## Contents

Preface………………………………………………………………………………………………………..xi

About the Authors………………………………………………………………………………….. xiii

1 PV Modeling………………………………………………………………………………………..1

1.1 From the Photovoltaic Cell to the Field………………………………………..1

1.2 The Electrical Characteristic of a PV Module………………………………3

1.3 The Double-Diode and Single-Diode Models………………………………7

1.4 From Data Sheet Values to Model Parameters…………………………… 12

1.4.1 Parameters Identification Assuming Rp → ∞……………….. 13

1.4.2 Parameters Identification Including Rp…………………………. 15

1.4.3 Parameters Identification Including Rp: Explicit

Solution………………………………………………………………………..16

1.4.4 Other Approaches Proposed in Literature…………………….. 17

1.5 Example: PV Module Equivalent Circuit Parameters

Calculation………………………………………………………………………………..20

1.6 The Lambert W Function for Modeling a PV Field……………………22

1.6.1 PV Generator Working in Uniform Conditions……………..22

1.6.2 Modeling a Mismatched PV Generator………………………….25

1.7 Example…………………………………………………………………………………….29

References………………………………………………………………………………………….. 32

2 Maximum Power Point Tracking………………………………………………………35

2.1 The Dynamic Optimization Problem………………………………………..35

2.2 Fractional Open-Circuit Voltage and Short-Circuit Current………40

2.3 Soft Computing Methods…………………………………………………………. 41

2.4 The Perturb and Observe Approach………………………………………….42

2.4.1 Performance Optimization: Steady-State and

Dynamic Conditions……………………………………………………..45

2.4.2 Rapidly Changing Irradiance Conditions……………………… 51

2.4.3 P&O Design Example: A PV Battery Charger………………..54

2.5 Improvements of the P&O Algorithm……………………………………….. 62

2.5.1 P&O with Adaptive Step Size……………………………………….. 62

2.5.2 P&O with Parabolic Approximation………………………………63

2.6 Evolution of the Perturbative Method……………………………………….68

2.6.1 Particle Swarm Optimization (PSO)………………………………68

2.6.2 Extremum Seeking and Ripple Correlation

Techniques………………………………………………………………..70

2.6.3 The Incremental Conductance Method………………………….71

2.7 PV MPPT via Output Parameters………………………………………………75

2.7.1 The TEODI Approach……………………………………………………. 76

2.8 MPPT Efficiency……………………………………………………………………….. 81

References…………………………………………………………………………………………..84

3 MPPT Efficiency: Noise Sources and Methods for Reducing

Their Effects………………………………………………………………………………………89

3.1 Low-Frequency Disturbances in Single-Phase Applications……..89

3.1.1 The Perturb and Observe Approach Applied to

Closed-Loop Switching Converters……………………………….95

3.1.2 Example of P&O Design for a Closed-Loop Boost

Converter……………………………………………………………………….99

3.2 Instability of the Current-Based MPPT Algorithms………………… 104

3.3 Sliding Mode in PV System…………………………………………………….. 108

3.3.1 Noise Rejection by Sliding Mode: Numerical Example…..114

3.3.2 MPPT Current Control by Sliding Mode……………………… 117

3.3.2.1 Basic Configuration of Sliding Mode with

Voltage Controller…………………………………………. 117

3.3.2.2 Voltage Controller Design………………………………122

3.3.3 Sliding Mode MPPT Controller: Numerical Example….. 123

3.4 Analysis of the MPPT Performances in a Noisy Environment…..126

3.4.1 Noise Attenuation by Using Low-Pass Filters……………… 129

3.4.2 Error Compensation by Increasing the Step

Perturbation………………………………………………………………… 131

3.4.3 ADC Quantization Error in the P&O Algorithm:

Numerical Example…………………………………………………….. 134

References………………………………………………………………………………………… 136

4 Distributed Maximum Power Point Tracking of Photovoltaic

Arrays………………………………………………………………………………………………. 139

4.1 Limitations of Standard MPPT……………………………………………….. 139

4.2 A New Approach: Distributed MPPT……………………………………… 139

4.2.1 DMPPT by Means of Microinverters…………………………… 140

4.2.2 DMPPT by Means of DC/DC Converters……………………. 142

4.3 DC Analysis of a PV Array with DMPPT………………………………… 145

4.3.1 Feasible Operating Regions…………………………………………. 145

4.3.2 Examples of Feasible Operating Regions…………………….. 147

4.3.3 I-V and P-V Characteristics of Boost-Based SCPVMs…… 152

4.3.4 I-V and P-V Characteristics of Buckboost-Based

SCPVMs………………………………………………………………………. 163

4.4 Optimal Operating Range of the DC Inverter Input Voltage…… 177

4.5 AC Analysis of a PV Array with DMPPT………………………………… 185

4.5.1 AC Model of a Single SCPVM……………………………………… 196

4.5.2 Small-Signal Model of a Photovoltaic Array with

DMPPT………………………………………………………………………..208

4.5.3 Stability of a String of SCPVMs…………………………………… 212

References………………………………………………………………………………………… 244

5 Design of High-Energy-Efficiency Power Converters for PV

MPPT Applications…………………………………………………………………………. 251

5.1 Introduction……………………………………………………………………………. 251

5.2 Power, Energy, Efficiency………………………………………………………… 252

5.3 Energy Harvesting in PV Plant Using DMPPT Power

Converters………………………………………………………………………………….. 258

5.4 Losses in Power Converters……………………………………………………..268

5.5 Losses in the Synchronous FET Switching Cells…………………….. 270

5.6 Conduction Losses………………………………………………………………….. 272

5.7 Switching Losses…………………………………………………………………….. 276

5.7.1 Turn ON……………………………………………………………………… 281

5.7.2 Turn OFF……………………………………………………………………..283

5.7.3 Thermal Analysis…………………………………………………………285

5.7.4 Example……………………………………………………………………….290

References…………………………………………………………………………………………308

Index………………………………………………………………………………………………………. 311

## Preface

Photovoltaic (PV) systems produce a significant amount of the electrical

energy used around the world. PV technology will be capable of offering a

great deal of support in the future to the rate of growth of advanced economies

as well as developing countries. The incentives provided at a first stage

by the European governments have resulted in the rapid growth of the PV

market and an increase in the number and quality of products offered by

industry. PV modules by many producers are now commercially available,

and a number of power electronic systems have been put on the market for

processing the electric power produced by PV systems, especially for gridconnected

applications.

The scientific literature concerning PV applications has been characterized

by a strong quantitative and qualitative growth in the past decade. A huge

number of papers have been written and continue to be published in many

journals, and there are many high-impact scientific journals specifically

devoted to PV systems. A significant number of scientific papers are dedicated

to control of the PV source. A simple search on the Reuters Thomson

website reveals that at the end of May 2012, about 600 papers include maximum

power point tracking (MPPT) among their keywords. Many authors have

contributed to the scientific field of circuits and systems, ensuring the best

operation of the photovoltaic generator, but a reference in this field is still

lacking.

Some books that assess the most significant improvements concerning the

connection of PV systems to the grid have been published recently. The most

recent advances in this field and the various solutions offered to researchers

as a starting point for their activities and to the industries for developing

new products are overviewed.

The aim of this book is to fill the gap in the field of control circuits, systems,

and techniques dedicated to the maximization of the electrical power

produced by a PV source. In the first part of the book, an overview of the

methods allowing a PV array working in uniform and mismatched conditions

to be modeled is given. Next, the ways in which the best MPPT performances

can be achieved are discussed. The design of the parameters

affecting the algorithm performances is treated. The maximization of the

energy harvested in mismatched conditions is then discussed, in terms of

both power architecture and control algorithms. Last, the design of the DC/

DC converter, which usually performs the MPPT function, is discussed, with

special emphasis on its energy efficiency.

This first edition of the book is the result of ten years of activity in the field

of PV systems. In this period, some of the points that have been investigated

in detail, with many relevant scientific and applicative results, were raised

from discussions with a number of persons. Researchers and friends from

academia, who are acknowledged for these fruitful discussions, and industry

design experts, from whom we received encouragement to continue our

studies, have had a significant role in helping us to write this book.

We also acknowledge out mentor, Professor Emeritus Luigi Egiziano, who

trusted in us and supported our research initiatives and academic growth.

Nicola Femia, Giovanni Petrone, Giovanni Spagnuolo, and Massimo Vitelli