solar photovoltaic energy generation and conversion.pdf

7/26/2019 SOLAR PHOTOVOLTAIC ENERGY GENERATION AND CONVERSION.pdf

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SOLAR PHOTOVOLTAIC ENERGY GENERATION AND CONVERSION

FROM DEVICES TO GRID INTEGRATION

by

HUIYING ZHENG

SHUHUI LI, COMMITTEE CHAIRTIM A. HASKEW

JABER ABU QAHOUQDAWEN LIMIN SUN

A DISSERTATION

Submitted in partial fulfillment of the requirementsfor the degree of Doctor of Philosophy

in the Department of Electrical & Computer Engineeringin the Graduate School of

The University of Alabama

TUSCALOOSA, ALABAMA

2013


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Copyright Huiying Zheng 2013ALL RIGHTS RESERVED


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ABSTRACT

Solar photovoltaic (PV) energy is becoming an increasingly important part of the world

renewable energy. In order for effective energy extraction from a solar PV system, this researc

investigates solar PV energy generation and conversion from devices to grid integration.

First of all, this dissertation focuses on IV and PV characteristics of PV modules anarrays, especially under uneven shading conditions, and considers both the physics and electric

characteristics of a solar PV system in the model development. The dissertation examines ho

different bypass diode arrangements could affect maximum power extraction characteristics of

solar PV module or array. Secondly, in order to develop competent technology for efficien

energy extraction from a solar PV system, this research investigates typical maximum pow

point tracking (MPPT) control strategies used in solar PV industry, and proposes an adaptive a

close-loop MPPT strategy for fast and reliable extraction of solar PV power. The researc

focuses especially on how conventional and proposed MPPT methods behave under highl

variable weather conditions in a digital control environment. A computational experiment syste

is developed by using MatLab SimPowerSystems and Opal-RT (real-time) simulatio

technology for fast and accurate investigations of the maximum power extraction under hig

frequency switching conditions of power converters. A hardware experiment system is built

compare and validate the conventional and the proposed MPPT methods in a more practic

condition. Advantages, disadvantages and properties of different MPPT techniques are studie


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evaluated, and compared. Thirdly, in order to develop efficient and reliable energy conversio

technologies, this dissertation compares the energy extraction characteristics of a PV system f

different converter configurations. A detailed comparison study is conducted to investigate wh

enhancements and impacts can be made by using different bypass diode schemes. It is found th

compared to micro-converter based PV systems, the central converter scheme with effectiv

bypass diode connections could be a simple and economic solution to significantly enhance P

system efficiency, reliability and performance. Lastly, the development of coordinated contro

tools for next-generation PV installations, along with energy storage units (ESU), provide

flexibility to distribution system operators. The objective of the control of this hybrid PV anenergy storage system is to supply the desired active and reactive power to the grid and at th

same time to maintain the stability of the dc-link voltage of the PV and energy storage syste

through coordinated control of power electronic converters. This research investigates thre

different coordinated control structures and approaches for grid integration of PV array, batte

storage, and supercapacitor (SC). In addition, other applications including single-phase Direc

Quadrature (DQ) control and ramp rate limit control are presented in this dissertation.

Index Terms solar photovoltaic, semiconductor physics, IV characteristics, PV

characteristics, bypassing diodes, uneven shading, power electronic converters, maximum pow

point tracking, digital control, computational and hardware-based experiments, battery an

supercapacitor, control coordination, single-phase DQ control, and ramp rate control.


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DEDICATION

This dissertation is dedicated to everyone who helped me and guided me through th

trials and tribulations of creating this research. In particular, the graduate school of th

University of Alabama and some knowledgeable and up-lifting professors in ECE departme

who stood by me throughout the time taken to complete this research.


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LIST OF ABBREVIATIONS AND SYMBOLS

I D Diffusion current

I S Drift current

I L Photogenerated current

R p Parallel resistance accounting for current leakage through the solar cell

R s Series resistance which causes an extra voltage drop between the junction voltagand the terminal voltage of the solar cell

I 0 Diode reverse saturation current

m Diode ideality factor

q Elementary charge

T Absolute temperature

k Boltzmann's constant

I c Output current of a solar device

P s Shading factor that the shaded cell is relevant to the unshaded cell

V d P-n junction diode voltages

V c Output voltage of a solar device

P c Generated power of a solar device

D N Net doping concentration in n-type region

A N Net doping concentration in p-type region

K Approximate constant with respect to temperature


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E g Band-gap energy of the semiconductor (eV)

S Ratio of the present solar irradiation over the nominal irradiation of 1000W/m2

I MPP Current at the maximum power point

I SC Short-circuit current of a PV array

k sc Ratio of current at the maximum power point to the short-circuit current

V MPP Voltage at the maximum power point

V OC Open-circuit voltage of a PV array

K oc Ratio of voltage at the maximum power point to the open-circuit voltage

a a I V Instant conductance

a a I V Incremental conductance

tanh( ) Hyperbolic function

SOC State of charge of battery

ib_ref Battery reference current

i sc_ref Supercapacitor reference current

V dc_ref Dc-link capacitor reference voltage

p sto_ref Storage units reference power

pdc_ref Dc-link capacitor reference power

p g_ref Grid reference power

p pv PV system generated power

p f Power losses in grid filter

id Grid d-axis current

iq Grid q-axis current

R f Resistance of grid filter


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X R Peak value of sinusoidal waveform

X I Corresponding imaginary orthogonal of X R

Initial phase

Fundamental frequency

T Transformation matrix from stationary frame to rotating frame

T -1 Transformation matrix from rotating frame to stationary frame

P(t) Instantaneous reactive power


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ACKNOWLEDGMENTS

I am pleased to have this opportunity to thank those who gave me an enormous amount o

help and guidance for this research project. My supervisor, Dr. Shuhui Li, has steered me fro

the early stages of problem formulation to the clarification and careful presentation of ideas

this dissertation. He has kept me on the right track while forcing me to discover the har

problems for myself. His enthusiasm for my research topic and tremendous expertise is ve

much appreciated and he has always made time to review my experimental objectives an

conclusions and give excellent guidance, despite his busy schedule.

I would also like to thank all of my committee members, Dr. Tim. A. Haskew, Jaber Ab

Qahouq, Dawen Li and Min Sun for their invaluable input, inspiring questions, and support

both the dissertation and my academic progress. I would like to thank Dean David Francko a

Dr. Haskew for their assistance at the most difficult time of this journey.

In addition, I would like to thank Dr. Bharat Balasubramanian for opening up a

transformative cooperative program with practical industrials, which provided me with

wonderful opportunity to apply knowledge to the work in Mercedes- Benz U. S. Internationa

Inc., Vance, Alabama.

In my long journey through the University of Alabama, the graduate school has bee

supporting me all the way to my graduation. With Graduate Council Fellowship, I accumulate

professional knowledge of industrial electrical engineering and adapted myself to the colorf

campus life. With the support of Graduate Student Research and Travel Support, I was able t


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present my work at international conferences, which is an excellent way to enhance knowled

about latest technological advancements in the field of electric power engineering, to learn abo

the culture of different host countries and cities, to show my work to all the professiona

researchers, and most importantly, to represent UA and the graduate program to the world!

Finally, I would like to thank my parents for instilling in me a love of learning and

encouraging my curiosity. There was never anything I needed that they did not try to provid

They have made me the person I am today.

Thanks to all of you.


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CONTENTS

ABSTRACT .......................................................................................................... ii

DEDICATION ..................................................................................................... iv

LIST OF ABBREVIATIONS AND SYMBOLS ...................................................v

ACKNOWLEDGMENTS .................................................................................. viii

LIST OF TABLES ............................................................................................. xiv

LIST OF FIGURES ..............................................................................................xv

LIST OF ILLUSTRATIONS ............................................................................. xix

CHAPTER 1 - INTRODUCTION .........................................................................1

CHAPTER 2- ENERGY EXTRACTION CHRACTERISTIC STUDY OFSOLAR PHOTOVOLTAIC CELLS, MODULES AND ARRAYS ......................6

2.1 Semiconductor Characteristics and Equivalent Model of a Solar Cell ............6

2.1.1 Silicon Solar Cell ...........................................................................................6

2.1.2 Photogenerated Current and Voltage ............................................................8

2.1.3 Equivalent Model of a Solar Cell ..................................................................9

2.2 Energy Extraction Characteristics of PV cells under Uneven ShadingConditions.............................................................................................................11

2.2.1 Two Series PV Cells under Uneven Shading Condition .............................11

2.2.2 PV Module under Uneven Shading Condition ............................................16

2.2.3 Model Validation .........................................................................................21

2.3 Bypassing Diode Impact to the Characteristics of Solar PV Cells ................22


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2.4 Energy Extraction Characteristics of PV Arrays under Uneven Shading .....26

2.5 Virtual Transient Experiment ........................................................................30

2.6 Conclusions ...................................................................................................33

CHAPTER 3 - A FAST AND RELIABLE APPROACH FOR MAXIMUMPOWER POINT TRACKING ..............................................................................35

3.1 Extracted Power Characteristics of a PV System ...........................................36

3.1.1 The Effect of Temperature ..........................................................................37

3.1.2 The Effect of Illumination Intensity ............................................................39

3.2 Conventional Fixed-step MPPT Methods ......................................................40

3.2.1 Short-Circuit Current Method .....................................................................41

3.2.2 Open-Circuit Voltage Method .....................................................................42

3.2.3 Perturb & Observe Method .........................................................................43

3.2.4 Incremental Conductance Method ...............................................................44

3.3 Adaptive MPPT Strategies .............................................................................45

3.3.1 Traditional Adaptive MPPT Methods .........................................................46

3.3.2 Proposed Hyperbolic -PI (H-PI) Adaptive MPPT Method .........................47

3.4 Computational Experiment .............................................................................49

3.4.1 MPPT under Step and Ramp Changes of Solar Irradiation .........................51

3.4.2 Sampling Rate Impact .................................................................................55

3.4.3 MPPT under Variable Solar Irradiation Condition .....................................57

3.5 Hardware Experiment and Comparison .........................................................58

3.5.1 Laboratory Setup and Design ......................................................................58

3.5.2 Experiment Analysis and Comparison ........................................................59

3.6 Conclusions ....................................................................................................61


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CHAPTER 4 - PV ENERGY EXTRACTION CHARACTERISTICS STUDYUNDER SHADING CONDITIONS FOR DIFFERENT CONVERTERCONFIGURATIONS ...........................................................................................63

4.1 Configurations of Grid-connected Solar PV Systems ....................................63

4.2 Power Converters Architecture of PV Arrays ................................................64

4.2.1 Central Dc/ac and Dc/dc Converters ...........................................................65

4.2.2 Central Dc/ac Inverter and String Dc/dc Converters ...................................66

4.2.3 Dc/dc Optimizers .........................................................................................66

4.2.4 Detached Microinverters .............................................................................67

4.2.5 Central and String Inverters ........................................................................69

4.3 PV Array Models for Different Converter Configurations ............................70

4.4 PV System Energy Extraction Characteristics without Bypass Diodes .........71

4.4.1 Central Converter Configuration .................................................................71

4.4.2 String Converter Configuration ...................................................................73

4.4.3 Micro-inverter Configuration ......................................................................74

4.5 PV System Energy Extraction Characteristics with Bypass Diodes ..............76

4.5.1 Central Converter Configuration .................................................................77

4.5.2 String Converter Configuration ...................................................................79

4.5.3 Comparison of Maximum Power Using Central, String and Micro

Converter Configuration .......................................................................................80

4.6 Conclusion ......................................................................................................83

CHAPTER 5 - COORDINATED CONTROL FOR GRID INTEGRATIONOF PV ARRAY, BATTERY STORAGE, AND SUPERCAPACITOR WITHRELATED ISSUES......84

5.1 Grid-connected PV and Energy Storage System ............................................85

5.1.1 Photovoltaic Arrays .....................................................................................86


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5.1.2 Rechargeable battery ...................................................................................86

5.1.3 Supercapacitor .............................................................................................86

5.1.4 Grid-Connected Converter ..........................................................................87

5.1.5 Integrated Control System ...........................................................................87

5.2 Coordinate PV Array, ESU and GCC Control ...............................................88

5.2.1 Control of Bi-directional Dc/dc Converters for ESUs ................................88

5.2.2 Direct-Current Vector Control of GCC .......................................................90

5.3 Coordinated Control Mechanisms for Grid Integration .................................93

5.3.1 Dc-link Voltage Control through ESUs ......................................................93

5.3.2 Power Balancing Control of ESUs ..............................................................94

5.3.3 Dc-link Voltage Control through GCC .......................................................95

5.4 Coordinated Control Evaluation and Comparison .........................................96

5.5 Other Applications of Coordinated Control .................................................103

5.5.1 Coordinated Control in Single-phase System ...........................................103

5.5.2 Coordinated Control Considering about Ramp Rate Limit .......................108

5.6 Conclusion ....................................................................................................115

CHAPTER 6 - CONCLUSIONS AND FUTURE WORK ................................117

6.1 Contributions of the Dissertation .................................................................117

6.2 Limitations and Future Work .......................................................................118

REFERENCES ...................................................................................................120


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LIST OF TABLES

3.1 Comparison of MPPT methods ......................................................................62

4.1 Comparison of maximum power extraction without bypass diodes fordifferent converter configurations ..................................................................76

4.2 Comparison of maximum power extraction under 50% shading factor 82

4.3 Comparison of maximum power extraction under 100% shading factor...82

5.1 Parameters of electrical components in grid-integrated PV system .............98

5.2 Comparison of ramp rate value before and after designed ramp ratecontrol in two scenarios ...............................................................................114


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LIST OF FIGURES

2.1. Diffusion current, drift current, and depletion zone of a p-n junction ...........7

2.2. Illustration of drift current as well as photogenerated current and voltage ....8

2.3. Solar cell equivalent circuit model .................................................................9

2.4. Solar cell I-V and P-V characteristics ...........................................................112.5. Two series PV cells with uneven shading.....................................................12

2.6. Characteristics of two series solar cells ........................................................14

2.7. A PV module connected to an external circuit .............................................18

2.8. Characteristics of PV module (one cell shaded) ...........................................19

2.9. Characteristics of PV module (18 cells shaded) ...........................................20

2.10. Schematics of a PV module connected with bypassing diodes, created by NI Multisim ..............................................................................................24

2.11. Characteristics of a PV module (3 cells with a bypass diode) ......................25

2.12. Characteristics of a PV module (9 cells with a bypass diode) ......................25

2.13. Characteristics of a PV module (18 cells with a bypass diode) ....................25

2.14. Bypass and blocking diodes in a solar PV generator ....................................27

2.15. PV array characteristics (without bypass diode) ...........................................30

2.16. PV array characteristics (one module with a diode) .....................................30

2.17. PV array characteristics (each cell with a bypass diode) ..............................30

2.18. Solar PV generator under an open-loop controlled dc/dc power converter.. 31


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2.19. Transient simulation results of a PV array relevant to the 100%shading condition applied in Fig. 2.16 .........................................................32

3.1. Configuration of grid-connected solar PV system ........................................36

3.2. Typical daily temperature and irradiation plots ............................................37

3.3. P-V characteristics of a PV array vs. temperature and voltage .....................38

3.4. Derivative of power over terminal voltage under different temperatures .....38

3.5. P-V characteristics of a PV array vs. irradiation and voltage .......................40

3.6. Derivative of power over terminal voltage under different irradiations ......40

3.7. Graphic relation of I MPP over I SC andV MPP overV OC ....................................41

3.8. Conventional MPPT methods of SCC and OCV ..........................................42

3.9. Flowchart of the fixed step P&O algorithm ..................................................44

3.10. Flowchart of the incremental conductance algorithm ...................................45

3.11. PI based MPPT control loop diagram of the PV system ..............................47

3.12. A tangent sigmoid function for adaptive MPPT ...........................................48

3.13. Control loop diagram of proposed adaptive MPPT ......................................48

3.14. Solar PV generator with the MPPT and grid-integration using SPS andOpal-RT RT-LAB .........................................................................................49

3.15. MPPT digital control module........................................................................50

3.16. Step and ramp changes of irradiation ............................................................52

3.17. Comparison of MPPT under step and ramp changes of solar irradiationlevels .............................................................................................................52

3.18. Dc-link voltage .............................................................................................54

3.19. Three-phase grid-side currents ......................................................................54

3.20. Dc/ac inverter power at the grid side ............................................................54

3.21. MPPT comparison under different sampling rates ......................................56


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3.22. MPPT comparison of under variable solar irradiation condition..................57

3.23. Hardware experiment setup for evaluation of MPPT algorithms ................59

3.24. Hardware experiment of captured maximum power using conventional

and proposed MPPT algorithms....................................................................614.1. PV array with central dc/ac and dc/dc converter structure ...........................65

4.2. PV array with central dc/ac inverter and string dc/dc converters .................66

4.3. Dc/dc optimizers per module and a central inverter .....................................67

4.4. Detached microinverter PV system ..............................................................68

4.5. PV array with central and string inverters ....................................................69

4.6. Characteristics of PV array with central converter .......................................72

4.7. Characteristics of series PV strings with shaded cells ..................................73

4.8. Characteristics of PV module under shading conditions ..............................75

4.9. Characteristics of PV array under shading conditions ..................................78

4.10. Characteristics of PV array for different bypass diode schemes ..................79

4.11. Characteristics of series PV strings...............................................................81

5.1. Configuration of grid-connected PV system with ESUs ..............................85

5.2. Block diagram of nested-loop battery control strategy .................................89

5.3. GCC converter schematic .............................................................................90

5.4. GCC direct-current vector control structure .................................................92

5.5. Control of dc-link voltage through ESUs .....................................................94

5.6. Power balance control structure of ESUs .....................................................95

5.7. Energy storage units connected converters control structure .......................96

5.8. Solar PV generator under the control of a dc/dc power converter usingSPS and Oparl-RT RT-LAB .........................................................................97

5.9. Solar PV array characteristics used in simulation .........................................98


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5.10. Simulation results of the control scheme in Section 5.3.1 ............................99



5.13. Solar irradiation over the nominal irradiation of 1000W/m2 ......................100

5.14. Three-phase grid-side currents ....................................................................102

5.15. Single-phase grid connected solar PV generator under the control of adc/dc power converter using SPS and Opal-RT RT-LAB .........................105

5.16. Simulation result of the proposed method applications in single-phaseinverter .......................................................................................................106

5.17. Energy storage units connected converters control structure .....................110

5.18. Hourly solar radiation data of two random days in Adair Casey ................110

5.19. Simulation results of scenario 1 ..................................................................111

5.20. Simulation results of scenario 2 ..................................................................111

5.21. Dc-link voltages of two solar irradiation scenarios ....................................114


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LIST OF ILLUSTRATIONS

4.1 Configuration of grid-connected solar PV system ...........................................64

5.1 Measured solar irradiance profiles for each day in August 2012 ..................109


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CHAPTER 1

INTRODUCTION

Investment in solar photovoltaic (PV) energy is rapidly increasing worldwide [1]. A grid

connected solar PV system consists of a PV generator that produces electricity from sunlight a

power converters for energy extraction and grid interface control [2, 3]. The smallest unit of

PV generator is a solar cell and a large PV generator is built by many solar cells that ar

connected together through certain series and parallel connections [4].

Although in most power-generating systems, the main source of energy (the fuel) can b

manipulated, this is not true for solar energies [5]. Industry must overcome a number of technic

issues to deliver renewable energy in significant quantities. Control is one of the major enablin

technologies for the deployment of renewable energy systems. Photovoltaic power requir

effective use of advanced control techniques. In all, safe and effective integration of PV systecannot be achieved without extensive use of control technologies at all levels.

Firstly, unlike a solar thermal panel which can tolerate some shading, PV modules ar

very sensitive to shading. Many brands of PV modules can be affected considerably even b

shading of the branch of a leafless tree. If enough cells are hard shaded, a module will no

convert any energy and will, in fact, become a tiny drain of energy on the entire system [2, 6].

existing research, most shading studies of a PV system focus mainly on how the I-V and P-

characteristics of an entire PV system are affected [7-12]. Different from the convention

approaches, Chapter 2 investigates the characteristics of shaded PV cells, modules, and arrays

integrating the semiconductor physics characteristics of PV cells and the electrical characteristi


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of the PV generators together and by investigating characteristic evaluation of unshaded cell

shaded cells, and PV modules of a PV system. The chapter first introduces the semiconduct

characteristics and model of a solar PV cell in Section 2.1. Section 2.2 presents a characterist

study of PV modules under uneven shading conditions and a strategy for validation of mode

and algorithms developed by using National Instruments (NI) Multisim software, a PSpice-bas

circuit simulation tool. Section 2.3 investigates how bypassing diodes affect and improve th

characteristics and performance of shaded cells, unshaded cells, and a PV module. Section 2

presents how the shading affects the performance of a PV array. Section 2.5 compares a transie

study of a PV array under an open-loop control condition through power electronic converterFinally, Section 2.6 concludes with the summary of main points.

Secondly, operation and control of a grid-connected solar PV system is importan

because the conversion efficiency of PV power generation is low (9-17%) [13], especially und

low irradiation conditions; the amount of electric power generated by a solar array change

continuously with weather conditions. The power delivered by a PV system of one or mor

photovoltaic cells is dependent on the irradiance, temperature, and the current drawn from t

cells. In general, there is a unique point on the I-V or P-V curve, called the maximum pow

point (MPP), at which the entire PV system operates with maximum efficiency and produces

maximum output power. The location of the MPP is not known, but can be located, eithe

through calculation models or by searching algorithms. To maximize the output power of a P

system, continuously tracking the MPP of the system is necessary. The primary challenges fo

maximum power point tracking of a solar PV array include: 1) how to get to a MPP quickly,

how to stabilize at a MPP, and 3) how to make a smooth transition from one MPP to anothe

under sharply changing weather conditions. In general, a fast and reliable MPPT is critical f


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power generation from a solar PV system. In order for effective design and development of sol

PV systems in electric power systems, it is important to investigate and compare operatin

principles, performance, and advantages or disadvantages of conventional MPPT techniqu

used in the solar PV industry, and develop new competent technology for fast and reliabl

extraction of solar PV power. In Chapter 3, the dissertation first presents an analysis of PV arr

characteristics and the impacts of temperature and solar irradiance on PV array characteristics

Section 3.1. Section 3.2 investigates conventional fixed-step MPPT techniques used in solar P

industry. Section 3.3 presents traditional adaptive MPPT techniques, and a propose

proportionalintegral (PI) based adaptive MPPT approach for fast and reliable tracking of Parray maximum power. Section 3.4 gives performance evaluation of the conventional an

proposed MPPT methods under stable and variable weather conditions through a computation

experiment strategy. Section 3.5 shows a hardware experiment evaluation of the convention

and proposed MPPT methods under more practical conditions in a dSPACE-based digital contr

environment. Finally, Section 3.6 concludes with the summary of main points.

Thirdly, to make a PV system more efficient and economic, it is necessary to analyz

different converter configurations. Many different converter structures have been developed an

used in a solar PV system. Typical configurations include a central dc/dc/ac converter [14],

central dc/ac inverter [15, 16], multi-string dc/dc converters plus a central dc/ac inverter [14, 17

string inverters [15, 16], dc/dc optimizers [16, 17] and microinverters [15, 17, 18]. For all th

different converter structures, the energy extraction characteristics and maximum power captu

capability for all the converter schemes under even solar irradiation are very similar. Howeve

under shading conditions, the energy extraction depends strongly on what converter structure

used in a PV system. Therefore, it is important to understand what the differences of energ


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extraction characteristics are when using different converter schemes. In [17, 19], it is pointe

out that the string converter system has the advantage in capturing the maximum power of eac

string of PV modules separately. In [15, 17], it is commented that micro converter PV system

effective to overcome shading impact and enhance PV system efficiency. But, no detaile

comparison studies have been conducted previously on PV array performance using differe

converter structures. This research first introduces configurations of grid-connected solar P

system in Section 4.1 and typical PV power converter architectures in Section 4.2 respectivel

PV array models for different converter configurations are discussed in Section 4.3.Section 4

and 4.5 investigate PV system energy extraction characteristics with and without bypass dioderespectively, for different converter schemes. Finally, Section 4.6 concludes with the summary

main points.

Last but not least, the control of energy storage is a key component in improving energ

efficiency, security and reliability, which allows the desired active and reactive power delivere

to the grid and at the same time to maintain the stability of the dc-link voltage of the PV an

energy storage system through coordinated control of power electronic converters. Batteries a

the technological solution most commonly employed to help make a PV power smooth an

dispatchable [20]. A battery stores electrical energy in the form of chemical energy. Normall

batteries perform three main functions in a grid-connected PV system: storing energy into th

batteries when the PV production is high and the grid demand is low, releasing energy to the gr

when the PV production is low or during grid peak demand intervals, and preventing larg

voltage fluctuations. Except for batteries, supercapacitor (SC) is usually used in conjunction wi

batteries to form an advanced PV energy storage system [20, 21]. However, unlike batterie

where the voltage remains relatively even over most of the batterys remaining charge levels,


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SCs voltage scales linearly with the remaining energy. This means additional circuitry i

required to make the SC energy usable. In order for effective design, development, and analys

of integrated PV and Energy storage units (ESU) systems, it is important to investigate operatin

principles, performance, and disadvantages and advantages of typical coordinated contr

techniques used in the PV and ESU systems. In chapter 5, this research first introduces gri

connected PV and ESU system in Section 5.1. Section 5.2 evaluates control technologie

associated with each individual PV system components. Section 5.3 investigates coordinate

control methods for the integrated PV system. Section 5.4 gives performance evaluation f

coordinated control of PV array and ESU integration with the grid. Other applications includinsingle-phase DQ control and ramp rate limit control are illustrated in Section5.5. Finally, chapt

5 concludes with the summary of main points in Section 5.6.

Taken as a whole, this research demonstrates some issues of PV energy generation an

conversion from devices to gird integration.


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CHAPTER 2

ENERGY EXTRACTION CHRACTERISTIC STUDY OF SOLAR PHOTOVOLTAIC CELLS

MODULES AND ARRAYS

To begin with any research in PV system, it is important to know the characteristics o

solar cells, modules, and arrays in order to operate the design, energy extraction and gri

integration of a solar PV generator.

2.1 Semiconductor Characteristics and Equivalent Model of a Solar Cell

In most of solar cells, the absorption of photons takes place in semiconductor material

resulting in the generation of the charge carriers and the subsequent separation of the photo

generated charge carries. Therefore, semiconductor layers are the most important parts of a solcell.

2.1.1 Silicon Solar Cell

A solar cell is a device that converts the energy of sunlight directly into electricity by th

photovoltaic effect [2]. Although there are many kinds of solar cells developed by using differe

semiconductor materials, the operating principle is very similar. The most commonly know

solar cell is configured as a large-area p-n junction made from silicon. When a piece of p-typ

silicon is placed in intimate contact with a piece of n-type silicon, a diffusion of electrons occu


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from the region of high electron concentration (the n-type side) into the region of low electro

concentration (p-type side). Similarly, holes flow in the opposite direction by diffusion. Th

forms a diffusion current I D from the p side to the n side (Fig. 2.1a). When the electrons diffuse

across the p-n junction, they recombine with holes on the p-type side. The diffusion of carrie

does not happen indefinitely because of an electric field which is created by the imbalance

charge immediately on either side of the junction which this diffusion creates. The electric fie

established across the p-n junction generates a diode that promotes charge flow, known as dri

current I S , that opposes and eventually balances out the diffusion current I D. The region where

electrons and holes have diffused across the junction is called the depletion zone (Fig.2.1b).

(a) Diffusion current I D from the p side to the n side

(b) Drift current I S from the n side to the p side and the depletion zone

Fig. 2.1. Diffusion current, drift current, and depletion zone of a p-n junction


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2.1.2 Photogenerated Current and Voltage

When a visible light photon with energy above the band-gap energy strikes a solar ce

and is absorbed by the solar cell, it excites an electron from the valence band. With thi

newfound energy transferred from the photon, the electron escapes from its normal positio

associated with its atom, leaving a localized "hole" behind [2]. When those mobile charg

carriers reach the vicinity of the depletion zone, the electric field sweeps the holes into the p-sid

and pushes the electrons into the n-side, creating a photogenerated drift current. Thus, the p-si

accumulates holes and the n-side accumulates electrons (Fig. 2.2), which creates a voltage thcan be used to deliver the photogenerated current to a load. At the same time, the voltage built u

through the photovoltaic effect shrinks the size of the depletion region of the p-n junction dio

resulting in an increased diffusion current through the depletion zone. Hence, if the solar cell

not connected to an external circuit (switch in the open position in Fig. 2.2), the rise of th

photogenerated voltage eventually causes the diffusion current I D balancing out the drift current

I S until a new equilibrium state is reached inside a solar cell.

Fig. 2.2. Illustration of drift current as well as photogenerated current and voltage


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2.1.3 Equivalent Model of a Solar Cell

When a solar cell is connected to an external circuit (i.e., switch in the close position i

Fig. 2.2), the photogenerated current then travels from the p-type semiconductor-metal contac

through the wire, powers the load, and continues through the wire until it reaches the n-typ

semiconductor-metal contact. Under a certain sunlight illumination, the current passed to th

load from a solar cell depends on the external voltage applied to the solar cell normally through

power electronic converter for a grid-connected PV system. If the applied external voltage

low, only a low photogenerated voltage is needed to make the current flow from the solar cell

the external system. Nevertheless, if the external voltage is high, a high photogenerated volta

must be built up to push the current flowing from the solar cell to the external system. This hig

voltage also increases the diffusion current as shown in Section 2.1.2 so that the net outpu

current of the solar cell is reduced.

Fig. 2.3. Solar cell equivalent circuit model

To analyze the behavior of a solar cell, it is useful to create a model which is electricall

equivalent. According to Section 2.1.2, an ideal solar cell can be modeled by a current sourc

representing the photogenerated current I L, in parallel with a diode, representing the p-n junction

of a solar cell. In a real solar cell, there exist other effects, not accounted for by the ideal mode


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Those effects influence the external behavior of a solar cell, which is particularly critical f

integrated solar array study. Two of these extrinsic effects include: 1) current leaks proportion

to the terminal voltage of a solar cell and 2) losses of semiconductor itself and of the met

contacts with the semiconductor. The first is characterized by a parallel resistance R p accounting

for current leakage through the cell, around the edge of the device, and between contacts o

different polarity (Fig. 2.3). The second is characterized by a series resistance R s, which causes

an extra voltage drop between the junction voltage and the terminal voltage of the solar cell f

the same flow of current.

The mathematical model of a solar cell is described by

0 1 ,

d qV d mkT

c L c d c s p

V I I I e V V I R

R (2.1)

where I L is proportional to the sunlight illumination intensity, m is the diode ideality factor (1 for

an ideal diode), the diode reverse saturation current I 0 depends on temperature,q is the

elementary charge,k is the Boltzmann's constant, and T is the absolute temperature [22]. For all

the studies presented in this dissertation, I L=6A, I 0=610-6A, R P =6.6 , RS =0.005 , andT =25 ,

which represents full sun condition used in [23]. Thus, characteristics of a solar cell can either b

simulated using a circuit simulation tool based on the equivalent circuit model or compute

directly by using MatLab based on (2.1). Important characteristics for a solar cell consist

output current I c and power P c versus output voltage V c characteristics. Figure 2.4 shows typical

I-V and P-V characteristics of a solar cell under ideal condition and with the consideration o

parallel and series resistance obtained by using a Spice simulation tool. As it can be seen fro

the figure, if the external voltage applied to the solar cell is low, the net output current of th

solar cell, depending primarily on the photogenerated current, is almost constant. Therefore,

the external voltage increases, more power is outputted from the solar cell. But, if the extern


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voltage is around the forward conduction voltage of the p-n junction diode, the net output curre

drops significantly and the output power reduces.

a) I-V characteristics b) P-V characteristics

Fig. 2.4. Solar cell I-V and P-V characteristics

(T = 25 C, I 0 = 6 10-10A, I L = 6A, R p =6.6 and R s = 0.005 )

2.2 Energy Extraction Characteristics of PV cells under Uneven Shading Conditions

In most conventional studies of a solar PV system, it is usually assumed that all the PV

cells and modules making up a solar PV generator are identical and work under the sam

condition [24- 26]. However, in reality, the characteristics of the cells and modules are subject

some variations. This may happen when uneven sunlight is applied to solar cells, unclean P

cells, variation and inconsistence of the cell parameters to be expected from manufacturin

process, or other conditions [2, 4].

2.2.1 Two Series PV Cells under Uneven Shading Condition

Figure 2.5 shows the configuration of two series connected PV cells. If both cells ar

identical and operate at the same condition, then, the concentration of the photon-excited char


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carriers are the same in both cells. Thus, the photogenerated current in one cell can flow throu

the second cell continuously and then to the external system, and the output voltage of the tw

cells is the summation of the photogenerated voltage of both cells.

IL 1

Rp1

Rs1

Vs

IL 2Rp2

Rs2

Fig. 2.5. Two series PV cells with uneven shading

Nevertheless, if the two cells operate at different conditions, such as one cell is at the fu

sun while the other is shaded, then, the photon-excited charge carriers in the unshaded cell a

more than the photon-excited charge carriers in the shaded cell. Thus, the photocurrent of th

unshaded cell cannot completely flow through the shaded cell due to the insufficient charg

carriers, causing the rest of the photon-excited charge carriers to be accumulated on the p- and

side of the unshaded cell. Then, the output voltage of the unshaded cell rises, which causes (

more diffusion current through the p-n junction of the unshaded cell (Fig. 2.2) and (b) some

the photogenerated current of the unshaded cell being pushed through the parallel resistance

the shaded cell until an equilibrium state is reached.

If assuming that the parameters of the two cells are identical, the mathematical model o

the series PV cells under the shading condition is described by


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11

0 1 11 ,

d qV

d mkT c L c d c s

p

V I I I e V V I R

R (2.2)

22

0 2 2(1 ) 1 ,

d qV d mkT

c s L c d c s p

V I p I I e V V I R

R

(2.3)

1 2 s c cV V V (2.4)

where p s stands for the shading factor that the shaded cell is relevant to the unshaded cell, and I L

represents the photogenerated current of unshaded cell under the full sun condition,V d1 and V d2

and V c1 and V c2 represent p-n junction diode voltages and output voltages of the unshaded and

shaded cells, respectively. Based on (2.2) to (2.4), a system of nonlinear equations can bdeveloped as

1 1 2 2 1 2, 0 , 0 d d d d f V V f V V (2.5)

Then, for a given voltage applied to the PV cells, voltageV d1 and V d2 can be solved

numerically by using Newton-Raphson algorithm in the following steps:

a) Initial estimation:

0 01 2,0dV d d V V (2.6)

b) Compute Jacobian matrix:

1 1 1 2

2 1 2 2

k k d d

k k d d

f V f V

f V f V

J (2.7)

c) Compute correction k d V and update PV cell voltage 1k

d V :

1k k k d d d

V V V (2.8)

d) Error calculation:

2 21 1

1 2

d dV Vk k err f f (2.9)


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e) Repeat steps b) to d) until a stop criterion is reached, such as |err| < ( is a

predefined threshold).

a) I-V characteristics of two cells b) P-V characteristics of two cells

c) Unshaded cell terminal voltage characteristics d) Unshaded cell P-V characteristics

e) Shaded cell terminal voltage characteristics f) Shaded cell P-V characteristics

Fig. 2.6. Characteristics of two series solar cells

For detailed study under shading condition, the I-V and P-V characteristics of the seriesPV cells can be obtained through either simulation of Fig. 2.5 or the numerical computatio

shown above. Although simulation of Fig. 2.5 is convenient to implement by using a circu

simulation tool, numerical computation approach is more practical for a large solar PV syste


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that contains thousands of solar cells. It is necessary to point out that the study based on bo

approaches can provide a cross validation mechanism.

Figure 2.6 shows the I-V and P-V characteristics under three shading conditions. The

shading factors are 0%, 50%, and 100%, where 0% represents the unshaded condition and 100

stands for the completely shaded condition. This shading representation is applicable to the re

of this research. Usually, the power dissipated by a shadowed cell increases cell temperatur

which changes the solar cell electrical properties by varying the values of I 0 and I L slightly.

However, detailed temperature change, involving complicated heat transfer issues, is very ha

to calculate. Therefore, the temperature change caused by the power dissipation of a shadowcell is not considered here. According to Fig. 2.6 as well as other results, the following remar

are obtained.

1) When both cells operate at the same condition and under the same illumination

intensity, the photogenerated voltages are the same (Figs. 2.6c and 2.6e) and the P-V

characteristics are identical for both cells (Figs. 2.6d and 2.6f). Compared to a single cell, th

output voltage and power at the maximum power point are increased.

2) If one cell is 100% shaded while the other is in full sun, the photogenerated curren

of the unshaded cell has to pass through the parallel resistor of the shaded cell. Moreover, t

push the current through the high parallel resistance, the photogenerated voltage of the unshad

cell must be high (Fig. 2.6c), which increases the diode drift current of the unshaded cell an

reduces the net output current significantly so that the actual output power is very low (Figs. 2.6

and 2.6d).

3) If one cell is partially shaded while the other is in full sun, the unshaded cell has

more photon-excited charge carriers than the shaded one. Therefore, part of the photon-excit


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charge carriers of the unshaded cell passes through the shaded cell and part of charge carriers

the unshaded cell has to pass through the parallel resistor of the shaded cell so that the termin

voltage of the shaded cell is reversed. Thus, the unshaded cell generates power while the shad

cell absorbs power (Figs. 2.6d and 2.6f), depending on the external voltage applied to the tw

series solar cells. Similarly, to push the current through the high parallel resistance, th

accumulated photogenerated voltage of the unshaded cell must be high (Fig. 2.6c), whic

increases the diode diffusion current of the unshaded cell so that the net current actually passin

through the parallel resistor of the shaded cell is very low (Fig. 2.6a).

4)

Under partial shading conditions, the power absorbed by the shaded cell isinfluenced by the applied external voltage. The higher the external voltage, the less the current

pushed through the parallel resistor of the shaded cell by the unshaded cell, the less the rever

terminal voltage of the shaded cell and the less the shaded cell absorbs power. When the extern

voltage is higher than the diode forward conduction voltage of the unshaded cell, the shaded c

basically starts to generate power (Fig. 2.6f). In other words, increasing external voltage appli

to the two series of cells could prevent the shaded cell from becoming a hot spot under an unev

shading condition. But, this special regularity cannot be seen effectively by just looking at th

overall P-V characteristics as shown by Fig. 2.6b.

2.2.2 PV Module under Uneven Shading Condition

Normally, solar cells are connected in series to form a module that gives a standard d

voltage. A module typically contains 28 to 36 cells in series (Fig. 2.7), to generate a dc outp

voltage of 12V in standard illumination condition. The 12V module can be used singly o


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connected in series and parallel into an array with a large voltage and current output, accordin

to the power demand by an application.

The I-V and P-V characteristics of a PV module under a shading condition are more

complicated, depending on how many cells are shaded and what the shading factor of each ce

is. Assume there are N cells in a PV module and the shading factor of theith PV cell in the

module is p i. Then, the mathematical model of a PV module under a shading condition is

described by:

0(1 ) 1 ,

diqV

dimkT c i L ci di c s

p

V I p I I e V V I R

R

(2.10)

1 2 ( 1) s c c c n cN V V V V V (2.11)

where p i stands for the shading factor of theith cell relevant to the full sun condition, I L

represents the full sun photogenerated current, and V di andV ci are the p-n junction diode voltages

and output voltages of the ith PV cell. Similar to Section 2.2.1, a system of N nonlinear equations

can be developed as shown by (2.12).

1 1 1, , 0 , , 0 d dN N d dN f V V f V V (2.12)

Then, for a given voltage applied to a PV module, voltageV d1, V d2, V dN can be solved

numerically by using Newton-Raphson algorithm in the following steps: 1) obtaining initia

estimation values of PV cell voltages, 2) computing the Jacobian matrix, 3) computing th

correction and updating PV cell voltages, 4) calculating the error, and 5) repeating steps (2)

(4) until a stop criterion is reached [27]. After the completion of the iteration, solutions ofV d1 ,

V d2 , V dN for all PV cells are available for both shaded and unshaded cells. It is necessary t

point out that the initial estimation is vital for the stability and convergence of the Newton

Raphson algorithm, which is achieved based on the knowledge and estimation of a commo


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voltage range for a shaded or unshaded PV cell. In addition, before the iteration process, PV ce

with the same shading factor are regrouped together, which can greatly reduce the number of th

nonlinear equations and accelerate the numerical computation. It is worth noting that th

Bishops numerical program based on an equivalent PVNet is another approach that wa

developed and used to investigate the electrical behavior of solar cell interconnection circuits

presented in [28].

Vs

Shade

Fig. 2.7. A PV module connected to an external circuit

The I-V and P-V characteristics of the PV module can be obtained through either

numerical computation or simulation of Fig. 2.7. Figure 2.8 shows the characteristics of a P

module when the shading factors of one cell are 0%, 50%, and 100%, respectively, while th

other cells are in full sun.


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a) I-V characteristics of PV module b) P-V characteristics of PV module

c) Unshaded cell voltage characteristics d) Unshaded cell P-V characteristics


Fig. 2.8. Characteristics of PV module (one cell shaded)

As it can be seen from the figure, if all the cells are in full sun irradiation and have th

same operating condition, the current from each cell is the same, and the output voltage an

power of the PV module are enhanced significantly due to the fact that more cells are connect

in series. But, this situation is completely different even when only one cell is shaded (Fig. 2.8and 2.8b). Due to the shading of one cell, part of charge carriers of the unshaded cells must g

through the parallel resistor of the shaded cell so that the terminal voltage of the shaded cell

reversed (Fig. 2.8e).Thus, the unshaded cells generate power while the shaded cell absorb


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power (Fig. 2.8d and 8f). Similarly, to push the current through the high parallel resistance of t

shaded cell, the accumulated photogenerated voltage of each unshaded cell must be high (Fi

2.8c) so that the net series voltage of all unshaded cells causes a high current through the parall

resistor of the shaded cell (Fig. 2.8a) and a high reverse terminal voltage on the shaded cell (Fi

2.8e), which results in a high absorbing power by the shaded cell especially when the extern

voltage applied to the PV module is low (Fig. 2.8f). This high absorbing power may damage th

shaded PV cell.

a) I-V characteristics of PV module b) P-V characteristics of PV module

c) Unshaded cell voltage characteristics d) Unshaded cell P-V characteristics


Fig. 2.9. Characteristics of PV module (18 cells shaded)


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Figure 2.9 shows the characteristics of the PV module when 18 out of the 36 cells ar

shaded. The shading factor, identical for all the 18 shaded cells, is 100%, 50% and none

Compared to Fig. 2.8, when there are more cells shaded in a PV module, the net output voltag

of the unshaded cells is smaller and is applied to the shaded cells in a distributed manner. Henc

the reverse voltage applied to the parallel resistor of each shaded cell is lower (Fig. 2.9e) and th

absorbing power by each shaded cell is decreased (Fig. 2.9f). Compared to Fig. 2.8f, the chan

for a shaded cell to become a hot spot is reduced, implying that a single shaded cell condition

more hazardous to affect proper function of a PV module.

2.2.3 Model Validation

The fundamental unit of a PV generator is a PV cell. For a PV array model, parameter

associated with a PV cell, such as R p and R s, must be identified first. These can be obtained

through parameter extraction, such as the procedure shown in [29, 30]. The parameter extractio

is not a focus of this paper. It is assumed that parameters of PV cells are available [31, 32]. Thuthe model validation focuses mainly on whether accurate current, voltage and power relations f

PV cells, modules and array can be obtained via the Newton-Raphson algorithm. Howeve

model validation through hardware experiments presents a big challenge for PV cells und

uneven shading conditions. This is due to the fact that that existing commercial available P

modules are not built in such a way that current or voltage of each individual cell can b

measured. To overcome the challenge, this dissertation uses NI Multisim, a well-develope

PSpice-based industry standard circuit simulation tool [33-35], to validate models and th

Newton-Raphson algorithm application in Section 2.2.2, which provides an accurate and fa

approach for model validation. Using the NI Multisim, a PV cell equivalent circuit is ver


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convenient to build by using professionally developed circuit components. The procedure for t

PSpice-based simulation includes: 1) drawing circuit schematics, as illustrated by Figs. 2.3, 2

and 2.7; 2) setting up circuit parameters of the PV system; 3) simulating the circuit; 4) plottin

the results. According to Fig. 2.3, each PV cell has four components, including two resistors, o

diode, and one ideal current source. For a PV module containing 36 cells, there would be 14

components.

The model validation involves the development of computer program using the Newton

Raphson algorithm and the building of the PV simulation system using NI Multisim. For th

PSpice-based simulation, each circuit component of a PV cell is treated as a different simulatioelement. Therefore, solar PV system simulation using NI Multisim is extremely expensive

terms of computing speed and memory requirements. However, for the computer program

especially developed for the PV system study, the PV cells having the same operating conditio

are first regrouped automatically before the simulation. Therefore, both the computing speed an

memory requirement are much more efficient, particularly for a large PV array. The resul

generated using the two different approaches are compared for different case studies, includin

PV cells (Fig. 2.6), PV modules (Figs. 2.8 and 2.9), and small-scale PV arrays. The compariso

always show the same results generated by both approaches (Figs. 2.6, 2.8, 2.9, 2.11, 2.12 an

2.13), demonstrating that it is effective and accurate to use the models and algorithm develope

in this chapter for small- and large-scale PV system studies (Section 2.4).

2.3 Bypassing Diode Impact to the Characteristics of Solar PV Cells

In photovoltaic industry, external bypass diodes in parallel with a series string of cells ar

normally utilized to mitigate the impacts of shading on P-V curves. The polarity of the bypass


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diode is reversed with respect to the PV cells [2]. Consequently, reverse bias of the cell

corresponds to the direct bias of the bypass diode which provides a bypass for the curre

generated by other cells. With bypass diodes, the I-V and P-V characteristics of a PV module are

more complicated [36].

Normally, a bypass diode is applied to a PV module or a group of series PV modules [7

12]. For research purpose, however, different bypass diode schemes within a PV module will b

studied in this dissertation. Figure 2.10 shows a bypass diode arrangement, in which a bypa

diode is applied to each three series PV cells. For a general case, it is assumed that there are M

bypass diodes with each bypass diode being applied to L=N/M series PV cells. Then, the currentand voltage relations of the PV cells connected with theith bypass diode and overall system

current and voltage are described by

0(1 ) 1 dijqV mkT ci ij L dij p I p I I e V R

(2.13)

1 2 ( 1) , pdi ci ci ci n ciL cij dij ci sV V V V V V V I R

(2.14)

0 1 2 ( 1)1 , pdiqV mkT

s ci s pd pd pd M pdM I I I e V V V V V

(2.15)

where p ij stands for the shading factor relevant to the full sun condition for the jth PV cell within

the ith bypass diode group,V dij and V cij represent p-n junction diode voltage and PV cell output

voltages of the jth PV cell within theith bypass diode group, I ci is the output current of the series

PV cells within theith bypass diode group, andV pdi represents the voltage applied to theith

bypass diode.Then, similar to (2.12), a system of N nonlinear equations can be developed and voltage

V d1 to V dN can be solved numerically by using Newton-Raphson algorithm for a given externa


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voltageV s applied to the PV module. If some of the PV cells within the PV module operate at th

same condition, the numerical computation could be simplified considerably.

Fig. 2.10. Schematics of a PV module connected with bypassing diodes, created by NI Multisim

Figures 2.11- 2.13 show the characteristic of the PV module when one PV cell in th

module is shaded for three different bypass diode arrangement schemes: three series cells with

bypass diode, nine series cells with a bypass diode, and eighteen series cells with a bypass diod

From the figures, other case studies, and comparison with Section 2.2, it is concluded that:

1) When a PV cell is shaded, there are two possible paths for the current generated b

other unshaded cells to pass through. One is through the shaded cell and parallel resistor of t

shaded cell; the other is through the bypass diode. The condition for the current passing throug

the bypass diode is that the resultant reverse voltage of the series cells in parallel with the bypa

diode must be larger than the forward conduction voltage of the bypass diode.


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a) I-V characteristics of PV

module

b) P-V characteristics of PV

module

c) Shaded cell terminal voltage

d) Shaded cell P-V

characteristics

Fig. 2.11.Characteristics of

a PV module

(3 cells with a bypass diode)


module

b) P-V characteristics of PVmodule


d) Shaded cell P-V

characteristics

Fig. 2.12. Characteristics of

a PV module



module

b) P-V characteristics of PVmodule


d) Shaded cell P-V

characteristics

Fig. 2.13. Characteristics of

a PV module



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2) When the bypass diode turns on, the voltage applied to the shaded cell equals to th

photogenerated voltages of the unshaded cells within the bypassing cell group plus the bypa

diode forward conduction voltage. Therefore, the less the PV cells within a bypassing cell grou

the smaller the reverse voltage which is applied to a shaded cell (Figs. 2.11c, 2.12c, and 2.13

and the less the shaded cell absorbs power (Figs. 2.11d, 2.12d, and 2.13d). In other words,

prevent a shaded cell from becoming a hot spot, the number of series PV cell within a bypassi

cell group should be properly designed.

3) With bypass diodes, the I-V and P-V characteristics of a PV module is more

complicated and different from the traditional understanding of the photovoltaic I-V and P-V characteristics. An important issue, as it can be seen from Figs. 2.11b, 2.12b, and 2.13b, is th

the P-V characteristics of a PV module may contain multiple peaks. Hence, using traditiona

maximum power point tracking approaches, one may get into a local peak point so that th

efficiency of the PV module would be reduced greatly.

By comparing Figs. 2.8 and 2.9 with Figs. 2.11-2.13, it can be been that bypass diodes o

a PV module can reduce absorbing power of shaded cells within the PV module and improve t

performance of PV system.

2.4 Energy Extraction Characteristics of PV Arrays under Uneven Shading

There are generally two ways to connect PV modules into an array. The first approac

connects modules in series into strings and then in parallel into an array. The second approac

first wires modules together in parallel then combines those units in series. Both connections a

equivalent if all the cells and modules are identical and work at the same condition. But,

sunlight is applied unevenly to different PV cells as well as shading or other impacts, the seco


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connection approach could cause many very bothersome problems [2]. Figure 2.14 shows

series-parallel PV array connection with a dc/ac power converter, in which the converter handl

both maximum power point tracking (MPPT) and grid interface control of the PV array [24]. A

the top of each string in Fig. 2.14, a blocking diode is used to prevent a shaded or malfunctioni

string from withdrawing current from the rest strings that are wired together in parallel.

Fig. 2.14. Bypass and blocking diodes in a solar PV generator

For the series-parallel connected PV array, the voltage applied to each string of the PV

modules is the same. However, the P-V and I-V characteristics of each string could be differe

depending on how many cells in a string are shaded and how much the shading factors are. Feach string, the mathematical procedure to obtain P-V and I-V characteristics is very similar

Section 2.3 except that the external voltage applied to each string equals to the sum o

photogenerated voltages of all series connected PV modules. Then, with the consideration th


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the output current of the PV array is the sum of currents of all parallel strings, characteristics

the PV array can be achieved quickly through numerical computation. It is necessary to point o

that for any PV cells having the same operating condition within a string, combining those P

cells into one mathematical equation could significantly accelerate the numerical computatio

speed.

Figures 2.15 to 2.17 show a comparative study of PV array characteristics for thre

different bypass diode conditions, i.e., no bypass diode employed, one bypass diode for each P

module, and one bypass diode for each PV cell. The PV array has a configuration of 10 paral

strings with each string containing 20 modules. Assume there are 19 shaded modules in the 1string, 17 in the 2nd string, 15 in the 3rd string and 1 in the last string. In each shaded modul

there is one shaded cell only, which is the worst condition that would damage a PV cel

according to Section 2.2. The shading factors are 0%, 50% and 100%, respectively. From th

figures, other case studies, and comparison with Section 2.3, the following properties ar

obtained:

1) If no bypass diodes are applied, the PV array characteristics can be shifted

significantly by shaded cells (Fig. 2.15a and Fig. 2.15b). The degree of the shift depends on ho

many strings contain shaded cells, how many shaded cells are in each string and how much th

shading factors are. When there is only one shaded cell in a string, all the photogenerate

voltages of the unshaded cells in that string are applied to the shaded cell (Fig. 2.15c), whic

would cause a high risk to damage the shaded cell due to the high absorbing power of the shade

cell (Fig. 2.15d).

2) If each PV module has one bypass diode, it is found that there is an improvement i

the PV array characteristics under shading conditions depending on the distribution of the shad


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cells in the PV array. For each string if the number of the shaded cells is the same, the be

situation is that all the shaded cells appear in one module. However, if the shaded cells ar

distributed evenly in different modules in a string, the enhancement of the PV array

characteristics is trivial (Figs. 2.16a and 2.16b). If there is only one shaded cell in a modul

then, all the photogenerated voltages of the unshaded cells in that module are applied to th

shaded cell (Fig. 2.16c). Compared to Fig. 2.15d, the absorbing power of the shaded cell und

100% shading condition is reduced a lot but changes very little for 50% shading condition

Another impact of the bypass diodes is that multiple peaks would result in the P-V characteristi

of the PV array. The extent of the multiple peaks depends on the distribution of the shaded celin the PV array as well as the number of parallel strings and the number of series modules

each string. For Fig. 2.16b, multiple peak impact can be seen clearly when the figure is enlarge

Hence, using traditional MPPT approaches [37-40], one may get into a local peak power point

that the efficiency of the PV module would be reduced greatly.

3) If each PV cell has a bypass diode, the influence of the shaded cells to the PV arra

characteristics is significantly reduced. Compared to both Figs. 2.15d and 2.16d, the absorbin

power of the shaded cell is very small (Fig. 2.17d). Under the condition that the number of t

shaded cells is significantly less than that of the unshaded cells, the P-V characteristics of the P

array is very close to the unshaded condition no matter how the shaded cells are distributed in th

PV array (Fig. 2.17b). Therefore, with a bypass diode for each PV cell, it is more convenient

manage the MPPT control of the PV array even under shading conditions, implying that a ne

solar PV cell design with a bypass diode would be a significant benefit for extraction an

management of solar PV energy.


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0 100 200 300 400 5000

20

40

60

Vs (V)

C u r r e n t

( A )

None50%100%

a) PV array I-V characteristics

0 100 200 300 400 5000

5

10

15

20

Vs (V)

P o w e r

( k W )

None50%100%

b) PV array P-V characteristics

0 100 200 300 400 500-40

-30

-20

-10

0

10

Vs (V)

V o l

t a g e

( V )

None50%100%


characteristics of the last string

0 100 200 300 400 500-300

-200

-100

0

100

Vs (V)

P o w e r

( W )

None50%100%

d) Shaded cell P-V

characteristics of last string

Fig. 2.15. PV array

characteristics

(without bypass diode)

0 100 200 300 400 5000

20

40

60

Vs (V)

C u r r e n t

( A )

None50%100%


0 100 200 300 400 5000

5

10

15

20

Vs (V)

P o w e r

( k W )

None50%100%


0 100 200 300 400 500-30

-20

-10

0

10

Vs (V)

V o l

t a g e

( V )

None50%100%



0 100 200 300 400 500-150

-100

-50

0

50

Vs (V)

P o w e r

( W )

None50%100%

d) Shaded cell P-V


Fig. 2.16. PV array

characteristics

(one module with a diode)

0 100 200 300 400 5000

20

40

60

Vs (V)

C u r r e n t

( A )

None50%100%


0 100 200 300 400 5000

5

10

15

20

Vs (V)

P o w e r

( k W )

None50%100%


0 100 200 300 400 500

-0.5

0

0.5

Vs (V)

V o l

t a g e

( V )

None50%100%



0 100 200 300 400 500-4

-2

0

2

4

Vs (V)

P o w e r

( W )

None50%100%

d) Shaded cell P-V


Fig. 2.17. PV array

characteristics

(each cell with a bypass diode)

2.5 Virtual Transient Experiment


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The behavior of the solar PV system is further examined under more realistic transien

conditions through a virtual experiment by using MatLab SimPowerSystens, which includes:

actual circuit connection of the solar PV array, 2) open-loop controlled power converte

including inductors and capacitors, and 3) losses of the system. Figure 2.18 shows the transie

simulation system. The dc voltage source stands for the dc-link voltage between the dc/d

converter and the dc/ac inverter (Fig. 2.14). The dc/dc converter is a boost converter, i.e., pow

flows from the PV array to the dc voltage source. The PV array is represented by a subsyste

containing all the PV modules in series and parallel. At each time instant, the Newton-Raphso

algorithm is used to find the current and voltage of each solar cell. The parameters of the solPV system are the same as those used in the characteristic study (Figs. 2.15-17). The number

series and parallel PV modules are 20 and 10, respectively. Major measurements include curren

voltage and power of PV cells, modules, and array under test. For power measurement, generat

sign convention is used, i.e., power generated by a PV cell, module, or array to the dc source

positive.

Fig. 2.18. Solar PV generator under an open-loop controlled dc/dc

power converter using SimPowerSystems


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0 1 2 3 4 5 6 7 80

100

200

300

400

500

600

Time(s)

V o l

t a g e

( V )

0 1 2 3 4 5 6 7 8

0

2

4

6

8

P o w e r

( k W )

Voltage

Power

a) PV array terminal voltage and power

0 1 2 3 4 5 6 7 8-30

-25

-20

-15

-10

-5

0

Time(s)

V o l

t a g e

( V )

0 1 2 3 4 5 6 7 8

-150

-125

-100

-75

-50

-25

0

P o w e r

( W )

Voltage

Power

b) Shaded cell terminal voltage and power of the

last string

Fig. 2.19. Transient simulation results of a PV array relevant to

the 100% shading condition applied in Fig. 2.16

In Fig. 2.18, the average power converter model [41] is used, in which the duty ratio is

ramp function of time, which causes the voltage applied to the PV array increases with the tim

until the full dc source voltage is reached. Figure 2.19 shows the transient results correspondi

to the 100% shading condition used in Fig. 2.16. The dc source voltage is 500V. As it can b

seen from Fig. 2.19a, the voltage applied to the PV array increases with time. The output powof the PV array increase, reaches maximum output power, and then decreases, a phenomeno

similar to Fig. 2.16b. The terminal voltage of the shaded cell is around -20V before the bypa

diode turns on (Fig. 2.19b) and the absorbing power of the shaded cell is about 120W (Fi

2.19b), which is consistent with the steady-state characteristics shown in Fig. 2.16d. Under th

uneven shading condition and a bypass diode for each PV module, the output power of the P

array also shows the multiple peaks (Fig. 2.19a) in the transient environment, which is consiste

with Fig. 2.16b. For all the other conditions, the results obtained through the transient simulatio

experiment agree with stead-state characteristic results, demonstrating that the models an


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Newton-Raphson algorithm are suitable for transient analysis of power converter controlled so

PV systems.

2.6 Conclusions

This chapter investigates IV and PV characteristics of solar PV cells, modules an

arrays and it focuses specifically on IV and PV characteristics of a solar PV system operate

under uneven shading and dissimilar conditions.

Under uneven shading conditions, the charge carriers of the unshaded cells have to g

through parallel resistors of the shaded cells. To push the current through the parallel resistor, th

accumulated photogenerated voltage of each unshaded cell must be high. The net photogenerat

voltage of all the unshaded cells causes: (1) a high current through the parallel resistors of th

shaded cells, (2) a high-reverse terminal voltage on each shaded cell, and (3) a high absorbin

power by each shaded cell, especially when the voltage applied to the PV cells is low. Thus, th

unshaded cells generate power, while the shaded cells absorb power, depending on the externvoltage applied to PV cells or modules.

Using bypass diodes, the voltage applied to the shaded cells equals the photogenerate

voltages of the unshaded cells within the bypass diode group plus the bypass diode forwar

conduction voltage. Thus, the less the PV cells within a bypass diode group, the smaller th

reverse voltage over shaded cells, and the less the shaded cells absorb power. To prevent shad

cells from becoming hot spots, the number of series PV cell within a bypassing diode grou

should be properly designed.

For a solar PV array, if no bypass diodes are applied, the PV array characteristics can b

shifted considerably by shaded cells depending on how many strings contain shaded cells an


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how many shaded cells are in each string. If there is only one shaded cell in a string, the shad

cell would be in the worst condition due to its high absorbing power. If each PV module has on

bypass diode, the improvement of the PV array characteristics depends on the distribution of t

shaded cells in the PV array. The best situation is that all the shaded cells appear in one modul

However, if the shaded cells are distributed evenly in different modules in a string, th

enhancement of the PV array characteristics is trivial. If each PV cell has a bypass diode, th

influence of the shaded cells on the PV array characteristics is significantly reduced in vario

aspects no matter how the shaded cells are distributed in the PV array, implying that a new sol

PV cell design with a bypass diode would be a significant benefit for energy extraction anmanagement of solar PV energy (Chapter 4).

The models developed in this chapter as well as the NewtonRaphson algorithm

applications are suitable for transient analysis of power converter-controlled solar PV system

making it possible to develop and test advanced MPPT control strategies for solar PV system

under shading conditions through virtual computer experiments.


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CHAPTER 3

A FAST AND RELIABLE APPROACH FOR MAXIMUM POWER POINT TRACKING

PV generation systems have two major problems: the conversion efficiency of electri

power generation is very low (9-17%) [42], especially under low irradiation conditions; th

amount of electric power generated by solar arrays changes continuously with weathe

conditions. The power delivered by a PV system of one or more photovoltaic cells is depende

on the irradiance, temperature, and the current drawn from the cells. In general, there is a uniq

point on the I-V and P-V curve, called the maximum power point (MPP), at which the entire P

system operates with maximum efficiency and produces its maximum output power. Th

location of the MPP is not known, but can be located, either through calculation models or b

searching algorithms. To maximize the

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