Photovoltaic Sources Modeling

A practical reference to support choosing, customising and handling the best PV simulation solution

This comprehensive guide surveys all available models for simulating a photovoltaic (PV) generator at different levels of granularity, from cell to system level, in uniform as well as in mismatched conditions. Providing a thorough comparison among the models, engineers have all the elements needed to choose the right PV array model for specific applications or environmental conditions matched with the model of the electronic circuit used to maximize the PV power production.

Key features:

• Multiple mathematical models are given for different application requirements.
• The shading effect is taken into account to improve the model accuracy.
• Procedures for parameter identification of the PV model are analysed and compared.
• Mathematical manipulations are introduced to some models to reduce their calculation time.
• The electronic interface effect on the power chain is analysed.
• Analytical expressions are used to design and control the power converter driving the PV field.

The book is an essential reference for R&D in the PV industry; designers of power converters for PV; PV systems designers; and practicing engineers.

Giovanni Petrone received a Ph.D. degree in Electrical Engineering from the University "Federico II" of Naples in 2004. He is Associate Professor of Electrical Engineering at the University of Salerno. He is a Member of the Technical Committee on Renewable Energy Systems of the IEEE Industrial Electronics Society and Associate Editor of the IEEE Journal of Photovoltaics. Giovanni has been coordinator of research projects in the field of power electronics for renewable sources. He is co-author of five international patents, of one book and of more than 40 papers published in international journals. He has been included in the 2015 list of Most Influential Minds from Thomson Reuters.

Carlos Andres Ramos-Paja received his Ph.D. degree in power electronics from the Universitat Rovira i Virgili-Spain in 2009. He is Professor at the Universidad Nacional de Colombia where he is an IEEE senior member. He was recognized with the “research merit award” from his faculty, and he is the principal investigator of some research projects funded by the Colombian government. He is co-author of one international patent and of more than 50 papers published in international journals.

Giovanni Spagnuolo received a Ph.D. degree in Electrical Engineering from the University "Federico II" of Naples in 1998. He is Full Professor of Electrical Engineering at the University of Salerno and an IEEE Fellow "for contributions to control of photovoltaic systems". He is also a Member of the Steering Committee and Editor of the IEEE Journal of Photovoltaics and Associate Editor of the IEEE Transactions on Industrial Electronics. From 2012 to 2014 he chaired the Technical Committee on Renewable Energy Systems of the IEEE Industrial Electronics Society. He is the principal investigator of industrial research projects and, for his University, of some FP7 and H2020 projects. He is co-author of five international patents, of one book and of more than 60 papers published in international journals. He is in the 2015 list of Most Influential Minds from Thomson Reuters.

Acknowledgements xi

Introduction xiii

Tables of Symbols and Acronyms xv

1 PV Models 1

1.1 Introduction 1

1.2 Modeling: Granularity and Accuracy 1

1.3 The Double-diode Model 2

1.4 The Single-diode Model 4

1.4.1 Effect of the SDM Parameters on the I–V Curve 5

1.5 Models of PV Array for Circuit Simulator 6

1.5.1 The Single-diode Model based on the Lambert W-function 10

1.6 PV Dynamic Models 11

1.7 PV Small-signal Models and Dynamic-resistance Modelling 14

References 17

2 Single-diode Model Parameter Identification 21

2.1 Introduction 21

2.2 PV Parameter Identification from Datasheet Information 21

2.2.1 Exact Numerical Methods 21

2.2.2 Approximate Explicit Solution for Calculating SDM Parameters 24

2.2.3 Validation of the Approximate Explicit Solution 27

2.3 Single-diode Model Simplification 30

2.3.1 Five-parameter versus Four-parameter Simplification 32

2.3.2 Explicit Equations for Calculating the Four SDM Parameters 34

2.4 Improved Models for Amorphous and Organic PV Technologies 37

2.4.1 Modified SDM for Amorphous PV Cells 37

2.4.2 Five-parameter Calculation for Amorphous Silicon PV Panels 38

2.4.3 Modified Model for Organic PV Cells 40

References 43

3 PV Simulation under Homogeneous Conditions 45

3.1 Introduction 45

3.2 Irradiance- and Temperature-dependence of the PV Model 45

3.2.1 Direct Effects of Irradiance and Temperature 45

3.2.2 Equations for “Translating” SDM Parameters 49

3.2.3 Iterative Procedure proposed by Villalva et al. 51

3.2.4 Modified PV Model proposed by Lo Brano et al. 52

3.2.5 Translating Equations proposed by Marion et al. 53

3.2.6 Modified Translational Equation proposed by Picault et al. 53

3.2.7 PV Electrical Model proposed by King et al. 56

3.2.8 Using the King Equation for Estimating the SDM Parameter Drift 59

3.3 Simplified PV Models for Long-term Simulations 61

3.3.1 King Equations for Long-term Simulations 63

3.3.2 Performance Prediction Model based on the Fill Factor 68

3.3.3 PV Modeling based on Artificial Neural Networks 69

3.4 Real-time Simulation of PV Arrays 71

3.4.1 Simplified Models including the Power Conversion Stage 72

3.5 Summary of PV Models 75

References 77

4 PV Arrays in Non-homogeneous Conditions 81

4.1 Mismatching Effects: Sources and Consequences 81

4.1.1 Manufacturing Tolerances 81

4.1.2 Aging 82

4.1.3 Soiling and Snow 83

4.1.4 Shadowing 83

4.1.5 Module Temperature 86

4.2 Bypass Diode Failure 87

4.3 Hot spots and Bypass Diodes 89

4.4 Effect of Aging Failures and Malfunctioning on the PV Energy Yield 90

References 94

5 Models of PV Arrays under Non-homogeneous Conditions 97

5.1 The use of the Lambert W-Function 98

5.2 Application Examples 102

5.2.1 The Entire I–V Curve of a Mismatched PV String 102

5.2.2 The Operating Point of a Mismatched PV String 104

5.3 Guess Solution by Inflection-point Detection 106

5.4 Real-time Simulation of Mismatched PV Arrays 108

5.5 Estimation of the Energy Production of Mismatched PV Arrays 109

References 111

6 PV array Modeling at Cell Level under Non-homogeneous Conditions 113

6.1 PV Cell Modeling at Negative Voltage Values 113

6.1.1 The Bishop Term 113

6.1.2 Silicon Cells Type and Reverse Behavior 115

6.2 Cell and Subcell Modeling: Occurrence of Hot Spots 116

6.2.1 Cell Modeling 117

6.3 Simulation Example 121

6.4 Subcell PV Model 123

6.5 Concluding Remarks on PV String Modeling 124

References 124

7 Modeling the PV Power Conversion Chain 127

7.1 Introduction 127

7.2 Review of Basic Concepts for Modeling Power Converters 129

7.2.1 Steady-state Analysis 132

7.2.1.1 Steady-state Values 133

7.2.1.2 Ripple Magnitudes 133

7.2.2 Converter Dynamics Analysis 134

7.3 Effects of the Converter in the Power Conversion Chain 136

7.3.1 Steady-state Model of the Power Conversion Chain 136

7.3.2 Analysis and Simulation using the Steady-state Model 139

7.3.3 Voltage Ripple at the Generator Terminals 143

7.3.4 I–V Curve of the Power Conversion Chain 148

7.4 Modelling the Dynamics of the Power Conversion Chain 151

7.5 Additional Examples 159

7.5.1 MIU based on a Buck Converter 159

7.5.2 MIU based on a Buck–Boost Converter 161

7.6 Summary 162

References 163

8 Control of the Power Conversion Chain 165

8.1 Introduction 165

8.2 Linear Controller 166

8.3 Sliding-mode Controller 172

8.3.1 Inductor Current Control 173

8.3.2 Capacitor Current Control 179

8.4 Summary 183

References 184

Index 000

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