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POWER ELECTRONICS for GREEN ENERGY CONVERSION Written and edited by a team of renowned experts, this exciting new volume explores the concepts and practical applications of power electronics for green energy conversion, going into great detail with ample examples, for the engineer, scientist, or student. Power electronics has emerged as one of the most important technologies in the world and will play a big role in the conversion of the present power grid systems into smart grids. Applications like HVDC systems, FACTs devices, uninterruptible power systems, and renewable energy systems totally rely on advances in power electronic devices and control systems. Further, the need for renewable energy continues to grow, and the complete departure of fossil fuels and nuclear energy is not unrealistic thanks to power electronics. Therefore, the increasingly more important role of power electronics in the power sector industry remains paramount. This groundbreaking new volume aims to cover these topics and trends of power electronic converters, bridging the research gap on green energy conversion system architectures, controls, and protection challenges to enable their wide-scale implementation. Covering not only the concepts of all of these topics, the editors and contributors describe real-world implementation of these ideas and how they can be used for practical applications. Whether for the engineer, scientist, researcher, or student, this outstanding contribution to the science is a must-have for any library.

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Table of Contents

Cover

Title Page

Copyright

Preface

1 Green Energy Technology-Based Energy-Efficient Appliances for Buildings

Nomenclature

Variables

1.1 Balance of System Appliances Needed for Green Energy Systems

1.2 Major Green Energy Home Appliances

1.3 Energy Savings Through Green Appliances

1.4 Conclusion

References

2 Integrated Electric Power Systems and Their Power Quality Issues

2.1 Introduction

2.2 Designing of a Hybrid Energy System

2.3 Classification of Hybrid Energy Systems

2.4 Power Quality Implications

2.5 Conclusion

References

3 Renewable Energy in India and World for Sustainable Development

3.1 Introduction

3.2 The Energy Framework

3.3 Status of Solar PV Energy

3.4 Boons of Renewable Energy

3.5 Energy Statistics

3.6 Renewable Energy Resources

3.7 Conclusion

Abbreviations

References

4 Power Electronics: Technology for Wind Turbines

4.1 Introduction

4.2 Power Converter Topologies for Wind Turbines

4.3 Quasi Z Source Direct Matrix Converter

4.4 Conclusion

References

5 Investigation of Current Controllers for Grid Interactive Inverters

5.1 Introduction

5.2 Current Control System for Single-Phase Grid Interactive Inverters

5.3 Simulation Results and Analysis

5.4 Experimental Results

5.5 Future Scope

5.6 Conclusion

References

6 Multilevel Converter for Static Synchronous Compensators: State-of-the-Art, Applications and Trends

6.1 Introduction

6.2 STATCOM Realization

6.3 STATCOM Control Objectives

6.4 Benchmarking of Cascaded Topologies

6.5 STATCOM Trends

6.6 Conclusions and Future Trends

References

7 Topologies and Comparative Analysis of Reduced Switch Multilevel Inverters for Renewable Energy Applications

7.1 Introduction

7.2 Reduced-Switch Multilevel Inverters

7.3 Comparative Analysis

7.4 Conclusion

References

8 A Novel Step-Up Switched-Capacitor-Based Multilevel Inverter Topology Feasible for Green Energy Harvesting

8.1 Introduction

8.2 Proposed Basic Topology

8.3 Proposed Extended Topology

8.4 Operational Mode

8.5 Standing Voltage

8.6 Proposed Cascaded Topology

8.7 Modulation Method

8.8 Efficiency and Losses Analysis

8.9 Capacitor Design

8.10 Comparison Results

8.11 Simulation Results

8.12 Conclusion

References

9 Classification of Conventional and Modern Maximum Power Point Tracking Techniques for Photovoltaic Energy Generation Systems

9.1 Introduction

9.2 MPPT Algorithms Based on Load Side Parameters

9.3 Conventional MPPT Algorithms

9.4 Soft Computing (SC) MPPT Techniques

9.5 Hybrid MPPT Techniques

9.6 Discussion

9.7 Conclusion

References

10 A Simulation Analysis of Maximum Power Point Tracking Techniques for Battery-Operated PV Systems

10.1 Introduction

10.2 Background of Conventional MPPT Methods

10.3 Simulink Model of PV System with MPPT

10.4 Results and Discussions

10.5 Conclusion

References

11 Power Electronics: Technology for Grid-Tied Solar Photovoltaic Power Generation Systems

11.1 Introduction

11.2 Grid-Tied SPVPGS Technology

11.3 Classification of PV Inverter Configurations

11.4 Analysis of Leakage Current in Nonisolated Inverter Topologies

11.5 Important Standards Dealing with the Grid-Connected SPVPGS

11.6 Various Topologies of Grid-Tied SPVPGS

11.7 Scope for Future Research

11.8 Conclusions

References

12 Hybrid Solar-Wind System Modeling and Control

12.1 Introduction

12.2 Description of the Proposed System

12.3 Model of System

12.4 System Control

12.5 Results and Interpretation

12.6 Conclusion

References

13 Static/Dynamic Economic-Environmental Dispatch Problem Using Cuckoo Search Algorithm

13.1 Introduction

13.2 Problem Formulation

13.3 Calculation of CO

2

, CH

4

, and N

2

O Emitted During the Combustion

13.4 The Cuckoo Search Algorithms

13.5 Application

13.6 Conclusions

References

14 Power Electronics Converters for EVs and Wireless Chargers: An Overview on Existent Technology and Recent Advances

14.1 Introduction

14.2 Hybrid Power System for EV Technology

14.3 DC/AC Converters to Drive the EV

14.4 DC/DC Converters for EVs

14.5 WBG Devices for EV Technology

14.6 High-Power and High-Density DC/DC Converters for Hybrid and EV Applications

14.7 DC Fast Chargers and Challenges

14.8 Wireless Charging

14.9 Standards

14.10 WPT Technology in Practice

14.11 Converters

14.12 Resonant Network Topologies

14.13 Appropriate DC/DC Converters

14.14 Single-Ended Wireless EV Charger

14.15 WPT and EV Motor Drive Using Single Inverter

14.16 Conclusion

References

15 Recent Advances in Fast-Charging Methods for Electric Vehicles

15.1 Introduction

15.2 Levels of Charging

15.3 EV Charging Standards

15.4 Battery Charging Methods

15.5 Constant Voltage Charging

15.6 Constant Current Charging

15.7 Constant Current-Constant Voltage (CC-CV) Charging

15.8 Multicurrent Level Charging

15.9 Pulse Charging

15.10 Converters and Its Applications

15.11 Design of DC-DC Converters

15.12 Results and Discussions

15.13 Conclusion

References

16 Recent Advances in Wireless Power Transfer for Electric Vehicle Charging

16.1 Need for Wireless Power Transfer (WPT) in Electric Vehicles (EV)

16.2 WPT Theory

16.3 Operating Principle of IPT

16.4 Types of Wires

16.5 Ferrite Shapes

16.6 Couplers

16.7 Types of Charging

16.8 Compensation Techniques

16.9 Power Converters in WPT Systems

16.10 Standards

16.11 Conclusion

References

17 Flux Link Control Modulation Technique for Improving Power Transfer Characteristics of Bidirectional DC/DC Converter Used in FCEVS

17.1 Introduction

17.2 GDAB-IBDC Converter

17.4 Dead Band Analysis of GDAB-IBDC Converter

17.5 Simulation and Results

17.6 Conclusion

References

Index

Also of Interest

End User License Agreement

List of Tables

Chapter 1

Table 1.1 The efficiency and durability of various electrolyte-based batteries [...

Table 1.2 Discharging rate and C rating of the battery [12].

Table 1.3 Power savings of major home appliances with green home appliances abou...

Table 1.4 List of few more common green appliances with their average energy con...

Table 1.5 Daily consumption of each appliance.

Table 1.6 Total per day energy consumption.

Chapter 2

Table 2.1 IEEE standard voltage and current limits.

Chapter 4

Table 4.1 Comparison of power converter topologies for wind turbine.

Table 4.2 Comparisons of simulations results of ZSDMC and QZSDMC.

Chapter 5

Table 5.1 Switching table for 1- phase inverter.

Table 5.2 Simulation parameters.

Table 5.3 Comparative valuation of current controllers.

Chapter 6

Table 6.1 Summary of multilevel converters characteristics.

Table 6.2 Overview of some STATCOMs commercially available.

Table 6.3 Position of the first harmonic group of the line voltage for cascaded ...

Table 6.4 Parameters for calculating current stress in semiconductor devices.

Table 6.5 Current stress in semiconductor devices.

Table 6.6 Parameters for calculating current stress in SM capacitor.

Table 6.7 Current stress in SM capacitor.

Table 6.8 Benchmarking of cascaded topologies. Remark: The characteristics are i...

Chapter 7

Table 7.1 Switching sequence of IPUC MLI (adapted from [11]).

Table 7.2 Switching states of single-phase seven-level grid-connected MLI [12] (...

Table 7.3 Switching sequence of a five-level single-phase T-MLI (adapted from [1...

Table 7.4 Switching states for the positive polarity of output voltage (adapted ...

Table 7.5 Switching states of 27-level asymmetric MLI (adapted from [21]).

Table 7.6 Switching states of a single-phase 13-level MLI (adapted from [23]).

Table 7.7 Switching-states of a single-phase five-level modified cascaded H-Brid...

Table 7.8 Switching states of a single-phase five-level grid-tied transformer-le...

Table 7.9 Switching states of a three-phase grid-tied five-level MLI (adapted fr...

Table 7.10 Switching sequence of IPUC MLI (adapted from [60]).

Table 7.11 Comparison based on total component count.

Table 7.12 Comparative analysis based on efficiency.

Table 7.13 Comparative analysis based on output current distortion.

Table 7.14 Comparative analysis based on output voltage distortion.

Chapter 8

Table 8.1 Switching states, output voltage and charge/discharge status of capaci...

Table 8.2 Switching states, output voltage and charge/discharge status of capaci...

Table 8.3 Standing Voltage (SV) and Normalized Standing Voltage (NSV) of Semicon...

Table 8.4 Standing Voltage (SV) and Normalized Standing Voltage (NSV) of Semicon...

Table 8.5 Parameter values used in efficiency and loss analysis.

Table 8.6 Comparison of proposed topology components with other topologies.

Table 8.7 Simulation results.

Table 8.8 Maximum voltage for switches/diodes.

Chapter 9

Table 9.1 Comparison of MPPT technique.

Table 9.2 GMPPT technique.

Chapter 10

Table 10.1 Simulation specifications [27].

Table 10.2 Performance comparison.

Chapter 11

Table 11.1 Overview of grid-tied PVPGS.

Table 11.2 Summary of the standards dealing with grid-tied inverters.

Table 11.3 Comparison of the various grid-tied inverter topologies.

Chapter 12

Table 12.1 Main challenges/possible solutions or mitigations for hybrid solarwin...

Table 12.2 Main parameters of the proposed hybrid system.

Chapter 13

Table 13.1 Generation limits and fuel cost coefficients of the western Algerian ...

Table 13.2 CSA solution of static economic dispatch/emission dispatch.

Table 13.3 Detailed results of CSA.

Table 13.4 Detailed CO

2

, N

2

O, and CH

4

emissions.

Chapter 14

Table 14.1 Characteristics of DC-fast chargers in the market [24–28].

Table 14.2 Features of the AC- coupled and DC-coupled systems [19].

Table 14.3 Details of charging levels [39].

Chapter 15

Table 15.1 EV Charging station standards.

Table 15.2 Battery parameters chosen for the study.

Table 15.3 Design equations for DC-DC converters.

Table 15.4 Specification of components and parameters usedin DC-DC converters un...

Table 15.5 Comparison of DC fast charging time for various converters.

Chapter 16

Table 16.1 Chargers available worldwide.

Table 16.2 Timeline of WPT as in [3].

Table 16.3 Comparison of contactless charging technologies.

Table 16.4 Various ferrite shapes.

Table 16.5 Different structures of coil.

Table 16.6.a Comparison of distinct coil structures.

Table 16.6b Laboratory prototype of different coils.

Table 16.7 Comparison of various topologies of compensation [17].

Table 16.8 Various AC/DC converter for fast charging [21].

Table 16.9 Isolated DC/DC converters for fast charging [21].

Table 16.10 Summary of various standards [16].

Chapter 17

Table 17.1 Simulation parameters of GDAB-IBDC converter.

Guide

Cover

Table of Contents

Title Page

Copyright

Preface

Begin Reading

Index

Also of Interest

End User License Agreement

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Scrivener Publishing

100 Cummings Center, Suite 541J

Beverly, MA 01915-6106

Publishers at Scrivener

Martin Scrivener ([email protected])

Phillip Carmical ([email protected])

Power Electronics for Green Energy Conversion

Edited by

Mahajan Sagar Bhaskar

Nikita Gupta

Sanjeevikumar Padmanaban

Jens Bo Holm-Nielsen

and

Umashankar Subramaniam

This edition first published 2022 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 © 2022 Scrivener Publishing LLCFor more information about Scrivener publications please visit www.scrivenerpublishing.com.

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Library of Congress Cataloging-in-Publication Data

ISBN 9781119786481

Cover image: Pixabay.comCover 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

Preface

Power electronics has emerged as one of the most critical technologies globally and will play a significant role in the conversion of the present power grid systems into smart grids. Applications like HVDC systems, FACTs devices, uninterruptible power systems, and renewable energy systems rely on advances in power electronic devices and control systems. Further, renewable energy needs continue to grow, and the complete departure of fossil fuels and nuclear energy is not unrealistic, thanks to power electronics. Therefore, power electronics’ increasingly critical role in the power sector industry remains paramount. This groundbreaking new volume aims to cover these topics and trends of power electronic converters, bridging the research gap on green energy conversion system architectures, controls, and protection challenges to enable wide-scale implementation.

This book presents topics and trends in power electronic converters, bridging the research gap on green energy conversion system architectures and control and protection challenges to enable their wide-scale implementation. Green energy sources based power systems are providing a much-needed solution for stationary as well as transportation based applications. Green energy sources combined with power electronics can handle low, high, and variable power requirements and provide a key element in stabilizing and managing the power when necessary. Green energy applications require two primary power electronics areas to be addressed: DC/DC converters for power regulation and DC/AC converters for connection to the primary grid apart from supplying load demands. DC microgrid energy distribution systems will probably encourage DC-DC power converter technology for green energy applications in interconnected power converters, isolated, non-isolated, resonant, multi-port, multilevel converters, high voltage gains, and medium/high voltage converters.

Furthermore, this will assist in the addition of storage systems, which are necessary to manage the unpredictability of the green energy supply. Grid-independent systems require DC/AC converters to use green energy sources as the primary power source. Inverters are commonly used to supply fixed AC power from DC sources such as fuel cells, solar panels, batteries, and variable AC sources like wind. Thus, advances in green energy technology require similar advances in power converter technology. Furthermore, the numerous experimental results and associated simulations contribute significantly to the book’s high quality.

Chapter 1 provides an elaborated view of green energy appliances, which goes a long way in reducing the electricity bill and the dependency on the utility. It also presents the optimization of the grid through load scheduling that helps reduce the peak load, which is one of the major concerns of any grid. Chapter 2 provides the design of different modes of hybrid energy systems to understand their operation that is possible under various variable constraints and PQ assessment with different dynamic and static controlling mechanisms. Chapter 3 describes the renewable energy scenario for sustainable development in India and the world by describing various supporting factors. This chapter also describes the various policies of the International Energy Agency (IEA) for sustainable energy development through renewable energy. Chapter 4 proposes a quasi Z source direct matrix converter based direct-drive wind energy conversion system to control the output voltage under different wind speeds and loading conditions. Simulation results validate the advantage of the converter over conventional matrix converters. Chapter 5 presents the design and analysis of the hysteresis current controller, a proportional integral current controller, a proportional resonant current controller, a dead beat current controller, and a model predictive current controller and their comparative performance assessment. Chapter 6 presents a survey on the application of multilevel converters for STATCOM realization. The development and the current state-of-the-art STATCOM technology are critically presented and discussed. Chapter 7 reviews the recent state-of-the-art trends in reduced-switch multilevel inverters (RSMLI) for renewable energy applications. The chapter provides an exhaustive review of the latest trends in RSMLI for renewable energy applications, their challenges, a comparative analysis of various RSMLIs, and their future developments. Chapter 8 proposes a basic switched-capacitive multilevel inverter topology with the following advantages: numerous voltage levels, voltage-boosting capability, self-voltage balancing ability, and the inherent negative voltage-level generation that reduces the number of switches bearing the maximum output voltage. In the suggested configuration, green energy sources with DC output voltage like photovoltaics, wind turbines (with rectified output voltage), fuel cells, and energy storage devices like batteries can be employed as the input sources. An assessment of different approaches for combining existing MPPT techniques to construct hybrid methods combining characteristics from both domains is carried out in Chapter 9. An overview of the existing MPPT classification for the photovoltaic system is provided. The classification includes conventional, hybrid, and modern MPPT techniques for PV energy generation systems. Chapter 10 proposes a comparative study and simulation analysis of conventional maximum power points tracking techniques like perturb and observe, incremental conductance, fractional short circuit current and fractional open circuit voltage with a nonlinear control approach named “ripple correlation control.” Simulations have been carried out for various levels of solar irradiance and for step irradiance inputs at a constant temperature to show all MPPT techniques’ performance concerning tracking speed and oscillations in output. Chapter 11 presents an overview of the power electronic technologies employed for the grid-tied inverter configurations. Various inverter topologies under the different classes have been classified based on the power rating. Also, some of the important grid codes and standards for selecting an inverter are discussed. Finally, the future trends in the grid-tied inverter topologies are discussed to show the directions for researchers. Chapter 12, modelling, simulation, and control of a grid-connected hybrid solar-wind system with two-level energy storage under different climatic conditions. The system proposed in this chapter includes a wind turbine system equipped with a Doubly Fed Induction Generator DFIG, a photovoltaic (PV) system, a hybrid super capacitor-battery energy storage system, and controlled power electronics converters. The hybrid system is connected to the grid using a three-level inverter with hybrid supercapacitor batteries for energy storage. In order to maximize the power of the PV system, the Particle Swarm Optimization (PSO) algorithm that generates the optimal current of the PV system is applied. Chapter 13 presents a static and dynamic economic dispatch study in electrical power systems using the Cuckoo Search Algorithm (CSA). With the problem formulation and the Cuckoo Search Algorithm, a description of the western Algerian electrical power system is presented, followed by a discussion of the simulation results. Chapter 14 discusses the existing technology and recent advances in power electronic devices used in EVs and wireless charging. In Chapter 15, the recent developments of DC-DC converters and control strategies for various charging techniques. The modelling and design of DC fast-charging techniques for electric vehicles are proposed. The proposed method consists of various DC-DC converters as a power conditioning unit, and a suitable charge control scheme is employed. The performance of the conventional charging methods is compared with selected converters for DC fast-charging technique, and its feasibility for level 3 charging is addressed. Chapter 16 presents recent studies aimed at achieving bidirectional charging in inductive power transfer and converters involved in fast-charging EV applications. This chapter will give a complete overview of the state-of-the-art couplers and their auxiliaries in different sections. Chapter 17 presents the mathematical modelling of the generic dual active bridge isolated bidirectional dc/dc converter (GDAB-IBDC) converter in both boost and buck modes. The flux link control modulation has been developed for the GDAB-IBDC converter.

Mahajan Sagar BhaskarNikita GuptaSanjeevikumar PadmanabanJens Bo Holm-NielsenUmashankar SubramaniamEditors

1Green Energy Technology-Based Energy-Efficient Appliances for Buildings

Avanish Gautam Singh1*, Rahul Rajeevkumar Urs2, Rajeev Kumar Chauhan3 and Prabhakar Tiwari4

1Politecnico di Milano, Milan, Italy2Northumbria University Newcastle, Newcastle, United Kingdom3Department of Electrical Engineering, Dayalbagh Educational Institute, Agra, Uttar Pradesh, India4Department of Electrical Engineering, Madan Mohan Malaviya University of Technology, Gorakhpur, India

Abstract

This chapter provides an elaborated view of green energy appliances, which goes a long way in reducing the electricity bill and the dependency on the utility. As the governments around the world are focusing on lowering the CO2 emission, green energy is penetrating the electrical market aggressively. These green appliances can be divided into two parts, wherein the first part includes the appliances that are fundamental units of the system and operates between source and the load like battery, charge controller, fuses, etc. The second part includes the daily household AC or DC appliances. The chapter is divided into various sections that provide the different perspective of appliances, like the mode of their operation or benefits of replacing AC appliances to DC appliances. Further, the chapter gives a quick view on balance of system for a typical islanded system that includes typical elements like batteries, charge controller, power conditioning devices, safety devices, meters, and instrumentation, along with the major home appliances, which consume maximum part of the daily energy consumption. The very next section presents the optimization of the grid through load scheduling that helps in reducing the peak load, which is one of the major concerns of any grid. The electrical appliances based on green energy contain few fundamental elements, which play a vital role in the flawless working of green energy grid; hence, the study of those elements is the main objective of this chapter. Before the last section, efficiency analysis of fundamental elements of grid-like grid-tied inverters, battery bank, and solar charge controller are shown. In the last section, a case study based on daily load profile appliance, which will provide an overview of daily overall energy saving could be possible with green appliances in comparison with conventional appliances. Photovoltaic, wind turbines, biomass, fuel cell, etc., are renewable energy sources that could be taken as a source, but this chapter considers PV as an energy source and presents the work accordingly.

Keywords: DC appliances, DC-building, DC-microgrid, energy conversion, green energy home appliances, converters, energy efficient home appliances, battery efficiency

Nomenclature

Acronyms

PHEVs

Plug-in Hybrid Electric Vehicles

BMS

Battery Management System

MPPT

Maximum Power Point Tracking

MPTT

Maximum Power Transfer Theorem

NEC

National Electric Code

EV

Electric Vehicle

AC

Air Conditioner, Alternating Current

DC

Direct Current

BOS

Balance of System

PCUs

Power Conditioning Units

PV

Photovoltaic

PEC

Power Electronic Converter

BB

Battery Bank

CFL

Compact Florescent Lamp

LED

Light Emitting Diode

SOC

State of Charge

Variables

μ

Converter Efficiency

D

Duty Cycle

V

o

Output Voltage

I

o

Output Current

R

eq

Equivalent Resistance

R

S

Series Resistance

R

LOAD

Load Resistance

j, i

Range Indicator

P

PV

Photovoltaic Array Power

P

L

Load Power

P

B

Battery Power

1.1 Balance of System Appliances Needed for Green Energy Systems

This section introduces the few fundamental power system appliances that are used in a green power system. In the process of installing a renewable energy system to the home whether grid-connected or islanded, an individual is required to invest in a few additional appliances that are also called as balance of system (BOS). These appliances are required to condition the electricity, and to safely transmit the power to the loads for utilization or store for future use.

The islanded grid, which is not connected to a utility, the number of fundamental appliances a consumer needs to purchase depends upon the additional functionalities like energy trading system, appliance scheduler etc. In the most basic system, the power generated by the system is directly utilized by the load. Further, if a consumer wants to use power when the system is not generating power, a battery bank and charge controller is required.

Depending upon consumers requirements, the balance of system appliances for the islanded system might be accountable to half of your total system costs. The system integrator will tell the consumer about the exact appliances required. Also, the balance of system for autonomous DC-grid includes charge controller, batteries, safety devices, power conditioning devices, meters, and instrumentation.

The grid-connected system needs the balance of system appliances for flawless and safely transmission of power to the loads and to comply with utility grid connection requirements. The consumer will need power conditioning devices (PCUs), safety devices, meters, and instrumentation.

1.1.1 Grid Interactive Inverters for Buildings with AC Wiring

The grid-interactive inverters convert DC power from Photovoltaic array into AC synchronous power. To extract the maximum power from the PV, maximum power point tracking (MPPT) algorithms are used.

This section focuses on inverters for grid-connected systems, net metering, including battery backup and non-battery backup inverters. The grid-tied models are divided into two parts one is micro-inverters other is central inverters [1].

1.1.2 Grid Interactive Inverter with No Battery Backup

To convert the DC supply of PV plant into AC supply, central inverter is used. For reduction of transmission losses, central grid-tie inverters are designed, which run on high voltage DC inputs and allows relatively large PV array to connect in series. Micro-inverters are the alternative for the central inverters, which are attached to each PV module to optimize the module output power by tracking each module’s Maximum Power Point.

Central inverters have a large range of input voltage that can reach up to 600VDC, this limit has set by the US National Electrical Code (NEC) and the maximum inverter input voltage is determined by a PV array total maximum open-circuit voltage (VOC