Intelligent Electrical Systems: A Step Towards Smarter Earth 9780429355998

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INTELLIGENT ELECTRICAL SYSTEMS A STEP TOWARDS SMARTER EARTH Edited by Satyajit Chakrabarti, Ayan Kumar Panja, Amartya Mukherjee, and Arun Kr. Bar

Intelligent Electrical Systems: A Step towards Smarter Earth

Satyajit Chakrabarti is Pro-Vice Chancellor, UEM a premier organization in education sector in India, started many entrepreneurial ventures. He is also Director of Institute of Engineering & Management (IEM) and University of Engineering & Management (UEM), Kolkata, India. Ayan Kumar Panja is Assistant Professor at IEM, Kolkata, India. Amartya Mukherjee is Assistant Professor at IEM, Kolkata, India. He has authored several books on embedded systems, IoT and sensor networks. Arun Kumar Bar is PhD from Jadavpur University, He has more than 20 years of teaching and research experience in the field of Mechanical Engineering.

Conference Proceedings Series on Information and Communications Technology Intelligent computing, data analysis and smart communication are currently among the paramount research domains in IT. This series consisting of conference proceedings mainly focuses on the recent advancement and research techniques in the field of intelligent information processing, data analysis, computing and smart communication. The series brings together latest research done in the area that addresses key challenges and issues in the domain of intelligent sensing, ubiquitous computing, cyber-physical systems, signal processing, data analysis, smart energy management, mechatronics, biomedical systems, smart city infrastructure and artificial intelligence.

Series Editor Nilanjan Dey is an Assistant Professor in the Department of Information Technology at Techno International Newtown, Kolkata, India. He is a visiting fellow of the University of Reading, UK. He was awarded his PhD. from Jadavpur University in 2015. He has authored/ edited more than 75 books with Elsevier, Wiley, CRC Press and Springer, and published more than 300 papers. He is the Editor-in-Chief of International Journal of Ambient Computing and Intelligence, IGI Global, Associated Editor of IEEE Access and International Journal of Information Technology, Springer. He is the Series Co-Editor of Springer Tracts in NatureInspired Computing, Springer Nature, and Series Co-Editor of Advances in Ubiquitous Sensing Applications for Healthcare, Elsevier, Series Editor of Computational Intelligence in Engineering Problem Solving and Intelligent Signal processing and data analysis, CRC. His main research interests include Medical Imaging, Machine learning, Computer-Aided Diagnosis, Data Mining etc. He is the Indian Ambassador of International Federation for Information Processing (IFIP) – Young ICT Group.

Other titles in the Series ICT for Competitive Strategies Proceedings of 4th International Conference on Information and Communication Technology for Competitive Strategies (ICTCS 2019), December 13th–14th, 2019, Udaipur, India. Edited by Durgesh Kumar Mishra, Nilanjan Dey, Bharat Singh Deora, Amit Joshi. Computer-Aided Developments: Electronics and Communication Proceeding of the First Annual Conference on Computer-Aided Developments in Electronics and Communication (CADEC-2019), Vellore Institute of Technology, Amaravati, India, 2–3 March 2019. Edited by Arun Kumar Sinha, John Pradeep Darsy.

Intelligent Electrical Systems: A Step towards Smarter Earth Proceedings of the International Conference on Industrial Electronics Mechatronics Electrical & Mechanical Power (IEMPOWER 2019), November 21–23, 2019, Kolkata, India.

Edited by Satyajit Chakrabarti, Ayan Kumar Panja, Amartya Mukherjee, and Arun Kr. Bar

First edition published 2021 by CRC Press 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487–2742 and by CRC Press 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN © 2021 by CRC Press, Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, LLC Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, access www.copyright.com or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. For works that are not available on CCC please contact [email protected] Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging in Publication Data A catalog record has been requested for this book ISBN: 978-0-429-35599-8 (eBook) Typeset in Minion Pro font Typeset by Ozone Publishing Services, Puducherry, India.

Contents Organizing Committee

xix

Acknowledgements

xxi

Preface

xxiii

Foreword

xxv

About the Editors Chapter 01

Design of One Adaptive Controller for a Dynamic Framework with Non-linear Parameterisation



xxvii

1

Samiran maiti and aChintya daS

1.1

INTRODUCTION

1

1.2

NON-LINEAR PARAMETERIZED FRAMEWORK

2

1.3

CONTROLLER DESIGN

3

1.2.1

Lyapunov Stability Analysis

4

1.4

RESULTS

5

1.5

CONCLUSION

8

REFERENCES

Chapter 02



8

A Comparative Study of Phasor Estimation Techniques

11

p. r. pattanaik, BaSanta. k. panigrahi, S. pati, S. k. Sanyal, and nakul Sahu

2.1

INTRODUCTION

11

2.2

PHASOR ESTIMATION TECHNIQUES

12

2.2.1

Discrete Fourier Transform Based Phasor Estimation

12

2.2.2

Discrete Wavelet Transform Based Phasor Estimation

13

2.2.3

Least Square Method Based Phasor Estimation

14

v

vi



Contents

2.3

2.4

RESULTS AND DISCUSSION

14

2.3.1

Signal Reconstruction

14

2.3.2

Total Vector Error

15

2.3.3

Transient Monitor

16

2.3.4

Effect of Noise

16

2.3.5

Effect of Harmonics

18

2.3.6

Effect of Sampling Frequency

18

CONCLUSION

REFERENCE

Chapter 03



19 19

Adaptive Fuzzy PID Controller for a Current Controlled Multilevel Inverter Fed Matrix Converter

21

g. mohapatra, m. k. deBnath, and k. k. mohapatra

3.1

INTRODUCTION

21

3.2

MULTILEVEL INVERTER

22

3.3

SYSTEM MODELLING

23

3.4

MATRIX CONVERTER

24

3.5

DIFFERENTIAL EVOLUTION ALGORITHIM (DEA)

24

3.6

PROPOSED CONTROLLER

24

3.7

SYSTEM BLOCK DIAGRAM

26

3.8

RESULT AND DISCUSSION

27

3.9

RESULT ANALYSIS

29

3.10

CONCLUSION

29

APPENDIX

29

REFERENCES

29

Chapter 04



Multi-Objective Optimization for Enhanced Surface Roughness and Microhardness of AA 6063/TiO2 Cast Aluminium Metal Matrix Nanocomposites Fabricated by Friction Stir Processing

31

laxmanaraju, lingaraju dumpala, and pavankumar r

4.1

INTRODUCTION

32

4.2

EXPERIMENTATION

33

4.3

RESULTS AND DISCUSSIONS

35

4.4

CONCLUSION

38

REFERENCES

39

Contents

Chapter 05





Self-Adaptive Multivariate q-Gaussian-based Capacitor Placement for Reactive Power Compensation in Distribution Feeders

vii

41

deBaShiS jana and ranjita Chowdhury

5.1

INTRODUCTION

41

5.2

PROBLEM FORMULATION

42

5.3

DISCUSSION

46

5.4

CONCLUSION

47

REFERENCES

Chapter 06



48

Differential Evolution Coupled Neural-based Prediction of Soil Water Content

49

Sayan Saha, kauShik majumder, Bitan ChakraBorty, and Sankhadeep Chatterjee

6.1

INTRODUCTION

49

6.2

BACKGROUND

50

6.3

METHODOLOGY

52

6.4

RESULTS & DISCUSSION

54

6.5

CONCLUSION

56

REFERENCES

Chapter 07



56

Numerical Investigation of Heat Conduction in a Rectangular Composite Plate with Sinusoidal Heat Input from Top Wall

59

deBarghya kar and Sumanta Banerjee

7.1

INTRODUCTION

59

7.2

METHODOLOGY

60

7.3

DISCUSSION

62

REFERENCES

Chapter 08



64

Analytical Modelling and Simulation of a Hot-Wall Condenser Applied to Domestic Refrigerator

65

S. n. Sapali and n. d. Shikalgar

8.1

INTRODUCTION

8.2 ANALYTICAL HEAT TRANSFER MODEL OF THE HOT-WALL CONDENSER 8.2.2

Variation of outside heat flux with contact angle in the hot-wall condenser

66 67 68

viii



Contents

8.3 8.4

NUMERICAL HEAT TRANSFER SIMULATION OF THE HOT-WALL CONDENSER WITH ANGULAR CONTACT

69

CONCLUSION

69

REFERENCES

Chapter 09



70

Design and Analysis of a Dual-Axis Solar Tracker with an In-built Low Cost Self-Cleaning Mechanism

71

moumita pramanik, tuhin kumar Barui, pankaj kumar giri, hiranmay Samanta, nirmal kumar deB, and hiranmay Saha

9.1

INTRODUCTION

71

9.2

DESIGN

72

9.3

OPERATION

74

9.4

RESULTS AND DISCUSSION

75

9.5

CONCLUSION AND FUTURE SCOPE

77

REFERENCES

Chapter 10



78

Indices based Comparative Performance Analysis of Standard Test Systems for Reliable Power System Operation

79

r. Chowdhury and d. jana

10.1

INTRODUCTION

79

10.2

METHODOLOGY

80

10.3

DISCUSSION

81

10.4

CONCLUSION

84

REFERENCES

Chapter 11



85

Natural Ground-Water Recharge Scenario in Kolkata and a Review of Artificial Recharging

87

j. Begam, S. Sarkar, S. Sarkar, and S. BhattaCharya

11.1

INTRODUCTION

88

10.2

METHODOLOGY

88

11.3

DISCUSSION

90

11.4

CONCLUSION

90

REFERENCES

91

Contents

Chapter 12



Performance Analysis of Grid Connected PV system under Varying Irradiance and Temperature



ix

93

B. tudu, a. BiSwaS, a. maji, k. Sardar, and k. k. mandal

12.1

INTRODUCTION

94

12.2

METHODOLOGY

95

12.3

DISCUSSION

96

12.4

CONCLUSION

103

ACKNOWLEDGMENT

103

REFERENCES

104

Chapter 13



Development of a Low Cost Autonomous Car Parking System: Towards Smart City

105

arjun dutta, ankur BhattaCharjee, and aBhijit kar gupta

13.1

INTRODUCTION

106

13.2

METHODOLOGY

107

13.2.1

Explanation

108

13.2.2

Explanation

108

13.3

DISCUSSION

109

13.4

CONCLUSION

110

REFERENCES

Chapter 14



111

Monitoring Static Security Assessment in Its Full Scope Using Common Artificial Neural Network

113

S. k. tiwary, j. pal, and C. k. Chanda

14.1

INTRODUCTION

114

14.2 ANN DEVELOPMENT AND APPLICATION TO TEST-BUS-NETWORK

114

14.3

RESULTS AND DISCUSSION

117

14.4

CONCLUSION

119

ACKNOWLEDGMENT

119

REFERENCES

120

Chapter 15



Modelling of Solar Cell Considering One Diode Model in MATLAB/Simulink Environment

123

SnehaShiS ghoShal, Sumit Banerjee, and Chandan kumar Chanda

15.1

INTRODUCTION

123

15.2

MODELLING OF SOLAR CELL

124

x



Contents

15.3

SIMULATION MODEL OF A SOLAR CELL

126

15.4

RESULTS AND DISCUSSION

127

15.5

CONCLUSION

128

REFERENCES

Chapter 16



128

Modelling of Intelligent Cooling of a Building in MATLAB/Simulink Environment

131

SnehaShiS ghoShal, Sumit Banerjee, and Chandan kumar Chanda

16.1

INTRODUCTION

16.2 THERMAL MODELLING OF A HOUSE REQUIRING COOLING LOAD

16.3

131 133

16.2.1

Thermostat subsystem

133

16.2.2

Chiller subsystem

133

16.2.3

House subsystem

134

16.2.4

Environment subsystem

135

SIMULATION MODEL OF A HOUSE REQUIRING COOLING LOAD

135

16.4

RESULT S AND DISCUSSION

136

16.5

CONCLUSION

137

REFERENCES

Chapter 17



137

Control and Monitor of Non-linear Gas Flow by Developing a Self-Adaptive Fuzzy Controller

139

a. k. pal, Sampa paul, indrajit naSkar, and a. mondal

17.1

INTRODUCTION

139

17.2

METHODOLOGY

140

17.2.1

Mathematical Modelling of the System

140

17.2.1.1 Modelling of Control Valve

140

17.2.1.2 Modelling of Gas Sensor

141

17.2.1.3 Modelling of Process

141

17.2.1.4 Overall Representation

142

Controller Design

143

17.2.2 17.3

RESULTS AND COMPARATIVE STUDY

145

17.4

CONCLUSION

148

REFERENCES

148

Contents

Chapter 18



Transient Stability Controlling and Assessment of a Congested Power System in a Deregulated Environment



xi

151

d. Sarkar, r. BrahmaChary, and S. d. Barma

18.1

INTRODUCTION

151

18.2

EIGEN VALUE ANALYSIS

153

18.3

STUDY OF THE IEEE 14 BUS TEST MODEL

155

18.4

CONGESTION STUDY IN THE IEEE14 BUS TEST SYSTEM

156

18.5

RESULT AND DISCUSSION

156

18.5.1

Analysis without using Facts Devices

156

18.5.2

Analysis with using Statcom Model

158

18.5.3

Analysis Using SVC Model

160

18.6

CONCLUSION

REFERENCES

Chapter 19



161 162

Bagasse Drying by Waste Heat Recovery from Surrounding Walls of the Combustion Chamber of a Jaggery Plant

163

a. B. Shinde, S. n. Sapali, and y. v. Sonone

19.1

INTRODUCTION

163

19.2

METHODOLOGY

164

19.2.1

165

19.3

Experimentation

DISCUSSION

166

19.3.1

Numerical Analysis

166

19.4

EXPERIMENTAL RESULTS

169

19.5

CONCLUSION

172

REFERENCES

Chapter 20



172

Study of Score Coefficient Functions for DBSCAN-based Photometric Invariant Approach in Vision Sensor-Based Shoe Detection for Human Tracking

173

p. paral, a. Chatterjee, and anjan rakShit

20.1

INTRODUCTION

173

20.2

PROPOSED RESEARCH FRAMEWORK

175

20.3

EXPERIMENTAL RESULTS

177

xii



Contents

20.4

20.3.1

Experimental Setup

177

20.3.2

Impacts of score coefficient functions on ACSAD distances

177

20.3.3

Performance Evaluations

178

CONCLUSION

179

ACKNOWLEDGMENT

180

REFERENCES

180

Chapter 21

Auto-adaptive Fuzzy Controllers with Automatic Setpoint Adjustment



181

a. k. pal, indrajit naSkar, Sampa paul, and j. ChakraBorty

21.1

INTRODUCTION

181

21.2

CONTROLLER DESIGN

182

21.2.1

184

Fuzzy Setpoint weighting (FSW) scheme

21.3

RESULT

186

21.4

CONCLUSION

188

REFERENCES

Chapter 22



188

An Application of Multivariate Control Chart for Online Process Monitoring in SMEs

191

S. Samanta and S. mondal

22.1

INTRODUCTION

191

22.2

METHODOLOGY

192

22.3

DISCUSSION

194

22.4

CONCLUSION

197

REFERENCES

Chapter 23



198

Analysis and Performance Indexing of Khagaria 132/33 kV Sub-station Using ETAP Load Flow Solutions

199

arChiSman kar, deBaShiS jana, Chiranjit dey, and ranjita Chowdhury

23.1

INTRODUCTION

200

23.2

METHODOLOGY & NETWORK FORMULATION

201

23.2.1

About ETAP

203

23.2.2

Khagaria Substation

204

23.3

RESULT ANALYSIS & DISCUSSION

205

23.4

CONCLUSION

208

REFERENCES

209

Contents

Chapter 24



Fractional Order PID controller for Setpoint Tracking and Load Rejection



xiii

211

Sudipta ghoSh, arijit Bhowmik, dipaBala Sarkar, anirBan Bhatta, and BiSwajit ChakraBorty

24.1

INTRODUCTION

212

24.2

CONTROLLER DESIGN

212

24.3

RESULTS

214

24.4

CONCLUSION

215

REFERENCES

Chapter 25



216

Analysis and Simulation of PWM-Based Half-Bridge and Full-Bridge Switch Mode Amplifier for Active Magnetic Bearing (AMB)

217

S. deBnath, p. k. BiSwaS, S. gupta, and j. laldingliana

25.1

INTRODUCTION

217

25.2 ACTIVE MAGNETIC BEARING

218

25.3

CLOSED LOOP SYSTEM OF AMB

219

25.4

POWER AMPLIFIER

220

25.4.1

221

Full bridge switch mode power amplifier

25.5

PULSE WITH MODULATION

221

25.6

SIMULATION RESULTS

222

25.7

CONCLUSION

225

ACKNOWLEDGEMENT

225

REFERENCES

225

Chapter 26



Design and Analysis of High-Speed Phase Locked Loop in 180 nm Technology

227

a. r. aBdul rajak, azeem gafoor mohammed, and deep Sehgal

26.1

INTRODUCTION

228

26.2

MATHEMATICAL MODEL FOR PLL

229

26.3 TRANSISTOR LEVEL IMPLEMENTATION AND RESULTS 26.3.1

Phase Frequency Detector (PFD)

231 231

26.4

CHARGE PUMP (CP)

233

26.5

LOOP FILTER DESIGN (LF)

235

26.6 VOLTAGE CONTROLLED OSCILLATOR (VCO)

235

26.7

DIVIDER (DIV)\

238

26.8

CONCLUSION

239

xiv



Contents

ACKNOWLEDGEMENTS

239

REFERENCES

239

Chapter 27



Design of APOD-PWM Based Multi-level Inverter using Cuk DC–DC Converter with MPPT

241

rajarShi dhar and SarBojit mukherjee

27.1

INTRODUCTION

242

27.2

SYSTEM DESIGN AND ANALYSIS

242

27.2.1

Tracking of MPPT

244

27.2.2

DC-DC Circuit

245

27.2.3

Proposed Multi-Level Inverter

247

27.2.4

Proposed Pwm Technique

248

27.3

SIMULATION RESULT AND ANALYSIS

249

27.4

CONCLUSION

253

REFERENCES

Chapter 28



253

Battery Storage Technologies: A Review

257

Bikram kumar Samanta, hiranmay Samanta, nirmal kr. deB, and hiranmay Saha

28.1

INTRODUCTION

258

28.2

METHODOLOGY

258

28.2.1

258

Lead Acid Battery

28.3

SODIUM SULFUR BATTERY

259

28.4

NICKEL CADMIUM BATTERY

260

28.5

LITHIUM-ION BATTERY

261

28.6 VANADIUM REDOX FLOW BATTERY

262

28.7

ZINC BROMIDE BATTERY

263

28.8

POLYSULPHIDE BROMINE

264

28.9

SODIUM-NICKEL CHLORIDE

264

28.10 DISCUSSION

264

28.11 CONCLUSION

267

REFERENCES

268

Chapter 29



Experimental Investigation of Solar Energy-Assisted DC Refrigerator

269

n. d. Shikalgar and S. n. Sapali

29.1

INTRODUCTION

269

29.2

DESIGN OF SOLAR PHOTOVOLTAIC PLANT

270

Contents



xv

29.3

EXPERIMENTAL STUDIES

271

29.4

RESULTS AND DISCUSSION

272

29.5

CONCLUSION

274

REFERENCES

Chapter 30



275

Automatic Speed Control of a Three Phase Induction Motor by Variable Frequency Drive

277

Sayantan Chanda, Chayan Bandopadhyay, maitreyee Banerjee, Shalini mondol, and ankur BhattaCharjee

30.1

MOTIVATION

277

30.2 V/F SPEED CONTROL METHOD

278

30.3 VARIABLE FREQUENCY DRIVE

278

30.4

CLOSED LOOP SIMULATION OF V/F SPEED CONTROL OF THREE PHASE INDUCTION MOTOR

279

30.4.1

Rectifier

280

30.4.2

L-C Filter

281

30.4.3

DC-DC Booster

281

30.4.4

PWM Generator

282

30.4.5

Inverter

283

30.4.6

Simulation Result

284

30.4.6.1 Inverter Output Voltage Curve

284

30.4.6.2 Rotor Speed Characteristics

284

FFT Analysis and Speed Analysis of Three Phase Induction Motor

284

30.4.7 30.5

CONCLUSION

REFERENCES

Chapter 31



285 286

OWEC: Optimised Weighted Ensemble Classifier Using Particle Swarm Optimisation

287

Syed fahim karim and ayan kumar panja

31.1

INTRODUCTION

287

31.2

BACKGROUND

288

31.3

OPTIMIZED WEIGHTED ENSEMBLE CLASSIFIER (OWEC)

289

31.3.1

Approach

290

31.3.2

Advantages

292

31.3.3

Results

292

31.4

FUTURE SCOPE

293

xvi



Contents

31.5

CONCLUSION

REFERENCES

Chapter 32



294 294

Detection of Disaster Affected Regions Using Drone-assisted Deep Learning Model

295

nikhil Singh, amitoSh Banerjee, Swadhin BhowmiCk, Sneha ChakraBorty, and

amartya mukherjee

32.1

INTRODUCTION

295

32.2

METHODOLOGY AND ALGORITHM

297

32.3

DISCUSSION

300

32.4

CONCLUSION

301

REFERENCES

Chapter 33



302

Enhancing Massive Open Online Courses with Brain Computing Interface and Artificial Intelligence

305

Sayantan pal, SaptarShi neogi, Sayanti dutta, Sumalyo datta, nilanjana Bandyopadhyay, and yaShaSwi raj

33.1

INTRODUCTION

305

33.2

METHODOLOGY

306

33.3

CONCLUSION

310

REFERENCES

Chapter 34



310

Application of Multi-Objective Particle Swarm Optimization Technique for Analytical Solution of Economic and Environmental Dispatch

313

S. roy, d. laha, a. daS, S. Chatterjee, m. BiSwaS, r. k. mandal, and B. k. ghoSh

34.1

INTRODUCTION

314

34.2

PROBLEM STATEMENT

314

34.3

METHODOLOGY

316

34.4

RESULT AND DISCUSSION

317

34.5

CONCLUSION AND FUTURESCOPE

318

REFERENCES

Chapter 35



318

Generation of Electricity From Harmful Gases using Fuel Cell

321

diptadip daS, Sayak Samanta, and praBal Saha

35.1

INTRODUCTION

322

35.2

METHODOLOGY

323

Contents

35.3 35.4

35.5



xvii

35.2.1

Materials Required

323

35.2.2

Fuel Cells

324

EXTRACTION OF OXYGEN

324

35.3.1

325

Extraction of Hydrogen

DISCUSSION

326

35.4.1

Parameters of fuel cell

326

35.4.2

Results

328

CONCLUSION

REFERENCES

Chapter 36



329 329

Exploring Potential Building Energy Saving through Daylight Harvesting through Light Pipe

331

v. aditya, BidiSha BhattaCharya, and gunjan kumar

36.1

INTRODUCTION

331

36.1.1

Aims of the Current Research

332

36.1.2

Problems and Factors that are to be Dealt

332

36.1.3

Research Problem

332

36.2

BACKGROUND INFORMATION

332

36.3

METHODOLOGY

333

36.3.1

Window-wall ratio

333

36.3.2

Energy Modelling and Simulation Result

333

36.3.3

Building Occupancy Schedule

334

36.3.4

Building Energy Simulation

335

36.3.5

Daylight calculation

336

36.3.5.1 Daylight analysis report Zone wise

337

36.4 36.5

DISCUSSIONS

338

36.4.1

339

Expected Cost for Light Pipe

CONCLUSION

REFERENCES

Chapter 37



339 339

Greenhouse Gas Mitigation for College Building

341

amulayan Bhargow, vivek kumar, aman kumar, ruStam alam, and nikeSh kumar

37.1

INTRODUCTION

341

37.2

METHODOLOGY

342

37.3

CONCLUSION

345

REFERENCES

345

Organizing Committee Chief Patron Dr. Satyajit Chakrabarti, President, IEM Kolkata. Patron Dr. Satyajit Chakrabarti, Director, IEM Kolkata. Dr. Amlan Kusum Nayak, Principal, IEM Kolkata. Conference Chair Dr. Arun Kumar Bar, Dean (Engg.), IEM Kolkata. Prof. Tapas Kr. Datta, Head, Dept. of EE, IEM Kolkata. Convenor Prof. Nikesh Kumar Singh, IEM Kolkata. Prof. Swetadri Ghosh, IEM Kolkata. Co-convenor Prof. Ayan Kumar Panja, IEM Kolkata. Prof. Amartya Mukherjee, IEM Kolkata. Prof. K. Yashaswi Raj, IEM Kolkata. Coordinator Prof. Somnath Hazra, IEM Kolkata. Prof. Prabir Kumar Das, IEM Kolkata. Organizing Committee Members Prof. Ranjita Chowdhury, IEM Kolkata. | Prof. Rajat Subhra Pal, IEM Kolkata. | Prof. Debashis Jana, IEM Kolkata. | Prof. Ankit Ray Ghatak, IEM Kolkata. | Prof. Subhendu Banerjee, IEM Kolkata | Prof. Nirban Kr. Saha, IEM Kolkata. | Prof. Debashish Ghosh, IEM Kolkata. | Prof. Aramita De, IEM Kolkata. | Prof. Avishek Ray, IEM Kolkata. | xix

xx



Organizing Committee

Prof. Aramita De, IEM Kolkata. | Prof. Arijita Das, IEM Kolkata. | Prof. Dipanwita Bhattacharya, IEM Kolkata. | Prof. Gunjan Kumar, IEM Kolkata. | Prof. Joydip Ray, IEM Kolkata. | Prof. Sudipta Swain, IEM Kolkata. | Prof. Mayurakshi Dev, IEM Kolkata. | Prof. Dwaipayan De, IEM Kolkata. | Prof. Sandip Kr. Chaudhury, IEM Kolkata.

Acknowledgements This book is itself an acknowledgement of cutting edge technological application in various aspects of our daily life. We are thankful to the researchers, the contributors and their enormous research effort towards the modern industrial applications. We are also thankful to our co-researchers, chief patron sir, patron sir, conveners, co-coordinators and all committee members.

Editors

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Preface In the modernized world, the intelligent systems are everywhere, starting from smart city, society office, home and, of course, in our day-to-day life. The introduction of the Industry 4.0 and the Society 4.0, however, increases the need for automated systems while also opening doors for advanced research on intelligent automated systems. In a modern industry, we often see highly smart pieces of equipment such as robotics arm in an assembly line, automatic spraying and welding systems, software control actuators to control the functionality of the deferent components of the industry without human intervention. In addition, the automatic navigation systems have become so popular and have eventually started replacing the manual driving systems. Furthermore, the drones have evolved to be the greatest technological advancement of navigation systems, in addition to advanced processing units and intelligent algorithms, which has made drone research go an extra mile. Currently, the introduction of the MEMS devices makes it possible to embed numerous pieces of sensing equipment in a credit card size board. Another big revolution is the open-source technology revolution. This ensures the advancement of hardware and software development to the next level by exploiting the power of community-driven project development. This book primarily emphasizes the current technological advancements in multidisciplinary fields such as control systems, power system design, internet of things and many more. The book also accumulates the recent research trends of various cutting-edge domain line machine learning, robotics and mechatronics applications, advanced control algorithm designs which are quite relevant to the contemporary researches on smart city, smart society and industry 4.0.

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Foreword On behalf of the local organizing committee and Institute of Engineering & Management, the hosting institution, I take immense pleasure in welcoming you to IEMPOWER 2019, Kolkata, for the Industrial Electronics Electrical & Mechanical Power (IEMPOWER-2019). Institute of Engineering & Management is one of the oldest premier technical institutes in Eastern India. It has been imparting quality engineering and management education since 1989. Being a NAAC-A grade institution, we have conducted numerous international conferences and workshops across India and abroad. IEEE IEMCON, IEEE UEMCON, IEEE CCWC, UEM Congress are some of the distinguished conferences organized by IEM in University of British Columbia, Vancouver Canada, Las Vegas, New York, Bangkok and Thailand every year. In the present era of clean energy and mitigation of carbon emission, renewable energy sources (Solar, Wind, Biogas, Micro and Mini Hydel etc.) have become need of the hour. In addition to this, power system and demand-side management can be addressed by the extensive use of energy storage devices whose efficient integration with renewable energy sources is a challenge. To make the integrated system smart in operation, we need an intelligent communication platform and various smart technologies (IoT-based, wireless communication). The entire system monitoring and control has to be executed by automation and supervisory control schemes. International Conference on Industrial Electronics Electrical & Mechanical Power (IEMPOWER-2019) is being organized by the Department of Electrical & Mechanical Engineering, Institute of Engineering & Management, Kolkata, during 21st–23rd November 2019 under the mentorship of the Institution of Engineers India (IEI) and ASME-IEM chapter. IEMPOWER-2019 aimed to provide a premier platform for Electrical, Electronics and Computer Engineers, researchers, scientists and academician from universities, research organizations and industries across the globe to present their work and research experiences in the emerging areas, such as Renewable Energy, Energy storage, Power Electronics & drives, Smart devices and communication systems, Artificial Intelligence, Robotics, Control and automation etc. We have invited speakers from Japan, Taiwan and premium universities of India, who

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Foreword

have kindly agreed to become part of this event. We are thankful to all IEM and UEM family members, participants and keynote speakers for helping us to build this exciting and highly technical conference program. We are very ambitious with this conference as in coming years we may plan to extend this conference at an international level with indexing in web of conferences.

Editors

About the Editors Dr. Satyajit Chakrabarti, who is the Pro-Vice Chancellor, UEM, a premier organization in education sector in India, has started many entrepreneurial ventures. He is also Director of Institute of Engineering & Management (IEM) and University of Engineering & Management (UEM), Kolkata. He received his PhD in computer science from NIT, Agartala. He has more than 12 years of experience in teaching and research. His primary research area includes Expert systems, Data mining, Nano Electronics and Nanotechnology. Apart from academia, he also has a huge industry experience. He was a Project Manager with extensive experience in planning, execution, monitoring, communicating with stakeholders, negotiating with vendors and cross-functional teams and motivating members. Ayan Kumar Panja has received his B.Sc. degree in Computer Science (Honors) in the year 2013 from Asutosh College, University of Calcutta, M.Sc. in Computer Science from St.Xavier’s College in the year 2015, Kolkata and M.Tech from University of Calcutta, Technology Campus. He is currently holding the position of Assistant Professor at Institute of Engineering and Management, Kolkata. His main research domain includes Machine Learning, Pattern Recognition, Audio Signal Processing, Wireless Communication and Sensor Networks. Amartya Mukherjee is an Assistant Professor at the Institute of Engineering & Management, Salt Lake, Kolkata, India. He holds a bachelor’s degree in computer science and engineering from West Bengal University of Technology and a master’s degree in computer science and engineering from the National Institute of Technology, Durgapur, West Bengal, India. His primary research interest is in embedded application development, including mobile ad-hoc networks and FANET, Internet of Things, mobile edge computing and machine learning. He has written several research articles and books in the field of wireless networking and embedded systems from Taylor & Francis, Elsevier, Springer and IEEE. His book Embedded Systems and Robotics With Open Source Tools is one of the bestselling books in the field of embedded application development.

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About the Editors

Dr. Arun Kumar Bar is a PhD holder from Jadavpur University. He has more than 20 years of teaching and research experience in the field of Mechanical Engineering, His Primary research area includes Mechatronics, Electrical Machines. He has written many research articles in well-known Journals and Conferences.

CHAPTER

1

Design of One Adaptive Controller for a Dynamic Framework with Non-linear Parameterisation Samiran Maiti1 and Achintya Das2 1Department of ECE, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata-741249, India. 2Department of ECE, Kalyani Government Engineering College, Kalyani, Nadia, West Bengal, Kalyani-741235, India. [email protected], [email protected]

ABSTRACT: This chapter represents a technique to design an adaptive controller for a non-linearly parameterised framework with obscure parameters. Contingent upon the variation of parameters such as lump inertia, rubbing coefficients, and a technique has been utilised to devise a versatile control for a non-linear system. Further, stability of the framework is guaranteed by reasonably choosing the Lyapunov capacity to develop the controller. The adequacy of the proposed plan is illustrated with a cart pendulum framework. Simulation results for a dynamic framework with non-linear parameterisation show the effectiveness of the present work. Keywords: Adaptive control, Non-linear system, Lyapunov stability theory, Non-linear parameterisation.

1.1 INTRODUCTION Adaptive control of non-linear framework has been a topic of broad research area. Most accessible adaptive controllers manage control issue of frameworks with non-linearities being linear in the obscure parameters. Non-linear parameterisation is exceptionally normal in numerous physical plants. Versatile control for non-linearly parameterised 1

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Intelligent Electrical Systems: A Step towards Smarter Earth

frameworks is a fascinating and challenging issue in control network. The Cart Pendulum (Ge, Hang, and Zhang, 1999) is an intrinsically flimsy framework with exceptionally nonlinear dynamics. This framework has a place with the class of under-incited mechanical frameworks having fewer control contributions than degrees of freedom. This renders the control task even more challenging making the Cart Pendulum framework a classical benchmark for the structure, testing, assessing, and looking at of changed control procedures. The aim of this contextual investigation is to balance out the Cart Pendulum to such an extent that the situation of the truck on the track is controlled rapidly and precisely with the goal that the pendulum is constantly raised in its reversed position during such developments. Reasonably, this straightforward mechanical framework is illustrative of a class of elevation control issues whose objective is to keep up the desired vertically arranged position consistently. The performance of the controlled frameworks is desired to be optimal which ought to be substantial likewise when connected in the genuine circumstance. Recently, a couple of specialists have endeavoured to research the keen computational frameworks with adaptable and perfect control design by applying certain methodologies for explicit applications. Ge, Hang, and Zhang (1999) presented controller design for a non-linear system. In 2006, Muskinja and Tovornik proposed counteraction for pendulum framework. Man and Lin (2010) also investigated control design for non-linear system. Huang, Guan, Fukuda, and Sekiyuma (2010) presented sliding mode speed control of a portable wheeled framework. In 2011, Razzaghi and Jalali discussed controller design for an inverted pendulum system. Swarnkar, Kumar, and Nema (2011) proposed analysis of versatile control system. Ghosh and Subudhi (2012) proposed controller design for cart pendulum framework. Ranjan and Rai (2012) discussed performance analysis of a system using versatile technique. Adhikary Mahanta (2013) proposed controller design for cart pendulum system using sliding mode technique. Yang et al. (2014) also proposed controller design under-actuated system. Pawar and Parvat (2015) presented versatile control design for inverted pendulum system. Orostica, Duarte-Mermoud, and Salinas (2016) discussed control of pendulum framework. In the present work, the distinction is observed in terms of modification as the performance of transient response being improved for dynamic framework with non-linear parameterisation using the adaptive technique in spite of parametric uncertainties. The remainder of the chapter is sorted out as follows: Section 1.2 – Non-linear parameterised framework, Section 1.3 – Controller design, Section 1.4 – Simulation results, finally, Section 1.5 – concludes the work.

1.2 NON-LINEAR PARAMETERISED FRAMEWORK The non-linear parameterised framework is considered as in Eq. (1.1): (dxi (t ) / dt ) = x (t ) , i = 1,...n - 1 i +1 (dxn (t ) / dt ) = (1 / g ( x(t ),q (t )))[ f ( x(t ),q (t )) + g ( x(t ))u (t )] y (t ) = xi (t )

(1.1)

Design of One Adaptive Controller for a Dynamic Framework

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3

where x(t ) = [ x1 (t ), x2 (t ),...., xn (t )] ÎÂn : state vector, u (t): control input and y(t): output. Functions f ( x(t ),q (t )) and g ( x(t ),q (t )) are characterised as in Eq. (1.2): k

f ( x(t ),q (t )) = å ql (t ) f l ( x(t )) = w Tf ( x(t ))q (t ) l =1 k

g ( x(t ),q (t )) = å ql (t )g l ( x(t )) = w gT ( x(t ))q (t )

(1.2)

l =1

where θ and k: number of unknown parameters. The following supposition that is made about the framework in Eq. (1.1) g ( x(t )) / g ( x(t ),q (t )) ¹ 0, "x(t ) ÎÂn . Without losing generality, it is assumed that g ( x(t )) > 0 and g ( x(t ),q (t )) > 0 "x(t ) ÎÂn .

i.

ii. q (t ) Î Sq , where Sq Ì Âk : compact set. iii. Framework has full relative degree n. iv. Framework (1): asymptotically steady.

1.3 CONTROLLER DESIGN Consider a virtual input v(t) as in Eq. (1.3): v(t ) = (1 / g ( x(t ),q (t ))[ f ( x(t ),q (t )) + g ( x(t ))u (t )]

(1.3)

Then control input u(t) is written as in Eq. (1.4): u (t ) = (1 / g ( x(t ))[ - f ( x(t ),q (t )) + g ( x(t ),q (t ))v(t )]

(1.4)

v(t) can be designed (Narendra, & Annaswamy, 1989; Slotine, & Li, 1991) as in Eq. (1.5): v(t ) = yd( n ) (t ) + cn ( yd( n -1) (t ) - y ( n -1) (t )) + .... + c1 ( yd (t ) - y (t ))

(1.5)

where c1,…,cn: constant coefficient and yd(t): desired trajectory. Hence, a stable estimator model for the framework is written as in Eq. (1.6): Ù

Ù

(d xi (t ) / dt ) = li ( xi (t ) - xi (t )) + xi +1 (t ) , i = 1,...n - 1 Ù

Ù

Ù

Ù

Ù

Ù

(d xn (t ) / dt ) = l n ( xn (t ) - xn (t )) + (1 / g ( x(t ),q (t )))[ f ( x(t ),q (t )) + g ( x(t ))u (t )] Ù

q (t ) : estimate of θ(t) and li , l n : negative constants. Subsequently, the estimation error dynamics of system is given as in Eq. (1.7): (dei (t ) / dt ) = li ei (t )

(1.6)

4

Intelligent Electrical Systems: A Step towards Smarter Earth Ù

Ù

(den (t ) / dt ) = ln en (t ) + (1 / wgT ( x(t ))q (t ))[w Tf ( x(t ))q (t ) + g ( x(t ))u (t )] -

T

g



Ù

Ù

( x(t )) q (t ))[w Tf ( x(t )) q (t ) + g ( x(t ))u (t )] - (1 / w gT ( x(t ))q (t ))[w Tf ( x(t ))q (t ) + g ( x(t ))u (t )] Ù

(den (t ) / dt ) = l n en (t ) +

Ù

(w gT ( x(t ))q (t ))[w Tf ( x(t )) q (t ) + g ( x(t ))u (t )] - (w gT ( x(t )) q (t ))[w Tf ( x(t ))q (t ) + g ( x( Ù

(Ùw gT ( x(tT)) q (t ))(w gT ( x(t ))q (t ))) T T T (w g ( x(t ))q (t ))[w f ( x(t )) q (t ) + g ( x(t ))u (t )] - (w g ( x(t )) q (t ))[w f ( x(t ))q (t ) + g ( x(t ))u (t )] Ù

) = l n en (t ) +

Ù

(w g ( x(t )) q (t ))(w g ( x(t ))q (t ))) T

T

Ù

(1.7)

Ù

∼

where e(t ) = x(t ) - x(t ) : estimation error and q (t ) = q (t ) - q (t ) : parameter error.

Eq. (7) can be rewritten as in Eq. (1.8): Ù ∼ ∼ Ù ∼ (w gT`` ( x(t )) q (t ))(w Tf ( x(t )) q (t )) - (w gT`` ( x(t )) q (t ))(w Tf ( x(t )) q (t )) - (w gT`` ( x(t )) q (t )) g (den (t ) / dt ) = l n en (t ) + Ù T T Ù ∼ ∼ Ù(w g ( x (t )) q (t ))(w ∼ g ( x (t ))q (t ))) T` T T` T T` (w g ` ( x(t )) q (t ))(w f ( x(t )) q (t )) - (w g ` ( x(t )) q (t ))(w f ( x(t )) q (t )) - (w g ` ( x(t )) q (t )) g ( x(t ))u (t ) t ) = l n en (t ) + (1.8) Ù (w gT ( x(t )) q (t ))(w gT ( x(t ))q (t ))) 1.3.1 Lyapunov Stability Analysis To establish the stability properties of the non-linear framework, consider the Lyapunov function as in Eq. (1.9): ∼ æ ∼T ∼ ö æ ö V ç e(t ),q (t )÷ = t1 (eT (t )e(t )) / 2 + t 2 ç (q (t ) q (t )) / 2÷ (1.9) è ø è ø

(

)

where t1 and t 2 : positive constants. Using adaptive law in Eq. (1.10–1.11): Ù Ù T` T T` T T ∼ t1 (w g q (t ))w f - w g (w f q (t )) - w g gu (t ) (d q (t ) / dt ) = - ( ) en (t ) Ù t2 (w gT q (t ))(w gT q (t )) Ù

(1.10)

Ù

T` T T` T T t (w g q (t ))w f - w g (w f q (t )) - w g gu (t ) (d q (t ) / dt ) = - ( 1 ) en (t ) Ù t2 T T (w q (t ))(w q (t )) Ù

g

(1.11)

g

Ù

Using estimate q (t ) in place of θ(t), the adaption law written as in Eq. (1.12) Ù

Ù

T` T T` T T t (w g q (t ))w f - w g (w f q (t )) - w g gu (t ) (d q (t ) / dt ) = - ( 1 ) en (t ) Ù t2 T 2 (w g q (t )) Ù

(1.12)

Derivative of Eq. (1.9) can be written as in Eq. (1.13) ∼

n -1

(dV (e(t ),q (t )) / dt ) = t1 å li ei2 (t ) + t1l n en2 (t ) £ 0 i =1

(1.13)

Design of One Adaptive Controller for a Dynamic Framework

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5

∼

Since (dV (e(t ),q (t )) / dt ) in Eq. (1.13) is negative. Thus, the adaptive control system is an asymptotics table. Utilising Hypothesis 2.1 in (Kristic, Kanellakopoulos, & Kokotovic, 1995), it tends to be ensured that eI (t ) ® 0 as t ® ¥ .

1.4 RESULTS To investigate the planned control technique for accomplishing the ideal transient reaction, the proposed control schemes have been actualised in simulation environment utilising MATLAB software. This discussed technique is applied to a cart pendulum framework. The structure goal is to manipulate the vertical edge of the cart pendulum system by controlling the balanced force. The cart pendulum framework (Kristic, Kanellakopoulos, and Kokotovic, 1995) described as in Eq. (1.14):

(dx1 (t ) / dt ) = x2 (t ) ( g sin x1 (t ) - (mlx2 2 (t )sin x1 (t ) cos x1 (t )) / ( M + m)) cos x1 (t ) / ( M + m) (dx2 (t ) / dt ) = + u 2 l ((4 / 3) - (m cos x1 (t ) / ( M + m))) l ((4 / 3) - (m cos 2 x1 (t ) / ( M + m))) ( g sin x1 (t ) - (mlx2 2 (t )sin x1 (t ) cos x1 (t )) / ( M + m)) cos x1 (t ) / ( M + m) dx2 (t ) / dt ) = + u (t ) 2 l ((4 / 3) - (m cos x1 (t ) / ( M + m))) l ((4 / 3) - (m cos 2 x1 (t ) / ( M + m))) y (t ) = x1 (t )

(1.14)

where x1(t) denotes the angular displacement, x2(t) the angular velocity, M denotes the lump inertia of cart, m: mass of pendulum, l signifying the half-length of pendulum, g: gravity constant. Consider suitable state variable as x1(t) and x2(t). The physical parameters belonging to the system taken as, M = 1 kg, m = 0.2 kg, l = 0.5 m, and g = 9.81 kg–m/s2. Therefore, the state space structure (Marc & Sastry, 1989; Wittenmark & Astrom, 2008) can be described as in Eq. (1.15): (dx(t ) / dt ) = f ( x(t ),q (t )) + g ( x(t ))u (t )

(1.15)

where x(t) denotes state vector, f(x(t)) and g(x(t)): smooth function. Equation (1.14) can be represented in the form of Eqs (1.1–1.2) with q k as: é

ù ú ú ú ú ê l ( M + m) ú ë3 û

éq1 ù ê ( M + m) ê q k = êêq 2 úú = ê - ml êëq3 úû ê 4

w f ( x(t )) and w g ( x(t )) are given as in Eq. (1.17): g sin x1 (t ) é ù ê 2 w f ( x(t )) = ê x2 (t )sin x1 (t ) cos x1 (t ) úú êë úû , 0

(1.16)

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0 é ù ê 2 w g ( x(t )) = êcos x1 (t )úú and g ( x(t )) = cos( x1 (t )) 1 ëê ûú

(1.17)

Control input u(t) considered as in Eq. (1.18) ÙT

ÙT

u (t ) = (1 / g ( x(t ))[ - q (t )w f + q (t )w g v(t )]

(1.18)

The adaption laws given as in Eq. (1.19): Ù

Ù

Ù

Ù

Ù

(d q1 (t ) / dt ) = -G1 (q 2 (t ) g sin x1 (t ) cos 2 x1 (t ) + q3 (t ) g sin x1 (t ))e2 (t ) / (q 2 (t ) cos 2 x1 (t ) + q3 (t )) 2 Ù

Ù

Ù

Ù

Ù

Ù

Ù

Ù

Ù 2 3 qqÙ2 (2(ttx))1//(tdt -G ttx))1xx(2t22))((ett )sin xx1 (2(ttx))1q 2 (t ) g sin x1 (t(()ddcos ) )+) == q (t )2g((qq sin (t ) /xx(1q((tt2))(cos t ) cos (tq) 1+(tq)3g(tsin )) 2 x1 (t ) cos x1 (t ) - u (t ) cos x1 (t ))e2 (t ) / (q 2 (t ) co 3( dt -G ( )sin cos 3 2 2 2 3 2 1 1 Ù

Ù

Ù

Ù

Ù

Ù

Ù

Ù

2 Ù 2 x (t ))e (t ) / 2(q (t ) cos 2 x (t ) + (d 1q(3t()tcos ) / dt ) = -G Ù -q sin (t ) g2x1sin x1 (t 2)Ùt ) ux2(2t ()tcos )sin3 xx11((tt)) ) cos u (t ) cos qt2)(2qx((tt))x+ (t )sin e2 (tx)1/(t()q1t ) + q23 (t )) 2 1 2 q 2 (t ) cos x1 ( (t ) gxsin x (t ))xe1 (t()t )-/ q(q13 (t()tg)1cos x(t()tcos ) + q x(1t())

2 3

Ù

1

3

1

2

2

1

3

Ù

Ù

Ù

Ù Ù 2 2 Ù Ù Ù q1 (tx) g(tsin xÙ1 ((tt)) gqt2)(/tx)dtx(t2))2=cos (t )sin 2 x1 (t ) cos x1 (t )3- u (t ) cos x1 (2t ))e2 (t ) / (2q 2 (t ) cos x1 (t 2) + q 3 (t )) )-cos ) q sin x ( t ) u ( t ) cos x ( t )) e ( t ) / ( q ( t ) cos x ( t ) + q ( t )) ( d q ( -G ( q ( t ) g sin x ( t ) q ( t ) x ( t )sin x ( t ) cos x ( t ) 1 1 1 2 1 3 31 1 1 1 22 2 1 1 3 Ù

Ù

Ù

q 2 (t ) x2 2 (t )sin x1 (t ) cos x1 (t ) - u (t ) cos x1 (t ))e2 (t ) / (q 2 (t ) cos 2 x1 (t ) + q3 (t )) 2

(1.19)

where, G1 , G 2 and G1 are positive gain. Figure 1.1. shows the output response of the framework. The cart velocity response is represented in Figure 1.2. The control input and output responses are delineated in Figure 1.3. The error response is delineated in Figure 1.4.

FIGURE 1.1 Output response.

Design of One Adaptive Controller for a Dynamic Framework

FIGURE 1.2 State response (x2).

FIGURE 1.3 Control input and output.

FIGURE 1.4 Error response.

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Intelligent Electrical Systems: A Step towards Smarter Earth

1.5 CONCLUSION In this paper, designing an adaptive controller for a non-linear parameterised framework is considered. The performance of the system with known and obscure dynamic within the sight of disturbance is examined as well. The controller guaranteed the strength of the cart pendulum framework in the upstanding position; likewise, it guaranteed the solidness of the inner elements of the framework. Theoretical analysis demonstrates that the controller can exhibit performance in the vicinity of parametric vulnerability. The simulation studies are conducted on cart pendulum framework to evaluate the proficiency of the work. Configuration using Lyapunov steadiness gives a stable versatile controller.

REFERENCES 1.

Ge, S. S., Hang, C. C., and Zhang, T., 1999. A direct adaptive controller for dynamic systems with a class of nonlinear parameterizations. Automatica, 35(4), 741–747. 2. Muskinja, N., and Tovornik, B., 2006. Swinging up and stabilization of a real inverted pendulum. IEEE Transactions on Industrial electronics, 53(2), 2004–2016. 3. Man, S. W., and Lin, S. J., 2010. Nonlinear control design for a class of under actuated system. IEEE International conference on Control Applications, 1439–1444. 4. Huang, J., Guan, H. Z., Matsuno, T., Fukuda, T., and Sekiyama, K., 2010. Sliding-mode velocity control of mobile-wheeled inverted-pendulum systems. IEEE Transactions on Robotics, 26(4), 241–247. 5. Razzaghi, K., and Jalali, A. A., 2011. A New Approach on Stabilization Control of an Inverted Pendulum Using PID Controller. International Conference on Control, Robotics and Cybernetics, 81–85. 6. Pankaj, S., Kumar, S. J., and Nema R. K., 2011. Comparative Analysis of MIT Rule and Lyapunov Rule in Model Reference Adaptive Control Scheme. Innovative Systems Design and Engineering, 2(4), 154–162. 7. Ghosh, A., Krishnan, R. T., and Subudhi, B., 2012. Robust proportional-integral derivative compensation of an inverted cart-pendulum system: an experimental study. IET Control Theory and Applications, 6(8), 1145–1152. 8. Ranjan, R., and Rai, P., 2012. Performance Analysis of a Second Order System Using MRAC. International Journal of Electrical Engineering and Technology, 3(3), 110–120. 9. Adhikary, N., and Mahanta, C., 2013. Integral backstepping sliding mode control for underactuated systems: Swing-up and stabilization of the cart-pendulum system. ISA Transactions, 52(6), 870–880. 10. Yang, C., Li., Z., Cui, R., and Xu., B., 2014. Neural network-based motion control of underactuated wheeled inverted pendulum models. IEEE Transactions on Neural Networks and Learning Systems, 25(11), 2004–2016. 11. Pawar, J. R., and Parvat, J. B., 2015. Design and Implementation of MRAC and Modifed MRAC technique for Inverted Pendulum. International Conference on Pervasive Computing, 1–6. 12. Oróstica, R., Duarte-Mermoud, A. M., and Salinas, J. C., 2016. Stabilization of inverted pendulum using LQR, PID and fractional order PID controllers: A simulated study. IEEE International Conference on Automatica, 1–7.

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13. Narendra, K. S., and Annaswamy, A., 1989. Stable Adaptive Systems. NJ, Prentice Hall, 705–752. 14. Slotine, J., and Li, W., 1991. Applied nonlinear control. NJ, Prentice Hall, 311–391. 15. Kristic, M., Kanellakopoulos, I., and Kokotovic, P. V., 1995. Nonlinear and Adaptive Control Design. New York, Jhon Wiley and Sons, 1st edition, 87–122. 16. Marc, B., and Sastry, S., 1989. Adaptive control stability, convergence, and robustness. NJ, Prentice-Hall, 1st edition, 294–323. 17. Wittenmark, B., and Astrom, K. J., 2008. Adaptive Control. Dover Publications, 2nd edition, 1–40.

CHAPTER

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A Comparative Study of Phasor Estimation Techniques P. R. Pattanaik, Basanta. K. Panigrahi, S. Pati, S. K. Sanyal, and N. Sahu SOA University, Bhubaneswar, India.

ABSTRACT: Phasor measurement units (PMU) are an essential part of modern power system. Phasor of alternating signals is widely used in protection and control schemes of power network. The sampled data of voltage and current signal are processed continuously through phasor estimation algorithms to obtain phasor values at each instant. Digital relays and controllers utilize these phasor values for system operation and control. Phasor estimation techniques based on discrete Fourier transform, discrete Wavelet transform, and least square method are briefly presented and a comparative assessment has been carried out. The performances of phasor estimators have been evaluated based on ‘Total vector error’ and ‘Transient monitor’ criterion. The effects of noises, harmonics, and sampling frequency have been studied and results are shown and discussed. A two-terminal system has been considered for simulation under Matlab®/Simulink™ environment. Keywords: Phasor estimation, Discrete Fourier transform, Discrete wavelet transform, Least square method, Total vector error, Transient monitor.

2.1 INTRODUCTION Phasor measurement units (PMU) are assigned for providing phasor values of voltage and current signal at critical buses. PMU used phasor estimation algorithm to extract phasor by processing real-time sampled data of analog signals provided by instruments transformer. PMU-based relaying was originally developed by American Electric Power Corporation. Signals of voltage and current are sampled using appropriate Nyquist filters, and phasors of sequential components are calculated using discrete Fourier transform (DFT) (Phadke et al., 2018). Phasor also plays an important role in wide area management system (WAMS) and in controlling Flexible AC transmission system (FACTS) devices. Relays need to be fast, accurate, and adaptive as operating conditions of modern power 11

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network are usually varying. An adaptive relay requires phasor data to adjust their setting according to prevailing conditions. Therefore, accurate phasor estimation becomes a necessity for the development of modern protective schemes (Xia and David, 1994; Sarangi, 2016). Technical literature survey suggests several phasor estimation techniques developed by researches. A DFT-based algorithm of fault detection and location in a transmission line is proposed in Jiang et al. (2000a) and (2000b). A computer measurement-based time synchronizing technique is used to calculate real-time phasors in Ree et al. (2010). A synchronized phasor measurement concerning research also includes frequency estimation, state estimation, instability prediction, and adaptive relaying. An impedance relaying scheme based on modal Kalman filtering (KF) is proposed in Si et al. (1990). Estimating phasor is modelled as a linear filtering problem and an adaptive algorithm for calculating real-time phasor values by quasi-second-order optimization technique is proposed in Abbas and Member (2012). Prony method is discussed as a dynamic estimator, and a comparative analysis with DFT-based method has been made in Serna and Member (2013). An artificial neural network-based algorithm is presented to estimate voltage magnitude of critical buses under normal and contingent states (Aravindhababu and Balamurugan, 2012). The concept of estimating phasors through discrete wavelet transforms (DWT) is given in Wong et al. (2001). A detailed analysis on the performance of DWT-based phasor estimation has been carried out and limitations are discussed in Brahma et al. (2008). Least square method (LSM) has been used to estimate phasors and frequency of signals in Nayak et al. (2014) and Pradhan et al. (2005). An investigation on the performance of LSM and KF-based phasor estimating algorithm is presented in Khodaparast and Khederzadeh (2017). In this chapter, a comparative assessment has been carried out between three phasor estimators based on DFT, DWT, and LSM. These techniques are tested under steady-state conditions by processing current signal obtained from a simulation model. Total vector error (TVE), a criterion set by IEEE C37. 118 standards for evaluating phasor estimation quality have been used while comparing the estimators. Another important index ‘Transient Monitor’ (TM) for evaluating phasor techniques performances has also been discussed. The effect of noises, harmonic, and sampling frequency is studied and discussed.

2.2 PHASOR ESTIMATION TECHNIQUES Phasors are rotating vectors used for the representation of alternating voltage and current signals. The decision regarding protection and control mostly depends upon the magnitude and phase angle of voltage and current. Therefore, phasor extraction method accuracy needs to be very high. The phasor estimation techniques based on DFT, DWT, and LSM are briefly discussed in the following sections. 2.2.1 Discrete Fourier Transform-Based Phasor Estimation A sinusoidal signal can be expressed as xk = X m cos( Wk + f )

(2.1)

A Comparative Study of Phasor Estimation Techniques



13

where Xm is the amplitude of signal, k is the sample number, φ is the phase angle in radians, and Ω= 2π/N (N is one cycle window length). DFT of the sinusoidal signal corresponding to fundamental frequency is X1 =

2 N

N -1

å k =0

xk e

-j

2P k N

where X1 is the phasor estimated in terms of peak and can also be represented as X 1 = X m e jf

(2.3)

The signal can be reconstructed by using phasor values at each instant as Ù

x k = [ X m e jf ]e jw0 kTs

(2.4)

where Ts is the sampling time and ω0 is the fundamental angular frequency 2.2.2 Discrete Wavelet Transform-Based Phasor Estimation DWT-based phasor extraction method requires one referenced sinusoidal signal (Wong et al., 2001). The referenced and the measured signals must be defined over a common clock pulse provided by GPS satellites. The signals then decomposed by the same wavelet function into low-frequency and high-frequency components. Only low-frequency component of the signals are considered for extraction as power system signals are of low frequency (50 Hz) with high magnitude. Let Aref and Ames be the vectors representing the approximation coefficient of referenced signal and measured signal, respectively. Then the phase angle φ can be calculated as æ Aref , Ames ö ÷ j = cos - 1ç ç | Aref | Ames | ÷ è ø

(2.5)

where operator is for dot product between two vectors. Now another sinusoidal signal is constructed with a phase angle value of φ, and a low frequency component is obtained using DWT. Let A1 be the vector representing the approximate coefficient of the new sinusoid. Then magnitude (Xm) of the required phasor is calculated as

Xm =

Ames A1

(2.6)

X1 phasor estimated in terms of peak and can be represented as

X 1 = X m e jj

(2.7)

The signal can be reconstructed by using phasor values at each instant as Ù

x k = [ X m e jf ]e jw0 kTs

(2.8)

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2.2.3 Least Square Method-Based Phasor Estimation A sinusoidal signal with a decaying DC component can be expressed as xk = X m sin(k w 0Ts + f ) + c0

- kTs e t

(2.9)

where c0 is value of decaying DC at t = 0 sec. The signal in state space representation can be expressed as

[ P ][ x ] = [Q ]

(2.10)

where é sin ( w0Ts ) cos ( w0Ts ) ê ê sin ( 2w0Ts ) cos ( 2w0Ts ) [ P ] = êê · · ê · · ê êsin ( N w0Ts ) cos ( N w0Ts ) ë

1

-Ts

1 · ·

-2Ts · ·

1 - NTs

(Ts ) ùú 2 ( 2Ts ) ú 2

ú ú ú ú 2 ( NTs ) úû

(2.11)

· ·

The state vector

[ X ] = éê X m cos f ë and the measurement vector

[Q ] = éë x ( t0 + Ts )

X m sin f c0

c0 t

c0 ù 2t2 úû

T

x ( t0 + 2Ts ) · · · · · x ( t0 + NTs ) ùû

(2.12)

T

(2.13)

The required vector containing phasor information can be obtained as

[X ] =

( éë P Pùû P ) *[Q] T

-1

T

(2.14)

The vector of reconstructed signal samples can be obtained as éÙù êQ ú = [ P ][ X ] ë û

(2.15)

2.3 RESULTS AND DISCUSSION A comparative assessment has been made between DFT-, DWT-, and LSM-based phasor estimation techniques. Highly accurate and fast phasor estimation is the requirement of modern relaying. Performances of each estimator have been evaluated based on parameters like TVE and TM. A normalised current signal of 50 Hz is sampled at 20 kHz used for steady-state testing. The test results are plotted and discussed in the following sections. 2.3.1 Signal Reconstruction The phasor values can be estimated through sampled data of the signal and any signal can be reconstructed through its phasor value as discussed in the phasor estimation techniques section.

A Comparative Study of Phasor Estimation Techniques

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15

Under steady-state conditions, the signal and the reconstructed signal should be equal in phase and magnitude. Accurate phasor estimation will result in overlapping of the real signal and estimated signal while plotting them in the time domain. A normalised steadystate current signal is obtained from simulation and its sampled data is processed through the phasor estimation techniques. The phasor values obtained are used to reconstruct the signal. The real signal and estimated signal are plotted in Figure 2.1. It can be seen that all the estimated signals are overlapping the real signal. The techniques satisfy the matching criterion of accurate phasor estimation. However, this visual criterion may fail to detect very small errors in phasor estimation and therefore cannot be set as an absolute standard to determine the quality of phasor estimation technique. 2.3.2 Total Vector Error Total vector error (TVE) is a parameter defined in IEEE C37.118 standard to evaluate the performance of the phasor estimation technique. Inaccurate phasor estimation produces considerable error in calculating magnitude and phase of signal. The TVE value of a phasor measurement technique should be below 1% under steady-state conditions. TVE can be mathematically defined as ®

TVE ( % ) =

®

Xe - X r ®

´ 100

(2.16)

Xr

It can be observed from Figure 2.2 that under steady-state condition, the values of DFT and LSM TVEs are approximately zero, whereas TVE value of DWT oscillates between 6.5% and 7.5% and therefore fails to satisfy the IEEE criterion of accurate estimation.

(a)

–2 0.4 2

Current (A)

(b)

Estimate

0

Current (A)

Current (A)

Real 2

0.45

0.5

0.55

0.6

0.45

0.5

0.55

0.6

0.5

0.55

0.6

0 –2 0.4 2 0

(c) –2

0.4

0.45

Time (s)

FIGURE 2.1 Current signal reconstruction under prefault conditions (a) DFT (b) DWT (c) LSM.

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Intelligent Electrical Systems: A Step towards Smarter Earth

TVE (%)

16

4

× 10−7

2

(a) 0 TVE (%)

0.48

0.5

0.51

0.52

0.53

0.54

0.55

0.49

0.5

0.51

0.52

0.53

0.54

0.55

0.49

0.5

0.51

0.52

0.53

0.54

0.55

8 7

(b) 6

0.48

TVE (%)

0.49

4

× 10

−6

2

(c) 0

0.48

Time (s)

FIGURE 2.2 TVE values in steady-state conditions prefault conditions (a) DFT (b) DWT (c) LSM.

2.3.3 Transient Monitor Transient monitor is another parameter used as a quality measure of phasor estimation techniques. TM index registers sudden change between actual and reconstructed signal. Mathematically, TM index can be expressed as follows: Ù é ù tn = ê xn - xn ú ë û

TM =

n=k

å

n=k - N

tn

(2.17) (2.18)

where tn is the estimation error at nth instant. For accurate phasor estimation, the value of TM should be zero. Estimation error and transient monitor index value have been calculated and results are shown in Figure 2.3. It can be observed that for steady-state condition tn and TM index of all the three techniques maintaining almost zero value. 2.3.4 Effect of Noise In this section, the effect of noise concentration on phasor estimation technique is studied. The current signal is contaminated with random white Gaussian noise. The level of noise contamination is increased from 0 dB to 100 dB SNR with a step size of 1 dB SNR. The TVE value of all three techniques is obtained at each step and plotted against the SNR level. It can be observed from Figure 2.4 that TVE value of phasor estimation

A Comparative Study of Phasor Estimation Techniques

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17

techniques vary inversely with SNR values. This means phasor estimation error increases with increase in noise level. DFT

DWT

LSM

TM (Amp)

0.2

(a)

0.1 0 −0.1 −0.2 0.4

TM (Amp)

3

0.45

0.5

0.55

0.6

0.5

0.55

0.6

Time (s)

× 10−6

2 1

(b) 0

0.4

0.45

Time (s)

TVE (%)

FIGURE 2.3 (a) Estimation error (b) Transient monitor.

(a)

150 100 50 0

0

20

40

60

80

100

60

80

100

60

80

100

TVE (%)

SNR (dB)

(b)

400 200 0

0

20

40

TVE (%)

SNR (dB)

(c)

4000 2000 0

0

20

40

SNR (dB)

FIGURE 2.4 Effect of noise (a) DFT, (b) DWT, (c) LSM.

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2.3.5 Effect of Harmonics The current signal is contaminated with third and fifth harmonics and their relative amplitude is successively increased from 1 to 50%. TVE of all the three-phasor estimation techniques is calculated for different total harmonic distortion (THD) values and results are plotted in Figure 2.5. The THD can be expressed as THD ( % ) =

X 32rms + X 52rms X 1rms

(2.19)

´ 100

It can be seen that DFT technique shows better performance than DWT- and LSM-based techniques against high THD values. 2.3.6 Effect of Sampling Frequency The number of samples per cycle increases with increment in sampling frequency. All the phasor estimation techniques compared in this chapter uses one cycle data of current samples. Increasing sampling frequency means the data processed at an instant also increases resulting in increment of computation time. The effect of sampling frequencies on phasor estimation accuracy of the techniques is studied in this section. The current signal is sampled with frequency from 1 kHz to 30 kHz. For each sampling frequency, TVE of different techniques is calculated and plotted in Figure 2.12. It is to be noticed that increasing sampling frequencies results in high estimation accuracy along with burden of high computational time. Therefore an optimal sampling frequency needs to be selected. The change in TVE value of DFT technique with varying sampling frequencies is almost negligible. 100

DFT DWT LSM

90 80 70

TVE (%)

60 50 40 30 20 10 0

0

20

40

60

THD (%)

FIGURE 2.5 Effect of harmonics.

80

100

TVE (%)

A Comparative Study of Phasor Estimation Techniques

(a)



19

0.4 0.2 0

0

5

10

15

20

25

30

25

30

25

30

TVE (%)

Sampling Frequency (kHz)

(b)

20 10 0

0

5

10

15

20

TVE (%)

Sampling Frequency (kHz) 10

(c)

0

5

0

5

10

15

20

Sampling Frequency (kHz) FIGURE 2.6

Effect of sampling frequencies (a) DFT (b) DWT (c) LSM.

2.4 CONCLUSION In this chapter, three-phasor estimation techniques based on DFT, DWT, and LSM are discussed and compared. The criterion based on total vector error and transient monitor have been considered to evaluate the performance of the techniques. The effects of noise content, harmonics, and sampling frequencies are studied. The DFT-based phasor estimation techniques is found to be more accurate and robust as compared to DWT and LSM.

REFERENCE 1. 2. 3.

4.

Abbas, S. A., and Member, S., 2012. A New Fast Algorithm to Estimate Real-Time Phasors Using Adaptive Signal Processing, 1–9. Aravindhababu, P., and Balamurugan, G., 2012. ANN based online voltage estimation. Applied Soft Computing Journal, 12, 313–319. https://doi.org/10.1016/j.asoc.2011.08.041 Brahma, S. M., Member, S., Kavasseri, R. G., and Member, S., 2008. Investigating the Performance of Discrete Wavelet Transform for Phasor Estimation in Digital Relays, PES General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century, July 2008, 1–6. Jiang, J., Lin, Y., Yang, J., Too, T., and Liu, C., 2000a. An Adaptive PMU Based Fault Detection / Location Technique for Transmission Lines — Part II: PMU Implementation and Performance Evaluation, 15, 1136–1146.

20

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5. 6.

7. 8.

9. 10.

11. 12. 13. 14. 15.

Intelligent Electrical Systems: A Step towards Smarter Earth Jiang, J., Yang, J., Lin, Y., Liu, C., and Ma, J., 2000b. An Adaptive PMU Based Fault Detection/ Location Technique for Transmission Lines Part I: Theory and Algorithms, 15, 486–493. Khodaparast, J., and Khederzadeh, M., 2017. Least square and Kalman based methods for dynamic phasor estimation: a review. Protection and Control of Modern Power Systems, 1–18. https://doi.org/10.1186/s41601-016-0032-y Nayak, P. K., Pradhan, A. K., Member, S., and Bajpai, P., 2014. Secured Zone 3 Protection During Stressed Condition, 1–8. Phadke, A. G., Bi, T., Hlibka, T., Adamiak, M., and Jauch, J., 2018. Phasor measurement units, WAMS, and their applications in protection and control of power systems. Journal of Modern Power Systems and Clean Energy, 6, 619–629. https://doi.org/10.1007/s40565018-0423-3 Pradhan, A. K., Routray, A., and Basak, A., 2005. Using Least Mean Square Technique, 20, 1812–1816. Ree, J. D. La, Member, S., Centeno, V., Member, S., Thorp, J. S., Fellow, L., Phadke, A. G., and Fellow, L., 2010. Synchronized Phasor Measurement Applications in Power Systems, 1, 20–27. Sarangi, S., 2016. Enhanced Alpha Plane Line Protection. Serna, D. O., Member, S., 2013. Synchrophasor Estimation Using Prony’s Method, 62, 2119–2128. Si, J. L. P. De, IEEE, Senior Member, Pedro, L., IEEE, Student Member, 1990. Modal Kalman Filtering Based Impedance Relaying, 6, 78–84. Wong, C., Leong, I., Lei, C., Wu, J., and Han, Y., 2001. A Novel Algorithm for Phasor Calculation Based on Wavelet Analysis, 00, 1500–1503. Xia, Y. Q., and David, A. K., 1994. Adaptive Relay Selting For Stand-Alone Digital Distance Protection. IEEE Transactions on Power Delivery, 9, 480–491.

CHAPTER

3

Adaptive Fuzzy PID Controller for a Current Controlled Multilevel Inverter Fed Matrix Converter G. Mohapatra, M. K. Debnath, and K. K. Mohapatra Siksha ‘O’ Anusandhan Deemed to be University, Bhubaneswar, Odisha, India.

ABSTRACT: Multilevel inverters (MLI), when used in voltage source inverter, have acquired wide utilization in industries. They are used, to obtain higher-output voltage with less total harmonic reduction (THD) with an increased number of levels. The matrix converter is used for ac to AC converter for variable frequency drives basically giving a good power factor improvement. This chapter aims in developing a simulation model of the matrix converter, established in Matlab Simulink with proper modulation technique. This also deals in controlling a PV-integrated three-phase Cascaded H Bridge (CHB) inverter, loaded with a matrix converter using the proportional resonant (PR) controller and adaptive fuzzy PID controller. The PR controller is helping to remove the steady-state error, and the fuzzy has the advantage of updated PI parameters. The superiority of fuzzy is emphasised based on THD reduction as compared to PR regulator. Keywords: Multilevel inverter, Matrix converter, Adaptive fuzzy PID.

3.1 INTRODUCTION In the context of large power handling and controlling the grid disturbance optimized control parameters and the use of a suitable controller is predominant in the recent era. The enormous amount of power requirement is fulfilled by the multilevel inverter (MLI) with an eye on the evaluation of the system performance, the fidelity of the device, and system prudential constraints (Rodriguez, 2002). In the field of cyclo converters, the

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Intelligent Electrical Systems: A Step towards Smarter Earth

matrix converters play a significant role in developing the desired output irrespective of the input for different frequency. By employing the proper modulation technique (Forzani, 2009), the input side power factor can be improved, which can eliminate the requirement of power factor correction devices at the cost of an increased number of switches. A trade-off is always desirable when selecting control between the converter components and the conventional system (Lahlou, 2017; Escobar, 2018; Zammit, 2017; Sefa, 2015; Teodorescu, 2006; Teodorescu, 2003). A new controlling method with variation of the fuzzy parameter is proposed for the inverter-fed matrix converter with the additional gain factor which can be optimised with differential evolution algorithm (DEA) considering the THD as the objective function. Tuning of the controller by modelling the same is customised to control the current with the PR controller, and the fuzzy controllers maintain the load power constant. Despite conventional PI regulator, the advantages of the PR controller and fuzzy controller for current control are discussed for different conditions by generating disturbances from the input as well as output side and the performances of the controllers are compared in the scale of Fast Fourier Transform (FFT), assuming a constant PV system.

3.2 MULTILEVEL INVERTER The ac to dc converter with distinct steps contains a cluster of IGBT and capacitor voltage sources as in Figure 3.1 to frame a MLI.

Sa1

Sa3

Outputa

V1 Sa4

Sa2

Outputn Sn1

Sn4

Sn3

Sn2

FIGURE 3.1 Represents the cascaded H bridge inverter.

Vn

U bn

Input Filter

3-Phase Input

U an

U cn

ia

daa

dab

dac

ib

dba

dbb

dbc

ic

dca

dcb

dcc

UB

iA

iB

23

UC

Output filter

UA



4-quadrant Switch

Adaptive Fuzzy PID Controller for a Current Controlled

Clamp Circuit

iC

Three -phase output

RL Load

N

FIGURE 3.2 Represents schematic diagram of matrix converter.

3.3 SYSTEM MODELLING The level, k, in the voltage per phase across the load of an MLI is explained by Eq. (3.1) (Escobar, 2018; Gholizade-Narm, 2014; Alesina, 1981; Iyer, 2018). The stretch of the load voltage U an on the basis of Fourier’s expansion is explained in Eq. (3.2). k=2s-1 ¥ 4Udc Uan ( wt ) = å xp x=1,3,5

(3.1) é cos ( hb1 ) + ..........ù ê ú sin ( hwt ) ë + cos ( hbs ) û

(3.2)

cos (b1 ) + ......................... + cos (bS ) = S´ M m cos ( 5b1 ) + ............................. + cos ( 5bS ) = 0

cos ( 7b1 ) + ............................. + cos ( 7bS ) = 0 .............................................................................. .............................................................................. cos ( xb1 ) + cos ( xb3 ) + ....... + cos ( xbS ) = 0

(3.3)

Inverter’s level can be evaluated from Eq. (3.2) to achieve the suitable angle of delay (b) as in Eq. 3.3 of the desired load potential using any iterative technique (Mohapatra, 2018; Mohapatra, 2019). Here is the number of H bridge of the inverter, Uaz is the individual source voltage for S number of sources, Uan is expressed as the inverter phase voltage, Udc is the voltage of the DC capacitor, h is the number of order of harmonic, and Mm gives the index required for modulation.

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Intelligent Electrical Systems: A Step towards Smarter Earth

3.4 MATRIX CONVERTER This converter, shown in Figure 3.2, is a set of four-quadrant switches connected to three input legs to synthesize one output leg voltage. To maintain constant input current, threeinput phase connection is mandatory (Dey, 2019).

3.5 DIFFERENTIAL EVOLUTION ALGORITHM (DEA) This is an evolutionary algorithm (Mohapatra, 2018) which is based upon the optimization of the objective function of the harmonic content and has the following steps: •

Initialize the number of operating parameters such as population, iteration.

•

Select the target vector as the minimum THD with the objective function as 2 2 4 2 ObjF = ( V1 - SM1 ) + ( V5 ) + ( V7 ) + ...... + ( Vz ) + THD

•

Calculate the values of the voltages from Eq. (3.2) for required harmonic percentages.

•

Evaluate the optimised value; if below the target, stop the operation, or else increase the iteration by 1 with generating the trial vector by cross over and mutant vector by mutant.

•

Selection of the best vector is done if the target is reached.

•

The PID parameters are updated.

3.6 PROPOSED CONTROLLER Proportional Resonant controller A proportional resonant (PR) is a controlling system with Hc(S) in Eq. (3.4) as the transfer function (Mohapatra, 2018), which is equivalent to a PI controller in structure as per Eq. (3.5) and can identify the frequencies near the resonance without disturbing the spread of the controller. The overall transfer function of the PR controller can be given in Eq. (3.6). Hc ( s ) =K P1+K I1 Gh =

å

K th

h =3,5,7

G PR (s)=

s s 2 +w2 s

s 2 +( wh )

2

2k p1s+c p1 2k p2s+c p2 2k p3s+cp3 + + +c p4 s 2 +w12 s 2 +w22 s 2 +w32

G F (s)=R f +

s 2 Lf1Cf +1

s3Lf1Lf 2Cf +s(Lf1+Lf 2 )

(3.4) (3.5) (3.6) (3.7)

Adaptive Fuzzy PID Controller for a Current Controlled

U dc 15%(MVAR) L Lf di =U dc , Lf = ,Cf = , R f =2x f 2 dt DI*mi *fsw Cf 2*p*fsw *U



25

(3.8)

The filter parameters of a LC filter can be designed as Lf, Cf, Rf and are the filter inductance, capacitance, and resistance with the lumped values as rL, rcf; R and L are the load components. GF(S) is the transfer function of the filter, and Fsw is the switching frequency and the filter coefficient as given in Eqs. (3.7) and (3.8). The complete PR controller, as given in Figure 3.3, takes the controller parameters as set with suitable tuning done by linearizing the system. The final block diagram of a PV-integrated three-phase MLI with a matrix converter employed with PR controller is given in Figure 3.5 and that with fuzzy controller in Figure 3.6. I∗ REF

+ G PR (s)

I ACTUAL

G INV (s)

G F (s)

−

FIGURE 3.3 Represents schematic diagram of PR controller. Knowledge based if and then Reference

Error

X

Inference engine

Fuzzifier

D-Fuzzification

Output

Process to be controlled

FIGURE 3.4 Represents schematic diagram of fuzzy controller. TABLE 3.1 Rule matrix table for KP and KI Output

r1

r2

r3

r4

r5

r1

n2

n2

m1

m1

r2

n2

m1

m1

s0

m1

n2

m1

m1

m1

s1

m1

m1

n2

n2

s1

s1

m1

m1

n2

r3 r4

CHANGE IN ERROR KP

r5

Output

r1

r2

r3

r4

r5

s0

s0

s0

m1

n2

n2

s0

s0

s0

m1

n2

n2

m1

m1

m1

m1

m1

n2

n2

m1

s0

s0

n2

n2

m1

s0

s0

CHANGE IN ERROR KI

r1

Negative Large

n2

Large

r2

Negative Small

m1

Medium

r3

Zero

s0

Small

r4

Positive Small

r5

Positive Large

Adaptive Fuzzy PID Controller The fuzzy controller, shown in Figure 3.4 (Mohapatra, 2018), has input as error and the rate of change of error. Here KP and KI are taken as outputs. The parameters are digitalized as defined in Eqs (3.6) and (3.7).

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Intelligent Electrical Systems: A Step towards Smarter Earth

Eri ( j )=Ila ( j )-Ilb ( j )

(3.9) (3.10)

¶Eri ( j )=Eri ( j )-Eri ( j-1)

Here Eri(j), ðEri(j), Il(a)j, Il(b)j, j are the error, change of error, reference current, actual current, and the parameter of discretization, respectively. A rule matrix table is developed as in Table 3.1.

3.7 SYSTEM BLOCK DIAGRAM A five-level, three-phase photovoltaic-operated, three-phase cascaded H bridge (CHB) inverter is developed in Matlab Simulink which is connected to a three-phase load with a matrix converter. The overall block diagrams with the controllers are given in Figures 3.5 and 3.6.

PWM Generator dq to abc Ɵ

3φ Load/ Grid

Matrix Converter

LCL Filter

3φ 5 LEVEL Inverter

PV System

3φ PLL

Ɵ

Id

PR Controller

Ʃ

PR Controller

Ʃ

−

abc to dq

+

Iq

−

Ɵ

3φ REF Current

abc to dq

Id*

+

Iq*

FIGURE 3.5 Explains the overall system arrangement to control the load current using PR

regulator.

Id

Ʃ

CONTROLLER

PI Controller

+

−

Iq

d/dt

+

abc to dq

Ɵ

Id*

−

abc to dq

Ʃ

Ɵ

3 φ _ Load/ Grid

d/dt

PI Controller dq to abc

Matrix Converter

LCL Filter

3φ _ 5L Inverter

PV System PWM Generator

Ɵ

PLL

Fuzzy Logic Controller

3 φ REF Current

Iq*

Fuzzy Logic Controller

FIGURE 3.6 Explains the diagram to control the load current using adaptive fuzzy PID regulator.

Adaptive Fuzzy PID Controller for a Current Controlled

3.8 RESULT AND DISCUSSION

Load Voltage (V)

200

Ua

Ub

Uc

100 0 –100 –200 0.04

0.06

0.08

0.1

0.12

0.14

0.16

Time (s) FIGURE 3.7 Explains the load voltage of the system.

Load Current (A)

Load Current in PID Controller Ia

5

Ib

Ic

0

–5 0.04

0.06

0.08

0.1

0.12

0.14

0.16

Time (s) FIGURE 3.8 Explains the load current with PID controller in loading of the system.

Load Current in Fuzzy Controller

Load Current (A)

5 Ic

Ib

Ia

0

–5

0.04

0.06

0.08

0.1

0.12

0.14

Time (S) FIGURE 3.9 Gives the load current with fuzzy PID controller in loading of the system.

0.16



27

28



Intelligent Electrical Systems: A Step towards Smarter Earth Load voltage in volts with PR controller Ua

100

Ub

Uc

0 –100 0.04

0.06

0.08

0.1

0.12

0.14

Load voltage in volts with fuzzy controller Ua

100

Ub

Uc

0 –100 0.04

0.06

0.08

0.1

0.12

0.14

Time (s)

FIGURE 3.10 Explains the load voltage of the system with PR and fuzzy PID controller with

voltage sag.

Load current in Amp with PR controller 10

Load Current (A)

Ia

Ib

Ic

5 0 –5 –10 0.04

0.06

0.08

0.1

0.12

0.14

Time (s)

FIGURE 3.11 Explains the load current of the system with PR controller with voltage sag. Load current in Amp with fuzzy controller 10

Load Current (A)

Ia

Ib

Ic

5 0 –5 –10 0.04

0.06

0.08

0.1

0.12

0.14

FIGURE 3.12 Explains the load current of the system with fuzzy controller with voltage sag.

Adaptive Fuzzy PID Controller for a Current Controlled

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29

18 with PR CONTROLLER

16

with FUZZY PID CONTROLLER

14

10

(expressed in pu)

PERCENTAGE OF THD

12

8 6 4 2 0 0

5

10

15

20

25

30

HARMONIC ORDER

FIGURE 3.13 Explains the THD variation of different controllers.

3.9 RESULT ANALYSIS A PV-integrated five-level system is developed with a voltage and load variation. Different controllers are analysed based on the harmonic content when the system is integrated with a matrix converter. The load current is forced to be stabilized with a set of controllers in Figures 3.8, 3.9, 3.11 and 3.12. A voltage variation of 0.8 pu is introduced for 0.06s–0.12s and is analysed in Figure 3.10 for voltage stability.

3.10 CONCLUSION A Matlab-simulated system of a five-level CHB is developed with a PV input. A matrix converter is connected and coupled with the load. The load current is stabilized with fuzzy controller in a better manner as compared to PR controller which is observed for different loading conditions. Voltage sag of 0.8 pu is inserted from the input side for a time interval of 0.06 s to 0.12 s, and the response of the system is analysed with PR and fuzzy controller is observed. The comparison of THD as described in the percentages of fundamental explains that the fuzzy PID is giving a better result as compared to PR.

APPENDIX PV voltage 70 V, Matrix output voltage 120 V, Load voltage 100 V, Reference current set 5A, Load current