Maria Carmela Di Piazza Gianpaolo Vitale Photovoltaic Sources Modeling and Emulation ^ Springer
Part I 1 From the Nuclear Fusion to the Radiated Energy on the Earth... 3 1.1 Inside the Universe 3 1.2 The Sun 5 1.2.1 Inside the Sun 5 1.3 From the Sun to the Earth 9 1.3.1 Finding One's Bearings on the Earth 11 1.3.2 The Greenhouse Effect 12 1.4 Tracking the Sun 12 1.5 Measuring Sunlight 15 1.6 Sunlight Emulation 16 1.7 Collecting Sunlight 17 1.8 Conclusions 17 Bibliography 18 2 From Radiated Energy to Electrical Energy: Physics of Photovoltaic Cells 19 2.1 Prologue: The Photoelectric Effect 19 2.2 Metals, Semiconductors, Insulators 21 2.3 Inside the Band Structure of a Semiconductor 22 2.4 Absorption of Light 23 2.5 Allowable States for Holes and Electrons 25 2.6 Energy Distribution for Holes and Electrons 25 2.7 Doping 27 2.8 Carrier Transport 29 2.8.1 Drift Current 30 2.8.2 Diffusion Current 32 2.8.3 Semiconductor Resistivity 33 XI11
xiv 2.9 Semiconductor Fundamental Equations 34 2.9.1 The Poisson's Equation 34 2.9.2 Continuity Equation 34 2.10 Minority Carrier Diffusion Equations 36 2.11 P-N Junction 37 2.12 P-N Junction Capacitance 41 2.13 The PV Cell 45 2.13.1 Minority Carriers Current Density 46 2.13.2 Optical Generation Rate 47 2.13.3 Recombination Rate 47 2.13.4 Current Versus Voltage Law of Photovoltaic Cell 47 2.14 Physical Model of a PV Cell 48 2.15 Semiconductor Types 49 2.15.1 Crystalline Silicon 50 2.15.2 Multicrystalline 50 2.15.3 Amorphous 50 2.15.4 Thin Film 51 2.15.5 Polymer Solar Cell 51 2.16 Conclusions 52 Bibliography 53 3 Photovoltaic Source Models 55 3.1 Introduction 55 3.2 Static Model 56 3.2.1 Circuit Model of a PV Cell 56 3.2.2 Diffusion Diode Non-Ideality 61 3.2.3 Parasitic Resistance Effects 61 3.2.4 Generalized Double Diode Model 63 3.2.5 Simplified Single Diode Model 63 3.3 Cell-Module/Field 71 3.4 Dynamic Model 73 3.4.1 Parallel Capacitance 73 3.4.2 Series Inductance 75 3.5 Modeling PV Fields under Nonuniform Illuminating Conditions 75 3.6 Conclusions 81 Bibliography 81 4 Parameter Identification for Photovoltaic Source Models 83 4.1 Introduction 83 4.2 Five-Parameter PV Model Formulation 84 4.3 Four-Parameter PV Model Formulation 85 4.4 Methods for the Parameter Extraction 86 4.4.1 Analytical Solution 86
xv 4.4.2 Numerical Solution 93 4.4.3 Heuristic Methods-Based Solution 102 4.5 Parameters Dependence on Temperature and Solar Irradiance 104 4.6 Identification of PV Model Parameters by Linear Regression Methods 107 4.7 PV Characteristic Representation Through Mapping Techniques 112 4.7.1 Look-Up-Table Approach 113 4.7.2 Neural Approach 113 (Hi 4.8 Examples of Matlab/Simulink Simulation of PV Electrical Characteristics 115 4.8.1 PV Field Array Model Identified by the Discrete Approach 117 4.8.2 PV Field Array Model Identified by the Regression Approach 118 4.8.3 PV Source Model Under Non-Uniform Irradiance 120 4.9 Conclusions 127 Bibliography 127 5 Photovoltaic Source Dynamic Modeling Issues 131 5.1 Introduction 131 5.2 Dynamic PV Model Formulation 132 5.3 Parameters Identification 137 5.4 Matlab/Simulink Simulation of PV Electrical Characteristics 142 5.4.1 V = f(i) Static Model Formulation 142 5.4.2 I = f(v) Static Model Formulation 143 5.4.3 S-Domain Dynamic Model 145 5.4.4 Nonlinear Junction Capacitance Implementation 146 5.4.5 PV Model Including Nonlinear Junction.. Capacitance. 148 5.4.6 Circuit Implementation Using PLECS 151 5.5 Conclusions 168 Bibliography 168 Part II 6 Photovoltaic Source Emulation 173 6.1 Introduction 173 6.2 PV Emulators: Concepts and Realization 175 6.2.1 Power Stage: A Survey of Proposed Solutions 175 6.2.2 Control Stage: PV Behavior Implementation 187 6.3 Dynamics and the Arbitrary Load Problem 191
xvl 6.4 Non-Ideal Operating Conditions 194 6.5 Rated Power 196 6.6 Modularity 196 6.7 Examples of Solutions Available on the Market 197 6.8 Conclusions 200 Bibliography 201 7 DC/DC Power Converters 203 7.1 Introduction 203 7.2 Linear Conversion 204 7.2.1 Linear Conversion by Voltage Divider 204 7.2.2 Linear Conversion by Series Regulator 205 7.3 Switching Conversion 206 7.4 Buck Converter 207 7.4.1 Continuous Operating Mode 207 7.4.2 Discontinuous Operating Mode 210 7.4.3 Continuous Operating Mode Including Parasitic Parameters 216 7.5 Boost Converter 217 7.5.1 Continuous Operating Mode 218 7.5.2 Discontinuous Operating Mode 221 7.5.3 Continuous Operating Mode Including Parasitic Parameters 224 7.6 Buck-Boost Converter 225 7.6.1 Continuous Operating Mode 226 7.6.2 Discontinuous Operating Mode 227 7.6.3 Continuous Operating Mode Including Parasitic Parameters 228 7.7 Comparison Among Buck, Boost, and Buck-Boost Topologies 229 7.8 Non-Ideal Behavior of Devices and Their Influence on the DC/DC Converter Operation 230 7.8.1 Inductor 230 7.8.2 Capacitor 231 7.8.3 Diode 232 7.8.4 Power Switch 234 7.9 State Space Representation 237 7.10 State Space Averaging 237 7.11 State Space Averaging of Buck Converter 240 7.12 State Space Averaging of Boost Converter 242 7.13 State Space Averaging of Buck-Boost Converter 246 7.14 Synopsis 250 7.15 Conclusions 250 Bibliography 251
xvii 8 Feedback Control of the DC/DC Converters for PV Source Emulation 253 8.1 Negative Feedback Classical Control 253 8.1.1 Closed-Loop Gain 253 8.1.2 Stability Analysis 254 8.2 Feedback Structure of a DC/DC Converter 259 8.2.1 Feedback Network Transfer Function 259 8.2.2 Pulse Width Modulator Transfer Function 259 8.2.3 Compensation Networks 260 8.3 Complete State Feedback (Pole Placement Technique) 264 8.4 Enhanced Pole Placement for Buck Converter 266 8.4.1 Simulink Implementation 270 8.5 DC/DC Converter-Based Emulation of a PV Source 272 8.5.1 DC/DC Power Converter Design Constraints 273 8.5.2 Selection of the Best Topology 274 8.6 Example of a FV Source Emulator Design 275 8.6.1 Power Stage Design 276 8.6.2 Pole Placement Voltage Controller 277 8.7 PLECS-Based Simulation of PV Source Emulator 278 8.8 Experimental Implementation of the PV Source Emulator 285 8.8.1 DC/DC Buck Converter 285 8.8.2 Control Board 286 8.8.3 DC/DC Boost Converter for the MPPT 289 8.9 Experimental Results 291 8.10 Conclusions 295 Bibliography 296