a challenge in the power sector to improvise the battery operating states. Switched mode DC-DC converters play an important role in this field. DC-DC converters are high frequency power converters and use high frequency switching. DC-DC converters are now used in automotive applications with low voltage and high efficiency [1]. DC-DC conversion is done by chopping either the input voltage or the current, named as choppers or switch mode power converters. All the power converters are closed loop converters as the efficiency of the system is increased. Choppers are always operated in forced commutation. Non-isolated DC-DC converters have major applications in DC microgrids [2]. High power DC-DC converters have applications in HVDC grid interconnection [3]. This chapter mainly concentrates on the classifications of DC-DC converters and their role in different applications in the present challenging world. It also highlights the importance of the control in DC-DC converters. As we all know, DC-DC converters are nonlinear systems as the input and the output of the systems are variable. There are several proposed converter topologies discussed in the past decades. All the proposed converters are designed to serve one specific application or another. Some of them are named based on their applications, such as buck, boost, and buck-boost converters. In this chapter we are going to classify the converters depending on their application areas so that it will be easy to contribute to research work for a better world.

1.2 Classifications of DC-DC Converters DC-DC converters are classified based on their working nature. Broadly, these are classified into three types: i. Linear mode DC-DC converter ii. Hard switching DC-DC converter iii. Soft switching DC-DC converter These converters are again subclassified based on their components and applications. These classifications are discussed in detail in this section. Detailed classification of DC-DC converter is shown in Figure 1.1.

DC-DC Converter Topologies for Sustainable Applications  5 Series Regulators

Linear Mode

Parallel Regulators Forward Isolated

DC-DC Converter

Flyback Push-pull Half bridge

Hard Switching

Buck

Non-Isolated

Boost Buck-Boost

Zero Current Switching (ZCS)

Soft Switching

SEPIC

Zero Voltage Switching (ZVS)

Cuk Zeta

Figure 1.1  Classification of DC-DC converter.

1.2.1 Classification of Linear Mode DC-DC Converters 1.2.1.1 Series Regulators The series voltage controller or series pass voltage controller utilizes a variable component set in arrangement with the load. By changing the obstruction of the arrangement component, the voltage dropped across it very well may be fluctuated to guarantee that the voltage over the load stays consistent. The circuit of the arrangement controller is shown in Figure 1.2.

Series Element Regulated Input Unregulated Input Load References

Figure 1.2  Series regulators.

6  DC-DC Converters for Sustainable Applications

R

Input Voltage

Zener Diode

Output Voltage

Figure 1.3  Parallel regulators.

1.2.1.2 Parallel Regulators One of the most widely recognized and basic types of shunt controller is the straightforward Zener diode controller circuit demonstrated as follows. Its activity is clear. Once over its least current, the Zener diode keeps up a practically consistent voltage over its terminals. The circuit of arrangement the controller is shown in Figure 1.3. In this circuit, the arrangement resistor drops the voltage from the source to the Zener diode and burden. As the Zener diode keeps up its voltage, any varieties in burden current do not influence the voltage over the Zener diode.

1.2.2 Classification of Hard Switching DC-DC Converter Hard switching DC-DC converters are sub classified into two major categories and are listed below. i. Isolated DC-DC Topologies ii. Non-Isolated DC-DC Topologies

1.2.2.1 List of Isolated DC-DC Topologies 1.2.2.1.1 Forward Converter Topology

A forward converter is a sort of DC-DC converter that, similar to the flyback and half-connect converters, can gracefully yield a voltage either

DC-DC Converter Topologies for Sustainable Applications  7 Db

L

Dc

C

R

V input

M

Da

Figure 1.4  Forward converter.

higher or lower than the info voltage and give electrical disengagement through a transformer [4, 5]. Albeit more unpredictable than a flyback, the forward converter configuration can yield higher yield power (for the most part up to 200W) alongside higher energy productivity. The circuit of arrangement controller is shown in Figure 1.4. The hardware on the optional (for example right) side is practically indistinguishable from a buck converter and forward converters store and convey energy similarly. The exchanging component, frequently a force MOSFET or IGBT, in a perfect world is either opened or cut off (or on) so the forward converter will shift back and forth between two unique states.

1.2.2.1.2 Flyback Converter

Flyback converters are one of the least difficult DC-DC converter geographies to incorporate electrical disengagement. Albeit for the most part they just suitable for lower range power supplies (up to 100W), they do have various focal points. Other than the converter’s intrinsic straightforwardness, maybe the best of these is that the plan does not need an extra inductor [6]. The transformer gives separation, but then additionally works as a couple of coupled inductors, putting away energy similarly as with an essential buck or lift converter. Supplanting the transformer with an arrangement inductor will, indeed, give us the lift converter geography. The circuit arrangement of the controller is shown in Figure 1.5.

8  DC-DC Converters for Sustainable Applications D V output

C

R

V input

M

Figure 1.5  Flyback converter.

The exchanging component, frequently a force MOSFET or IGBT, is preferably either opened or stopped (or on) so the buck converter circuit will shift back and forth between two distinct states.

1.2.2.1.3 Push-Pull Converter

A push–pull converter is a sort of DC-to-DC converter, an exchanging converter that utilizes a transformer to change the voltage of DC power flexibly [7]. The distinctive element of a push-pull converter is that the transformer essentially is provided with current from the info line by sets of semiconductors in a balanced push-pull circuit. The circuit of arrangement controller is shown in Figure 1.6. Da

L R C

N1

V input

N2

+ –

Db

Sa

Sb

Figure 1.6  Push-pull converter.

V output

DC-DC Converter Topologies for Sustainable Applications  9 The semiconductors are, on the other hand, turned high to low, quickly changing the corresponding current in the transformer. Alternatively, the current absorber is in the line over the two exchanging cycle. These differ from buck-help converters, in which the information current is provided by a solitary semiconductor which is turned here and there, so current is just drawn from the line during a large portion of the exchanging cycle. During the other, a large portion of the yield power is provided by energy put away in inductors or capacitors in the force flexibly. Push–pull converters have steadier info current, make less commotion on the information line, and are more productive in higher force applications.

1.2.2.1.4 Half-Bridge Converter

A half-bridge converter is a kind of DC-DC converter that, as flyback and forward converters, can gracefully a yield voltage either higher or lower than the information voltage and give electrical separation by means of a transformer. Albeit more mind boggling than a flyback or forward converter, the half-bridge converter configuration can yield higher power (conceivably up to 500W) and use parts that are more modest and affordable. The circuit arrangement of the controller is shown in Figure 1.7. The essential side capacitors are utilized to create a consistent mid-point voltage, a large portion of the info voltage, over the essential winding [8, 9]. This implies that the exchanging components need to withstand a larger portion of the voltage than those of a comparable forward converter [10].

Vca

Ca

Da

Vin Cc

C

Cb Vcb

Figure 1.7  Half-bridge converter.

Db

Vout

10  DC-DC Converters for Sustainable Applications

1.2.2.2 Classification of Non-Isolated DC-DC Converters The above topologies are broadly classified into 6 categories and they are listed below: 1. 2. 3. 4. 5. 6.

Cuk-Converter Single-Ended Primary Inductance Converter (SEPIC) Boost Converter Buck-Boost Converter Buck Converter Zeta Converter

1.2.2.2.1 Cuk-Converter

Cuk-converters are the extended version of boost converters, also we can say they are derived from boost converters. The operation of the Cukconverter is discussed here. The output voltage Vo is calculated using the expression shown below. A Cuk-converter is operated in two modes: continuous conduction mode and discontinuous conduction mode [11, 12]. The operation of continuous and discontinuous conduction mode is discussed in detail below. The Cuk-converter is shown in Figure 1.8. From the figure, S and D1 are on during switch on and D is off and D is on during switch off and S and D1 are off.

VO =



p Vin 1− p

(1.1)



Continuous Conduction Mode Average inductor voltage is zero in a steady state condition, therefore the voltage is given as

VC1 = VCO = VO Lb

Vin

M

Figure 1.8  Cuk-converter.

(1.2)

Ca

D

Cb

R

Vout

DC-DC Converter Topologies for Sustainable Applications  11 Voltage across the capacitors C1 and C are equal during the switch on period. Assuming the value of capacitors C and C1 are large, the voltage across them are given as

VC = VC1 = VO

(1.3)

IL being the inductor current increases during the switch on period and during switch off period, it decreases. The voltage values across inductor L are given as VI and - (VC - VI). Therefore,

pTVI = (1–p)T(VC–V1)

(1.4)

Hence,

VO = VC = VC1 = VCO =



1  V 1− p



(1.5)

Discontinuous Conduction Mode During discontinuous conduction mode, the current across the inductor iL increases when its switch is on and during switch off, the current decreases from pT to (1-p)mT. The corresponding voltage across the inductors are given as V I and –(vc – vI).



∴ pTVI = (1 – p)mT(Vc – VI)

(1.6)

 p  Vc =   1 +  V1  (1 − p)m 

(1.7)

Hence,



Assuming C, C1, and CO are very large values,



  p Vo = Vc = Vco =   1 +  V1  (1 − p )m 

(1.8)

12  DC-DC Converters for Sustainable Applications

1.2.2.2.2 Single-Ended Primary Inductance Converter (SEPIC)

SEPIC converters are derived from boost converters. The working of SEPIC converters is discussed here. A circuit diagram of a SEPIC converter is shown in Figure 1.9. The output voltage VO is calculated using the equation shown below. The SEPIC converter is operated in two different modes: continuous conduction mode and discontinuous conduction mode [13, 14].

VO =



p Vin 1− p

(1.9)



Continuous Conduction Mode The average voltage across the inductor in the steady state over a period is given by:

VC = VI

(1.10)

The voltage across the capacitors C1 and C is the same during switch on period. We have assumed the capacitors C1 and C are large and the voltage across them is given by:

VC1 =VC = VI

(1.11)

Average voltage across the inductor LO during steady state over a period is given as:

VC2 =VC0 = V0

(1.12)

Current across the inductor iL increases during switch on period and the value of current decreases during switch off period. Voltage across the inductors L is given as V and I – (Vc – Vc1 + Vc2 – VI).

La

Ca

Vin M

D

Lb

Cb

R

Figure 1.9  Single-Ended Primary Inductance Converter (SEPIC).

Vout

DC-DC Converter Topologies for Sustainable Applications  13

∴ pTVI = (1 – p)TVc – Vc1 + Vc2 – VI)



(1.13)

Hence,

Vo =



1  VI = Vco = Vc2 1− p

(1.14)



VT gain in the continuous conduction mode is given as:

M  =



Vo 1 = VI 1 − p

(1.15)



Discontinuous Conduction Mode In DCM, the inductor current iL increases during the switch on period and current decreases during the switch off period from pT to (1 – p)mT. Voltage across the inductors L is given as V and -(VC-VC1+VC2−VI ). Thus,

pTVI = (1 – p)T(VC-VC1+VC2−VI )

(1.16)

and

VC= VI  VC1=VC= VI  VC2= VCO = VO

(1.17)

Hence,



VO = 1 +

p V (1 − p )m I

(1.18)



So, the real DC voltage transfer gain in the Discontinuous Current Mode is given as:



M DCM = 1 + p2 (1 − p)

R 2 fLeq



(1.19)

14  DC-DC Converters for Sustainable Applications

1.2.2.2.3 Boost Converter

Boost converters are nothing but step-up DC/Dc converters which operates in the second quadrant. Boost converter operation can be derived from quadrant II chopper. A circuit diagram of the Boost Converter is shown in Figure 1.10. Voltage across the output represented by:

VO  =



T 1 Vin  =   Vin T − ton 1− p



(1.20)

1 f f = Chopping frequency ton = Switch-on time p = Duty cycle

where T  =

p=



ton T

(1.21)

1.2.2.2.4 Buck-Boost Converter Topology

The above topology is a step up or step-down converter. These topologies perform in the third quadrant. The working circuit of the Buck-boost converter is given in Figure 1.11. O/p voltage represented as

VO  =



p ton Vin  = Vin T − ton 1− p



(1.22)

Where



T  =

1 f



(1.23)

F= frequency ton = switch-on schedule p= conduction obligation cycle



p  =

ton T

(1.24)

DC-DC Converter Topologies for Sustainable Applications  15 D

L Vin

M

C

Vout

R

Figure 1.10  Boost converter.

D

M Vin

L

C

Vout

R

Figure 1.11  Buck-boost converter topology.

By utilizing the above topology, it is difficult to get the required voltage level, which can be different from the actual value.

1.2.2.2.5 Buck Converter

This topology is a step-down DC-DC topology, which steps down the voltage from the primary end to the secondary end. This can also be interpreted as stepping up the current from input to the output. Normally, these converters consist of a couple of transistors, a capacitor, and an inductor [15]. These converters provide much higher efficiency than linear regulators and are normally simpler in design but fail to step-up the current. The circuit arrangement of the controller is shown in Figure 1.12.

1.2.2.2.6 Zeta Converter

The Zeta converter is a non-linear fourth order converter and with regards to energy input it can be used as buck-boost-buck converter. It can be used

M Vin

Figure 1.12  Buck converter.

Lb D

Cb

R

Vout

16  DC-DC Converters for Sustainable Applications Ca

M Vin

La

Lb D

Cb

R

Vout

Figure 1.13  Zeta converter.

as a boost-buck-boost converter with regards to the output [16]. The circuit diagram of a Zeta converter is shown in the Figure 1.13.

1.2.3 Classification of Soft Switching DC-DC Converter 1.2.3.1 Zero Current Switching (ZCS) The above converter is one among the DC-DC topology family. This converter neutralises the switching loss during the turn-off period. Switching losses are minimized during the turn-on period of the operation [17]. ZCS converter operation is not affected by the diode capacitance, as there is a large capacitor placed at the output end prior to resonance.

1.2.3.2 Zero Voltage Switching (ZVS) Similar to that of the ZCS, zero voltage switching also neutralizes the losses during capacitor turn-on. These converters are good for high frequency applications. Voltage stress proportional to the load will appear for one end of the switching operation.

1.3 Applications of DC-DC Converters in Real World DC-DC converters have wide applications in the present day. Varying from small scale to large scale applications, DC-DC converters play an important role. A wide variation of voltage levels is required in daily appliances to provide continuous, uninterrupted supply and these converters are very useful. Applications of DC-DC converters are listed in the Table 1.1, shown below [18].

DC-DC Converter Topologies for Sustainable Applications  17 Table 1.1  Applications of DC-DC converters. Sl. no.

Converter

1

Application Series Regulators

2

Linear Mode DC-DC Converters

Parallel Regulators

Use in all power supplies to electronic contraptions to control voltage and spare the gadget from harm; Utilized with the alternator of inward burning motors to direct the alternator yield; Utilized for gadget circuits to flexibly include an exact measure of voltage

3

Isolated DC-DC Converters

Forward Converter

Power metering, modern programmable logic controllers (PLCs), insulated-gate bipolar transistor (IGBT) driver power supplies, mechanical fieldbus, and modern robotization

4

Flyback Converter

5

Push-pull Converter

6

Half-bridge Converter

7 8 9

Non-Isolated DC-DC Converters

Cuk-Converter Single-Ended Primary Inductance Converter (SEPIC)

10

Boost Converter

11

Buck-Boost Converter

12

Buck Converter

13

Zeta Converter

The converter is anticipated for huge force electronic applications where regularly the converters are taken care of DC supplies at a commonplace voltage level of around a couple of kV

(Continued)

18  DC-DC Converters for Sustainable Applications Table 1.1  Applications of DC-DC converters. (Continued) Sl. no.

Converter

14

Soft Switching DC-DC Converters

15

Application Zero Current Switching (ZCS) Zero Voltage Switching (ZVS)

Use of delicate exchanging in DC-DC converters has made astounding progress in power gadgets innovation regarding a decrease in exchanging misfortunes, improving in influence thickness, minimization of electromagnetic impedance (EMI), and decrease in the volume of DC-DC converters

1.4 Conclusion Application of DC-DC converters is vital in the modern world. As the world is moving towards electric vehicles, DC-DC converters play a very important role. This chapter gives a brief of different types of converters and their basic operations. Every converter has its own application areas and is important. Applications of every converter are listed in this chapter in brief. Overall, the operation and control of DC-DC converters is explained.

References 1. H. Matsumori, T. Kosaka, K. Sekido, K. Kim, T. Egawa and N. Matsui, “Isolated DC-DC Converter utilizing GaN power device for Automotive Application,” 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), Anaheim, CA, USA, 2019, pp. 1704-1709. 2. P. Odo, “A Comparative Study of Single-phase Non-isolated Bidirectional DC-DC Converters Suitability for Energy Storage Application in a DC Microgrid,” 2020 IEEE 11th International Symposium on Power Electronics for Distributed Generation Systems (PEDG), Dubrovnik, Croatia, 2020, pp. 391-396. 3. Z. W. Khan, H. Minxiao, C. Kai, L. Yang and A. u. Rehman, “State of the Art DC-DC Converter Topologies for the Multi-Terminal DC Grid Applications:

DC-DC Converter Topologies for Sustainable Applications  19 A Review,” 2020 IEEE International Conference on Power Electronics, Smart Grid and Renewable Energy (PESGRE2020), Cochin, India, 2020, pp. 1-7. 4. Luo, F.L. and Ye, H., Positive output super-lift converters, IEEE Transactions on Power Electronics, 18, 105, 2003. 5. Luo, F.L. and Ye, H., Positive output super-lift Luo-converters, in Proceedings of IEEE- PESC’2002, Cairns, Australia, 2002, p. 425. 6. A.M. Trzynadlowski, Introduction to Modern Power Electronics, third ed., Wiley, New York, NY, 2015. 7. P.T. Krein, Elements of Power Electronics, second ed., Oxford University Press, New York, NY, 2014. 8. Luo F. L. and Ye H., Advanced DC/DC Converters, CRC Press, LLC, Boca Raton, 2003. 9. Luo F. L. and Ye H., Ultra-Lift Luo-Converter, in IEE-EPA Proceedings, 152, 1, 2005, pp. 27-32. 10. Ioinovici, Power Electronics and Energy Conversion Systems, Fundamentals and Hard-Switching Converters, Wiley, New York, NY, 2013. 11. Luo, F.L., Seven self-lift DC/DC converters: voltage-lift technique, IEE Proceedings on Electric Power Applications, 148, 329, 2001. 12. M.K. Kazimierczuk, Pulse-Width Modulated DC-DC Power Converters, second ed., Wiley, New York, NY, 2015. 13. Luo, F.L., Double output Luo-converters: advanced voltage lift technique, IEE-Proceedings on Electric Power Applications, 147, 469, 2000. 14. M.K. Kazimierczuk, Class-D voltage-switching MOSFET power amplifier, IEE Proc. Electric Power Appl. 138 (1991) 285–296. 15. Luo, F.L., Positive output Luo-converters: voltage lift technique, IEE Proceedings on Electric Power Applications, 146, 415, 1999. 16. K. Lee, Z. Pantic, S.M. Lukic, Reflexive field containment in dynamic inductive power transfer systems, IEEE Trans. Power Electron. 29 (2014) 4592–4602. 17. Cúk, S., Basics of switched-mode power conversion: topologies, magnetics, and control, in Cúk, S., Ed., Advances in Switched-Mode Power Conversion, Irvine, CA, Teslaco, 1995, vol. 2. 18. N. Mohan, T.M. Undeland, W.P. Robbins, Power Electronics: Converters, Applications and Design, third ed., John Wiley & Sons, New York, NY, 2003.

2 DC-DC Converters for Fuel Cell Power Sources M. Venkatesh Naik1*, Paulson Samuel1 and Srinivasan Pradabane2 Electrical Engineering Department, MNNIT Allahabad, Uttar Pradesh, India 2 Electrical Engineering Department, NIT Warangal, Telangana, India

1

Abstract

In this chapter, various topologies of DC-DC converters for use with Polymer Electrolyte Membrane Fuel Cells (PEMFC) are emphasized. The non-isolated type of DC-DC converters are examined as they are of special interest. A 24 kW, 180 V PEMFC source is considered as the power source and the input and output voltages and input and output currents are plotted. In addition, the ripples present in the FC currents have been evaluated for each converter under study for common loads. The non-inverting type buck boost converters, like buck boost converters (BBC) and interleaved buck boost converters (IBBC), are studied and their steady state performances are presented. Further, the proposed converters’ multi-device buck boost converters (MDBBC) and multi-device multi-phase interleaved buck boost converter (MDMPIBBC) are compared with existing BBC and IBBC topologies for an FC power source whose terminal voltage varies from 28.0 V at full load and 45.0 V at no load. From the study it is shown that the proposed MDMPIBBC converter gives smaller ripple current with lower sizes of passive component parameters. The converter configurations for integrating an FC source with a DC link feeding a 400 V, 50 Hz inverter is proposed. Keywords:  DC-DC power converters for fuel cells, buck boost converters for fuel cells

*Corresponding author: [email protected] S. Ganesh Kumar, Marco Rivera Abarca and S. K. Patnaik (eds.) Power Converters, Drives and Controls for Sustainable Operations, (21–70) © 2023 Scrivener Publishing LLC

21

22  DC-DC Converters for Sustainable Applications

2.1 DC-DC Boost Converter in Fuel Cell (FC) Applications Fuel cells are low voltage high current (LVHC) devices. The FC stack output voltage is around 50V. The power converters connected with these devices should provide high voltage gain to reach the high output voltage and less input ripple current [1–3]. For automotive, grid-connected, and portable applications, the PEMFC type FCs are most appropriate due to their high power density, low temperature, and faster transient response for the dynamic loading conditions [4–6]. An FC, when utilized as a part of various applications as listed in Table 2.1, requires DC-DC voltage transformation in view of the higher DC link voltage needed. Since the DC link voltage (VDC) is usually higher than the FC stack voltage, DC-DC boost converters are utilized [7–9]. For the requirement of a DC link voltage smaller than the FC stack voltage, buck converters are used and such applications include portable power and battery charging. A special case is when the regulated voltage falls inside the FC unregulated voltage range and requires the use of buckboost converters. All the distinctive types of DC-DC converters are classified in Figure 2.1. Considering the switching approaches, there are two basic types: hard switching and soft switching converters. Based on isolation between the input and output side, the converters are further classified as non-isolated and isolated converters. The distinctively non-isolated type converters are boost, buck, buck-boost, Cuk, and Sepic converters. Considering the number of switches connected in the topologies, isolated converters are further classified as single switch and multiple switch Table 2.1  DC link voltage levels in various applications. DC link voltage levels

Applications

42 V

Automobile systems

48 V, 120 V

Parallel grid or standalone systems

270 V or 350 V

Aircraft

350 V – 750 V

Electric transit bus system (350V); Tramway and tramcar, locomotive systems (750V)

270 V – 540 V

Electric automotive

400 V – 480 V

Stand alone or parallel grid connection

DC-DC Converters for Fuel Cell Power Sources   23

DC-DC Converters

Linear

Series regulator

Soft switching (Resonant)

Hard switching

Parallel regulator

Boost

Buck

Buckboost

ZCS

Isolated converters

Non-Isolated

Cuk

Sepic

Multiple switch

One switch

FlyBoost Forward back

Figure 2.1  Classification DC-DC converters for sustainable applications.

Cuk

Sepic

Push pull

Half bridge

Full bridge

ZVS

24  DC-DC Converters for Sustainable Applications converters. The single switch converters are boost, forward, flyback, Cuk, and Sepic converters and push-pull, half bridge, and full bridge converters go under the multiple switch class. The DC link voltage or the input DC voltage requirement for the single and three phase DC-AC inverters are 400 V and 750 V, respectively (230 V single phase and 415 V three phase supply system). Figurer 2.2 depicts such a system with a commercially existing PEMFC stack manufactured by Ballard Power Systems Limited. The output voltage of the stack is 65.0 V at  no load and 45.0 V at full load condition. For a 45 V, 6 kW PEMFC under rated operating condition, the FC terminal voltage Vfc is 45.0 V at a rated current Ifc of 133.33 A. The FC stack voltage is low and thus, a few such stacks are connected in series to get some sensible voltage at full load. For instance, four such stacks can be connected in series to get 180.00 V at full load and utilizing a boost converter, this voltage can be improved to the required DC link voltage, i.e., VDC = 400 V, 750 V, and so on. The DC-DC converter should be designed for high input current on the FC side and high output voltage. The fuel cell often draws some ripple current, which appears as an AC current on the top of the average DC current Ifc. The ripple current in the fuel cell results in reduction of FC life span and unnecessary tripping as it gets overloaded with an extra current magnitude. The circuit diagram of a boost converter with an FC stack is shown in Figure 2.3. Here, four PEMFC stacks are connected in series to get 180 V as the input voltage to the converter. Lb is the boost inductor, Cf is the filter capacitor, T is the IGBT switch, D is the diode, and Rlb and Rcf are the internal resistances of boost inductor and filter capacitor, respectively. The input

Idc

Ifc Vfc

133.33A 45V- 65V

Ifc

H2

+

+ Ballard 9SSL

Vfc -

O2

H2O

Iac

DC-DC Boost Converter

325V/ DC- AC Inverter + 230V/ 625V Filter 440V -

Heat

Figure 2.2  Block diagram of FC system connected to single or three phase stationary load.

DC-DC Converters for Fuel Cell Power Sources   25 +DC D Ifc

Io

Lb

RLb

Rcf

+ PEMFC stacks in series

Vfc

Ro

Vo

Cf

T

-DC

Input voltage (V)

Figure 2.3  PEMFC stack associated with boost converter.

180.5 180 179.5 179

250 200

0.0402

0.0404

0.07

0.08

0.0406

150 100 0

0.01

0.02

0.03

0.04

0.05

0.06

0.09

0.1

0.09

0.1

Output voltage (V)

400 300 340

200

338 100 0

0.0402 0

0.01

0.02

0.03

0.04

0.05

0.0403 0.06

0.0404

0.07

0.08

Time (sec)

Figure 2.4  Input and output voltage waveforms of boost converter to DC load.

FC output current (A)

26  DC-DC Converters for Sustainable Applications 250

136

200

132

134

0.0404 0.0405 0.0406 0.0408 0.0407

150 100 50 0

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Time (Sec)

Figure 2.5  Ripple current in fuel cell output current with boost converter.

and output voltage waveforms of the boost converter are shown in Figure 2.4. Also, the ripple present in FC output current is shown in Figure 2.5.

2.2 DC-DC Buck Converter Buck converters are required when the voltage required is less than the voltage of the FC stack or stacks. As shown in Figure 2.6, a buck converter is associated with four PEMFC stacks of rating 6 kW, 45 V, whereas the no load voltage of the stack is 260 V. Ifc is the stack output current, Vfc is the stack output voltage, T is the MOSFET switch, D is the diode, L is the buck inductance, C is the filter capacitance, and Ro is the output resistance. For portable applications, smaller voltages are required, such as 42 V and 48 V, as given in Table 2.1. The FC stack rated voltage usually lies in the range of 12 V – 72 V. Any convenient voltage lesser than the FC rated voltage can be effectively obtained by utilizing a buck converter with a certain duty ratio. As the voltage range is small, the MOSFET is suitable for the switching device in L

Ifc + PEMFC Stacks Vfc in series

Io

T

D

-

Figure 2.6  PEMFC stack associated with buck converter.

C

Ro

Vo

DC-DC Converters for Fuel Cell Power Sources   27 260 231

Duty cycle D=0.7

Vfc

230.5

Input and Output voltages (V)

240

2.96 2.962 2.964 2.966

220

2.96

200

Vo

180

159.12 159.1 2.96 2.962 2.964 2.966

160 Ro=15 Ω 140

0

1

Ro=15 Ω

Ro=7.5 Ω 2

3 Time (Sec)

4

5

6

Figure 2.7  Input and output voltages of buck converter for load disturbance.

the circuit. Figure 2.7 depicts the variation in FC stack voltage and load voltage for a load disturbance. The input voltage for the converter is 230 V with duty cycle 0.7 and the output voltage of the converter is 160 V. The FC voltage is unregulated and varies as the load current varies.

2.3 DC-DC Buck-Boost Converter Figure 2.8 shows a single switch buck-boost converter connected with a PEMFC stack. The output polarity is opposite to the FC voltage polarity and output voltage varies with the duty cycle of the switch T. Another possible topology of a buck-boost converter is obtained by combining a boost converter with a buck converter and this topology results in a single inductor non-inverting type buck-boost converter. Fuel cells are unregulated voltage sources and non-inverting DC-DC buck-boost converters are used to regulate the output voltage when the derived voltage is within the FC terminal voltage range. These types of conventional converters, when integrated with FC sources, experience high component stress and have low efficiency [10].

28  DC-DC Converters for Sustainable Applications Ifc

D

+

+

T

PEMFC Stacks Vfc in series

L

C

Io

Ro

Vo

-

-

Figure 2.8  PEMFC stack associated with buck-boost converter.

The buck-boost converter is simulated with a PEMFC stack connected at the input side of the converter. The stack is rated for 180.0 V at rated load and 260.0 V at no load. The duty cycle of the switch is controlled to observe the variation in FC voltage and its ripple. Figure 2.9 shows the variation in converter output voltages for buck and boost operating modes. For D = 0, the voltage across the load is zero as there is no energy transfer. The buck operation is initiated at t = 2.0s and continued until t = 5.3s, with

300

Vfc

200

Input and output voltges (V)

100 0 -100 -200

D = 0.7

D=0

D = 0.25 Vo

-300 -400 -500

0

1

2

3 Time (Sec)

4

5

6

Figure 2.9  FC output voltage variation with buck-boost converter in buck and boost modes.

DC-DC Converters for Fuel Cell Power Sources   29 a duty cycle D = 0.7. During this period, the FC voltage has higher ripple compared to the boost operation. The converter is operated under boost operation with D = 0.25 during 5.4 s < t < 6.2 s.

2.4 DC-DC Cuk-Converter The Cuk converter is fundamentally a boost converter followed by a buck converter. The non-isolated Cuk converter, as shown in Figure 2.10, has the output voltage of opposite polarity to the FC voltage. The circuit comprises of two inductors ‘L1’ on the FC source side and ‘L2’ on the load side, two capacitors ‘C’ in the middle which act as energy storage elements, with ‘Cf’ on the load side, a switch ‘T’ (usually MOSFET), and a diode ‘D’. The capacitor ‘C’ is used to transfer the energy from input to the output with the help of the switch ‘T’ and diode ‘D’. The Cuk converter is simulated with a PEMFC source of 180 V at loaded condition and 260 V at no load condition. The FC terminal and output voltage of the Cuk converter are shown in Figure 2.11. During the time period, at 0 < t Ts, the current in Lb2 is forced to flow through diode D2 as shown in Figure 2.20(a), as the inductor Lb2 current tends to decrease, the voltage induced in the inductor Lb1 is reversed to that shown in Figure 2.20(b). The voltage across the load becomes vLb2 + Vfc, i.e., the voltage across the Lb1 adds to the supply voltage to force the inductor Lb1 current into the load. During Mode-II, for (Ts/2 < t < Ts): When T2 is on, the inductor Lb2 is connected to the Vfc and inductor stores the energy during T2 on period (Ts/2 < t < Ts). When the switch T1 is off during the period Ts/2 < t < Ts, the current in Lb1 is forced to flow through the diodes D1, as shown in Figure 2.20(b). +DC

D1 IFC

IL1

RLb1

+

+

IL2 RLb2

+

Lb1

+

D2

-

Lb2

Io

Rcf

-

Vo

Ro VFC Cf

T1

T2

-

-DC

(a)

+DC D2

D1 Ifc

+

IL1

RLb1

+

Lb1

-

IL2

RLb2

+

Lb2

-

+

Io

Rcf

Vo

Ro Vfc Cf

T1

-

T2

(b)

-DC

Figure 2.20  Conduction equivalent circuit of MPIBC during switching cycle when: (a) T1 is ON; (b) T2 is ON.

DC-DC Converters for Fuel Cell Power Sources   37 T1

1 0.5

T1on

T1off

T2off

T2on

0

T2

1 0.5 0 Vfc (V)

178.541 178.5405

0.05 V

178.54

Ifc (A)

137.364 137.362

0.02 A

137.36 Vo (V)

350.4

Io (A)

350.6

66.75

0.1 V

66.8

66.7 0

0.05 A Ts/2

Ts

3Ts/2

2Ts Time (S)

Figure 2.21  Switching signals for T1,T2, fuel cell current & voltage, converter current & voltage waveforms of MDBC.

As the inductor current tends to decrease, the voltage induced in the inductor Lb1 is reversed to that shown in Figure 2.20(a). The voltage across the load becomes vLb1 + Vfc, i.e., the voltage across the Lb1 adds to supply voltage to force the inductor Lb1 current into the load. The FC stack output voltage Vfc = Vin = 178.5 V and average output voltage Vout measured during simulation is 350.5 V, according to the converter Vin 178 output voltage equation Vout = = = 356 V . As shown in 1 − (q × D ) 0.5 Figure 2.21, the output voltage Vout is 350.5 V, the remaining 5.5 V being the voltage drop in ESR of inductors and switch and diode on-state resistance. Whereas the voltags drop in parasitic conventional boost converter was 20.0 V and in MDBC 10.0 V, but in MPIBC it is 5.5 V and this is achievable with reduced ripple current in MPIBC with interleaving technique. The MPIBC has higher efficiency compared to the BC and MDBC because of the reduced passive component losses.

2.6.3 Multi-Device Multi-Phase Interleaved Boost Converter In multi-device multi-phase interleaved boost converters (MDPIBC), the number of phases (p) is two and number of devices per phase (q) is

38  DC-DC Converters for Sustainable Applications also  two. Figure 2.22 illustrates the two-phase multi-device interleaved boost converter topology integrated with a PEMFC stack. Where Lb1 and Lb2 are boost inductors and RLb1 and Rlb2 are the ESRs of Lb1 and Lb2, respectively. T1 and T2 are the IGBT switches connected in phase-I and T3 and T4 +DC P=2 q=2

PEMFC Stacks in series

+

Ifc

RLb1

+

RLb2

D1

Lb1

D2

D4

D3

Io Rcf

Lb2

-

Cf

Vfc T1

T2

T3

Vo

Ro

T4

-DC

Figure 2.22  Multi-device multi-phase interleaved boost converter connected with PEMFC stack.

T1on

T1off

T2on

T2

T1

1 0.5 0 1 0.5 0 1 0.5 0 1 0.5 0 178.41 178.405 178.4 137.745 137.74 T3

T3on

Io (A) Vo (V)

Ifc (A)

Vfc (V)

T4

T4on

352.8 352.6 352.4 64.15 64.1 64.05 Mode I

Ts/4 Ts/2 3Ts/4 Ts Mode II Mode III Mode IV

5Ts/4

3Ts/2

Figure 2.23  Voltage and current waveforms in different operating mode.

7Ts/4 2Ts Time (Sec)

DC-DC Converters for Fuel Cell Power Sources   39 are the IGBT switches connected in phase-II, D1 and D2 are the diodes of phase-I and D3 and D4 are diodes in phase-II, Cf is the output filter capacitor, Rcf is the ESR of output capacitor, p is the number of phases, and q is the number of devices per phase. Figure 2.23 shows the different modes of operation of the converter along with voltage and current waveforms at the input and output. During Mode–I, for (0 < t < Ts /4): In this mode, the switch T1 is on, the inductor Lb1 is connected to the FC voltage Vfc, the inductor stores the energy during the Ton period, and the supply current flows though the path shown in Figure 2.24(a). The switches T2,T3 and T4 are turned off, and the current in Lb2 is forced to flow through diodes D3 and D4, as shown in Figure 2.24 (a). As the inductor Lb2 current tends to decrease, the voltage induced in the inductor Lb2 is reversed to that of shown in Figure 2.24(a). The voltage across the load vLb2 + Vfc, i.e., the voltage across the Lb2, adds to the supply voltage to force the inductor Lb1 current into the load. During Mode–II, for (Ts/4 < t < Ts /2): In this mode, the switch T3 is on, the inductor Lb2 is connected to the Vfc, the inductor stores the energy during T3on period, and the current flow path is shown in Figure 2.24(b). The other switches, T1,T2, and T4, are turned off and the current in Lb1 is forced to flow through the diodes D1 and D2, as shown in Figure 2.24(b). As the inductor current tends to decrease, the voltage induced in the inductor Lb1 is reversed to that shown in Figure 2.24(b). The voltage across the load vLb1 + Vfc, i.e., the voltage across the Lb1 adds to the supply voltage to force the inductor Lb1 current into the load. During Mode–III, for (Ts/2 < t < 3Ts /4): In this mode, the switch T2 is turned on, the inductor Lb1 is connected to the FC voltage Vfc, the inductor stores the energy during the Ton period, and the supply current flows though the path, as shown in Figure 2.24(c). The switches T1,T3, and T4 are turned off and the current in Lb2 is forced to flow through the diodes D3 and D4, as shown in Figure 2.24(c). As the current in inductor Lb2 tends to decrease, the voltage induced in inductor Lb2 is reversed to that shown in Figure 2.24(c). The voltage across the load vLb2 + Vfc, i.e., the voltage across the Lb2, adds to the supply voltage to force the inductor Lb2 current into the load. During Mode – IV for (3Ts /4 < t > Ts): In this mode, the switch T4 is turned on, the inductor Lb2 is connected to the Vfc, the inductor stores the energy during T4on period, and the current flow path is shown in Figure 2.24(d). The other switches, T1,T2, and T3, are turned off and the current in Lb1 is forced to flow through diodes D1 and D2, as shown in Figure 2.24(d). As

40  DC-DC Converters for Sustainable Applications + Ifc

RLb1

+

+

RLb2

+

Lb1 Lb2

D1

D2

D3

D4

IO

Rcf

-

-

Cf Vfc T1

T2

T3

VO

RO

T4

-

(a) + Ifc

RLb1

+

+

RLb2

+

Lb1 Lb2

D1

D2

D3

D4

IO

Rcf

-

VO

RO

-

Cf Vfc T1

T2

T3

T4

-

(b) + Ifc

RLb1

+

+

RLb2

+

Lb1 Lb2

D1

D2

D3

D4

IO

Rcf

-

VO

RO

-

Cf Vfc T1

T2

T3

T4

-

(c) + Ifc

RLb1

+

+

RLb2

+

Lb1 Lb2

D1

D2

D3

D4

IO

Rcf

-

Cf

VO

RO

-

Vfc T1

T2

T3

T4

-

(d)

Figure 2.24  Equivalent circuits of MDMPIBC for interval shown in Figure 2.23: (a) Mode I; (b) Mode II; (c) Mode III; (d) Mode IV.

DC-DC Converters for Fuel Cell Power Sources   41 the inductor current tends to decrease, the voltage induced in inductor Lb1 is reversed to that shown in Figure 2.24 (d). The voltage across the load vLb1 + Vfc, i.e., the voltage across the Lb1 adds to the supply voltage to force the inductor Lb1 current into the load. As shown in Figure 2.23, the FC stack output voltage Vfc = Vin = 178.4 V and average output voltage Vout during simulation is 352.6 V, according Vin 178 to converter output voltage equation Vout = = = 356.8 V . As 1 − (q × D ) 0.5 shown in Figure 2.23, the output voltage across load Vout is 352.6V, with the remaining 4.2 V being the voltage dropped in the ESR of inductors and switch and diode on state resistance. Whereas the voltage drop in parasitic conventional boost converters is 20.0 V, in MDBC 10.0 V, and in MPIBC 5.5 V, in MDMPIBC it is 4.2 V and this is achievable with reduced ripple current and multi-devices per phase along with interleaving operation. The MDMPIBC have higher efficiencies compared to the BC, MDBC, and MPIBC because of the reduced passive component losses. The steady state current waveforms of the two phase multi device interleaved boost converter at an FC current demand of 137.86 A (Vfc = 178.4V) is shown in Figure 2.25.

137.8615

FC current (Amps)

137.861 137.8605 137.86 137.8595

Inductor currents ILb1 and ILb2 (Amps)

137.859 ILb1 ILb2

74 72 70 68 66 64 Ts/4

Ts/2

3Ts/4

Ts

5Ts/4

3Ts/2

7Ts/4

2Ts

Figure 2.25  Steady state current waveforms of two-phase multi-device interleaved boost converter at FC current demand of 137.86 A (Vfc = 178.4V).

42  DC-DC Converters for Sustainable Applications Table 2.2  Comparison among DC-DC boost converters for ripple reduction. Parameter

BC

MDBC

MPIBC

MDMPIBC

Boost Inductor, Lb (µH), Rb (mΩ)

750 68

375 34

375 34

187.5 17

Boost Capacitor Cf (µF) Rcf (mΩ)

550 0.697

275 1.394

320 1.15

160 2.3

Input Voltage (V)

180.0

177.0

178.5

178.4

Output Voltage (V)

340.0

354.0

350.5

352.5

Voltage Lost in Parasitic (V)

20.0

10.0

5.5

4.2

Duty Ratio (D)

0.5

0.25

0.5

0.25

No. of Phase (p), No. of Devices per Phase (q)

1,1

1,2

2,1

2,2

Effective ‘D’ (q×D)

0.5

0.5

0.5

0.5

Ripple Current pk-pk

4.8

4.5

0.02

0.002

Average FC Current

134

140.5

137.36

137.74

Steady State Ripple Current Percentage (%)

3.58

3.20

0.014

0.00145

The comparison among the conventional and multi-phase DC-DC converters is given in Table 2.2, from which it is apparent that the MDMPIBC uses smaller values of components, has higher output voltage compared to the other converters, and the current ripple in the FC current is the least among them. Hence, the MDMPIBC is preferred over other converters when used for high power applications.

2.7 The Proposed High Gain Multi-Device Multi-Phase Interleaved Boost Converter The commonly used single switch boost converters, when employed to get high gain voltage, require the use of high duty ratio, but with extreme high

DC-DC Converters for Fuel Cell Power Sources   43 duty ratio the ripple current in the FC current increases and in addition, the efficiency of the converter reduces due to increased conduction losses. Another alternative to get high voltage gain is by employing cascaded boost converters; these converters provide high voltage gain without the use of a high duty ratio [24]. The strategy for switched capacitor/inductor and voltage lift techniques are additionally fit for furnishing high voltage gain and with favorable circumstances incorporate a smaller size, lighter weight, reduced cost, and reduced conduction losses. The disadvantages include several diode/capacitor structures when a high voltage gain is required, complex circuits, and for high power applications, the single switch may suffer due to the high current of FC devices [25–27]. From the discussion about the disadvantages of using single switch DC-DC boost converter topologies for high power DC-DC conversion, it is evident that single switch topologies are not appropriate for high power and high step up transformation. To carry large FC currents with reduced ripple, interleaved control based switched capacitor cell boost converters are preferred [28]. However, in these too, the voltage stresses of the power devices remain high. A few other converter topologies based on interleaved control with cross coupled inductors and diode capacitor cells are presented for high step up gain in addition to high efficiency [29–37]. In this thesis, a high gain multi-device multi-phase interleaved boost converter (HGMDMPIBC), as shown in Figure 2.26, is proposed to obtain high voltage gain. The converter structure works on the principle of parallel input and series output connection. The HGMDMPIBC boosts the FC voltage four times with a smaller duty ratio of 0.25. The advantages of the proposed converter are high voltage gain, low output voltage ripple, FC current ripple, and low device stresses. In some applications, like traction +DC

D1

PEMFC Stack Ifc +

RL RL

RC1

D2

Io +

L C1 L

Ro

Vo

Vfc -

C2

T1

T2

T3

RC2

T4 Do

-DC

Figure 2.26  High gain multi-phase multi-device interleaved boost converter.

44  DC-DC Converters for Sustainable Applications and transient bus systems, a DC link voltage of 750 V is required. These voltages are possible with the proposed HGMDMPIBC, which is derived from the MDMPIBC shown in Figure 2.22.

2.7.1 Operating Principle of HGMDMPIBC The converter is derived from the multi-device boost converter and can be divided in two parts, as shown in Figures 2.27 (a) and (b). The multi-device boost converter is integrated with the other form of MDBC shown in 27 (b), in which the diodes are placed in a negative DC link rail. This forms the parallel input and series output structure and it is named a high gain multi-device multi-phase interleaved boost converter. The proposed converter has several advantages: 1)  Obtains the double the voltage gain as that of MDMPIBC 2)  Lowers ripple in FC current and output voltage +DC

RLb

Lb

D1

RCf

T1

T2

+DC

Vin T1

-

Cf

Lb

RCf

Vo

Ro

+ Vin

RLb

+

D2

T2

D2 Cf

+ + R V o o -

D1 -DC

-DC

(a)

(b) +DC

D1 Ifc

RLb1 RLb2

RCf1

D2

Io

Lb1

+ Cf1

Lb2

Ro

-

Cf2

Vfc T1

T2

T3

Vo

RCf2

T4 Do

(c)

-DC

Figure 2.27  Development of proposed converter from basic converters: (a) Multi-device boost converter; (b) Output series multi-device boost converter; (c) Modified multidevice multi-phase interleaved boost converter.

DC-DC Converters for Fuel Cell Power Sources   45 3) Reduces device stress as there are multiple devices per phase 4) High voltage gain is achievable with smaller duty ratio and hence the conduction losses are less, which results in higher efficiency of the system. Figure 2.28 shows the input/output voltage and current waveforms of the converter under continuous conduction mode. The duty cycles of the 360° ). The duty cycle of switches are interleaved with a 900 phase shift (θ = p×q the individual switches is D = 0.25.

T2

T1

During mode – I, for (0 < t < Ts/4): In this mode, the switch T1 is on, the inductor Lb1 is connected to the FC voltage Vfc and inductor stores the energy during the Ton period and the supply current flows though the path shown in Figure 2.29 (a). The switches T2, T3, and T4 are turned off, the current in Lb2 flows through the Cf1 and Cf2, and as the inductor Lb2 current tends to decrease, the voltage induced in the inductor Lb2 is reversed to that of shown in Figure 2.29 (a). The voltage across the load vLb2+ Vfc = VCf1+VCf2,

1 0.5 0 1 0.5

T3

0 1 0.5 0

Vfc

T4

1 0.5 0 180.5 180

0.5V

Ifc

179.5 136 134

1.5A

Vo

132 750.5 750

0.2V

Io

749.5 29.91 29.9 29.89 0

0.01A Mode-1

Ts/4

Mode-2

Ts/2

Mode-3 Mode-4 Ts 3Ts/4

5Ts/4

Figure 2.28  Input and output waveforms of HGMDMPIBC.

3Ts/2

7Ts/4

2Ts

46  DC-DC Converters for Sustainable Applications +DC

(a) D1 RLb1 RLb2

RCf1

D2

Io +

Lb1 Cf1

Lb2

Ro

-

Cf2

Vfc T1

T2

T3

Vo

RCf2

T4 Do

-DC

(b)

+DC

D1 RLb1 RLb2

RCf1

D2

Io +

Lb1 Cf1

Lb2

Ro

-

Cf2

Vfc T1

T2

T3

Vo

RCf2

T4 Do

-DC

(c)

+DC

D1 RLb1 RLb2

RCf1

D2

Io +

Lb1 Cf1

Lb2

Ro

-

Cf2

Vfc T1

T2

T3

Vo

RCf2

T4 Do

-DC

(d)

+DC

D1 RLb1 RLb2

RCf1

D2

Io +

Lb1 Cf1

Lb2

Ro

-

Cf2

Vfc T1

T2

T3

Vo

RCf2

T4 Do

-DC

Figure 2.29  Operating intervals of proposed HGMDMPIBC: (a) Only T1 On; (b) Only T3 On; (c) Only T2 On; (d) Only T4 On.

DC-DC Converters for Fuel Cell Power Sources   47 i.e., the voltage across the Lb2, adds to the supply voltage to force the inductor Lb2 current into the load. During mode – II, for (Ts /4 < t < Ts /2):- In this mode, the switch T3 is on, the inductor Lb2 is connected to the Vfc, and the inductor stores the energy during T3 on period and the current flow path is shown in Figure 2.29 (b). The other alternate switches T1,T2, and T4 are turned off and the current in Lb1 is forced to flow through diodes D1 and D2, as shown in Figure 2.29 (b). As the inductor current tends to decrease, the voltage induced in inductor Lb1 is reversed to that shown in Figure 2.29 (b). The voltage across load vLb1 + Vfc, i.e., the voltage across the inductor Lb,1 adds to the supply voltage to force the current into the load inductor Lb1. During mode – III, for (Ts /2 < t < 3Ts /4): In this mode, the switch T2 is turned on, the inductor Lb1 is connected to the FC voltage Vfc, the inductor stores the energy during the Ton period, and the supply current flows though the path shown in Figure 2.29 (c). Switches T1, T3, and T4 are turned

VT1

400 356V

200 0

VT2

400 356V

200 0

VT4

VT3

500 0

394V

-500 500 0

394V

-500

Icf1

50 0

31.5A

-50 Icf2

50 0

32 A

-50 Vcf1

358 356 354

Vcf2

394 392 390 0

Mode-1

Mode-2

Mode-3

Mode-4

Ts

2Ts

Figure 2.30  Voltage stress in power switches, voltage, and current in capacitors Cf1 and Cf2.

48  DC-DC Converters for Sustainable Applications off and the current in Lb2 flow in Cf1 and Cf2 is shown in Figure 2.29 (c). As the current in inductor Lb2 tends to decrease, the voltage induced in the inductor Lb2 is reversed to that shown in Figure 2.29 (c). The voltage across load vLb2  +Vfc, i.e., the voltage across the Lb2, adds to the supply voltage to force the inductor Lb2 current into the load. During mode – IV for (3Ts /4 < t < Ts): In this mode, switch T4 is turned on, the inductor Lb2 is associated with the Vfc, the inductor stores the energy amid T4 on period, and the current flow path is shown in Figure 2.29 (d). Alternate switches T1,T2, and T3 are turned off and the current in Lb1 is compelled to course through the diodes D1 and D2, as shown in Figure 2.29 (d). As the inductor current tends to diminish, the voltage affected in inductor Lb1 is turned around to that shown in Figure 2.29 (d). The voltage across the load is vLb1 +Vfc, i.e., the voltage across the Lb1 adds to the supply voltage to drive the inductor Lb1 current into the load. The device stress of the HGMDMPIBC is shown in Figure 2.30. The voltage across the switch amid the turned off condition is around half of the output voltage. Additionally, the current through and voltage across the output capacitors Cf1 and Cf2 are also shown. The HGMDMPIBC can have high voltage gain with less device stress and high efficiency.

2.8 Non-Inverting Buck-Boost Converters for Low Voltage FC Applications The FC sources are unregulated voltage sources and require power converter devices to get a regulated output voltage. Figure 2.31 shows the non-inverting buck-boost converter in which the boost converter is cascaded with the buck converter. These converters are used to regulate the voltage from the unregulated FC voltage source. For example, the Horizon RL2 S2 Ig

RL1

L1

Vg G1

Cd

D1 C1 + S1

-

G2

L2

C2 D2

vc1 R d

Figure 2.31  Schematic circuit diagram of non-inverting buck-boost converter.

+ -

Io Vo Ro

DC-DC Converters for Fuel Cell Power Sources   49 FC model ECS-1000 has a voltage range variation of 45 V at no load and 28 V at full load. In order to get a regulated voltage of 36 V, the buck-boost converters are integrated with the fuel cell stacks.

2.8.1 Single Switch Non-Inverting Buck-Boost Converter The cascaded association of a conventional buck-boost converter is shown in Figure 2.31. The converter works either in buck or boost mode depending upon the source voltage and the control method. If the source voltage is less than the output voltage, the converter works in boost mode and if the source voltage is higher than the output voltage, the converter works in buck mode. Normally, the FC stack voltage varies from no load to full load and, consequently, to get the steady output voltage required for a few applications like, battery charging/discharging, portable applications etc., these buck-boost converters are used [38]. As shown in Figure 2.31, Vg is the average input voltage to converter, Ig is average input current, L1 is the boost inductor, RL1 is the ESR of the boost inductor, S1 is the boost switch, D1 is the boost side diode, C1 is the boost side filer capacitor, Cd is the damping capacitor, Rd is the damping resistor, S2 is the buck switch, D2 is the buck side diode, L2 is the buck inductor, RL2 is the ESR of the buck inductor, C2 is the output capacitor, and Ro is the load resistor. When the circuit is operating under the boost mode, the buck switch S2 is switched continually with duty cycle D = 1 and boost switch S1 is operated in pulse width modulation (PWM). Under the buck operation mode, the boost switch S1 is turned off with D = 0 and S2 is operated in PWM. The S1 and S2 are controlled to get the required voltage at the output of the converter. The equivalent circuits of the buck and boost operating modes are illustrated in Figure 2.32 (a) and (b) respectively. A PEMFC stack of ECS-1000 is considered as the input power source for the converter. The no load voltage of the stack is 45 V and at load 28 V, whereas the required output voltage of the converter is 36 V. When the FC voltage is at 28 V, the buck boost converter operates as shown in Figure 2.32 (a). The switch S1 is operated with D = 0.11 to get 36 V at the output and S2 in boost mode is shown as short circuited due to the full conduction of it with 100% duty cycle. The current and voltage waveforms under boost operation are shown in Figure 2.33. When the FC voltage is at 45 V, the buck boost converter operates as shown in Figure 2.32 (b). The switch S2 is operated with D = 0.11 to get 36 V at the output and S1 is turned off with the 0% duty cycle. The typical current and voltage waveforms under buck operation of the converter are shown in Figure 2.33.

50  DC-DC Converters for Sustainable Applications RL2

Cd

D1

L1

RL1

Ig

C1

Vg

L2

S1

C2

+ -

Vc1

Rd

+

Vo - Ro

Io

G1 (a)

L1

Ig RL1

S2 Vg

L2

RL2

C1 + -

Cd

G2

Vc1

C2

D2

+ -

Io Vo

Ro

Rd (b)

Figure 2.32  Equivalent circuit of buck-boost converter: (a) Boost mode; (b) Buck mode. 1

VGS

0.5 0 10.5

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

IL1 10 7.505 7.5

IL2

7.495 7.5 7.5 7.4999 36.0001

Io

Vo

36 35.9999 37 36.8

0.065

Vc1

36.6 0.065

Ts

2Ts

3Ts

Figure 2.33  Voltage and current waveforms of buck-boost converter operated in boost mode.

DC-DC Converters for Fuel Cell Power Sources   51 Table 2.3  Passive component values applied for buck-boost converter.

1 0.5

Component

Value

Boost Inductor L1 in µH

320

Internal Resistance of L1 in mΩ

26

Buck Inductor L2 in µH

240

Internal Resistance of L2 in mΩ

20

Boost Capacitor C1 in µF

94

Buck Capacitor C2 in µF

94

Damping Resistor Cd in µF

940

Damping Resistor Rd in Ω

0.5

VGS2

0 6.576 6.574

7.5

7.5

44.2 44 43.8

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

Io

7.498 36.01 36 35.99

0.065

IL2

7 7.502

0.065

IL1

6.572 8

0.065

Vo

Vc1

Ts

2Ts

3Ts

Figure 2.34  Voltage and current waveforms of buck-boost converter operated in buck mode.

52  DC-DC Converters for Sustainable Applications From Figure 2.33, it can be observed that the FC ripple current is 0.52 A, whereas the mean FC current is 10.25 A and the ripple percentage is 5%, which is acceptable for satisfactory operation of FC devices, but the passive component values used for these converters are high. The passive component values used in the simulation are given in Table 2.3. The load current and voltages are 7.5 A and 36 V, respectively. The ripple in boost capacitor C1 is observed as 0.4 V with a value of 94 µF. From Figure 2.34, it is observed that the FC current ripple is approximately 0.02. Due to the buck operation, the ripples are mainly presenting in the output inductor L2. In buck mode, the S2 is operating with a duty cycle of 0.81 to get 36 V at the output side. The boost capacitor voltage is equal to the input voltage 45 V, as switch S1 is opened. However, the size of the passive components can be reduced by employing the interleaved buck-boost converter.

2.8.2 Interleaved Buck-Boost Converter The conventional type of buck-boost converter, when associated with FC devices for voltage regulation, has certain drawbacks such as high input/ output current ripple, high noise level, complicated control system, current limitation, and less system efficiency [39–41]. An interleaving technique is applied to have several benefits such as low ripple current, high efficiency, low component stress, high power density, and better thermal property [42–44]. Figure 2.35 represents the two phase non-inverting interleaved buck boost converter (IBBC) in which the interleaved boost converter is

IL21 RL21

L21

IL22 RL22

L22

S3 G3

D1 IL11 RL11 Ig

IL12 RL12

Cd

L11 C1 +

L12

G1

VC1

- Rd

G4

D3

Io

D4

S2

S1 Vg

S4

D2

G2

Figure 2.35  Schematic circuit diagram of interleaved buck-boost converter.

C2

+ Vo -

Ro

DC-DC Converters for Fuel Cell Power Sources   53 cascaded with an interleaved buck converter to operate it as a voltage regulation device. In IBBC, the number of phases is two and the number of devices per phase is one on both the buck and boost side of the converter. This converter can work either in buck or boost depending on the supply voltage extent. The circuit when working under boost and buck modes are shown in Figures 2.36 (a) and (b), respectively. In boost mode of operation, switches S1 and S2 are operated in PWM, whereas the buck switches S3 and S4 are persistently on with the unity duty cycle. In buck operation mode, buck switches S3 and S4 are worked in PWM, whereas the boost switches S1 and S2 are turned off with the zero duty cycle. With the end goal of examining the steady state waveforms, the IBBC is interfaced with a PEMFC power source whose terminal voltage at no load is 45 V and 28 V at full load, whereas the required converter output voltage is 36 V. The selected duty cycles for boost switches are D1 = D2 = 0.11 IL21 RL21 IL22 RL22 D1 IL11 RL11 Ig

IL12 RL12

D2

L22 Io

Cd

L11 L12

+

C2

C1 + V C1

-

Vo Ro

- Rd S1

Vg

L21

S2

G1

G2 (a)

S3

Ig

Vg

IL11 RL11

L11

IL12 RL12

L12

S4

C1

+ -

Cd

G3

L21

IL22 RL22

L22

G4 D3

VC1

IL21 RL21

C2 D4

Io

+ -

Rd (b)

Figure 2.36  Equivalent circuit diagrams of IBBC: (a) Boost mode; (b) Buck mode.

Vo Ro

54  DC-DC Converters for Sustainable Applications 1

VGS1

0.5 0 1

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

VGS2

0.5 0 11

Ig

10 9 6

IL11

5 4

0.065

6

IL12

5 4 7.505

Io

7.5 7.495 3.755

IL21

3.75 3.745 3.755 3.75

IL22

3.745 36.0001 36

Vo

35.9999 37.2 37 36.8

VC1

Ts

2Ts

Figure 2.37  Steady state voltage and current waveforms of IBBC in boost mode for Vg= 45V.

3Ts

DC-DC Converters for Fuel Cell Power Sources   55 1

VGS3

0.5 0 1 0.5 0 6.546

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

VGS4

Ig=6.544A

6.544 6.542 3.273

0.065

IL11=3.272A

3.272 3.271 3.273

0.065

IL12=3.272A

3.272 3.271

0.065

8 7.5 7 5 4 3 5

Io=7.5A 0.065

IL21=3.8A

0.065

IL22=3.7A

4 3 36.01 36 35.99 44.4

0.065

Vo=36V

0.065

VC1=44.15V

44.2 44

0.065

Ts

2Ts

Figure 2.38  Steady state voltage and current waveforms of IBBC in buck mode for Vg = 45V.

3Ts

56  DC-DC Converters for Sustainable Applications for Vg = 28 V and for buck switches, the duty cycles are D3 = D4 = 0.81 for Vg = 45 V. The steady state voltage and current waveforms in boost and buck mode are shown in Figures 2.37 and 2.38. The passive component parameter values used as a part of the simulation study are shown in Table 2.4. The parameter qualities are reduced considerably as that of the parameters used in the conventional buck boost converter. This is possible by interleaving the procedure of operation and this operation makes the effective inductor current frequency (100 kHz) twofold of the switching frequency, ‘fs ’ (50 kHz). As it can be seen, the size of the LC component is inversely proportional to the switching frequency. Further, FC ripple current is 0.5 A with the reduced passive component values. The ripple in boost capacitor voltage is limited to 0.4 V. The IBBC works in buck mode when the supply voltage lies in the extent 36 V to 45 V. For example, the simulation has been carried for the Vg = 45 V and operating duty cycles for switches S3 and S4 are 0.81. During this mode, the boost switches are turned off forever. Figure 2.44 demonstrates the steady state voltage and current waveforms of IBBC in buck mode of operation with Vg = 45 V. The FC ripple current is smaller because of the buck operation, whereas the ripple in the output current is 0.75 A. Because of the smaller size of inductance employed for buck inductors, likewise the ripple in boost capacitor voltage is limited to 0.15 V. Table 2.4  Passive component values for IBBC. Component

Value

Boost Inductor L1 in µH

160

Internal Resistance of L1 in mΩ

13

Buck Inductor L2 in µH

120

Internal Resistance of L2 in mΩ

13

Boost Capacitor C1 in µF

47

Buck Capacitor C2 in µF

68

Damping Resistor Cd in µF

470

Damping Resistor Rd in Ω

2.2

DC-DC Converters for Fuel Cell Power Sources   57

2.9 Proposed Multi-Device Buck-Boost Converter for Low Voltage FC Applications A multi-device buck-boost converter (MDBBC), as shown in Figure 2.39, is proposed in this thesis work and in this converter, the number of phases ‘p’ is one and the number of devices per phase ‘q’ are two. By paralleling the device per phase, the effective inductor current frequency is doubled to the switching frequency. The MDBBC operates either in boost or buck mode, depending on the supply voltage extent. For the converter operated in boost mode, the boost switches are operated in PWM mode and buck switches are turned permanently with the unity duty cycles of the buck switches. In buck operating condition, the buck switches are operated in PWM and boost switches are turned off permanently with zero duty cycle. The proposed MDBBC is analyzed through computer simulations and the passive component parameters used in the circuit are the same as that of the IBBC shown in Table 2.5. The respective results in both buck and boost mode are presented in Figure 2.40. The converter is fed with an input voltage of 28 V for boost mode and 45 V during buck mode. The FC ripple current is only 0.4 A during the buck and boost operating condition, whereas in IBBC, it was 0.5 A with the same passive component parameters. Also, the MDBBC has higher efficiency compared to the IBBC and BBCs.

S3 G3

RL2

L2

S4 D1 IL1 or Ig

RL1

D2

L1

Cd C1

+ -

Vg

S1 G1

G2

S2

VC1

G4 C2 D3

D4

+V

o

- Ro

Rd

Figure 2.39  Proposed multi-device buck-boost converter for portable FC application.

Io

58  DC-DC Converters for Sustainable Applications IL1 (Amps)

10.4 10.2 10

0.4 A

9.8 0.035

Io (Amps)

7.5002

0.035

0.035

0.035

0.0351

1mA

7.5002

7.5001

0.035

36.0011

0.035

0.035

0.035

0.035

0.0351

36.001

1mV

36.0009

Vc1 (Volts)

Vo (Volts)

0.035

0.035

0.035

0.035

0.035

0.035

0.0351

36.2

0.35V

36 35.8

0.035

0.035

0.035

0.035

0.035

0.0351

Time (Secs)

Vo (Volts)

Io (Amps)

IL2 (Amps)

(a) 7.8 7.6

0.4A

7.4 7.2

0.035

0.035

0.035

0.035

0.0351

0.02A

7.5 7.498

0.035

0.035

0.035

0.035

0.035

0.0351

36.01

0.01V

36 35.99 0.035

Vc1 (Volts)

0.035

7.502

0.035

0.035

0.035

0.035

0.0351

44.2

0.2V

44.1 44

0.035

0.035

0.035

0.035

0.035

0.0351

Time (Sec)

(b)

Figure 2.40  Steady-state voltage and current waveforms of MDBBC: (a) In boost mode for Vg = 28 V; (b) In buck mode for Vg = 45 V.

DC-DC Converters for Fuel Cell Power Sources   59

2.10 The Proposed Multi-Device Multi-Phase Interleaved Buck-Boost Converter for Low Voltage FC Applications In multi-device multi-phase interleaved buck boost converters (MDMPIBBC), as shown in Figure 2.41, the number of phases and devices per phase are two (p = q = 2), whereas on the buck side p = 2 and q = 1. The advantage of connecting multiple devices per phase was already discussed in the previous sections. Here, in this converter, the FC ripple current is further reduced due to the multiple devices per phase and the passive component parameters get reduced to half that of IBBC and the proposed MDBBC and is reduced to four times that of BBC. Due to the reduced components size, the system becomes lighter in weight and occupies smaller area and the device selection also becomes easier as the lower rating devices can be used as current flow through them is decreased. With the end goal of comparing the proposed MDMPIBC with BBC, IBBC, and MDBBCs, the converter is simulated by connected a PEMFC stack of voltage range 28 V at full load and 45 V at no load. The converter is fed with 28 V during the boost mode and 45 V during buck mode for a requirement of output voltage Vo = 36 V for battery charging applications. In boost operating mode, the switches S1, S2, S3, and S4 are operated in PWM and buck switches S5 and S6 are turned on permanently with unity duty cycles. The suitable duty cycle required for boost switches to get 36 V at the output is 0.055. In buck operating mode, the boost switches are turned off permanently and buck switches are operated in PWM. The suitable duty cycle required for buck switches to get 36 V at the output is 0.81. The steady state voltage and current waveforms during the boost and buck modes are delineated in Figures 2.42 and 2.43.

S5

G5

RL2

L2

RL2

L2

S6 IL11 IL12 Ig

RL11 RL12

D1

L11

D3

D4

Cd C1

L12

+ -

S1 Vg

D2

G1

S2 G2

S3 G3

S4

G6 D5

Vc1

D6

C2

+ -

Vo

Io

Ro Rd

G4

Figure 2.41  Proposed multi-device multi-phase interleaved buck-boost converter for FC low voltage applications.

60  DC-DC Converters for Sustainable Applications 1 0.5

VGS1

0 1 0.5 0 1 0.5

0.5 0 10.5

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065 Ts

0.065

0.065

0.065

0.0651

VGS3

0 1

0.065

VGS2

VGS4 Ig=10.25A

10 5.8 5.6 5.4 5.2 5

IL1=5.4A 0.065

5.4 5.2 5 4.8 4.6 4.4

IL2=4.85A

7.505

Io=7.5A

0.065

7.5 7.495 3.755

0.065

IL21=3.75A

3.75 3.745 3.755 3.75 3.745 36.0002

0.065

IL21=3.75A 0.065

Vo=36V

36 35.9998 37.2

0.065

VC1=37V

37 36.8

0.065

2Ts

Figure 2.42  Steady-state voltage and current waveforms of MDMPIBBC in boost operating for Vg = 28 V.

3Ts

DC-DC Converters for Fuel Cell Power Sources   61 1

VGS3

0.5 0 1 0.5

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065

0.065

0.065

0.065

0.0651

0.065 Ts

0.065

0.065 2Ts

0.065

0.0651 3Ts

VGS4

0 6.546

0.065

Ig=6.544A

6.544 6.542 3.273

0.065

IL11=3.272A

3.272 3.271 3.273

0.065

IL12=3.272A

3.272 3.271 8 7.5 7

Io=7.5A

5

IL21=3.8A 4 3 5

0.065

IL22=3.7A

4 3 36.01

0.065

Vo=36V

36 35.99 0.065 44.4

VC1=44.15V

44.2 44

0.065

Figure 2.43  Steady-state voltage and current waveforms of MDMPIBBC in buck operating for Vg = 45 V.

62  DC-DC Converters for Sustainable Applications Table 2.5  Passive component values for MDMPIBBC. Component

Value

Boost Inductor L1 (µH)

80

Internal Resistance of L1 (mΩ)

6.5

Buck Inductor L2 (µH)

60

Internal Resistance of L2 (mΩ)

5

Boost Capacitor C1 (µF)

23

Buck Capacitor C2 (µF)

34

Damping Resistor Cd (µF)

230

Damping Resistor Rd (Ω)

4.2

As shown in Figure 2.42, the converter switching gate pulses are phase shifted by 90°, which is selected according to the expression (360/(p×q)), where p = q = 2 and the phase shifting angle comes to be 90°. The FC ripple current drawn with MDMPIBBC is 0.5 A for the halved passive component parameters which is used for IBBC and MDBBCs. The LC components used in MDMPIBBC are presented in Table 2.5. The ripple in boost capacitor is limited to 0.3 V (0.8 %).

2.11 Converter Configurations for Integrating FC with 400 V Grid Voltages To interface a FC stack with a 400 V grid, certain configurations must be used. Because a single FC stack cannot generate such high DC link voltage, to get the three phase 400 VL-L voltage at the output of 3-phase inverter, a DC link voltage of around 625 V is required. Various configurations have been suggested in the next section to achieve this.

2.11.1 Series Configuration In the series configuration, appropriate numbers of FC stack with lower ratings are connected in series. By connecting the stacks in series, the required voltage is generated for input of the DC-DC converter. The DC-DC converter boosts the FC stack voltage to the required DC link voltage, which is shown in Figure 2.44. In this configuration, the DC link voltage of 625 V is

DC-DC Converters for Fuel Cell Power Sources   63 generated with the help of MDMPIBC converter with a duty cycle of 0.25. Initially, considering the Ballard FC model 1120ECS, whose output voltage is 45 V at full load and 65 V at no load, such FC stacks can be connected in series to get the appropriate voltage levels to feed a DC-DC converter. Seven FC stacks of rating 45 V are taken to get 325 V as input voltage to the MDMPIBC, which can amplify it to 625 V with a voltage gain of two. The steady state voltage and current waveforms of FC voltage and DC link voltages are depicted in Figure 2.45. The advantage of this configuration Vdc +

PEMFC stack 1

+

PEMFC stack 2

DC link

PEMFC stack 3

+

325 V

PEMFC stack 4

625V

Three phase inverter

3-phase 400 V, 50Hz AC supply

Three phase inverter

3-phase 400 V, 50Hz AC supply

-

PEMFC stack 5

DC-DC converter

PEMFC stack 6

625V

PEMFC stack 7

Figure 2.44  DC series configuration for obtaining DC link voltage for three phase 400 V, 50 Hz inverter. 700 600 Voltage (V)

500

625V

325V

400 300 FC output voltage DC link voltage

200 100 0

0

0.02

0.04

0.06

0.08

0.1

Time (Sec)

Figure 2.45  Steady-state FC voltage and DC link voltages in DC series configuration.

64  DC-DC Converters for Sustainable Applications is that smaller rated FC units may be connected in series and only one DC-DC power converter is necessary. The main disadvantages are faced during the outage of any single FC unit which affects the complete system and thus has lower reliability.

2.11.2 DC-Distributed Configuration In a DC distributed configuration, each FC module is associated with a corresponding DC-DC converter to obtain the DC link voltage for the input of a. three phase inverter, as shown in Figure 2.46. In this configuration, the FC module consists of several stacks in series to get the appropriate voltage level. Each FC module contains seven FC stacks of 45 V rating and the total module voltage comes out to be 325 V and this voltage is given as the input for the MDMPIBC for getting the DC link voltage of 625 V shown in Figure 2.47. The converter operates at duty cycle 0.25 to obtain the DC link voltage of 625 V. The lesser value of duty cycle ensures a smaller ripple in FC current and high efficiency of the DC-DC converter. The reliability which is affected in the series configuration is solved by using this configuration, as during the outage of any FC module during maintenance and replacement, the other FC modules can supply power continuously without disturbing the system function. The additional advantage is that several inverters can be fed with the same DC bus and DC Distribution

+

FC Module

+ 325V

FC Module

325V

FC Module

325V

FC Module

325V

+ + + -

DC-DC Converter

+

DC-DC Converter

+

DC-DC Converter DC-DC Converter

-

+ +

-

625 V

625 V

625 V

625 V

-

+ 625 V

Three phase inverter

FC Module

325V

+ -

DC-DC Converter

+ -

+ 625 V

625 V -

Three phase inverter

3-phase 400 V, 50Hz AC supply 3-phase 400 V, 50Hz AC supply

Figure 2.46  DC distributed configuration for obtaining DC link voltage for multiple three phase inverters.

DC-DC Converters for Fuel Cell Power Sources   65 700 600

625V

Voltage (V)

500 325V

400 300 200

FC output voltage DC link voltage

100 0

0

0.02

0.04

0.06 Time (Sec)

0.08

0.1

Figure 2.47  Steady-state FC voltage and DC link voltages in DC distributed configuration.

share the AC load. The disadvantage is that when the output voltage of the DC-DC converters are not equal, circulating currents are developed which interfere with the operation of the system and there is a higher device count in this configuration compared to the series configuration.

2.12 Conclusions Several DC-DC converter topologies suitable for PEMFC stacks have been discussed and the different DC-DC boost and buck-boost converter topologies have been classified based on the operation. The DC-DC converter performances have been analyzed by considering an input source PEMFC stack of 24 kW, 180 V rating. Furthermore, the advantages of multi-device and multi-phase converter topologies in boost and buck-boost mode are clearly emphasized with respect to the parameters like FC ripple current, device count, LC parameters size, and the voltage gain. It has been shown that the FC current ripple is decreased to a very small value by operating the boost converter with multi-device multi-phase topology named MDMPIBC, also the LC component parameters were smallest for this topology. A DC-DC converter called HGMDMPIBC has been proposed and its steady state performance has been presented with the various waveforms. The proposed converter is capable of boosting up to four times the input voltage with the smaller duty cycle of 0.25. The input voltage fed to the converter is 180 V and 750 V was obtained, which is 2 times higher than the MDMPIBC case. Several buck boost converter topologies for low voltage applications have been analyzed in steady state operation.

66  DC-DC Converters for Sustainable Applications The proposed converter topologies called MDBBC and MDMPIBBC are briefly described with the steady state voltage and current waveforms. Additionally, the converter configurations for interfacing the FC source with 400 V AC grid systems are suggested and their advantages and ­disadvantages during the integration have been discussed.

References 1. N. Femia, M. Fortunato, G. Lisi, G. Petrone, and G. Spagnuolo, “Guidelines for the optimizations of the P&O technique in grid-connected double-stage photovoltaic systems,” in Proc. ISIE, 2007, pp. 2420–2425. 2. Yangbin Zeng;Hong Li;Wencai Wang;Bo Zhang;Trillion Q. Zheng, HighEfficient High-Voltage-Gain Capacitor Clamped DC–DC Converters and Their Construction Method IEEE Transactions on Industrial Electronics vol. 68, no. 5, pp. 3992–4003, May 2021 3. M. H. Todorovic, L. Palma, and P. N. Enjeti, “Design of a wide input range DC–DC converter with a robust power control scheme suitable for fuel cell power conversion,” IEEE Trans. Ind. Electron., vol. 55, no. 3, pp. 1247–1255, Mar. 2008. 4. Jiawei Zhao;Daolian Chen;Jiahui Jiang, “Transformerless High Step-Up DC-DC Converter With Low Voltage Stress for Fuel Cells,” IEEE Access., vol. 9, no. 1, pp. 10228–10238, Dec. 2021. 5. A. Emadi, Y. J. Lee, and K. Rajashekara, “Power electronics and motor drives in electric, hybrid electric, and plug-in hybrid electric vehicles,” IEEE Trans. Ind. Electron., vol. 55, no. 6, pp. 2237–2245, Jun. 2008. 6. M. Ehsani, Y. Gao, and A. Emadi, Modern Electric, Modern Hybrid, and Fuel Cell Vehicles. New York: Taylor & Francis Group, 2005. 7. Jianjun Ma;Miao Zhu;Yunwei Li;Xu Cai, “Dynamic Analysis of Multimode Buck–Boost Converter: An LPV System Model Point of View,” IEEE Transactions on Power Electronics, vol. 36, no. 7, pp. 8539–8551, July. 2021. 8. Zahra Saadatizadeh; Ebrahim Babaei; Frede Blaabjerg; Carlo Cecati, “ThreePort High Step-Up and High Step-Down DC-DC Converter With Zero Input Current Ripple,” IEEE Transactions on Power Electronics, vol. 36, no. 2, pp. 1804–1813, Feb 2021. 9. H. Kim, C. Yoon, and S. Choi, “A three-phase zero-voltage and zero current switching DC–DC converter for fuel cell applications,” IEEE Trans. Power Electron., vol. 25, no. 2, pp. 391–398, Feb. 2010. 10. R.W. Erickson and D. Maksimovic, Fundamentals of Power Electronics, 2nd ed. Norwell, MA, USA: Kluwer, Jan. 2001. 11. O. Hegazy, J. Van Mierlo, and P. Lataire, “Analysis, control and implementation of a high-power interleaved boost converter for fuel cell hybrid electric vehicle,” Int. Rev. Electr. Eng., vol. 6, no. 4, pp. 1739–1747, 2011.

DC-DC Converters for Fuel Cell Power Sources   67 12. Pongsiri Mungporn; Phatiphat Thounthong; Burin Yodwong; Chainarin Ekkaravarodome; Anusak Bilsalam; Serge Pierfederici; Damien Guilbert; Babak Nahid-Mobarakeh; Nicu Bizon; Zahir Shah; Surin Khomfoi; Poom Kumam; Piyabut Burikham, “A Novel High-Gain DC-DC Converter Applied in Fuel Cell Vehicles ,” IEEE Transations on Vehicular Technology, vol. 69, no. 11, pp. 12673–12774, Feb 2020. 13. M. Kabalo, B. Blunier, D. Bouquain, and A. Miraoui, “State-of-the-art of DC–DC converters for fuel cell vehicles,” in Proc. IEEE Vehicle Power and Propulsion Conf., Lille, France, Sep. 1–3, 2010, pp. 1–6. 14. A. R. Prasad, P. D. Ziogas, and S. Manias, “Analysis and design of a three phase offline DC–DC converter with high-frequency isolation,” IEEE Trans. Ind. Appl., vol. 28, no. 4, pp. 824–832, Jul./Aug. 1992. 15. D. de Souza Oliveira, Jr. and I. Barbi, “A three-phase ZVS PWM DC/DC converter with asymmetrical duty cycle for high power applications,” IEEE Trans. Power Electron., vol. 20, no. 2, pp. 370–377, Mar. 2005. 16. D. S. Oliveira, Jr. and I. Barbi, “A three-phase ZVS PWM DC/DC converter with asymmetrical duty cycle associated with a three-phase version of the hybridge rectifier,” IEEE Trans. Power Electron., vol. 20, no. 2, pp. 354–360, Mar. 2005. 17. H. Kim, C. Yoon, and S. Choi, “A three-phase zero-voltage and zero current switching DC–DC converter for fuel cell applications,” IEEE Trans. Power Electron., vol. 25, no. 2, pp. 391–398, Feb. 2010. 18. J. Lai, “A high-performance V6 converter for fuel cell power conditioning system,” in Proc. IEEE VPPC 2005, pp. 624–630. 19. R. L. Andersen and I. Barbi, “A three-phase current-fed push–pull DC–DC converter,” IEEE Trans. Power Electron., vol. 24, no. 2, pp. 358–368, Feb. 2009. 20. S. Lee and S. Choi, “A three-phase current-fed push-pull DC-DC converter with active clamp for fuel cell applications,” in Proc. APEC 2010, pp. 1934–1941. 21. H. Cha, J. Choi, and P. Enjeti, “A three-phase current-fed DC/DC converter with active clamp for low-DC renewable energy sources,” IEEE Trans. Power Electron., vol. 23, no. 6, pp. 2784–2793, Nov. 2008. 22. S. V. G. Oliveira and I. Barbi, “A three-phase step-up DC-DC converter with a three-phase high frequency transformer,” in Proc. IEEE ISIE 2005, pp. 571–576. 23. H. Cha, J. Choi, and B. Han, “A new three-phase interleaved isolated boost converter with active clamp for fuel cells,” in Proc. IEEE PESC 2008, pp. 1271–1276. 24. S.V., J-P F, and Y. L, “Optimization and design of a cascaded DC/DC converter devoted to grid-connected Photovoltaic systems,” IEEE Trans. Power Electron., vol. 27, no. 4, pp. 2018–2027, Apr. 2012

68  DC-DC Converters for Sustainable Applications 25. B.Axelrod, Y.Berkovich, and A. Ioinovici, “Switched-capacitor/switchedinductor structures for getting transformer less hybrid DC-DC PWM converters,” IEEE Trans. Circuits Syst. I, vol. 55, no. 2, pp. 687–696, Mar. 2008. 26. M. Prudente, L. L. P fitscher, G. Emmendoerfer, E. F. Romaneli, and R. Gules, “Voltage multiplier cells applied to non-isolated DC-DC converters,” IEEE Trans. Power Electron., vol. 23, no. 2, pp. 871–887, Mar.2008. 27. F. L. Luo and H. Ye, “Positive output super-lift converters,” IEEE Trans.n Power Electron, vol.18, no. 1, pp. 105–113, Jan. 2003. 28. G. V. T. Bascope and I. Barbi, “Generation of a family of non- isolated DC-DC PWM converters using new three-state switching cells,” in 2000 IEEE 31st Annual PESC, 2000, pp. 858-863 vol.2. 29. G. V. T. Bascopé, R. P. T. Bascopé, D. S. Oliveira, Jr., S. A. Vasconcelos, F. L. M. Antunes, and C. G. C. Branco, “A high step-up DC-DC converter based on three-state switching cell,” in IEEE Proc. Int. Symp. Ind. Electron., 2006, pp. 998–1003. 30. E. A. S. da Silva, T. A. M. Oliveira, F. L. Tofoli, R. P. T. Bascopé, D. S.b. Oliveira Jr, “A novel interleaved boost converter with high voltage gain for UPS applications,” 9th Brazilian Power Electronics Conference, 2007. 31. G A. L. Henn, R. N. A. L. Silva, P P. Praca, L H. S. C. Barreto, and D S. Oa, Jr. “Interleaved-boost converter with high voltage gain,” IEEE Trans. Power Electron., vol. 25, no. 11,pp. 2753–2761, Nov. 2010. 32. C. M. Lai, C. T. Pan, and M. C. Cheng, “High-efficiency modular high step-up interleaved boost converter for DC-micro grid applications,” IEEE Trans. Ind. Applications., vol. 48, no. 1, pp. 161–171, Jan/Feb. 2012. 33. Araujo, S.V, Torrico-Bascope, R.P, Torrico-Bascope, G.V, “Highly efficient high step-up converter for fuel-cell power processing based on three-state commutation cell,” IEEE Trans on Ind Electron, vol.57, no.6, pp.1987–1997, June 2010. 34. B R Lin, and C H Chao “Analysis of an interleaved three-level ZVS converter with series-connected transformers,” IEEE Trans. Power Electron., vol. 28, no. 7, pp. 3088–3099, Jul. 2013. 35. W. Li and X. He, “A family of interleaved DC/DC converters deduced from a basic cell with winding-cross-coupled inductors (WCCIs) for high step-up or step-down conversions,” IEEE Trans. Power Electron., vol. 23, no. 6, pp. 1791–1801, Jun. 2008. 36. W. Li, Y. Zhao, J. Wu, and X. He, “Interleaved high step-up converter with winding-cross-coupled inductors and voltage,” IEEE Trans. Power Electron., vol. 27, no. 1, pp. 133–143, Jan. 2012. 37. F. Forest, E. Labouré, T. A. Meynard, and J. J Huselstein, “Multicell interleaved fly back using intercell transformers,” IEEE Trans. Power Electron., vol. 22, no. 5, pp. 1662–1671, Sep. 2007. 38. Calvente, L. Martinez-Salamero, P. Garces, R. Leyva, and A. Capel, “Dynamic optimization of bidirectional topologies for battery charge/discharge in

DC-DC Converters for Fuel Cell Power Sources   69 satellites,” in Proc. 32nd IEEE Annu. Power Electron. Spec. Conf. (PESC), 2001, vol. 4, pp. 1994–1999. 39. J. M. Blanes, R. Gutierrez, A. Garrigos, J. L. Lizan, and J. M. Cuadrado, “Electric vehicle battery life extension using ultra capacitors and an FPGA controlled interleaved buck-boost converter,” IEEE Trans. Power Electron., vol. 28, no. 12, pp. 5940–5948, Dec. 2013. 40. Y. Cho and J. Lai, “High-efficiency multiphase dc-dc converter for fuel-cellpowered truck auxiliary power unit,” IEEE Trans. Veh. Technol., vol. 62, no. 6, pp. 2421–2429, Jul. 2013. 41. H. Liao, T. Liang, L. Yang, and J. Chen, “Non-inverting buck-boost converter with interleaved technique for fuel-cell system,” IET Power Electron., vol. 5, no. 8, pp. 1379–1388, Sep. 2012. 42. J. E. Larminie and Dicks, Fuel Cell Systems Explained. New York Wiley, 2002. 43. L. Palma and P. N. Enjeti.: ‘A modular fuel cell, modular DC–DC converter concept for high performance and enhanced reliability’, IEEE Trans. Power Electron., 2009, 24(6), pp. 1437–1443. 44. C.Cecati, F. Ciancetta, and P. Siano, “A multilevel inverter for photovoltaic systems with fuzzy logic control,” IEEE Trans. Ind. Electron., vol. 57, no. 12, pp. 4115–4125, Dec. 2010.

3 High Gain DC-DC Converters for Photovoltaic Applications M. Prabhakar* and B. Sri Revathi School of Electrical Engineering (SELECT), Vellore Institute of Technology, Chennai, India

Abstract

In this chapter, the synthesis, design and experimental details of some high gain DC-DC converter topologies are discussed. The chapter begins by exploring the high gain requirements, drawbacks of the classical boost converter and some gain extension methods. The detailed method of combining various gain extension techniques to synthesise some high gain DC-DC converter topologies are described. The elements used in the converters are designed using basic principles that govern the proper operation of all power converters. Experimental results along with the key inferences are elaborated to validate and appreciate the adopted synthesis methodology. Finally, the converters discussed in this chapter are compared among themselves and the concluding remarks are summarised. Keywords:  DC-DC power converter, power conversion, distributed energy sources, high voltage gain, interleaved boost converter, coupled inductor, voltage multiplier cell

3.1 Introduction Recently, due to rapid depletion of fossil fuels and issues concerning environmental pollution, green energy sources like photovoltaic (PV) cells are being used proficiently for electrical energy conversion. The twin challenges of meeting the present-day electrical energy demand while causing the least damages to the environment are both massive *Corresponding author: [email protected] S. Ganesh Kumar, Marco Rivera Abarca and S. K. Patnaik (eds.) Power Converters, Drives and Controls for Sustainable Operations, (71–126) © 2023 Scrivener Publishing LLC

71

72  DC-DC Converters for Sustainable Applications and contradictory. Distributed renewable energy resources (DRER) lend a great helping hand to confront this situation besides being environment friendly [1, 2]. Hence, among energy conscious planners, there is a significant inclination to efficiently convert and utilise electrical energy from never exhausting, secure, and non-polluting energy resources like solar, wind, etc. [3–5]. Globally, solar PV has an installed capacity of 630GW [6]. With particular reference to Indian context, the potential capacity of solar PV is of the order of 750GW, while the installed capacity amounts to only 34.6GW [7]. The huge gap between the potential and installed capacities is one of the motivations to carry out this research work in a flourishing field. Generally, photovoltaic (PV) panels yield low voltage across their output terminals; the typical voltage ratings lie in the range of 12V to 60V DC. On most occasions, their voltage magnitude is insufficient to directly supply the loads which require about 110V or 230V and the majority of the loads operate from AC supply. The customary practice of interfacing the load with the PV panel(s) is through an inverter and transformer combination which provides the necessary voltage gain besides matching the electrical energy form. For systems with larger power ratings that range from a few kilowatts (kWs) to megawatts (MWs), a common practice is to connect many panels in series to meet the load voltage magnitude. The power level is also increased as many panels are put to use. However, during partial-shading and fault condition, the net system voltage (and power level) drops drastically. Parallel connection of PV panels definitely comes to the rescue as far as higher power levels (in the range of few kWs to few MWs) are concerned. Nevertheless, from a system view point, the voltage level remains the same as the chosen panels’ voltage rating. Unfortunately, parallel-­ connected PV configuration fails to meet the high voltage required at the load end. Power electronic converters play a significant role in the PV-load interface. The converters aid in efficiently and easily meeting the electrical energy requirement of the load both in terms of voltage gain and form (AC and DC). Considering the tremendous technical and commercial scope that is available for attaining the required standardization levels, a few high gain DC-DC converters are explored in this chapter.

3.1.1 Role of DC-DC Converter in Renewable Energy System The standard DC voltage is about 380V [8] to suit the input of the full bridge inverter in the single phase 230V AC grid-connected power systems.

High Gain DC-DC Converters for PV Applns.  73 For DC distribution, a DC voltage level of 1.1kV is preferred [9]. Thus, the need for an efficient high gain DC-DC converter to act as an interface between the loads and PV input is reiterated. In order to obtain 230V AC from an inverter, a DC bus voltage of 380V is required. To obtain the DC link voltage, conventionally, series connected PV panels are employed, as shown in Figure 3.1(a). However, in the case of series connected PV arrays, due to module mismatch and partial shading conditions, the generated power output drastically decreases. To overcome these problems, a high-performance utility interactive PV generation system with a Generation Control Circuit (GCC) is applied. However, due to the use of numerous power devices, the cost becomes prohibitive and dissuades the users from employing such systems. The parallel connected PV configuration shown in Figure 3.1(b) is more efficient than the series connected configuration due to the possibility of tracking the maximum power point (MPP) of individual PV panels. Figure 3.1(c) shows the schematic arrangement of a grid connected PV fed system in which the individual parallel connected PV panels operate at maximum power points through an appropriate MPP tracking algorithm. Generally, a Power Conditioning System (PCS) is required to significantly step up the voltage level obtained from the parallel connected PV

Solar PV Panel

(a)

Solar PV Panel

(Parallel Connected) (0-60V)

1ф Grid

1ф Inverter

(Series Connected)

Large Transformer

3ф Inverter

3ф Grid

(b) Solar PV Panel

(Parallel Connected) (0-60V)

MPPT 1

DC-DC Conv. 1

MPPT 2

DC-DC Conv. 2

MPPT 3

3ф Inverter

DC-DC Conv. 3

(c)

Figure 3.1  Conventional grid connected PV systems.

Large Transformer

3ф Grid

74  DC-DC Converters for Sustainable Applications configuration before connecting to the load [10]. Thus, high step-up DC-DC converters are usually used at the front-end, as shown in Figure 3.2(a). In the system shown in Figure 3.2(a), employment of a high step-up DC-DC converter reduces the size of the power transformer and the overall system cost [11]. The high gain DC-DC converters are broadly classified as isolated (with transformer) and non-isolated (without transformer) converters. The isolated DC-DC converters in Figure 3.2(a) employ a transformer whose turns ratio is suitably designed to meet the required gain. In these converters, the main switches suffer from high voltage spikes and consequently, higher switching power loss due to leakage inductance of the transformer. The non-isolated DC-DC converters in Figure 3.2(b) do not require transformers and are capable of achieving high gains using passive components itself.

Solar PV Panel

(Parallel Connected) (0-60V)

High Gain DC-DC Converter

3ф Inverter

3ф Grid

With Transformer (Isolated)

PCS (a) 3ф Inverter

Solar PV Panel

(Parallel Connected) (0-60V)

High Gain DC-DC Converter

DC Distribution Lines (1.1kV, 2.2kV etc.,)

Without Transformer (Non-Isolated)

PCS

(b)

Figure 3.2  Grid tied PV systems with high gain DC-DC converter.

3ф Grid

High Gain DC-DC Converters for PV Applns.  75 Therefore, non-isolated high step-up DC-DC converters are compact, more efficient, and best suited for PV fed applications.

3.1.2 Classical Boost Converter (CBC) Figures 3.3(a) and 3.3(b) show the power circuit diagram of a CBC and a photograph of a prototype converter. The basic operating principle of a CBC is elaborated in [12, 13]. The voltage gain (M) of a CBC is derived from the volt-second balance principle and given by:



M=

Vo 1 = Vin 1 − D

(3.1)

where D is duty ratio of the switch. The prototype version of a 24V/48V, 48W, 50kHz boost converter is fabricated by designing the inductor (L) considering operation under continuous conduction mode (CCM). The experimental results obtained from the prototype converter are presented to appreciate the voltage gain capability. From Figure 3.3(c), the voltage gain obtained from the prototype converter is observed. When the switch operates at a duty ratio of D=0.5, an output voltage of 46.9V is obtained. The negligible difference between the expected value (48V) and the actual value is attributed to the voltage drop across the stray resistance of the inductance and diode. To achieve a higher voltage gain of M=5 and higher values, the switch should be operated at a duty ratio of D=0.8 (for M=5) and D>0.8 (for higher values of M). To comprehend the problems of operating the switch at extreme duty ratios (D>0.8), especially at high switching frequencies (say f=50kHz), the same prototype converter (shown in Figure 3.3(b)) was operated at D=0.82. The experimental results obtained at D=0.82 and depicted in Figure 3.3(d) clearly show that the power converter is not capable of providing the expected output voltage (M>5). While the switch remains turned ON for 82% of the total time period (T), energy is stored in the inductor. Energy transfer from inductor to capacitor occurs through the diode as long as the switch is turned OFF (18% of T). At extreme duty ratios, the available duration for energy transfer (from L to C) is short. Resultantly, only a fraction of energy transfer occurs, leading to reduced output voltage. Moreover, as energy transfer is insufficient, power transferred to the load also reduces.

76  DC-DC Converters for Sustainable Applications D

L IDiode Input

L1 Vin

S1

C

Output

S

D1

+ -

ISwitch

C1

L O A D

+

Vo -

(a)

(b)

(c)

(d)

Figure 3.3  (a) Power circuit diagram of classical boost converter (CBC). (b) Photograph of experimented CBC, (c) Experimental results of CBC at D=0.5, CH1: input voltage, CH2: gate pulse, CH3: voltage across the switch, and CH4: output voltage, (d) Experimental results of CBC at D=0.82, CH1: input voltage, CH2: voltage across the switch, CH3: current through the switch, and CH4: current through the diode.

The switch conducts for a longer duration and results in excessive power loss. Further, only a small duration is available to completely turn ON the fast-recovery power diode. Consequently, both the switch and the diode conduct simultaneously. This results in an incremental voltage drop and power loss. Thus, operating the CBC at extreme duty ratios of D>0.8 is not preferred to obtain high voltage conversion ratios. Besides the problem of extreme duty ratios, the input current ripple in a CBC is quite high, even at safe duty ratio values. In Figure 3.4, channel 2 (CH2) shows the input current waveform captured using digital storage oscilloscope (DSO) when the prototype CBC was tested at D=0.5. Generally, a smooth input current (or ripple-free input current) is preferred for PV

High Gain DC-DC Converters for PV Applns.  77 Tek

Trig’d

M Pos: 0.000s

1

2 3

4 CH1 50.0V CH3 5.00A

CH2 2.00V CH4 50.0A

M 5.00µs 13–Jan–16 16:57

MEASURE CH1 Pos Width 10.38µs CH2 Mean 4.40A

CH2 Pk–Pk 1.04A CH3 Pk–Pk 5.60A CH4 Pk–Pk 84.0V CH1/867mV 50.4308kHz

Figure 3.4  Experimental results obtained from prototype CBC to demonstrate input current ripple, CH1: gate pulse, CH2: input current, CH3: current through the switch, and CH4: voltage across the switch.

application. Therefore, in the subsequent sections, methods to enhance the voltage gain and reduce the input current ripple are discussed.

3.2 Gain Extension Mechanisms Generally, gain extension circuits are included as additional circuits or blocks along with CBC to achieve higher voltage conversion ratios. Various techniques of extending the voltage gain are elaborated in [10, 14–17]. In this chapter, the following gain extension techniques are described: (a)  voltage-lift capacitor (Clift) or voltage-lifting technique (b)  coupled inductor (CI) (c)  voltage multiplier cells (VMCs)

3.2.1 Voltage-Lift Capacitor (Clift) The voltage gain of a CBC is given by (3.1) and its implications are well understood through the discussions presented in 3.1.1. In order to enhance the voltage gain, a capacitor is used as an intermediate energy storage

78  DC-DC Converters for Sustainable Applications L1

D1 S1

Cell 1

To rest of the circuit Voltage-Lift Capacitor (Clift)

L2 Cell 2 + -

Vin S2

Figure 3.5  Schematic circuit diagram of voltage-lift technique using Clift.

element. Figure 3.5 shows the schematic circuit diagram in which a voltage-lift capacitor (Clift) is employed as a gain extension component. The main purpose of Clift is to act as an energy buffer and clamp the voltage available from cell 1 with the output from cell 2. In other words, without Clift, the output from cell 1 has to be connected to the ground terminal and the voltage gain in such a case would then be same as that of CBC. Thus, by judiciously changing the connection alone and not using additional components, the voltage gain is doubled.

3.2.2 Coupled Inductor (CI) In boost derived converters, replacing the simple energy storage inductor with a coupled inductor (CI) results in extended voltage gain and enhanced power handling capability. Compared to transformer-based converters, the primary and secondary windings of CI store and transfer energy in a complimentary manner and a magnetic core is utilised in a better manner [18–20]. However, the power switches are subjected to voltage spikes caused by the dynamic current flowing through the leakage inductance of the coupled inductor. The resonance between leakage inductance and the stray capacitor of the output diode may cause EMI issues and increases the output diode voltage stress further. To suppress the voltage stress on the switch and recycle the leakage inductance energy, passive lossless clamp circuits with resistor capacitor diode (RCD) snubbers are employed [21]. The energy stored in leakage inductance of the CI is recycled to the load when the switch turns OFF. Thereby, the voltage spike impressed on it is limited [22, 23]. By employing soft-switching techniques, power switches with a reduced voltage rating are employed to improve efficiency [24, 25].

High Gain DC-DC Converters for PV Applns.  79 Hence, by using CIs with proper turns ratios, the voltage conversion ratio is extended. The power handling capacity of the converter also increases. However, an alternative energy recovery mechanism must be employed to reduce the switch voltage stress due to leakage inductance. By placing multiple windings on a single magnetic core, the cost, weight, and size of the converter is reduced [26, 27]. However, designing and manufacturing a multi-winding CI in a single magnetic core is slightly complicated.

3.2.3 Voltage Multiplier Cells (VMC) The concept of voltage multiplier cells (VMC) which use two diodes and two capacitors per cell was introduced to significantly enhance the voltage gain of a CBC without using additional magnetic elements [28] by employing VMCs along with CBCs. As the switch is located nearer to the input port, the voltage stress impressed on it is exactly similar to that of a CBC with only a fraction of the output voltage. Moreover, each voltage multiplier diode is also subjected to a minimal voltage stress which is the difference between two adjacent stages and similar to that of a CBC. Thus, gain extension is achieved besides reducing the switch stress [28–31]. Generally, VMCs offer high voltage gain using a compact and modular circuit structure. However, when a voltage gain of more than 10 is required, a greater number of components must be used. Resultantly, the power circuit is subjected to incremental voltage drops and power dissipation across the additional devices employed. Therefore, power handling capability is limited [32]. Thus, when VMCs are employed, a judicious trade-off between the voltage gain (component count) and power handling capacity must be made. The generic structure of a VMC network is depicted in Figure 3.6. The multiplier elements are named as CM1, CM2 and DM1, DM2. By adopting one or more of the above-described gain extension techniques, the proposed high gain DC-DC converters (HGCs) are synthesized, as elaborated in the next section. CM1

Input

DM1

DM2 Output CM2

Reference Node

Figure 3.6  Generic structure of Voltage Multiplier Cell (VMC).

80  DC-DC Converters for Sustainable Applications

3.3 Synthesis of High Gain DC-DC Converters To obtain higher voltage conversion ratios which are of the order of 10 and more, one or more of the gain extension techniques described earlier must be incorporated in the CBC. Further, the current ripple content at the input side must be reduced for easily implementing maximum power point tracking (MPPT) algorithms. An interleaving mechanism is a well-­ established technique to reduce input current ripple. Hence, the HGCs discussed in this chapter will be synthesised from a basic interleaved boost converter (IBC). The synthesis methodology is discussed in detail subsequently.

3.3.1 Concept of Interleaving An interleaved boost converter (IBC) is obtained by operating two or more CBCs in parallel with each other. An interleaving technique has the beneficial features of reduced input current ripple and reduced current stress on the switch with consequent increment in power transfer efficiency while still maintaining good power density [33]. The switches used in different phases of IBC are triggered with equal phase displacement. By splitting the input current into two or more parallel paths, conduction losses occurring on the switches reduce and result in enhanced efficiency compared to a CBC [34, 35]. Figure 3.7 shows the arrangement of a generic N-phase IBC. Understandably, “N” identical boost converters are connected in parallel. Resultantly, the total input current is shared by the identical CBCs. In another perspective, the overall power rating of the generic N-phase IBC will be N-times the power rating of an individual CBC. Thus, IBC helps in handling higher power at reduced current stress on the switches. To understand the concept of input current sharing and input current ripple reduction due to interleaving technique, a 24V/48V, 96W, 50kHz prototype two-phase IBC was constructed and tested. Figures 3.8(a) and 3.8(b) show the power circuit diagram and photograph of the prototype IBC which was fabricated and tested. From Figure 3.8(c), the voltage gain capability of IBC is evident and the same as that of CBC. Further, the total input current is shared equally among the interleaved phases. Consequently, by using the components with ratings similar to a CBC, more power can be transferred from the input to the output port using an IBC. As the interleaved phases are equally displaced from each other (by 180° in the two-phase IBC), the input current is almost

High Gain DC-DC Converters for PV Applns.  81

LN iL

Lo

ad

DN

N

SN CN

L O A D

L3 iL

So

ur ce

S3

L2 iL

D2

Vin

+ -

iL

C2

D1

1

Co nv er

S2

L1

Vo -

te

rN

C3

2

iin

Co nv er

D3

3

+

S1 C1

Co nv er Co nv er

te

r3

te

r2

te

r1

Figure 3.7  Schematic arrangement of generic N-phase IBC.

ripple free as depicted in Figure 3.8(d). Thus, by operating the switches in an IBC with 180°, the current ripple at the input side is cancelled. Further, compared to CBC, the power handling capability is enhanced in an IBC. The voltage gain capability of an IBC is the same as that of a CBC. In the next sub-section, some boost derived converters which possess slightly higher voltage gain capabilities are explored. In the classical two-phase IBC, as the output from each stage is grounded through the filter capacitor, the voltage obtained at the output port is the same as that of the CBC. To enhance the voltage gain of IBC, the voltage output from one stage is “lifted” through a lift-capacitor and applied at the output node of the next stage. Since the outputs from the multiple phases of IBC act in an additive manner, the conversion ratio gets multiplied by the number of interleaving channels ‘m’. This technique is often referred to as a voltage lift technique [36, 37]. To appreciate the voltage-lift concept, the circuit diagram of a two-phase IBC employing voltage-lift technique is shown in Figure 3.9(a) and a lab prototype of the same (shown in Figure 3.9(b)) is constructed and practically tested.

82  DC-DC Converters for Sustainable Applications

iL2

L2

D2

S2 C0 iL1

L1

D1

L O A D

iin

Vin + -

+

Vo -

S1

(a) Trig’d

Tek

(b) M Pos: 0.000s

MEASURE CH1 Mean 23.9V

1

CH2 Pos Width 10.43µs

2 3

CH2 Freq 49.14kHz

Trig’d

Tek

M Pos: 2.000µs

CH1 Mean 2.13A

CH1 Pk-Pk 2.48A CH2 Mean 2.20A

1

2

CH3 Pos Width 10.28µs CH4 Mean 48.0V

4 CH1 50.0V CH3 5.00A

CH2 50.0V CH4 20.0A

M 10.0µs 9–Aug–16 18:00

CH2 / 6.60V 49.1585kHz

MEASURE

CH2 Pk–Pk 2.56A

3 CH1 2.00A CH3 2.00A

CH2 2.00A

M 5.00µs 10–Aug–16 15:24

(c)

CH3 Pk–Pk 480mA CH1 / 2.48A 28.6200kHz

(d)

Figure 3.8  (a) Power circuit diagram of interleaved boost converter, (b) Photograph of experimented interleaved boost converter, (c) Experimental results of interleaved boost converter: CH1: input voltage, CH2: voltage across switch, CH3: voltage across the diode, and CH4: output voltage, (d) Experimental results of interleaved boost converter: CH1: current through interleaved phase 1, CH2: current through interleaved phase 2, CH3: input current.

From basic principles, the voltage gain of a two-phase IBC with voltage lift technique is derived as:



M 2-Ph IBC with Clift =

Vo 2 = Vin 1 − D

(3.2)

As demonstrated through experimental results shown in Figure 3.9(c), the output voltage is twice that of classical IBC. Further, the total input current is equally shared among the two interleaved phases and the input current ripple is negligible as observed from Figure 3.9(d). Therefore, compared to CBC and IBC, for the same duty ratio, the voltage gain is doubled

High Gain DC-DC Converters for PV Applns.  83

iL2

L2

D2 D0

S2

C0

CLift iL1 iin Vin + -

L O A D

+

Vo -

L1 S1

(a) Tek

Trig’d

(b) M Pos: 0.000s

MEASURE CH1 Mean 24.0V

1

CH2 Pos Width 9.670µs CH2 Freq 50.26kHz CH3 Pos Width 9.840µs CH4 Mean 93.2V

2

3 4 CH1 20.0V CH3 20.0V

CH2 20.0V CH4 20.0V

M 10.0µs 23–May–17 16:52

(c)

CH2 / 6.40V 50.2699kHz

Trig’d

Tek

M Pos: 0.000s

MEASURE CH1 Mean 1.89A CH1 Pk-Pk 1.92A

1

CH2 Mean 1.93A

2

CH2 Pk–Pk 2.24A CH3 Pk–Pk 320mA

3 CH1 2.00A CH3 2.00A

CH2 2.00A

M 5.00µs 23–May–17 17:05

(d)

CH1 / 2.56A 50.2391kHz

Figure 3.9  (a) Power circuit diagram of IBC with voltage lift technique, (b) Photograph of experimented IBC with Clift, (c) Experimental results of interleaved boost converter: CH1: input voltage, CH2: voltage across switch S1, CH3: voltage across switch S2 and CH4: output voltage, (d) Experimental results of interleaved boost converter: CH1: current through interleaved phase 1, CH2: current through interleaved phase 2, CH3: input current.

in a two-phase IBC with voltage-lift technique. In this chapter, all the ­converters are synthesised from an interleaved configuration employing voltage-lift technique.

3.3.2 Interleaving Mechanism with Coupled Inductors (CIs) In the IBC structure, discrete inductors are employed as energy storage elements at the source end. By replacing them with coupled inductors (CIs), the primary winding of the CIs serve as conventional boost inductors (energy storage inductor) while the secondary windings are utilised to further extend the voltage gain obtained from the IBC structure. The number of turns in the CI windings are adjusted to meet the steep step-up requirements. If required, the voltage gain is further extended by connecting

84  DC-DC Converters for Sustainable Applications suitable gain extension cells. Thus, an additional degree of freedom to enhance the voltage gain is obtained. Due to the use of CIs with suitable turn ratios, a significant part of gain extension occurs at the secondary side of CIs. Consequently, voltage stress on the switches is significantly reduced. In addition, as CIs efficiently transfer the energy from the primary to their secondary side, the overall power handling capability of the converter is also enhanced. However, leakage inductance of the CIs causes voltage spikes and results in increased voltage stress on the power switches. The incremental voltage stress on the power switches are suppressed by using an energy recycling network and the voltage multiplier cell (VMC) at the secondary side.

3.3.3 VMCs at Secondary Side of CIs As discussed in Section 3.2.3 and depicted in Figure 3.6, VMC comprises of two diodes and two capacitors. Generally, VMCs are used to extend the voltage gain of a CBC [28]. In the HGCs discussed in this chapter, since the secondary winding of the CIs are available for gain extension, a VMC network is embedded across the secondary winding of the CIs. The multiplier capacitors store the energy available across the secondary windings and discharge the stored energy to the load in a cyclic manner. Thus, higher voltage gain is obtained by using a VMC network in conjunction with secondary winding of CIs. Moreover, as the stored energy from the CIs is transferred to the multiplier capacitors, power handling capability is also enhanced. As the VMCs are embedded at the secondary side of the CIs, stored energy in the leakage inductance is also recycled within the diode-­capacitor network formed by the VMC. As a result, the voltage spikes (due to the energy stored in the leakage inductance) that appear across the switches are reduced. All the proposed HGCs described in this chapter employ one or more VMC networks to enhance the overall voltage gain. All the HGCs that are described in this chapter are systematically developed by judiciously adopting the above-mentioned synthesis procedures. The techniques are graphically summarised in Figure 3.10. Further details about the HGCs are presented subsequently.

3.4 Development of High Gain DC-DC Converters (HGCs) All the proposed HGCs are based on 3-phase IBC which employs (a) CIs instead of discrete inductors, (b) a voltage-lift capacitor, and (c) one or

High Gain DC-DC Converters for PV Applns.  85 D1 L3P Z3

Clift

L2P Z2

Dlift

L1P Z1

Vin + –

LS L1P

L1S

L2P

L2S

L3P

(a)

DM2 CM2

L3S

(b)

CM1

DM1

(c)

Figure 3.10  Hybrid strategies used in proposed HGCs. (a) Stage 1 – IBC with voltage lift technique and primary winding of CIs; (b) Stage 1 – primary and secondary winding of the CIs; (c) Stage 2 – VMC network.

more VMCs connected at the secondary side of the CIs. The development of each converter is described subsequently.

3.4.1 HGC with 3 CIs, Clift, and VMC Figure 3.11 shows the power circuit diagram of the proposed HGC-1. In Stage 1, Clift and Dlift act as a voltage lifting network and aid in enhancing the voltage gain of Stage 1. In Stage 2, the secondary windings are connected in series and one VMC network is embedded into them. The  detailed

Stage 1 L3P Z3

Stage 2 D1 DIBC

DM1 Clift

L2P Z2

L2S

L3S

+

CM1

D0

DM2

CM2

Dlift

L1P Vin

L1S

Z1

–

Figure 3.11  Power circuit diagram of proposed HGC-1.

+

C0

L O A V0 D –

86  DC-DC Converters for Sustainable Applications operating principle and the characteristic behaviour of various circuit parameters are elaborated subsequently. For ease of understanding and added clarity, the following valid assumptions are made: (i) All the semiconductor devices used in the converter are ideal (ii) The current flowing through the CIs and load are continuous (continuous conduction mode (CCM)) (iii) All three switches are switched ON for a brief time interval to charge the primary inductors L1P, L2P, and L3P The working of HGC-1 is elaborated through Mode 1 to Mode 6. Figure 3.12 depicts the circuit equivalent during the operation.

L3P Z3 L2P Z2 L1P

D1 DIBC Clift

L3S

L2S

DM1

L1S CM1 CM2 DM2

C0

Dlift

L3P

D0 + V0 LO -

+ Z1 V - in

A D

D1 DIBC

Z3 L2P

Clift

Z2 L1P

Dlift

Z3 L2P Z2 L1P

D1 DIBC Clift

L3S

L2S

DM1

L1S CM1

L3P

D0

CM2 DM2 C0

Dlift

+ V0 LO -

Z2 L1P

D1 DIBC Clift

L3S DM1

A D

Z3 L2P Z2 L1P

(e)

C0

D1 DIBC Clift

L3S

L2S

DM1

L1S CM1

+ V0 LO A D

D0

CM2 DM2 C0

Dlift

+ V0 LO -

+ Z1 V - in

L2S

L1S CM1

L3P

D0

CM2 DM2

+ V0 LO -

+ Z1 V - in

CM2 DM2

A D

(d)

C0

Dlift

D0

+ Z1 V - in

(c) Z3 L2P

DM1

L1S CM1

(b)

+ Z1 V - in

L3P

L2S

-

(a) L3P

L3S

A D

Z3 L2P Z2 L1P

D1 DIBC Clift

L3S DM1

L2S

L1S CM1

D0

CM2 DM2 C0

Dlift

+ V0 LO -

+ Z1 V - in

(f)

Figure 3.12  Equivalent circuit diagram of proposed converter during various operating modes: (a) to (f) represent Mode 1 to Mode 6.

A D

High Gain DC-DC Converters for PV Applns.  87 Mode 1: (t0- t1) At time t=t0, Switch Z1 is turned OFF while Z2 and Z3 remain turned ON. Stored energy in the primary winding, L1P, starts discharging to its secondary winding, L1S. The charging and discharging rates of L1S and L1P, respectively, are the same. Energy transfer from L1P to L1S occurs through the path comprising of Dlift, Clift, and DIBC. The current through Dlift is same as the current through L1P and is expressed as:



iL1 P = iDlift (t ) = n (iDM 1 (t ) + iCM 2 (t ))



(3.3)

In Stage 2, secondary winding of the CIs along with the VMC acts as voltage source and meets the load demand through CM1 and D0. The potential developed across Clift forward biases diode DM1 and helps in charging the multiplier capacitor CM2. When CM2 is completely charged, DM1 turns OFF while DM2 is forward biased. Multiplier capacitor CM2 charges CM1 and supplies the load simultaneously. Current through capacitor CM1 is given by:



iCM 1 (t ) =

1 (nVL1P − vCM 1 ) × t n L py 2



(3.4)

where Lpy = L1P+L2P+L3P and ‘n’ is the turns ratio of CIs. When CM1 is completely charged (by CM2), diode DM2 is reverse biased and DM1 starts to conduct. Thus, the multiplier diodes in the VMC network operate in a complimentary manner and contribute to the energy transfer process in Stage 2. In all the subsequent modes, the VMC network operates in a similar manner as explained above. Mode 1 ends when I L2 P = I L2 P ,max.. Mode 2: (t1- t2) Mode 2 begins at t2 when Z2 is switched OFF. Switches Z1 and Z3 are maintained in their respective OFF and ON states. Turning OFF Z2 initiates the energy transfer from L2P to L2S through Clift and DIBC. As Z3 is conducting, D1 remains reverse biased. Current through switch Z3 is expressed as:



iL3 P = iZ3 (t ) = n (iCM 1 (t ) + iDM 1 (t ))

(3.5)

Diode Dlift continues to remain in forward biased condition till Z1 is ON. L1P continues to discharge its stored energy till its current decreases to a

88  DC-DC Converters for Sustainable Applications minimum value, I L1 P ,min , and marks the end of Mode 2. At time t=t2, Clift is charged to a value (with respect to ground) given by:

VClift (i ) =



1 Vin 1− D

(3.6)

where D represents the duty ratio of each switch. Mode 3: (t2- t3) To charge L1P, Z1 is turned ON while switches Z2 and Z3 are maintained in their OFF and ON states respectively. Diodes Dlift and D1 remain reverse biased. L2P continues to discharge and charges L2S while L3P continues to store energy. The rate of rise and fall of current through the CIs’ windings are same. In Stage 2, the VMC network comprised of DM1, CM1, DM2, and CM2 operate in a manner as detailed in Modes 1 and 2. Current through CM2 is governed by:



iCM 2 (t ) =

V0 − (VC1 + nVL1 P + VCM 2 ) ×t n 2 L py

(3.7)



When the current through L3P reaches its maximum value, I L3 P ,max , at time t=t3, Mode 3 ends. Mode 4: (t3 - t4) The beginning of Mode 4 is marked at time t=t3 when L3P is completely charged. Switch Z3 is turned OFF to enable energy transfer from L3P to L3S followed by the load, while switches Z1 and Z2 are retained in their ON and OFF states respectively. D1 and DIBC are in the ON state and participate in the energy transfer process. The current through Z1 is given by:



iZ1 (t ) = niD0 (t ) =

V0 − (VC1 + nVL1 P + VCM 2 ) ×t n 2 L py

(3.8)



The current through L2P reaches its minimum value, I L2 P ,min,, at time t=t4, when the transfer of energy from L2P to the load through L2S and the VMC network is completed, marking the end of Mode 4. Voltage across Clift and ground at instant t4 is equal to:



VClift (ii ) =

2 Vin 1− D

(3.9)

High Gain DC-DC Converters for PV Applns.  89 VGE(Z1) 0 VGE(Z2)

t

0 VGE(Z3)

t t

0 IL1P

IL1,max

IL1S

IL1,min

0

t

IL

IL2,max

2P

IL2S

IL2,min

0

IL3S

t

IL3,max

IL3P

IL3,min

0

t

VD1

0

t

3V0 3+2nk

VD

lift

0

VZ1 IZ1 0

t

V0 3+2nk

3V0 3+2nk

t

VZ2 IZ2

3V0 3+2nk

0

t

VZ3 IZ3

V0 3+2nk

0 t0

t1

t2

t3

t4

t t5

t6

Figure 3.13  Waveforms depicting some key circuit parameters of HGC-1.

90  DC-DC Converters for Sustainable Applications Mode 5: (t4- t5) At time t=t4, switch Z2 is turned ON to charge L2P towards supply voltage Vin. Switching state of Z1 and Z3 is same as Mode 4. L3P discharges to the load and L1P continues to store energy. D1 remains ON while CM1 and CM2 continue to charge and discharge respectively. Current through D1 is given by

iD1 (t ) = niD0 (t )



(3.10)

At the end of Mode 5, the current through L1P reaches its maximum value at t=t5. Thus, L1P is ready to transfer its stored energy. Mode 6: (t5- t6) As L1P is completely charged, switch Z1 is turned OFF allowing L1P to transfer its stored energy to the load through L1S. Switches Z2 and Z3 are maintained in their respective ON and OFF states. Primary winding L2P charges while L3P discharges to the load through the diodes D1, DIBC, and D0. At time instant t=t6, Clift is completely charged. The potential difference between the top plate of Clift and ground is given by:

VClift (iii ) =



3 Vin 1− D

(3.11)

Current through D0 (and load current I0) is governed by Lpy and is expressed as:



iD0 (t ) =

3Vin + VCM 2 (1 − D ) − V0 (1 − D ) ×t n 2 L py (1 − D )



(3.12)

At the end of Mode 6, one switching cycle is complete. Figure 3.13 depicts the waveforms of key circuit parameters of the HGC-1. The equations for designing the elements of HGC-1 are elaborated subsequently.

3.4.1.1 Design Details of HGC-1 From the basic volt-second balance principle, the voltage gain of the proposed HGC-1 under steady-state conditions can be easily derived. For better understanding, the voltage gain of the HGC-1 can be two derived by intuitively cascading the voltage gain obtained from Stage 1 and Stage 2. The voltage gain is given by:

High Gain DC-DC Converters for PV Applns.  91



M HGC −1 =

V0 3 + 2nk = Vin 1− D

(3.13)

where ‘n’ and ‘k’, respectively, are the turns ratio and coupling co-efficient of the CIs while ‘D’ is the duty ratio of the switches. Voltage Stress on Power Switches and Diodes used in HGC-1 Voltage stress experienced by power switches Z1 and Z2 is equal to the potential across Clift. Therefore, voltage stress impressed across the switches is given by:

VZ1 = VZ2 =

V0 3V0 = 2 1 + nk 3 + 2nk 3

(3.14)

Due to asymmetry caused by Clift, the voltage stress on Z3 is relatively lower and given by:



VZ3 =

V0 3 + 2nk

(3.15)

When Z1 conducts, Dlift is reverse biased while D1 remains reverse biased when Z3 conducts. Therefore, D1 blocks a voltage level obtained across Stage 1 given by (3.14), while voltage stress on Dlift is given by (3.15). From the operating principle, voltage stress on DM1, DM2, and D0 is given by:



V0 2 1 + nk 3



VDM 2 = VD0 = V0 − VCM 2

VDM 1 = VCM 2 −

(3.16)

(3.17)

The voltage stress on the semiconductor devices is inversely proportional to n and k. Therefore, to minimize the voltage stress across the switches and diodes, a careful choice of n is essential. In addition, the CIs are properly designed and manufactured to ensure that the value of k is higher and voltage stress on the power switches is reduced.

92  DC-DC Converters for Sustainable Applications The practical value of k is determined to be 0.88. Figure 3.14 shows the operating point of the proposed converter. Operating the switches at D=0.55 and using CIs with n=3 yields the required voltage gain of about 18.4 when k=0.88. Figures 3.15 (a) and (b) clearly show that the magnitude of voltage stress impressed on the switches is very much reduced to only 36% (Z1, Z2) and 12% (Z3) of the output voltage (V0). Current Stress on Semiconductor Devices of HGC-1 From the input-output power balance principle of an ideal power converter, the average input current (Iin) is derived as:

Iin =



3 + 2nk I0 1− D

(3.18)

Total input current is shared by the three interleaved phases of Stage 1. Current through Z1 is greater than Z2 and Z3 due to the asymmetry in Stage 1 caused by Clift. Current through Z1 is given by (3.19). Switches Z2 and Z3 carry equal currents given by (3.20).

36 34 40 32

Voltage Gain (M)

35

30

30 25 20

28 26

Operating Point is at M=18.4 when D=0.55, n=3 and k=0.88

10 1 0.98 0.96 Coe 0.940.92 ffic 0.9 ien 0.88 t of Cou 0.86 plin 0.84 g (k 0.82 ) 0.8

24

X: 0.55 Y: 0.88 Z: 18.4

15

22 20 0.8 0.7 0.5

0.4

0.6 (D) Ratio Duty

18 16 14

Figure 3.14  Performance plot of the proposed HGC-1 showing the variation in voltage gain (M) versus duty ratio (D) for various values of k when turns ratio is n=3 and the operating point.

0.7 0.6

0.55

0.5 0.5

0.4 0.3

0.45

Voltage Stress on Z1 and Z2is 36.2% of Output Voltage (0.362 V0) when n=3, k=0.88 and D=0.55

3.5

4

0.1

0.16

0.05

X: 3 Y: 0.88 Z: 0.1206

1

0.3

0.1

0.85 0.8

Tu

0.12

0.9

)

tio (n) rns Ra

0.14

Voltage Stress on Z3 is 12% of Output Voltage (0.12 V0) when n=3, k=0.88 and D=0.55

0.95

(k ng

3

2.5

2

0.35

0.18 0.15

pli

1

1.5

0.4

0.2

ou fC

0.2 1 0.98 0.96 Co 0.94 ffi cie 0.92 nt 0.9 of Co 0.88 up lin 0.86 g (k 0.84 ) 0.82 0.8

X: 3 Y: 0.88 Z: 0.3623

0.2

0.25

to ien ffic Co

Voltage stress on Z1 and Z2/Output voltage

0.65

0.6

Voltage across switch Z3/Output voltage

High Gain DC-DC Converters for PV Applns.  93

1

1.5

(a)

3

2.5

2

Turns Ratio

3.5

4

(n)

(b)

Figure 3.15  Performance plots of HGC-1 showing the variation in voltage stress on the switches compared with output voltage for various values of k and n for D=0.55: (a) voltage stress on Z1 and Z2; (b) voltage stress on Z3.





I Z1 =

6 + 4nk 2 I 0 = Iin 3(1 − D ) 3

I Z 2 = I Z3 =

3 + 2nk 1 I 0 = Iin 6(1 − D ) 6

(3.19)

(3.20)

A current flows through Dlift when switch Z1 is in the OFF state. As the switch conducts for 55% of the total time period, diode Dlift conducts for the remaining 45% of the total time period. Similarly, D1 conducts when Z3 is turned OFF. Correlating the conducting intervals of Dlift-Z1 and D1-Z3 combinations, current through Dlift and D1 is derived as:

9 + 6nk 3 I 0 = Iin 5(1 − D ) 5

(3.21)

9 + 6nk 3 I 0 = Iin 20(1 − D ) 20

(3.22)

I Dlift =

I D1 =

Determination of Primary Inductance Value of CIs used in HGC-1 The primary winding of CIs is designed to ensure continuous input current with low ripple content as preferred for PV application. Considering the input current ripple (∆Iin), the appropriate value of inductance offered by primary windings (L1P, L2P and L3P) is obtained using (3.23).

94  DC-DC Converters for Sustainable Applications

L1P = L2 P = L3 P =



Vin D 3 f S Iin



(3.23)

The inductance value of secondary winding of the CIs is determined from:

Lsy = n2Lpy

(3.24)

Generally, tight coupling between the primary and secondary windings of the CIs is preferred. However, due to minor manufacturing imperfections, the value of coupling coefficient is less than 1. For an individual CI, its practical value of coupling coefficient (kpractical) is determined from (3.25).

k practical = 1 −



LS LO

(3.25)

where LO and LS are the inductance values measured across primary winding (of an individual CI) when secondary winding is open and short-circuited, respectively. In the proposed converter, the average value is computed and denoted as ‘k’. Determination of CIs’ Turns Ratio The voltage gain of HGC-1 is derived and given by (3.13). From (3.13), the voltage gain of the converter is dependent on the values of D and n. The turns ratio of the CIs is determined from (3.26).



n=

V0 (1 − D ) 3 M (1 − D ) − 3 − = 2kVin 2k 2k

(3.26)

To meet the high voltage gain requirement, incorporating a greater number of turns in the windings leads to an increase in size of the CIs, whereas lesser value of ‘n’ translates to operating the switches at extreme duty ratios. Due to the practical difficulties encountered while operating the switches at extreme duty ratios, the value of D is fixed at D=0.55. The proposed HGC-1 is expected to operate from a 60V DC input and yield 1.1kV DC at the output port. Based on the voltage gain requirement, the value of ‘n’ is computed as n=3.

High Gain DC-DC Converters for PV Applns.  95 Design of Capacitors Considering the output power (P0), output voltage (V0), switching frequency (fs), and output voltage ripple (ΔV0), the value of output capacitance is obtained from (3.27).



C0 =

P0 D V0 f s V0



(3.27)

The value of CM1, CM2, and Clift depends on energy transferred through them individually and the voltage ripple across each capacitor. Therefore, the rating of each capacitor is obtained from (3.27) by substituting the voltage impressed across each capacitor and the individual ripple voltage. The proposed HGC-1 is fabricated and tested from a 60V DC input. When the switches are operated at a duty ratio of D=0.55 and 100kHz switching frequency, the HGC-1 is designed to deliver 3kW at 1.1kV to the load. The primary inductances are designed considering 15% current ripple at the input side. Some of the experimental results obtained from the prototype converter are discussed subsequently.

3.4.1.2 Experimental Results of Prototype HGC-1 and Discussion The TMS320F28027 Piccolo digital signal processor (DSP) is used for generating the required gate pulses. A signal conditioning unit is employed to interface the gate pulses obtained from DSP and the SCALE driver boards (2AP043512) which are used for isolating and driving the power IGBTs. The close proximity between the driver board and power module aids in reducing EMI issues. The key waveforms are captured using four channel isolated a Tektronix TPS2024B digital storage oscilloscope (DSO) and standard accessories. Figure 3.16 shows the waveforms obtained from the DSO. In the oscilloscope waveform, Channels 1 to 3 (CH1, CH2 and CH3) correspond to gate pulses applied to the power switches used in HGC-1 and the voltage obtained across the output terminals is depicted in CH4. Gate pulses with a moderate duty ratio (D=0.55) and 120° phase delay between the three interleaved legs provide the required output voltage which is in accordance with the value predicted using (3.13). The output voltage is fairly constant with negligible ripple content, proving the design of the output capacitor. Further, the voltage gain capability of HGC-1 is validated. During experimentation, the voltage stress experienced by switches Z1 and Z3, with respect to the output voltage, is depicted through

96  DC-DC Converters for Sustainable Applications Tek

Trig’d

M Pos: 0.000s

MEASURE CH1 Pos Width 5.815µs

1

CH2 Pos Width 5.845µs

2 3

CH3 Pos Width 5.870µs CH3 Freq 100.9kHz CH4 Mean 1.10kV

4 CH1 50.0V CH3 5.00A

CH2 2.00V CH4 50.0A

M 2.50µs 11–Apr–17 18:05

CH1 / 8.00V 100.862kHz

Figure 3.16  Oscilloscope waveforms of HGC-1 showing experimental results obtained while testing HGC-1 under full-load conditions; gate pulses (CH1, CH2, CH3) and output voltage (CH4).

Figures 3.17(a) and (b). The turn ON and turn OFF instants of the power switches are in perfect agreement with their respective gate pulses. Further, as the majority of the gain extension happens at Stage 2, the voltage stress magnitude of Z1 and Z3 is reduced and in close agreement with (3.14) and (3.15). The voltage spikes appearing across the switches are caused by the leakage inductance of the CIs. However, their magnitudes are much reduced and not alarming since most of the stored energy is recycled at Stage 2 through the elements present in the VMC network. To verify the dynamic performance of the HGC-1, input voltage applied to the converter is varied from 48V to 72V (80% to 120% of the rated input voltage) while maintaining a constant load. Figure 3.18(a) illustrates the variations in the output voltage. The variation in output voltage is much less. From theoretical computations, the duty ratio variation is between 0.6386 and 0.458 to maintain a constant output voltage. At input voltage levels higher than the specified value, the efficiency is expected to be slightly higher due to marginally lower input current magnitude which causes reduced losses. To obtain the converter performance when the load varies, the results are obtained through simulation and experimentation. The output voltage variation of the proposed converter for 75%, 100%, and 125% of the

High Gain DC-DC Converters for PV Applns.  97 Trig’d

Tek

M Pos: 0.000s

MEASURE

1

CH1 Pos Width 5.913µs

2

CH1 Freq 100.8kHz CH2 Pk–Pk 392V CH3 Mean 1.10kV

3

CH4 Off Mean

CH1 20.0V CH3 500V

CH2 200V

M 2.50µs 11–Apr–17 18:57

Trig’d

Tek

M Pos: 0.000s

CURSOR Type Amplitude

1

Source CH2

2

V 128V Cursor 1 0.00V

3

CH1 / 4.76V 100.854kHz

Cursor 2 128V

CH1 50.0V CH3 1.00kV

CH2 100V

M 2.50µs 11–Apr–17 19:00

(a)

CH1 / 3.00V 100.842kHz

(b)

Figure 3.17  Experimental waveforms of HGC-1 obtained while testing HGC-1 under full-load conditions: (a) gate pulse applied to Z1 (CH1), voltage stress on Z1 (CH2), and output voltage (CH3); (b) gate pulse provided to Z3 (CH1), voltage stress on Z3 (CH2), and output voltage (CH3).

Tek 60V 1

48V

Scan

DISPLAY

72V 48V

60V Input Voltage Vin

Output Voltage Vo

Scan

Persist Off Format YT

M 10.0s 14–Jun–17 12:39

(a)

CH1 / 0.00V 3.5kW

Li

H

N

Complex SAC control

6&0

0,3

L

MPC

N

Y

Y

30kW

H

H

N

Phase shift PWM

12&0

2,1

L

BC

Y

N

N

30Kw

L

L

Y

Single pulse control

1&1

1,1

L

IBC

Y

Y

Y

30Kw

H

M

Y

Phase shift PWM

S1… Sn&D1… Dn

L1… Ln,1

L

MDC

Y

Y

Y

30kW

H

H

Y

Phase shift PWM

8&0

4,1

L

Y-Yes, N-No, H-High, L-Low, M-Moderate, Li-limited, PWM-Pulse width modulation, SW-switch, D-diode, L-inductor, C-capacitor, SAC-sinusoidal amplitude control.

130  DC-DC Converters for Sustainable Applications achieve control on the loosely coupled coils’ primary and secondary side (that acts as a basic transformer but is separated in the air gap with a distance) in the circuit. By choosing a suitable DC-DC converter, the voltage and power levels can be controlled. The power flow from the primary converter (high-frequency inverter) to the secondary converter (DC-DC converter) to the battery is controlled by DC-DC converters. A general description of ICPT is given in Figure 4.1, which illustrates the DC-DC converter’s role in the circuit. The receiving side control is focused based on the battery or the storage type embedded in the vehicle. The converter’s design has to be low in size and weight ratio and simple in structure. A typical storage system is used based on the load type, i.e., light-duty and heavy-duty vehicles. For heavy-duty vehicles, the storage system must not be bulky and must be low cost as the vehicles takes a huge load and driving range. For low-duty vehicles, the converter design’s efficiency must be high and independent of the load characteristics. The onboard charged circuit has to be designed with cost-effective power electronics parts. The battery storage system and the battery management system (BMS) will increase the design cost for ICPT systems. To achieve a high-efficiency IPT battery charging, the power converters used at the transmitter and receiver sides must be designed with a high conversion ratio. DC-DC converters’ indispensable role is to regulate the voltage, current, and power fed to the battery. The topologies classification is shown in Figure 4.2. The various topologies are discussed in this section. The comparisons based on their components, advantages, and drawbacks with their suitability for battery electric vehicle (BEV) ICPT applications [5–7] are enumerated in Table 4.1.

4.2 Isolated Converters 4.2.1 Bridge Type These converters are provided with isolation between the source and the load. The isolation can be capacitor isolation or transformer isolation which is shown in Figure 4.3. The full-bridge (FB) type is a suitable converter for battery vehicles. The negative half cycle of the voltage waveform will help in the regenerative braking mode of the vehicle. It pertains to bidirectional power flow control [8, 9]. The duty cycle (D) of the converter should be greater than 50%. The converter operates with a zero voltage switching (ZVS) condition, i.e., the voltage in the next switching period is forced to zero at the ton instant of the switch. The pulse width modulation

Converters for EV Energy Storage System  131

Vg1

S1

Vdc Vg2

Vg3 a

S2

S3

irab Vg4

C

S4

RL

b

Figure 4.3  Isolated DC-DC full-bridge converter (FBC).

technique (PWM) is incorporated to maintain the ZVS condition and provide control signals to the switches of the converter.

4.2.2 Z-Source Type The Z-source converter shown in Figure 4.4 is operated with ZVS and Zero current switching (ZCS) condition. It is like the operation of dual bridge converters, and also it pertains to bidirectional power flow control. The architecture is constructed like the two half-bridge converters connected between the source and the load with isolation [10]. The converter and control operation is better with the FBDC, as the diode rectifier circuit is not needed. The diode rectifier deteriorates the performance of the converter with high conduction losses. The design of capacitor C0 is large in volume and size. The power density of the battery can be increased when connected with this converter. It is not suitable for applications >10kW. The PWM shown in Figure 4.5 can be implemented for switching.

4.2.3 Sinusoidal Amplitude High Voltage Bus Converter (SAHVC) The voltage gain is fixed so that high voltage will be supplied to the battery. The high voltage bus converter is used for power levels < 3.5kW. The circuit is complex with multi-windings of the transformer connected for isolation as shown in Figure 4 6. The power transformer is attached to each switch for fixating the high step-up voltage. The control is not as simple as in FBDC and ZVSDC. It involves complex sinusoidal amplitude control (SAC) for achieving a pure sinusoidal waveform. The converter’s operating frequency is in padlock with the resonant frequency of the resonant tank present in the circuit [11]. It is similar to the FBDC and the half-bridge converter is cascaded with multi-windings and isolation.

132  DC-DC Converters for Sustainable Applications

Vg1

C1

S1

Vg3

C3 S3

Vdc Vg2

RL

C0 S4

S2

C4

Vg4

C2

Figure 4.4  Isolated DC-DC Z-source converter (ZSC).

Vg1,Vg2 0°

180° T1,T2

Vg3,Vg4

T3,T4

T1,T2

T3,T4

360°

90°

Vo Vdc

T/2

3T/2

2T

T

Vdc

Figure 4.5  Phase shift PWM for switching. S5 Vdc

S3

S1

C0

Cres S2

S4

Figure 4.6  Sinusoidal amplitude high voltage isolated converter.

S6

RL

Converters for EV Energy Storage System  133 L S1

S3

S1

S3

Vdc S2

S4

C0 S2

Battery

S4

L Storage system

S1

S3

S2

S4

Figure 4.7  Isolated multi-port converter (MPC).

4.2.4 Multiport Converter A multi-winding isolation shown in Figure 4.7 is provided between the source and the load. The number of input ports is increased and interconnected by a multi-winding transformer (linear transformer). The input source is connected by an interleaved technique where the input current will be split to the converter legs with the identical inductors. The parallel shifting is carried out for the converters connected with hybrid energy storage systems (HESS). It pertains to bidirectional power flow control. The number of components increases and the complex switching technique makes it difficult to apply for a single battery charging application.

4.3 Non-Isolated Converter 4.3.1 Conventional Converters These converters are used in medium and high power applications where the voltage level is also in a moderate range. The conventional Cuk and SEPIC converters are not suitable for BEV, but find application in energy storage and hybrid energy storage systems. These converters are current-fed converters [12, 13]. For step-up and step-down applications, the buck-boost

134  DC-DC Converters for Sustainable Applications LB

DB

SB

Battery

CB

Figure 4.8  Non-isolated boost converter (BC).

converter is used and it circulates a high inrush current in the circuit and affects the output current delivered to the battery. Operating at resonance can be employed with a SEPIC converter. The number of energy storage elements is high and requires a large volume of filter capacitor, which increases the size and volume of converters. An uncomplicated and convenient structure that is the most pervasive in BEV applications shown in Figure 4.8 is the boost converter (BC). The only drawback is that the voltage gain is low, which is < 1. The single switch creates an ease in design relative to architecture, cost, and control strategy. The circuit operation and switching control technique depend on the fine-tuning of the duty cycle D.

4.3.2 Interleaved Converter To increase the voltage ratio and for high step-up operation, interleaved converters are introduced for battery applications [14]. The input current source is cleaved into the path of individual inductors connected to the legs of the converter. All inductors are wound on a separate magnetic core. The voltage gain is improved in the ratio of 1: 2 with two inductors, as shown in Figure 4.9. These are also referred to as interleaved N-phase converters where N denotes the number of phase or the number of inductors used for

D1

D2

Dn

L1 L2

C0

Ln S1

S2

Sn

Figure 4.9  Non-isolated interleaved boost converter (IBC).

Battery

Converters for EV Energy Storage System  135 the interleaving technique. The size of energy storage elements is reduced and with an equal number of inductors (L1…. Ln ). The current delivered is equalized, which is an essential feature for the battery charging scenario. 360° The switches S1 and S2 are phase-shifted with the expression . The N control signals to the converter switch are also interleaved, which results in low input current and output voltage ripples.

4.3.3 Multi-Device Interleaved The converter is like the multiport isolated seen in Figure 4.7 but with distinction in the internal stage of the converter topology with interleaving technique and non-isolation as shown in Figure 4.10. The switch count is high and makes it difficult to operate in transient conditions. Control and synchronization of the switches are difficult. It is suitable for energy storage and hybrid storage systems. The switch count is increased, but the resonant and storage elements are reduced. It is less complex compared to MPC.

L1

S1

S3

Cf Battery

L2

S2

S4

L1 S1 Storage system

S3

L2 S2

S4

Figure 4.10  Non-isolated DC-DC multi-device converter (MDC).

136  DC-DC Converters for Sustainable Applications

4.4 Design of DC-DC Converter with Integration of ICPT and Battery Implementation with Digital Control Loop 4.4.1 Design of DC-DC for BEV with the Integration of ICPT From the Table 4.2 enumerated above, the BC is the most suitable for ICPT charging of electric vehicles. Figure 4.1 is replicated as the simulation circuit shown in Figure 4.11, which is done in MATLAB Simulink with a rating of 3.7 V per cell of lithium battery. The model with 6.2Ah is taken as a load. The high-frequency inverter is designed with the ICPT standards of 85kHz. The design includes an H-bridge inverter model, resonant transmitter, and receiver coils with k 2T0, the converter will operate in discontinuous current conduction mode of operation and switches are turned on at zero current and will be naturally turned off due to L-C tank circuit. But in case of T0 < Ts < 2T0, the inductor current becomes continuous and the next half cycle will start before ending of the previous cycle. Again if Ts < T0, the inductor current becomes almost sinusoidal and less harmonic distortion. But in both the continuous current conduction mode, the size of the inductor becomes significantly large. Furthermore, a compromise between sizing of the passive components and the switching frequency can be carried out so that overall compactness of the converter with satisfied performance has be obtained in experimentation. Keywords:  DC-DC converter, harmonic distortion, series load resonant

5.1 Introduction One of the significant considerations in the power electronics field is to maintain energy efficient switch mode power supplies. It has literally motivated next generation engineers to come up with new designs that drastically improve power conversion. In distributed energy generation systems *Corresponding author: [email protected] S. Ganesh Kumar, Marco Rivera Abarca and S. K. Patnaik (eds.) Power Converters, Drives and Controls for Sustainable Operations, (149–158) © 2023 Scrivener Publishing LLC

149

150  DC-DC Converters for Sustainable Applications like solar systems, fuel cell power systems, and vertical axis aero-­generators, DC-DC Series Load Resonant (SLR) converters widely used to achieve better power quality. SLR converters are a subset of DC-DC converters that can be operated with either Zero Voltage Switching (ZVS) turn on, i.e., above the resonant frequency or Zero Current Switching (ZCS) turn off, i.e., below the resonant frequency. Thus, switching losses are minimized and the converter is particularly applicable for high power and high frequency operation. To allow bi-directional energy transfer, an uncontrolled rectifier is used, which controls the output power [1]. Depending on the switching frequency and resonant frequency, current through the inductor may be continuous or discontinuous. The choice of diodes depending upon the improvement of efficiency for these modes of operations has been described in [2] where a comparative study has been analyzed with general purpose P-N diodes, Schottkey diodes, and Super Barrier Rectifier diodes in the circuit. To achieve fast tracking converter output voltage, a fuzzy based control algorithm is very much suitable so that irrespective of sudden load disturbance, the converter can establish a satisfactory output voltage with efficiency [3]. This proposed work investigates an SLR converter containing a tank circuit, as shown in Figure 5.1, with soft switching topology that is used for DC-DC conversion. The SLR converter consists of a half bridge DC-AC inverter followed by an L-C tank circuit and it converts the AC to DC voltage through an uncontrolled rectifier to control output DC energy. A filter capacitance may be introduced at the output of the uncontrolled rectifier to minimize DC voltage ripple. This analysis has been done considering all power electronic devices that are ideal so that there is no switching loss in the device. The series L-C tank circuit is connected in series with the output of the DC-AC half-bridge inverter that will provide a resonant frequency and characteristic impedance.

Vdc 2 Vdc 2

T +

T -

D +

D -

iL

+ Vc-

Lr

Cr

Vin

Figure 5.1  Series load resonant DC-DC converter.

Cf Vo

R

Series Load Resonant Converter  151

5.2 Theoretical Background As the L-C tank circuit is connected at the output of the half bridge inverter, it is obvious that the current through the inductor will be sinusoidal in nature. Depending on the ratio of switching frequency ωS to resonating frequency ω0, there are three possible modes of operation. a)  Discontinuous Conduction Mode (DCM) of SLR Converter → Switching frequency is less than half of resonating frequency: 1 This operation defines ω s < ω 0 , i.e., Ts > 2T0. As the tank circuit con2 tains Lr and Cr, the current and voltage waveforms should be sinusoidal in nature. In a steady state when switch T + is turned on, the inductor current starts increasing from its zero initial value. As the input voltage of the half bridge inverter is Vdc, the capacitor remains operational until the voltage across it reaches equal to the DC supply voltage. Now, applying KVL to the circuit of Mode I shown in Figure 5.2 when the switch T + is conducting,



Vdc di (t ) 1 = v L (t ) + vc (t ) + Vo (t ) = L L + iL (t )dt + Vo (t ) (5.1) 2 dt C

∫

In frequency domain, Equation (5.1) can be expressed as:



Vdc Vo 1 V (0) − = L[sI L (s ) − I L (0)] + I L (s ) + c Cs 2s s s

(5.2)

where IL(0) = initial inductor current and Vc(0) = initial capacitor voltage. The inductor current in the frequency domain can be equated as



s   V − 2Vc (0) − 2Vo   ω 0   (5.3) I L (s ) =  dc   2 2  + I L (0)  2    s +ω0   s + ω 0 2  2ω 0 L

or, in time domain, the inductor current will be



 V − 2Vc (0) − 2Vo  iL (t ) =  dc  sin ω ot + I L (0)cosω 0t  2ω 0 L

(5.4)

152  DC-DC Converters for Sustainable Applications D+

T+

T-

D-

Modes of operation

vc iL 1/2Vdc

Vc0= 2V0

Vdc

+ _ Vo

iL

Cr

Lr 1/2Vdc

T+ operating

+ _ II

+ _ -Vo

iL

D+ operating

Vc0= -2V0

ω0t

-1/2Vdcdc

T0 Ts

II

+ _ III

III

Lr

Cr

Lr

-Vdc

I

+ _ I

ω0t2

ω0t1

ω0t0

Cr

Lr

iL

+_ -Vo

-1/2Vdc

T- operating

+ _

Cr iL

+ _ Vo

IV D- operating

IV

1 Figure 5.2  Discontinuous conduction mode of SLR at ω s < ω 0 . 2

Now, substituting the value of IL(s) from Equation (5.3),

Vc (s ) =

s  Vdc − 2Vc (0) − 2Vo   1  I L (0)  ω 0  Vc (0) − 2 +  2+    s s + ω O  ω 0C  s 2 + ω 0 2  2 s

 as

(5.5) Similarly, voltage across capacitance in the time domain can be written

vc (t ) =

I (0)  Vdc − 2Vc (0) − 2Vo  (1 − cosω 0t ) + L sin ω 0t + Vc (0)   ω 0C 2



(5.6)

Now, at ω0t = 0, iL(t) = IL(0) = 0 and vc(t) = Vc(0) and at ω0t = π, iL(t) = 0

∴  vc(t) = Vdc – Vc(0) – 2Vo

(5.7)

Now, 180° subsequent to 1st half cycle, the switch T + is naturally turned off, the inductor current reverses, and then it will start to free-wheel through the diode D + since another switch T − is not yet turned on, as shown in Mode II of Figure 5.2. After free-wheeling the inductor current, i.e., IL(0) = 0, diode D + is conducting and remains 0 as no switches are on. Applying KVL,

Vc(0) = −Vc(0) and Vo = −Vo



Series Load Resonant Converter  153

 V + 2Vc (0) + 2Vo  This gives This gives iL (t ) =  dc  sin ω ot  2 ω L 0

(5.8)

 V + 2Vc (0) + 2Vo  Similarly, Similarly, vc (t ) = dc (1 − cosω 0t ) − Vc (0) (5.9)   2    At

ω0t = π,

iL(t) = 0 vc(t) = Vdc + Vc(0) + 2Vo

(5.10)

Equating Equation (5.7) and Equation (5.10),

Vdc – Vc(0) – 2Vo = Vdc + Vc(0) + 2Vo Vc(0) = −2Vo

(5.11)

Similar analysis can be applied for the next half cycle when T − is turned ON, which gives the initial voltage across the capacitor as Vc(0) = 2Vo. The corresponding diagram has been depicted in Mode III of Figure 5.2. As in the case of the positive half cycle, T − will be turned off naturally and the inductor current reverses, which will start to free-wheel through the diode D −, as shown in Mode IV of Figure 5.2. b)  Continuous Conduction Mode of Series Load Resonant Converter → Switching frequency is greater than half of resonating frequency, but less than resonating frequency: 1 This operation defines ω 0 < ω s < ω 0 , i.e., T0 < Ts < 2T0. When T + is 2 turned on, the inductor current starts rising with a finite value in a positive direction and it is conducted for less than 180° at a switch voltage of Vdc, as shown in Mode I of Figure 5.3. Then, the inductor current reverses and will start to free-wheel through D + and, consequently, T + turns off naturally. The corresponding circuit diagram is depicted as Mode II of Figure 5.3. When switch T − is turned on, the inductor current will transfer to

154  DC-DC Converters for Sustainable Applications Modes of operation T+

D+ iL

Lr

D-

T-

1/2Vdc

vc

+ _ I

ω0t1

ω0t0

ω0t

ω0t2

T0

Cr

_+

1/2Vdc

Cr iL

+ _

+ _ -Vo

iL

II D+ operating

T+ operating Lr

-1/2Vdc

+_ Vo

iL

Cr

Lr

Lr

_+ -Vo

Cr

II -1/2Vdc + _

iL

+_ Vo

Ts

I

II

III

III T- operating

IV

IV D- operating

1 Figure 5.3  Continuous conduction mode of SLR at ωs < ω0 . 2

T − from D +. Compared with discontinuous conduction mode, D + will conduct for less than 180° because of early switching on T −. This next half cycle is shown as Mode III and Mode IV operations, respectively, of Figure 5.3. In this mode of operation, switching loss arises because of the switching turn on at a finite current and finite voltage. The free-wheeling diode has a good reserve recovery characteristic, as it can avoid large reverse current spikes through the switches. c)  Continuous Conduction Mode of Series Load Resonant Converter → Switching frequency is greater than resonating frequency: This operation defines ωs > ω0 i.e., Ts < T0. In this mode of operation, the switches are forced to turn off at a finite current but are turned on at zero voltage and zero current. Initially, T + starts conducting at zero current and inductor current starts rising, as shown in Mode I of Figure 5.4. After turning off the T +, the positive inductor current transfers from T + to Modes of operation D+

T+

D-

T-

iL

1/2Vdc

vc

+ _ I

ω0t1 ω0t0

ω0t2

-1/2Vdc

+ _

+ _ Vo

iL

iL

+_ -Vo

II

III

IV

Figure 5.4  Continuous conduction mode of SLR at ωs > ω0.

+ _ Vo

iL

II D+ operating Lr

T0

I

Cr

+ _

Cr

III T- operating

Ts

-1/2Vdc

T+ operating Lr

ω0t

Lr

Cr

Lr

1/2Vdc

+ _

Cr iL

+ _ -Vo

IV D- operating

Series Load Resonant Converter  155 D −, which is shown as Mode II of Figure 5.4 and a similar operation will continue for the next half cycle, i.e., T − ensures to flow inductor current in a negative direction and after switching off of T −, the inductor current will switch over to D + accordingly, which is depicted as Mode III and Mode IV, respectively, of Figure 5.4.

5.3 Simulation Results The entire circuit has been simulated in a MATLAB Simulink environment. The theoretical analysis has been verified with simulation with the value of inductance and capacitance of the tank circuit, as depicted in Table 5.1, where corresponding angular resonant frequencies are also mentioned that will satisfy the criterion with respect to a switching frequency of 50 Hz. Figure 5.5 shows the discontinuous inductor current operation with the tank circuit parameter values mentioned in Table 5.1. Corresponding waveforms for the capacitor voltage and DC load voltages are also shown. It is clear from the figure that the initial capacitor voltage is almost equal to -50 V and the steady-state DC load voltage can be approximated as 20 V, i.e., Vc(0) ≈ 2Vo, which validates the theoretical analysis as shown in Figure 5.2. Figure 5.6 shows the continuous current mode of operation with the specified value of the tank circuit parameters mentioned in Table 5.1, which defines the angular resonant frequency of 451.75 rad/sec. Since the switching frequency is 314.16 rad/sec and lies in between 225.88 rad/sec and 451.75 rad/sec, the selection of passive components satisfies criteria 2,

Table 5.1  Parameters related to different resonant frequencies and mode of operation.

Sl. no.

Value of resonant inductance (mH)

Value of resonant capacitance (µF)

Angular resonant frequency (rad/sec)

Mode of operation

1.

10

10

3162

DCM

2.

490

10

451.75

CCM

3.

500

22

301.51

CCM

156  DC-DC Converters for Sustainable Applications Inductor current at L = 10 mH, C = 10uF and Resonant Frequency = 3162 rad/sec

3

Current (Amp)

2 1 0 -1 -2 -3 0.1

0.105

0.11

0.115

0.12

0.125

0.13

0.125

0.13

Capacitor voltage at L = 10 mH, C = 10uF and Resonant Frequency = 3162 rad/s 100

Voltage (Volt)

50 0 -50 -100 0.105

0.1

0.11

Voltage (Volt)

0.115

0.12

DC output voltage at L = 10mH, C = 10uF and Resonant Frequency = 3162 rad/sec

30 20 10 0 -10

0

0.1

0.2

0.3

0.4

0.5 Time (Sec)

0.6

0.7

0.8

0.9

1

1 Figure 5.5  Discontinuous conduction mode of operation at ω s < ω 0 . 2 Inductor current at L = 490 mh, C = 10uF and Resonant Frequency = 451.75 rad/sec

Current (Amp)

0.5

0

-0.5 0.8

0.81

0.82

Voltage (Volt)

0.83

0.84

0.85

0.86

0.87

0.88

0.89

0.9

0.87

0.88

0.89

0.9

0.7

0.8

0.9

1

Capacitor voltage at L= 490 mH, C = 10 uF and Resonant Frequency = 451.75 rad/sec

200 100 0 -100 -200 0.8

0.81

0.82

Voltage (Volt)

0.83

0.84

0.85

0.86

DC output voltage at L = 490 mH, C = 10 uF Resonant Frequency = 451.75 rad/sec

30 20 10 0 -10 0

0.1

0.2

0.3

0.4

0.5 Time (Sec)

0.6

Figure 5.6  Continuous conduction mode of operation at

1 ω0 ω0.

5.4 Conclusion From the experimental simulation work, it is evident that a Series Load Resonant (SLR) DC-DC converter with soft switching topology exhibits sinusoidal current wave shape either in CCM or DCM depending upon the selection of the passive components, on which resonant frequency depends. For a fixed switching frequency, it has been found that if Ts > 2T0, the converter will operate in a discontinuous current conduction mode of operation and switches are turned on at zero current and will be naturally

158  DC-DC Converters for Sustainable Applications turned off due to L-C tank circuit. But, in the case of T0 < Ts < 2T0, the inductor current becomes continuous and the next half cycle will start before ending of the previous cycle, as shown in Figure 5.6. Again, if Ts < T0, the inductor current becomes almost sinusoidal and less harmonic distortion is found, as shown in Figure 5.7. But, in both the continuous current conduction mode, the size of the inductor becomes significantly large. Furthermore, a compromise between sizing of the passive components and the switching frequency can be carried out so that overall compactness of the converter with satisfied performance can be obtained.

References 1. A. Vuchev, N. Bankov, A. Lichev, and Yasen Madankov, “Load Characteristics of a Series Resonant DC-DC Converter with an Symmetrical Controlled Rectifier”, 25th International Scientific Conference Electronics (ET), 2016. 2. T. Taufik, M. McCarthy, S. Watkins, and Makbul Anwari, “Performance Study of Series Loaded Resonant Converter Using Super Barrier Rectifiers”, IEEE Region 10 Conference TENCON, 2009, pp. 1-5. 3. T. S. Sivakumaran, and S. P. Natarajan, “Development of Fuzzy Control of Series-Parallel Loaded Resonant converter-Simulation and Experimental Evaluation”, India International Conference on Power Electronics, 2006, pp. 360-364.

6 Review on Different Methodologies of DC-AC Converter Pushparajesh V.1*, Marulasiddappa H. B.2 and Nandish B. M.2 *

Dept. of Electrical & Electronics, FET, JAIN - A Deemed to be University, Bengaluru, Karnataka, India 2 Dept. of Electrical & Electronics, Jain Institute of Technology, Davanagere, Karnataka, India 1

Abstract

This chapter reviews different methods of converting from DC to AC. This elaborates on single phase multilevel inverters (MLI) which have more advantages over conventional two level inverters. The necessity of pure energy and saving energy has caused a sudden increase in power generation and use of variable speed drives (VSD). Controlling the speed and torque of variable speed drives is very much necessary to increase efficiency of conversion. MLIs are the better choice compared to two level inverters, while conversion from DC to AC for different applications like Flexible AC transmission systems (FACTS), Variable speed drives, renewable energy power generation, and for utility applications. Presently, MLI plays a major role in DC-AC conversion. Various topologies are involved in improving overall efficiency of conversion, they are: diode clamped, flying capacitor, cascaded, and new hybrid MLIs are the important topologies used in various applications. This chapter explains various aspects of these topologies with respect to operation and switching pattern. It gives a detailed structure of new hybrid MLI topology for nine level operations using a stepped wave modulation technique. With the use of the stepped wave modulation strategy used in the MLI network, it is possible to achieve low Total Harmonic Distortion (THD) in the output waveform without using a filtering device. This chapter also elaborates the comparison of new hybrid MLI topology with other topologies that include cascaded, flying capacitor, and diode clamped MLI topologies. Nine levels are produced using two different input voltages in new hybrid MLI. It gives more quality output waveforms by giving more levels than other MLIs. *Corresponding author: [email protected] S. Ganesh Kumar, Marco Rivera Abarca and S. K. Patnaik (eds.) Power Converters, Drives and Controls for Sustainable Operations, (159–174) © 2023 Scrivener Publishing LLC

159

160  DC-DC Converters for Sustainable Applications Keywords:  Two level inverter, MLI, THD

6.1 Introduction Basically, converters which convert DC to AC are called inverters. Voltage source inverters (VSI) and current source inverters (CSI) are the two basic types of inverters. Basically, we should design inverters more efficiently [1]. It is possible to control voltage, frequency, and power of the entire circuit using the inverter circuit. There may be an electronic inverter or a combination of an electronic and mechanical power inverter. Figure 6.1 gives different types of inverters. Voltage source inverters are then classified into two level inverters and MLI. Two level inverters are also called conventional VSI and its representation is given above in Figure 6.2. When the upper switch of the leg in on, VDC appeared across the load and VDC appears across the load if another one is on. Therefore, at any instant of time, one switch has to be turned on and other must be turned off. Conventional VSI output voltage contains 2-levels, hence it is called a two level inverter. Presently, many industries deal with medium and high power applications. AC drives are connected to a medium voltage system in the range of megawatts. Usually, conventional VSI is employed for converting DC to AC, but a conventional two level inverter produces more harmonic distortions and high voltage stresses on switches. Due to this, it is not more

DC-AC Converter

Current source inverter (CSI)

PWM CSI

Load commutated inverter

Figure 6.1  Different types of inverters.

Voltage source inverter (VSI)

Two level inverter

Multilevel inverter

Review of DC-AC Converter  161 + V dc/2

Vdc/2

a

n

V dc

Van

Load -V dc/2

-Vdc/2

-

Figure 6.2  Circuit diagram of two level inverter.

efficient for conversion purposes. Hence, to overcome these drawbacks, MLIs are being used. As the name indicates, they produce a greater number of output voltage levels and, in turn, gives lesser harmonic distortion. MLI generates the output levels in steps which look like a staircase and resemble the sinusoidal waveform. The MLI are very much suited for medium and high voltage applications [2]. There are many advantages over a conventional 2-level inverter [3]. MLI produces a good quality of waveform, lowers the dv/dt on switch, and lowers the harmonic distortion. A cascaded connection between different MLI topologies is explained [4–7]. There are 3 basic multilevel inverters: flying capacitor multilevel inverters, Neutral Point Clamped multilevel inverters, and cascaded H-bridge multilevel inverters [8–12]. The following Figure 6.3 shows representation of an MLI system.

DC supply

Multilevel Inverter

Driver Circuit

Microcontroller

Figure 6.3  Representation of MLI.

Load

162  DC-DC Converters for Sustainable Applications

6.2 Different Multilevel Inverter Topologies There are various multilevel inverters and a few important topologies include: i)  ii)  iii)  iv) 

Diode clamped MLI (DCMLI) Flying capacitor MLI (FCMLI) Cascaded H-bridge (CHMLI) MLI New hybrid MLI (NHMLI)

Nowadays, these topologies are also applied for low voltage applications. There is always a problem in development of inverters with respect to its quality of waveform [13]. These are explained briefly in following sections.

6.2.1 Diode Clamped MLI (DCMLI) It was initially explained in 1981 by Nabae, Takashi [14]. It is called a neutral point converter. This type of MLI is a commonly used topology. In this topology, diodes are mainly used to reduce the voltage stress on each switch. This requires (n-1) inputs for n level inverters. It is possible to increase the quality of the sinusoidal signal by raising the voltage steps because this waveform comes closer to a sinusoidal one. The representation circuit for a 5-level DCMLI is given in Figure 6.4. Vs

L1

Ds1

L2

Ds2

L3

Ds3

C1 D1 V4 D2

D7

D3

D8

D11

L4

Ds4

D4

D9

D12

L5

D s1

D5

D10

L6

D s2

L7

D s3

C2 V3 0

Vdc

C3

1

1

V2 D6 C4

L8 V1

Figure 6.4  5-level diode clamped MLI.

1

D s4 1

A

Review of DC-AC Converter  163 This type of topology consists of three legs and the above diagram gives 5-levels. The five levels are Vdc, 2Vdc, 0, -Vdc, and -2Vdc. This type of topology has an application in medium speed AC drives and static VAR compensation. According to following switching Table 6.1, power semiconductor switches are on and off. High means on state and low means off state. g- number of level Number of main switches required = 2(g-1). Number of diodes required = 2(g-1) Quantity of clamping diodes required = (g-1) *(g-2) Quantity of dc bus capacitors = (g-1) For g = 5 Number of main switches required = 8 Number of diodes required =8 Quantity of clamping diodes required = 12 Quantity of dc bus capacitors =4 Advantages: ¾¾ It gives more efficiency at fundamental frequency ¾¾ Groups of capacitors are made for pre-charging ¾¾ In this topology, all phases use a common DC bus which, in turn, minimizes the use of capacitance ¾¾ It requires minimum cost

Table 6.1  Switching pattern of DCMLI topology. V0

L1

L2

L3

L4

L5

L6

L7

L8

Vdc/2

H

H

H

H

L

L

L

L

Vdc/4

L

H

H

H

H

L

L

L

0

L

L

H

H

H

H

L

L

-Vdc/4

L

L

L

H

H

H

H

L

-Vdc/2

L

L

L

L

H

H

H

H

*H-high (on state), L-low (off state).

164  DC-DC Converters for Sustainable Applications

6.2.2 Flying Capacitor MLI This topology finds more usefulness over DCMLI in industrial applications [15]. It consists of capacitors and is used to transfer the voltage to devices. This topology will not use the clamping diodes. It is represented below in Figure 6.5. A major drawback is a load voltage of only 50% of the source voltage. This can be used in reactive power compensation and also for induction motor controlling purposes. We can calculate the number of DC sources by using: Ndc = n − 1 Then, the number of main switches required is 2(g -1). Number of diodes required = 2(g -1) Clamping diodes required = 2(g -1) DC bus capacitors = (g -1) Quantity r of balancing capacitors = (g -1)(g -2)/2 For g = 5. The requirement of components is given below Switches = 8 Diodes = 8 Clamping diodes = 8 DC bus capacitors = 6

+ Vdc L1 C1 L2 C4 L3 C7

C2

L4

C8

S

V

C9

C5

a

L5 L6

C6 L7 C3 L8 - Vdc

Figure 6.5  Five level flying capacitor MLI.

Review of DC-AC Converter  165 Table 6.2  Switching pattern of FCMLI topology. V0 (volts)

L1

L2

L3

L4

L5

L6

L7

L8

Vdc

H

H

H

H

L

L

L

L

Vdc/2

H

H

H

L

H

H

H

L

0

H

H

L

L

H

H

H

L

-Vdc/2

H

L

L

L

H

H

H

L

-Vdc

H

L

L

L

H

H

H

H

The switching states for a 5-level MLI are given below. According to following switching Table 6.2, power semiconductor switches will on and off. Advantages: ¾¾ Both powers can be controlled ¾¾ Phase redundancies are possible This topology has the disadvantage of high switching losses [3].

6.2.3 Cascaded H-Bridge MLI CHMLI topology is the most commonly used topology for different applications. This topology was first initiated in 1975. This topology has

D1 V

L3

D3

L1 L2 D2

L4

D4 L O A D

D1* V

L5

L6

D2*

L7

L8

Figure 6.6  Circuit diagram of cascaded MLI for 5-levels.

D3*

D4*

166  DC-DC Converters for Sustainable Applications superiority in getting maximum levels compared to other topologies. A diagram of this topology is given in Figure 6.6. In an H-bridge inverter, at any instant of time, one switch has to turn on from each leg and one should turn on from the upper arm or lower arm. No two switches from the same leg should turn on, as it causes a short circuit. In this topology, both DC input sources are equal values. The above Figure 6.6 gives a cascaded MLI diagram. Depending on switching Table 6.3 given below, the respective switches are in a conduction state or closed to give the respective output voltages. For example, to get a 2V DC as an output voltage, switches S1 and S4 in the upper H-bridge have to turn on and switches S1* and S4* in the lower H-bridge are in the on state. The states of switches in on/off for a 5-level MLI are given below in Table 6.3. According to the following switching Table 6.3, switches will be on and off. Number of switches required are   2*(g -1). Total diodes required = 2(g -1) = 2(g -1) Total clamping diodes required Total dc bus capacitors = (g-1)/2 For g = 5 Number of main switches required = 8 Number of diodes required =8 Number of clamping diodes required = 8 Number of dc bus capacitors =2

Table 6.3  Switching states. V0

L1

L2

L3

L4

L5

L6

L7

L8

2Vdc

H

L

L

H

H

L

L

H

Vdc

H

L

L

H

H

H

L

L

0

H

H

L

L

H

H

L

L

-Vdc

L

H

H

L

L

L

H

H

-2Vdc

L

H

H

L

L

H

H

L

Review of DC-AC Converter  167

6.2.4 New Hybrid Cascaded MLI This topology is similar to cascaded H-bridge MLI topology, except the ratio of two sources is 1:3. That is, if the input voltage of the upper bridge circuit is taken as Vdc, then the input voltage of the lower H-bridge is considered as 3Vdc. For example, if V1=Vdc=50V, then V2=3Vdc=150V. There are many control techniques for MLI. For asymmetrical DC input voltage we propose a stepped wave modulation technique. This is explained in detail in the next section.

6.2.4.1 Stepped Wave Modulation Topology (SWMT) This is one of the techniques which is well suited for MLI topology. This technology gives lower harmonic distortion without the use of a filter circuit. This paper [16] explains the asymmetric modulation technique for MLIs. This technique will not sample like sinusoidal signals. It will divide complete waves into small intervals and then control each intervals separately, which leads to control amplitude of the voltage. This technique for MLI reduces harmonic distortion and increases fundamental voltage. The below Figure 6.7 shows an SWMT waveform. From the Figure 6.7, there is an output voltage V0=0 for ωt=0. At ωt=α1, the voltage is V0= V1 and at ωt=α2, the output voltage level is V2 and so on, until the output voltage is Vs at Π/2. The next quarter wave output voltage decreases in steps until it reaches zero at Π-α1. For the other part of the waveform, this entire process is repeated with negative values in output voltage. For the next cycle, this procedure will be repeated. Vout

+VS +V(S-1) +V2

ω

+V1 π-α π

π-α

...

π-α

Figure 6.7  Stepped wave modulation waveform.

π-α(s-1)

π/2

π-α

π-α

a(S-1)

a3

a2

a1

...

168  DC-DC Converters for Sustainable Applications

6.2.4.2 Fourier Series of Proposed Waveform For any number of DC sources, s, n, and an are followed as:

an =



4E [cos(nα 1) + cos(nα 2) +…cos(nan )] nπ

(6.1)

or

an =



4E nπ

∑

s

[cos(nak )

k =1



(6.2)

The Fourier series of the quarter wave symmetry of the output voltage is given by

Vout (ω t ) =



∑

 4E  n=1  nπ ∞

∑

s

[cos(nak )]sin(nω t ) 

k =1

(6.3)

where αk = switching angles ‘S’ represents the number H-bridge cells ‘n’ represents the odd harmonic order ‘E’ represents amplitude of DC voltages Odd harmonic components are given by



h1 =

4E π

hn =

4E nπ

∑

S

[cos(ak )

k =1

(6.4)



and



∑

S

[cos(nak )

k =1



(6.5)

As we know it, half wave symmetry even order harmonics are zero. Therefore, output voltage contains only odd order harmonics and to reduce harmonic distortion, the switching angles need to be adjusted. Total amount of harmonics present in the signal is described as total harmonic distortion, calculated by:

Review of DC-AC Converter  169

THD =



∑n∞=2 H 2n H1

(6.6)

6.2.4.3 Proposed Topology (New Hybrid MLI) New hybrid MLI topology is explained for S=2, i.e., the number of stages is equal to 2. It has a number of output voltage levels equal to 3S. Two DC voltage sources, V1 and V2, are used as input sources. This topology has a maximum number of output step sin comparison to remaining inverters. The circuit diagram for the new hybrid CMLI is shown in Figure 6.8. It is called a new hybrid because DC input voltages are selected in the ratio 1:3. Here, we considered Vdc1=V1 and Vdc2=v2. Inputs are in the ratio 1:3. That is, if V1= Vdc, then V2=3Vdc. According to following switching Table 6.4, power semiconductor switches will be on and off. In the following Table 6.4, ‘0’ represents opening of a switch and ‘1’ represents closing of a switch.

L1

L3

+

-

Vdc1

L4

L2

VO

L5

L7

+

-

Vdc2

L8

L6

Figure 6.8  Circuit diagram of nine level new hybrid MLI.

170  DC-DC Converters for Sustainable Applications Table 6.4  Switching states of switching devices. V0 (volts)

L1

L2

L3

L4

L5

L6

L7

L8

0

L

L

L

L

L

L

L

L

V1

L

H

H

L

L

L

H

H

V2 - V1

H

L

L

H

L

H

H

L

V2,

H

H

L

L

L

H

H

L

V1 + V2

L

H

H

L

L

H

H

L

- V1.

H

L

L

H

L

L

H

H

V1 - V2

L

H

H

L

H

L

L

H

-V2.

H

H

L

L

H

L

L

H

- V1 - V2

H

L

L

H

H

L

L

H

Switching states are obtained from the stepped wave modulation technique. Figure 6.9 shows the output voltage waveform of a 9-level new hybrid MLI topology. 5Vdc 4Vdc 3Vdc 2Vdc Vdc 0 -Vdc -2Vdc -3Vdc -4Vdc -5Vdc 0

0.002

0.004

0.006

0..008

0.01

0.012

Time (seconds)

Figure 6.9  9-level new hybrid MLI topology.

0.014

0.016

0.018

0.02

Review of DC-AC Converter  171 2(g -1). Total main switches required are Total diodes required = 2(g -1) Total clamping diodes required = 2(g -1) Total dc bus capacitors = (g -1)/2 For Q = 5 Number of main switches required = 8 Number of diodes required =8 Number of clamping diodes required = 8 =2 Number of dc bus capacitors Circuit Operation: The frequency of output voltage is 50Hz. Therefore, the time period is T=1/f=1/50=20ms. From Figure 6.9, there are a total 16 levels in complete waveform. Hence, duration of each level is 1.25ms. As we know, the sine wave is symmetrical in nature. Therefore, one fourth of the sine wave has five modes of operation. Mode 1: 0 ≤ t ≤ 1.25 Mode 2: 1.25 ≤ t ≤ 2.5 Mode 3: 2.5 ≤ t ≤ 3.75 Mode 4: 3.75 ≤ t ≤ 5 Mode 5: 5 ≤ t ≤ 6.25 Circuit operation is explained below. Mode 1: 0 ≤ t ≤ 1.25: Here, all switches are in the off condition and therefore, output voltage is zero for this period, i.e., for t=1.25ms. Mode 2: 1.25 ≤ t ≤ 2.5: Here, operation L3, L4, L6, and L8 are in the on condition and other switches are in the open state. Hence, V1 will appear across load terminals. Mode 3: 2.5 ≤ t ≤ 3.75: In this mode of operation, L1, L 2, L7, and L8 are in closed condition and the others are in the open state. Hence, output voltage V2-V1 will appear across the load terminals.

172  DC-DC Converters for Sustainable Applications Mode 4: 3.75 ≤ t ≤ 5: Only L1, L3, L7, and L8 are in the on condition and the other switches are in the off state. Hence, the output voltage V2 will appear across the load terminals. Mode 5: 5 ≤ t ≤ 6.25: This is the last mode of operation. During this mode of operation, only L3, L4, L7, and L8 are in the on condition. Hence, the output voltage V1+V2 will appear across load terminals. This topology along with the stepped wave modulation technique reduces the total harmonic distortion in the output voltage.

6.3 Comparison between Various MLI The following Table 6.5 gives a comparison of all MLI topologies with respect to various parameters. From the table it is shown that a new hybrid MLI topology has a fewer number of components and lower value of total harmonic distortion.

Table 6.5  Comparison table of MLIs. MLI topology

DCMLI

FCMLI

CHMLI

New hybrid MLI

Number of Switches

2*(g-1)

2*(g -1)

2*(g -1)

2*(g -1)

Number of Main Diodes

2*(g -1)

2*(g -1)

2*(g -1)

2*(g -1)

Number of Clamping Diodes

(g -1)*(g -2)

2*(g -1)

2*(g -1)

2*(g -1)

DC Bus Capacitors

(g -1)

(g -1)

(g -1)/2

(g-1)/2

Balancing Capacitors

0

(g -1)*(g -2)/ 2

0

zero

Average Output Voltage

Low

Low

Medium

High

THD

High

High

Medium

Low

g-number of levels.

Review of DC-AC Converter  173

6.4 Conclusion Different methods to convert DC to AC are explained here. This explains multilevel inverters (MLI) which have more advantages over conventional two level inverters. Many methods are present to improve overall efficiency of conversion, a few of them are: diode clamped, flying capacitor, cascaded, and new hybrid MLIs. Circuit diagrams and switching tables for different multilevel inverters are explained. This chapter gives a detailed structure of new hybrid MLI topology for 9-level operations by using a stepped wave modulation technique. With the use of stepped wave modulation strategy used in an MLI network, this can be possible for achieving low THD in the output waveform without using a filtering device.

References 1. Xu Jun, Han Kailing, “The single phase inverter design for photovolataic systems”, 2016 International Symposium on Computer, Consumer, and Control, pp 341-344. 2. L. Tolbert, F.Z. Peng, and T.G. Habetler, “Multilevel Inverters for Electric Vehicle Applications,” IEEE Power Electronics in Transportation, pp. 79-84, Dearborn, MI, October 22-23, 1998. 3. Jos Rodrguez, Jih-Sheng Lai, Fang ZhengPeng “Multilevel Inverters: A Survey of Topologies, Controls, and Applications,” IEEE Transactions On Industrial Electronics, Vol. 49, No. 4, August. 4. L. M. Tolbert and X. Shi, “Multilevel power converters,” in Power Electronics Handbook, ed: Elsevier, 2018, pp. 385-416. 5. A. Khodaparast, E. Azimi, A. Azimi, M. E. Adabi, J. Adabi, and E. Pouresmaeil, “A New Modular Multilevel Inverter Based on Step-Up Switched-Capacitor Modules,” Energies, vol. 12, p. 524, 2019. 6. R. R. Karasani, V. B. Borghate, P. M. Meshram, H. M. Suryawanshi, and S. Sabyasachi, “A three-phase hybrid cascaded modular multilevel inverter for renewable energy environment,” IEEE transactions on power electronics, vol. 32, pp. 1070-1087, 2016. 7. P. Kala and S. Arora, “A comprehensive study of classical and hybrid multilevel inverter topologies for renewable energy applications,” Renewable and Sustainable Energy Reviews, vol. 76, pp. 905-931, 2017. 8. J. Rodriguez, S. Bernet, P. K. Steimer, and I. E. Lizama, “A survey on neutralpoint-clamped inverters,” IEEE Transactions on Industrial Electronics, vol. 57, pp. 2219-2230, 2009.

174  DC-DC Converters for Sustainable Applications 9. V. Dargahi, K. A. Corzine, J. H. Enslin, M. Abarzadeh, A. K. Sadigh, J. Rodriguez, and F. Blaabjerg, “Duo-active-neutral-point-clamped multilevel converter: An exploration of the fundamental topology and experimental verification,” in 2018 IEEE Applied Power Electronics Conference and Exposition (APEC), 2018, pp. 2642-2649. 10. A. K. Sadigh, V. Dargahi, and K. A. Corzine, “New active capacitor voltage balancing method for flying capacitor multicell converter based on ­logic-form-equations,” IEEE Transactions on Industrial Electronics, vol. 64, pp. 3467-3478, 2016. 11. C. D. Fuentes, C. A. Rojas, H. Renaudineau, S. Kouro, M. A. Perez, and T. Meynard, “Experimental validation of a single DC bus cascaded H-bridge multilevel inverter for multistring photovoltaic systems,” IEEE Transactions on Industrial Electronics, vol. 64, pp. 930-934, 2016. 12. B. Wu and M. Narimani, “Cascaded H‐bridge multilevel inverters,” 2017. 13. P. Sachis, I. Echeverria, A. Ursua, O. Alonso, E. Gubia, L. Marroyo,” Electronics Converter for the Analysis of Photovoltaic Arrays and Inverters”, IEEE 2003, pp. 1748-1753. 14. Beser, E.; Camur, S.; Arifoglu, B.; Beser, E.K.Design and application of a novel structure and topology for multi-level inverter,” in Proc. IEEE SPEEDAM, Tenerife, Spain, 2008, pp. 969 – 974. 15. S.G. Lee, D.W. Kang, Y.H. Lee and D.S. Hyun, “The carrier-based PWM method for voltage balance of flying capacitor multilevel inverter”, Power Electronics Specialists Conference. 1 (2001) 126-131. 16. Ding, K., Cheng, K. W. E., & Zou, Y. P. (2012). “Analysis of an asymmetric modulation method for cascaded multilevel inverters”.  IET Power Electronics, 5(1), 74-85.

7 Grid Connected Inverter for Solar Photovoltaic Power Generation K.K. Saravanan* and M. Durairasan Department of Electrical and Electronics Engineering, University College of Engineering, Thirukkuvalai, Tamil Nadu, India

Abstract

The MATLAB Simulink model analysing the seven level, nine level, and fifteen level is ensured. The variation of output voltage and current magnitudes are measured, which depend upon the load changes and the measured Total Harmonic Distortion (THD) that has been compared with the different inverter configurations. The modelling methodology by variation of solar radiation supplies constant input power to the inverter and grid connected system. The Zero Voltage Switching (ZVS) technique is implemented in this described model. The complex system is simplified and it has enhanced the efficiency and improved the electromagnetic interference. The optimal utilisation of a Dynamic Voltage Restorer (DVR) is recovering the voltage sags which reduces 10% and swells up to 190% of its rated value. Household application is adopted in the medium and highpower rating for varying the mismatch load and addressing power quality issues, stability problems, voltage sags, short duration voltage swell, and power interruption, which are eliminated by introducing the DVR system in the modified PV Simulink model. The grid system is connected with a high performance single stage inverter system. The modified circuit does not convert the lowlevel photovoltaic array voltage into high voltage. The converter is applied in solar DC power into high quality AC power and is utilized in the grid. Total harmonic distortion was reduced to the IEEE-519 standard permissible level. Keywords:  Zero Voltage Switching (ZVS), Dynamic Voltage Restorer (DVR), Total Harmonic Distortion (THD), Electromagnetic Interference (EMI)

*Corresponding author: [email protected] S. Ganesh Kumar, Marco Rivera Abarca and S. K. Patnaik (eds.) Power Converters, Drives and Controls for Sustainable Operations, (175–202) © 2023 Scrivener Publishing LLC

175

176  DC-DC Converters for Sustainable Applications

7.1 Single Phase Seven Level Inverter Fed Grid Connected PV System A singlephase grid connected seven level inverter is typically utilized for private or low control utilizations of power ranges that are under 10 KW. Enhancing its output waveform diminishes it agreement with substances and, consequently, additionally the extent of the channel utilized and the level of Electromagnetic Interference (EMI) produced by the inverter’s exchanging operation. Multilevel inverters are promising; they verge on sinusoidal output voltage waveforms, produce output current with better consonant profile, have less pushing of electronic sections inferable from reduced voltages, trade adversities that are lower than those of customary two level inverters, and have a smaller channel size and lower EMI, all of which make them less costly and at the high cut-off from that point of minimization [1].

7.1.1 Seven Level Inverter Topology The modified single stage seven level inverter was produced from the five level inverter. It involves a solitary stage ordinary H-bridge inverter, two bidirectional switches, and a capacitor voltage divider framed by C1, C2, and C3, as shown in Figure 7.1. The modified H-bridge topology is altogether worthwhile over different topologies, i.e., less power switch, power diodes, and less capacitor for inverters of the same number of levels. Photovoltaic (PV) arrays were associated with the inverter through a DC–DC converter.

Dpv

Lb

Lf

Db SW2

SW1

C1 SW5

PV Cpv

SWb

a

Grid Voltage

C2

b SW6

SW3

SW4

Lf

Figure 7.1  Modified single phase seven level grid connected inverter for photovoltaic systems.

Grid Connected Inverter for PV System  177 The utility matrix, as opposed to a load, was utilized by the power produced by the inverter which conveyed the power to the power system [3].

7.1.2 PWM Technique for Seven Level Inverter A novel PWM modulation method is introduced to create the PWM switching signals. Three reference signals (Vref1, Vref2, and Vref3) were contrasted, as well as a carrier signal (Vcarrier). The reference signals having the same frequency and amplitude were in phase with an offset value equivalent to the amplitude of the carrier signal [4]. Table 7.1 shows output voltage and switching conditions of a seven level inverter. Each reference signal is compared with the carrier signal. When Vref1 exceeds the peak amplitude of Vcarrier, Vref2 is compared with Vcarrier until it exceeds the peak amplitude of Vcarrier. At that point, ahead, Vref3 receives responsibility and is contrasted with Vcarrier until it achieves zero. Once Vref3 achieved zero, Vref2 would be looked at until it achieved zero [5].

Table 7.1  Output voltage according to switches’ ON–OFF condition. Switching states SW1

SW2

SW3

SW4

SW5

SW6

Output voltage Vo (volts)

On

Off

Off

On

Off

Off

Edc

Off

Off

Off

On

On

Off

2 E dc 3

Off

Off

Off

On

Off

On

1 E dc 3

Off

Off

On

On

Off

Off

0

Off

On

Off

Off

On

Off

1 − E dc 3

Off

On

Off

Off

Off

On

2 − E dc 3

Off

On

On

Off

Off

Off

Edc

178  DC-DC Converters for Sustainable Applications From that point forward, Vref1 would be contrasted, as well as Vcarrier. For one cycle of the fundamental frequency, the proposed inverter worked through six modes. The six modes are described as follows: Mode 1: 0 10 MVA

IEEE 1547.6

Draft recommended practice

IEEE 1547.7

IEEE 1547.8

Conducting Distributed Impact Studies Guide

Implementation, Strategies, Methods and Procedures

Figure 20.6  IEEE 1547.

this section are (i) to review and evaluate common microgrid standards, (ii) to present Taiwanese research work to establish a microgrid standard for industry applications, and (iii) to suggest realistic tests of essential microgrid standards and how these tests can be performed at a low-voltage AC microgrid in Taiwan in real-time. The international non-governmental, non-profit norm body is the International Electrotechnical Commission. Relevant standards for all relevant electrical and mechanical technology are prepared and issued by the IEC [57]. Technical specifications and guidelines for the development, management, and design of renewable energy and hybrid rural electrification systems are provided by IEC TS 62257 (Figure 20.7).

IEC TS 62257 Recommendation for small Renewable Energy and Hybrid System for Rural Electrification

Microgrid: Recent Trends and Control  623

IEC TS 62257-1

Rural Electrification General Introduction

IEC TS 62257-2

From Requirements to a range of Electrification System

IEC TS 62257-3

Project Development and Management

IEC TS 62257-4

System Design and Selection

IEC TS 62257-5

Protection against Electrical Hazards

IEC TS 62257-6

Acceptance, Operation, Maintenance and

IEC TS 62257-7

Generators

IEC TS 62257-8

Selection of Batteries and its Management Systems

IEC TS 62257-9-1

Micropower Systems

IEC TS 62257-9-2

Microgrids

Figure 20.7  IEC TS 62257.

20.8 Challenges of MG Controls There will be a significant rise in MG installations and integration in LV distribution systems in the future. Therefore, distribution systems will be more significant with a greater number of MGs and differ in characteristics from the current conventional distribution systems for which the design of suitable control strategies must be done for anticipating the difference. The aim of MG controls is optimizing production and consumption of heat, gas, and electricity for improving the overall efficiency. There is a possibility of conflicting requirements and limited communication for controlling a large number of small-scale RES with different characteristics,

624  DC-DC Converters for Sustainable Applications which will be challenging. When it comes to linear and nonlinear loads in the same bus connection under normal and islanding modes of bus connection, electricity distribution will become critical. The challenging part in the decentralized or centralized controller is the required control action with the loss of input parameters. Large mismatches may be caused between generation and loads during transitions from grid-connected mode to an islanded mode, which causes severe frequency and voltage control problems. The connection and disconnection process involves a larger number of micro sources at the same time. Thus, the “plug-and-play” capability creates a serious problem. Operating in the same control frequency for different types of loads is typical and maintaining the stability in such a system during the operation becomes more critical and quite challenging.

20.8.1 Future Trends The development of power converters remains a challenge. The analysis of these is performed but has not been thoroughly studied under MG scenarios. The plug-and-play capability must be studied. Modularization of power converters must be included in the designing process to improve performance. Further research must be done in reactive power-sharing, frequency, and voltage deviations. Multiple MG management control techniques have to be improved for the enhancement of efficiency, reliability, and stability analysis. Studies in energy management strategies must be developed for controlling the flow of energy. MG reduces fossil fuel dependency and increases the overall efficiency, reliability, and power quality of the electric grid. The important aspects of MG are grid integration and energy management schemes for proper operation. An overview of MG control and different energy management schemes has been reviewed for improved and stable operation of the MG and optimizing the use of renewable energy resources. The challenges of MG control and the future trends of the MG are also discussed in this chapter.

Acknowledgement The authors thank AICTE for the financial support through MODROB scheme.

References 1. S. Monesha, S. Ganesh Kumar, M. Rivera. Microgrid Energy Management and Control: Technical Review. 2016 IEEE Conf. on Automatica (ICAACCA). pp. 1-7, 2016.

Microgrid: Recent Trends and Control  625 2. Monesha S, Ganesh Kumar S, Rivera M. Methodologies of Energy Management and Control in Microgrid. IEEE Latin America Transactions, Vol. 17, No. 2, Sept. 2018, p. 2345-2353. 3. Monesha S, Ganesh Kumar S. Microgrid: Structures, Curb Methods, Standards and Challenges. Journal of Electrical Engineering, Vol. 20, No. 1, 2020, p. 67-75. 4. P Basak, S, Chowdhury, S, Halder nee Dey and S.P, Chowdhury. A literature review on integration of distributed energy resources in the perspective of control, protection and stability of microgrid. Renew. Sustain. Energy Rev. vol.16, pp. 5545-5556, 2012. 5. Q. Jiang, M. Xue and G. Geng. Energy Management of Microgrid in GridConnected and Stand-Alone Modes. IEEE Trans. On Power Systems. Vol. 28, no. 3, pp. 3380-3389, Aug 2013. 6. Nikos Hatziargyriou. Microgrids Architectures and Control. IEEE press, Wiley, 2014. 7. H. Jaiyi, J. Chuanwen and XuRong. A review on distributed energy resources and microgrid. Renew. Sustain. Energy Rev. vol. 12, pp. 2472-2483, 2008. 8. Robert H. Lassester. Microgrids and Distributed Generation. Journal of Energy Engineering, American Society of Civil Engineers. Sept 2007. 9. E. Planas, Jon Andreu, J.I. Garate and I. M. de Algeria, Edorta. AC and DC technologies in microgrids: A review. Renew. Sustain. Energy Rev. vol. 43, pp. 726-749, 2015. 10. P. Silva and C. Marques de Sa Medeiros. A Promising Future To DC Power System: A Review. IEEE Latin America Trans. vol. 15, no. 9, pp. 1639-1642, 2017. 11. J. Silva de Souza, Y. Percy Molina, C. Silva de Araujo, W. Pereira de Farias and I. Santos de Araujo. Modified Particle Swarm Optimization Algorithm for Sizing Photovoltaic System. IEEE Latin America Trans. vol. 15, no. 2, pp. 283-289, Feb. 2017. 12. E. Hossain, E. Kabalci, R. Bayindir and R. Perez. Microgrid testbeds around the world. Energy Convers Manage. vol. 86, pp. 132-153, 2014. 13. T.S. Ustun, C. Ozansoy and A. Zayegh. Recent developments in microgrids and example cases around the world-A review. Renew. Sustain. Energy Rev. vol.15, pp. 4030-4041, 2011. 14. Wang, C., Yang, X., Wu, Z., Che, Y., Li Guo, Zhang, S., Liu, Y.: A Highly Integrated and Reconfigurable Microgrid Testbed with Hybrid Distributed Energy Sources. In: IEEE Transactions On Smart Grid, Vol. 7, No. 1, Jan 2016, p. 451-459. 15. J.A. Pecas Lopes, C. L. Moreira and A. G. Madureira. Defining Control Strategies for Microgrids Islanded Operation. IEEE Trans. On Power Systems Vol. 21, no. 2, pp. 916-924, May 2006. 16. M. Mehrasa, E. Pouresmaeil and J. P. S. Catalao. A Multifunction Control Strategy for the Stable operation of DG units in Smart Grids. IEEE Trans. On Smart Grid. vol. 6, no. 2, pp. 598-607, Mar. 2015.

626  DC-DC Converters for Sustainable Applications 17. E. Pouresmaeil, M. Mehrasa, O. Erdinc and J.P.S. Catalao. A Control Algorithm for the stable operation of interfaced converters in microgrid systems. 5th IEEE PES Innovative Smart Grid Technologies Europe. pp. 1-6, Oct 2014. 18. M. Mehrasa, E. Pouresmaeil and MA Shokridehaki. Stability Analysis for Operation of DG Units in Smart Grids. IEEE 5th International Conference on Power Engineering, Energy and Electrical Drives. 2015, pp. 447-452. 19. D. Stimoniaris, D. Tsiamitros and E. Dialynas. Improved energy storage management and PV- Active power control infrastructure and strategies for microgrids. IEEE Trans. On Power Systems. vol. 31, no. 1, pp. 813-820, Jan 2016. 20. R. Zamora and A.K. Srivastava. Controls for microgrids with storage: Review, challenges and research needs. Renew. And Sustain. Energy Reviews. vol 14, 2009-2018, 2010. 21. M.N. Ahmed, M. Hojabri, A.M. Humada, H.B. Daniyal and H.F. Frayyeh. An overview on microgrid control strategies. International J. of Engineering and Advanced Tech.. vol. 4, no. 5, pp. 93-98, June 2015. 22. C. Ahumada, R. Cardenas, D. Saez and J.M. Guerrero. Secondary control strategies for frequency restoration in islanded microgrids with consideration of communication delays. IEEE Trans. On Smart Grid. Vol. 7, no. 3, pp. 1430-1441, May 2016. 23. M. R. Miveh, M. F, Rahmat, A. A. Ghadimi and M. W. Mustafa. Control techniques for three-phase four-leg voltage source inverters in autonomous microgrids: A review. Renew. Sustain. Energy Rev. vol. 54, pp. 1592-1610, Feb 2016. 24. Il-Yop Chung, W. Liu, D.A. Cartes, E. G. Collins and Seung-Il Moon. Control Methods of Inverter-Interfaced distributed generators generators in a microgrid system. IEEE Trans. On Indus. Apps. Vol. 46, no. 3, pp. 1078-1088, May/ June 2010. 25. J. A. M. Roque, R. O. González, J. J. R. Rivas, O. C. Castillo, and R. M. Caporal. Design of a New Controller for an Inverter Operation in Transitional Regime Within a Microgrid. IEEE Latin America Trans. Vol. 14, No. 12, 4724-4732, Dec 2016. 26. L. Meng, E.R. Sanseverino, A. Luna, T. Dragicevic, Juan C. Vasquez and Josep M. Guerrero. Microgrid supervisory controllers and energy management systems: A literature review. Renew. Sustain. Energy Rev. vol. 60, pp. 1263-1273, July 2016. 27. L. Olatomiwa, S. Mekhilef, M.S. Ismail and M. Moghavvemi. Energy management strategies in hybrid renewable energy systems: A review. Renew. Sustain. Energy Rev. vol. 62, pp. 821-835 2016. 28. Il-Yop Chung, W. Liu, D.A. Cartes, E. G. Collins and Seung-Il Moon. Control Methods of Inverter-Interfaced distributed generators in a microgrid system. IEEE Trans. On Indus. Apps. Vol. 46, no. 3, pp. 1078-1088, May/June 2010.

Microgrid: Recent Trends and Control  627 29. Yunwei LI. Overview of control, integration and energy management of microgrids. J. Mod. Power Syst. Clean Energy. vol. 2, no.3, pp. 212-222, 2014. 30. J.P. Torreglosa, P.Gracia-Trivino and L.M. Fernandez-Ramirez. Control strategies for DC networks: A systematic literature review. Renew. Sustain. Energy Reviews. vol. 58, pp. 319-330, 2016. 31. Palizban O, Kauhaniemi K, Guerrero JM. Microgrids in active network management – Part I: Hierarchical control, energy storage, virtual power plants, and market participation. Renew. Sustain. Energy Reviews. vol. 36, 428-439, 2014. 32. E Unamuno and JA Barrena. Hybrid ac/dc microgrids-Part II: Review and classification of control strategies. Renew. Sustain. Energy Rev. vol. 53, pp. 1123-1134, 2015. 33. M. Marzband, A. Sumper, JL. Dominguez-Garcia and R. Gumara-Ferret. Experimental validation of a real time energy management system for microgrids in islanded mode using a local day-ahead electricity market and MINLP. Energy Convers Manage. vol. 76, pp. 314-322, 2013. 34. M.S. Mahumoud, S. Azher Hussain and M.A. Abido, . Modeling and control of microgrid. Journal of the Franklin Institute. vol. 351, pp. 2822-2859, 2014 35. J.M. Guerrero, M. Chandorkar, Tzung-Lin Lee and P.C. Loh. Advanced control architectures for intelligent microgrids-part I: Decentralized and Hierarchical control. IEEE Trans. On Indus. Electrons. Vol. 60, no. 4, pp. 1254-1262, Apr 2013. 36. Koohi-Kamali S, Rahim NA and Mokhlis H. Smart power management algorithm in microgrid consisting of photovoltaic, diesel, and battery storage plants considering variations in sunlight, temperature, and load. Energy Convers Manage. vol. 84, pp. 562-582, 2014. 37. J.M. Guerrero, P.C. Loh, Tzung-Lin Lee and M. Chandorkar. Advanced control architectures for intelligent microgrids-part II: power quality, energy storage, and AC/DC microgrids. IEEE Trans on Indus. Electronics. vol. 60, no. 4, pp. 1263-1270, Apr 2013. 38. A. Khorsandi, M. Ashourloo, H. Mokhtari and R.Iravani, . Automatic droop control for a low voltage dc microgrid. IEEE Trans. IET Generation, Trans., Distribution. Vol. 10, no. 1, pp. 41-47, Jan 2016. 39. S. Daspupta, S.N. Mohan, S.K. Sahoo and S.K. Panda, . Lyapunov FunctionBased current controller to control active and reactive power flow from a renewable energy source to a generalized three-phase microgrid system. IEEE Trans on Indus. Electronics. vol. 60, no. 2, pp. 799-813, Feb 2013. 40. L. Valverde, C. Bordons and F.Rosa. Power management using model predictive control In a hydrogen-based microgrid. IECON 2012-38th Annual Conference on IEEE Industrial Electronics Society. vol. 22, no. 5, pp. 56695676, 2012. 41. A.Mehrizi-Sani and R. Iravani. Potential-function based control of a microgrid in islanded and grid-connected modes. IEEE Trans. On Power Systems. vol. 25, no. 4, pp. 1883-1891, Nov 2010.

628  DC-DC Converters for Sustainable Applications 42. M. Mehrasa, E. Pouresmaeil, H. Mehrjerdi, Bo Nørregaard Jørgensen, João P.S. Catalão. Control technique for enhancing the stable operation of distributed generation units within a microgrid. Energy Convers. Manage. vol. 97, pp. 362-373, 2015. 43. M. Mehrasa, M Ebrahim Adabi, Edris Pouresmaeil, Jafar Adabi. Passivitybased control technique for integration of DG sources into the powergrid. Electric. Power and Energy Syst. vol. 68, pp. 281-290, 2014. 44. Ganesh Kumar, S., Hosimin Thilagar, S., Rivera, M.: Cost Effective Control of a Partially Flat Boost Converter fed DC motor. IEEE International Conference on Automatica (ICA-ACCA), Oct 2016, p. 19-21. 45. Ganesh Kumar, S., Hosimin Thilagar, S.: Load Torque Estimation and Passivity Based Control of Buck Converter. The Mediterranean Journal of Measurement and Control, Vol. 9, No. 2, 2013, p. 51- 57. 46. Ganesh Kumar, S., Hosimin Thilagar, S.: Sensorless Load Torque Estimation and Passivity Based Control of Buck Converter Fed DC Motor. The Scientific World Journal, No. 1, 2015, p. 0-15. 47. Ganesh Kumar, S., Hosimin Thilagar, S.: Soft Sensing of Speed in Load Torque Estimation For Boost Converter fed DC motor. International level conference on IECON 2013 - The 39th Annual Conference of the IEEE Industrial Electronics Society, Austria, Nov 2013. 48. Arathy, R., Ganesh Kumar, S., Rivera, M.: 2016, Investigation on Passivity Based Control for Electrical Applications. In: Proceedings of the International level conference on IEEE CHILECON 2017, CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies, Chile, 18-20 Oct 2017. 49. J. A. Dias, P. J. A. Serni, A. M. Bueno and E. P. Godoy. Study of Communication Between Distributed Generation Devices in an Smart Grid Environment. IEEE Latin America Trans. Vol. 16, No. 3, 777-784, March 2018. 50. Y. Lopes, D. C. M. Saade, C. V. N. Albuquerque, N. C. Fernandes and M. Z. Fortes. Quality of Service for Wireless Network Implementation in Advanced Metering Infrastructure. IEEE Latin America Trans. Vol. 15, No. 10, 18751880, Oct 2017. 51. C. Marcelino, M. Baumann, P. Almeida and E. Wanner e M. Weil. A New Model for Optimization of Hybrid Microgrids Using an Evolutive Approach, IEEE Latin America Trans. Vol. 16, No. 3, 799-805, March 2018. 52. Sechilariu, M., Locment, F.: Urban DC Microgrid Intelligent Control and Power Flow Optmization, Elsevier, 2016. 53. Nallusamy, S., Velayutham, D., Govindarajan, U., Parvathyshankar, D.: Power quality improvement in a low-voltage DC ceiling grid powered system. IET Power Electronics, Vol. 8, No. 10, Oct 2015, p. 1902-1911. 54. E.K. Lee, W. Shi 2, R. Gadh and W. Kim. Design and Implementation of a Microgrid Energy Management System., Sustainability. Vol. 8, 1143, 1-19, 2016.

Microgrid: Recent Trends and Control  629 55. David Wenzhong Gao, Energy Storage for Sustainable Microgrid, Elsevier, 2015. 56. Han, H., Hou, X., Yang, J., Jifa Wu, Mei Su, Josep M. Guerrero: Review of Power Sharing Control Strategies for Islanding Operation of AC Microgrids. IEEE Transactions on Smart Grid, Vol. 7, No. 1, Jan 2016, p. 200-214. 57. Li Fusheng, Li Ruisheng, Fengquan, Z.: Microgrid Technology and Engineering Application, Elsevier, 2016.

21 Control Techniques in Sustainable Applications R. Dhanasekar1*, L. Vijayaraja1 and S. Ganesh Kumar2 DEEE, Sri Sairam Institute of Technology, Chennai, Tamil Nadu, India DEEE, College of Engineering Guindy, Anna Univeristy, Chennai, Tamil Nadu, India 1

2

Abstract

In recent years, renewable energy sources (RES) have played a vital role to meet the power demand with the quality of power. In RES, the power electronic converters are effective for changing characteristics of voltage and current. The introduction of control system techniques in the engineering field has made development in various renewable energy applications. The control techniques has the ability to give robust performance and is insensitive to parameter variations. Recently, sliding mode controls have become attractive due their robust performance. In variable structure systems, a sliding mode control is an efficient tool for complex non-linear multi-variable plants. In recent years, Passivity-based Control (PBC) has been adopted in RES due to its robustness against parameter uncertainties. The system which comprises PBC achieves the desired control parameters with no peak overshoots and oscillations. Model Predictive Control (MPC) has been a likely control technique for power electronic converters because of its quick reaction and high control data transfer capacity. This chapter deals with the concepts of Sliding Mode Control, Passivity-based Control and Model Predictive Control in Sustainable Applications. Keywords:  Renewable energy sources, sliding mode control, passivity-based control, model predictive control

*Corresponding author: [email protected] S. Ganesh Kumar, Marco Rivera Abarca and S. K. Patnaik (eds.) Power Converters, Drives and Controls for Sustainable Operations, (631–658) © 2023 Scrivener Publishing LLC

631

632  DC-DC Converters for Sustainable Applications

21.1 Introduction Nowadays, control methodologies play a major role in renewable energy system integration with the grid. A non-linear Sliding Mode Controller (SMC) is implemented in various power conversion stages in grid integration. In SMC, relay function, signum function, Hysteresis function, and equivalent control are presented to regulate the flow of active and reactive power in the grid, load, and converters. During improper loaded conditions in the non-linear loads, the Sliding Mode Controllers diminish the total harmonic distortion and maintain the unity power factor [1]. The dead time effects introduce voltage distortion in the output voltage of the inverter. The dead time effects in the inverter output eliminated the super twisting second order Sliding Mode Technique in the three phase grid integrated renewable energy systems. The proposed algorithm reduces the chattering and fast response in the frequency variations on the grid side. The super twisting second order sliding mode algorithm is compared with a PI controller to validate the performance [2]. The maximum power is extracted by the Maximum Power Point Tracking (MPPT) technique in a Photovoltaic (PV) system. To extract the maximum power, a non-­ linear back stepping sliding mode (BSSM) MPPT algorithm is proposed. The proposed BSSM MPPT algorithm gives robust output, low steady state error, fast speed tracking, eliminates the peak overshoot, and provides stable response under load and environmental variations [3]. In renewable energy systems, wind energy plays a vital role in industrial development. The voltage fluctuations occur due to the uncertain parameters and disturbance on the load side. So, a novel control methodology called the adaptive sliding mode controller and sliding mode observer is proposed in the converter located at the load side to enhance the stability of the overall system. The reactive power is compensated by the adaptive sliding mode controller in the static compensator interconnected in a wind-diesel hybrid system [4]. The active power control and maximum power extraction and two sliding mode controllers is proposed for the variable speed wind turbine integrated with a Double-fed Induction generator. The Proportional Integral SMC and Supertwisting Second Order SMC are implemented in rotor side converters to eliminate the chattering effect and enhance the tracking [5]. The power is controlled in doubly fed induction generators by an adaptive sliding mode neuro-fuzzy controller. The proposed sliding mode control algorithm is used to train the online parameters for the type-2 fuzzy membership functions. The time derivative of active and reactive power is

Control Techniques in Sustainable Applications  633 regulated by type-2 fuzzy membership functions. The simulation results of the proposed controller are compared with the classical proportional integral controller [6]. Interconnection and Damping Assignment-Passivity Based Controls (IDA-PBC) are proposed for the enhancement of energy management and damping improvement. The DC-DC converters are the gateway between the renewable energy system and DC microgrid. The proposed controller is implemented for the inverter in the grid side and DC-DC converters which are connected with fuel cells and battery backup. Depending on the battery state and the availability of the grid parameters, the IDA-PBC is tuned. The integral term is added with IDA-PBC to eliminate the steady state error [7]. A capacitive coupled grid connected inverter (CGCI) is the gateway between the distribution grid and renewable energy sources. A non-liner passivity based controller is designed to achieve asymptotic stability for tracking the current in GGCI with fast response [8]. A passivity controller based on a perturbation observer is designed for a voltage source converter with multi-terminal direct current systems. The observer is designed to estimate the no linear effects, faults in the grid, and variation of output power. The estimated parameters are fully compensated by the passivity based controller. The output DC voltage and reactive power in the rectifier side and the output AC voltage and active power in the inverter side is regulated by the proposed controller [9]. In PV systems, the DC-DC converters are used as a gateway between the solar panels and the load. A passivity based controller is implemented to regulate the load variations [10]. A non-linear passivity based controller is proposed to extract the maximum power from the windmill to regulate the DC link voltage and power factor in the grid [11]. In a hydro-turbine governing system, an Adaptive Model Predictive Controller is proposed as a load/frequency controller. The proposed controller is validated in both load control mode and frequency control mode. The controller is implemented using Hildreth’s algorithm as a quadratic programming solver [12]. In recent years, integrated renewable energy sources with the power grid have emerged. Model Predictive Controller (MPC) is proposed to attain optimal power in predicting the generation of renewable energy. MPC is designed by the combination of genetic algorithm with a state space model [13]. In large multi-connected systems, the Model Predictive Controller is implemented for load frequency control. The desired output is achieved and the interconnected system comprises of six power plants with renewable energy sources under load variations [14]. Due to the presence of inverters in storage systems, frequency regulation is the major challenge. The future behavior of the system is predicted

634  DC-DC Converters for Sustainable Applications by the new virtual inertia emulator-based model predictive control. The control technique is compared with a proportional and proportional integral controller [15]. Section 21.2 describes the sliding mode control techniques in sustainable applications. Section 21.3 describes the Passivity-based Control (PBC) in sustainable applications to improve the performance of voltage stability and Section 21.4 describes the Model Predictive Control (MPC) in sustainable applications.

21.2 Sliding Mode Control Techniques in Sustainable Applications Nowadays, renewable energy systems play a vital role in the generation of electric power. A multi-input single output DC to DC converter is used to utilize the energy resources with different voltage and power levels to achieve the desired output voltages. The DC to DC converters are non-­linear in nature because of their characteristics. Due to the switching sequence of converter, the control structure is a challenging one. To improve the control point of view, many researchers used various non-­ linear controllers to achieve the voltage levels in the output. Recently, the Sliding Mode Controller (SMC) is attractive due to its robustness and uncertainty to parameter variations. To attain the desired output, the SMC forces the trajectory in the exact location by using a high speed switching technique. A double input single output DC to DC converter is presented in [16] with sliding mode control. Figure 21.1 shows the renewable energy system in the hybrid using the sliding mode control technique. Figure 21.2 shows the dual input single output DC-DC converter. The voltages V1 and V2 are sources from wind and solar PV array. The converter consists of two switches, Q1 and Q2, and the DC link capacitor. The two sources V1 and V2 are interconnected with capacitor C. The sliding surface is given in Equation (21.1).



S=

where λ is a positive constant.

d  +λ  dt 

n−1

e(t )



(21.1)

Control Techniques in Sustainable Applications  635

PMS G

Diode Bridge Rectifier

Double Input Single Output DC-DC converter

Load

Wind Turbine PV array

Battery

Sliding Mode Controller

Figure 21.1  Renewable energy system in hybrid using sliding mode control technique.

L1

V1

D1

Q1

+ –

C L2

V2

Q2 + –

D2

Figure 21.2  Dual input single output converter.

R

636  DC-DC Converters for Sustainable Applications The error is given in Equation (21.2).

e(t) = vref – vactual

(21.2)

The control input consists of equivalent control Ueq and switching control Usw and is given in Equation (21.3).

U = Ueq + Usw

(21.3)

The equivalent control regulates the nature of the system and the switching control reduces the system uncertainties. Figure 21.3 shows SMC with a Dual Input single output converter. The controller contains two loops. The inner loop contains current control and outer loop contains voltage control. Table 21.1 shows the effectiveness of SMC in A Multi Input DC-DC Converter [16].

Input Voltage

DC-DC Converter

Control Input U

Inductor current

Actual Voltage

+

Current Controller

PI CONTROLLER

Voltage Controller

Reference Voltage

Figure 21.3  SMC with dual input single output converter.

Table 21.1  Performance of SMC. Parameters

SMC performance

Settling Time

0.135 sec

Chattering

0.2V

Transients

No overshoots

Control Techniques in Sustainable Applications  637 In [17], for a hybrid standalone system, an advanced power management system is presented. The hybrid system consists of a PV panel, fuel cell, and battery system. The output from the PV panel, fuel cell, and battery system is connected commonly in a DC bus through DC-DC converters. The PV panel is connected to a DC bus by a boost converter which adopted the Maximum Power Point Technique. The second order SMC is adopted for MPPT control. The battery system is connected to DC bus through a Bidirectional Buck-Boost Converter. Figure 21.4 shows the structure of hybrid system. Figure 21.5 shows the Second Order SMC for a Boost Converter. The actual voltage Vac is compared with the reference voltage Vref generated DC Bus

PV Panel

Boost Converter MPPT

Battery

DC-AC Converter

Buck Boost Converter

Load

SMC Super Capacitor

Figure 21.4  Structure of hybrid system.

Boost Converter

Vpv

IL

MPPT Algorithm

Second Order SMC Vref

Figure 21.5  Second order SMC for boost converter.

Vac

638  DC-DC Converters for Sustainable Applications from the MPPT algorithm. VPV and IL are the panel output voltage and inductor current on the boost converter. Consider X1 = IL and X2 = Vout. The sliding surface is given as in Equation (21.4).

∫

S = e + K edt





(21.4)

where error e = (x2 – x2) The second order SMC is expressed as in Equation (21.5) 2

S = (e + Ke )



(21.5)

The region of the control input is in between 0 and 1. The super twisting algorithm is expressed as:

u = u1 + u2

(21.6)

where u1 = −k1 sgn(s) 0.5

u2 = − k2 S sgn(s ) K1〉0 and K2〉0 The results in [17] show that the second order SMC prevents the battery from overcharge during heavy loads and very bad weather conditions. It increases the efficiency of the overall system by disconnecting critical loads under heavy loaded conditions. The efficiency of the solar system is attained by an MPPT algorithm. In [18], for the standalone solar PV system, a fractional integral terminal sliding mode MPPT algorithm is adopted for the maximum extraction of solar power. For DC to DC conversion, a Buck Boost Converter is used. To generate the reference voltage, a Radial Basis Function Neural Network (RBFNN) is trained. The proposed controller is compared with the Proportional Integral Derivative Controller and Perturb and Observe algorithm. Figure 21.6 shows the structure of the Fractional Order Integral Terminal SMC Algorithm with a PV panel. RBFNN is trained to provide the reference voltage Vref . The irradiance and temperature is input to the network and the three neurons are used in the hidden layer. Figure 21.7 shows the structure of a Radial Basis Function Neural Network (RBFNN).

Control Techniques in Sustainable Applications  639 IPV PV Panel

Radial Basis Function Neural Network

Buck Boost Converter

VPV

Vref

+ -

Load

Fractional Order Integral Terminal SMC Algorithm

Figure 21.6  Fractional order integral terminal SMC algorithm with PV panel. Hidden Layer H-1 Input Layer Irradiance Output Layer H-2

Vref

Temperature

H-3

Figure 21.7  Structure of radial basis function neural network (RBFNN).

The modeling of a Buck-Boost Converter is given as in Equation (21.7).



dv pv i pv iL = − u dt c1 c1 v diL v pv = u − 0 (1 − u) dt L L v dvc 2 iL = (1 − u) − 0 dt c2 Rc 2

(21.7)

640  DC-DC Converters for Sustainable Applications where Vpv, ipv, iL, V0, c1, c2, and u are the PV panel array output voltage, PV panel array output current, inductor current, output voltage, input capacitor voltage, output capacitor voltage, and the control input. The state space model is given as in Equation (21.8).

i pv x 2 − φ c1 c1 − x (x + x ) x 2 = 3 + 1 3 φ L L x x x x 3 = 2 − 3 − 2 φ c 2 Rc 2 c 2 x 1 =



(21.8)



where x1, x2, x3, and ϕ are the average values of PV panel array output voltage, PV panel array output current, output voltage, and control input. The sliding surface is given as in Equation (21.9).

S = e + Ke1

(21.9)

Error e = x1 – x1ref m

where e1 = e n sgn(e ) m The region of is bound between 0 and 1. n The equivalent control is defined as:



.   m c1  I pv n φeq = − x1ref + Ke sgn(e )  x 2  c 2

(21.10)

The fractional order terminal SMC is given as:

ϕc =ϕeq + ϕsw Where ϕsw = λ1(S) + λ2 sgn(S) Where λ1 and λ2 are positive values The proposed controller is compared with a PID controller and PO algorithm for various resistive loads and climatic conditions. The proposed

Control Techniques in Sustainable Applications  641 controller is investigated under the parameters such as error, overshoot, and settling time. Fast terminal sliding mode control with direct power control is designed for the maximum power extraction from the PV panel. The system consists of two cascaded loops. Perturb and Observe (PO) algorithms acted as an inner loop in which the PV panel voltage Vpv and current Ipv are the input parameters. The Perturb and Observe (PO) algorithm generates the reference active power. The reference active power and actual active power are compared and the error signal is given to the fast terminal SMC. The fast terminal sliding mode control acted as an outer loop in which the active power error and reactive power error are the input parameters. A sinusoidal pulse width modulation technique is adopted for the generation of gate pulses. The gate pulses from the sinusoidal pulse width modulator are given to the inverter. Figure 21.8 shows the structure of the grid connected PV panel with fast terminal SMC [19]. The sliding surfaces are chosen with active and reactive power, as given in Equation (21.11).

S = [ S p Sq ]

T



r

Sp = e p + γ p

∫

l e p dt + δ p  e p dt   

∫

Sq = eq + γ q

∫

l eq dt + δ q  eq dt   

∫

r



(21.11)

The active and reactive powers are given as Equation (21.12).

1 ( v gα i gα + v g β i g β ) 2 1 Q = − ( v g β i gα + v gα i g β ) 2 P=−



(21.12)

The final control law is the combination of equivalent control and switching control (discontinuous control). The final control law is given to the sinusoidal pulse width modulator. The sinusoidal pulse width modulator generates appropriate pulses to the inverter. The stability of the control

642  DC-DC Converters for Sustainable Applications

T1 PV Panel

T3

R

L

C

Grid T4

T2

Pref PO Algorithm

Fast Terminal SMC

P

Control Signal

Qref Q

Figure 21.8  Grid connected PV panel with fast terminal SMC.

law is analyzed by Lyapunov Stability Theorem. The tuning parameters in the sliding surface are properly selected to attain minimum settling time and steady state error. The simulation is carried out in MATLAB for both steady state and transient conditions. From the results, the fast terminal sliding mode control performs better results in converging time. Even in the presence of disturbances, the active and reactive power are independently controlled. Due to controller robustness, the Total Harmonic Distortion (THD) is 3-5% for the grid current [19]. A voltage mode second order sliding mode controller is proposed to extract the maximum power from the wind energy conversion systems. Sensorless maximum power point tracking is implemented to track the optimum voltages. A PID sliding surface is chosen and the control law is generated in the second order [20]. Figure 21.9 shows the wind energy conversion system with a second order PID sliding surface. The PMSG is connected to the wind turbine without gearbox arrangements. PMSG is connected to the load through a rectifier and boost converter. The reference voltage is generated from the MPPT technique and the generated voltage given to the second order SMC. The control system variables are given as:

X1 = Vref – Vin

Control Techniques in Sustainable Applications  643 Wind Turbine

PMSG

Uncontrolled Rectifier

Boost Converter

Resistive Load

Vin Io MPPT Vo

Vref

Second Order PID Sliding Mode Controller

u

Driver Circuit

Vo

Figure 21.9  Wind energy conversion system with second order SMC.

X 2 = X 1



The PID sliding surface is defined as in Equation (21.13) t

∫

S = PX1 + I X1 dt + D X 1

0

(21.13)



The control signal is given as in Equation (21.14).



u = 1+

LC β    1 P βλ  I + −  − X1 − X 2   X 2  − D(Vo − Vref + X1 ) RC D D D D 



(21.14)

Table 21.2 shows the comparison of classical SMC and second order SMC. From Table 21.2 it is clear that the performance of second order SMC is good in terms of integral absolute error (IAE), integral square error (ISE), and integral of time with absolute error (ITAE). The results are validated by wind speed profiles from 5m/s to 12m/s. The proposed controller is compared with classical SMC in terms of ripple voltage content, steady state error, and the extraction of average power [20]. With proper change in the switching states, the SMC changes the subsystems structures at any time. Due to these features, SMC plays an important role in power converters and drives. In [21], the implementation of SMC in DC drives, AC drives, and special machines is discussed. The chattering effect in the drives is reduced by the implementation of higher order SMC. Third order SMC is discussed in [22] to control the speed of a permanent magnet DC motor.

644  DC-DC Converters for Sustainable Applications Table 21.2  Comparison of classical SMC and second order SMC. Integral Absolute Error (IAE)

Integral Square Error (ISE)

Integral of Time with Absolute Error (ITAE)

Classical Sliding Mode Controller

22.86

274.5

95.49

Second order Sliding Mode Controller

15.03

226.1

63.18

Non–linear controller

21.3 Passivity-Based Control in Sustainable Applications A passivity based controller based on a decoupling method is proposed for a T-Type neutral point clamped photovoltaic grid connected inverter. First, based on the operation and basic principle Euler-Lagrange (EL) model for T-Type neutral point clamped, a photovoltaic grid connected inverter is designed with inductor and capacitor components. Secondly, by damping injection method a passivity based controller is designed. Third, a PI controller together with a passivity based control is adopted to regulate the DC voltage. The proposed controller achieves the dynamic decoupling current under a synchronous rotating dq coordinate system. Also, it improves the quality of current in the grid side inverter under

PV Panel

DC-DC Converter

T-Type Neutral Point Clamped Inverter

3-Phase AC Grid

Passivity Based Controller

Figure 21.10  T-Type neutral point clamped photovoltaic grid connected inverter.

Control Techniques in Sustainable Applications  645 disturbances. There are two types in a photovoltaic grid connected system: one stage and two stages. Later, it developed as a DC-DC converter with a grid side inverter, as shown in Figure 21.10. PV output voltage is given to the DC-DC converter. The output from the DC-DC converter is given to the grid-side inverter which is converted to AC. A T-Type neutral point clamped is implemented due to its minimum loss, loop current in symmetrical path, and reliability [23]. The system is passive such that t

∫

t

T

∫

H ( x (t )) − H ( x (0)) ≤ u y dt − Q( x )dt

0

0

(21.15)



where T ≥ 0 x(t), y(t) are the input and output state vectors The passivity based controller was proposed and implemented experimentally for a 10Kw prototype which shows performance of the system for various grid side currents [23]. For DC microgrid applications, passivity based control is presented for wind energy conversion systems with switched reluctance generators (SRG). The output voltage is stabilized for constant power loads. The system operates under the maximum power point tracking technique for voltage stabilization. Using the Euler-Lagrange System, a switched reluctance generator with a microgrid is modeled which improves the stability and ripple reduction in the DC link. An adaptive technique is adopted with a passivity based controller to deal the inductance in a time varying manner and back EMF of SRG. The closed loop stability is analyzed by Lyapunov Theorem. The reduction in voltage ripple and speed tracking is achieved by the proposed controller [24]. Figure 21.11 shows a passivity based control for a wind driven system. A Switched Reluctance Generator operates under self excited mode and it is connected to the DC link capacitor through a boost converter. The DC link capacitor supplies constant power loads. The battery pack consists of lead acid batteries and is connected to a bidirectional DC-DC converter. The bidirectional converter is used because the DC link voltage is not always equal to the voltage across the battery at all the conditions and the charging/discharging of batteries which creates ripples. The bidirectional converter minimizes these problems. The proposed controller reduces the undamped oscillations, increases the stability of the system, and minimizes

646  DC-DC Converters for Sustainable Applications Wind Turbine

SRG

SRG Converter

Constant Power Load

Current PWM Controller

Bidirectional DC/DC Converter

Battery

PWM Controller

Passivity Based Controller with Back Emf Coefficient Calculation

Figure 21.11  Passivity based controller for wind driven system.

the destabilizing effect in constant power loads. Also, it tracks the rotor speed and reduces the DC link voltage ripples [24]. A passivity based linear feedback control (PBFLC) is proposed in a wind energy conversion system with a permanent magnet synchronous generator to achieve the maximum power point tracking (MPPT) at the grid side voltage source converter and improves the fault ride through capability in the grid side converter. To regulate the desired tracking error, linear

Wind Turbine

Multi Pole Synchronous Generator

Generator Side Voltage Source Converter

Passivity Based Linear feedback Control

Grid Side Voltage Source Converter

AC Grid

Passivity Based Linear feedback Control

Figure 21.12  Multi-pole synchronous generator with passivity based linear feedback control.

Control Techniques in Sustainable Applications  647 feedback control is employed with auxiliary inputs. Step changes in wind speed, random wind speed variation, and fault ride through are analyzed [25]. Figure 21.12 shows the structure of a synchronous generator with passivity based linear feedback control. The energy from the wind is captured and given to PMSG. The system consists of back-to-back voltage source converters (VSC). The generator side converter controls the active power and reactive power. The generator side converter and grid side converter are independently controlled and the power grid and the PMSG are decoupled by the DC link capacitor. The PBFLC is designed for both grid side VSC and generator side VSC. The contributions in the paper [25] are given as: i) The transient response of PMSG is improved. ii) The closed loop system is fully investigated so that the proposed controller is accepted to implement both in industry and academics. iii) The performance of the controller is good and achieves MPPT for all the desired speeds. The passivity based control method is employed for a small hydropower system with a Permanent Magnet Synchronous Generator (PSMG). The overall system is connected to the grid through the back-to-back converter. In passivity based control, two methods such as standard passivity based control and PI passivity based control are implemented. The intrinsic characteristic of the model is considered for this control approach. The control law is designed to ensure stability by Lyapunov’s Theory [26]. Figure 21.13 shows a hydro system with PMSG integrated with the grid. The system comprises of electrical, mechanical, and hydraulic components. The PMSG is integrated with the grid through back-to-back converters. The proposed controller is tested with the conventional method in a 13.2kv feeder for a standard passivity based controller, PI passivity based controller, and classical PI controller. The results prove that the proposed method attains stability and good performance [26]. The Passivity-Based Control technique is presented to regulate the output current of the buck-boost converter. The buck-boost converter is connected in between the DC microgrid and the permanent magnet synchronous generator (PMSG) for the pitch angle control, wind turbine calculations, and regulation of torque in the rotor [27]. Figure 21.14 shows the integration of a wind energy conversion system with the DC microgrid. To ensure constant torque in the generator and to

648  DC-DC Converters for Sustainable Applications Small Hydro Power System

PMSG

AC-DC Converter

Standard/PI Passivity Based Controller

DC-AC Converter

Grid

Standard/PI Passivity Based Controller

Figure 21.13  Small hydro system integrated with grid.

Wind Turbine

Pitch Angle Control

PMSG

Un Controlled Rectifier

VO IL

Buck Boost Converter

Load

Passivity Based Controller

Figure 21.14  Wind energy conversion system with DC microgrid.

protect the over speed of the rotor, pitch angle control is installed. A buckboost converter is connected in between the rectifier and DC microgrid through a DC link capacitor. The performance of the controller is validated through MATLAB simulation results [27]. An Adaptive Passivity Based Control is proposed to mitigate the instability issues in a buck converter fed DC microgrid. A non-linear disturbance observer (NDO) is designed based on Passivity Based Control to control the load variation and line variation. To improve the performance of the system in disturbance, the non-linear disturbance observer is connected in parallel with the Adaptive Passivity Based Controller [28]. Figure 21.15 shows the Structure of a DC microgrid system. The sources for the system consist of a battery system and PV panels. The resistive load and constant power load (CPL) are connected in parallel. The load bus voltage will be in oscillating nature if the resistive load is higher than CPL.

Control Techniques in Sustainable Applications  649 Source Bus

PV Panel

Load Bus

Resistive Load

Buck Converter

Boost Converter

CPL

DC-DC Bidirectional Converter

Battery

DC-AC Bidirectional Converter

AC Grid

Figure 21.15  Structure of DC microgrid system with PV panel and battery system.

This leads the system to be unstable. So, a non-linear control is implemented to make the system in equilibrium state. Figure 21.16 shows the control block diagram of a passivity based controller. The reference inductor current is generated by the given equation as

I Lref =



Vo P 1 + + (Voref − Vo ) R Vo R

Vref

ILref ILref

P 1 V = O + + (Voref –Vo ) R VO R

u=

Vo

Figure 21.16  Control block diagram of passivity based controller.

(21.2)

1 E

U (Vo + R(ILref –iL ))

650  DC-DC Converters for Sustainable Applications The control signal is generated as



u=

1 (Vo + R( I Lref − iL )) E

(21.3)

where E is the supply voltage for the buck converter, R is the load resistor, Vo is the output voltage, Iref is the reference inductor current, iL is the actual inductor current in a buck converter, and u is the control signal. The performance of the system is compared for Passivity Based Control, Integral Passivity Based Control, and Passivity Based Control with NDO. In disturbance conditions such as line variations, the Passivity Based Control with NDO has less overshoot and fast settling [28].

21.4 Model Predictive Control in Sustainable Applications The Model Predictive Control (MPC) is employed for grid connected systems which comprise of a photovoltaic (PV), wind turbine (WT), and battery. The advantage of the proposed system is that the customers can reduce the energy cost consumed from the grid side. The simulation result shows the effectiveness of the proposed controller under external disturbances. Also, optimal power flow is achieved with reduction in cost. Figure 21.17 shows the diagram of the Hybrid System consists of a PV panel, wind turbine system, and battery system. The PV panel, wind turbine system, and battery system are connected to a common DC bus through converters. Inverters are employed to connect the DC bus and AC bus. The output from the AC bus is given to the main grid. Nowadays, Demand Side Management (DSM) plays an important role in hybrid renewable energy systems. Time of Use (TOU) in employed in the DSM to analyze the electricity cost for different periods. In peak periods to pay maximum cost, in standard periods to pay standard cost, and off peak periods to pay minimum cost [29]. The cost and savings of energy for MPC and an open loop control strategy are analyzed. The analysis is shown below in Table 21.3. The cost is analyzed for Moroccan currency for both the methods. From the Table 21.3, it is clear that the daily electricity costs is reduced by the TOU tariffs. By comparing the open loop and MPC methods, the MPC approach enhances the energy management system and reduces the costs under disturbances [29]. Figure 21.18 shows the control structure of the plant which consists of optimizer and MPC.

Control Techniques in Sustainable Applications  651 DC Bus

PV Array

DC-DC Converter

Wind Plant

AC-DC Converter

AC Bus

Main Grid

DC-AC Converter AC Load

Battery Bank

DC-DC Converter

PV, Wind, Load and Battery Power

MATLAB

Optimal Power flow

Electricity Price

Figure 21.17  Structure of hybrid system.

Table 21.3  Comparison between open loop control and model predictive control. Control method

Baseline cost (MAD/Day)

Optimal cost (MAD/Day)

Sales (MAD/ Day)

Cost savings (%)

Open Loop Control

265.04

198.07

27.71

25.27

Model Predictive Control

265.04

172.72

14.40

34.83

652  DC-DC Converters for Sustainable Applications U(t)

y(t) Open Loop Plant

MPC

Cost Function

Optimizer

Constraints

Figure 21.18  Control structure of plant.

Model predictive control based MPPT technique is proposed for photovoltaic (PV) systems with high gain DC-DC converters. A high gain DC-DC converter is proposed for utilizing maximum power from the PV module. The voltage gain is about ten times of the input voltage obtained from the proposed topology. Two voltage and one current sensor are needed for the conventional MPPT technique. In the proposed topology, only two sensors are required. The model predictive control based MPPT technique is operated in both fixed and adaptive step changes [30]. Figure 21.19 shows that the new high gain DC-DC converter consists of two diodes, two inductors, two switches, and one capacitor in the output side. The voltage gain for the proposed converter is given as in Equation (21.4).



=

1+ D where D is the duty cycle 1− D

(21.4)

The discrete time model derived for the high gain converter by the forward Euler method is given as in Equation (21.5).



on I pv (k + 1) =

 2T  V (k ) + I pv (k )  L  pv

off I pv (k + 1) =

 2T  V (k ) − Vo ] + I pv (k )  L  [ pv



(21.5)

Control Techniques in Sustainable Applications  653 D1

L1

V+

C1

D2

D0

L2

Q1

C0

R0

Q2

Figure 21.19  High gain DC-DC converter.

where T is sampling time, L is inductance, Vpv is output voltage from PV, on Ipv is output current from PV, I pv is predicted PV current when the switch off is in the OFF state, and I pv is predicted PV current when the switch is in the ON state. Figure 21.20 shows the control signal generation for the proposed system. Both simulation and hardware results are analyzed for a 150W DC-DC converter prototype and it is compared with the analytical analysis. In the proposed algorithm, the voltage sensor at the output side is replaced with an observer and it optimizes the cost of the system [30].

IPV(K) VPV(K)

Adaptive incremental conductance

I*PV(K+1)

Control Signal Optimization

Prediction

IPV(K+1)

Figure 21.20  Control signal generation for proposed system.

654  DC-DC Converters for Sustainable Applications Due to the simplicity and fast dynamic response, model predictive control (MPC) plays a vital role in the power converters. MPC act as current regulator for the voltage source inverter in dual mode operation. From the PV panel, the voltage source inverter (VSI) provides the desired current to the load in islanded mode. Also, the VSI acts as an active power filter for reactive power compensation. Model predictive current control is applied to the two level H-bridge converter. The two level H- bridge converter works to compensate the reactive power and feed the voltage to the load [31]. Figure 21.21 shows the structure of a) Islanded VSI and b) Grid connected Active Power Filter. PV panels act as a power source for both islanded and grid connected VSI. Figure 21.22 shows the control block of the predictive current controller with two level VSI. The main objective of the MPC is to control the load current. The whole process comprises of three states. The first state is to identify all the switching states, the second is to initialize the switching state and calculate the cost function, and the third one is to apply the switching state. The results are validated by MATLAB/Simulink. The simulation results prove that the PCC has good current tracking response [31].

PV System

Voltage Source Inverter

Passive Filter

Load

(a) Load

Electric Power Grid

PV System

Voltage Source Inverter

Passive Filter (b)

Figure 21.21  Structure of (a) Islanded VSI and (b) Grid-connected active power filter.

Control Techniques in Sustainable Applications  655 Iref(k+1) IL(k+1)

Minimization of cost function

U

Voltage Source Inverter

IL(k) Predictive Model

Figure 21.22  Control block of predictive current controller.

21.5 Conclusion Renewable Energy Sources are portrayed by the capacity to change fluctuating environmentally friendly power into storable and changeable power. Various non-linear control techniques are emerging to control the parameters in the integration of grids. In this chapter, a review of Sliding Mode Control, Passivity-based Control, and Model Predictive Control in sustainable applications and its latest trends are discussed. Recently. Sliding Mode Control, Passivity-Based Control, and Model Predictive Control are adopted with renewable energy sources. These control techniques provides good performance and are insensitive to variations in parameters. The control techniques control the non-linear parameters and provide the output with no peak overshoots and oscillations.

Acknowledgement The authors thank RUSA 2.0 (PO 2) project for the financial support and the Department of Electrical and Electronics Engineering, Anna University.

References 1. V. Rajakumar, K. Anbukumar and I. Selwynraj A, “Sliding mode c­ ontroller-based voltage source inverter for power quality improvement in microgrid,” in IET Renewable Power Generation, vol. 14, no. 11, pp. 1860-1872, 17 8 2020, doi: 10.1049/iet-rpg.2019.1305. 2. D. Memije, O. Carranza, J. J. Rodriguez, R. Ortega and F. E. Rodarte, “Reduction the Dead-Time Effects on the Inverter in Renewable Energy Conversion Systems by Applying Sliding Mode Control,”  2020 IEEE 11th

656  DC-DC Converters for Sustainable Applications International Symposium on Power Electronics for Distributed Generation Systems (PEDG), Dubrovnik, Croatia, 2020, pp. 429-434, doi: 10.1109/ PEDG48541.2020.9244426. 3. R. Khan, Z. A. Khan, W. Ahmad, U. H. Khan, Z. Alam and I. U. Haq, “GRNN based Backstepping Sliding Mode Control Scheme for Maximum Power Extraction of Photovoltaic System,” 2020 International Conference on Emerging Trends in Smart Technologies (ICETST), Karachi, Pakistan, 2020, pp. 1-6, doi: 10.1109/ICETST49965.2020.9080706. 4. Y. Mi, Y. Song, Y. Fu and C. Wang, “The Adaptive Sliding Mode Reactive Power Control Strategy for Wind–Diesel Power System Based on Sliding Mode Observer,” in IEEE Transactions on Sustainable Energy, vol. 11, no. 4, pp. 2241-2251, Oct. 2020, doi: 10.1109/TSTE.2019.2952142. 5. M. R. Lat Leily, S. Tohidi, F. Hashemzadeh and A. M. Shotorbani, “Novel sliding mode controller for power control of a doubly fed induction generator in variable speed wind turbine,” 2019 Iranian Conference on Renewable Energy & Distributed Generation (ICREDG), Tehran, Iran, 2019, pp. 1-6, doi: 10.1109/ICREDG47187.2019.194147. 6. H. Moradi, Y. Alinejad-Beromi, H. Yaghobi and D. Bustan, “Sliding mode type-2 neuro-fuzzy power control of grid-connected DFIG for wind energy conversion system,” in IET Renewable Power Generation, vol. 13, no. 13, pp. 2435-2442, 7 10 2019, doi: 10.1049/iet-rpg.2019.0066. 7. S. Samanta, S. Barman, J. P. Mishra, P. Roy and B. K. Roy, “Design of an interconnection and damping assignment-passivity based control technique for energy management and damping improvement of a DC microgrid,” in IET Generation, Transmission & Distribution, vol. 14, no. 11, pp. 2082-2091, 5 6 2020, doi: 10.1049/iet-gtd.2019.1075. 8. C. Gui-ping, L. Long-fu, L. Yong and C. Jie, “Passivity-based control of multi-functional single-phase capacitive-coupling grid-connected inverter for renewable energy integration and reactive power compensation,”  2018 13th IEEE Conference on Industrial Electronics and Applications (ICIEA), Wuhan, 2018, pp. 1785-1790, doi: 10.1109/ICIEA.2018.8397998. 9. Y. Sang, B. Yang, W. Yao and L. Jiang, “Design and implementation of perturbation observer-based robust passivity-based control for VSC-MTDC systems considering offshore wind power integration,” in  IET Generation, Transmission & Distribution, vol. 12, no. 10, pp. 2415-2424, 29 5 2018, doi: 10.1049/iet-gtd.2017.1693. 10. D. A. M. Cirino, R. D. Zamora and E. I. O. Rivera, “Passivity Based Controller for Photovoltaic Modules Using Zeta Converter,” 2017 IEEE 44th Photovoltaic Specialist Conference (PVSC), Washington, DC, 2017, pp. 3044-3049, doi: 10.1109/PVSC.2017.8366613. 11. R. Cisneros, F. Mancilla-David and R. Ortega, “Passivity-Based Control of a Grid-Connected Small-Scale Windmill With Limited Control Authority,” in IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 1, no. 4, pp. 247-259, Dec. 2013, doi: 10.1109/JESTPE.2013.2285376.

Control Techniques in Sustainable Applications  657 12. M. Beus and H. Pandžić, “Application of an adaptive model predictive control algorithm on the Pelton turbine governor control,” in  IET Renewable Power Generation, vol. 14, no. 10, pp. 1720-1727, 27 7 2020, doi: 10.1049/ iet-rpg.2019.1291. 13. X. Chen, W. Cao, Q. Zhang, S. Hu and J. Zhang, “Artificial IntelligenceAided Model Predictive Control for a Grid-Tied Wind-Hydrogen-Fuel Cell System,” in  IEEE Access, vol. 8, pp. 92418-92430, 2020, doi: 10.1109/ ACCESS.2020.2994577. 14. H. H. Ali, A. M. Kassem, M. Al-Dhaifallah and A. Fathy, “Multi-Verse Optimizer for Model Predictive Load Frequency Control of Hybrid MultiInterconnected Plants Comprising Renewable Energy,” in IEEE Access, vol. 8, pp. 114623-114642, 2020, doi: 10.1109/ACCESS.2020.3004299. 15. N. Sockeel, J. Gafford, B. Papari and M. Mazzola, “Virtual Inertia Emulator Based Model Predictive Control for Grid Frequency Regulation Considering High Penetration of Inverter-Based Energy Storage System,” in  IEEE Transactions on Sustainable Energy, vol. 11, no. 4, pp. 2932-2939, Oct. 2020, doi: 10.1109/TSTE.2020.2982348. 16. S. E. Mahjoub, M. Ayadi and N. Derbel, “Sliding Mode Controller for a Dual Input – Single Output Converter in a Hybrid Power System,” 2020 5th International Conference on Renewable Energies for Developing Countries (REDEC), Marrakech, Morocco, Morocco, 2020, pp. 1-6, doi: 10.1109/ REDEC49234.2020.9163855. 17. T. Alnejaili, S. Drid, D. Mehdi, L. Chrifi-Alaoui and H. Sahraoui, “Sliding mode control of a multi-source renewable power system,”  2015 3rd International Conference on Control, Engineering & Information Technology (CEIT), Tlemcen, 2015, pp. 1-6, doi: 10.1109/CEIT.2015.7233129. 18. Z. A. Khan, L. Khan, Q. Khan and F. W. Karam, “Fractional Integral Terminal Sliding Mode MPPT Control for Photovoltaic System,”  2019 15th International Conference on Emerging Technologies (ICET), Peshawar, Pakistan, 2019, pp. 1-6, doi: 10.1109/ICET48972.2019.8994613. 19. Elaheh Heydari, Ali Yazdian Varjani, Demba Diallo, “Fast terminal sliding mode control-based direct power control for single-stage single-phase PV system, “Control Engineering Practice, Volume 104, 2020, 104635, ISSN0967- 0661, https://doi.org/10.1016/j.conengprac.2020.104635. 20. Dursun, Emre & Kulaksız, Ahmet. (2020). Second-order sliding mode voltage - regulator for improving MPPT efficiency of PMSG-based WECS. International Journal of Electrical Power & Energy Systems. 121. 106149. 10.1016/j.ijepes.2020.106149. 21. R. Dhanasekar, S. G. Kumar and M. Rivera, “Sliding mode control of electric drives/review,” 2016 IEEE International Conference on Automatica (ICAACCA), Curico, 2016, pp. 1-7, doi: 10.1109/ICA-ACCA.2016.7778466. 22. R. Dhanasekar, S. G. Kumar and M. Rivera, “Third Order Sliding Mode Control of Buck Converter Fed Permanent Magnet DC Motor,” 2018 IEEE International Conference on Automation/XXIII Congress of the Chilean

658  DC-DC Converters for Sustainable Applications Association of Automatic Control (ICA-ACCA), Concepcion, 2018, pp. 1-4, doi: 10.1109/ICA-ACCA.2018.8609812. 23. J. Wang, X. Mu and Q. Li, “Study of Passivity-Based Decoupling Control of T-NPC PV Grid-Connected Inverter,” in  IEEE Transactions on Industrial Electronics, vol. 64, no. 9, pp. 7542-7551, Sept. 2017, doi: 10.1109/TIE. 2017.2677341. 24. M. M. Namazi, S. M. S. Nejad, A. Tabesh, A. Rashidi and M. Liserre, “PassivityBased Control of Switched Reluctance-Based Wind System Supplying Constant Power Load,” in  IEEE Transactions on Industrial Electronics, vol. 65, no. 12, pp. 9550-9560, Dec. 2018, doi: 10.1109/TIE.2018.2816008. 25. B. Yang et al., “Passivity-based linear feedback control of permanent magnetic synchronous generator-based wind energy conversion system: design and analysis,” in IET Renewable Power Generation, vol. 12, no. 9, pp. 981-991, 9 7 2018, doi: 10.1049/iet-rpg.2017.0680. 26. W. Gil-González, A. Garcés and O. B. Fosso, “Passivity-Based Control for Small Hydro-Power Generation With PMSG and VSC,” in IEEE Access, vol. 8, pp. 153001-153010, 2020, doi: 10.1109/ACCESS.2020.3018027. 27. J. S. Velez, S. Ospina and E. Giraldo, “Passivity-Based Control for a BuckBoost Converter Applied in Small Wind Generation Interconnected to DC Microgrid,”  2019 IEEE 4th Colombian Conference on Automatic Control (CCAC), Medellín, Colombia, 2019, pp. 1-6, doi: 10.1109/CCAC. 2019.8920939. 28. M. A. Hassan, E. Li, X. Li, T. Li, C. Duan and S. Chi, “Adaptive PassivityBased Control of dc–dc Buck Power Converter With Constant Power Load in DC Microgrid Systems,” in IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 7, no. 3, pp. 2029-2040, Sept. 2019, doi: 10.1109/ JESTPE.2018.2874449. 29. M. Azaroual, M. Ouassaid and M. Maaroufi, “Model Predictive Control and Optimal Cost for A Grid-Connected Photovoltaic/Wind/Battery System,”  2020 5th International Conference on Renewable Energies for Developing Countries (REDEC), Marrakech, Morocco, Morocco, 2020, pp. 1-6, doi: 10.1109/REDEC49234.2020.9163878. 30. O. Abdel-Rahim and H. Wang, “A new high gain DC-DC converter with model-predictive-control based MPPT technique for photovoltaic systems,” in CPSS Transactions on Power Electronics and Applications, vol. 5, no. 2, pp. 191-200, June 2020, doi: 10.24295/CPSSTPEA.2020.00016. 31. F. Martinez, T. Morel, H. Fretes, J. Rodas, Y. Kali and R. Gregor, “Model Predictive Current Control of Dual-Mode Voltage Source Inverter Operations: Islanded and Grid-Connected,”  2020 5th International Conference on Renewable Energies for Developing Countries (REDEC), Marrakech, Morocco, Morocco, 2020, pp. 1-6, doi: 10.1109/REDEC49234.2020.9163850.

22 Optimization Techniques for Minimizing Power Loss in Radial Distribution Systems by Placing Wind and Solar Systems S. Angalaeswari*, D. Subbulekshmi and T. Deepa SELECT, VIT, Chennai, India

Abstract

The scope of the naturally available sources in power system generation is inevitable nowadays due to the benefits of integration of the distributed generation. The distributed sources, for example wind and solar, have a major role in the power system filed as they are more abundant in nature, have less pollution and a low operation cost, and are eco-friendly. Depending on the distribution, the network has been classified into mesh and radial. Traditional power generation, transmission, and distribution have a radial structure in general and the non-conventional energy sources have to be placed at optimal location to increase the power generation with less loss. Based on the connected loads in the distribution network, the incurred system has been determined for standard bus systems. The placing of the distributed sources and their sizing has to be determined optimally, otherwise it may give adverse effect. Identifying optimal location and rating of the distributed sources could be efficiently done with optimization techniques. These techniques may be classical, analytical, and evolutionary methods. Each method has its own merits and drawbacks. This chapter is going to elaborate on various optimization techniques for the reduction of power loss in radial networks by placing wind/solar energy sources at optimal locations with optimal ratings identified by the optimization algorithms. Keywords:  Radial distribution network (RDN), power loss minimization, optimization algorithms, distributed generation

*Corresponding author: [email protected] S. Ganesh Kumar, Marco Rivera Abarca and S. K. Patnaik (eds.) Power Converters, Drives and Controls for Sustainable Operations, (659–680) © 2023 Scrivener Publishing LLC

659

660  DC-DC Converters for Sustainable Applications

I. Introduction 22.1 Distribution Systems Owing to the exhaustion of fossil fuels and awareness of the global environment, renewable sources are occupying more space in power generation recently. Moreover, these non-conventional energy sources are freely available in nature, cause less pollution, and are low maintenance and user friendly. All the consumers can easily generate the power from major resources like solar and wind that can be utilized for their own use. The excess power could be exported to the utility grid and this way, it is more economical. The power generation and consumption at the consumer end itself leads to the concept of distributed generation and these sources are called distributed generators (DGs). Owing to the integration of the DGs into the existing grid, the reliability is enhanced by reducing the losses and the quality of the supply is improved considerably [1]. Relieved transmission and distribution capacity, improved grid performance with great asset utilization, supporting reactive power, and management of load and energy are the main advantages of the DGs addition [2]. Moreover, the conventional grid is strengthened by sharing the peak load and enhanced voltage profile, improving the load factor also. Integrating DGs with the utility grid improves the system security and efficiency [3]. The commonly used renewable sources are solar, wind, fuel cell, micro turbines, and diesel generators. These DGs reduce the line losses, increasing the efficiency of the transmission and distribution while connecting at the consumer end. Hence, the power quality and voltage stability are increased significantly at the consumer side. When the power is generated and distributed at the load end, the distribution network is benefitted. Hence, the distribution network is focused much more on the power systems. Based on the configuration, the distribution is classified into a radial network, ring, or mesh network. In the practical network, power is generated at a generating station which is the sole entity and it is transmitted via long transmission lines in the distribution substations. The voltage level is reduced to a lower value depending on the applications and it is supplied to the consumers using the distribution network.

Power Loss minimization in RDS  661

22.2 Radial Distribution Network The general structure of radial distribution network systems (RDN) is presented in Figure 22.1, in which the generated power is distributed to various loads after lowering the voltage. Because of the simple structure and the low initial installation cost, RDN is more popular. The resistance to the reactance (R/X) ratio of this RDN is very high and the generation load is also distributed, which leads to an ill conditioned or weak system in nature. The real power loss in the RDN can be determined by considering the system shown in Figure 22.2, in which the power is transferred from bus i to bus j. The power losses occurring in the line is written in Equations (22.1) and (22.2).

Pijloss = Rij

Pj2 + Q 2j Vj2

(22.1)



Loads

Generating station Feeder Step up transformer

Loads

Figure 22.1  General structure of Radial Distribution Network (RDN). Vi δi

~

PGi,QGI

Vj δj

Pij , Qij

Pji , Qji Zij =Rij +jXij

Pi ,Q i Bus i PDi ,QDi

Figure 22.2  Two bus system with nodes.

PGj , QGj Pj ,Qj

Bus j PDj ,QDj

~

662  DC-DC Converters for Sustainable Applications loss ij

Q



Pj2 + Q 2j = Xij Vj2

(22.2)



where Pijloss and Qijloss are considered as the active and imaginary power losses in the distribution line, Rij is the resistance and Xij is the reactance of the line, Pj and Qj are the active and imaginary power flowing in bus j, and Vj is to be the magnitude of the voltage at ‘j’ bus. Consider totally N bus in the RDN system and the active power loss ‘PL’ in kW can be determined using the formula [4]:





PL = ∑iN=1 ∑ Nj =1 α ij ( Pi Pj + QiQ j ) + βij (Qi Pj − PQ i j ) 

α ij =

Rij Rij cos(δ i − δ j ) ; βij = sin(δ i − δ j ) VV VV i j i j

Zij = Rij + jXij





(22.3)

(22.4) (22.5)

where Zij is the impedance formed with resistance and reactance in the line, Vi and Vj are the magnitudes of the voltages with the phase angles of δi, δ, and Pi, Pj, Qi, and Qj are real and reactive powers at nodes. The total power comprises of real and reactive power components. Because of the high ratio of R/X in RDN, the foremost portion of the power loss happened due to the real power loss. Hence, this plays a more significant role in economic operation than the reactive power loss, so the focus is narrowed down to the real power loss reduction. Reducing the real power loss is a more challenging and important task as the power loss is considered as a function of square of the current flowing in the circuit [4] and the resistance. Hence, the objective is to reduce the current flowing in the distribution line by placing the power generating devices nearer to the loads, which reduces the current dispatched from the particular to other loads. The system losses are reduced in this way, which improves the voltage profile and the efficiency.

22.3 Power Loss Minimization There are numerous objectives considered in the RDN for improving system performance, such as voltage stability improvement, reducing power

Power Loss minimization in RDS  663 losses, and minimizing the fuel cost in an economical point of view. In most of the research areas, single or multi-objectives are considered for meeting out the desired performance, among which the real power loss minimization is chosen in this chapter since it is the primary one from an operational point of view. There are various methods for loss minimization like placement of distributed generation, placing capacitors, and doing reconfiguration in the RDN. Since the capacitor is generating reactive power, thereby reducing the reactance in the transmission line, it will reduce the reactive power loss in the total loss equation [5]. Addition of shunt capacitors could be done for the power flow control, reducing power loss for the improvement of voltage, and improving the stable condition. Moreover, placing a capacitor can also be implemented for the high voltage network and it deals with only the reactive component, therefore this method is not suitable for real power reduction in RDN. Feeder reconfiguration and DG placement are applied for a low voltage distribution network. Reconfiguration could be performed by varying the switching operation for changing the loads between the feeders. This operation has to be performed by keeping the radial network as such. The main drawback associated with this method is its complex decision-­ making process and the computation for the reconfiguration process and the configuration of protection devices. Owing to various advantages of DGs and considering the environmental aspects, placing DGs for active power loss reduction is presumed to be the best method in RDN systems. DGs are to be placed at the proper locations with correct rating to reduce the power loss, otherwise, it will give an opposite effect. Hence, optimization methods can be applied in the RDN for the placement of DGs along with optimal rating. In this chapter, the various optimization methods are going to be discussed along with their constraints. While solving the power loss minimization of real power loss, there are various constraints or limitations to be considered. The main parameters in RDN are the active and reactive power and the magnitude of voltage and its phase angle. Several constraints of equalities and inequalities are power balance equation, voltage limits, and active and reactive power limits, which are to be specified. For practical cases, transformer tapping also is mentioned. a) Net Power Flow Constraints



PGi − PDi = ∑ Nj =1 VV i j Gij cos (δ i − δ j ) + Bij sin(δ i − δ j )



(22.6)

664  DC-DC Converters for Sustainable Applications



QGi − QDi = ∑ Nj =1 VV i j Gij sin (δ i − δ j ) − Bij cos(δ i − δ j ) (22.7)

where PDi and QDi are the active and reactive power demand at node i and the conductance of the line is Gij, whereas the susceptance is Bij. The total DG capacity is restricted to total loads of the network. b) DG power generation constraints:

PGmin ≤ PGi ≤ PGmax

(22.8)

c) The voltage constraint is

Vmin ≤ Vi ≤ Vmax

(22.9)

where Vmin and Vmax are the minimum and maximum node voltage limit.

22.4 Optimization Techniques The true power loss in RDN is assigned proportional to the power flow in each branch. Based on the power flow results, the loss has to be allocated among the branches [6]. The classical power flow methods are not efficient for the distribution networks for the load flow calculations. So, dedicated load flow methods such as forward/backward (F/B) sweep load flow are considered in the literature. For calculating the power, the current in each branch is determined as follows:



Iij =

Vi ∠δ i − Vj ∠δ j Zij

(22.10)



The power loss for any RDN is calculated based on any of the load flow methods and it is being considered as the base case results. As discussed in the previous section, placement of DG is more preferable than other methods. Since the network is radial in nature, the loads are connected at various feeders. The power is fed from the generating station to various loads through the feeder. The current and the power loss in the feeder, which have more loads, are high compared to other feeders. Hence, the DGs have

Power Loss minimization in RDS  665 to be placed at the feeder from which more loads are connected. This is considered as the optimal place for the DG and also, the sizing or rating of DG should be more optimal from an economical point of view. Otherwise, the excess power will be unutilized and not meaningful. Hence, the objective is chosen as the reduction of the active power loss in RDN by suitably placing DG with its optimal sizing. While doing so, if the DGs are placed other than at the best location, this leads to an increase in power loss in the system. The various optimization techniques are useful in determining the ideal location and optimal rating. The count of variables in the problem is based on the selections required in the solution. In this chapter, optimal location and rating are the two solutions needed, hence the numbers of decision variables are considered as two. There are various types of DGs available such as: i) real power injecting DG with unity power factor, ii) reactive power injecting DGs such as capacitors and synchronous compensators, iii) injecting both active and reactive power, and iv) DGs observing reactive power but injecting active power such as induction generators deployed in wind power generation. Solar (PV) systems are becoming very popular in the renewable energy field as they are very clean and freely available in nature [7]. The DGs considered in this chapter are wind turbines and solar systems. The modeling of these DGs is referred from [8, 9]. In mathematical problem analysis, there are various conventional methods available for the optimization of any objective function along with its constraints. In the literature, conventional methods like analytical and sensitivity based evolutionary algorithms, such as naturally inspired and non-naturally inspired intelligent algorithms and hybrid algorithms are presented. Depending on the objective function, it may be linear programming, mixed non-linear programming, newton method, quadratic and sequential quadratic programming, index-based method, sensitivity-based method, dynamic programming, or Eigen value-based methods. There are modified algorithms such as simplified analytical and efficient analytical algorithms found in the papers. Evolutionary algorithms are mostly inspired by nature via the various species. With the behavior of birds and insects, the particle swarm optimization (PSO) method was proposed by taking its position and velocity as variables. Among the population called a swarm, the best particles find the candidate solution. The shortest movement of the species to reach its destination is being considered as the optimization method. Various modified PSO algorithms such parameter improved PSO [4] and modified PSO are proposed in the literature.

666  DC-DC Converters for Sustainable Applications Based on survival of the fittest, species either emigrate or immigrate to an island, which has a better habitat suitability index. These indices are founded with the best suitability index variables which are independent. In a particular habitat, rainfall, temperature, and geographical location determine the suitability index. Rate of immigration and rate of emigration can be evaluated as a function of the number of species on that island. The population on an island could be considered as the tuning parameter for obtaining the optimum value. When both immigration and emigration rates are equal, it is called an equilibrium number of species [10]. This kind of optimization is called bio-geography based optimization (BBO), in which the habitats with a low index have a high immigration rate and the habitats having a high index have a high emigration rate. Modified [11] and improved BBO [12] algorithms are utilized in various literature for active power loss reduction in RDN. Based on Darwin’s theory of evolution, the genetic algorithm (GA) has evolved in optimization algorithms. This is slowly changing the process based on the population. The individual chromosome is called the solution and it has a set of genes. For each individual, the fitness value is being evaluated and it defines the quality of the solution. Choosing the best is called mating and the members in the mating pool are called parents. Offspring will be generated from the parents and cross-over and mutation are applied in this step to generate the best among the offspring by the process of recombination. Rate of crossover and mutation has to be chosen to reduce the number of generations. Though GA provides a list of best solutions, it is being suffered from computational analysis and it may not converge to the optimal solution for improper implementation. The authors [13] have implemented GA for active power loss reduction in RDN for the selection of DG. The Ant-Lion algorithm (ALO) is evolved from the hunting habit of ant lions. This is based on the random walk of the agents and its selection [14]. These ant lions form traps by digging the sand, forming a circular cone, and hiding there. The insects which fall on this dig are swollen by these ant lions and consumed there. The main operators in this are the random walk of the ants, the trap, building the trap, prey catch, elitism, and rebuilding of the pit [14]. Initially, the most preferable DG location can be chosen using loss sensitivity factors and then this ALO is deployed for reducing the DG location and sizing [15]. Whale optimization algorithms are formed by the shooting nature of humpback whales, which uses the method of chasing randomly and hunting by bubble net method [16]. These whales swim around the prey and form a circle shape or ‘9’ shape path. It uses an exclusive method called

Power Loss minimization in RDS  667 bubble net feeding method and this technique can be utilized for solving the economic dispatch problem, fuel consumption problem, beam design, and pressure vessel design problems, etc. The whale’s best location at each iteration is updated and the encircling prey is also updated. Due to its exploitation and exploration ability, it has been applied in power loss minimization problems in the electrical field. The bat algorithm (BA) for the best location and rating of DG is applied in RDN using the varying nature of loudness and pulse rate generation of the bats [17]. The unique nature of bats is the echolocation identification of the bats and it emits sonar signals which hit the object and bounce back. The delay time between emission and the echo are evaluated by the bats to find the shortest path for reaching the objects. The velocity and position of the bats with varying loudness and pulse rate are considered as the variables updated at every iteration. Population, movement of bats, local search, pulse rate, and loudness are the major variables in BA. A shuffled bat algorithm is implemented in [18] for the addition of multiple DGs by increasing load demand by 20%. A shuffled frog leap algorithm (SFLA) is proposed in [19] for the reconfiguration with DG placement. The frogs are randomly sitting on the ponds for food and shuffling happens between the frogs sitting within the pond and between the ponds. This behavior of the frogs has high accuracy in searching the best solution over other methods. Similar to jellyfishes, the salps are moving towards the front by pumping the water back. Due to its unique swarming nature, it is found in deep oceans and forms a swarm called a chain [20]. The entire inhabitants are divided into leaders and supporters. The frontrunner is leading the salp chain and the remaining are the members in the followers. They move to find food in the shortest path, hence its position and velocity are presumed as the decision variables. This algorithm is implemented in [21] for DG location and rating, thereby reducing the true power loss and operating cost of the utility grid. A mutated salp swarm algorithm is adopted in [22] for the distribution of real and reactive power sources in RDN. A bacterial forging (BFOA) optimization algorithm uses the group foraging of swarms of Escherichia coli bacteria which is present in human intestines [23]. The bacterium sends signals to other bacteria for communication and it makes the decision by considering the factors. The chemotaxis process helps to take steps in the search space and it is more effective than other methods. In each location, the fitness value is calculated and analyzed. The main process involved in this algorithm is swarming, reproduction, chemotaxis, and dispersion and it uses the friendly movement of the bacteria at a longer distance.

668  DC-DC Converters for Sustainable Applications Cuckoo search follows the removal of bad eggs in a nest. A good solution is the eggs of cuckoos and it is carried to the next generation. Cuckoos are laying their eggs in other birds’ nests and remove the eggs in that nest. Sometimes, female cuckoos produce eggs with various patterns and colors of the host species. To avoid loss of the eggs due to the host birds, these cuckoos lay their eggs in the nest in which the bird simply puts in its eggs and takes care of them. Immigration of cuckoos is chosen as the variable for the optimization problems [24] and this algorithm is adopted in various fields such as nurse scheduling for duty allocation, the traveling salesman problem for finding the shortest path, etc. Invasive weed optimization emerges from the inspiration of weed growth which is heavier than other plants. This growth is a harm and threat to the other plants. These weeds have good stability and adaptability. Attacking weeds use the sources available in the field and grow new weeds. Based on the qualification of the value, weeds are ranked and form a colony [25]. The plants with less rank are eliminated from the competition and the surviving plants move to the next generation for production. A stud krill herd algorithm is proposed by Gandomi and Alavi based on the natural phenomenon in view of the biological process. The individual is adopted to live in nature and it is evaluated by its movement, which is forced by other individuals, its hunting behavior, and the unsystematic dispersion [26]. Based on the selection and crossover operators, the optimization is performed for obtaining the best fitness function. This has been implemented in RDN for the DG placement to get minimum power loss. The detailed presentation of a stud krill herd is explained in [Wang] for various optimization problems. The coyote optimization algorithm (COA) is based on the community deeds of coyotes and its adjustment in nature. It differs from the grey wolf algorithm in such a way that this COA gives the organization and common practice amongst the coyotes [27]. The improved version of COA is implemented in [28] for the optimal installation of solar systems in RDN for power loss reduction, reduced capacity, improved voltage profile, and minimized harmonic distortion. Based on hybrid optimization algorithms of salp swarm and whale algorithms, multi-DG’s are placed at optimal locations with an optimal rating in 13 and 123 node RDN. The software named OpenDSS engine has been adopted to find the power flow parameters [29]. Reactive power dispatch has been done optimally to minimize the real power loss, minimize the voltage deviation, and enhance the stability of the voltage using an artificial Bee colony algorithm in [30].

Power Loss minimization in RDS  669 For voltage profile improvement, the optimal reconfirmation has been proposed in [31] using the modified selective PSO, keeping various loading situations. The algorithm is tested in an IEEE 33 system and it is observed that this proposed modified algorithm has significant reduction in real power loss by increasing the minimum voltage profile. In [32], the mixed algorithm of binary PSO and shuffled frog leap has been proposed for the power loss reduction on 33 and 69 bus systems. Reconfiguration has also been developed with same hybrid algorithms for voltage improvement and cost saving objectives. Wind energy is being considered as an addition to DG in the radial distribution networks to reduce the power loss, taking the factors of kernel density estimation and Monte Carlo simulation, load demand and air density effect in an hourly manner, and modelling of single and multi-wake methods [33]. The real time data is taken for the wind system data and the various wind systems are connected for the wake losses method. This has been done in IEEE 28 and 69 radial distribution networks. In [34], wind farms running with doubly fed induction generators are taken for the power loss minimization system. The losses of all the components in the systems including generators, filters, and power converters are also considered and the objectives are solved using the distributed optimal reactive power control method. The alternating direction method of multipliers is used for solving the control objectives. The optimal DG placement problem has been sorted out using a new algorithm called chaotic maps integrated stochastic fractal search in [35] implemented in 33, 69, and 118 networks which is mentioned in appendix with Figure 22.1A, Figure 22.2A and Figure 22.3A respectively. Various constraints such as real and reactive power balance, voltage limits, current limits, capacity limits of DGs, power factor limits, location of the DG, and penetration levels of DG are considered for the objective function. For the reconfiguration to reduce the power loss, the improved selective binary PSO is proposed for 33 and 94 node distribution systems by taking the activation function as a square of the branch current and the resistance of the line [36]. Radiality structure has been considered as one among the constraints. Adopting teacher learning based optimization (TLBO) for placing the energy storage systems for enhancing the reliability of the radial network has been proposed in [37] considering 30 and 69 bus systems. The results are being compared with other popular techniques to prove the validity of the proposed algorithm. The capacitor placement of multi-period based switchable has been proposed in [38] for energy loss reduction and to improve the voltage profile. The factor of number of segments is being considered for the yearly loss

670  DC-DC Converters for Sustainable Applications calculation. The popular load flow methods such as direct load flow and backward/forward sweep have been adopted and tested in 10 bus, 33 bus, 69 bus, and 85 bus systems. An adaptive PSO and modified gravitational search algorithm have been implemented for the single and multi-­objective DG placement for a unity power factor and optimal power factor [39]. For compensation of the reactive power of the distribution systems, DGs and shunt capacitors have been added in the optimal location with optimal size in [40]. The method of mutated salp swarm algorithm has been adopted to stray away from local minima and to increase the population and this has been tested in 33 and 69 distribution systems. The hybrid classical and metaheuristic algorithms of SQP and PIPSO have been implemented in [41] for power loss reduction with voltage improvement. The SQP, which runs on quadratic programming, is more sensitive to initial value selection. Hence, parameter improved PSO has been implemented first and the results are taken as the initial values for the SQP algorithm, thereby the losses are reduced. Active power filters have been adopted for harmonics reduction using an extended non-linear load position based APF current injection algorithm in [42]. Considering three cases, the size and cost of APF is determined using a grey wolf algorithm and tested in a 69 bus system. In a similar way, there are many such optimization algorithms such as harmonic search, artificial bee colony, ant colony, plant growth simulation algorithm, differential evolution, artificial immune systems, flower pollination, paddy field algorithm, fish swarm algorithm, intelligent water drop algorithm, firefly algorithm, and fireworks that have been planned for the loss decrease problem in RDN. To validate the optimization algorithms in the practical case, various test systems are being considered. Most of the algorithms have been tested in these systems and the results are related with the results and/or other algorithms to propose superiority over other methods. The structure and the line details are presented at the end of the chapter for understanding the RDN system.

22.5 MATLAB Tools for Optimization Techniques The optimization algorithms presented in the previous section have been implemented in MATLAB by writing the logic as coding. In order to simplify the burden on the researchers, popular conventional techniques are developed as tailor made functions and implemented in MATLAB as readily available.

Power Loss minimization in RDS  671 In MATLAB, an optimization tool is available under the APPS option. This could be opened either by directly clicking on the optimization icon in the tool bar or we can type ‘optimtool’ in the command window. Recently, MATLAB has introduced an alternative for an optimization app, which can be opened using new live script and one has to set the options about the solver and all. Since there are many objectives to be attained for a single optimization problem, a multi-objective optimization problem is chosen in some cases. In the MATLAB toolbox, the following functions are available. For all the functions, the equality and inequality constraints have to be entered as a matrix in A or B for inequality linear constraints and Aeq or Beq for equality linear constraints. Also, the upper and lower limits have to be specified. It is preferable to specify the initial values for the variables. For some specific functions, the nonlinear constraints are to be given as a separate function. The entire m file and the corresponding constraint functions are to be saved in the same running folder. 1. fmincon – Constrained nonlinear minimization – This is for the minimization of an objective function with constraints. In this, various methods can be employed such as interior point, trust region, sequential quadratic programming, and the active set method. 2. fgoalattain - mMultiobjective goal attainment – This function is defined for solving multi-objective optimization problems. 3. fminbnd - Single-variable nonlinear minimization with bounds - This has a single objective function with the left and right end points specified. 4. fminmax - Minimax optimization - It is used to find the minimum of a set of multi-variable functions. 5. fminsearch - Unconstrained nonlinear minimization This function is used without constraints for nonlinear minimization. Similarly, there are many such defined functions available in the optimization toolbox. The evolutionary algorithms such as GA and simulated annealing are defined in this tool box. Some sample programming is given in this chapter for understanding the function and the constraints. Considering the linear programming with three variables x, y, and z, Minimize f=7x-3y+8z

672  DC-DC Converters for Sustainable Applications Subject to the inequality constraints 2x+4y≥ 5 3x-z ≤8 and equality constraints 4x-y+z=20 The solution for the above linear programming with the constraints is 60 at the 7th iteration.

Similarly, consider the given objective function chosen as



Minimize f(x) = 5x2 + 20 cos (2x)

Using genetic algorithm, one can find the fitness value using this toolbox as -9.04 at the 5th iteration.

Power Loss minimization in RDS  673

Since the chosen power loss minimization objective function is quadratic in nature, the quadratic function is considered as follows, the value is 0.5, and it shows that it is non-convex. Quadratic programming



1 minimize f ( x ) = x12 − 2 x 22 + 4 x1x 2 − x1 + 3x 2 2 Subject to the constraints

x1 – 3x2 ≤ 5; –2x1 + 4x2 ≤ 6;

H= [1 -4; -4 4]; f=[-1; 3]; A=[1 -3; -2 4]; B=[5;6];

674  DC-DC Converters for Sustainable Applications

In the same way, after identifying the objective function and the constraints, the values should be entered in the toolbox in the specified locations and the simulation should be run.

22.6 Conclusion In this chapter, the concept of a radial distribution network and its associated active power loss in the RDN is discussed. The various load flow methods adopted in RDN are presented. The review of various methods of power loss minimization such as capacitor placement, DG placement, and feeder reconfiguration are referred from the literature. The need for obtaining the best location and optimal rating is discussed in the previous section. Conventional and evolutionary optimization algorithms and their origins are elaborated in the chapter to get a nutshell of the algorithms. In the last section, the optimization tools available in MATLAB are discussed by taking some examples to understand the way of entering the functions and the constraints with the initial values appropriately.

Power Loss minimization in RDS  675

References 1. S.Angalaeswari, K.Jamuna. Active Power Loss Minimization in Radial Distributed Micro grid Incorporating Distribution Generator: Emerging Trends in Electrical, Communications and Information Technologies, Lecture Notes in Electrical Engineering, 394, Springer, pp.no.353-360, 2015. 2. S.Angalaeswari, K.Jamuna. Constrained Power Loss Minimization of DC Micro grid Using Particle Swarm Optimization: Proceedings of the International Conference on Data Engineering and Communication Technology, Advances in Intelligent Systems and Computing 468, Springer, 379-389, 2015. 3. Attia El Fergany Optimal allocation of multitype distributed generators using backtracking search optimization algorithm, I. Journal of Electrical Power and Energy Systems, 64, 1197–1205, 2015. 4. Angalaeswari S, Jamuna.K Optimal Placement and Sizing of Real Power Supporting DG in Radial Distribution Networks: IEEE Conference on Women in Engineering (WIECON-ECE), 342-345, 2015. 5. Kalambe S. & Agnihotri G.Loss Minimization Techniques Used in Distribution Network: Bibliographical Survey, Renewable and Sustainable Energy Reviews, 29, 184-200, 2014. 6. S. S. Kashyap and M. De, “Loss allocation and loss minimization for radial distribution system including DGs,” IET Renewable Power Generation, vol. 11, no. 6, pp. 806-818, 2017. 7. Sujitha N., Partha Sarathi Subudhi, Krithiga S., S. Angalaeswari, T. Deepa, D.Subbulekshmi, “Grid tied PV system using modular multilevel inverter” International Journal of Power Electronics and Drive System (IJPEDS), vol. 10, No. 4, pp. 2013-2020, 2019. 8. S. Angalaeswari, K. Jamuna, “ Design and implementation of a robust iterative learning controller for voltage and frequency stabilization of hybrid microgrids” Computers and Electrical Engineering, vol. 84, 106631, 2020. 9. A. Rakesh Kumar, Deepa Thangavelusamy, Sanjeevikumar Padmanaban, and Dwarkadas P. Kothari, “A modified PWM scheme to improve AC power quality for MlIS using PV source” I.Journal of Power and Energy Systems, 39(1), 34-41, 2019. 10. Simon, D., “Biogeography-based optimization” IEEE Transactions on Evolutionary Computation. 12: 702–713, 2008. 11. Duong, M.Q.; Pham, T.D.; Nguyen, T.T.; Doan, A.T.; Tran, H.V., Determination of Optimal Location and Sizing of Solar Photovoltaic Distribution Generation Units in Radial Distribution Systems. Energies, vol. 12, 174, 2019. 12. S. Angalaeswari, A. Arunagiri and K. Jamuna, “Improved biogeography based optimization technique for loss minimization in power distribution networks,” 2017 International Conference on Power and Embedded Drive Control (ICPEDC), Chennai, pp. 26-31, 2017.

676  DC-DC Converters for Sustainable Applications 13. Sattianadan D., Sudhakaran M., Dash S.S., Vijayakumar K., “Power Loss Minimization by the Placement of DG in Distribution System Using GA. Swarm, Evolutionary, and Memetic Computing. SEMCCO,Lecture Notes in Computer Science, 7677. Springer, Berlin, Heidelberg, 2012. 14. E.S.Ali, S.M.Abd Elazim,A.Y.Abdelaziz, Ant Lion Optimization Algorithm for optimal location and sizing of  renewable distributed generations, Renewable Energy, 101, 1311-1324, 2017. 15. E.S. Ali, S.M. Abd Elazim, A.Y. Abdelaziz, Ant Lion Optimization Algorithm for renewable Distributed Generations, Energy, 116, 445-458, 2016. 16. D.B. Prakash, C. Lakshminarayana, Multiple DG placements in radial distribution system for multi objectives using Whale Optimization Algorithm, Alexandria Engineering Journal, 57, 2797–2806, 2018. 17. R. Prakash and B. C. Sujatha, “Optimal placement and sizing of DG for power loss minimization and VSI improvement using bat algorithm,” National Power Systems Conference (NPSC), Bhubaneswar, 1-6, 2016. 18. Chandrasekhar Yammani, Sydulu Maheswarapu and Sailaja Kumari Matam, Optimal placement and sizing of distributed generations using shuffled bat algorithm with future load enhancement, International transactions on Electrical Energy Systems, 26, 274–292, 2016. 19. Onlam, A.; Yodphet, D.; Chatthaworn, R.; Surawanitkun, C.; Siritaratiwat, A.; Khunkitti, P. Power Loss Minimization and Voltage Stability Improvement in Electrical Distribution System via Network Reconfiguration and Distributed Generation Placement Using Novel Adaptive Shuffled Frogs Leaping Algorithm, Energies, 12, 2019. 20. Seyedali Mirjalili, Amir H.Gandomi, Seyedeh Zahra Mirjalili, Shahrzad Saremi, Hossam Faris, Seyed Mohammad Mirjalili, “Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems” Advances in Engineering Software, vol. 114,pp. 163-191, 2017. 21. Tolba, M.; Rezk, H.; Diab, A.A.Z.; Al-Dhaifallah, M. A Novel Robust Methodology Based Salp Swarm Algorithm for Allocation and Capacity of Renewable Distributed Generators on Distribution Grids, Energies, vol.11, 2556, 2018. 22. Khalil Gholami, Mohammad Hasan Parvaneh, ‘A mutated salp swarm algorithm for optimum allocation of active and reactive power sources in radial distribution systems ‘Applied Soft Computing, vol. 85, 105833, 2019. 23. Mohamed Imran A, Kowsalya M,‘Optimal size and siting of multiple distributed generators in distribution system using bacterial foraging optimization’, Swarm and Evolutionary Computation, vol. 15, pp. 58–65, 2014. 24. Ms. Anuja. S. Joshi, Mr. Omkar Kulkarni, Dr. Kakandikar G. M., Dr. Nandedkar V.M., “Cuckoo Search Optimization- A Review” Materials Today: Proceedings 4, 7262–7269, 2017. 25. D.Rama Prabha,T. Jayabarathi, ‘Optimal placement and sizing of multiple distributed generating units in distribution networks by invasive weed optimization algorithm’ Ain Shams Engineering Journal, vol. 7,pp. 683–694, 2016.

Power Loss minimization in RDS  677 26. Li, Q.; Liu, B. Clustering Using an Improved Krill Herd Algorithm. Algorithms, vol. 10, 56, 2017. 27. Mohammed H. Qais, Hany M. Hasanien, Saad Alghuwainem, Adnan S. Nouh, “Coyote optimization algorithm for parameters extraction of three diode photovoltaic models of photovoltaic modules” Energy, vol. 187, 116001, 2019. 28. Thang Trung Nguyen, Thai Dinh Pham, Le Chi Kien and Le Van Dai, “Improved Coyote Optimization Algorithm for Optimally Installing Solar Photovoltaic Distribution Generation Units in Radial Distribution Power Systems” Hindawi-complexity, 34 pages, 2020. 29. Khalid Mohammed Saffer Alzaidi, Oguz Bayat and Osman N. Uçan, “Multiple DGs for Reducing Total Power Losses in Radial Distribution Systems Using Hybrid WOA-SSA Algorithm”, Hindawi International Journal of Photoenergy, vol. 2019, Article ID 2426538, 20 pages. 30. M. Ettappan, V. Vimala, S. Ramesh, V. Thiruppathy Kesavan, Optimal Reactive Power Dispatch for Real Power Loss Minimization and Voltage Stability Enhancement using Artificial Bee Colony Algorithm, Microprocessors and Microsystems (2020), doi:https://doi.org/10.1016/j.micpro.2020.103085. 31. Ayodeji Olalekan Salau, Yalew Werkie Gebru, Dessalegn Bitew, “Optimal network reconfiguration for power loss minimization and voltage profile enhancement in distribution systems”, Heliyon 6 (2020) e04233. 32. Abdurrahman Shuaibu Hassan, Yanxia Sun, Zenghui Wang, “Multi-objective for optimal placement and sizing DG units in reducing loss of power and enhancing voltage profile using BPSO-SLFA”, Energy Reports 6 (2020) 1581–1589. 33. Routray A, Mistry KD, Arya SR, Wake Analysis on Wind Farm Power Generation for Loss Minimization in Radial Distribution System, Renewable Energy Focus (2020), doi: https://doi.org/10.1016/j.ref.2020.06.001 34. Sheng Huang, Peiyao Li, Qiuwei Wu, Fangxing Li, Fei Rong, “ADMMbased distributed optimal reactive power control for loss minimization of DFIG-based wind farms”, Electrical Power and Energy Systems 118 (2020) 105827. 35. Thanh Long Duong, Phuoc Tri Nguyen, Ngoc Dieu Vo et al., A newly effective method to maximize power loss reduction in distribution networks with highly penetrated distributed generations, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2020.11.003 36. Raoni Pegado, Zocimo Ñaupari, Yuri Molina, Carlos Castillo, “Radial distribution network reconfiguration for power losses reduction based on improved selective BPSO”, Electric Power Systems Research 169 (2019) 206–213. 37. Preet Lata, Shelly Vadhera, “Reliability Improvement of Radial Distribution System by Optimal Placement and Sizing of Energy Storage System using TLBO”, Journal of Energy Storage 30 (2020) 101492.

678  DC-DC Converters for Sustainable Applications 38. Omid Sadeghian, Arman Oshnoei, Morteza Kheradmandi, Behnam Mohammadi-Ivatloo, “Optimal placement of multi-period-based switched capacitor in radial distribution systems”, Computers and Electrical Engineering 82 (2020) 106549. 39. Ahmad Eid, “Allocation of distributed generations in radial distribution systems using adaptive PSO and modified GSA multi-objective optimizations”, Alexandria Engineering Journal (2020) 59, 4771–4786. 40. K. Gholami and M.H. Parvaneh, A mutated salp swarm algorithm for optimum allocation of active and reactive power sources in radial distribution systems, Applied Soft Computing Journal (2019), doi: https://doi. org/10.1016/j.asoc.2019.105833. 41. Angalaeswari, S.; Sanjeevikumar, P.; Jamuna, K.; Leonowicz, Z. Hybrid PIPSO-SQP Algorithm for Real Power Loss Minimization in Radial Distribution Systems with Optimal Placement of Distributed Generation. Sustainability 2020, 12, 5787. https://doi.org/10.3390/su12145787. 42. A. Lakum and V. Mahajan, A novel approach for optimal placement and sizing of active power filters in radial distribution system with nonlinear distributed generation using adaptive grey wolf optimizer, Engineering Science and Technology, an International Journal, https://doi.org/10.1016/j. jestch.2021.01.011

Power Loss minimization in RDS  679

Appendix 01 02

19

03

20 21 22

04

23

05

24

06

25

07 08

26

09

27

10

28

11

29

12

30

13

31

14

32

15

33

16 17 18

Figure 22.1A  Single line diagram of IEEE 33 system.

40 41

39

42

43

44

45

46

38 37 47

36

01

02

03 28

04

48

05

49

06

56

58 59

30 31

33

08

09

66

10

11

12

13

14

15

16

55

54

53

68

69

18 19

60

32

07

67

52 51

17

57

29

50

34

61

35

62

63

64

27

20

65

26

Figure 22.2A  Single line diagram of IEEE 69 bus system.

25

24

23

22

21

680  DC-DC Converters for Sustainable Applications 12 13 14 15 16 17 10 11 2 4 5

18 19 20 21 22 23 24 6

7

8

31 32 33 34 36

96

63

35

47

45 46

48 49

50 51 52 53 54

37

55 56 57 58

64

27

38 39 40 41 42 43 44

30

1

26

9

3 28 29

25

59

60

97

98

61 62

99

89 90 91 92 93 94 95 65 66 67 68

78 79

100

80 81

86 87

69

82

70 71 72

73

74

83 84 85

88

112

101 102 103 104 105 106 107 108 109 110 111 114 115 116 117 118

Figure 22.3A  Single line diagram of IEEE 118 bus system.

113

75 76 77

23 Passivity Based Control for DC-DC Converters Arathy Rajeev V.K. and Ganesh Kumar S.* DEEE, CEG Campus, Anna University, Chennai, Tamil Nadu, India

Abstract

The control of an electrical drive system plays a vital role in our day to day life. The total energy of a system is the algebraic sum of stored energy and dissipated energy in the system. We could control the system by adjusting the dissipated energy in the system by injecting damping to the system. This control is known as passivity based control. The system should be passive in nature to apply this control. On an analogous, 90% of the physical system in the world is passive. In this chapter, we discuss how to apply passivity based control to an electrical drive system step by step. The control law is generated for three considered cases and sensitivity analysis is done in MATLAB for finding the sensitive parameters in a DC drive system. Keywords:  DC-DC converters, Lyapunov’s stability, passivity based control

23.1 Introduction Power converters are widely used for the conversion of electrical energy of one form to another. These converters control the flow of energy [1]. The control of converters can be effectively done by representing the system in Euler-Lagrange form. The method of passivity based control (PBC) is an energy-based method of control. As a sum of stored energy and dissipated energy, the total energy of the system is expressed. This method deals with the shaping of energy, as well as the injection and tracking of damping, which is done via the Hamiltonian operator. Control based on passivity *Corresponding author: [email protected] S. Ganesh Kumar, Marco Rivera Abarca and S. K. Patnaik (eds.) Power Converters, Drives and Controls for Sustainable Operations, (681–730) © 2023 Scrivener Publishing LLC

681

682  DC-DC Converters for Sustainable Applications is defined by satisfying the matching condition of dissipated energy. The basic development of control law using PBC for DC-AC converters is discussed in this chapter. The stability of the system is physically related to the energy storage and dissipation that occurs in the system. This energy dissipated from the elements should be shaped using power converter circuits in such a way that the system becomes stable throughout the operating cycle. The control method which does this process is said to be dissipativity based control or passivity based control [2]. This control uses electrical parameters as references to the controller. In this methodology, the closed loop system is made passive and oscillations in the system are suppressed by injecting damping constants. The rate of damping injection is based on the nature of the load and the type of oscillation. Systems are modeled in terms of conservative forces, dissipative forces, and elements of energy acquisition in PBC. The error in energy satisfies Lyapunov’s stability and dissipation matching condition for the control function of PBC for any system [3]. Control and stability of nonlinear systems is a significant field in engineering as practically all systems have nonlinearity. Hysteresis nonlinearity is the capacity of the system to memorize the previous outputs. In electromechanical systems the reverse in current in an actuator also requires an extra current to reverse the field. This results in hysteresis loops and the area of this loop is directly proportional to energy lost to the device. This energy interpretation of the system can provide the maximum variation of gain possible in a system before going unstable [3]. As energy is one of the fundamental concepts, the control has a wide area of application. Here, we talk about applying the control for electrical systems, mainly DC drives. The energy shaping method is well known in mechanical systems. Here, the nonlinearity is converted to a passive operator that controls the energy lost by the device. A DC motor’s feedback control is achieved through the DC-DC converter’s pulse width modulation (PWM). An average small-signal model controlling DC-DC converters supports the application of linear control theory [4], which produces satisfactory results in many applications. In certain cases, this approach offers minimal performance or may even fail. During sudden load changes, such situations can involve tight monitoring of the reference voltage. This kind of issue [4] would be alleviated by ­passivity-based regulation. It is based on measurements of the energy in the device. If any system’s model is converted to its energy outlook, it is easy to enforce PBC. Based on the required reference trajectories, PBC is designed to achieve stabilized performance trajectories.

Passivity Based Control for DC-DC Converters  683 In motorized seatbelt systems, wearable exoskeletons, robots, and battery-powered vehicles, load torque estimation of the DC motor is essential. The torque sensor is eliminated due to the knowledge of the inversion of the plant model and the load torque estimation is successfully completed [5]. Estimating the load torque of the DC motor using the online algebraic approach is now gaining more interest because of its rapid estimation without any tuning requirement and model inversion. As feedback variables for estimating the load torque and speed, both armature current and armature voltage are used. Torque can be estimated without a speed sensor and therefore, the number of sensors is also reduced. Therefore, it is proposed to implement online algebraic load torque estimation without a speed sensor. In this scheme, speed is estimated using feedback variables, such as armature current and armature voltage, through the corresponding mathematical model. Because of the choice of the mathematical model and its corresponding variables for speed estimation, the scheme can be referred to as soft sensing [5], which is otherwise referred to as sensor-less.

23.2 Passivity Based Control For power electronic circuits, passivity-based controllers are commonly synthesized with a stability goal in mind, i.e., to achieve a constant output voltage or a constant current in the branches of the circuit. Euler Lagrange equations were previously used in this context to derive PBC in various electronic power circuits and also in some mechanical systems [5]. In such a way that the non-linear terms in the torque equations are eliminated, a unified framework for the control of different DC motor configurations using PBC was derived. For the switching function using PBC, fundamental equations are derived such that the tracking error can be stabilized to zero. Using mathematical modeling of electrical drives, the system has to be represented by both mechanical and electrical subsystems. When the output of a converter is connected to the machine, the number of variables that depend on the system stability increases. In other words, the system is more complicated depending on the controllability [6]. The feedback decomposition of a general electrical drive system is represented in Figures 23.1 and 23.2. The parameters controlling the physical system are represented in the figure. Usually, the electrical parameters that control a converter are the current in inductor and capacitor voltage. The motor is controlled by speed which is related to input voltage and load torque which is related to current [7].

684  DC-DC Converters for Sustainable Applications

V

Electrical Subsystem

TE +

θ, ω

Mechanical Subsystem

–

TL

Figure 23.1  Feedback decomposition block diagram. U1

e1

y2

y1

H1

H2

e2

U2

Figure 23.2  Passivity analysis system.

The passivity based control technique is an energy based control technique where the system should be passive in nature. The above figure represents a Lur’e type system where both outputs are products of Hamiltonian and error, which can be mathematically expressed by the equations as follows:

y1 = H1 ∗ e1 = H1(u1 – y2)

(23.1)

y2 = H2 ∗ e2 = H2(u2 – y1)

(23.2)

In the above system, if U2=0, H1 is passive and H2 is strictly passive, this means any system is passive if it is free from external disturbance parameters influencing the output of the entire system. This theorem should be verified before applying the control. In the case of power electronic converters, they are strictly passive in nature [8]. For power converters, the formation considers the following behaviour traits such as: 1. It is possible to define conservative forces by the product of skew symmetry and state vector. In the system’s stability consideration, the skew symmetry matrix does not arbitrate. 2. The product of a constant symmetric positive semi-definite matrix and state vector can be defined by dissipative forces.

Passivity Based Control for DC-DC Converters  685 This force appears in the system due to the resistances and friction of the system. 3. The control inputs can be formulated from a constant matrix multiplying with the input vector. 4. The external forces are signified by a time varying or alternatively constant vector field. In PBC, conservative forces, dissipative forces, and energy acquisition elements play a key role during modeling given in Figure 23.3. The energy error should satisfy Lyapunov’s stability and dissipation matching condition for the control function of PBC for any system [9]. The passivity based control can be accomplished by many methods like: 1) Energy shaping damping injection method (ESDI) 2) Exact tracking error dynamics passive output feedback method (ETEDPOF) 3) Exact static error dynamics passive output feedback method (ESEDPOF) System selection

Flat ?

N

Indirect reference profile generation

Y Direct reference profile generation

PBC PBC Control input to plant Control input to plant

Figure 23.3  General flowchart for PBC.

686  DC-DC Converters for Sustainable Applications

23.3 Control Law Generation Using ESDI, ESEDPOF, ETEDPOF 23.3.1 Energy Shaping and Damping Injection (ESDI) To verify the system stability, it should satisfy Lyapunov’s stability theory. To make the system stable, the incremental energy should be zero. To achieve the same, we inject damping to the system. This is an output feedback dynamic controller that enhances the closed loop energy. ESDI method is the very basic method of PBC, which is an output feedback controller [2]. Considering a linear time invariant controllable single output system, such as

Pẋ(t) = (J – R)x(t) – bu

(23.3)

where J is skew symmetric and R is symmetric in nature. Now, the desired system can be represented by



ẋ*(t) = (J − R)x*(t) + R1(x – x*) + bu

(23.4)

Here, a damping factor R1 is added to the system matrix which depends on the tracking error in the system. The damping factor injects the error to the system to minimize or maximize the stored energy in the system to the desired value where, R + R1 > 0. From the above equation, the control law can be derived as



bT u = T ( Px *(t ) − ( J − R )x *(t ) − R1 ( x − x *)) b b

(23.5)

Considering the Hamiltonian operator, the state space equation will be modified as follows:





x (t ) = ( J − R ) y = bT

∂H − bu ∂x

∂H ∂x

(23.6)

(23.7)

Passivity Based Control for DC-DC Converters  687 The control law generated from the above equation can be given as



u = −γ bT

∂H = −γ y ∂x

(23.8)

From the above control law it is clear that PBC is an output feedback controller.

23.3.2 Exact Tracking Error Dynamics Passive Output Feedback (ETEDPOF) In this method, the average system model differentiates the stabilization error exact dynamic model. The energy management structure of the error dynamics is demonstrated in a generalized Hamiltonian form. So, the passive output is associated with the error dynamics [10]. These error dynamics are identified by a time invariant feedback controller. If the dissipation matching condition is satisfied, then the equilibrium point will be a semi-globally asymptotically stable equilibrium for a closed loop system [11–13]. The Hamiltonian of the physical system symbolizes the energy function (H) and is written including the state vector ‘x’, which can be expressed as:



1 H = xMx T 2

(23.9)

where M is a constant and positive definite matrix. The partial derivative of Equation (23.9) with respect to ‘x’, gives Equation (23.10) as: T



 ∂H    = Mx ∂x 

(23.10)



Generally, any averaged state model can be represented as: T



 ∂H(x)   = (J(u) − R) + bu + ∈ x(t)  ∂ x 



(23.11)

688  DC-DC Converters for Sustainable Applications Matrix J is skew-symmetric in nature, which will not affect system stability, as:

xTJ(u) x=x J(u) xT=0

(23.12)

The term ‘bu’ is the energy acquiring term. External disturbances such as load torque, etc. are introduced in ′∈′. R is symmetric and positive semi-definite, i.e.,

RT = R ≥ 0

(23.13)

It is possible to express the J(u) skew symmetry matrix as:



J(u) = J0 + J1u

(23.14)

The desired machine profile is achieved using Bezier polynomials in an offline fashion. For this required system profile, it is assumed that the desired open-loop dynamics should be convinced by a state reference trajectory x*(t) and it is defined by: T



 ∂H(x*)   = (J(u*) − R) + bu*+ ∈* x*(t)  ∂ x* 



(23.15)

The matrix J(u) is skew-symmetric, which is related to an average control input ‘u’ and it satisfies the following expansion property:



J(u) = J(u*) + (u − u*)

∂J(u) ∂u

(23.16)

∂J(u) is a skew-symmetry constant matrix. ∂u Under steady-state conditions, state trajectory ‘x’ will reach x* and control input ‘u’ becomes u*. Now, Equation (23.15) is customized to:

where

T



 ∂H(x*)  0 = [J(u*) − R] + bu*+ ∈  ∂ x* 

(23.17)

Errors in the system’s state trajectories should be detected to adjust the control input in order to enforce a closed-loop process. These errors in the trajectory of state (e) and input of control (eu) are determined as follows:

Passivity Based Control for DC-DC Converters  689

 ∂H(e)  e = x − x*   ∂e 



T

(23.18)



eu = u − u*

(23.19)

On differentiating Equation (23.18) with respect to time ‘t’:



ė = ẋ

(23.20)

Adding and subtracting the required steady-state values to Equation (23.20) yields: T

T

 ∂H(e)   ∂H(x*)  e = [J(u) − R] + be u + ∈+[J(u) − R] + bu* (23.21)  ∂e   ∂ x*  If the value for ∈ obtained from Equation (23.17) is substituted in Equation (23.21), then the error dynamics will become: T

 ∂H(e)   ∂H(x*)  e = [J(u) − R] + be u + [J(u) − J(u*)]   ∂e   ∂ x* 

T



(23.22)

On using Equation (23.15) in Equation (23.22), error dynamics of the system is modified into: T T ∂H(e)    ∂J(u)   ∂H(x*)     e = [J(u) − R] e + b+  ∂e    ∂u   ∂ x*    u T



T

∨  ∂H(e)   ∂H(e)  e = [J(u) −R + be u    ∂e   ∂e 



(23.23)

(23.24)

where



  ∂J(u)   ∂H(x*)  T   ∨ b = b +        ∂u   ∂ x*   

(23.25)

690  DC-DC Converters for Sustainable Applications T

 ∂H(e)  ” is a conservative term which will not affect the The “J(u)  ∂e  stability property of the system: T



 ∂H(e)   ∂H(e)    J(u)  =0 ∂e ∂e 

(23.26)



The other remaining terms exactly coincide with the tangent linearization part of the dynamics. The passive output tracking error is given by:

 ∂H(e)  e y = y − y* =b   ∂e  ∨



T

(23.27)

T



A linear time-varying average incremental passive output feedback controller is simply given by:



∨  ∂H(e)  e u = −γe y = −γ bT   ∂e 

T

(23.28)



When substituting Equation (23.20) in Equation (23.16), the error dynamics of the system will become: T



T

T

∨ ∨  ∂H(e)   ∂H(e)   ∂H(e)  e = J(u) (23.29) −R − b γ bT   ∂e   ∂e   ∂e 

T



∨ ∨  ∂H(e)   ∂H(e)  e = J(u) − (R + b γ bT )   ∂e   ∂e 

T



(23.30)

Now, with the skew symmetry property of J(u), Ḣ(e) is given by: T



 = −  ∂H(e)  R   ∂H(e)  < 0 H(e)  ∂e   ∂e 



(23.31)

Passivity Based Control for DC-DC Converters  691 Equation (23.23) is negative definite if dissipation matching condition (23.24) is satisfied.

 = (R + b∨ γ b∨ T ) R



(23.32)



The fulfilment of the matching state of dissipation will usually be in two ways and both forms are explained below:  >0 Case I: R This means that it is strictly satisfied with the dissipation matching condition and Equation (23.26) will become a negative definite.  ≥0 Case II: R Here, the condition of dissipation matching is not strictly met. LaSalle’s theorem [10–12] is used in these cases to evaluate the global asymptotic stability of the origin of the tracking error space. According to the theorem of LaSalle, the following conclusions can be drawn as follows: Suppose that there is a positive definite function, H: RnàR, whose derivative satisfies the inequality Ḣ ≤ 0 and, in addition, if the largest invariant set found in the set {x: Ḣ = 0} is equal to {0}, then the system is globally asymptotically stable. The machine can be semi-globally asymptotically stable due to the boundary existence of control input [0 and 1] in the power electronic converters. Now, the condition of dissipation matching and the average control input are given by: T

  ∂J(u)   ∂H(x*)  T    ∂J(u)   ∂H(x*)  T   (R + b γ b ) = R = R +  b +     γ b +       ∂u   ∂ x*     ∂u   ∂ x*   (23.33) ∨

∨

T



T

∨  ∂H(e)  u = u* −γ b  = u* −γ bT Me   ∂e  ∨

T



(23.34)

where ‘γ’ represents the coefficient of damping injection whose value can be considered low to prevent amplification of noise. The control input to regulate the speed of the DC motor is therefore obtained. In Equation (23.34), the control function (u) clearly indicates the absence of a derivative term, which simplifies the controller [4].

692  DC-DC Converters for Sustainable Applications S

Rm

L i

E

D

iam C

v

Lm

Rfm M

Ef

ω*

i

J

Lfm

ω

v

u

CONTROLLER

Figure 23.4  Exact tracking error dynamics passive output feedback (ETEDPOF) control of buck converter.

23.3.3 Exact Static Error Dynamics Passive Output Feedback This method is comparable to the aforementioned method by which the controller is derived by identifying the passive output static error dynamics. In this method, the control law consists of no derivative terms. This control can be implemented by systems where accuracy is not a concern. The control law is the same as that of ETEDPOF, but the dynamic terms become null during reference profile generation shown in Figure 23.4.

23.4 Control Law Generation Using ETEDPOF Method for DC Drives 23.4.1 Buck Converter Fed DC Motor The average model of the buck converter-fed DC motor is developed using the ETEDPOF method [5] and is given in Equations (23.35)–(23.38)





L

di = − v + uE dt

(23.35)

dv = i − i am dt

(23.36)

C

Passivity Based Control for DC-DC Converters  693



Lm J

di am = v − R mi am − kω dt

(23.37)

dw = ki am − Bω − TL dt

(23.38)

The state vector when the above equations are written in matrix form is:

x(t)T = (i, v, iam, ω)

(23.39)

  −1 0 0   0 L      0   x 1 (t)   1 −1   x1   E    0 0      L   0    C C (t) x x 2     2 + u+  0   x 3 (t)  =  1 − Rm −k   x3   0      0      x   0   −TL  L L L m m m  (t) x 4  4     0   J        k −B   0 0  J J   (23.40) where k—Torqueconstant (N.m/A) L—Inductance of buck converter (henry) C—Capacitance of buck converter (farad) Rm—Armature resistance of motor (Ohm) Lm—Armature inductance of motor (henry) u—Average input for control i—Current input (ampere) v—Armature voltage or output converter voltage (volt)  2πN  ω—Angular velocity of motor   60  TL—Torque produced by load (Nm) iam—Armature current of motor (ampere) N—Speed of the motor (RPM) J—Inertia of motor (kg.m2) B—Coefficient of friction (Nms) E—Voltage input (volt)

694  DC-DC Converters for Sustainable Applications The buck converter-fed DC motor model shown in the above equation demonstrates that it is a system of conservative and dissipative forces for energy management. Since ETEDPOF includes energy-based operations, further modification of Equation (23.40) in terms of energy function is mandatory and can be rewritten as: T

 ∂H(x)   = [J − R] + bu + ∈ x(t)  ∂ x 



(23.41)

where T

 ∂H(x)   = Mx ;  ∂x 



(23.42)



Matrix M is given by:



  M=   

L 0 0 0

0 C 0 0

0 0 Lm 0

0 0 0 J

     

(23.43)

The matrices ‘b’ and ‘ϵ’ are given by:



E bT =  , 0, 0,0  ; L 

(23.44)



−T ∈T = 0,0,0, L  J  

(23.45)

Passivity Based Control for DC-DC Converters  695 and the matrices J and R are given by:



  0   1  LC J=   0    0 



    R=    

−1 LC

0

0

−1 LmC

0

1 LmC

0

−k JLm

0

k JLm

0

0

0 0

0 0

0

0

0

0

0 0 Rm L2m 0

0 0 0 B J2

        

           

(23.46)

(23.47)

The matrix ‘J’ is independent of ‘u’ and it is of skew-symmetry in nature. Matrix R is symmetric and positive semi-definite:

RT =R ≥ 0

(23.48)

As a result, the modified average buck converter-fed DC motor model is achieved through fundamental principles of the system’s energy management structure. This derived model may be used under no load and loaded conditions in the deriving control law using the ETEDPOF control for a buck converter-fed DC motor. ETEDPOF control is essential for speed regulation and it is developed on the basis of error stabilization dynamics, which are further discussed. For speed regulation, load torque estimation is essential under loading conditions. The primary purpose of the current work is to control the speed of a DC motor under no-load and load conditions for a given speed profile (ω*). In an offline method with Bezier polynomials, the desired speed profile is acquired. The control function (u) is developed by following the procedure discussed earlier.

696  DC-DC Converters for Sustainable Applications



u = u* −

γE (i − i*) L

(23.49)

where the constant ‘γ’ is termed as the damping injection coefficient and must be > 0. In this case, the dissipation matching condition is verified using Equation (23.32). Final dissipation matching matrix 2Ř for the buck converter system is specified by:



 γ E2  2  L  0 R =  0    0 

0

0

0

0

0 Rm L2m

0

0 0

0

0 B J2

    ≥0     

(23.50)

It is realized that the Ř matrix is not strictly satisfying the dissipation matching condition. Hence, the control law makes the origin of error space as an asymptotically stable equilibrium point by virtue of LaSalle’s theorem [13]. To verify the stability of the system stability using LaSalle’s theorem:



 = −  ∂H(e)  (R)   ∂H(e)  H(e)  ∂e   ∂e 

T

T



(23.51)

 ∂H(e)  = Me. Substitute Equation (23.49) and It is known that   ∂e  T  ∂H(e)    in Equation (23.50), then Ḣ(e) ≤ 0. Ḣ(e) can be obtained by ∂e  substituting the required matrices in Equation (23.50) and it is given by:



 = −( γe12 E 2 + e32R m + e 24B) H(e)

(23.52)

When Ḣ(e) = 0 and if errors e1, e3, and e4 become zero, then ė1 = ė3 = ė4 = 0. On substituting these values in Equation (23.24), e2 = 0. Hence, the error dynamics of the system converges to zero and the system becomes globally

Passivity Based Control for DC-DC Converters  697 asymptotically stable by virtue of LaSalle’s theorem. As the control input is bounded in nature [i.e., 0, 1], system stability is not global. In Equation (23.49), the inductor current plays a significant role in control operation, and hence, it can be articulated as the more sensitive variable. This sensitive nature of the inductor current is investigated in the coming section. Equation (23.49) points towards the control input derived using the ETEDPOF method. This control law makes the system semi-globally asymptotically stable for a given or desired speed profile (ω*).

23.4.2 Boost Converter Fed DC Motor ETEDPOF implementation with ω* as the desired speed profile use the armature voltage (v) and boost inductor current (i) as feedback signals is shown in Figure 23.5. Using Kirchhoff ’s laws and Newton’s laws, the average model for a boost converter-fed DC motor can be obtained and is expressed as:

L



di = −(1 − u)v + E dt

(23.53)

dv = (1 − u)i + i am dt

(23.54)

C



L

Rm

D

i E

Lm

iam

S

J

M v

C

ω i u

v CONTROLLER

Figure 23.5  ETEDPOF control of boost converter.

iam ω*

698  DC-DC Converters for Sustainable Applications

Lm



J



di am = v − R mi am − kω dt

(23.55)

dw = ki am − Bω − TL dt

(23.56)

Equations (23.53)–(23.56) can be written as below:   −(1 − u) 0 0 0    E  L    x 1 (t )   (1 − u)   x1   L  −1  0 0       C C x  x 2 (t )  =   2 +  0   x 3 (t )   1 − Rm −k   x3   0  0      x   −TL  L L L m m m  ( ) x t  4      4     J k B −     0 0   J J   (23.57) with the state vector

x(t)T = (i, v, iam, ω)

(23.58)

where L—Inductance of converter (H) C—Capacitance of converter (F) Rm—Armature resistance of motor (Ohm) Lm—Armature inductance of motor (H) u—Average control input i—Current input (A) v—Converter output voltage or Armature voltage (V) By the Hamiltonian operator, the state space equation can be given as follows: T



 ∂H(x)   = [J(u) − R] +∈ x(t)  ∂ x 

(23.59)

Passivity Based Control for DC-DC Converters  699 where T

 ∂H(x)    = Mx ; ∂x 



(23.60)



Matrix M is given by:



  M=   

L 0 0 0

0 C 0 0

0 0 Lm 0

0 0 0 J

     

(23.61)

The matrix ϵ is given by:



E −T ∈T =  ,0,0, L  J  L

(23.62)

and the matrices J and R are given by:



 0    (1 − u)  LC J=  0    0  

−(1 − u) LC

0

0

−1 LmC

0

1 LmC

0

−k JLm

0

k JLm

0

0

           

(23.63)

700  DC-DC Converters for Sustainable Applications



    R=    

0 0

0 0

0

0

0

0

0 0 Rm L2m 0

0 0 0 B J2

        

(23.64)

Thus, the average model of a boost converter-fed DC motor is changed based on the energy management formation. By following the procedure explained in previous Section (23.3.2), a natural feedback control law may be written as:



u = u* − γ(iv* − vi*)

(23.65)

where the constant ‘γ’ must be > 0. Here, the dissipation matching condition is strictly satisfied and the final matrix is given by:



 *2  γ x22 L   * *  − γ x1 x 2 LC R =   0    0 

γ x1* x 2* − LC

0

0

0

0

0

Rm L2m

0

0

0

B J2

γ x1* C2

2

     >0      

(23.66)

 is a positive definite matrix. R  is positive definite whenever t ≥ 0, the origin of the error space Since R is asymptotically stable. As the control input is in a bounded nature of u between 0 and 1, the result is not global [14]. When ‘u’ semi-globally reaches to u*, output voltage, current of the boost converter, and speed of the motor will attain stability.

Passivity Based Control for DC-DC Converters  701

23.4.3 Luo Converter Fed DC Motor For the analysis, which is the luo converter-fed DC motor, a sixth-order non-flat system is derived in this section. The luo converter-fed DC motor has three relative degrees, which is less than the system order. This validates the unstable internal dynamics of the luo inductor converter current and the voltages of the capacitor that are related to velocity. Reference trajectories are therefore derived in an indirect way [15]. Figure 23.6 embodies the luo converter with a dynamic load for ETEDPOF implementation. ETEDPOF can be realized with inductor currents (i1 and i2) capacitor voltage (v1). For the current work, a primary positive output luo converter is taken with the available wide variety of pump circuits. A linear average model for a Luo converter feeding DC motor can be developed using Kirchhoff ’s laws and Newton’s laws. Field circuit equations are absent because of the choice of the armature control method for speed control. The linear average model that was developed is provided by:



di1 uE (1 − u) = − v1 dt L1 L1

(23.67)



di 2 uE uv 1 v 2 = + − dt L 2 L 2 L 2

(23.68)

S

C1

L2 i2

E

v1 L1

l1

Rm

iam D

C2

v2

Rfm

Lm M

Ef Lfm

ω

u

i1

i2 v1 CONTROLLER

Figure 23.6  ETEDPOF control of luo converter.

ω*

J

702  DC-DC Converters for Sustainable Applications



dv 1 (1 − u)i1 ui 2 = − dt C1 C1

(23.69)



dv 2 i 2 i am = − dt C 2 C 2

(23.70)



di am v 2 R m k = − i am − ω dt Lm Lm Lm

(23.71)



dω k B T = i am − ω − L dt J J J

(23.72)

where i1—Input side inductor current (A) i2—Output side Inductor current (A) v1—Input side Capacitor voltage (V) v2—Output side Capacitor voltage (V) iam—Armature current of the motor (A) u—Input control variable E—Voltage supplied to the system (V) Employing matrix notation with the aid of Hamiltonian system given in Equation (23.11), with the state vector shown in Equation (23.73).

xT(t) = (i1, i2, v1, v2, iam, ω)

(23.73)

and the matrices b, ∈, J(u), and R are given from Equation (23.74) to Equation (23.77):



bT =  E L , E L , 0, 0, 0, 0  2  1 

(23.74)



−T ∈T = 0 , 0 , 0 , 0 , 0, L  J  

(23.75)

Passivity Based Control for DC-DC Converters  703

 0    0    (1 − u)  LC 1 1 J(u) =   0    0    0  

−(1 − u) L1C1 u L 2C1

0

0

0

−1 L 2C 2

0

0

0

0

0

0

0

0

−1 L mC 2

0

0

0

1 L mC 2

0

−k JL m

0

0

0

k JL m

0

0 0 -u L 2C1 1 L 2C 2

                 

(23.76)



     R=     

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0

0

0

0

0

0

0

0

0 0 0 0 Rm L2m 0

0 0 0 0 0 B J2

          

(23.77)

Matrix J is skew-symmetric in character. R is symmetric and also ­ ositive–semi-definite, i.e., p

RT =R ≥ 0

(23.78)

The skew symmetry matrix J(u) can be given as



J(u) = J0 + J1u

(23.79)

704  DC-DC Converters for Sustainable Applications where J0 and J1 are skew symmetry constant matrices which are specified in Equations (23.80) and (23.81)

 0    0    1  LC 1 1 J0 =   0    0    0  



0

−1 L1C1

0

0

0

0

0

−1 L 2C 2

0

0

0

0

0

0

0

1 L 2C 2

0

0

−1 L mC 2

0

0

0

1 L mC 2

0

−k JL m

0

0

0

k JL m

0

 0    0   J1 =  −1  LC  1 1 0   0  0 

0 0 −1 L 2C1 0 0 0

1 L1C1 1 L 2C1

0

0

0

0

0

0

0

0 0 0

0 0 0

0 0 0

 0    0    0   0  0   0 

         (23.80)         

(23.81)



The total stored energy of the system is prearranged as



1 H(x) = x T M x 2

where the matrix ‘M’ is given by

(23.82)

Passivity Based Control for DC-DC Converters  705



 L1   0  0 M=  0  0   0

0 L2 0 0 0 0

0 0 C1 0 0 0

0 0 0 C2 0 0

0 0 0 0 Lm 0

        

0 0 0 0 0 J

(23.83)

which is positive definite and constant. Thus, the average model of luo converter-fed DC motor is obtained. The ETEDPOF control law can be developed by replacing the necessary matrices in Equation (23.26) and it is specified as follows: (23.84)

u = u* + γ[v 1 i1* − v 1*i1 − v 1*i 2 + v 1 i *2 − E(i1 − i1* ) − E(i 2 − i *2 )]

In the present scenario, the dissipation matching condition is not satisfied strictly and the final dissipation matching matrix is given by: 2   E + x 3*   γ    L1   2   E + x 3*   γ   L1L2     −γ ( E + x 3* )( x1* + x 2* ) R =  L1C1   0   0    0  

−

 E + x 3*  γ  L1L2 

2

 E + x 3*  γ  L2 

2

γ ( E + x 3* )( x1* + x 2* ) L2C1

−

γ ( E + x 3* )( x1* + x 2* ) L1C1

0

0

0

−

γ ( E + x 3* )( x1* + x 2* ) L2C1

0

0

0

0

0

0

0 Rm L2m

0

 x* + x*  γ 1 2  C1 

2

0

0

0

0

0

0

0

0

0

0

0 B J2

         ≥0         

(23.85)

 is positive semi-definite whenever t ≥ 0, the control law (23.84) Since R makes the origin of error space an asymptotically stable equilibrium point by virtue of LaSalle’s theorem. Stability Proof of System: Error dynamics in the luo converter and first derivative of energy can be expressed as: T T ∂H(e)    ∂J(u)   ∂H(x*)     e = [J(u) − R] e + b+  ∂e    ∂u   ∂ x*    u

(23.86)

706  DC-DC Converters for Sustainable Applications



 = −  ∂H(e)  (R + b∨ γ b∨ T ) ∂H(e)  H(e)  ∂e   ∂e 

T



(23.87)

and it is calculated as

 = −{γ[(E + x *3 )e1 ]2 + γ[(E + x *3 ]2 e1e 2 − 2 γ[(E + x *3 )(x1* + x *2 )e1e3 ] H(e) + γ[(E + x *3 )]2 e1e 2 + γ[(E + x *3 )e 2 ]2 − γ[(E + x *3 )(x1* + x *2 )e 2e3 ] + γ[(x1* + x *2 )e3 ]2 + γR me5 + γBe6 }

(23.88)





 = 0 and e = e = e = e = e = 0 → e = 0. This indicates that when H(e) 1 2 3 5 6 4 LaSalle’s theorem is recognized and the origin of error space is globally asymptotically stable. Therefore, due to the bounded nature of control input between 0 and 1, the origin of error space is semi-globally asymptotically stable [15].

23.5 Sensitivity Analysis In power systems, power electronics, and control engineering, sensitivity analysis demonstrates an important role. Sensitivity is used in power systems to identify dominant parameters for slow oscillation generation [4]. More sensitivity provides better insights into the performance of the system that cannot be obtained from conventional simulation [16]. Sensitivity is used in power electronics to decide the variation of the state variable and steady-state determination [15]. In addition, sensitivity analysis effectively calculates the tolerance region between the actual characteristics and behavior acquired in a power electronic circuit through the design process. Sensitivity analysis is favored as a tool in the Posicast control of buck converters and in optimal control due to the above-mentioned benefits [4]. Sensitivity is used in the continuity of this control engineering application for the evaluation of various control techniques based on variations in parameters. Sensitivity can be used in discrete systems in addition to these applications to learn the local and global effects of discrete systems due to disturbances in sampling frequency on system performance [17] and in sampled systems. It can be concluded from the above that sensitivity analysis is an important tool used in a variety of fields, such as power systems, power electronics,

Passivity Based Control for DC-DC Converters  707 control engineering, etc. To date, sensitivity analysis is rarely used to identify the more sensitive variables used in the control law of ETEDPOF and the control law derived from ETEDPOF for fourth and sixth order systems is discussed in this section. For power converters, sensitivity analysis can be done by following the algorithm shown below. Step 1: Recognize the output variable. In the current scenario, it is the speed of the motor. Step 2: Recognize the state variables of the physical system. Step 3: Number of equations compulsory for analysis = (Order of the system)-1 Step 4: Acquire the relation between output variable and each state variable in the frequency domain. For a flat system, developed expressions are attained in terms of converter and motor parameters only. In contrast, for a partially flat system, expressions will be in requisites of control input in addition to converter and motor parameters. Step 5: Discover the gain margin and phase margin values for a range of values of load torque in the case of a flat system. For a partially flat system, margin values get hold of various values of load torque as well as various values of control input. Step 6: Sensitive variables can be recognized based on the margin values obtained through the aforementioned procedure and it is discussed in the following subsections.

23.5.1 Sensitivity Analysis of Buck Converter The order of the flat system here is four and three expressions are therefore developed, which are shown in Equations (23.89)-(23.91). The values of the gain margin and phase margin are intended for transfer functions obtained between ω(s)&iam(s), ω(s)&v(s), and ω(s)&i(s). From Equations (23.89)-(23.91) for the load torque variations and based on the machine specifications, both margins are obtained (Table 23.1). The negative margin values obtained for the inductor current are found to have gain and phase margin values that make that variable more sensitive [4, 17].



ω(s) =

i am (s) TL − a1s + a 2 k(a1s 2 + a 2s)

(23.89)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

∞

∞

∞

∞

∞

∞

∞

∞

∞

∞

∞

GM (dB)

19.7

18.8

17.8

16.9

15.9

14.9

13.9

12.9

11.9

10.9

9.88

PM (degrees)

GM—gain margin; PM—phase margin; dB—decibel.

% Load torque

S. no.

Armature voltage

∞

∞

∞

∞

∞

∞

∞

∞

∞

∞

∞

GM (dB)

90.3

90.3

90.3

90.2

90.2

90.2

90.2

90.2

90.2

90.1

90.1

PM (degrees)

Armature current

Table 23.1  Sensitivity analysis for ETEDPOF control of buck converter-fed DC motor.

−97.4

−97.4

−97.4

−97.4

−97.4

−97.4

−97.4

−97.4

−97.4

−97.4

−97.4

GM (dB)

−88.9

−88.9

−88.9

−88.9

−88.9

−88.9

−88.9

−88.9

−88.9

−88.9

−88.9

PM (degrees)

Inductor current

708  DC-DC Converters for Sustainable Applications

Passivity Based Control for DC-DC Converters  709

 R   TL m   k   v(s)   − ω(s) =  2   3 2  a 3s + a 4 s + a 5   a 3s + a 4 s + a 5 s 

(23.90)

   1 TL     i(s)   k − ω(s) =  3   2 4 3 2  a 6 s + a 7 s + a 8 s + a 2   a 6 s + a 7 s + a 8 s + a 2 s 

(23.91)



where

J B JL  BR m  BL m + JR m   + k ;  ; a2 = ; a3 = m ; a4 = ; a5 =     k k k k k J CJL m  CBR m  BL m + JR m  + Ck + . ;a 7 = C ; a8 = a6 =    k k k k

a1 =

The above examination and expression (23.9) show that the inductor current is more sensitive than other variables and that this sensitive variable is inherently selected as a control variable in the ETEDPOF method [21].

23.5.2 Sensitivity Analysis of Boost Converter For a flat system, previous sensitivity analysis is performed, whereas it is complicated for a fourth-order partially flat boost converter with dynamic load. For a partially flat system [40], both gain and phase margin values are derived from the expressions (23.92)-(23.94) that are linked to input and load torque control, whereas for a flat system referred to earlier, only load torque is associated. For the specifications of the machine, margin values are calculated along with load and controller input variations (u). It is clear from the margin values obtained from the equations below that the sensitive variable [17] is the inductor current shown in Figure 23.7.



ω(s) =



(23.92)

i am (s) TL − a 4bs + a 5b ks(a 4bs + a 5b )

(23.93)

ω(s) =

ω(s) =

v(s) R m TL − 2 a1bs + a 2bs + a 3b ks(a1bs + a 2bs + a 3b ) 2

i(s) TL − 2 3 (a 6bs + a 7bs + a 8bs + a 9b ) k(1 − u)s(a 6bs + a 7bs 2 + a 8bs + a 9b ) 3

(23.94)

710  DC-DC Converters for Sustainable Applications (b)

PHASE MARGIN vs TL and u

GAIN MARGIN vs TL and u 0

0

Gain margin (dB)

Phase margin (degrees)

(a)

-20 -40 -60 -80

-100 0

20

10 15 20 0 Load torque (counts) Control input (counts) 5

10

-10 -20 -30 -40 -50 0

15 20 15 20 0 5 10 Load torque (counts) Control input (counts) 5

10

Figure 23.7  Margin plots for ω(s) vs i(s): (a) phase margin; (b) gain margin.

where

JL m BL + R m J BR m J B + k; a 4b = ; a 5b = ; ; a 2b = m ; a 3b = k k k k k  CJL m   CBL m + CJR m   CBR m J  + ; a 6b =  a 7b =  ; a 8b =     k(1 − u)    (1 − u)k k  k(1 − u) 

a1b =

 B  a 9b =  .  (1 − u)k  23.5.3 Sensitivity Analysis of a Luo Converter The method can be accepted for a sixth order partially flat luo converter [21] with dynamic loads, similar to a partial flat boost converter and the expressions are observed in (23.95)—(23.99). Converter voltage ‘v1’ and current ‘i1′ vary with load, as well as controller input, among those provisions while other parameters diverge with load only:



Speed ω(s) =

Speed ω(s) =

v(s) R m TL − (23.95) 2 a18 s + a19 s + a 20 ks(a18 s + a19 s + a 20 ) 2

Speed ω(s) =

i am (s) TL − a 21s + a 22 ks(a 21s + a 22 )

(23.96)

i 2 (s) TL − 2 3 (a 23s + a 24 s + a 25 s + a 26 ) ks(a 23s + a 24 s 2 + a 25 s + a 26 ) 3

(23.97)

Passivity Based Control for DC-DC Converters  711

v 1 (s) (a 27 s + a 28 s + a 29 s 2 + a 30 s + a 31 ) TL − 4 3 kus(a 27 s + a 28s + a 29s 2 + a 30 s + a 31 )

Speed ω(s) =

4

3

i1 (s) (a 32 s + a 33s + a 34 s3 + a 35 s 2 + a 36 s + a 37 ) TL u − 5 4 k(1 − u)s(a 32 s + a 33s + a 34 s3 + a 35 s 2 + a 36 s + a 37 )

Speed ω(s) =

5

(23.98)

4

(23.99)

where

JL m BL + R m J BR m J B + k; a 21 = ; a 22 = a 26 = ; ; a19 = m ; a 20 = k k k k k L CJ BL C +  R m JC 2  a 23 = m 2 ; a 24 = m 2 k k 2 BR mC 2 + k C 2 + J LL CJ a 25 = ; a 27 = 2 m 2 ; k ku* L (BL mC 2 +  R m JC 2 ) L (BR mC 2 + k 2C 2 + J) + L m J a 28 = 2 ; a 29 = 2 ; ku* ku* BL + BL m + JR m 1  BR m L JL C C  + k ; a 32 = 2 m 1 2 a 30 = 2 ; a 31 =   ku* u* k ku*(1 − u*) L C (BL m C 2 + R m JC 2 ) ; a 33 = 2 1 ku*(1 − u*) a18 =

 L C (BR m C 2 + k 2C 2 + B L m + R m J + J) + JL m  a 34 =  2 1  ku*(1 − u*)    L C J  u*   + m 2  ku  1 − u*   L C B + (BL m + J R m ) u*(BL m C 2 +  R m JC 2 ) + a 35 = 2 1 ;  ku*(1 − u*) k(1 − u*)  BR m + k 2   u*(BR mC 2 + R 1k 2C 2 +  J)  C1   +    ;  u*(1 − u*)  k k(1 − u*) L B u* u* T + a 37 = k 1 − u* 1 − u* k a 36 =

712  DC-DC Converters for Sustainable Applications

60 40 20 0 -20 15

(b)

Gain margin-Inductor current i1

0 2 4 6 8 0 10 Load torque (counts) Control input(counts) 10

5

Phase margin (degrees)

Gain margin (dB)

(a)

80 60 40 20 0 -20 15

Phase margin (Inductor current-i1)

12 8 10 4 6 2 0 0 Load torque (counts) Control input (counts) 10

5

Figure 23.8  Frequency response of inductor current (i1): (a) gain margin; (b) phase margin.

(b)

Gain margin (Capacitor voltage-v1) 40 30 20 10 0 15

10

5

4

6

8

10 12

Phase margin (degrees)

Gain margin(dB)

(a)

0 0 2 Load torque (counts) Control input (counts)

Phase margin (Capacitor voltage-v1) 200 100 0 -100 -200 15

10

5

Load torque (counts)

2

4

6

8

10 12

0 0 Control input (counts)

Figure 23.9  Frequency response of capacitor voltage (v1): (a) gain margin; (b) phase margin.

Gain margin (Inductor current- i2) 5 0 -5 -10 -15 15

10

5

Load torque (counts)

0 0

5

10

Phase margin (Inductor current-i2)

(b)

15

Control input(counts)

Phase margin(degrees)

Gian margin (dB)

(a)

20 0 -20 -40 -60 -80 15

10

5

4

6

8

10 12

0 0 2 Load torque (counts) Control input (counts)

Figure 23.10  Frequency response of inductor current (i2): (a) gain margin; (b) phase margin.

Passivity Based Control for DC-DC Converters  713 From the investigation made above, it is accomplished that capacitor voltage (v1), inductor current (i1), and inductor current (i2) are considered as more sensitive variables and these variables are essentially used in ETEDPOF implementation [4]. Frequency response of various parameters are shown in Figures 23.8, 23.9 and 23.10. Therefore, in the cases of fourth-order and sixth-order systems, the sensitivity analysis carried out signifies the sensitive variables.

23.6 Reference Profile Generation 23.6.1 Boost Converter Fed DC Motor The control law of a DC motor as observed in Equation (23.65) needs three reference variables, these are current, voltage, and control input reference. Since we approximate the speed of the system, the voltage and current equations are condensed to the following equations in terms of speed. The dynamic variation in speed is measured as we develop the control law by means of ETEDPOF method [5]. The derivative terms cancels in case of ESEDPOF method as we deal with static error of the system in this method.

L R m  *(t) + a 2ω *(t) + a 3ω *(t) + T v*(t) = a1ω k



i am * (t) = a 4ω *(t) + a 5ω *(t) +



L T k

(23.100)

(23.101)

where



a1 =

JL m BL + R m J BR m J B ; a2 = m ; a3 = + k; a 4 = ; a 5 = ; k k k k k

A fifth order Bezier polynomial is used for identifying the speed profile using the current and voltage trajectory. The polynomial for this system is given as,



ω*(t) = ωini for t < tini; ω*(t) = ωfin for t > tfin; ω*(t) = ωini + [Δ3 − 15Δ4 + 6Δ5](ωfin – ωini) else

(23.102)

714  DC-DC Converters for Sustainable Applications with ∆ =

t − t ini . At static conditions, (23.3) and (23.4) become t fin − t ini

ˆR R B T v =  m  + k  ω + L m  K  K



i am =



 B T ω+ L k k

(23.103)

(23.104)

Using (23.38) and (23.39), we could parameterize inductor current to obtain (23.41)

1 1 HB (t) = L(i*(t))2 + C(v*(t))2 2 2



1 (2HB *(t) − C(v*(t))2  ) L

i*(t) =



(23.105)

(23.106)

HB *(t) attained using the Bezier polynomial is given by: HB *(t) = HBinitial for t t ; fin

3 4 5 * H = B (t ) H Binitial + (H Bfinal − H Binitial )[∆ − 15∆ + 6∆ ] For other values of � t



(23.107)

where 2



1  i amini v ini  1 HBinitial = L  + Cv ini 2  2  E  2



1  i amfin v fin  1 + Cv fin 2 HBfinal = L   2  E  2

(23.108)

2



v ini =

R   BR m  + k ω ini + m T L  k  k

(23.109)

(23.110)



Passivity Based Control for DC-DC Converters  715

i amini =









v fin =

 B T ω ini + L k k

R   BR m  + k ω fin + m T L  k  k i amfin =

 B T ω fin + L k km

(23.111)

(23.112)

(23.113)

The desired control input is given by:

1  1 − u*(t) = [Cv*(t) + i am *(t)] i*

(23.114)

23.6.2 Luo Converter Fed DC Motor In order to extend the developed feedback law, the generation of voltage and current references for the Luo converter circuit is required, i.e., v1*(t), i2*(t) and i1*(t). In order to understand a smooth starter, reference trajectories must be calculated in terms of speed and load torque. Reference trajectories can be deliberated easily for the differentially flat system. The relative grade of the system is 3 for the Luo converter-fed DC motor and it is a non-flat system. By incessantly differentiating the output variable, users can obtain a relative degree until the control input is reached [15]. In the third step, in the Luo converter with dynamic load, the control input is achieved and thus the relative degree becomes three. The relative degree is therefore not equal to the order of the system, which is equal to six. The system is thought to be a non-flat system because of this fact. The subsequent reference trajectories for v1*(t), u*, and i1*(t) are created from the elementary working principle of the Luo converter which is described below. Figures 23.11 and 23.12 show workings of the Luo converter during the switch in turned on and off conditions. Variations in the i1 and i2 inductor currents are insignificant during high-frequency operation. Inductor current profile i1 is achieved by equating the amount of charge in the capacitor when the switch is on (Figure 23.11) and off (Figure 23.12). It is possible to express the charge balance equation according to Faraday as:

716  DC-DC Converters for Sustainable Applications L2

+ v1C1

S (ON)

i2

i1

E

L1

iD

iam

+

C2

M

v2

Figure 23.11  Converter status when switch is on (field circuit of motor is omitted). L2

C1

S (OFF)

i2 iam

+ v1

E

i1

L1

iD

C2

+

M

v2

Figure 23.12  Converter status when switch is off (motor field circuit is omitted).

(Charge during switch off condition)Q+ = Q-(Charge during switch on condition) (23.115) (1-u)*T*i1= u*T*i2

(23.116)

where “T” symbolize the time period for one switching. From (23.116), the reference profile for i1 is given by



i1* =

u* * i2 1 − u*

(23.117)

Passivity Based Control for DC-DC Converters  717 Since capacitor C2 performs as a low-pass filter, the load current iload = i2. Therefore,

i1* =



u* * i load 1 − u*

(23.118)

Source current is given by isource = i1 + i2 when the switch is on and it is equal to zero when the switch is off. Thus, the average source current (isourcea) is presented in Equation (23.120):



u   i sourcea = i source = i1 + i1 = i1  1− u 



(23.119)

Hence, the load current is given by



i am =

u i1 1− u

(23.120)

v2 =

u E 1− u

(23.121)

and the output voltage is



when the switch is on, inductor current i1 increases and is excited by a potential difference, E. Gradually, current i1 decreases when the switch is off. Therefore,

uTE=(1-u)Tv1

v 1* =

u* E = v *2 1 − u*

(23.122) (23.123)

Hence, variations in capacitor voltages are equal, i.e.,



v 1* = v *2

(23.124)

718  DC-DC Converters for Sustainable Applications From this, it can be found that, for a given voltage profile v *2 , v 1* will follow v *2 . Hence, the control input, inductor current i1, and other profiles are expressed as:

v *2 E + v *2

(23.125)

u* * i2 1 − u*

(23.126)

u* =



i1* =

v *2 =

L LmJ (BL m + R m J) BR m + k 2 RmT  * + ω ω * + ω* + k k k k

L mC 2 J (BL mC 2 + R m JC 2 ) BR mC 2 + k 2C 2 + J * +  * + ω ω ω * k k k  T B + ω* + L k k 

(23.127)

i 2* =



v 1* = v *2

(23.128)

(23.129)

For the generation of reference trajectories of the Luo converter voltage v 2 * and inductor current i 2 *, differential parameterizations in the expressions of the given angular velocity and the approximate load torque are carried out and the equations are given in (23.127) and (23.128). To describe the trajectory, the Bezier polynomial of the fifth order is used. Therefore, the trajectories of the given velocity profile and its equivalent current and voltage profiles have been obtained in this section. These reference values are used under a variety of loading conditions for sensor-less operation of a Luo converter-fed DC motor. In order to modernize the value of the load torque under closed-loop operation, the evaluation of the load torque is essential and this method is explained in the next section. The estimation of load torque is necessary for the speed control of DC motors under various load conditions. The space constraint limits the use of a torque sensor and is therefore more cost-effective for the observer scheme [17].

Passivity Based Control for DC-DC Converters  719

23.7 Load Torque Estimation In the speed control of electric motors when operated under loaded conditions, load torque estimation is crucial. The torque of the load can be obtained using torque sensors [18]. As it should be mounted on the shaft of  the motor, the torque sensor is not preferred and is also costly. To estimate the load torque applied to the motor, observers are therefore employed. The benefits for observers are: 1) Better accuracy 2) Less expensive to produce 3) More reliable than sensed signals 4) It provides an inviting alternative for designers to add new sensors or upgrade existing ones Hence, an observer can be used for the load torque estimation. Based on order of the system, the observers are of two types: full-order and reduced-order observers. If the order of the observer is equal to the system order, then it is known as a full-order observer, otherwise it is known as a reduced-order observer [19]. As a reduced order observer uses a smaller number of states, it is preferred and it is developed for electrical machines.

23.7.1 Reduced-Order Observer for Load Torque Estimation A Reduced-Order Observer (ROO) approach for the load torque approximation of the DC motor [9, 19] was proposed by Linares-Flores et al. (2012). Using the calculated speed and armature current, the load torque from the mechanical model of the DC motor is obtained as:



dξ = −λξ + λkiam (t ) + λ(λJ − B)ω dt

(23.130)

Setting ξ = τL + λωJ, τL = ξ − λωJ. Clearly, for λ ≫ 0, the observation error e τL , where e τL = τL − τL , exponentially congregates to zero. Implementation of ROO is shown in Figure 23.14. Here, ROO can be chosen by connecting switch ‘S’ to the speed

720  DC-DC Converters for Sustainable Applications signal. Considering the speed, armature current deliberated from the DC motor, tuning gain λ, and the motor parameters J, k, B, Rm, Lm, the expression for ROO is realized in Equation (23.130). This estimated load torque ˆL is employed in ETEDPOF implementation along with other feedback T signals received from the power converter. In Figure 23.14, the ROO scheme with a speed sensor is explained in detail. The speed sensor requires mounting space and this will amplify the hardware circuit’s complexity [18]. ROO is implemented without a speed sensor to avoid this impenetrability and this system is well-known as the Sensorless Reduced Order Observer (SROO) approach, which is explained in the next sub-section.

23.7.2 SROO Approach for Load Torque Estimation Equation (23.130) specifies the ROO approach for estimating load torque using armature current and speed as feedback variables [20]. If a speed sensor is not utilized in the approach, the scheme can be expressed as an SROO approach. Due to all these merits, a sensorless scheme is favored in this chapter. A Sensorless Reduced Order Observer (SROO) based estimation of load torque is established in Equation (23.131) and this scheme diam (t )   in is projected by replacing speed ‘ω’ by v(t ) − Rmiam (t ) − Lm dt   Equation (23.130). The resultant expression is: k

dξ = − λξ + λ kiam (t ) + dt

di (t ) λ (λ J − B) v(t ) − Rmiam (t ) − Lm am  dt   k (23.131)

SROO can be executed by connecting the switch ‘S’ to the armature voltage sensed from the DC motor (Figure 23.13). Figure 23.14 corresponds to the MATLAB implementation of SROO. For SROO, the convergence rate will vary based on the value of λ. However, for a high value of λ, the estimation will turn out to be unstable. Hence, it is observed that SROO could not approximate load torque quickly. This demerit of SROO leads to instability at high values of tuning gain. To keep away from these difficulties and tuning prerequisites, an online algebraic approach has been proposed by Jesús Linares-Flores et al. (2010) for load torque estimation [20].

Passivity Based Control for DC-DC Converters  721 Speed profile Load torque Power Converter

Controller

Speed

DC motor

Feedback signals from converter

λ, Rm, Lm, J, k, B

v iam

Reduced Order Observer

TL

S

Figure 23.13  ETEDPOF implementation with ROO/SROO. 1 In_λ

2 In_iam

×

k Rm

ω

B

–

3 In_v

d dt

Lm

–

+ _

× ×

k-1

+ ω

_

×

∫

+_

Out-τL 1

+

× J

Figure 23.14  Implementation of SROO.

23.7.3 Load Torque Estimation Using Online Algebraic Approach The necessary variation between the online algebraic approach and the conventional parameter estimation techniques lies in the fact that a valid dynamic parameter estimation formula is developed on the basis of an electromechanical model which, in terms of measured in-situ signals, is instantly exploitable or calculated. The parameter is frequently estimated in a very small amount of time in the online algebraic approach; its numerical result is refurbished to the controller expression whenever necessary. The penalty for long-term or short-time errors happening during the

722  DC-DC Converters for Sustainable Applications estimation of the parameter formula or computational rearrangement in the interval are imagined to be taken care of by the controller as if, during this small time interval, a feedback loop had disturbances occur. The online algebraic estimation technique is used for load torque estimation due to the merits stated above and can be achieved from the mechanical model of DC motor, which can be expressed as: τL =

2 (t − t i )2

 J 

t

t

∫ ω(τ)dτ − J(t − t )ω(t) + k ∫ (t − t ) i  i

ti

ti

i

am

(τ)d τ − B

t



∫ (t − t )ω(τ)dτ  i

ti

(23.132)

Load torque values are determined based on the constraints pointed out below:

n(t) τˆ L = τˆ L (t i − ) for t [t i , t i + δ]; for t > t i + δ d(t)



t  t n(t) = 2  J ω(τ)d τ − J(t − t i )ω(t) + k (t − t i )i am (τ)d τ − B ti  ti t t  k (t − t i )i am (τ)d τ − B (t − t i )ω(τ)d τ  ; d(t) = (t – ti)2 And ti = ksT, ks = 0,1,2, ……., T ≫ δ ti ti  where δ is reset time. The implementation of the online algebraic approach is explained in Figure 23.15. OAA needs time to renew the load torque (ti) and reset time

∫

With

∫

∫

∫

Speed profile Load torque Power Converter

Controller

DC motor

Feedback signals from converter

iam

v

Reset J, k,B, Rm, Lm, ti

TL

Speed

Online Algebraic Approach

Figure 23.15  ETEDPOF implementation with OAA/SAA.

S

t

∫ (t − t )ω(τ)d ti

i

Passivity Based Control for DC-DC Converters  723 to eradicate past errors in assessment with ROO. As a consequence, it becomes quicker to estimate. For the DC drive system, OAA may therefore be preferred. The load torque was estimated in this work with a decrease in the number of sensors being evaluated with a system based on a reduced order observer [18]. It can however be understood that load torque can be estimated without a speed sensor and therefore, for OAA, this scheme is selected. In the coming subsection [9], this Sensorless Online Algebraic Approach (SAA) is discussed.

23.7.4 Sensorless Online Algebraic Approach (SAA) for Load Torque Estimation The estimated load torque using the online algebraic approach commencing the fundamental model of the DC motor with a speed sensor for a boost rectifier fed DC motor is cost effective [9]. Therefore, the present sensorless scheme is an enhanced method of the work done by the earlier researchers. diam (t )   For sensorless mode, substituting speed ‘ω’ by v(t ) − Rmiam (t ) − Lm dt   k in Equation (23.131), we get the expression in Equation (23.133), which is τL =

2  J (t − t i )2 

t

di am (t)   1    v(t) − R mi am (t) − L m dτ dt   ti  k 

∫

di (t)   1  − J(t − t i )   v(t) − R mi am (t) − L m am   + k dt   k  B

∫ (t − t )i

di (t)    1  (t − t i )   v(t) − R mi am (t) − L m am   dt  dt    ti k 

∫

t

t

ti

i

am

(τ)d τ − (23.133)





Figure 23.16 shows the approximation of load torque by means of SAA in which sensorless mode is selected as an alternative of speed by connecting switch “S” to armature voltage. The need to update the estimated load torque for every fraction of a second is highlighted by further SAA estimates. As a result, past torque values are omitted and it turns out that the reaction time for the torque estimation is instantaneous. Figure 23.16 illustrates the MATLAB implementation of SAA in which the armature voltage and the armature current are operated as feedback

724  DC-DC Converters for Sustainable Applications 1 in_iam

2k

× X0

(t-tini)

+

∫

+

_ clock

reset

tini

2J

Rm _ Lm

d dt

ω

X0

_ +

k

-1

∫

+

reset

× ÷

outτL

in_v 2 B clock

×

∫

X0

(t-tini)

+

1

_

_ reset

tini 2J

_

× ×

Figure 23.16  Implementation of SAA.

variables. The reset time is selected to be 0.03 seconds. For each rising edge of the counter, resetting is completed. The characteristics of SROO and SAA were examined in a meticulous way. With a system order of four, i.e., buck converter-fed DC motor drive systems [19], SROO and SAA are implemented equally in flat converters.

23.8 Applications of PBC In many physical systems, PBC is an extensively used method of control. The commonly implemented PBC method is the ESDI method and has a

Passivity Based Control for DC-DC Converters  725

PBC

ETEDPOF

ESDI

Fexible Manipulators

Transient stability in grid

DC motor system

Figure 23.17  Applications of PBC in electrical systems.

DC motor system

ESEDPOF

DC-DC Converters

DC motor system with solar power

IDA-PBC

DC-DC Converters

Power system stability

726  DC-DC Converters for Sustainable Applications wide range of applications [21] and it is shown in Figure 23.17. To control the position of robot manipulators, the ESDI method is used. The regulation problem of manipulators in this section is that the output variable may differ from the joint position. This is corrected by the Jacobian transpose control that depicts the closed loop system’s set of equilibrium and asymptotically stable equilibrium. Thus, the system’s local stability is achieved [22]. Transient stability is a big concern in power systems. Improvement of transient stability is mentioned by means of the PBC method [23]. The authors have derived a transient energy function in the prescribed paper that takes into account the physical properties of the power system. The energy variation is captured by the energy function desired. In order to recover stability, the developed controller mechanically injects damping. For DC-DC converter fed wind power generation, any PBC method can be used where motor operation is based on system requirements [24]. For disturbance rejection, the ESDI method is preferred, while the ETEDPOF method is used for exact output tracking and the ESEDPOF method is appropriate for static error compensation [25]. The estimation of sensor-­ less load torque by means of the ETEDPOF method has been demonstrated experimentally. The author used the LaSalle theorem to calculate the stability of the DC motor supplied by the buck converter. In [26–28], passivity based control is implemented in a DC motor with load torque estimation to enhance the current controller performance of the machine. The switching and control of passivity is discussed in detail in [29] and [30]. In addition, different nonlinear control techniques were compared to a passivity-based control technique. Passivity-based controllers can monitor the flow of active and reactive power in grid-connected systems [31– 33]. [34] discusses the efficiency of passivity-based control when operating an induction machine with adaptive observers. The use of the energy principle to control power electronic converters in the grid system reduces grid system losses. Microgrids are the future of electrical power systems. The power generated by various means is fed to the nearby consumers. DC and AC microgrids have been analyzed using passivity based control in [35–39]. This control can be used to assess the grid’s stability. Passivitybased regulation in spacecraft is the focus of recent research [40].

23.9 Conclusion The control of DC drives using passivity based control is discussed in this chapter. Control based on passivity is an energy-based method of control. The condition for passivity by means of the Lyapunov stability equation

Passivity Based Control for DC-DC Converters  727 should be convinced by the system here. The sum of stored and dissipated energy will be the total energy in a passive system. The real system is purchased in the desired state by adding a damping factor to control the dissipated energy. A general procedure is explained for deriving the control law using control based on passivity. It explains from scratch the reference generation and control law generation of passivity-based control for DC drives. To verify the generated control law for the system, the sensitivity analysis results of the buck converter, boost converter, and luo converter fed DC motor are obtained and discussed. Sensitivity analysis of buck, boost, and luo converters fed to the DC motor was performed in this chapter. For research, frequency response analysis is used. We come to the following conclusions and infer certain points from the sensitivity analysis carried out such as: a. The inductor current is believed to be a sensitive variable in a buck converter with an online variable load. b. ETEDPOF is evaluated using MATLAB in the aforementioned system to substantiate the nature of the sensitivity. The results verify ETEDPOF’s supremacy against a range of speed references and different load torque conditions. c. The current flow through the input inductor and the voltage across the load are determined as sensitive in a boost converter. d. The capacitor voltage (v1) or capacitor voltages (v2), inductor current (i1), and inductor current (i2) are measured as more sensitive variables in a luo converter. Two reduced order observers were measured in the buck converter fed DC motor system. SAA and SROO are two load torque estimation techniques examined in this chapter. Using different load torques, they were inspected. It is monitored based on the theoretical results that SAA performs better than SROO. This is because of the facts below: a. Any arbitrary value can be set to the initial condition value of the load torque by choosing the reset time. Past measured torque values are omitted and at each reset time the current values are restructured. b. SAA also doesn’t have tuning involved. Without any reconfiguration to any drive system, this SAA can be used.

728  DC-DC Converters for Sustainable Applications It can therefore be concluded that SAA can estimate any type of load torque in a differentially flat system of the fourth order, buck converter-fed DC motor. The system is converted into a cost-effective system due to the lack of speed and torque sensors. This approach is extended to boost the fed DC motor systems of converters and luo converters.

References 1. N. Mohan, T. M. Undeland, and W. P. Robbins, Power Electronics, Converters, Applications, and Design, 3rd ed. New York: Wiley, 2003. 2. Ortega R, Loria A, Nicklasson H, Sira-Ramirez H, “Passivity based control of Euler-Lagrange systems: Mechanical, electrical & electromechanical applications”, Springer, London; 1998. 3. Sira-Ramirez, H.J.; Silva-Ortigoza, R.Control Design Techniques in Power Electronics Devices; Springer: London, UK, 2006. 4. GK Srinivasan, HT Srinivasan, M Rivera, “Low-Cost Implementation of Passivity-Based Control and Estimation of Load Torque for a Luo Converter with Dynamic Load”, Electronics 9(11), 2020. 5. S. Ganesh Kumar and S. Hosimin Thilagar, “Sensorless Load Torque Estimation and Passivity Based Control of Buck Converter Fed DC Motor”, in Scientific World Journal, Hindawi Publishing Corporation, Vol. 2015, pp. 15, Feb. 2016. 6. V. K. A. Rajeev, M. Rivera and S. G. Kumar, “Investigation on passivity based control for electrical applications,” 2017 CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies (CHILECON), Pucon, pp. 1-6, 2017. 7. Romeo Ortega, Iven Mareels, “Energy-Balancing Passivity-Based Control,” in Proceedings of the American Control Conference Chicago, Illinois, June 2000. 8. J. Linares-Flores and H. Sira-Ramírez, “DC motor velocity control through a DC-to-DC power converter,” in Proceeding of 43rd IEEE Conference on Decision and Control, pp. 5297-5302, 2004. 9. Jesus Linares-Flores, Hebertt Sira-Ramirez, Edel F. Cuevas-Lopez and Marco A. Contreras-Ordaz, “Sensorless Passivity Based Control of a DC Motor via a Solar Powered Sepic Converter-Full Bridge Combination,” in Journal of Power Electronics, August 2011. 10. Kumar, S.G.; Thilagar, S.H. Soft Sensing of Speed in Load Torque Estimation for Boost Converter Fed DC Motor. In Proceedings of the 39th Annual Conference of the IEEE Industrial Electronics Society, Vienna, Austria, 10–14 November 2013; pp. 3758–3763. 11. Romeo Ortega, Arjan J van der Schaft, Iven Mareels, Bernhard Maschke, “Putting energy back in control”, IEEE Control System Magazine, Pp.18-33, 2001.

Passivity Based Control for DC-DC Converters  729 12. Romeo Ortega, Arjan J van der Schaft, Iven Mareels, Bernhard Maschke, “Energy shaping revisited” Proceedings of IEEE on International Conference on Control Applications, pp.121-126, 2000. 13. Ganesh Kumar S, Hosimin Thilagar S. Implementation of passivity based controller for buck converter. European Journal of Scientific Research. 2013;94(3):405-413. 14. Jesús Linares-Flores, Jorge L. Barahona-Avalos, Hebertt Sira-Ramírez, and Marco A. Contreras-Ordaz, “Robust Passivity-Based Control of a Buck– Boost-Converter/DC-Motor System: An Active Disturbance Rejection Approach,” in IEEE Transactions on Industry Applications, Vol. 48, No. 6, Nov./Dec. 2012. 15. Ganesh Kumar S, Hosimin Thilagar S. Passivity based control of luo converter. Journal of Electrical Engineering. 2013;13(1):159-166. 16. H. Sira-Ramírez and S. K. Agrawal, “Differentially Flat Systems,” New York, USA: Marcel Dekker, 2004. 17. GK Srinivasan, HT Srinivasan, M Rivera, “Sensitivity Analysis of Exact Tracking Error Dynamics Passive Output Control for a Flat/Partially Flat Converter Systems”, Electronics 9(11), 2020. 18. Ganesh Kumar S, Hosimin Thilagar S. Sensorless load torque estimation and passivity based control of buck converter fed DC motor. The Scientific World Journal. 2015;15. 19. Ganesh Kumar S, Hosimin Thilagar S. Load torque estimation and passivity based control of buck converter. The Mediterranean Journal of Measurement and Control, Published by SOFT MOTOR. 2013;9(2):51-57. 20. Linares-Flores, J.; Sira-Ramírez, H.; Yescas, E.; Sanjuan, J.J.V. A Comparison Between the Algebraic and the Reduced Order Observer Approaches for on-Line Load Torque Estimation in a Unit Power Factor Rectifier-DC Motor System. Asian J. Control vol.14, pp.45–57, 2010. 21. A. Tofighi and M. Kalantar, “Power management of PV/battery hybrid power source via passivity-based control,” Renewable Energy, vol. 36, no. 9, pp. 2440–2450, 2011. 22. R. Kelly, “Regulation of Manipulators in Generic Task Space: An Energy Shaping Plus Damping Injection Approach,” in IEEE Transactions On Robotics And Automation, Vol. 15, No. 2, April 1999. 23. Monesha S, Kumar SG, Rivera M. Methodologies of energy management and control in microgrid. In IEEE Latin America Transactions. 2018;16(9):2345-2353. 24. Kim, S.-K. “Passivity-Based Robust Output Voltage Tracking Control of DC/ DC Boost Converter for Wind Power Systems” Energies, 11, 1469,2018. 25. Feng, Q.; Nelms, R.; Hung, J. Posicast-Based Digital Control of the Buck Converter. IEEE Trans. Ind. Electron., vol.53, pp.759–767, 2006. 26. Albrecht Gensior, Hebertt Sira-Ramírez, Joachim Rudolph, Henry Güldner, “On some nonlinear current controllers for three-phase rectifiers” IEEE Transactions on Industrial Electronics, vol. 56(2), pp.360-370, 2009.

730  DC-DC Converters for Sustainable Applications 27. Barkan Ugurlu, Masayoshi Nishimura, Kazuyuki Hyodo, Michihiro Kawanishi, Tatsuo Narikiyo, “A framework for sensorless torque estimation and control in wearable exoskeletons”, Proceedings of 12th IEEE International Workshop on Advanced Motion Control, pp.1-7, 2012. 28. Campos-Delgado DU, Palacios E, Espinoza Trejo DR, “Passivity based control of nonlinear DC motors configurations and sensor less applications”, Proceedings of IEEE, pp.3379-3384, 2007. 29. Daniel Liberzon, “Switching in systems and control”, Birkhauser, Boston, 2003. 30. Escobar G, Ortega R, Sira Ramirez H, Vilain JP, Zein I, “An experimental comparison of several nonlinear controllers for power converters”, Proceedings of IEEE, pp.66-82, 1999. 31. George Ellis, “Observers in control systems – A practical guide”, Academic Press, 2002. 32. Hebertt Sira-Ramírez, Ramón Silva-Ortigoza, “Control design techniques in power electronics devices”, Springer, London, 2006. 33. Patrone M, Feroldi D, “Passivity-based control design for a grid-connected hybrid generation system integrated with the energy management strategy”, Journal of Process Control, vol.74, pp.99-109, 2019. 34. Ramzi Salim, Abdellah Mansouri, Azeddine Bendiabdellah, Sofyane Chekroun, Mokhtar Touam, “Sensorless passivity based control for induction motor via an adaptive observer”, ISA Transactions, vol.84, pp.118-127, 2019. 35. Yonghao Gui, Baoze Wei, Mingshen Li, Josep M. Guerrero, Juan C. Vasquez, “Passivity-based coordinated control for islanded AC microgrid”, Applied Energy, vol.229, pp.551-561, 2018. 36. Hans F, Schumacher W, Chou S, Wang X, “Passivation of current-controlled grid-connected VSCs using passivity indices”, IEEE Transactions on Industrial Electronics, vol.66(11), pp.8971-8980, 2019. 37. Montoya OD, Gil-González W, Garces A, “Control for EESS in three-phase microgrids under time-domain reference frame via PBC theory”, IEEE Transactions on Circuits and Systems II: Express Briefs, vol.66(12), pp.20072011, 2019. 38. Hassan MA, Li E, Li X, Li T, Duan C, Chi S, “Adaptive passivity-based control of Dc–Dc buck power converter with constant power load in DC Microgrid Systems”, IEEE Journal of Emerging and Selected Topics in Power Electronics, vol.7(3), pp.2029-2040, 2019. 39. Spanias C, Lestas I, “A system reference frame approach for stability analysis and control of power grids”, IEEE Transactions on Power Systems, vol.34(2), pp.1105-1115, 2019. 40. Ti Chen, Jinjun Shan, Hao Wen, “Distributed passivity-based control for multiple flexible spacecraft with attitude-only measurements”, Aerospace Science and Technology, vol.94, no.105408, 2019.

24 Modeling, Analysis, and Design of a Fuzzy Logic Controller for Sustainable System Using MATLAB T. Deepa*, D. Subbulekshmi and S. Angalaeswari SELECT, VIT, Chennai, India

Abstract

Designing a controller for a multi-variable system is very difficult task. In this chapter, the distillation column of a Multi Input Multi Output (MIMO) system with delay elements is used for analysis. The MATLAB tool is used for analyzing the wood and berry distillation column. Various steps involved for finding the stability of the wood and berry distillation column are discussed here. Also, design of a PID Controller and Fuzzy Logic Controller (FLC) for an MIMO system using MATLAB/Simulink is presented. First, find the transfer function of the system. This system transfer function has the delayed element, so Pade approximation is used for determining the transfer function and to find the poles and zeros of the MIMO system, then to determine the feedback gain matrix using pole placement technique. The Singular Value Decomposition (SVD) and Relative Gain Array (RGA) of the MIMO system are also very challenging. The PID parameters are optimized using various optimization techniques. How to design an FLC for a proposed system is developed. In this chapter, using a MATLAB tool is used to find the SVD and RGA techniques. By using frequency domain analysis (Nyquist stability), the behavior and stability of the system is determined. Using Fuzzy block in MATLAB/Simulink, the fuzzy logic controller is designed for the proposed system. Keywords:  MIMO system, PID controller, optimization techniques, pade approximation, SVD, RGA

*Corresponding author: [email protected] S. Ganesh Kumar, Marco Rivera Abarca and S. K. Patnaik (eds.) Power Converters, Drives and Controls for Sustainable Operations, (731–748) © 2023 Scrivener Publishing LLC

731

732  DC-DC Converters for Sustainable Applications

24.1 Introduction The majority of industrial plants in nature are multivariable. There are several output variables to be managed and outputs are often coupled with more than one input variable. Processes with the same number of inputs and outputs are known as square systems, while input and output processes are known as non-square systems. The interaction between the loops allows the manipulated variable to influence more than one controlled variable and thus it is difficult to obtain the mathematical model and develop the MIMO process control scheme. Load disruptions occur during operations, which can result in the configuration of the change control requiring measurement of the measure/ dynamic RGA interaction. The loop where the load disturbances push the device away from its desired behavior is called closed loop undesired. Therefore, loop interactions will lead to instability if they are not taken into account in both model formulation and control system design. The ill effect of loop interaction can be alleviated by making a correct choice of input-output pairings, thereby minimizing interactions. In chemical engineering, distillation is one of the most significant unit operations. The aim of a distillation column is to separate a mixture of components into two or more different compositional products. The physical concept of distillation splitting is the difference in component volatility. The separation happens in a vertical column where heat is applied to a bottom reboiler and removed from the top condenser. A vapor stream formed in the reboiler rises through the column and is forced into contact with a fluid stream flowing down the column from the condenser. The literature has followed a broad variety of methods from complex computer simulations, basic black box models, and analog and digital hardware experimental experiments. Each approach may have its merits, but there is no universal solution that can be extended to all processes of distillation and in reality the control problems of a particular column of distillation may be special. In the end, the overriding philosophy behind all investigations into the performance of different control schemes will be profit. The key distillation control problems are: ¾¾ Interactions between control loops ¾¾ The process’s non-linearities ¾¾ The time variance of process parameters ¾¾ The process’s slow dynamics

FLC for Sustainable System using MATLAB  733 ¾¾ The use of slow and unreliable sensors and analyzers ¾¾ The great load changes that may occur This paper [1] discussed the control strategy of a fuzzy logic controller, along with the architecture of the Adaptive-Network-based Fuzzy Inference Method (ANFIS) expanded to cope with multivariable systems. This enables the parameters of both the membership functions and their consequents to be fine-tuned. The aim of this paper [2, 6] is to create an adaptive control system for a binary distillation column’s distillate output flow rate. Changes in the concentration of the inlet compound cause the mechanism to be disrupted. For a binary distillation column, a fuzzy logic control scheme has been suggested [3, 8]. The top and bottom product compositions are managed by two different fuzzy inference systems. Based on the error signal and its first difference, the scheme employs fuzzy rules and logic to decide the optimal outputs. Finally, the fuzzy based scheme’s findings were compared to the traditional results. A decentralized controller for a binary distillation column is introduced in this paper [4, 7]. Then, an H-infinity controller designed for maintaining closed-loop stability and diagonal dominance is guaranteed by solving them and applying the built controller to the device. This controller was designed for the crude oil system [5] also. In this paper [9, 10], distributed control systems (DCS) are used to control a binary distillation column using fuzzy supervisory PI control. The fuzzy supervisors then adjust the parameters of the on-line PI controls to keep the top and bottom temperatures of the distillation column constant, even though the feed flow rate varies. The performance of a cyclic distillation column designed to operate at the maximum driving force is compared to alternative sub-optimal designs [11]. The results suggest that operation at the largest driving force is less sensitive to disturbances in the feed and inherently has the ability to efficiently reject disturbances. The paper [12] explains the robust algorithm, which ensures that the compensation of perturbations with a high level of precision and simulations show that the proposed scheme is successful. This paper [13, 15] tells about the importance of controllers like PID and direct quadratic controllers for nonlinear systems like the magnetic levitation system. The author [14] has designed the controller in a pH neutralization process, which is also the same as the principle of the distillation column.

734  DC-DC Converters for Sustainable Applications

24.2 Modeling of MIMO System The MIMO model can be represented as

 y1   y 2

 12.8e − s   16.7 + 1 =   6.6e −7 s   10.9s + 1

−18.6e −3s 21s + 1 −19.4e −3s 14.4s + 1

    u1   u2  

  

(24.1)



Here, y1 – distillate methanol y2 – water u1 – reflux flow rate u2 – steam flow rate

24.3 Analysis of MIMO System Using MATLAB clc; Enter the numerator 1, n1 is given by: n1=12.8; Enter the denominator 1, d1 is given by: d1=[16.7 1]; tf is used to get the transfer function. g1 is given by: g1=tf(n1,d1); Transfer function g1: 12.8 ---------16.7 s + 1 The first delay value is 1, so the below comment is used to get the delayed element. g1.inputdelay=1; Convert in to a transfer function using Pade approximation. q1=pade(g1,1); Transfer function: -12.8 s + 25.6 --------------------16.7 s^2 + 34.4 s + 2 The same procedure is repeated to find the other transfer function also. n2=-18.9;

FLC for Sustainable System using MATLAB  735 d2=[21 1]; g2=tf(n2,d2); Transfer function: -18.9 -------21 s + 1 g2.inputdelay=3; q2=pade(g2,3); Transfer function: 18.9 s^3 - 75.6 s^2 + 126 s - 84 ----------------------------------------21 s^4 + 85 s^3 + 144 s^2 + 100 s + 4.444 n3=6.6; d3=[10.9 1]; g3=tf(n3,d3); Transfer function: 6.6 ---------10.9 s + 1 g3.inputdelay=7; q3=pade(g3,7); Transfer function: -6.6 s^7 + 52.8 s^6 - 203.7 s^5 + 484.9 s^4 - 762 s^3 + 783.8 s^2 - 485.2 s + 138.6 ------------------------------------------------------------------------------10.9 s^8 + 88.2 s^7 + 344.3 s^6 + 831.7 s^5 + 1332 s^4 + 1410 s^3 + 920 s^2 + 302.5 s + 21 n4=12.8; d4=[-19.4 1]; g4=tf(n4,d4); Transfer function: -12.8 ---------19.4 s - 1 g4.inputdelay=3; q4=pade(g4,3); Transfer function: 12.8 s^3 - 51.2 s^2 + 85.33 s - 56.89 -------------------------------------------------

736  DC-DC Converters for Sustainable Applications 19.4 s^4 + 76.6 s^3 + 125.3 s^2 + 79.56 s - 4.444 The overall transfer function is given by: g=[q1 q2;q3 q4]; Transfer function from input 1 to output... -12.8 s + 25.6 #1: --------------------16.7 s^2 + 34.4 s + 2 -6.6 s^7 + 52.8 s^6 - 203.7 s^5 + 484.9 s^4 - 762 s^3 + 783.8 s^2 - 485.2 s + 138.6 #2: --------------------------------------------------------------------------10.9 s^8 + 88.2 s^7 + 344.3 s^6 + 831.7 s^5 + 1332 s^4 + 1410 s^3 + 920 s^2 + 302.5 s + 21 Transfer function from input 2 to output... 18.9 s^3 - 75.6 s^2 + 126 s - 84 #1: ----------------------------------------21 s^4 + 85 s^3 + 144 s^2 + 100 s + 4.444 12.8 s^3 - 51.2 s^2 + 85.33 s - 56.89 #2: ------------------------------------------------19.4 s^4 + 76.6 s^3 + 125.3 s^2 + 79.56 s - 4.444 The transfer function with delay element is G=[g1 g2;g3 g4]; Transfer function from input 1 to output... 12.8 #1: exp(-1*s) * --------- 16.7 s + 1 6.6 #2: exp(-7*s) * --------- 10.9 s + 1 Transfer function from input 2 to output... -18.9 #1: exp(-3*s) * ------- 21 s + 1 -12.8 #2: exp(-3*s) * --------- 19.4 s - 1 [z,p,k]=zpkdata(g); z=   [ 2] [3x1 double]

FLC for Sustainable System using MATLAB  737   [7x1 double] [3x1 double] p=   [2x1 double] [4x1 double]   [8x1 double] [4x1 double] k=   -0.7665 0.9000   -0.6055 0.6598 Transfer function to state space data is [a,b,c,d]=ssdata(ss(g)); To find the poles of the system or roots of the system, p=pole(g); The poles are p= -2.0000 -0.0599 -0.7673 + 1.5488i -0.7673 - 1.5488i -1.1629 + 1.0049i -1.1629 - 1.0049i -1.4205 -1.3595 + 0.4969i -1.3595 - 0.4969i -0.0917 -1.2259 + 1.1696i -1.2259 - 1.1696i -1.5481 -0.0476 -1.2259 + 1.1696i -1.2259 - 1.1696i -1.5481 0.0515 To find the zeros of the system, z=zero(g); Zeros are 1.0e+002 *   1.6231   0.0002 + 0.0223i   0.0002 - 0.0223i   0.0200

738  DC-DC Converters for Sustainable Applications   0.0123 + 0.0117i   0.0123 - 0.0117i   -0.0200   -0.0123 + 0.0117i   -0.0123 - 0.0117i   0.0155   -0.0155   0.0001 + 0.0105i   0.0001 - 0.0105i   -0.0006   -0.0000 + 0.0014i   -0.0000 - 0.0014i To find the feedback gain matrix K using the pole placement technique, K=place(a,b,p); Columns 1 through 14 -0.0003 -0.0024 0.0489 0.0532 0.0502 0.0551 0.0381 0.0308 0.0217 -0.0027 -0.0035 -0.0035 -0.0049 -0.0101 0.0006 0.0046 0.6827 0.1648 -0.1167 -0.3720 -0.4136 -0.4682 -0.4700 -0.1532 -0.0288 -0.0344 -0.0349 0.0314 Columns 15 through 18 -0.0076 -0.0076 -0.0118 -0.0285 -0.0198 -0.0243 -0.0174 0.0741 To draw the Nyquist plot, %nyquist(g); Figure 24.1 gives the nyquist plot for the given transfer function. Singular value decomposition of a MIMO system is very tedious. Using the SVD comment to get the values of U, S, and V: [U,S,V]=svd(k); U=   -0.7972 -0.6038   -0.6038  0.7972 S= 1.4828 0   0 0.0265 V=   0.6586  -0.7525   -0.7525 -0.6586 Another method to find the relative gain array: rga=k.*pinv(k’);

FLC for Sustainable System using MATLAB  739 rga =   -12.8863 13.8863   13.8863 -12.8863 The below comment is used find the condition number. CN=cond(k); CN = 56.0274 To draw the multivariable Nyquist plot: [kc1,tc1]=upug(); kc1 = 0.9561 tc1 = 3.2500 [kc2,tc2]=upug1(); kc2 = 0.2939 Nyquist Diagram From: In(1)

From: In(2)

15

Imaginary Axis

To: Out(1)

10 5 0 -5 -10 -15 6

To: Out(2)

4 2 0 -2 -4 -6 -5

0

5

10

15 -20 Real Axis

Figure 24.1  Nyquist plot.

-10

0

10

740  DC-DC Converters for Sustainable Applications tc2 = 3.8694 f=2.1259 kz1=kc1/f; kz2=kc2/f; ti1=tc1*f; ti2=tc2*f; kz1 = 0.4497 kz2 = 0.1382 ti1 = 6.9091 ti2 = 8.2259 n5=[(kc1*ti1) kc1]; d5=[ti1 0]; b1=tf(n5,d5); b1.outputdelay=0; n6=0; d6=[ti1 0]; b2=tf(n6,d6); b2.outputdelay=0; n7=0; d7=[ti1 0]; b3=tf(n7,d7); b3.outputdelay=0; n8=[kc2*ti2 kc2]; d8=[ti2 0]; b4=tf(n8,d8); b4.outputdelay=0; b=[b1 b2;b3 b4]; Transfer function from input 1 to output...    6.606 s + 0.9561 #1: ---------------   6.909 s #2: 0 Transfer function from input 2 to output... #1: 0    2.417 s + 0.2939

FLC for Sustainable System using MATLAB  741 #2: ---------------   8.226 s Transfer function from input 1 to output...    -84.55 s^2 + 156.9 s + 24.48 #1: ------------------------------   115.4 s^3 + 237.7 s^2 + 13.82 s   -43.6 s^8 + 342.5 s^7 - 1295 s^6 + 3008 s^5 - 4570 s^4 + 4449 s^3 2456 s^2 + 451.8 s + 132.5 #2: ---------------------------------------------------------------------------  75.31 s^9 + 609.4 s^8 + 2379 s^7 + 5746 s^6 + 9202 s^5 + 9741 s^4 + 6357 s^3 + 2090 s^2 + 145.1 s   gb=g*b; Transfer function from input 2 to output...    45.69 s^4 - 177.2 s^3 + 282.4 s^2 - 166 s - 24.69 #1: -----------------------------------------------------   172.7 s^5 + 699.2 s^4 + 1185 s^3 + 822.6 s^2 + 36.56 s    30.94 s^4 - 120 s^3 + 191.2 s^2 - 112.4 s - 16.72 #2: -----------------------------------------------------   159.6 s^5 + 630.1 s^4 + 1031 s^3 + 654.4 s^2 - 36.56 s k=[1 0;0 1]; j=k+gb; detj=(j(1,1)*j(2,2)-j(1,2)*j(2,1)); d=-1+detj; nyquist(d); Multivariable nyquist plot for the given system shown in Figure 24.2. To find the phase margin and gain margin of the system: m=allmargin(d) m=   GainMargin: [0 0.0068 2.1251]   GMFrequency: [0 0.0589 1.8901]   PhaseMargin: 32.8192   PMFrequency: 0.7614   DelayMargin: 0.7523   DMFrequency: 0.7614    Stable: 0 grid; H = freqresp(d,f);

742  DC-DC Converters for Sustainable Applications Nyquist Diagram

300

0 dB 200

Imaginary Axis

100

0

-100

-200

-300 -16000

-14000

-12000

-10000

-8000

-6000

-4000

-2000

0

2000

Real Axis

Figure 24.2  Multivariable nyquist plot.

c=abs(H/(1+H)); lcm=20*log10(c); ll=db(lcm) ll = 10.1916

24.4 Optimization Techniques for PID Parameter 24.4.1 Controller Design 24.4.1.1 PID Controller Design Figure 24.3 shows the block diagram of the PID controller with the MIMO system. Here, the MIMO system is the distillation column. The inputs are the reflux flow rate and stream flow rate. The outputs are distillate methanol and water. The PID controller may be a centralized controller or decentralized controller. The controllers are derived depending upon the relative Gain Array (RGA) method. The PID controller parameters are found out using the Ziegler Nichols method.

FLC for Sustainable System using MATLAB  743 Input

PID Controller

MIMO system

Output

Feedback signal

Figure 24.3  Block diagram of PID controller.

24.4.2 Optimization of PID Controller Parameter PID parameters are optimized using various optimization techniques. Some of the optimization techniques are Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Bacteria Foraging (BF), Biogeography based Optimization (BBO), Gravitational Search Algorithm (GSA), Cuckoo Search Algorithm, Crow Search Algorithm etc. Also, hybrid optimization techniques like GA-PSO, BF-PSO, and GSA-PSO. Figure 24.4 shows the block diagram of a PID controller with GA. Here, the PID parameters are tuned by GA and it is sent to the MIMO system. The output is fed back to the input and the error is calculated. Figure 24.5 to Figure 24.10 show the block diagram of a PSO tuned PID controller, BF tuned PID controller, BBO tuned PID controller, GSA tuned Input

GA tuned PID Controller

MIMO system

Output

Feedback signal

Figure 24.4  Block diagram of PID controller with GA. Input

PSO tuned PID Controller

MIMO system

Output

Feedback signal

Figure 24.5  Block diagram of PID controller with PSO. Input

BF tuned PID Controller

MIMO system

Feedback signal

Figure 24.6  Block diagram of PID controller with BF.

Output

744  DC-DC Converters for Sustainable Applications Input

BBO tuned PID Controller

MIMO system

Output

Feedback signal

Figure 24.7  Block diagram of PID controller with BBO. Input

GSA tuned PID Controller

MIMO system

Output

Feedback signal

Figure 24.8  Block diagram of PID controller with GSA. Input

Cuckoo tuned PID Controller

MIMO system

Output

Feedback signal

Figure 24.9  Block diagram of PID controller with Cuckoo search algorithm. Input

Crow tuned PID Controller

MIMO system

Output

Feedback signal

Figure 24.10  Block diagram of PID controller with crow search algorithm.

PID controller, Cuckoo tuned PID controller, and Crow tuned PID controller, respectively.

24.5 Fuzzy Logic Controller Using MATLAB/ Simulink A fuzzy logic controller with a MIMO system is shown in Figure 24.11. Replacing the PID controller block in the Simulink and putting in the fuzzy block will give a fuzzy logic controller. Here, there are two input errors and a derivative error used. A 5 by 5 membership function and 25 rules are used. Figures 24.12 and 24.13 show the output of the fuzzy logic controller.

FLC for Sustainable System using MATLAB  745 Input

Fuzzy Controller

Output

MIMO system

Feedback signal

Figure 24.11  Block diagram of fuzzy controller.

Volume (m3)

1.5 1 0.5 0 0

20

40 60 Temperature (F)

80

100

80

100

Figure 24.12  Output y1 using fuzzy controller.

Volume (m3)

1

0.5

0 0

20

40 60 Temperature (F)

Figure 24.13  Output y2 using fuzzy controller.

24.6 Conclusion Further investigation into how to introduce refining segments can be improved. There is continuous research that tries to improve refining. As of now, there are continuous research bunches concentrating on the most proficient method to make refining sections increasingly effective to save the enormous measures of vitality expected to play out this sort of

746  DC-DC Converters for Sustainable Applications partition. These gatherings are concentrating on strategies for stricter controls on temperature. This is helped by propelling in warm protection, just as there is new increasingly productive pressing for the segments. As innovation improves so do the potential outcomes and standpoint for refining. With more vitality, well-disposed advancements and this expensive partition method can turn out to be more earth benevolent. In this section, the requirement for refining segment control and distinctive control strategies utilized are introduced. The scientific model of the refining segment utilized in this work is likewise given. The neural and fluffy demonstrating approach is additionally quickly clarified. The Pade approximation technique is used for the approximation. The Nyquist plot technique is used for checking the stability analysis of the multivariable system.

References 1. Fernandez de Canete et al, “”An Adaptive Neuro-Fuzzy Approach to Control a Distillation Column” Neural Comput & Applic, 9, 211–217, 2000. 2. Petia Koprinkova-Hristova et al, Adaptive Control of Distillation Column using Adaptive Critic Design, International Conference on Process Control, June 6–9, 2017. 3. Amit Kumar Singh et al, Comparative performance analysis of Fuzzy Logic Controller for the Composition control of Binary Distillation Column, Neural Comput & Applic, 9, 515–519, 2000. 4. Iman Makaremi, Batool Labibi, Control of a Distillation Column: A Decentralized Approach, Proceedings of the 2006 IEEE International Conference on Control Applications Munich, Germany, October 4-6, 2006. 5. David Sotelo, Design and implementation of a control structure for quality products in a crude oil atmospheric distillation column, ISA Transactions, 75, 573–584, 2017. 6. Samruddhi Chavan, Design and simulation of model predictive control for multivariable distillation column, 3rd IEEE International Conference on Recent Trends in Electronics, Information & Communication Technology (RTEICT-2018), MAY 18th & 19th 2018. 7. Rakesh Kumar Mishra, Tarun Kumar Dan, Design of an Internal Model Control for SISO Binary Distillation Column, IEEE International Conference on Emerging Trends in Computing, Communication and Nanotechnology (ICECCN 2013). 8. Xin Wang et al, Dynamic behavior and control strategy of cryogenic distillation column for hydrogen isotope separation in CFETR, Fusion Engineering and Design, 160, 11, 1-7, 2018.

FLC for Sustainable System using MATLAB  747 9. Poramade Cheingjong, Suvalai Pratishthananda, Fuzzy Supervisory PI Control of a Binary Distillation Column via Distributed Control Systems, 10th Intl. Conf. on Control, Automation, Robotics and Vision Hanoi, Vietnam, 17–20 December 2008. 10. Samruddhi Chavan et al, Implementation of fuzzy logic control for FOPDT model of distillation column, IEEE International Conference on Recent Trends in Electronics, Information & Communication Technology (RTEICT-2019), MAY 17th & 18th 2019. 11. Bastian B, Integrated Process Design and Control of Cyclic Distillation Columns, IFAC Papers OnLine 51-18 (2018) 542–547. 12. Igor B. Furtat, Robust Algorithm for Control of Distillation Column, Proceedings of 2017 4th International Conference on control, Decision and Information Technologies (CoDIT’17) / April 5-7, 2017, Barcelona, Spain. 13. D. Subbulekshmi et al, Execution of various Types of Controllers to Fix the Ball Position of Magnetic Levitation System, International Journal on Emerging Technologies 11(3): 809-815 (2020). 14. Naregalkar Akshay, Data Driven Design of IMC-fractional Filter PI Controller for Sewage Waste Water Process, Journal of Adv Research in Dynamical & Control Systems, Vol. 11, No. 3, 2019. 15. T. Deepa G. S. Renjini, Evaluation of Time Response Analysis using Fuzzy PI Controller for Luo Converter, International journal of control theory and applications, 9, 2, 771-780.

25 Development of Backstepping Controller for Buck Converter R. Sureshkumar1* and S. Ganesh Kumar2 1

Electronics and Instrumentation Engineering, Kongu Engineering College, Perundurai, Erode, India 2 Electrical and Electronics Engineering, College of Engineering, Guindy, Chennai, India

Abstract

The backstepping controller (BC) is aimed for stabilizing the output voltage and angular velocity of a direct current motor. Motor armature voltage is regulated via a step down converter. In this chapter, a backstepping controller is developed for a buck converter with resistive load and a permanent magnet direct current motor. Virtual control law is developed for stabilizing the voltage/angular velocity. Lyapunov’s theorem is used for verifying the convergence of error in output voltage/ angular velocity. In order to test the performance of BC, a simulation study is completed and presented for BC and a Proportional Integral controller. MATLAB is used for simulating the buck converter system with a resistive load and dynamic load. Keywords:  Backstepping controller, PM DC motor, buck converter, motor load, resistive load

25.1 Introduction There are three main types of Switch Mode Power Converters (SMPC), respectively called Boost, Buck, and Buck-Boost. Recently, the increasing requirements of power electronics in automatic control applications and the wide range of applications like computers, battery-operated vehicles, and industrial controllers, etc. require SMPC fed DC drive systems used *Corresponding author: [email protected] S. Ganesh Kumar, Marco Rivera Abarca and S. K. Patnaik (eds.) Power Converters, Drives and Controls for Sustainable Operations, (749–778) © 2023 Scrivener Publishing LLC

749

750  DC-DC Converters for Sustainable Applications in more precise speed or position control applications. From an automatic control viewpoint, a switched power converter fed drive constitutes an interesting case study as it is a variable-structure nonlinear system. Its rapid structure variation is accounted for using averaged models. Various non­linear control and adaptive control methods for non-linear systems have been proposed. Among many others, those control methods include: input-output linearization with or without adaptive control, feedback linearization, flatness methods, passivity techniques, and pseudo linearization. In this chapter, the problem of controlling switched power converters is approached using the backstepping technique and it is compared with a conventional PI controller. While feedback linearization methods require precise models and often cancel some useful nonlinearity, backstepping designs offer a choice of design tools for accommodation of uncertain nonlinearities and can avoid wasteful cancellations. In this project, the backstepping approach is applied to a specific class of switched power converters, namely DC-to-DC Buck converters. In the case where the converter model is fully known, the backstepping nonlinear controller can achieve the control objectives, i.e., output voltage tracking and speed tracking. In the past decade, research on backstepping control is increasing. The backstepping control is a non-linear system recursive method of the controller design procedure. Applying those design methods, control objectives such as position and velocity can be achieved. This design method requires whole system dynamics. Jianguo Zhou et al. (2000) discusses an adaptive mode of backstepping control for a separately excited DC motor with disturbances such as the inertia and load torque that are considered for the shaft output speed and the rotor induced EMF reference achieved. The simulation results clearly analyzed the proposed controller [1]. Fadil et al. (2003) explained the nonlinear and adaptive controls of buck power converters using the backstepping control approach. Both adaptive and non-adaptive versions are designed. The compared result explains the performance of backstepping and passivity-based controllers [2]. Liu et al. (2003) presented an adaptive multiple input and output backstepping controller improved performance in a DC motor based on controller parameter proper tuning speed reference achieved and demonstrated [3]. Suzana Uran et al. (2003) explained the buck converter control with a state controller. The system state-space model was used to design the Proportional Integral and State controller. Simulations of the switched and average power performances are explained [4].

Backstepping Controller for Buck Converter  751 Shoei-Chuen Lin et al. (2004) presented a Voltage Regulation of a Buckfed DC-DC Converter using an adaptive method of Backstepping Sliding Mode Control. The reduced order model is obtained and an adaptive sliding mode control was proposed to control buck fed DC-DC converters and was implemented using a computer simulation [5]. Fadil et al. (2006) includes the DC-DC converter dynamics in DC motor velocity adaptive control. Adaptive and non-adaptive techniques were designed and analyzed using simulation [6]. Hamit Erdem et al. (2007) explained and analyzed the performance of Fuzzy, PI, and Sliding Mode Controllers for DC-DC Converters and detailed the application of DC/DC fed converter drives [7]. Sreenu Kancherla et al. (2008) presented on the nonlinear method of Current Mode Control for a Buck Converter fed DC drive for various modes. The outer voltage controller uses a PI controller instead of an inductor and the switch current is measured. The average output voltage and inductor current are controlled and implemented using hardware [8]. Chen Lanping et al. (2009) explained an adaptive scheme of backstepping control for a DC motor system with disturbances. Here, the system is modelled by using a state reconstruction technique, the conventional backstepping method, and compensated uncertainties and load disturbance [9]. Raja Ismail et al. (2009) discussed the Buck converter fed DC drive based on smooth trajectory control. The PI and PI-type FLC designed the time and frequency domain. Both method performances are compared the terms of duty cycle [10].

25.2 Buck Converter With R-Load A Buck Converter is a circuit constituted of power electronic components connected as shown Figure 25.1. The circuit is operated according to the Pulse Width Modulation (PWM) principle. This means that time is shared in intervals of length T (also called sampling period). Within any period, the switch is closed during a period fraction. Then, the voltage source E provides the energy to the load resistances R and the inductances L. The diode D is blocked. During the rest of the sampling period (1-u)T, the switch is not conducting, the diode freewheeling assures the continuity of the current, and the discharge of energy is inductance in load resistance. The output voltage V may therefore be lower than the input voltage E. It is worth noting that the value of u varies from one sampling period to another. The variation of u determines the value of output voltage.

752  DC-DC Converters for Sustainable Applications PWM

T g D

i

m S

L

Mosfet +

ia

E

D

C

V

R

Figure 25.1  Buck converter circuit with R-load.

25.2.1 Mathematical Model The dynamic model of a Buck converter fed R-load is a second order system and the mathematical equations are given below.





L

di = − v + Eu dt

(25.1)

dv = i − ia dt

(25.2)

C

where v - Output voltage (V) i - Input current (A) ia - Output current (A) E - Input voltage (V) L - Filter inductor (H) C - Filter capacitor (F) R - Resistive load (Ω) Vd - Desired output voltage (V) u - Control input

25.2.2 Buck Converter with PMDC Motor Consider a Permanent Magnet DC motor with its armature circuit loaded to a DC-DC power converter of Buck type, as shown in Figure 25.2.

Backstepping Controller for Buck Converter  753 PWM

T g D

i

m S

ia

L

Mosfet

J f +

E

C

D

V

eb

M TL

Figure 25.2  Buck converter circuit with motor load.

25.2.3 Mathematical Model The dynamic model of a Buck converter fed motor-load is a fourth order system and the dynamic equations are given below.





(25.3)

dv = i − ia dt

(25.4)

di a = v − R mi a − k eω dt

(25.5)

C





di = − v + Eu dt

L

Lm

J

dω = k mi a − fω − TL   dt

where i - Converter input current (A) ia - DC motor armature current (A) v - Converter output voltage (V) ω - Motor angular velocity (rad/sec) TL - Load torque (N-m) J - Moment of inertia (kg*m2) f - Friction co-efficient (N-m/rad) u - Control input km - Torque constant ke - EMF constant

(25.6)

754  DC-DC Converters for Sustainable Applications

25.3 Controller Design The nonlinear systems do not obey the principle of superposition. The linear systems are systems which satisfy the principle of superposition. In all practical engineering systems there will be some nonlinearity due to friction, inertia, stiffness, backlash, hysteresis, saturation, and deadzone. The effect of the nonlinear components can be avoided by restricting the operation of the component over a narrow limited range. Moreover, most of the automatic control systems operate within a narrow range, e.g., the speed controller of an electric drive for a constant speed operation of 1500 rpm will be required to operate between 1450 to 1550 rpm. Similarly, an automatic voltage controller will be operating within 5% tolerance of the specified voltage. Thus, the characteristics of components may be considered linear over this limited range. Further, some components behave linearly over their working range, e.g., a spring when loaded gets extended. As the load is increased, the load-displacement curve is a linear system within working range. However, when the load is increased beyond the maximum of the working range, the spring material starts to yield and it becomes permanently deformed. It can be concluded that the spring behaves linearly over its working range and beyond this range it is nonlinear. Although nonlinearities in systems may be due to imperfections in a physical device, sometimes we deliberately introduce nonlinear devices or operate the devices in nonlinear regions with a view to improve system performance. This section explains the PI and Backstepping controller design details.

25.3.1 Basic Block Diagram for PI/Backstepping Controller The general block diagram for a backstepping controller with load is shown below (Figure 25.3). The converter output (voltage or speed) is fed to the load. Then, the controller will decide the necessary action to achieve the reference value. The controller output signal is to control the buck converter to keep the reference value in the buck converter output.

25.3.2 Conventional PI Controller Design The control action of a proportional-plus-integral controller is defined by the following equation:

Backstepping Controller for Buck Converter  755 POWER SUPPLY

BUCK CONVERTER

LOAD

PWM

PI/BACKSTEPPING CONTROLLER

REFERENCE VOLTAGE/SPEED

Figure 25.3  Basic block diagram for PI/backstepping controller with load.



u = K pe(t) +

Kp Ti

t

∫ e(t)dt 0

(25.7)

or the transfer function of the controller is



1   G(s) = k p  1 +   Ti s 

(25.8)

where Kp-Proportional gain constant Ti-Integral time constant e (t)-Error value Both Kp and Ti are adjustable. The integral time adjusts the control action, while a change in the value of Kp affects both the proportional and integral parts of action. The inverse of the integral time Ti is called the reset rate. The reset rate is the number of times per minute that the proportional part of the control action is duplicated. The reset rate is measured in terms of repeats per minute. The PI controller introduces a zero at s = -1/Ti and a pole at origin. Thus, the characteristic of the PI controller is infinite gain at zero frequency. This improves the steady-state characteristics. However, inclusion of the PI control action in the system increases the type number of the compensated system by 1 and this causes the compensated system to be less stable or

756  DC-DC Converters for Sustainable Applications even make the system unstable. Therefore, the values of Kp and Ti must be chosen carefully to ensure a proper transient response. By properly designing the PI controller it is possible to make the transient response to a step input exhibit relatively small or no overshoot. The speed response, however, becomes much slower. This is because the PI controller, being a lowpass filter, attenuates the high-frequency components of the signal.

25.3.3 Backstepping Controller Design Backstepping is a recursive Lyapunov-based scheme proposed in the beginning of the 1990s. The technique was comprehensively addressed by Krstic, Kanellakopoulos, and Kokotovic. The idea of backstepping is to design a controller recursively by considering some of the state variables as “virtual controls” and designing for them intermediate control laws. Backstepping achieves the goals of stabilization and tracking. The proof of these properties is a direct consequence of the recursive procedure because a Lyapunov function is constructed for the entire system including the parameter estimates. The control objective is to design a robust controller for achieving desired voltage or speed. The backstepping design to achieve the voltage or speed tracking is described with a step by step procedure. Backstepping starts with the system equation which is the farthest from the control input and reaches the control input at the last step. Consider an Nth order system for the design. Backstepping design procedure starts in output side (voltage or speed) and is derived when the intermediate control law finally reaches the control input (duty ratio) of system. Backstepping control design for Nth order system block diagram is shown in Figure 25.4.

u

1 s

....

State N control law

virtual control3

Step N

1 s

x3

state3

virtual control2

Step3

Figure 25.4  N-step backstepping control.

1 s

x2

state2

1 s

state1

virtual control1

Step2

Step1

x1 Output

Backstepping Controller for Buck Converter  757

25.3.4 Backstepping Control Algorithm Backstepping controller for Nth order system can be explained in a step by step procedure: 1. 2. 3. 4.

Define all state variables. Number of Backsteps = Number of state variables Find the state variable to be controlled (SVC) Define Virtual State Variable (VSV) = SVC-DV, where DVDesired Value 5. Find the virtual control law in such a way that the augmented Lyapunov function for the VSV will become negative definite. 6. Repeat the steps equal to the number of state variables. 7. Find the value of control input in terms of other state variables in the last step so that the corresponding Lyapunov function will be negative definite.

25.3.5 Controller Design for Buck Converter with R-Load The state space models of Buck converter with R-load equations are given below:



x 1 =

x 2   x1   − C RC

(25.9)

x1   uE + L L

(25.10)

x 2 = −

where x1-Average input current x2 - Average output voltage Step 1: For the voltage tracking objective, find the tracking error

z1 = x1 – Vd

(25.11)

758  DC-DC Converters for Sustainable Applications and its derivative as:



z 1 = x 1 − Vd

(25.12)

1 The first Lyapunov function is chosen as: V1 = z12  (25.13) 2 Then. Then, the derivative of V1 is V 1 = z1 z 1

(25.14)

Substituting the z 1 value in the above equation becomes



V 1 = z1 (x 1 − V d )

(25.15)



x  x   V 1 = z1   2 − 1 − Vd  C RC 

(25.16)



x In (25.19), 2 can be viewed as the virtual control and define the folC lowing stabilizing function:



∝1  = −c1 z1   +

x1    + Vd RC

(25.17)

where c1 is the positive constant. The second regulated variable is chosen as



z2 =

x2 − ∝1  C

V 1 = z1 z 1 = −c1z12  + z1z 2

(25.18) (25.19)

When z2 = 0, then only the above Lyapunov function will be negative definite. So, to compensate, the second regulated variable chooses the appropriate virtual control law shown in Step 2. Step 2: Hence, the derivative of the second regulated variable is calculated as



z 2 = x 2

x 2  1  −∝ C

(25.20)

Backstepping Controller for Buck Converter  759

∝⋅1 = c12z1 − c1z 2 +



x2 x1  + Vd 2 −  RC  RC

(25.21)

Applying the Lyapunov function to stabilize the second state:



V 2 = z1 z 1 + z 2 z 2

(25.22)



V 2 = −c1z12  − c 2z 22  + z 2 ( z1 + z 2 + c 2 z 2 )

(25.23)

u=

LC  x2  1 1  2 d  x1 + V  −z1 –c 2 z 2 + c1 z1 − c1z 2 + 2 − 2 2 −   E  RC R C  CL

(25.24) The control law is

u=

LC  2 x2  1 1  d  . x1 + V  (c1 − 1)z1  –(c1 + c 2 )z 2 + 2 − 2 2 −  E RC R C CL 

(25.25)

Controller Design for Buck Converter with PM DC Motor The Buck converter fed DC motor is a fourth order system. Therefore, four steps are involved in the backstepping controller design procedure. These four steps are explained below:







f k T x 1 = − x1 + x 2 − L J J J x 2 = −

k R x x1 − m x 2 + 3 Lm Lm Lm x 3 =

x4 x2 − C C

(25.26)

(25.27)

(25.28)

760  DC-DC Converters for Sustainable Applications

x 4 = −



x 3 uE + L L

(25.29)

where x1 - Average angular velocity x2 - Average motor armature current x3 - Converter output voltage x4 - Converter inductor current Step 1: First find the Tracking error

z1 = x1 – ωr

(25.30)

Take its derivative

z 1 = x 1 − ω r

(25.31)

f k T z 1 = − x1 + x 2 − L − ω r J J J

(25.32)





Applying the Lyapunov function, stabilize the first state

1 V1 = z12 2

(25.33)



V 1 = z1 z 1

(25.34)



V 1 = z1 z 1 = −c1z12  + c1z12  + z1 z 1

(25.35)



V 1 = −c1z12  + z1 (c1 z1 + z 1 )

(25.36)

Take the derivative of V1:







f k T   V 1 = −c1z12  + z1  c1z1 − x1 + x 2 − L  − ω r    J J J

(25.37)



Backstepping Controller for Buck Converter  761 k x 2 can be viewed as the virtual control and define the folJ lowing stabilizing function: In (25.42)

f T ∝1 = x1 + L + ω r − c1  z1 J J



(25.38)

where c1 is the positive constant. The second regulated variable is chosen as:

z2 =



k x 2 − ∝1  J

(25.39)

Pr oofWhen : When Step1negative is negative definite Proof: thethe Step1is definite

f T   V 1 = −c1z12  + z1  c1  z1 − x1  + z 2 + ∝1 − L   − ω r    J J



f T z 1 = − x1 + z 2 + ∝1  − L   − ω r = −c1z1 + z 2 J J

(25.40)

(25.41)

Put ∝1 in z 1



z 1 = −c1z1 + z 2

(25.42)

When z2 = 0, then only above the Lyapunov function will be negative definite. So, we compensate the second regulated variable by choose the appropriate virtual control law, shown in Step 2. Step 2: Find the next state error and find ∝.1 . We can substitute the follwing equations and stabilize the second state using virtual variable:



z2 = z 2 =

k x 2 − ∝1 J k x 2 − ∝.1 J

(25.43)

762  DC-DC Converters for Sustainable Applications Take its derivative





f  r − c1 z 1 ∝.1 = x 1 + ω J

(25.44)

f f k T   r − c1 z 1 ∝.1 =  − x1 + x 2 − L  + ω J J J J 

(25.45)



k  f k  f f   k k   R z 2 =   ∗  −  ∗   x1 +   m ∗  −  ∗   x 2   J J   J Lm     Lm J   J J   +

k fT  r + c1 (−c1z1 + z 2 ) x 3 + 2L − ω JL m J



(25.46)

Applying the Lyapunov function, stabilize the second state:



V 2 = −c1z12  + z1z 2 + z1 z 2



V 2 = −c1z12  − c 2z 22  + z 2 (c 2z 2 + z1 + z 2 )

(25.47)



(25.48)

k x 3 can be viewed as the virtual control and define the followJL m ing stabilizing function. Second state virtual control variable Then,







 kk22 ff22 fT kR fk fk fT  kR ∝∝22== −− 22xx11++ mm −− 22xx22−− 2L  2L   JL  JL JJ JLmm JJ  JLmm JJ  ω r r++cc1122zz11−−cc11zz22−−cc22zz22−−zz11 ++ω ∝2 = b1x1 + b2 x 2 −



(25.49)

f TL 2  (25.50) 2 + ω r + (c1 − 1)z1 − (c1 + c 2 )z 2 J

 k2 f 2  fk   kR where b1 =  − 2  , b2 =  m + 2   JL m J   JL m J 



(25.51)

Backstepping Controller for Buck Converter  763 Step 3: Similarly, find the error variable to stabilize the state:



z3 =

k x 3   − ∝2 JL m

(25.52)

z 3 =

k x 3 − ∝.12 JL m

(25.53)

r + (c12 − 1) z 1 − (c1 + c 2 ) z 2 ∝. 2   = b1 x 1 + b2 x 2 + ω



z 3 =



k  x4 x2  . − ∝2 − JL m  C C 

(25.54) (25.55)

k  x4 x2  r + (c12 − 1) z 1 –(c1  + c 2 ) z 2 ) − ( b1 x 1 + b2 x 2 + ω Z 3 = − JL m  C C 

(25.56)

z 3 =





k  x4 x2    f k T  −  b1  − x1 + x 2 − L  − JL m  C C    j j J 

R x    k r + (c12 − 1) z 1 − (c1 + c 2 ) z 2  x1 − m x 2 + 3  + ω + b2  −  Lm Lm Lm  



(25.57)

kkxx bb kk bb RR  bb  bb kk bb ff   kk  rr zz33 == 22 ++ 11  xx11−− ++ 11 −− 22 mm xx22 −− 22 xx33 44 −−ω ω  LLmm JJ  jj LLmm  LLmm JL JCLmm JLmmcc  JCL bb TT ++(c (c1133−−cc11)z )z11−−(c (c1122 −−cc2222 ++cc11cc22−−1)z 1)z22++(c (c11++cc22)z )z33++ 11 LL JJ 

(25.58)



Similarly, apply the Lyapunov function to stabilize the third state:



V 3 = −c1z12  − c 2z 2 2 − c 3z 32  + z 3 (c 3z 3 +  z 2 + z 3 )

(25.59)



764  DC-DC Converters for Sustainable Applications

 b2 k2  b1fb2 k  b1fk  b2 k kb1f  2  2  2  +  2 3 (c V 3 = −c1z12 V−3c=2z−2 2c−  z−z2c3+2(c z(2 2z3z3−3c+3 z z 3 + (zz3 (c 3zx31 +−+ z 2 + (zx3 1 −  + −3cV −−c3cz31z3z32 + 1 + 1zc 1 3z 2z3z2 =  x1 −  L m2 J3  L m  JCL J m  LmJCL mJ  kx   f ( z  b21k +k b12fRmbx1k−  b2bkR2 m  b1kkxb4 2b2Rm kx 43 b2  b3z23k+  zb21+ 2 2 3 2 3 24− c 2 − (c (c x 21−− cω x+31(c (c + 1 r)z ++(zz 33 (c c 2c+ c11c−2 (c1 − )z2ω1+−r c+(c −L − J + 1 x−2−JCL x+3 x+2 − − −xω r+ 1c 1 )z 1− 12 1− − 3+ 1 1− c   L + J  x31+  m m  J L L JL c J L L JL c  JCL m m J L m m JL mc m m  m m m m kx 4 b T  b T  2 2 b T  2 −31)z 2 + (c− + −r (c − 1ω + 1(c −2 c+3 22+(c+1c1+1ccL22−)z1)z c1 2 )z )3 +2 +1(c1L + c) 2 )z 3 + 1 L  ) 1 c−2 c+12 )z − 1)z ωr x+3(c+13JL− cc1 )z c1c1 21 (c J  J  m m J  (25.60) 1 TL  )  J  k x 4 can be viewed as the virtual control and define the JL mC following stabilizing function. Third state virtual control variable is In (25.58),

bb1TTL bb1kk bb2RR m bb2  bb kk bb ff   kk ∝33==−− 22 ++ 11 xx11++ ∝ ++ 1 −− 2 m xx22++ 2 xx33−− 1 L JCLmm JJ  LLmm JJ  JCL LLmm  LLmm JJ  

rr −−(c  (c1133−−cc11)z )z11++(c (c1122−−cc2222++cc11cc22−−2)z 2)z22−−(c (c11++cc22++cc33)z )z33 (25.61) ω ++ω

b1 TL bb2T b r − (c13 − c12)z1 +2 (c12 − c 22 + c1c 2 − 2)z 2 3ω r − x13+= b−4bx32x+1 + b2 4xx32 −+ L1 xL 3+−ω ∝3 = − b3 ∝ (c+ 1 − c1 )z1 + (c1 − c 2 + c1c 2 − 2)z 2 J m Lm J − (c + c + (25.62) − (c1 + c 2 + c13 )z 3 2 c 3 )z 3



bk bR  b k bf  k where b3 =  2 + 1  , b4 =  + 1 − 2 m  Lm  JCL m J  J Lm  Step 4: Similarly, find the state error variable of the next state applying the Lyapunou function



z4 =

k x 4 −∝3  JCL m

(25.63)

Backstepping Controller for Buck Converter  765

k x 4 −∝.3 JCL m

(25.64)

k  x 3 uE  . −∝3 − + JCL m  L L 

(25.65)

z 4 =

z 4 =



bb . . . . ∝∝ bb3 3x x1 1++bb4 4x x2 2++ 2 2x x3 3++ωω(4) (c(c1313−−c1c)z 3 3==−− 1 1 (4)−− 1 )z LLmm 22 22   ++(c(c1 1 −−c c2 2++c1cc1c2 −2 −2)2)z z2 −2 −(c(c1 1++c c2 2++c c3 )3 z) z3 3 (25.66)



kk TTL  RRm xx3   kk  ff .   ∝ ∝3.3 ==−−bb33−− J xx11++ J xx22 −− J L ++bb44−−L m xx11−− L mm xx22 ++L m3   Lm  J J J  Lm Lm  b x x  . 3 1 + (c122 + c 222 + c1c 2 − 2) z2 ++ b22  x44 −− x22  ++ω . − (c1 3− c1 )z (4) ω − − (c c )z   (4) 1 1 1 + (c1 + c 2 + c1c 2 − 2) z 2 LLm  CC CC  m  −−(c (c11++cc22 ++cc33))zz33 (25.67) kk TT    kk RR xx   bb  xx xx    f f .3 .3==−− ∝∝ bb3 3 −− xx1 1++ xx2 2−− L L ++bb4 4 −− xx1 1−− mmxx2 2++ 3 3 ++ 2 2  4 4−− 2 2   J J JJ J J    LLmm LLmm LLmm  LLmm CC CC  . . ) +(c(c1212++c c22 22++c1cc1 c2 −2 −2)( 2)(−−c c2z2z2 +2 +z z3 )3 ) ++ωω(4) (c(c1313−−c1c)( −−c1cz11z1++z z2 )2 + (4)−− 1 )(

−−(c(c1 −1 −c c2 +2 +c c3 )( −−c c3z3z3 +3 +z z4 )4 ) 3 )(





(25.68)

R x  k  x uE  k T   k  f zz4 == k −− x33 ++ uE ++bb3 −− f xx1 ++ k xx2 −− TLL  −−bb4 −− k xx1 −− Rmm xx2 ++ x33  4 3 J 1 2 4 L 1 L 2 L      JCL L L J J  Lmm  J JCLmm  L L  J J  Lmm Lmm  bb2  xx4 xx2  . 3 2 2 . + (c1 3 − c1 )( − c1z1 + z 2 ) − (c1 2 + c 22 + c1 c 2 − 2)( − c 2z 2 + z 3 ) −− 2  4 −− 2  −−ω (4) + (c1 − c1 )( − c1z1 + z 2 ) − (c1 + c 2 + c1 c 2 − 2)( − c 2z 2 + z 3 )  ω(4) LLm  C C C C m ++(c (c1 −−cc2 ++cc3 )( )(−−cc3zz3 ++zz4 )) (25.69) 1



2

3

3 3

4





766  DC-DC Converters for Sustainable Applications

z 4 =

uE JLCL m

bk b  b k b f b R +  4 − 3  x1 +  4 m − 3 + 2  x 2  Lm  Lm J  J L mC 

b  b bT  −k . + − 4  x 3 − 2 x 4 − 3 L − ω (4)  JLCL m L m  CL m J + (−c14 + c12 )z1 + (c13 + c 32 + c12c 2 + c1c 22 − 2c 2 − c1 )z 2 − (c12 + c 22 + c 32 + c1c 2 + c1c 3 + c 2c 3 − 2)z 3 + (c1 + c 2 + c 3 )z 4



(25.70)

Similarly, apply the Lyapunov function and stabilize the final state.

V 4 − c1z12  − c 2z 2 2 − c 3z 32  − c 4z 2 4 + z 4 (c 4z 4 + z 3 + z 4 )



(25.71)

Final control law is

u=

b T JLCLm  b2 . − (−c14 − c12 )z1 x 4 + 3 L + ω (4)  b5 x1 − b6 x 2 + b7 x 3 + E  CL m J

− (c13 + c 32 + c12 c 2 + c1c 22 − 2c 2 − c1 )z 2 + (c12 + c 22 + c 32 + c1c 2 + c1c 3 + c 2c 3 − 3)z 3 −(c1 + c 2 + c 3 + c 4 )z 4 }

(25.72)



bk b  b   −b k b f  b R  k + 4 . where b5 =  4 + 3  , b6 =  4 m + 3 + 2  , b7 =   Lm  Lm  JLCL m L m  J  J L mC  b R b k b k b     b6 =  4 m + 3 + 2  , b7 =  + 4 .    Lm J L   C JLCL L m m m The PI and Backstepping controller with R load and PM DC motor load design procedures were explained.

25.4 Simulation Results The circuit parameters for a Buck converter with R load are shown in the Table 25.1. The load resistance of a Buck converter with a PI/Backstepping Controller under load variation condition is shown in Figure 25.5.

Backstepping Controller for Buck Converter  767 Table 25.1  Buck converter with R load circuit parameters. S. no.

Parameters

Symbols

Values

1

Load Resistance

R

30 Ω, 40 Ω

2

Filter Inductor

L

20 mH

3

Filter Capacitance

C

68

4

Supply Voltage

E

15V

5

Desired Voltage

Vd

5V

Resistive load

60

Resistance (Ohms)

50 40 30 20 10 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (sec)

Figure 25.5  Resistive load.

The load resistance is changed from 30Ω to 40 Ω at 0.4 seconds. Then, again, the load resistance is changed from 40Ω to 30 Ω at 0.6 Seconds. The output voltage of a Buck converter with a PI controller is shown in Figure 25.6. During the load variation from 30Ω to 40Ω, the output voltage exhibits overshoot and it is settled at 0.057 sec. When the load resistance is PI controller output voltage for Buck converter with R load

8

Output voltage (volts)

7

kp=1 ki=200

6 5 4 3 2 1 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time (sec)

Figure 25.6  PI controller output voltage for buck converter with R load.

0.9

1

768  DC-DC Converters for Sustainable Applications Backstepping controller output voltage for Buck converter with R load

8

Output voltage (volts)

7

c1=100 c2=390

6 5 4 3 2 1 0

0

0.1

0.2

0.3

0.4

0.5 Time (sec)

0.6

0.7

0.8

0.9

1

Figure 25.7  Backstepping controller output voltage for buck converter with R load.

decreased from 40Ω to 30 Ω, the output voltage exhibits overshoot and the settling time was 0.057 sec. The output voltage of a Buck converter with a Backstepping controller is shown in Figure 25.7. During the load variation periods, the settling times were 0.0326 sec and 0.055 sec. Though the overshoot for a Backstepping controller is more than a PI Controller, the settling time was less. These details are mentioned in Table 25.2 The Buck converter with PM DC motor parameters is shown in Table 25.3. The load torque of the PM DC motor with load torque variation is shown in Figure 25.8. The load torque is changed and varies from (0.05 0.07) N-m at 1.5 sec. Then, again, the load torque is changed to vary from (0.07 - 0.05) N-m at 2.5 sec. The output speed of a PI controller with a Buck converter fed PM DC motor is shown in Figure 25.9. During the load variation from 0.05N-m to 0.07 N-m, the speed exhibits undershoot and the settling time for the response is 0.550 sec. When the load torque is decreased from 0.07 N-m to 0.05 N-m, the speed exhibits overshoot and the settling time was 0.550 sec. The output speed response of a Buck converter fed PM DC motor with a Backstepping controller is shown in Figure 25.10. During the load torque variation profile at 1.5 seconds, the settling time was 0.062 sec and at 2.5 seconds, the settling time was 0.062 sec. These details are mentioned in Table 25.4.

25.5 Hardware Details The general block diagram for a closed loop control Buck converter with a UC3524 controller with load is shown below (Figure 25.11). The converter output (voltage) is fed to the controller UC3524. Then, the controller will

Backstepping Controller for Buck Converter  769

Table 25.2  R Load output comparison. PI controller

Backstepping controller

S. no.

Time (sec)

Desired voltage (V)

Load resistance (Ω)

Overshoot/ undershoot (V)

Settling time (sec)

Overshoot/ undershoot (V)

Settling time (sec)

1

0.0 - 0.4

5.0

30

-

0.290

-

0.0920

2

0.4 – 0.6

5.0

40

5.48

0.057

6.18

0.0326

3

0.6 – 1.0

5.0

30

4.47

0.057

4.00

0.055

770  DC-DC Converters for Sustainable Applications

Load torque (N-m)

Table 25.3  Buck converter with PM DC motor load circuit parameters.

0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

S. no.

Parameters

Symbols

Values

1

Filter Inductor

L

20e-3 H

2

Filter Capacitor

C

400e-6 F

3

Motor Constant

K

0.046

4

Moment of Inertia

J

7.06e-5 kg*m2

5

Friction Coefficient

F

8.42e-4 N-m/rad

6

Motor Inductor

Lm

2.63e-3 H

7

Motor Resistance

Rm

2.0 Ω

8

Supply Coltage

E

12 V

9

Load Torque

TL

0.05 N-m, 0.07 N-m

10

Desired Speed

ωd

50 rad/sec

PM DC Motor load

0

0.5

1

1.5

2 Time (sec)

2.5

3

3.5

4

Figure 25.8  PM DC motor load torque. PI controller output speed for Buck converter with PM DC motor

80

Load torque (N-m)

70

kp=0.0072 ki=0.1

60 50 40 30 20 10 0

0

0.5

1

1.5

2 Time (sec)

2.5

3

3.5

Figure 25.9  PI controller output speed for buck converter with PM DC motor.

4

Backstepping Controller for Buck Converter  771 Backstepping controller output speed for Buck converter with PM DC motor

80 Output speed (rad/sec)

70

c1=5000 c2=7000 c3=2250 c4=100

60 50 40 30 20 10 0

0

0.5

1

1.5

2 Time (sec)

2.5

3

3.5

4

Figure 25.10  Backstepping controller output speed for buck converter with PM DC motor.

decide the necessary action to achieve the reference value. The controller output signal is to control the Buck converter switching period to keep the reference value in the Buck converter output.

25.5.1 Buck Converter Specifications The most common power converter topology is the Buck power converter, sometimes called a step down power converter. Power supply designers choose the Buck power converter because the output voltage is always less than the input voltage in the same polarity and is not isolated from the input. The Buck converter circuit diagram is shown in Figure 25.12. The buck regulator circuit is a switching regulator, as shown in Figure 25.11. It uses an inductor and a capacitor as energy storage elements so that energy can be transferred from the input to the output in discrete packets. The advantage of using switching regulators is that they offer higher efficiency than linear regulators. The one disadvantage is noise or ripple; the ripple will need to be minimized through careful component selection. To reduce output voltage ripple, the switching frequency should be increased but this lowers efficiency. This means that the selection of the switching devices will be an important issue. The output voltage ripple can also be reduced by increasing the output capacitance; this means a large capacitor in practical design.

772  DC-DC Converters for Sustainable Applications

Table 25.4  PMDC motor load output comparison. PI controller

S. no.

Time (sec)

Desired speed (rad/sec)

1

0.0 - 1.5

2

1.5 – 2.5

3

2.5 – 4.0

Backstepping controller

Load torque (N-m)

Overshoot/ undershoot (rad/sec)

Settling time (sec)

Overshoot/ undershoot (rad/sec)

Settling time (sec)

50.0

0.05

-

0.770

-

0.1210

50.0

0.07

45.0

0.550

-

0.0620

50.0

0.05

55.0

0.550

-

0.0620

Backstepping Controller for Buck Converter  773 POWER SUPPLY

BUCK CONVERTER

LOAD

PWM

UC 3524

REFERENCE VOLTAGE

Figure 25.11  Buck converter with UC3524 controller. main MOSFET

Vdc

Control Circuit

Inductor

Diode

Capacitor

Load

Figure 25.12  Buck converter.

The input current for a Buck power converter is discontinuous due to the power switch and the current pulses from zero to maximum every switching cycle. The output current for a Buck power converter is continuous because the output current is supplied by the output inductor/capacitor combination. The Buck converter constructed for this thesis is 1.0kW with a reference voltage of output voltage 225V and nominal input voltage of 313V. This combination of Vout and Vin yields a steadystate duty ratio of 0.71. The MOSFET switching frequency selected is 22kHz. The buck converter filter inductance value is 2.15mH and filter capacitance value is 0.1µF.

25.5.2 Advanced Regulating Pulse Width Modulator The UC3524 semiconducting device can do the operations of regulated power supply, inverters, etc. The high power drive application controller is designed by using UC3524. It is operated on the principle of pulse width

774  DC-DC Converters for Sustainable Applications VREF

VIN

EB

CB

CA

EA

S/D

COMP

16

15

14

13

12

11

10

9

REFERENCE REGULATOR

S/D

CURRENT AMP

+

OSCILLATOR

_

_

+

ERROR AMP

1

2

3

4

5

6

7

8

INV INPUT

NON INV INPUT

OSC OUT

CL SENSE(+)

CL SENSE(--)

RT

CT

GND

Figure 25.13  Advanced regulating pulse width modulator.

modulation techniques. The UC3524 analog controller connection diagram is shown in Figure 25.13.

25.5.3 Principles of Operation The UC3524 is an operating fixed frequency PWM, voltage regulator, and control circuit. The frequency depends on a one-timing resistor (RT), one-timing capacitor (CT), and a constant charging current for CT. The UC3524 has an internal 5V regulator for the purpose of reference, internal circuit control, and external interfacing. Also, a voltage divider is used to set operating modes. Based on the feedback signal, UC3524 can produce PWM signals so that the desired output voltage is achieved. The oscillator frequency of UC3524 is related with RT and the CT relationship is given below.



Frequency f =

1.18 R TC T

(25.73)

Backstepping Controller for Buck Converter  775 where RT – Timing resistor CT – Timing capacitor The hardware details of Buck converter circuit components and an advanced regulating pulse width modulator UC3524 controller were explained.

25.6 Hardware Results This chapter explains the hardware results for the closed loop control of a Buck converter with a UC3524 controller. The Buck converter experimental setup of a closed loop control Buck converter with a UC3524 controller is shown in Figure 25.14. The buck  converter input voltage waveform is shown in Figure 25.15. Here, the buck converter input DC voltage is 313 volts and reference output voltage is 225 volts.

Figure 25.14  Buck converter with UC 3524 experimental setup.

776  DC-DC Converters for Sustainable Applications

TPS 2014 - 3:44:41 PM 3/18/2011 Figure 25.15  Buck converter DC input voltage.

Figure 25.16 represents the PWM signals for the buck converter under unloaded conditions to achieve the corresponding output voltage shown in Figure 25.17.

TPS 2014 - 3:27:00 PM 3/18/2011 Figure 25.16  UC3524 controller PWM output signal.

Backstepping Controller for Buck Converter  777

TPS 2014 - 3:22:08 PM 3/18/2011 Figure 25.17  Buck converter output voltage.

The buck converter with UC 3524 controller output voltage is shown in Figure 25.17. Here, the reference value 225V is reached.

25.7 Conclusion This book chapter describes the Backstepping controller design scheme for a Buck converter with R load and a PM DC motor. Step by step control design and stability analysis are given and the effectiveness of backstepping controller design is demonstrated through computer simulations. In addition, PI controller performance is compared with the Backstepping controller. Simulation results with R-load with load disturbance reveals that the output voltage settling time for PI controllers is more than a Backstepping Controller and the overshoots are higher in the backstepping controller than in the PI controller. A simulation study with DC motor with load disturbance indicates that the output speed settling time for the PI controller is more than the Backstepping Controller. The simulation results have clearly illustrated that the proposed backstepping controllers are quite effective and efficient for a PM DC machine. The closed loop operation of a Buck converter with a UC3524 controller is implemented and tested under no-load conditions.

778  DC-DC Converters for Sustainable Applications

References 1. Jianguo Zhou, Youyi Wang and Rujing Zhou. Adaptive backstepping control of separately excited DC motor with uncertainties. IEEE International Conference on Power System Technology, Page(s): 91 - 96 vol. 1, 2000. 2. El Fadil. H, Giri. F, Haloua. m and Ouadi. H “Nonlinear and Adaptive Control of Buck Converters”. IEEE Conference on Decision and Control, Hawali USA, Dec 2003. 3. Liu. Zuo Z, Luo.Fang L, and Rashid Muhammad H. “Adaptive MIMO Backstepping Controller for High-Performance DC motor field weakening”. Taylor & Francis on Electric Power Components and Systems, 31: 913–924, 2003. 4. Uran, S and Milanovic, M. State controller for buck converter. IEEE Region 8 Conference EUROCON 2003 , pp: 381 – 385, vol. 1, 2003. 5. Shoei-Chuen Lin and Ching-Chih Tsai. Adaptive voltage regulation of PWM buck DC-DC converters using backstepping sliding mode control. IEEE International Conference on Control Applications, pp: 1382 - 1387, vol. 2, 2004. 6. El Fadil and Giri.F, “Accounting of DC –DC Power converter dynamics in DC motor velocity adaptive control”. IEEE Conference on Control, Applications, Germany, Oct 2006. 7. Erdem, H. Comparison of fuzzy, PI and fixed frequency sliding mode controller for DC-DC converters. IEEE International Aegean Conference on Electrical Machines and Power Electronics, pp: 684 – 689, 2007. 8. Sreenu Kancherla and Tripathi. R.K. “Nonlinear Average Current Mode Control for a DC-DC Buck Converter in Continuous and Discontinuous conduction modes”. Tencon IEEE conference, pp: 1-6, 2008. 9. Chen Lanping, Ma Zhenghua, Duan Suolin. “Adaptive Speed Controller Design Based on Backstepping for DC Motor System with Parameter Uncertainities”. IEEE conference on intelligent computing and Intelligent system, Shanghai, pp: 140-144, 2009. 10. Raja Ismail. R. M. T, Ahmad. M. A. and Ramli. M. S. “Modelling & Simulation Speed Control of Buck-converter Driven Dc Motor Based on Smooth Trajectory Tracking”. Third Asia International Conference, pp: 97–101, 2009.

26 Analysing Control Algorithms for Controlling the Speed of BLDC Motors Using Green IoT V. Evelyn Brindha1 and X. Anitha Mary2* Department of Electrical and Electronics Engineering, Karunya Institute of Technology and Sciences, Coimbatore, Tamil Nadu, India 2 Department of Robotics Engineering, Karunya Institute of Technology and Sciences, Coimbatore, Tamil Nadu, India

1

Abstract

In recent days, Brushless Direct Current (BLDC) are gaining popularity in many fields because of its higher efficiency, noiseless operation and speed of operation are high. One of the disadvantages of BLDC motor is that it requires sophisticated control algorithms to control the speed. In this chapter, BLDC motor is discussed with various control algorithms like PI, PID and artificial intelligence techniques using MSP430 microcontroller. Later the application of Green IoT that helps in remote controlling of motor in an energy efficient way is also discussed. Keywords:  Motor, BLDC, control algorithms, Green IoT

26.1 Introduction Conventional DC motors, though highly efficient, are subjected to wear and require frequent maintenance. On the other hand, Brushless Direct Current (BLDC) motors are without brushes for commutation, which results in less spark and maintenance cost. In a BLDC motor, the rotor is

*Corresponding author: [email protected] S. Ganesh Kumar, Marco Rivera Abarca and S. K. Patnaik (eds.) Power Converters, Drives and Controls for Sustainable Operations, (779–788) © 2023 Scrivener Publishing LLC

779

780  DC-DC Converters for Sustainable Applications made up of a permanent magnet and stator with coil windings. To know the position of the rotor, the motor has inbuilt position sensors like photo­ transistors, photodiodes, half effect devices, and incremental encoders. The square wave generated from the motor is given to the driver module to control the speed of the motor. In recent days, BLDC have gained popularity in many fields such as aerospace, consumer, medical instrumentation, and industrial automa­ tion because of its higher efficiency, noiseless operation, and high speed of operation. One of the disadvantages of the BLDC motor is that it requires sophisticated control algorithms to control the speed. Various algorithms like PI, PID, and other artificial intelligence techniques are used to control the speed of the motor. In recent days Green IoT plays an important role in remote control of motors. It not only controls the speed of the motor, but also does it in an energy efficient way. In this chapter, a BLDC motor is discussed with various control algo­ rithms like PI, PID, and artificial intelligence techniques using an MSP430 microcontroller. Later, the application of Green IoT to help in remote con­ trolling of motors in an energy efficient way is also discussed. Since BLDC motors are weightless, reliable, and have high efficiency, they are broadly applied in various industries. Hence, controlling the speed of the these remotely using IoT would be very useful.

26.2 Working of BLDC Motor As the name suggests, it is a DC motor that is brushless and has no com­ mutator, but rather employs a control unit, rotary encoders, or hall sensors. In a BLDC motor, the permanent magnets are attached to the rotor. On the stator, the current carrying conductors or armature winding are situated. Electrical switches are used to transform electrical energy into mechanical energy. Figure 26.1 shows the different parts of the BLDC motor. The main difference between brushed and brushless motor are as follows: 1. Speed range is high when compared to brushed, as BLDC does not require brushes and commutators, thereby noise is reduced and requires less maintenance. 2. The characteristics of speed/torque are high as mechanical parts involved are less and thereby reduce building cost. 3. As there are no electrical and friction losses, efficiency is higher.

Controlling the Speed of BLDC Motors Using Green IoT  781 Rotar

Stator

Hall effect sensor

Permanent magnet

Figure 26.1  Parts of BLDC motor (Source: [1]).

26.3 Speed Control of Motor To know the position of the rotor and rotor movement in terms of turns, either sensored commutation or sensorless commutations are used. The sensored commutation uses hall sensors and sensorless commutation analyses the back emf generated in the stator winding and has the dis­ advantage of no emf generated, which produces a jerk during starting of the motor. In order to have good starting torque, hall effect sensors are used. Figure 26.2 shows the different types of BLDC motor depending on the turns as single phase, two phase, and three phases [2]. The speed controller of the BLDC motor is important to find the work­ ing of motors at the desired speed, which can be controlled using vari­ able DC voltage or current. There are two types of speed control: open and closed. (I) Open Loop Speed Control In an open loop controller, the output is not fed back and thereby has the advantage of simplicity and lower cost (Figure 26.3). The control input can be analog or digital. The analog controller input will be given in the form of a potentiometer which increases or decreases the PWM duty cycle. The variable PWM duty cycle helps in varying the speed of the motor. The controller used can be any microcontroller. For implementation, an MSP430 microcontroller is used. The analog input is fed to a 12 bit ADC which counts from 0 to 212, representing 0% to 100%.

782  DC-DC Converters for Sustainable Applications

(a)

(b)

(c)

Figure 26.2  Different phases of BLDC motors: (a) single phase; (b) two phase; (c) three phase.

Control Input

Open loop speed controller

Driver circuit

BLDC Motor

Figure 26.3  Open loop control.

In the case of a sensored BLDC motor, the hall sensor signal is fed to the microcontroller through the GPIO pins. The PWM signal is fed to the driver module for running the motor. Figure 26.4 shows the flow chart for open loop speed control of a BLDC motor. The time taken from input phase to the output phase is approximately 9 microseconds. (ii) Closed Loop Control The closed loop control uses feedback to regulate the speed of the motor to the desired rate. It consists of an input block, closed loop controller, motor driver feedback block, and motor or actuator (Figure 26.5). In open loop control, the speed of the motor depends on the current input, but in closed loop, the speed depends on the current input and feed­ back (actual motor speed). Various algorithms like PI and PID control­ lers can be used to control the speed by updating the PWM duty cycle. The speed input is given to the microcontroller using a potentiometer.

Controlling the Speed of BLDC Motors Using Green IoT  783 START

Initializing phase: 1. Configure Microcontroller 2. Set system clock to 16 MHz 3. Connect hall sensor wires to GPIO pins 4. Set Timer B in PWM mode Start of Conversion ADC by enabling ISR

Conversion process of PWM signal

NO End of conversion (return from ISR) YES Digital input to the driver module

STOP

Figure 26.4  Flowchart of open loop speed control using MSP430.

Input

Micro-Controller (control algorithm)

Feed back control

Figure 26.5  Closed loop speed control.

BLDC Driver unit

Motor

784  DC-DC Converters for Sustainable Applications The  12  bit ADC will give the counts to timer B. By varying the Kp and Ki values, the PWM duty cycle update can be given to the driver module through timer B. Here, Kp and Ki are the tuning parameters called propor­ tional and integral constants (Figure 26.6). For a 3 phase BLDC motor, given the number of poles to be 6, the maxi­ mum speed required is 4000 rpm and the maximum electrical rotation per second is given by Equation 26.1:

required maximumspeed noof poles ∗ 60 2 4000 6 (26.1) = ∗ = 200 60 2

Maximumelectricalrotation =



One electrical rotation has six hall states and the maximum speed in rpm is given by Equation 26.2.



200*6 = 1200 rpm

(26.2)

The difference between expected speed and measured speed gives the proportional error and these errors are accumulated to give the integral error. PI controller output = (Kp * proportional error)+ Ki* Integral error) A PI controller can be used as a PID by inserting the Kd value. PID duty cycle = desired duty cycle + (PI controller output)/division factor. Apart from PI and PID, recently algorithms like fuzzy controllers, arti­ ficial neural networks, and machine learning based algorithms are used. Shanmugasundram et al. [3] uses various controllers like fuzzy logic and hybrid neural networks to control the speed. PID for speed control is implemented with neural network controllers [4–7]. Optimization algo­ rithms like particle swarm optimization [8], adaptive fuzzy logic [9], bio­ inspired algorithms [10], and firefly algorithms [11–13] are used for tuning the controller parameters of PID controllers.

Controlling the Speed of BLDC Motors Using Green IoT  785 START

Initializing phase: Configure Microcontroller 1. Set system clock to 16 MHz 2. Connect hall sensor wires to GPIO pins 3. Set Timer B in PWM mode 4. configure Timer A as feedback timer

Start of Conversion ADC bv enabling ISR

Conversion process of PWM signal

NO

End of conversion (return from ISR) YES

Select the value of Kp, Ki depending on the desired PWM cycle

Execute PI controller 1. Compute errors 2. Implement controller equations 3. Send PI controller output to update PWM duty cycle.

Is desired speed achieved

STOP

Figure 26.6  Flowchart for closed loop speed control with MSP430 microcontroller.

786  DC-DC Converters for Sustainable Applications

26.4 Speed Control of BLDC Motor with FPGA The Field Programmable Gate Array (FPGA) is the sensorless control tech­ nique which uses a PWM control scheme like a microcontroller. FPGA consists of a combinational logic block which is interconnected using programmable horizontal and vertical channels. The logic blocks are sur­ rounded by input/output blocks in order to communicate with the user. In high speed applications, there is a problem of undesirable commuta­ tion delay, which can be overcome by measuring the voltage and current control scheme [14]. The analog input can be given to the ADC convertor using the potentiometer. The voltage variations are fed to the FPGA for programming control algorithms. Further, it can be given to the inverter/ driver module to the BLDC motor for controlling the speed (Figure 26.7).

26.5 Advancements in Green IoT for BLDC Motors The Internet of Things has the potential to change the world. The world has completely taken a different shape and we can divide into two eras: an era before IoT and an era after IoT. Though all things and objects existed, they were not connected before IoT. But now, each and every object and thing is connected with each other. These things can interact, collaborate, and share their experiences with each other. An IoT system or solution built by using energy effectual hardware and software components in order to enable reduction of power consumption is known as the Green Internet of Things (GIoT). Green IoT design should concentrate on green design, green man­ ufacturing, green adoption, green energy, and eventually green recycling and/or green disposal, thus reducing its effect on the environment.

Potentiometer

ADC

FPGA (Algorithm for position control of rotor)

Inverter

BLDC Motor

Figure 26.7  FPGA based BLDC speed control.

Controlling the Speed of BLDC Motors Using Green IoT  787 BLDC uses electronics for brushes and commutators which have the ability to operate in multiple speeds. The BLDC is otherwise called an ECM or Electronically Commutated Motors Because of green fan technol­ ogy, the materials used are lighter and thereby increase the efficiency. Solar panels with green technology can be used for continuous power supply. For the speed control, the microcontroller can be substituted with node MCU which has an inbuilt Wifi module. Thus, the monitored parameters like voltage, current, and speed can be monitored remotely either with a mobile app or remote station.

26.6 Conclusion The speed control of BLDC can be controlled using various algorithm like PID and PI with a closed loop control scheme. This algorithm is pro­ grammed using an MSP430 microcontroller. With advancements in green technology, the BLDC can be fabricated with lightweight materials, higher efficiency, and remote controlling.

References 1. Working of BLDC motor https://robu.in/brushless-dc-motor-workingprinciple-construction-applications/ 2. Difference between 2-phase and 3-phase https://www.bldcpump.com/diffe​ rence-between-2-phase-and-3-phase/ dt June 22, 2018 3. Shanmugasundram, R.; Zakaraiah, K.M.; Yadaiah, N. Modeling, simulation and analysis of controllers for brushless direct current motor drives. J. Vib. Control 2013, 19, 1250–1264. 4. Arulmozhiyal, R.; Kandiban, R. Design of fuzzy PID controller for brush­ less DC motor. In Proceedings of the 2012 International Conference on Computer Communication and Informatics, Coimbatore, India, 10–12 January 2012; pp. 1–7. 5. Premkumar, K.; Manikandan, B. Adaptive neuro-fuzzy inference system based speed controller for brushless DC motor. Neurocomputing 2014, 138, 260–270. 6. Al-Maliki, A.Y.; Iqbal, K. FLC-based PID controller tuning for sensorless speed control of DC motor. In Proceedings of the 2018 IEEE International Conference on Industrial Technology (ICIT), Lyon, France, 20–22 February 2018; pp. 169–174. 7. Mamadapur, A.; Mahadev, G.U. Speed Control of BLDC Motor Using Neural Network Controller and PID Controller. In Proceedings of the 2019

788  DC-DC Converters for Sustainable Applications 2nd International Conference on Power and Embedded Drive Control (ICPEDC), Chennai, India, 21–23 August 2019; pp. 146–151. 8. Liu, L.; Liu, Y.J.; Chen, C.P. Adaptive neural network control for a DC motor system with dead-zone. Nonlinear Dyn. 2013, 72, 141–147. 9. Ibrahim, H.; Hassan, F.; Shomer, A.O. Optimal PID control of a brushless DC motor using PSO and BF techniques. Ain Shams Eng. J. 2014, 5, 391–398. 10. Ramya, A.; Balaji, M.; Kamaraj, V. Adaptive MF tuned fuzzy logic speed con­ troller for BLDC motor drive using ANN and PSO technique. J. Eng. 2019, 2019, 3947–3950. 11. Potnuru, D.; Mary, K.A.; Babu, C.S. Experimental implementation of Flower Pollination Algorithm for speed controller of a BLDC motor. Ain Shams Eng. J. 2019. 12. Wang, M.S.; Chen, S.C.; Shih, C.H. Speed control of brushless DC motor by adaptive network-based fuzzy inference. Microsyst. Technol. 2018, 24, 33–39. 13. Templos-Santos, J.L.; Aguilar-Mejia, O.; Peralta-Sanchez, E.; Sosa-Cortez, R. Parameter Tuning of PI Control for Speed Regulation of a PMSM Using BioInspired Algorithms. Algorithms 2019, 12, 54 14. Merugumalla, M.K.; Kumar, N.P. FFA-based speed control of BLDC motor drive. Int. J. Intell. Eng. Inform. 2018, 6, 325–342.

Index AC MG, 600, 601, 602 Acoustic noise, 340, 345, 472 Adaptive control, 602, 733, 746, 750, 751, 778 ADC converter, 783, 784, 785, 786 Agent-based control, 613 Alternate Phase Opposite Disposition (APOD), 208 Alternating Current (AC), 123, 126, 343, 392 Analogue to Digital Converter (ADC), 278 Angles, 168, 183, 187, 204–215, 223-230, 240, 248-264, 414, 424, 425, 490, 564, 562 Anisotropy, 464, 476, 490, 491 Ant-Lion algorithm, 666 Application of PBC, 724, 726 Armature winding, 780 Asymmetric, 204, 248, 293, 391 Automatic unmanned battery charging system, 517, 521 Average Voltage (VAVG), 274 Backlash, 754 Backstepping controller, 749, 750, 751, 753, 754, 756, 757, 759, 761, 763, 765, 766, 767, 768, 769, 771, 772, 773, 775, 777, 778 Bacteria foraging, 743 Bacterial forging (BFOA) optimization algorithm, 667 Bat algorithm, 667, 676 BBI (Buck Boost Inverter), 195

Bidirectional DC–DC Converters (BDC), 437, 442 Bidirectional power flow control for MPC with HESS, 144 Binary equivalent, 213, 214, 215, 224, 227, 228, 229, 230, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264 Biogeography based optimization, 675, 743 Bone, 337, 338, 339, 340, 341, 361, 362, 363, 365 Boost, 4, 5, 10, 12, 14, 15, 16, 17, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 41, 42, 43, 44, 48, 49, 50, 51, 53, 56, 57, 59, 62, 66, 67, 58, 71, 75, 78, 80, 81, 82, 83, 123 Boost converter, 4, 10, 14, 15, 16, 17, 443, 713 Boost/Boost-up resistance, 375 Brushless DC motor (BLDC), 337, 339, 341, 342 Brushless Direct Current (BLDC) motors, 779, 787 Buck converter, 7, 8, 10, 15, 17, 26, 749 Buck converters, 26 Buck-boost converter, 27, 28, 30, 48, 49, 50, 51, 52, 57 Carrier wave, 180, 208 Cascaded, 203, 208, 209, 210, 211, 212, 213, 215, 216, 217, 218, 219, 221 Cascaded H-bridge inverters, 293, 393

789

790  Index CBMLI (Cascaded Bridge Multi Level Inverter), 182 CB-PWM, 560 CCM (Continuous Conduction Mode), 75, 86, 149, 155, 157, 543, 612 Cdg/Miller capacitance, 377 Ceiling DC MG, 602 Central Control, 603, 608, 614, 619 Centralized Energy Management System, 606 Challenges of MG control, 623, 624 Closed loop speed control, 783, 785 Cogging, 412, 414, 421, 424, 433 Communication-based energy management scheme, 605, 608 Compact, 75, 79, 103, 105, 107, 112, 125, 293, 303, 304, 311, 443, 559, 560 Component count, 79, 105, 112, 117, 118 Component utilisation ratio, 117, 118 Configuration, 72, 73, 74, 83 Continuous MPC, 347, 348 Control design based on transfer function, 616 Control input, 636, 638, 640, 685, 688, 691, 697, 700, 707, 710–713, 718, 752, 753, 756, 757, 781, 782 Control law generation, 686, 692, 727 Control strategy of HESS, 447 Cost function, 339, 340, 343, 346, 347, 348, 349, 350, 351, 352, 353, 354, 360, 361, 583, 584, 585, 587, 589, 590, 618, 654 Coupled inductor, 7, 43, 68, 71, 77, 78, 83, 101, 105, 122, 124, 125, 323, 344, 519 Coupling coefficient, 94, 113, 114, 115, 117 Coyote optimization algorithm, 668 Cp/Piezo capacitance, 371 Crest factor, 279, 290

Crow search algorithm, 290, 743 Crystal oscillator, 278 CSI (Current Source Inverter), 183 Cuckoo search, 668, 676, 744 Cuckoo search algorithm, 744 Cuk-converter, 10, 17, 29 Current harmonics, 337, 339, 340, 346, 352, 353, 355, 357, 359, 360 Current stress, 80, 92, 98, 110, 114, 115, 116, 117, 118, 119 Current vector, 342, 351, 416 d axis, q axis inductance, 342, 361 Damping injection, 691, 617, 649, 682, 685, 686, 690, 696, 729 Data analysis and communication, 604 DC distribution, 64, 73, 74, 116, 121, 122, 125, 126, 601, 602 DC MG, 600, 601, 602 DC/Direct current, 370 DC-DC converter, 3, 71, 72, 73, 74, 75, 79, 80, 84, 122, 123, 124, 176, 540, 541, 542, 543, 544, 548, 553, 555, 557 DC-to-DC buck converters, 750 Dead zone, 754 Decentralized Energy Management System (DEMS), 607 DFIG, 556, 585, 590 Different structures of MG, 600 Digital form, 225, 248 Digital Pulse Width Modulation (DPWM), 203 Digital Switching Function (DSF), 204, 205, 215, 224, 231, 232, 234, 236, 248, 265, 266 Digital Switching Pattern (DSP), 206, 210, 231 Diode clamped MLI, 162 Diode-clamped inverters, 293, 301 DIR, 273 Direct Current (DC), 203, 471, 614, 633, 749, 779, 787

Index  791 Direct Lyapunov Control (DLC), 598, 617 Direct Torque Control (DTC), 298, 343, 344, 345, 346, 347, 348, 355, 560, 578 Distributed control, 613, 615, 616, 733 Distributed generation, 597, 659, 660, 663 Distributed generator, 621, 660 Drive cycle, 464, 509, 512 Droop control, 616 Dual boost converter, 442, 444, 445, 457, 459 Dual In Pack (DIP) Switch, 278 Dual output, 533, 536, 537, 540, 545, 548, 550 DVR (Dynamic voltage restorer), 185, 186, 187 Dynamic model, 687, 752, 753 Electric vehicle, 317, 318, 319, 411, 540, 541, 542, 543, 552, 557 Electric Vehicle Service Equipment (EVSE), 317, 318, 320 Electric vehicles, 394 EMC-Electromagnetic Compatibility, 176 EMF constant, 753 EMI-Electromagnetic Interference, 137, 175, 176, 294 EN/Enable, 375 Energy management schemes, 605, 624 Energy storage system for MG, 608 Equal phase-switching angle algorithm, 203, 208, 209 ESDI, 686 ETEDPOF, 687 Euler-Lagrange form, 645, 652, 681, 683, 728 EV charging stations (EVCS), 317, 318, 319, 320, 326, 536 Extreme duty ratios, 75, 76, 94

FACTs, 294, 296, 312 Faster Adoption and Manufacturing of Electric Vehicle (FAME I), 318 FC system, 24 Feed forward-switching angle algorithm, 203, 208, 209 Feedback decomposition, 683, 684 Field Oriented Control (FOC), 343, 344, 347, 355, 360 Field Programmable Gate Array (FPGA), 203, 204, 291, 292, 519, 786 Finite Control Set MPC (FCSMPC), 347, 348, 360 Fluke Power Analyzer (FPA), 279, 289 Flux density, 412, 414, 415, 421, 422, 464, 487, 488, 489, 498, 503, 506 Flux linkage, 464, 476, 478, 480, 481, 482 Flux ripple, 338, 340, 345, 346, 354, 356, 357 Flying capacitor inverter system, 391 Form Factor (FF), 274 Forward/backward (F/B) sweep load flow, 664 Fourier series, 168 Frequency, 204, 208 Frequency response, 712, 713, 727 Full load, 96, 97, 104, 106, 115 Fuzzy, 731, 733, 744, 745, 751 Fuzzy logic controller, 731, 733, 744 Generation, 18, 68, 73, 121, 203 Genetic algorithm, 666 Global warming, 463, 464 Gm/transconductance, 370 Gravitational search algorithm, 743 Grinding mills, 393 Half equal phase-switching angle algorithm, 203, 208, 209, 218, 235 Half height-switching angle algorithm, 203, 208, 209 Hall effect sensors, 337, 339, 341, 781

792  Index Hamiltonian, 681, 683, 684, 687, 698 Hard switching DC-DC converter, 4, 6 Hardware Description Language (HDL), 203, 204, 205 Harmonic component, 168, 421, 423 HBI - H bridge inverter, 181 H-Bridge, 204, 205, 206, 207, 208, 391 HESS types, 441, 447, 448, 449 High frequency switching, 4 High Gain Multi-Device Multi-Phase Interleaved Boost Converter (HGMDMPIBC), 43 High voltage gain, 71, 79, 94, 104, 111, 120, 122 High-frequency transformer (HFT), 137, 144 HVDC, 4, 294, 312, 394, 559 Hybrid AC/DC MG, 602, 627 Hybrid cascaded MLI, 167 Hybrid energy management systems, 133, 147, 440, 437 Hybrid Energy Storage System (HESS), 133, 147, 440, 437 Hybrid power, 1, 8, 517, 518, 528, 531 Hysteresis, 139, 333, 682, 754

Joint Test Action Group (JTAG) Programmer, 278

ICPT system, 128, 129, 130, 136 IEEE 33 system, 669, 679 IEEE 69, 679 IEEE and IEC Standards, 621 IEEE specifications, 392 IGBT switches, 38, 39 Incremental conductance, 193, 194, 195, 533, 538, 552 Incremental interleaved, 71, 76, 79, 80, 82, 83, 84, 92, 95, 98, 101, 103, 114, 116, 122 Interleaved boost converter, 43, 44, 444, 454, 455, 456 Inverter, 24, 62, 63, 64, 73, 108, 130, 136, 150, 160, 162, 173, 204, 206 Isolated DC-DC full-bridge converter (FBC), 131

Master/Slave control, 615 MATLAB, 127, 136, 139, 155, 175, 180, 181, 183, 195, 199, 216, 231, 277, 295, 297, 298, 340, 354, 357, 400, 749 MATLAB SIMULINK, 136, 139, 155, 175, 180, 181, 195, 216, 231, 268, 277, 295 MATLAB/Simulink, 297, 298, 340, 354, 357, 391, 400, 405, 530, 545, 654, 731 Maximum electrical rotation, 784 Maximum torque per ampere (MTPA), 353, 507 Metal oxide semiconductor field effect transistor, 206, 207, 210 MG concept, 599

LaSalle’s Theorem, 696, 697, 705, 706 LCC (Inductance Capacitance Capacitance), 136, 145, 146, 147, 559 Leakage, 74, 78, 79, 84, 96, 114, 117, 128, 137, 477, 480, 486 Lift converter, 7, 19, 68, 371, 372 Light Emitting Diode (LED), 278 Linear mode DC-DC converter, 4, 5 Liquid Crystal Display (LCD), 278 Load torque estimation, 628, 683, 695, 719, 720, 721, 722, 723, 728, 729 Load variation, 97, 326, 633, 648, 678, 766, 767 Loss distribution inductance, 100, 101, 111, 113, 116 Luo converter, 437, 442, 445, 456, 457, 459, 701, 710, 715, 718, 727, 728, 729 Lyapunov, 598, 617, 620, 627, 642, 645, 647, 681, 682, 685, 686, 726, 749, 756, 757, 758, 759, 761, 762, 763, 766

Index  793 MG control layer, 603 Microgrid, 4, 18, 116, 120, 121, 122, 125, 126, 335, 461, 536, 597, 598, 599, 601–629, 633, 645, 647 MIMO, 348, 731, 732, 734, 738, 742, 743, 744, 745, 778 MLI, 159, 176, 160, 161–173, 203–311 Model predictive control, 337, 339, 341, 343, 345, 346, 347, 348, 349, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 363, 364, 365, 366, 618 Moderate, 95, 114, 117, 119, 133, 204, 375, 376, 381, 382 Modern robotization, 17 Modular, 68, 69, 79, 104, 112, 116, 120, 125, 126, 147, 173, 200, 298, 301, 302, 312, 313, 535, 551, 559, 608, 624, 675 Modulating wave, 203, 205, 208 Modulation index, 178, 179, 208 Motor angular velocity, 753 MPP (Maximum Power Point), 192 MPPT (Maximum Power Point Tracking), 73, 80, 180, 185, 188, 189, 191, 192, 194, 195, 196, 537, 538, 552, 611, 632, 637, 638, 642, 643, 646, 647, 652, 657, 658 MSP430 microcontroller, 779, 781, 785, 787 Multi-Agent System (MAS) Based Distributed Control, 613 Multi-device boost converters (MDBC), 33 Multilevel inverter, 69, 159, 161, 162, 173, 174, 176, 182, 183, 193, 199, 200, 291, 292, 294, 295, 297, 298, 299, 300 Multi-phase converter, 32, 65 Multi-phase interleaved boost converter, 35, 37, 38, 42, 44 Multi-winding transformer, 133

National Electric Mobility Mission Plan (NEMMP), 318 Negative half/cycle, 130, 231 Negative Voltage, 242 NITI Aayog, 318 N-Level, 205, 280 Non-Inverting Buck-Boost Converters, 48 Non-isolated boost converter (BC), 134 Non-isolated DC-DC converters, 4, 10, 68, 74 Non-isolated DC-DC multi-device converter (MDC), 135 Non-isolated interleaved boost converter (IBC), 134 Nonlinear controller, 634, 730, 750 Number, 79, 81, 83, 94, 105, 112, 114, 115, 118, 707, 719, 723, 732, 739, 755, 757, 784 Online algebraic approach, 683, 720, 721, 722 OPAL-real time lab, 337, 340, 357 Open loop control, 782 Operating regions, 412, 424 Optimization, 66, 67, 68, 139, 194, 200, 313, 314, 348, 349, 514, 515, 519, 555, 588, 598, 603, 604, 607, 608, 616, 617, 621, 625, 628, 633, 639, 731, 742, 743 Optimization techniques, 604, 659, 664, 665, 670, 731, 742, 743 Orthopaedic, 337, 338, 339, 340, 341, 342, 351, 357, 361, 363 Output Enabled (OE), 273 Overview of MG Control, 611 P & O MPPT (Perturb and Observe MPPT), 192 P&O (Perturb & Observe), 192

794  Index Parallel, 5, 6, 17, 33, 34, 43, 44, 57, 72, 73, 74, 80, 125, 133, 146, 158, 187, 189, 196, 279, 292, 294, 388, 438 Parasitic conventional boost converter, 37 Particle swarm optimization, 364, 519, 598, 625, 665, 675, 743, 784 Passivity based control, 617, 628, 633, 644, 645, 646, 647, 648, 649, 650, 656, 681, 682, 683, 684, 685, 687, 689, 691, 693, 695, 697, 699, 701 Peak Voltage (VPEAK), 268, 290 PEMFC stacks, 24, 26, 65 Period, 75, 93, 110, 130, 143, 171, 191, 195, 215, 225, 248 Permanent magnet synchronous motor (PMSM), 337, 339, 340, 341, 342, 343, 344, 347, 349, 351, 353, 362 Phase Disposition (PD), 208 Phase Opposite Disposition (POD), 208 Phase shift PWM for switching, 132 Photo Voltaic (PV), 186 Photovoltaic, 175, 193, 195, 199, 200, 201, 202, 292, 293, 296, 297 PI controller, 352, 360, 588, 632, 644, 647, 747, 750, 751, 755, 756, 767, 768, 769, 770, 777 PID controller, 640, 731, 733, 742, 743, 744, 782, 784, 787 PM/piezomotors, 368 PMDC Motor, 437, 449, 451, 452, 454, 455, 458, 466, 752, 772 Positive half/cycle, 215, 224, 248, 265 Positive Voltage, 206, 241 Power Conditioning System (PCS), 73, 74 Power converter, 3, 71, 75, 92, 110, 127, 130, 145, 146, 149, 159, 173, 175, 191, 203, 279, 293, 317, 319, 337, 352 Power converters, 21, 22, 71, 127, 130, 145, 149, 159, 175, 203, 279, 293, 317, 319, 352

Power flow control by current regulation, 611 Power flow control by voltage regulation, 612 Power handling capacity, 79, 101, 392 Power loss minimization, 659, 662, 663, 667, 669, 673, 674 Power rating, 3, 72, 80, 98, 199, 319, 321, 391, 466, 558, 570 Power switching converter, 3 PQ control, 614, 615 Predictive control, 139, 337, 338, 339, 341, 342, 343, 345, 347, 349, 350, 351, 353, 355, 357, 359, 360, 361, 562 Programmable logic controllers (PLCs), 17 Programmable Read Only Memory (PROM), 278 Proton exchange membrane fuel cell, 295 Push-Pull converter, 8 PV (Photovoltaic), 71, 72, 73, 74, 75, 77, 79, 81, 83, 85, 87, 89, 91, 176 PWM (Pulse Width Modulation), 49, 129, 131, 160, 177, 178, 203, 204, 751 PWM duty cycle, 781, 782, 784, 785 PZT/piezoelectric, 368 Quadrant, 14, 204, 208, 209, 210, 213, 214, 215, 223, 224 Quadratic boost converter, 533, 535, 536, 537, 539, 540, 543, 544, 546, 547, 550, 552 Quasi, 147, 248, 387, 389, 551 R1 to R7/Resistances, 368 Radial distribution network, 659, 661, 669, 674, 675 Real-time optimization, 604 Recursive method, 389, 750 Reduced order observer, 723, 727, 728, 729

Index  795 Reference profile generation, 713 Reluctance, 463, 464, 471, 472, 475, 476, 482, 490, 491, 498, 503, 513, 514 Reluctance torque, 414, 415, 424, 427 Renewable energy sources, 120, 200, 251, 319, 322, 392, 518, 534, 553, 599, 611, 631, 655 RES (Renewable Energy Sources), 200 Resistive load, 206, 305, 690, 749, 752, 767 Resistive-inductive load, 209 Resolution, 205, 210, 215, 225, 248, 266, 268, 274, 276, 277, 278, 279, 280, 286, 287, 288, 290, 341 REXT/Resistor, 368 R-load, 211, 401, 403, 751, 752, 753, 757 Role, 16, 72, 73, 117, 130 Root Mean Square (RMS), 203, 268 Root Mean Square Voltage (VRMS), 268, 274, 278 Rotor, 476, 477, 478, 481, 482, 485, 486, 487, 488, 489, 490, 491, 493, 496, 497 RS232 port, 278 Scaling value, 215, 224, 248 Selective Harmonic Elimination (SHE), 204 Sensitivity analysis, 419, 515, 681, 706, 707, 708, 709, 710, 727, 729 Sepic converter, 12, 22, 24, 30, 31, 32, 134, 456, 728 Series voltage controller, 5 Shuffled frog leap algorithm, 667 Sine wave, 84, 171, 196, 203, 208 Sliding mode controllers, 632, 751 SMC control for BC converter, 142

Soft switching converters, 22 Soft switching DC-DC converter, 4, 16 Solar charging, 519, 520, 530 Solar irradiation, 181, 189, 190 Space vector modulation, 345, 560, 561, 578, 591 SROO approach, 720 State of dissipation, 691 Stator resistance, 342 Steady state, 10, 12, 31, 41, 42, 53, 54, 55, 56, 63, 65, 66, 151, 755 Steady state current waveforms, 41 Step-down converter, 14 Strictly passive system, 684 Stud krill herd algorithm, 668 Switch mode power converters, 4, 149, 749 Switching Angle Algorithm (SAA), 203, 205 Switching frequency, 151, 153, 154, 155, 156, 157, 158, 340, 345, 352, 360 Switching loss, 98, 101, 113, 114, 116, 137, 150, 154, 183, 184, 205, 297, 298, 326, 332, 344, 346, 353, 582, 586 Switching pattern, 159, 163, 165, 203, 205, 206, 210, 215, 216, 231, 241, 265, 268, 280 Symmetric, 67, 98, 116, 124, 129, 204, 248, 391, 686, 688, 695, 703 Symmetric inverter, 293, 307, 311, 313, 394, 408 Synthesis, 71, 80, 83, 84, 101, 104, 110, 112, 122 Synthesized resistor transistor logic, 279 System generator, 204, 216, 231, 268

796  Index THD, 159, 266, 268, 269, 270, 275, 277, 290, 298, 308, 313, 361 Topology, 31, 204, 205, 206, 222, 296, 308, 313, 314, 323, 324, 326, 391, 392, 407 Torque, 337, 338, 339, 340, 343, 344, 345, 346, 347, 348, 349, 350, 351, 353, 361, 362 Torque equation, 415, 417, 683 Torque ripple, 337, 338, 339, 340, 344, 345, 348, 351, 353, 354, 355, 356, 357, 359, 360, 361, 500, 502, 503, 504, 505, 512, 513, 515 Total harmonic distortion, 159, 172, 175, 182, 183, 185, 199, 290 , 291, 298, 319, 402, 632 Triangular, 203, 205, 208 Trinary Cascaded Hybrid MLI circuit, 208, 210, 223, 240, 266, 277 Turns ratio, 74, 79, 87, 91, 92, 93, 94, 110, 111, 115, 118 UC3524 controller, 768, 773, 775, 776, 777 Unequal, 109, 203, 204, 206, 222, 240, 294, 295, 305, 307, 392, 616 UPS (Uninterruptable Power Supply), 68, 121, 163, 186, 187, 199, 373, 534, 615 Urban DC MG, 600, 602 Very High Speed Integrated Circuit Hardware Description Language (VHDL), 204, 210, 280 Virtual control, 749, 756, 758, 759, 761, 762, 764

Voltage level, 16, 22, 63, 72, 73, 91, 96, 97, 111, 119, 120, 121, 122, 133, 161, 167, 169, 180, 203, 303, 311, 384, 396, 399, 3407, 439, 618, 634, 660 Voltage multiplier cell, 68, 77, 79, 124, 125 Voltage source inverter, 199, 293, 297, 311, 350, 354, 393, 654 Voltage sources, 27, 48, 169, 296, 303, 305, 307, 308, 324, 391, 394, 396, 407 Voltage stress, 16, 43, 78, 79, 84, 91, 92, 93, 95, 96, 97, 109, 115, 116, 117, 118, 160, 162, 182, 204, 205, 300, 392, 535 Voltage vector, 339, 342, 344, 346, 347, 348, 349, 350, 352, 354, 416, 417 VSI control, 614 WECS, 553, 554, 555, 556, 557, 558, 559, 560, 564, 567, 569 Weighting factor, 340, 346, 349, 350, 351, 352, 353, 390 Whale optimization algorithms, 666 Xilinx Spartan FPGA, 273, 279 Zener diodes, 377 Zero, 222, 240, 273 Zero current switching (ZCS), 16, 18, 131, 150, 325, 326, 328 Zero Voltage Switching (ZVS), 16, 18, 130, 150, 175, 323, 324, 325, 326 ZVS, 323, 324, 325, 326

Also of Interest Check out these related titles from Scrivener Publishing HYDROGEN ELECTRICAL VEHICLES, Edited by Mehmet Sankir and Nurdan Demirci Sankir, ISBN: 9781394166381. Hydrogen electrical vehicles are an essential component of the “Green New Deal” and this book covers cutting-edge technologies designed for fuel-cell-powered cars. DESIGN AND DEVELOPMENT OF EFFICIENT ENERGY SYSTEMS, edited by Suman Lata Tripathi, Dushyant Kumar Singh, Sanjeevikumar Padmanaban, and P. Raja, ISBN 9781119761631. Covering the concepts and fundamentals of efficient energy systems, this volume, written and edited by a global team of experts, also goes into the practical applications that can be utilized across multiple industries, for both the engineer and the student. NOW AVAILABLE! Electrical and Electronic Devices, Circuits, and Materials: Technical Challenges and Solutions, edited by Suman Lata Tripathi, Parvej Ahmad Alvi, and Umashankar Subramaniam, ISBN 9781119750369. Covering every aspect of the design and improvement needed for solid-state electronic devices and circuit and their reliability issues, this new volume also includes overall system design for all kinds of analog and digital applications and developments in power systems. NOW AVAILABLE! Green Energy: Solar Energy, Photovoltaics, and Smart Cities, edited by Suman Lata Tripathi and Sanjeevikumar Padmanaban, ISBN 9781119760764. Covering the concepts and fundamentals of green energy, this volume, written and edited by a global team of experts, also goes into the practical applications that can be utilized across multiple industries, for both the engineer and the student. NOW AVAILABLE!

Check out these other related titles from Scrivener Publishing INTELLIGENT RENEWABLE ENERGY SYSTEMS: Integrating Artificial Intelligence Techniques and Optimization Algorithms, edited by Neeraj Priyadarshi, Akash Kumar Bhoi, Sanjeevikumar Padmanaban, S. Balamurugan, and Jens Bo Holm-Nielsen, ISBN 9781119786276. This collection of papers on artificial intelligence and other methods for improving renewable energy systems, written by industry experts, is a reflection of the state of the art, a must-have for engineers, maintenance personnel, students, and anyone else wanting to stay abreast with current energy systems concepts and technology. NOW AVAILABLE! SMART CHARGING SOLUTIONS FOR HYBRID AND ELECTRIC VEHICLES, edited by Sulabh Sachan, Sanjeevikumar Padmanaban, and Sanchari Deb, ISBN 9781119768951. Written and edited by a team of experts in the field, this is the most comprehensive and up to date study of smart charging solutions for hybrid and electric vehicles for engineers, scientists, students, and other professionals. NOW AVAILABLE! Microgrid Technologies, edited by C. Sharmeela, P. Sivaraman, P. Sanjeevikumar, and Jens Bo Holm-Nielsen, ISBN 9781119710790. Covering the concepts and fundamentals of microgrid technologies, this volume, written and edited by a global team of experts, also goes into the practical applications that can be utilized across multiple industries, for both the engineer and the student. NOW AVAILABLE! Progress in Solar Energy Technology and Applications, edited by Umakanta Sahoo, ISBN 9781119555605. This first volume in the new groundbreaking series, Advances in Renewable Energy, covers the latest concepts, trends, techniques, processes, and materials in solar energy, focusing on the stateof-the-art for the field and written by a group of world-renowned experts. NOW AVAILABLE! Energy Storage 2nd Edition, by Ralph Zito and Haleh Ardibili, ISBN 9781119083597. A revision of the groundbreaking study of methods for storing energy on a massive scale to be used in wind, solar, and other renewable energy systems. NOW AVAILABLE!

Nuclear Power: Policies, Practices, and the Future, by Darryl Siemer, ISBN 9781119657781. Written from an engineer’s perspective, this is a treatise on the state of nuclear power today, its benefits, and its future, focusing on both policy and technological issues. NOW AVAILABLE! Zero-Waste Engineering 2nd Edition: A New Era of Sustainable Technology Development, by M. M. Kahn and M. R. Islam, ISBN 9781119184898. This book outlines how to develop zero-waste engineering following natural pathways that are truly sustainable using methods that have been developed for sustainability, such as solar air conditioning, natural desalination, green building, chemical-free biofuel, fuel cells, scientifically renewable energy, and new mathematical and economic models. NOW AVAILABLE!

WILEY END USER LICENSE AGREEMENT Go to www.wiley.com/go/eula to access Wiley’s ebook EULA.