solar photovoltaic energy generation and conversion … · 2016-11-03 · solar photovoltaic energy...

SOLAR PHOTOVOLTAIC ENERGY GENERATION AND CONVERSION

—FROM DEVICES TO GRID INTEGRATION

by

HUIYING ZHENG

SHUHUI LI, COMMITTEE CHAIR

TIM A. HASKEW JABER ABU QAHOUQ

DAWEN LI MIN SUN

A DISSERTATION

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy

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

The University of Alabama

TUSCALOOSA, ALABAMA

2013

ii

ABSTRACT

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

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

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

First of all, this dissertation focuses on I–V and P–V characteristics of PV modules and

arrays, especially under uneven shading conditions, and considers both the physics and electrical

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

different bypass diode arrangements could affect maximum power extraction characteristics of a

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

flexibility to distribution system operators. The objective of the control of this hybrid PV and

energy storage system is to supply the desired active and reactive power to the grid and at the

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

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

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

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

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

Index Terms – solar photovoltaic, semiconductor physics, I–V characteristics, P–V

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

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

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

iv

DEDICATION

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

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

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

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

v

LIST OF ABBREVIATIONS AND SYMBOLS

ID Diffusion current

IS Drift current

IL Photogenerated current

Rp Parallel resistance accounting for current leakage through the solar cell

Rs Series resistance which causes an extra voltage drop between the junction voltage and the terminal voltage of the solar cell

I0 Diode reverse saturation current

m Diode ideality factor

q Elementary charge

T Absolute temperature

k Boltzmann's constant

Ic Output current of a solar device

Ps Shading factor that the shaded cell is relevant to the unshaded cell

Vd P-n junction diode voltages

Vc Output voltage of a solar device

Pc Generated power of a solar device

DN Net doping concentration in n-type region

AN Net doping concentration in p-type region

K Approximate constant with respect to temperature

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Eg Band-gap energy of the semiconductor (eV)

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

IMPP Current at the maximum power point

ISC Short-circuit current of a PV array

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

VMPP Voltage at the maximum power point

VOC Open-circuit voltage of a PV array

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

a aI V Instant conductance

a aI V Incremental conductance

tanh() Hyperbolic function

SOC State of charge of battery

ib_ref Battery reference current

isc_ref Supercapacitor reference current

Vdc_ref Dc-link capacitor reference voltage

psto_ref Storage units reference power

pdc_ref Dc-link capacitor reference power

pg_ref Grid reference power

ppv PV system generated power

pf Power losses in grid filter

id Grid d-axis current

iq Grid q-axis current

Rf Resistance of grid filter

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XR Peak value of sinusoidal waveform

XI Corresponding imaginary orthogonal of XR

φ Initial phase

ω 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 of

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

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

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

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

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

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 Abu

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

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

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 a

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

Inc., Vance, Alabama.

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

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

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

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

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

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

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

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 provide.

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 OF SOLAR 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 Shading Conditions.............................................................................................................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 MAXIMUM POWER 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 STUDY UNDER SHADING CONDITIONS FOR DIFFERENT CONVERTER CONFIGURATIONS ...........................................................................................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 INTEGRATION OF PV ARRAY, BATTERY STORAGE, AND SUPERCAPACITOR WITH RELATED 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 for different 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 rate control 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 ...........................................................11

2.5. 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 IMPP over ISC and VMPP over VOC ....................................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 and Opal-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 irradiation levels .............................................................................................................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....................................................................61

4.1. 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 using SPS and Oparl-RT RT-LAB .........................................................................97

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

xviii

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 a dc/dc power converter using SPS and Opal-RT RT-LAB .........................105

5.16. Simulation result of the proposed method applications in single-phase inverter .......................................................................................................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

xix

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

1

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 and

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

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

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

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

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

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

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

effective use of advanced control techniques. In all, safe and effective integration of PV system

cannot be achieved without extensive use of control technologies at all levels.

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

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

shading of the branch of a leafless tree. If enough cells are hard shaded, a module will not

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

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

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

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

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

2

of the PV generators together and by investigating characteristic evaluation of unshaded cells,

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

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

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

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

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

characteristics and performance of shaded cells, unshaded cells, and a PV module. Section 2.4

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

study of a PV array under an open-loop control condition through power electronic converters.

Finally, Section 2.6 concludes with the summary of main points.

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

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

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

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

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

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

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

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

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

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

maximum power point tracking of a solar PV array include: 1) how to get to a MPP quickly, 2)

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

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

3

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

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

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

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

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

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

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

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

proportional–integral (PI) based adaptive MPPT approach for fast and reliable tracking of PV

array maximum power. Section 3.4 gives performance evaluation of the conventional and

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

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

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

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 analyze

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

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

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 the

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

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

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

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

4

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

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

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

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

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

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

system in Section 4.1 and typical PV power converter architectures in Section 4.2 respectively.

PV array models for different converter configurations are discussed in Section 4.3.Section 4.4

and 4.5 investigate PV system energy extraction characteristics with and without bypass diodes,

respectively, for different converter schemes. Finally, Section 4.6 concludes with the summary of

main points.

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

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

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

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

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

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

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

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

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

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

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

where the voltage remains relatively even over most of the battery’s remaining charge levels, a

5

SC’s voltage scales linearly with the remaining energy. This means additional circuitry is

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

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

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

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

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

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

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

coordinated control of PV array and ESU integration with the grid. Other applications including

single-phase DQ control and ramp rate limit control are illustrated in Section5.5. Finally, chapter

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 and

conversion from devices to gird integration.

6

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 of

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

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 materials,

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 solar

cell.

2.1.1 Silicon Solar Cell

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

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

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

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

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

7

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

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

forms a diffusion current ID 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 carriers

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

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

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

current IS, that opposes and eventually balances out the diffusion current ID. The region where

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

(a) Diffusion current ID from the p side to the n side

(b) Drift current IS 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

8

2.1.2 Photogenerated Current and Voltage

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

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

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

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

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

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

accumulates holes and the n-side accumulates electrons (Fig. 2.2), which creates a voltage that

can be used to deliver the photogenerated current to a load. At the same time, the voltage built up

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

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

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

photogenerated voltage eventually causes the diffusion current ID balancing out the drift current

IS 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

9

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 in

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

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

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

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

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

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

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

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

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

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 electrically

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

representing the photogenerated current IL, 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 model.

10

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

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

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

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

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

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

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

the same flow of current.

The mathematical model of a solar cell is described by

0 1 ,

dqVdmkT

c L c d c sp

VI I I e V V I R

R (2.1)

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

an ideal diode), the diode reverse saturation current I0 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, IL=6A, I0=6⋅10-6A, RP=6.6Ω, RS=0.005Ω, and T=25 ,

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

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

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

output current Ic and power Pc versus output voltage Vc characteristics. Figure 2.4 shows typical

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

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

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

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

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

11

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

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 = 25C, I0 = 6 10-10A, IL = 6A, Rp =6.6 and Rs = 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 same

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

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

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

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 are

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

12

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

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

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

IL1

Rp1

Rs1

Vs

IL2

Rp2

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 full

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

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

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

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

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

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

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

the shaded cell until an equilibrium state is reached.

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

the series PV cells under the shading condition is described by

13

1

10 1 11 ,

dqV

dmkTc L c d c s

p

VI I I e V V I R

R (2.2)

2

20 2 2(1 ) 1 ,

dqVdmkT

c s L c d c sp

VI p I I e V V I R

R

(2.3)

1 2 s c cV V V (2.4)

where ps stands for the shading factor that the shaded cell is relevant to the unshaded cell, and IL

represents the photogenerated current of unshaded cell under the full sun condition, Vd1 and Vd2

and Vc1 and Vc2 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 be

developed as

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

Then, for a given voltage applied to the PV cells, voltage Vd1 and Vd2 can be solved

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

a) Initial estimation:

0 01 2,0

dV d dV V (2.6)

b) Compute Jacobian matrix:

1 1 1 2

2 1 2 2

k kd dk k

d d

f V f V

f V f V

J (2.7)

c) Compute correction kdV and update PV cell voltage 1k

dV :

1k k kd d d V V V (2.8)

d) Error calculation:

2 21 11 2

d dV Vk kerr f f (2.9)

14

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 series

PV cells can be obtained through either simulation of Fig. 2.5 or the numerical computation

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

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

15

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

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 rest

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

which changes the solar cell electrical properties by varying the values of I0 and IL slightly.

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

to calculate. Therefore, the temperature change caused by the power dissipation of a shadowed

cell is not considered here. According to Fig. 2.6 as well as other results, the following remarks

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, the

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 current

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

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

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

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

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-excited

16

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

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

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

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

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

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

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

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 is

influenced by the applied external voltage. The higher the external voltage, the less the current is

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

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

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

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

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

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

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 dc

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

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

17

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

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 cell

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

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

described by:

0(1 ) 1 ,

diqV

dimkTc i L ci di c s

p

VI p I I e V V I R

R

(2.10)

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

where pi stands for the shading factor of the ith cell relevant to the full sun condition, IL

represents the full sun photogenerated current, and Vdi and Vci 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 dNf V V f V V (2.12)

Then, for a given voltage applied to a PV module, voltage Vd1, Vd2, … VdN can be solved

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

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

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

(4) until a stop criterion is reached [27]. After the completion of the iteration, solutions of Vd1,

Vd2, … VdN for all PV cells are available for both shaded and unshaded cells. It is necessary to

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 common

18

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

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

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

Bishop’s numerical program based on an equivalent PVNet is another approach that was

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

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 PV

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

other cells are in full sun.

19

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 the

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

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

in series. But, this situation is completely different even when only one cell is shaded (Fig. 2.8a

and 2.8b). Due to the shading of one cell, part of charge carriers of the unshaded cells must go

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

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

20

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

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

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

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

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

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

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)

21

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

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 voltage

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

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

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

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

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, parameters

associated with a PV cell, such as Rp and Rs, must be identified first. These can be obtained

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

is not a focus of this paper. It is assumed that parameters of PV cells are available [31, 32]. Thus,

the model validation focuses mainly on whether accurate current, voltage and power relations for

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

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

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

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

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

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

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

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

22

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

PSpice-based simulation includes: 1) drawing circuit schematics, as illustrated by Figs. 2.3, 2.5

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

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

diode, and one ideal current source. For a PV module containing 36 cells, there would be 144

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 the

PSpice-based simulation, each circuit component of a PV cell is treated as a different simulation

element. Therefore, solar PV system simulation using NI Multisim is extremely expensive in

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 conditions

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

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

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

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

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

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

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 are

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

23

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

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

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 be

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

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 current

and voltage relations of the PV cells connected with the ith bypass diode and overall system

current and voltage are described by

0(1 ) 1 dijqV mkT

ci ij L dij pI 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 pdMI I I e V V V V V

(2.15)

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

the ith bypass diode group, Vdij and Vcij represent p-n junction diode voltage and PV cell output

voltages of the jth PV cell within the ith bypass diode group, Ici is the output current of the series

PV cells within the ith bypass diode group, and Vpdi represents the voltage applied to the ith

bypass diode.

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

Vd1 to VdN can be solved numerically by using Newton-Raphson algorithm for a given external

24

voltage Vs applied to the PV module. If some of the PV cells within the PV module operate at the

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 the

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

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

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 by

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

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

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

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

25

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


module


d) Shaded cell P-V

characteristics

Fig. 2.12. Characteristics of

a PV module



module


module


d) Shaded cell P-V

characteristics

Fig. 2.13. Characteristics of

a PV module


26

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

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

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

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

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

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

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 that

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

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

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 of

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

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 approach

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

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

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

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

27

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

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

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

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

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 different

depending on how many cells in a string are shaded and how much the shading factors are. For

each string, the mathematical procedure to obtain P-V and I-V characteristics is very similar to

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

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

28

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

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

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

cells into one mathematical equation could significantly accelerate the numerical computation

speed.

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

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

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

strings with each string containing 20 modules. Assume there are 19 shaded modules in the 1st

string, 17 in the 2nd string, 15 in the 3rd string … and 1 in the last string. In each shaded module,

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

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

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

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 how

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

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

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

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

cell (Fig. 2.15d).

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

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

29

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

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

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 module,

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

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

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 characteristics

of the PV array. The extent of the multiple peaks depends on the distribution of the shaded cells

in the PV array as well as the number of parallel strings and the number of series modules in

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

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

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 array

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

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

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

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

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

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

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

management of solar PV energy.

30

0 100 200 300 400 5000

20

40

60

Vs (V)

Cur

rent

(A

)

None

50%100%

a) PV array I-V characteristics

0 100 200 300 400 5000

5

10

15

20

Vs (V)

Pow

er (

kW)

None

50%100%

b) PV array P-V characteristics

0 100 200 300 400 500-40

-30

-20

-10

0

10

Vs (V)

Vol

tage

(V

)

None

50%100%


characteristics of the last string

0 100 200 300 400 500-300

-200

-100

0

100

Vs (V)

Pow

er (

W)

None

50%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)

Cur

rent

(A

)

None

50%100%


0 100 200 300 400 5000

5

10

15

20

Vs (V)

Pow

er (

kW)

None

50%100%


0 100 200 300 400 500-30

-20

-10

0

10

Vs (V)

Vol

tage

(V

)

None

50%100%



0 100 200 300 400 500-150

-100

-50

0

50

Vs (V)

Pow

er (

W)

None

50%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)

Cur

rent

(A

)

None

50%100%


0 100 200 300 400 5000

5

10

15

20

Vs (V)

Pow

er (

kW)

None

50%100%


0 100 200 300 400 500

-0.5

0

0.5

Vs (V)

Vol

tage

(V

)

None

50%100%



0 100 200 300 400 500-4

-2

0

2

4

Vs (V)

Pow

er (

W)

None

50%100%

d) Shaded cell P-V


Fig. 2.17. PV array

characteristics

(each cell with a bypass diode)

2.5 Virtual Transient Experiment

31

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

conditions through a virtual experiment by using MatLab SimPowerSystens, which includes: 1)

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

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

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

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

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

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

algorithm is used to find the current and voltage of each solar cell. The parameters of the solar

PV system are the same as those used in the characteristic study (Figs. 2.15-17). The number of

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

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

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

positive.

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

power converter using SimPowerSystems

32

0 1 2 3 4 5 6 7 80

100

200

300

400

500

600

Time(s)

Vol

tage

(V

)

0 1 2 3 4 5 6 7 80

2

4

6

8

Pow

er (

kW)

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)

Vol

tage

(V

)

0 1 2 3 4 5 6 7 8-150

-125

-100

-75

-50

-25

0

Pow

er (

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 a

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

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

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

seen from Fig. 2.19a, the voltage applied to the PV array increases with time. The output power

of the PV array increase, reaches maximum output power, and then decreases, a phenomenon

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

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

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

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

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

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

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

33

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

PV systems.

2.6 Conclusions

This chapter investigates I–V and P–V characteristics of solar PV cells, modules and

arrays and it focuses specifically on I–V and P–V characteristics of a solar PV system operated

under uneven shading and dissimilar conditions.

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

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

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

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

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

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

unshaded cells generate power, while the shaded cells absorb power, depending on the external

voltage applied to PV cells or modules.

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

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

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

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

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

should be properly designed.

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

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

34

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

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

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

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

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

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

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

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

PV cell design with a bypass diode would be a significant benefit for energy extraction and

management of solar PV energy (Chapter 4).

The models developed in this chapter as well as the Newton–Raphson algorithm

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

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

under shading conditions through virtual computer experiments.

35

CHAPTER 3

A FAST AND RELIABLE APPROACH FOR MAXIMUM POWER POINT TRACKING

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

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

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

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

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

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

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

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

searching algorithms. To maximize the output power of a PV system, continuously tracking the

maximum power point of the system is necessary.

There are many different approaches to maximizing the power from a PV system. These

range from using simple voltage relationships, to more intelligent and adaptive based algorithms.

Typical MPPT techniques that have been proposed in the literature include the Short-Circuit

Current method [43], Open-Circuit Voltage method[44], Perturb and Observe (P&O) methods

[45, 46], Incremental Conductance (IC) methods [47, 48, 49], and Adaptive P&O method [50,

51], and Intelligent and Fuzzy Logic methods [52, 53]. These techniques vary between each

other in many aspects, including simplicity, convergence speed, system stability, and MPP

tracking effectiveness. The primary challenges for maximum power point tracking of a solar PV

array include: 1) how to get to a MPP quickly, 2) how to stabilize at a MPP, and 3) how to

36

smoothly transition from one MPP to another for sharply changing weather conditions. In

general, a fast and reliable MPPT is critical for power generation from a solar PV system.

3.1 Extracted Power Characteristics of a PV System

A grid-connected solar PV system consists of three parts (Fig. 3.1): an array of solar

cells, power electronic converters, and an integrated control system [44, 45]. The control system

of a solar PV array contains two parts: one for MPPT and the other for grid interface control [49-

52]. Both control functions are achieved through power electronic converters. In general, the

dc/dc converter implements the MPPT function while the dc/ac converter performs the grid-

interface control.

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

The power extracted from a PV array Pa is determined by the terminal voltage Va and

output current Ia of the array. The terminal voltage Va depends on the control of the dc/dc

converter while the output current Ia depends on temperature, irradiation level, and the PV array

37

terminal voltage. During a day, solar irradiation and temperature fluctuates over time [54] (Fig.

3.2), causing the MPP of the PV array changes continuously. Consequently, the PV system

operating point must be adjusted constantly to maximize the energy produced.

0 4 8 12 16 20 2450

60

70

80

90

Tem

pera

ture

(F

)

Time (Hour)

0 4 8 12 16 20 240

200

400

600

800

1000

Sol

ar Ir

radi

atio

n(W

/m2)

Temp

Irra

Fig. 3.2. Typical daily temperature and irradiation plots [54]

3.1.1 The Effect of Temperature

Temperature affects solar cell characteristics primarily in the following two ways:

directly via T in the exponential term in (3.1) and indirectly via its effect on the reverse-diode

saturation current I0 and the photo-generated current IL. The dependence of the reverse-diode

saturation current I0 on temperature for a silicon solar cell is:

3

0

gq E

m k TI K T e

(3.1)

where K is the approximate constant with respect to temperature, Eg is the band-gap energy of

the semiconductor (eV), m is the diode ideality constant, k is Boltzmann constant, and T (K) is

the temperature of the p–n junction. The photo-generated current IL is also influenced by the

temperature too as the following:

38

,( )L L n In

EI I K T

E (3.2)

where IL,n is the photo-generated current at the nominal condition, ΔT is the difference between

actual temperature T and nominal temperature Tn (25C), respectively, E is the irradiation on the

device surface (W/m2), and En is the nominal irradiation (1000 W/m2).

0 100 200 300 400 500 600 700025

5075

100

0

5

10

15

20

25

Vs (V)T ( oC)

P(k

W)

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

(Nc=36, Ns=30, Np=10, Rp=6.6and Rs=0.005)

0 100 200 300 400 500 600 700-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

Vs (V)

dP/d

V (

kW/V

)

T=0T=20

T=40

T=60

T=80T=100

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

Then, based on (3.1) and (3.2), characteristics of a PV array versus the PV cell

temperature and the terminal voltage of the array can be obtained as shown by Fig.3.3.

39

According to Fig. 3.3, as the temperature increases, the maximum power production of the PV

array drops greatly and the MPP voltage reduces, indicating that PV arrays perform better on

cold days than hot ones. Figure 3.4 shows the derivative of the output power versus PV array

terminal voltage for several constant temperatures. For each constant temperature, the voltage

corresponding to the zero derivative represents the required voltage for MPP. The derivative has

a stable positive value before reaching the MPP, and then drops sharply around the MPP. As

temperature increases, the zero derivative point shifts to the left.

3.1.2 The Effect of Illumination Intensity

The photo-generated current is affected by the irradiance intensity. First, without

consideration of temperature impact by the irradiance levels, the short-circuit current of a solar

cell is directly proportional to the irradiance intensity over a wide operating range. Assume that S

stands for the ratio of the present solar irradiation over the nominal irradiation of 1000W/m2 and

the short-circuit current of the solar cell at 1000W/m2 is defined by IL1. Then, the short-circuit

current under S is IL = SIL1. Second, the impact of irradiation to the temperature of solar cells is

determined by:

n nT T E E (3.3)

where is a constant value between a range of 25-35.

Figure 3.5 shows the characteristics of the PV array as the irradiance intensity changes

from 0W/m2 to 1000W/m2. It can be seen from Fig. 3.5 that there is a peak power production

corresponding to each solar irradiation. As the irradiance level increases, the maximum power

increases greatly and the MPP voltage drops slightly due to the temperature rise according to

40

(3.3). Figure 3.6 shows the derivative of PV array power versus terminal voltage of the PV array

for several constant irradiation levels. Compared to Fig. 3.4, as the irradiation level changes, the

shift of the terminal voltage corresponding to zero derivatives is much smaller.

0100200300400500600700

00.25

0.50.75

1

05

10152025

SVs (V)

P (

kW)

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

0 100 200 300 400 500 600 700-0.04

-0.02

0

0.02

0.04

0.06

0.08

Vs (V)

dP/d

V (

kW/V

)

s=0.2

s=0.4

s=0.6s=0.8

s=1

Fig.3.6. Derivative of power over terminal voltage under different irradiation

3.2 Conventional Fixed-step MPPT Methods

There have been reported many traditional MPPT methods for solar PV generators. In

general, the MPPT control is achieved by varying the terminal voltage applied to the PV

generator. Typical MPPT techniques include fixed-step MPPT: Short-Circuit Current method

41

[43], Open-Circuit Voltage method[44], Perturb and Observe (P&O) methods [45, 46],

Incremental Conductance (IC) methods [47, 48, 49].

3.2.1 Short-Circuit Current Method

The SCC method is based on the observation that IMPP is about linearly proportional to

ISC of a PV array (Fig. 3.7a) , i.e.,

( ) ( )MPP SC SCI S k I S (3.4)

where kSC is a constant. According to (3.4), the SCC controller (Fig. 3.8a) generates a control

signal to the dc/dc converter based on the error signal between the actual current of the PV array

Ia and the IMPP calculated from (3.4).

0 10 20 30 40 50 60 700

20

40

60

ISC

(A)

I MPP

(A)

a) Graphic relation of IMPP over ISC

300 350 400 450 500 550 600 650 700200

300

400

500

600

VOC

(V)

VM

PP (

V)

b) Graphic relation of VMPP over VOC

Fig. 3.7. Graphic relation of IMPP over ISC and VMPP over VOC

42

This method requires measurements of ISC. Therefore, a static switch in parallel with the PV

array is needed in order to create the short-circuit condition for each solar irradiation level

change, which could cause a large oscillation of PV array output power. Another disadvantage is

that the computation of IMPP is very sensitive to kSC, and the relation between IMPP and ISC is not

100% linear. Thus, a small deviation of IMPP, calculated by (3.4), can easily reduce the output

power of the PV array greatly.

*MPPI

d

ai

SCI SCk

a) Control scheme of SCC

*MPPV

d

av

OCV OCk

b) Control scheme of OCV

Fig. 3.8. Conventional MPPT methods of SCC and OCV

3.2.2 Open-Circuit Voltage Method

The OCV method is based on the observation that VMPP is about linearly proportional to

VOC of a PV array (Fig. 3.7b), i.e.,

( ) ( ) MPP OC OCV S k V S (3.5)

43

where kOC is a constant. Based on (3.5), a close-loop control scheme is developed to bring the PV

array voltage to VMPP calculated from (3.5) (Fig. 3.8b). Similar to the SCC method, the OCV

method requires measurements of VOC. Thus, a static switch in series with the PV array is

necessary in order to create the open-circuit state for each weather condition change, which

would also cause a large oscillation of PV array output power. In addition, since VOC varies with

temperature and other factors and the relation of VMPP and VOC is affected by shading, actual

VMPP for a practical PV application is difficult to get.

3.2.3 Perturb & Observe Method

The P&O method is the most commonly used MPPT technique for PV arrays. It operates

by periodically perturbing the array terminal voltage or current and comparing the PV output

power with that of the previous perturbation cycle.

In general, if an increased perturbation of PV array operating voltage causes an increase

of output power, the control system moves the operating point in the same direction; otherwise

the perturbation is changed to the opposite direction. The process continues until the MPP is

reached [55-57]. There are many different P&O methods available in the literature. In the classic

P&O technique [41] (Fig. 3.9), the perturbations of the array operating point have a fixed

magnitude. In the optimized P&O technique [55, 56], an average of several samples of the array

power is used to adjust the perturbation magnitude.

44

( ) & ( )a aV k I k ( ) & ( )a aV k I k( 1) & ( 1)a aV k I k

refVrefV refV refV

0?aP

( ) ( ) ( )

( 1) ( 1) ( 1)

( ) ( 1)

( ) ( 1)

a a a

a a a

a a a

a a a

P k V k I k

P k V k I k

P P k P k

V V k V k

0?aV 0?aV

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

3.2.4 Incremental Conductance Method

The IC method is based on the principle that ideally the following equation holds at the

MPP [47, 51]:

0a a a aI V I V (3.6)

Also, when the operating point in the P-V plane is to the right of the MPP,

0 ;a a a aI V I V when the operating point is to the left of the MPP, 0.a a a aI V I V Thus,

the direction in which the MPP operating point must be perturbed can be determined by

comparing the instant conductance a aI V to the incremental conductance .a aI V Using the IC

45

method (Fig. 3.10), it is theoretically possible to know when the MPP is reached and when the

perturbation should be stopped.

( ) & ( )a aV k I k ( ) & ( )a aV k I k( 1) & ( 1)a aV k I k

refVrefV

0?aI

0?aI

refV refV

0?aV

aI

( ) ( 1)

( ) ( 1)a a a

a a a

I I k I k

V V k V k

/ ?a a aV I V

aI / ?a a aV I V

Fig.3.10. Flowchart of the incremental conductance algorithm

3.3 Adaptive MPPT Strategies

In a PV system, the maximum power point tracking speed and tracking accuracy are the

key factors for a MPPT control algorithm. These factors directly relate to the duty ratio

adjustment of the dc/dc converter. When the PV system operating point is away from the MPP,

the tracking speed must be accelerated, i.e., the regulation of the duty ratio should be large.

When the operating point is around the MPP, the regulation of the duty ratio must be small to

46

avoid system oscillation. However, conventional fixed-step MPPT algorithms as shown by

Section 3.2 are unable to meet those MPPT requirements [58, 59], resulting in many

disadvantages such as instability, oscillations near MPP, poor adaptability to the external

environment, and low system robustness. Thus, adaptive MPPT approaches have been proposed

recently, including M-factor adaptive-step MPPT, fuzzy logic based MPPT [52, 53], neural

networks MPPT [60, 61] and ripple correlation control (RCC) MPPT [62, 63], etc. However,

some of them may still be inappropriate in respective of suppleness in applications and accuracy

at different occasions. For example, RCC lacks the mathematical foundation and careful stability

analysis that is attractive for control design. RCC is limited to first-order high-pass filters, which

approximate the derivative at low frequencies [63].

The proposed method is developed based on observations obtained from Figs. 3.4 and

3.6: 1) on the left side of the MPP, a adP dV is positive; 2) On the right side of the MPP, a adP dV

is negative; 3) Around the MPP, the | a adP dV | drops sharply so that the adjustment of the duty

ratio of the dc/dc converter should be small; 4) At the MPP, a adP dV =0 and therefore the duty

ratio should remain unchanged.

3.3.1 Traditional Adaptive MPPT Methods

In conventional adaptive MPPT methods, the perturbation value changes during the hill

climbing process [50, 55]. Typical adaptive P&O methods use power derivative information to

determine the next perturbation operation. It is based on the observation that the derivative is

positive on the left side of the MPP, zero at the MPP, and negative on the right side of the MPP

(Fig. 3.4 and 3.6). Thus, a scaling factor (SF) perturbation strategy is developed as shown by

47

(3.7), in which M is a constant coefficient and the multiplication of M with the derivative

determines an adaptive adjustment of the duty ratio in the next perturbation cycle [55]. Hence,

the duty ratio adjustment is scalable rather than fixed. Similar to the IC method, the perturbation

stops theoretically when the MPP is reached.

( ) ( 1) a

a

dPd k d k M

dV (3.7)

Another conventional adaptive duty ratio strategy is based on a proportional-integral (PI)

control mechanism (Fig. 3.11). The error signal to the controller is generated by comparing

a adP dV with a zero power derivative reference value. The duty ratio of the dc/dc converter is

regulated continuously until the MPP is reached, i.e., 0.a adP dV

aV

aI D

0

a

a

dP

dV

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

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

The proposed adaptive MPPT strategy has adopted the advantage of the inner close-loop

control mechanism for the duty-ratio regulation. But, it introduces a hyperbolic function (3.8)

into the MPPT design.

48

tanh a ay k dP dV (3.8)

where k is a constant value which is tuned to meet a fast and reliable MPPT requirement for a

typical solar PV array. The output of the sigmoid function (Fig. 3.12) is close to 1 if |dPa /dVa| is

large while around a adP dV =0, the output reduces greatly. This hyperbolic function enables a

more accurate and stable, and much faster tracking properties under dynamic condition. The

control diagram of the proposed H-PI method is shown by Fig. 3.13, the measured voltage and

current are first processed through a low-pass filter. Then, the power over voltage derivative is

processed by a hyperbolic function and the adjustment amount of the duty-ratio is determined by

a PI controller. Finally, a new duty-ratio computed from this block is applied to the power

converter for the next control cycle.

-1 -0.5 0 0.5 1-1

-0.50

0.51

x

y=

tanh

(4*x

)

Fig.3.12. A tangent sigmoid function for adaptive MPPT

aV

aI tanh( )a

a

dPk

dV

D

0

a

a

dP

dV

Fig.3.13. Control loop diagram of proposed adaptive MPPT

49

One issue for the proposed MPPT is the computation associated with the tanh()

function. In general, the tanh() can be calculated very quickly in a digital control system.

According to a large number of experiments performed over a 2GHz PC, the average

computation time of tanh() in MatLab is about 10ns. Compared to the controller sampling time,

the computation time of tanh() is much smaller and ignorable. For tanh() implementation in a

DSP chip, the additional computational effort is even more insignificant.

3.4 Computational Experiment

To evaluate and compare different MPPT approaches, a computational experiment

platform of the integrated PV array and power converter system is developed. The experiment

system mainly includes three parts: a PV array module, a power converter module, and a control

module.

Fig.3.14. Solar PV generator with the MPPT and grid-integration using

SimPowerSystems (SPS) and Opal-RT RT-LAB

50

The PV array module has a series-parallel PV panel connection configuration. An

external bypass diode in parallel with each PV panel is also considered [23]. In addition,

blocking diodes are included at the top of each string [23]. The PV array module consists of 10

parallel strings with each string having 20 series panels. Each string of PV panels is represented

by a subsystem containing all the PV panels in series (Fig. 3.14). The mathematical model of a

PV panel is developed according to (2.1) and Fig. 2.3. Major measurements of the PV generator

include current and voltage of each PV panel, current and voltage of the PV array, and the output

power of the PV array. The generator sign convention is used, i.e., power transferred to the grid

is positive.

The power converter is a dc/dc boost converter. The dc voltage source shown in Fig. 3.14

represents the dc-link voltage (Fig. 3.1). For a fast and accurate simulation, the converter

modules from Opal-RT RTE-Drive toolbox are used. These converter modules can be integrated

with the RTE PWM signal generation function from the Opal-RT RT-EVENTS toolbox to

generate very fast and accurate drive pulses for a precise simulation of power converters [64].

The switching frequency is 10kHz, and losses of the power converters and the system are

considered.

cf

cf

Fig.3.15. MPPT digital control module

51

Modern MPPT algorithms are usually implemented by using the digital control

technology. The MPPT control module of this paper is developed with detailed consideration of

digital control system natures, including the sample and hold, digital signal processing, and time

delays (Fig. 3.15). The measured voltage and current signals first pass through sample and hold

blocks, which converts measured “continuous” signals to “discrete” signals. Then, a digital

filtering mechanism is applied to remove high frequency components caused by noises or rapid

switching of power converters. A time delay block is applied to account for potential delay

between digital and physical systems. The comparison in this section focuses mainly on IC fixed

step, traditional scaling factor (SF) adaptive, and the proposed hyperbolic-PI based (H-PI) MPPT

methods.

3.4.1 MPPT under Step and Ramp Changes of Solar Irradiation

The temperature during a day normally does not change sharply, but solar irradiation

levels could vary quickly from one value to another. To test and compare MPPT algorithms

under abrupt changes of solar irradiation levels, a solar irradiation curve with step and ramp

changes is generated (Fig. 3.16). The irradiation increases suddenly from 400W/m2 to 1000W/m2

at 1.5s, stays at 1000W/m2 between 1.5s to 2.2s, and drops to 600W/m2 at 2.2s. At 2.9s, there is a

ramp change of solar irradiation levels. The solar irradiance level increases gradually until it

reaches 900W/m2 at 3.2s, maintains at this value for a period of 0.6s, and drops slowly to

700W/m2 at 4s.

The PV array maximum power, along with the captured power by using IC, SF and H-PI

methods under the step and ramp changes of solar irradiation levels, is presented by Fig. 3.17a.

The sampling rate of the MPPT control module is 0.1ms.

52

1.5 2 2.5 3 3.5 4 4.50.4

0.6

0.8

1

Time (s)Ir

radi

atio

n (k

W/m

2)

Fig. 3.16. Step and ramp changes of irradiation

a) PV array output power b) Current & voltage of SF & H-PI MPPT

c) A zoomed in a) at a step change d) A zoomed in a) at an increasing slope

e) Changes of duty ratio f) P-V locus at the increasing slope

Fig. 3.17. Comparison of MPPT under step and ramp changes of solar irradiation levels

0 50 100 150 200 250 300 350 4000

4

8

12

16

Vs (V)

Ou

tpu

t Po

we

r(kW

)

IC

SF

S-PIPV curve (S=0.6)

PV curve (S=0.9)

Max Power Points

H‐PI

1.5 2 2.5 3 3.5 4 4.5-6

-4

-2

0

2

4x 10

-3

Time(s)

detD

IC SF S-PIH‐PI

3.14 3.16 3.18 3.2 3.22 3.2413.5

14

14.5

15

Time(s)

Out

put

Pow

er (

kW)

Max IC SF S-PIH‐PI

1.5 1.51 1.52 1.53 1.54 1.55 1.56

16

16.2

16.4

16.6

Time(s)

Out

put

Pow

er (

kW)


1.5 2 2.5 3 3.5 4 4.5260

280

300

320

340

Vo

ltag

e (

V)

1.5 2 2.5 3 3.5 4 4.530

40

50

60

Cur

rent

(A

)

1.5 2 2.5 3 3.5 4 4.5

50

Voltage (SF) Voltage (S-PI)

(H‐PI)

(H‐PI)

Time (s) 1.5 2 2.5 3 3.5 4 4.5

8

10

12

14

16

Time(s)

Out

put

Pow

er (

kW)


53

The current and voltage waveforms of the proposed MPPT are shown by Fig. 3.17b.

Figures 3.17c and 3.17d are the zoom-in plots of Fig. 3.17a. Figure 3.17e presents the duty-ratio

adjustment during the MPPT control. Figure 3.17f shows, for the three MPPT methods, the

power vs. voltage locus for a slope change of the solar irradiation level from 0.6kW/m2 to

0.9kW/m2 around 3sec (Fig. 3.16).

For the IC method, it is quite stable under sharp and gradient solar irradiation changes.

The primary issue of the IC method is a continuous perturbation in duty ratio (Fig. 3.17e) even

when the solar irradiance level is stable. The extent of the oscillation depends on the perturbation

step selected. The smaller the perturbation step, the smaller the oscillation. However, if the

perturbation step is too small, the MPPT speed would be affected.

For the SF method, there is a very small oscillation when the irradiation level remains at

a stable level, at which the power over the voltage derivative is close to zero (Fig. 3.17 e). But,

for changing irradiation levels, the output power of the PV array oscillates a lot as demonstrated

by time-domain waveforms (Figs. 3.17c and 3.17d) and the power vs. voltage locus plot (Fig.

3.17f). This results from a sharp change of around the MPP (Fig. 3.4 and 3.6), causing unstable

variation in duty ratio.

The proposed H-PI approach shows the best performance (Figs. 3.17a, 3.17c, 3.17d, and

3.17f). This is due to the fact that the duty ratio adjustment of the H-PI method is tuned based on

the power and voltage derivative that is preprocessed through a hyperbolic function as shown by

(3.8). As it can be seen in Fig. 3.17e, the change in duty ratio has a smoothly continuous value

during an abrupt or ramp change of solar irradiation, and is around zero when the solar

irradiation is stable.

54

1.5 2 2.5 3 3.5 4 4.51,150

1,175

1,200

1,225

1,250

Time(s)

DC

link

Vol

tage

(V

)

Fig. 3.18 Dc-link voltage

3.5 3.52 3.54 3.56 3.58 3.6-1,000

-500

0

500

1,000

Time(s)

Grid

-sid

e C

urre

nt (

A)

Fig. 3.19 Three-phase grid-side currents

1.5 2 2.5 3 3.5 4 4.5-50

-25

0

25

50

Time(s)

Grid

Pow

er (

kW)

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

The PV voltage and current oscillate continuously (Fig. 3.17b), particularly under

changing solar irradiation conditions. This causes more oscillation of the instantaneous power of

the PV array. This issue is critical and must be considered in the design of the low-pass filters

55

(Fig. 3.15) to assure fast and robust MPP tracking, particularly for the adaptive MPPT techniques

(Figs. 3.11 and 3.13). The power vs. voltage locus as shown by Fig. 3.17f illustrates more clearly

how the maximum power is tracked by using three different MPPTs approaches. As it can be

seen from the figure, the proposed adaptive MPPT is more reliable and efficient in tracking the

MPP than the conventional adaptive MPPT.

The dc-link voltage is very stable (Fig. 3.18) under the direct-current vector control

strategy applied to the dc/ac inverter, which is an important factor for the MPPT. The three-

phase current waveform on the grid side is shown by Fig. 3.19 and the instantaneous grid power

is shown by Fig. 3.20. As shown by Fig. 3.20, the grid power follows the captured PV power.

However, due to the existence of harmonics and unbalance in the grid three-phase currents, there

are oscillations in the grid power, which is similar to the instantaneous grid power in other

renewable energy applications [65, 66].

3.4.2 Sampling Rate Impact

When designing a digital control system, sampling rate is usually predefined. After that,

the perturbation rate for each MPPT technique should be designed independently until an

acceptable performance is obtained. Figure 3.21 shows the maximum power tracking by using

the three different MPPT techniques under the sampling rate of 1ms per sample and 10ms per

sample, respectively.

As shown by Fig. 3.21a, all the MPPT methods can track MPP when the sample time is

1ms. However, when the sample time is 10ms, there will be a big notch in the captured power by

IC and SF method (Fig. 3.21b). An examination of power vs. voltage locus (Fig. 3.21c) reveals

more detailed information about the MPP tracking using the three different MPPT approaches.

56

The figure, consistent with Fig. 3.17f, demonstrates that the proposed adaptive MPPT is more

reliable. Overall, the proposed method responds much faster and is more stable under different

irradiation conditions.

1.5 2 2.5 3 3.5 4 4.5

8

10

12

14

16

Time(s)

Out

put

Pow

er (

kW)

Max IC SF H-PI

a) 1ms per sample

1.5 2 2.5 3 3.5 4 4.5

8

10

12

14

16

Time(s)

Out

put

Pow

er (

kW)

Max IC SF H-PI

b) 10ms per sample

c) Power vs. voltage locus at the increasing slope change (10ms)

Fig. 3.21. MPPT comparison under different sampling rates

0 50 100 150 200 250 300 350 4000

4

8

12

16

Vs (V)

Ou

tpu

t Po

we

r(kW

)

IC

SF

S-PIPV curve (S=0.6)

PV curve (S=0.9)

Max Power Points

H‐PI

57

It is needed to point out that the sampling rate determines the waiting time for the next

perturbation. From this point of view, the sampling rate concept is not exactly equivalent to the

cutoff frequency notion normally used in the digital signal processing field. In a MPPT algorithm

for a PV array, the low-pass filters shown in Fig. 3.15 help to remove noises while the sampling

rate determines how fast to conduct the next perturbation. The impact of the sampling rate can be

seen from Fig. 3.21. In general, as the sampling time increases, it is slower to track the maximum

power.

3.4.3 MPPT under Variable Solar Irradiation Condition

In reality, solar irradiation level changes constantly over time [67]. Therefore, it is

important to evaluate and compare MPPT performance under variable irradiance conditions. For

this purpose, a variable solar irradiation curve is generated (Fig. 3.22a).

0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Time (s)

Irra

diat

ion

(kW

/m2)

a) Variable solar irradiation levels b) PV array maximum and output power

Fig.3. 22. MPPT comparison under variable solar irradiation condition

Figure 3.22b compares the MPP tracking using different MPPT algorithms and the

parameters of the MPPT algorithms are the same as those used in Fig. 3.17. As shown by the

0.5 1 1.5 2 2.50

5

10

15

20

Time(s)

Out

put

Pow

er (

kW)


58

figure, among the three algorithms, the proposed H-PI method is the most effective to track the

MPP. For the IC method, the fixed step perturbation disables the fast changing requirement in

duty ratio to track the MPP. For the SF method, a stable adaptive adjustment based on the

derivative information is hard to obtain in tracking the MPP under fast changing weather

conditions.

3.5 Hardware Experiment and Comparison

In this chapter, not only the software simulation but also the hardware experiment has

been applied for the comparison of different MPPT schemes.

3.5.1 Laboratory Setup and Design

A hardware laboratory test system of Fig. 3.14 is built for further investigation of the

conventional and proposed MPPT algorithms. Figure 3.23 shows the testing system with the

following setups. 1) An Agilent E4360A solar simulator is used to represent an actual PV array

[68]. The solar simulator can generate real output voltage and current with relation that is

equivalent to a practical PV panel or array. By using the solar simulator, it is possible to repeat

the same solar irradiation condition to test and compare different MPPT algorithms through this

hardware experiment which is otherwise impossible. Another advantage is that the maximum

output power of the simulated PV array can be calculated based on the experiment settings so

that one can determine whether a MPPT algorithm is effective or not in a hardware experiment.

Due to these reasons, solar simulators have been widely used by many researchers around the

world for evaluation of a PV control system [69]. 2) The dc/dc converter is built by using a

59

LabVolt MOSFET power converter. 3) The capacitor connected to the output terminal of the

simulator is formed by several LabVolt capacitors in parallel. 4) A smoothing inductor is

employed for the dc/dc converter. 5) The solar simulator is controlled by a dSPACE digital

control system [70].

The control system collects output voltage and current signals of the solar simulator, and

sends a control signal to the converter based on control demands generated by different MPPT

algorithms. Although the dSPACE system is not a digital device used for practical applications,

it is a digital control system based on modern DSP chips [71]. Using the dSPACE system, a

MPPT digital controller can be quickly built and tested before converting it to a practical digital

control device.

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

3.5.2 Experiment Analysis and Comparison

60

The rated values of the hardware experiment system (Fig.3.23), including the power

converter and the PV simulator, are different from those used in the computational experiment

(Fig.3.14). In general, the rating of the hardware experiment system is lower than the rating of a

practical PV array. Therefore, parameters of the MPPT controllers must be retuned. To ensure

that the controllers work properly, the retuned MPPT algorithms for both the conventional and

proposed techniques are evaluated in simulation first before the hardware experiment, where the

simulation time step for the controllers is the same as the sampling time used in the dSPACE

digital control system. Another big challenge, that is different from the simulation, is that noises

are more significant than expected. One strategy to reduce the noises is to increase the strength

of the measured signals.

Because of the noises, it is very hard to tune MPPT parameters for IC and SF algorithms,

especially for the SF algorithm. This is due to the fact that a noise can result in a high notch in

the calculated power during the next sampling time, causing a large variation in power derivative

and thus affecting the stability of the SF algorithm. However, for the proposed H-PI algorithm, a

stable MPPT algorithm is much easier to obtain. The test sequence is scheduled as the following

with t=0s as the starting point for data recording. Around t=20s, there is an increase of the solar

irradiation. A small increase of the solar irradiation appears near t=40s. Close to t=60s, there is a

large decrease of the irradiation. At about t=80s, the sequence repeats itself. The PV simulator

voltage and current are not only collected by the dSPACE system but also monitored by

oscilloscopes and/or meters. Figure 3.24 shows the captured maximum power by all the three

algorithms. Again, the proposed H-PI approach has the best performance because for the

proposed H-PI approach, the power derivative is smoothly processed before it is applied to the PI

controller. In addition, PI controller can responds much faster than an open-loop scheme.

61

0 20 40 60 80 100

6

8

10

12

Time

Out

put

Pow

er (

W)

IC

SF

S-PI

a) Captured output power in a long time range

40 45 50 55

11.2

11.4

11.6

11.8

12

12.2

Time

Out

put

Pow

er (

W)

IC SF S-PI

b) A zoom in of the captured output power

Fig. 3.24. Hardware experiment of captured maximum power using

conventional and proposed MPPT algorithms

3.6 Conclusions

This chapter proposes a fast and robust MPPT technique and compares it with typical

conventional MPPT algorithms used in solar PV industry (Table 3.1).

Among the three most popular conventional MPPT algorithms (fixed step P&O, IC and

adaptive P&O), the fixed step P&O and IC methods have continuous oscillation even when the

solar irradiance level is constant in the power converter switching environment; the adaptive

P&O method has very small oscillation if the solar irradiance level is stable. For the proposed

MPPT approach, it has the least oscillation and the highest stability.

The sampling rate affects the design of the perturbation rate. This result indicates that a

match between the sampling rate and the perturbation step is important. If the sampling rate is

too slow, a stable and reliable MPPT would be hard to achieve. Again, the proposed method is

more stable and reliable under different sampling rate conditions.

Under the variable irradiance levels, the proposed H-PI approach has better performance

than conventional methods, indicating that the power derivative information is valuable in

62

tracking and capturing maximum PV array power under changing weather conditions. The

comparison between the traditional and proposed adaptive methods shows that the hyperbolic

processing of the derivation is important for high performance of a solar PV system.

Table 3.1. Comparison of MPPT methods

MPPT

Technique

True

MPPT Complexity

Oscillation

around MPP

Sensed

Parameters

SCC No Low No Current

OCV No Low No Voltage

P&O Yes Low Yes V/C

IC Yes Medium Yes V/C

SF Yes Low No V/C

RCC Yes Low No V/C

Fuzzy/Neural Yes High No Varies

Proposed H-PI Yes Low No V/C

In the hardware experiment, the unexpected noises would drastically influence the power

increment or power derivative calculation in the next perturbation step. Because of the noises, it

is very hard to tune the MPPT parameters for IC and SF algorithms, especially for the SF

algorithm. However, for the proposed H-PI approach, the power derivative is smoothly

processed before it is applied to the PI controller; in addition, PI controller can respond much

faster than an open-loop scheme. The comparison demonstrates that the proposed H-PI approach

is much easier to tune and has the best performance.

63

CHAPTER 4

PV ENERGY EXTRACTION CHARACTERISTICS STUDY UNDER SHADING

CONDITIONS FOR DIFFERENT CONVERTER CONFIGURATIONS

A solar PV energy conversion system requires power converters for maximum power

extraction and grid integration. At present, many different converter structures have been

developed and used in a solar PV system. For all the different converter structures, the energy

extraction characteristics and maximum power capture capability for all the converter schemes

under even solar irradiation are very similar. However, under shading conditions, the energy

extraction depends strongly on what converter structure is used in a PV system.

4.1 Configurations of Grid-connected Solar PV Systems

A grid-connected solar PV system consists of three parts: an array of solar panels, power

electronic converters, and an integrated control system [13, 72]. Normally, solar cells are

connected in series to form a module that gives a standard dc voltage. For an application,

modules are connected into an array to produce sufficient current and voltage to meet a demand

[23]. There are generally two ways to connect PV modules into an array. The first approach

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

first wires modules together in parallel and then those units are combined in series. Ideally, both

series-parallel and parallel-series connections are equivalent if all the cells and modules are

64

identical and work at the same condition. But, if sunlight is applied unevenly to different PV

cells, the second connection approach could cause many very bothersome problems [23].

The control system of a solar PV system contains two parts: one for maximum power

point tracking (MPPT) and the other for grid interface control [38, 39]. Both control functions

are achieved through power electronic converters. On the dc side, MPPT optimizes the power

output by varying the closed loop system voltage. On the ac side, these inverters ensure that the

sinusoidal output is synchronized to the grid frequency (60Hz). Illustration 4.1 shows a

residential grid connected solar system.

Ill. 4.1.Configuration of grid-connected solar PV system [73]

4.2 Power Converters Architecture of PV Arrays

Power electronic converters, a critical component in a PV system, have the following

typical architectures: 1) central dc/ac and dc/dc converter structure, 2) central dc/ac converter

and string dc/dc converter structure, 3) central dc/ac converter and dc/dc optimizer structure, 4)

detached micro-inverter structure, and 5) central and string inverter structures.

65

4.2.1 Central Dc/ac and Dc/dc Converters

This PV array structure consists of a dc/dc converter for maximum power extraction of a

whole PV array, a dc/ac converter for interface of the PV array to the grid, and a dc-link between

the two converters (Fig. 4.1). The MPPT control is achieved through the regulation of the dc

voltage applied to the array and the grid interface control stabilizes the dc-link voltage and

adjusts the reactive power sent to the grid [38, 39].Hence, the control of the two converters is

decoupled. It is a cost-effective approach to develop large MW-scale solar PV systems. The

primary disadvantage of the central converter configuration is that a large power loss may occur

in the energy harvest when mismatch or varying shading happens among the PV panels within

the array. Normally, a bypass diode is applied to a PV module [23]. At the top of each string, a

blocking diode is used to prevent a shading or malfunctioning string from withdrawing current

from the rest strings that are wired together in parallel.

Fig. 4.1. PV array with central dc/ac and dc/dc converter structure

66

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

This PV array structure consists of a central dc/ac converter for interface of the PV array

to the grid and multiple dc/dc converters with each dc/dc converter responsible for MPPT of one

PV string [14, 17] (Fig. 4.2) while the dc/ac inverter stabilizes the dc-link voltage and adjusts the

reactive power sent to the grid by the whole array. The key difference between Figs. 4.1 and 4.2

is that each dc/dc converter performs MPPT of a string rather than a whole PV array. The string

converter structure is likely to provide better power harvest than a central converter structure

because each string is tracked independently. Multiple self-contained string converters may offer

some advantage by eliminating the single point of failure, but will have a higher installation cost.

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

4.2.3 Dc/dc Optimizers

Dc/dc optimizers place a dc/dc converter to each PV module and provide one, large

67

central inverter that aggregates the power from all optimizers [16, 17] (Fig. 4.3). The optimizers

provide MPPT at the module level while the dc/ac inverter accomplishes the same control

functions as shown in Sections 4.2.1 and 4.2.2. The dc outputs of each module are joined in

series and parallel to be collected and then converted to ac power by a central inverter. With

additional equipment to purchase and install, dc/dc optimizers add to the initial cost of a PV

system. The added module-level hardware also imposes a penalty on overall system-level

efficiency by introducing an additional stage of loss power conversion. Furthermore, some dc/dc

optimizer systems also require a separate command-and-control device to operate.

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

4.2.4 Detached Microinverters

Detached microinverters involve placing a small inverter in close proximity to each PV

module (Fig 4.4). Arrays of panels are connected in parallel to each other, and then to the grid

feed. Hence, each microinverter is responsible for: 1) MPPT control of a module by regulating

68

the dc voltage applied to the module and 2) control of the reactive power sent to the grid by each

module. Similar to dc/dc optimizers, detached microinverters offer enhanced energy harvest by

performing MPPT at the module level, therefore, a single failure of panel or inverter will not take

the entire string offline. Also, they produce grid-matching power directly at the back of the

panel, and different ratings of solar panels can be added to an array even if they don't match the

original types. In addition, a micro-inverter on each module as the inverter’s anti-islanding

capability will shut down the module energy production when the system is disconnected, which

can significantly limit the risk to firefighters under emergency conditions according to proposals

of 2014 NEC [74].

Fig. 4.4. Detached microinverter PV system

However, the MPPT and reactive power control functions of a module are not decoupled,

which is a disadvantage for this PV system architecture because the two control requirements

may not be met at the same time as reported in [14]. Also, microinverters need to be installed

individually on the racking near each module. Today’s microinverters have a five- to fifteen-year

warranty, much shorter than the life of PV modules. As such, it would be necessary to replace all

of the nonintegral microinverters at least once during the lifetime of the system.

69

4.2.5 Central and String Inverters

For both central and string inverter configurations, there is no dc/dc converter in the PV

system [15-17]. Thus, the inverters need to handle both MPPT and grid interface control

functions at the string or array level. Similar to Section 4.2.4, a disadvantage for these PV system

architectures is that the MPPT and reactive power control requirements may not be met at the

same time. In the central inverter PV structure, a single and large inverter is connected to many

PV modules wired in series to form strings with up to 600V of open-circuit voltage (1,000V in

Europe) [16] (Fig. 4.5a). In the string inverter PV structure, each string of series PV modules is

connected to one string inverter. Then, inverters for all the strings are connected in parallel

before feeding into the grid (Fig. 4.5b).

a) Central inverter (b) String inverter

Fig. 4.5. PV array with central and string inverters

In summary, from the maximum power extraction standpoint, there are basically three

70

different configurations: 1) one dc voltage applied to the whole PV array for MPPT control

(Figs. 4.1 and 4.5a), 2) multi-independent dc voltages applied to multiple strings of series PV

modules (Figs. 4.2 and 4.5b), and 3) one independent dc voltage for each PV module (Figs. 4.3

and 4.4). For detailed evaluation of the three different configurations, it is important to be able to

assess power and voltage characteristics at individual cell, module, and array levels. However,

such a study is difficult to be conducted experimentally because the existing commercial PV

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

measured. To overcome the challenge, a numerical algorithm developed in Chapter 2 for

simulation study of PV cell, module, and array characteristics under different converter schemes.

It is also important to indicate that a large PV array usually consists of thousands of cells. Thus, a

rigorous computational approach is very important.

4.3 PV Array Models for Different Converter Configurations

Detailed mathematical and simulation model of a PV cell, module and array have been

described Section 2.2. The PV Array model with consideration of different converter

configurations will especially be analyzed and validated.

For the micro inverter structure, the energy extraction characteristics of each module is

computed separately based on the PV module model (Sections 2.2.2 and 2.3) while the total

energy extraction of a PV array is the summation of energy from all the modules. For the string

converter structure, the voltage applied to each string is different (Sections 4.2.2 and 4.2.5). For

each string, the mathematical model and procedure to obtain P-V and I-V characteristics is very

similar to Sections 2.2.2 and 2.3 except that the external voltage applied to each string equals to

the sum of photogenerated voltages of all series connected PV modules. The output power of the

71

array is the sum of the output powers of all strings. For the central converter structure with the

standard series-parallel connected PV array (Section 4.2.1), 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

different depending on how many PV cells in a string are shaded and how much. The model and

procedure for energy extraction computation of each string is similar to that of the string

converter structure while the total output current of the PV array is the sum of currents of all

parallel strings.

4.4 PV System Energy Extraction Characteristics without Bypass Diodes

Based on the analysis shown in Section 4.2, PV system characteristic studies are

conducted for the following three converter configurations, i.e., a power converter for an entire

array, for each string, and for each panel.

4.4.1 Central Converter Configuration

For a typical series-parallel connected PV array with central converter configuration, 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 different depending on how many PV cells in a string are

shaded and how much. The mathematical procedure to obtain P-V and I-V characteristics is

based on Sections 2.2. The output current of the PV array is the sum of currents of all parallel

strings.

72

0 100 200 300 400 5000

5

10

15

20

Vs (V)

Pow

er (kW

)

None

50%100%

a) P-V characteristics of PV array

0 100 200 300 400 500-40

-30

-20

-10

0

10

Vs (V)

Vol

tage

(V

)

None

50%100%

b) Shaded cell terminal voltage characteristics of the last string

0 100 200 300 400 500-300

-200

-100

0

100

Vs (V)

Pow

er (W

)

None

50%100%

c) Shaded cell P-V characteristics of the last string

Fig. 4.6. Characteristics of PV array with central converter

Figure 4.6 shows the PV array characteristics. The PV array has a configuration of 10

parallel strings with each string containing 20 series modules. Assume there are 19 shaded

modules in the 1st string, 17 in the 2nd string, 15 in the 3rd string … and 1 in the last string. In

73

each shaded module, there is only one shaded cell, which represents the worst condition that may

damage a PV cell [75, 76]. The shading factor is 0, 50% and 100%, respectively. From the

figures and other case studies, it is found that the PV array characteristics can be shifted

significantly under shading conditions (Fig. 4.6a). The degree of the change depends on how

many strings contain shaded cells and how many shaded cells are in each string. When there is

only one shaded cell in a string, all the photogenerated voltages of the unshaded cells in that

string are applied to the shaded cell (Fig. 4.6b), which would cause a high risk to damage the

shaded cell due to the high absorbing power of the shaded cell (Fig. 4.6c).

4.4.2 String Converter Configuration

For a PV array with the string converter configuration, the voltage applied to each string

of PV modules is different. Therefore, the P-V and I-V characteristics of each string are

independent from those of other strings. Under the MPPT control strategy, each string captures a

different power. The total output power of the array is the summation of the maximum powers

captured by all strings.

0 100 200 300 400 5000

0.5

1

1.5

2

Vs (V)

Pow

er (

kW)

shade factor=100%

Average max

strings 1-10

0 100 200 300 400 5000

0.5

1

1.5

2

Vs (V)

Pow

er (

kW)

shade factor=50%

Average max

strings 1-10

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

74

Figure 4.7 shows the P-V characteristics of all strings under the same shading conditions

used in Fig. 4.6. In the figure, the constant line represents the maximum power of the PV array

divided by the number of all strings. From the figure and other analysis, the following properties

are found.

1) When there is no shaded cell in the PV array, all the strings have the same P-V

characteristics. The output power of the PV array under the MPPT control strategy is the

maximum power of one string multiplied by the number of all strings.

2) When there are shaded cells in the PV array, the P-V characteristics of each string

would be different from other strings depending on the distribution of the shaded cells and the

shading factors of shaded cells. The average maximum power lies between the maximum

captured powers of the least and the most shaded strings.

3) Similar to Fig. 4.6, the most damaging condition for a PV cell is when there is only

one shaded cell in a long string, which would cause a high risk to damage the shaded cell due to

the high absorbing power of the shaded cell.

4.4.3 Micro-inverter Configuration

For the micro-inverter configuration, each PV module is connected to the grid via its own

inverter. Hence, the P-V and I-V characteristics of each module are independent from those of

other modules. Under the MPPT control strategy, each module captures a different power. The

total output power of the PV array is the summation of the maximum powers captured by all the

PV modules.

75

0 5 10 15 20 250

0.025

0.05

0.075

0.1

Vs (V)

Pow

er (

kW)

None

50%

100%

a) P-V characteristics of PV array

0 5 10 15 20 25-100

-75

-50

-25

0

25

Vs (V)

Pow

er (

W)

None

50%

100%

b) Shaded cell terminal voltage characteristics of the last string

0 5 10 15 20 25-20

-15

-10

-5

0

5

Vs (V)

Vol

tage

(V

)

None

50%100%

c) Shaded cell P-V characteristics of the last string

Fig. 4.8. Characteristics of PV module under shading conditions

Figure 4.8 shows the P-V characteristics of a PV module with one shaded cell for shading

factor of 0, 50%, and 100%, respectively. As it can be seen from the figure, shading of even one

single cell could cause significant drop of PV module output power (Fig. 4.8a). Under the

shading condition, a high reverse terminal voltage would appear on the shaded cell (Fig. 4.8b),

76

which results in a high absorbing power by the shaded cell especially when the external voltage

applied to the module is low (Fig. 4.8c). Similarly, the most demanding situation is when there is

only one shaded cell in the PV module.

Table 4.1 compares maximum power that can be captured by the PV array for the three

power converter configurations under the same shading condition used in Fig. 4.6. In general, if

there is no shaded cell, the captured maximum power is the same for all the three converter

configurations. However, under shading conditions, the micro-converter configuration based PV

system has the highest energy yield while the central converter configuration one has the lowest

energy production.

Table 4.1. Comparison of maximum power extraction without bypass diodes

for different converter configurations

Shading factor

Configuration 50% 100%

Central converter 13.65 kW 7.34 kW

String converter 13.79 kW 7.76 kW

Micro converter 15.71 kW 11.39 kW

4.5 PV System Energy Extraction Characteristics with Bypass Diodes

In the PV industry, bypass diodes are normally adopted in central and string converter

configurations [38]. For the micro converter configuration, it is reasonable to assume that bypass

diodes are not used.

77

4.5.1 Central Converter Configuration

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

[39]. For research purpose, however, the dissertation considers different bypass diode schemes

within a PV module, such as a bypass diode for every one, two, or three series PV cells. As

discussed in Chapter 2, 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.

Figure 4.9 compares characteristics of the PV array for different bypass diode conditions.

From the figures, other case studies, and comparison with Section 4.2.1, the following properties

are obtained:

1) If each PV module has one bypass diode, the PV array characteristics is improved

depending on the distribution of the shaded cells in the PV array. For each string, the best

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

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

characteristics is trivial (Fig. 4.9a). If there is only one shaded cell in a module, then, all the

photogenerated voltages of the unshaded cells in that module are applied to the shaded cell.

Compared to Fig. 4.6, the absorbing power of the shaded cell under 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 appear in the P-V characteristics (Fig. 4.9a), making it harder for

the MPPT control of the PV array.

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

characteristics is significantly reduced. Compared to Fig. 4.9c, the absorbing power of the

shaded cell is very small (Fig. 4.9d). If the number of the shaded cells is significantly less than

78

the number of the unshaded cells, the P-V characteristics of the PV array is very close to the

unshaded condition no matter how the shaded cells are distributed in the PV array. In addition, it

is more convenient to manage the MPPT control of the PV array even under shading conditions

when there is a bypass diode for each PV cell.

3) As fewer cells are in parallel with a bypass diode, the peak power of the PV array

increases and the multi-peak impact to the P-V characteristics of the PV array reduces (Fig.

4.10).

0 100 200 300 400 5000

5

10

15

20

Vs (V)

Pow

er (

kW)

None

50%

100%

a) PV array characteristics

(one bypass diode per module)

0 100 200 300 400 5000

5

10

15

20

Vs (V)

Pow

er (

kW)

None

50%

100%

b) PV array characteristics

(one bypass diode per cell)

0 100 200 300 400 500-150

-100

-50

0

50

Vs (V)

Pow

er (

W)

None

50%

100%

c) Shaded cell characteristics

(one bypass diode per module)

0 100 200 300 400 500-4

-2

0

2

4

Vs (V)

Pow

er (

W)

None

50%

100%

d) Shaded cell characteristics

(one bypass diode per cell)

Fig. 4.9. Characteristics of PV array under shading conditions

79

0 100 200 300 400 5000

5

10

15

20

Vs (V)

Pow

er (

kW)

shade factor=50%

full-sunn=1

n=2

n=3

4n=6

n=9

n=12

n=18n=36

a) PV array characteristics under 50% shading

0 50 100 150 200 250 300 350 400 450 5000

5

10

15

20

Vs (V)

Pow

er (

kW)

shade factor=100%

full-sun

n=1n=2

n=3

4

n=6

n=9

n=12n=18

n=36

b) PV array characteristics under 100% shading

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

4.5.2 String Converter Configuration

With the same bypass diode layouts, the only difference between the string and central

converter configurations is that the voltage applied to each string of series PV modules is

different. Due to the bypass diode impact, the characteristics of PV strings would be different

from Fig. 4.7. Figure 4.11 shows the P-V characteristics of all strings under the same shading

80

conditions used in Fig. 4.6 for different bypass diode schemes. Again, the constant red dot line

represents the maximum power of the PV array divided by the number of all strings.

If each module has one bypass diode, the characteristics of each string has multiple

peaks, requiring that the MPPT algorithm must be designed to be able to locate the maximum

power production of each string. If there are more bypass diodes within a module, the multiple

peaks moves from low voltage range to high voltage range in general, resulting in more power

production from each string under the same shading conditions. If one bypass diode is applied to

every one or two PV cells, the energy yield of each string is significantly increased and the peak

power of each string is closer to ideal peak power under the nonshading condition, making it

easier to develop and design MPPT algorithm.

4.5.3 Comparison of Maximum Power Using Central, String and Micro Converter Configuration

One important issue for the evaluation and comparison of the power production using

micro, string, and central converter configurations is how much power can be extracted for

different converter structures. Tables 4.2 and 4.3 compares the maximum power of the PV array

that can be captured by using different converter configurations for varying bypass diode

arrangements under the same shading condition used in Fig. 4.6. The comparison shows:

1) When the number of PV cells of each bypass diode is small, the difference among

the maximum power extracted by using the three different converter structures is very small.

2) The micro-converter based PV system has the highest power capture capability

while the power production of central converter based PV system is the lowest. The difference

between the highest and the lowest power is more obvious as the number of PV cells contained

in each bypass diode increases.

81

0 100 200 300 400 5000

0.5

1

1.5

2

Vs (V)

Pow

er (

kW)

shade factor=100%

Average max

strings 1-10

a) a bypass diode per module

0 100 200 300 400 5000

0.5

1

1.5

2

Vs (V)

Pow

er (

kW)

shade factor=100%

Average max

strings 1-10

b) a bypass diode per 18 cells

0 100 200 300 400 5000

0.5

1

1.5

2

Vs (V)

Pow

er (

kW)

shade factor=100%

Average max

strings 1-10

c) a bypass diode per 9 cells

0 100 200 300 400 5000

0.5

1

1.5

2

Vs (V)

Pow

er (

kW)

shade factor=100%

Average max

strings 1-10

d) a bypass diode per 6 cells

0 100 200 300 400 5000

0.5

1

1.5

2

Vs (V)

Pow

er (

kW)

shade factor=100%

Average max

strings 1-10

e) a bypass diode per cell

Fig. 4.11. Characteristics of series PV strings

82

Table 4.2. Comparison of maximum power extraction under 50% shading factor (kW)

Configuration

n Central converter String converter Micro converter

1 19.0610 19.1124 19.1127

2 18.7270 18.8392 18.8395

3 18.3700 18.5661 18.5664

4 17.9912 18.2929 18.2932

6 17.1742 17.7466 17.7470

9 15.8272 16.9274 16.9277

12 14.7374 16.1083 16.1087

18 13.9460 14.7711 15.7179

Table 4.3. Comparison of maximum power extraction under 100% shading factor (kW)

Configuration

n Central converter String converter Micro converter

1 19.0475 19.1012 19.1014

2 18.7120 18.8277 18.8280

3 18.3535 18.5543 18.5546

4 17.9730 18.2808 18.2811

6 17.1517 17.7340 17.7343

9 15.7945 16.9137 16.9140

12 14.3236 16.0934 16.0938

18 11.3022 14.4531 14.4535

83

3) In reality, however, a larger number of bypass diodes is not used in micro-converter

based PV systems. Thus, when the number of PV cells of each bypass diode is small, such as 1 to

4 as shown by Tables 4.2 and 4.3, the central converter based PV system is much more efficient

than micro-converter based PV system. In addition, the reactive power compensation ability of

central-converter based PV system is higher [14, 77].

4.6 Conclusion

This chapter compares the energy extraction characteristics of a solar PV system for

different converter schemes, including central, string and micro converter configurations. The

chapter particularly focuses on how energy extraction characteristics of a PV array are affected

by uneven shadings using different converter structures. Without shading, the PV system has the

same energy yield for all the three converter schemes. Under shading and without bypass diodes,

the micro converter based PV system has the highest energy yield while the central converter

based PV system has the lowest energy production. However, the micro converter based PV

system is costly and is still unable to prevent energy loss caused by the shading within PV

panels.

It is found that with bypass diodes, the efficiency of a PV system can be improved

significantly especially when the number of PV cells within a bypass diode is small. Simulation

studies show that the difference among the maximum extracted power is trivial under shading

conditions for the three different converter structures for PV modules with large number of

bypass diodes. The study shows that the central converter based PV system with properly built-in

bypass diodes is an effective and economic approach to improve efficiency, performance, and

reliability of a PV system.

84

CHAPTER 5

COORDINATED CONTROL FOR GRID INTEGRATION OF PV ARRAY, BATTERY

STORAGE, AND SUPERCAPACITOR WITH RELATED ISSUES

The intermittent nature of PV energy and quick fluctuations of load demanding require

energy storage units (ESU) which generally consists of storage battery and supercapacitor (SC)

[78, 79]. Batteries are the technological solution most commonly employed to help make a PV

system [80-84], whose power output cannot be controlled, smooth and dispatchable. A battery

stores electrical energy in the form of chemical energy. For a PV-battery system to function

effectively the electrochemical processes must work in both directions—in other words, the

system must be rechargeable. Normally, batteries perform three main functions in a grid-

connected PV system: storing energy into the batteries when the PV production is high and the

grid demand is low, releasing energy to the grid when the PV production is low or during grid

peak demand intervals, and preventing large voltage fluctuations.

Except for batteries, SC is usually used in conjunction with batteries to form an advanced

PV energy storage system [85-87]. However, unlike batteries, where the voltage remains

relatively even over most of the battery’s remaining charge levels, a capacitor’s voltage scales

linearly with the remaining energy. This means an additional circuitry is required to make the SC

energy usable.

For the PV array, a boost converter is usually connected to the dc link to raise the input

voltage and then transfer the high voltage dc energy to ac energy through a grid-connected

converter [88]. Bidirectional dc–dc converters are required to interface the ESU, including

85

batteries and SC, to the dc link for controlling the power flow. The coordinated control of the

entire system is critical. Currents and voltages of PV array, SCs, battery, dc link, and grid are

input signals used to modulate PWM signals to power electronic converters. The modulation

algorithm has to be specified for each converter control topology and has to generate control

signals to fulfill basic functions such as dc link voltage control, ESU control, grid active and

reactive power control, and MPPT control, which has resulted in many different control

strategies for the integrated PV and ESU system [87-94].

5.1 Grid-connected PV and Energy Storage System

A typical grid-connected solar PV and energy storage system consists of five parts (Fig.

5.1): an array of solar cells, battery storage, SC, power converters, and an integrated control

system.

bi

pvv

bv

scv

pvi

sci

g gv i

dcvgi

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

86

5.1.1 Photovoltaic Arrays

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

voltage. Modules are connected into an array to produce sufficient current and voltage to meet a

demand for a gird-connected application [90, 92, 95]. Usually, the PV modules are first

connected in series into strings and then in parallel into an array. The power produced by a PV

array is dependent on the irradiance and temperature. In general, there is a unique point on the P-

V curve of the PV array, called the maximum power point (MPP), at which the entire PV system

operates with maximum efficiency and produces its maximum output power. To maximize the

output power of a PV system, continuously tracking the MPP of the system is necessary (Chapter

3). This is accomplished through the control of the dc/dc converter connecting the PV array to

the dc-link capacitor.

5.1.2 Rechargeable battery

A rechargeable battery is one or more electrochemical cells that convert stored chemical

energy into electrical energy during a discharge process or convert electrical energy into

chemical energy during a charge process [95]. The electrical energy storage system in a PV

system is expected to be designed with adequate energy capacity and output peak power to

satisfy grid integration needs [88, 89]. In an integrated PV and battery storage system, the battery

is connected to the dc-link also through a dc/dc converter which controls the charge and

discharge of the battery.

5.1.3 Supercapacitor

87

Unlike batteries, SCs store their energy in an electrostatic field. The most significant

advantage of SCs over batteries is that they are capable of very fast charges and discharges [81,

82, 87]. Disadvantages are that their power is available only for a very short duration and their

self-discharge rate is much higher than that of batteries. Thus, SCs can supply power when there

are surges or energy bursts, while batteries can supply the bulk energy over a longer time period

[81, 82, 87].The combination of the two is crucial for diverse energy storage needs of both fast

and slow fluctuating solar power [81, 87, 89].

5.1.4 Grid-Connected Converter

The grid-connected converter (GCC) converts dc to grid compatible ac [88, 96]. In

addition, the purpose of a GCC includes: managing the active power transferred from dc to ac

side or stabilizing the dc-link voltage, and controlling the reactive power absorbed from the ac

grid, depending on the coordinated control system design (Section 5.3).

5.1.5 Integrated Control System

The control system of an integrated PV system has three levels: device level at PV array,

battery and SC, PV system central control level (PVCC), and distribution management system

(DMS) level [79, 93, 97]. At the device level, the energy is either captured from the PV array or

generated from ESUs. At the PVCC, the power production is determined based on the optimal

overall profits to operate the PV, ESUs and GCC. The central controller sends out power

references to PV, ESUs and GCC based on commends from DMS, while each individual device

control system ensures that the power reference from the PVCC is reached. At the DMS level,

88

the power production of the integrated PV system is managed to meet the overall grid demands

and stability and reliability needs.

5.2 Coordinate PV Array, ESU and GCC Control

The development of coordinated control for next-generation PV installations, along with

ESUs, provides flexibility to distribution system operators. The control objective of this hybrid

PV and energy storage system is to supply the desired active and reactive power to the grid and

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

system through coordinated control of power electronic converters.

MPPT control for PV Array has been studied and investigated in Chapter 3. Hereby, the

control of bi-directional dc/dc converter for ESUs and direct-current vector control of GCC will

be discussed.

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

Unlike the PV array which requires only one-directional power flow, ESUs require bi-

directional power flow. Due to its simplicity and robustness, the bi-directional buck/boost

converter is used in this dissertation to interface the SC or battery ESUs with the dc voltage bus.

In general, the dc/dc converter acts as a boost converter during ESU discharge mode and as a

buck converter during ESU charge mode.

Both constant-current and constant-voltage control schemes are developed. The two

control techniques are then integrated together to meet ESUs charge and discharge requirements.

89

Figure 5.2 shows the block diagram for battery control. Similar current control strategy is also

used to control the SC.

Dbi

bv

_b refv

_b refi

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

For battery control, the switch block passes through the top input or the bottom input

based on the value of SOC in the middle. If the switch is in the upper position, the system

operates in the constant-voltage control mode. If the switch is in the bottom position, the system

operates in the constant-current control mode. The reference current can be either positive or

negative. Assume that the current flowing into the dc-link is positive. Then, if the reference

current is positive, the system implements constant-current discharging control function; if the

reference current is negative, the system implements constant-current charging control function.

SOC is the main factor to decide the battery status from current control to voltage control. When

SOC is below 70%, constant-current charging mechanism is applied; when SOC is above 70%,

the system switches to constant-voltage charging mechanism. In order for a smooth transition

from current to voltage control, the same value of reference current before transition should be

the initial value of the voltage controller. While the battery is in discharging mode, the constant-

current control mechanism is applied and the power provided by the battery to the grid can be

regulated by adjusting the reference discharging current.

90

5.2.2 Direct-Current Vector Control of GCC

Figure 5.3 shows the schematic of the GCC, in which a dc-link capacitor is on the left,

and a three-phase voltage source, representing the voltage at the Point of Common Coupling

(PCC) of the ac system, is on the right. The following dynamic equations can be obtained:

1

1

1

a a a a

b b b b

c c c c

v i i vd

v R i L i vdt

v i i v

(5.1)

where L and R are the inductance and resistance of the grid filter and abcv , abci , and 1abcv are

instantaneous space vectors of the PCC voltage, line current, and converter output voltage,

respectively.

Fig. 5.3 GCC converter schematic

By using the abc-dq transformation with its d-axis aligned to the voltage vector of the

PCC, full equation in Eq. (5.1) be described in the synchronously rotating reference frame as

follows:

1

1

d d d q d

sq q q qd

v i i i vdR L L

v i i vdt i

(5.2)

91

where ωs is the angular frequency of the grid's PCC voltage, and. Using space vectors, (5.2) is

expressed by the complex equation in (5.3), in which vdq, idq and vdq1 are instantaneous space

vectors of the PCC voltage, line current, and converter output voltage, respectively. In the

steady-state condition, (5.3) becomes (5.4), where Vdq, Idq and Vdq1 stand for the steady-state

space vectors of PCC voltage, grid current, and converter output voltage, respectively.

1dq dq dq s dq dq

dv R i L i j L i v

dt (5.3)

1dq dq s dq dqV R I j L I V (5.4)

In the grid's PCC voltage-oriented frame [98-103], the instantaneous active and reactive

powers absorbed by the GCC from the grid are proportional to the grid's d- and q-axis currents,

respectively, as shown by (5.5) and (5.6):

( ) d d q q d dp t v i v i v i (5.5)

( ) q d d q d qq t v i v i v i (5.6)

In terms of the steady-state condition, Vdq=Vd+j0 if the d-axis of the reference frame is

aligned along the PCC voltage position. Assuming that Vdq1=Vd1+j Vq1 and neglecting the grid

filter resistance, the current flowing between the PCC and the GCC according to (5.4) is:

1 1( ) /( ) /dq d d f q fI V V jX V X (5.7)

Where Xf stands for the grid filter reactance.

Supposing that passive sign convention is applied, i.e., power flowing toward the GCC is

positive, the power absorbed by GCC at the PCC is:

1 1/ , ( ) /conv d q f conv d d d fP V V X Q V V V X (5.8)

92

The basic principle of the direct-current vector control is to use d- and q-axis currents

directly for active and reactive power or dc-link voltage and reactive power control of the GCC

[96]. Unlike the conventional standard vector control approach that generates a d- or q-axis

voltage from a GCC current-loop controller, the direct-current vector control structure outputs a

current signal at the d- or q-axis current-loop controller (Fig. 5.4). In other words, the output of

the controller is a d- or q-axis tuning current, while the input error signal tells the controller how

much the tuning current should be adjusted during the dynamic control process. The

development of the tuning current control strategy has adopted intelligent control concepts [104],

e.g., a control goal to minimize the absolute or root-mean-square (RMS) error between the

desired and actual d- and q-axis currents through an adaptive tuning strategy.

PI+ _

PI

+

_+_+

PI

+

_ __

PI

+ _

PI

+ _

PI

+ _

Fig. 5.4. GCC direct-current vector control structure

Due to the nature of a voltage-source converter, the d-and q-axis tuning current signals,

i’d and i’

q, generated by the current-loop controllers must be transferred to d- and q-axis voltage

signals v*d1 and v*

q1 to control the GCC. This is realized through (5.11), which is equivalent to

93

the transient d-q equation (5.2), after being processed by a low pass filter in order to reduce the

high oscillation of d and q reference voltages applied directly to the converter.

* ' '1

* ' '1

d f d s f q d

q f q s f d

v R i L i v

v R i L i

(5.11)

The initial values of the GCC PI current-loop controllers are tuned by minimizing the

RMS error between the reference and measured values.

5.3 Coordinated Control Mechanisms for Grid Integration

In grid integration of the integrated PV system, the PVCC receives active and reactive

power commends from the DMS and then determines how to control PV array, ESUs and GCC.

Normally, the PV array is controlled for maximum power extraction. Thus, depending on the

active power or dc-link voltage control for the GCC (Fig. 5.4), three coordinated control

strategies are implemented.

5.3.1 Dc-link Voltage Control through ESUs

In this control scheme, the GCC operates in PQ control mode by maintaining the PCC

active and reactive power output according to the grid control commend. Hence, the dc-link

voltage must be controlled via ESUs [79, 89]. In general, if the PV generated power is more than

the GCC output power, the dc-link voltage goes up so that the ESUs must operate in charging

mode to reduce the voltage; if the PV power is less than the GCC output power, the dc-link

voltage drops so that the ESUs must operate in discharging mode to increase the dc-link voltage.

94

Usually, a battery bank has a high energy density whereas it has relatively slow response

speed. On the other hand, SC has a low power density but fast response speed. Therefore, in the

control design of ESUs, SC should be responsible for fast transient energy exchange whereas

battery should take care of relatively steady-state energy charge or discharges. This results in a

control design as shown by Fig. 5.5, in which the error signal between measured and reference

dc-link voltage generates a current reference iref through a PI controller and then a low-pass filter

is applied to obtain the battery reference current ib_ref while the rest is used as the SC reference

current isc_ref . This strategy is simple but may result in unstable dc-link voltage when the SC

and/or battery reach their lower or upper energy storage limits.

refi _b refi

bi

_sc refi

bv

dcv1/ dcv

dcv1/ dcv

_dc refV

dcv

Fig. 5.5. Control of dc-link voltage through ESUs [87]

5.3.2 Power Balancing Control of ESUs

In this control scheme, the GCC operates in PQ control mode too, requiring that the dc-

link voltage must be controlled by ESUs. However, different from Section 5.3.1, the reference

current signals to the battery and SC are determined through a power balance relation as shown

in Fig. 5.6. In the figure, pf represents the power losses in the grid filter which is calculated by:

95

2 2f f d qp R i i (5.12)

where, id and iq are grid d- and q-axis currents, respectively, and Rf is the resistance of grid

filter. The error signal between measured and reference dc-link voltage generates a dc-link

capacitor power reference, pdc_ref. The summation of grid reference power pg_ref, pdc_ref and ppv is

the total instantaneous generated power in the power system. By subtracting loss power from the

filter pf , the charging or discharging power to ESUs is obtained. Similarly, through a low-pass

filter, the battery reference current ib_ref is obtained while the rest is used as the SC reference

current isc_ref.

The primary issues associated with this scheme is that the variation of system parameters,

such as Rf, or the inaccuracy of the power balance calculation, such as neglect of power

converter losses, could affect control effectiveness of the dc-link voltage. In addition, the slow

response speed of the power balance computation and the lower or upper energy storage limits of

the SC and/or battery could affect the dc-link voltage control too.

_g refp fp

_dc refp

pvp

_sto refp _b refp

_sc refp

_dc refV dcv

pvv

pvi

bv

scv

_b refi

_sc refi

Fig. 5.6. Power balance control structure of ESUs [89]

5.3.3 Dc-link Voltage Control through GCC

96

In this control scheme, the GCC is responsible for dc-link voltage control and the grid

reactive power or bus voltage control. Although this GCC control strategy can maintain a very

stable dc-link voltage, power management of ESUs must be determined through power balance

computation. Similar to the ESU control method described in Section 5.3.1, the summation of

grid reference power pg_ref with pf and actual dc-link capacitor power pdc is the power that should

be outputted by the combined PV array and ESUs before the dc-link capacitor (Fig. 5.7). Then,

the SC and battery reference currents can be obtained in the same way as described in Section

5.3.2. Due to the variation of system parameters and the inaccuracy of the power balance

calculation, the actual output power at PCC could be slightly different from the grid reference

power pg_ref by using this control scheme.

_g refp fp dcp

pvp

_sto refp _b refp

_sc refppvv

pvi

bv

scv

_b refi

_sc refi

Fig. 5.7. Energy storage units connected converters control structure

5.4 Coordinated Control Evaluation and Comparison

To evaluate different control schemes, a computational experiment platform of the grid-

integrated PV system with ESUs is developed. The experiment system mainly includes: a PV

array module, a battery bank, a SC, four power converter modules, and four corresponding

97

control modules for these converters (Fig. 5.8). The parameters used in the simulation study are

shown in Table 5.1.

The PV array has a series-parallel connection configuration having 10 parallel strings

with each string consisting of 50 series panels. The converter modules are from Opal-RT RTE-

Drive toolbox. These converter modules can be integrated with the RTE PWM signal generation

function from the Opal-RT RT-EVENTS toolbox to generate drive pulses for very fast and

accurate simulation of power converters [64]. Figure 5.9 shows I-V and P-V characteristics of

the PV array. The control modules are developed with detailed consideration of digital control

system natures, including sample and hold, digital signal processing, and time delays. The

measured voltage and current signals first pass through sampling blocks, which converts

measured “continuous” signals to “discrete” signals. Then, a digital filtering mechanism is

applied to remove high frequency components caused by noises or rapid switching of power

converters [13].

Fig. 5.8. Solar PV generator under the control of a dc/dc power converter

using SPS and Opal-RT RT-LAB

98

0 200 400 600 800 1000 12000

20

40

60

80

Cur

rent

(A

)

0 200 400 600 800 1000 12000

30

60

Voltage (V)

Pow

er (

kW)

Fig. 5.9. Solar PV array characteristics used in simulation

Table 5.1 Parameters of electrical components in grid-integrated PV system with ESUs

Parameters Value Parameters Value

L1 0.3mH C1 0.3mF

RL1 0.5Ω +1.2mH RL2 1mΩ +33mH

RL3 0.9Ω +1.2mH RL4 1mΩ +33mH

Cdc 16mF Lf1 0.55mH

Lf2 0.55mH Cf 2.5μF

Figures 5.10-12 show results of a case study for the three control schemes presented in

Section 5.3. The solar irradiation is initialized at a value of S=0.75 (Fig. 5.13), where S stands

for the ratio of the present solar irradiation over the nominal irradiation of 1000W/m2. Then, it is

simulated as a parabola curve starts at t=6s with a highest value of S=1 at t=12s. Finally, S

maintains at a value of 0.75 after t=18s.

99

5 10 15 20-50

-25

0

25

50

Time (s)

P(k

W)a

nd Q

(kV

ar)

PV

GridQ

a) Active power of PV system

and grid along with grid side

reactive power

5 10 15 20-50

-25

0

25

50

Time (s)

P(k

W)a

nd Q

(kV

ar)

PV

GridQ



reactive power

5 10 15 20-50

-25

0

25

50

Time (s)

P(k

W)a

nd Q

(kV

ar)

PV

Grid

Q



reactive power

5 10 15 201400

1450

1500

1550

1600

Time (s)

Dc-

link

Vol

tage

(V)

b)Dc-link voltage

5 10 15 201400

1450

1500

1550

1600

Time (s)

Dc-

link

Vol

tage

(V)

b)Dc-link voltage

5 10 15 201400

1450

1500

1550

1600

Time (s)

Dc-

link

Vol

tage

(V)

b)Dc-link voltage

5 10 15 20310

320

330

340

Time (s)

ES

U V

olta

ge (

V)

battery

SC

c) Battery & SC voltage profiles

5 10 15 20310

320

330

340

Time (s)

ES

U V

olta

ge (

V)

battery

SC


5 10 15 20310

320

330

340

Time (s)

ES

U V

olta

ge (

V)

battery

SC


5 10 15 200

15

30

45

60

Time (s)

Cur

rent

(A

)

5 10 15 2069.5

70

70.5

SO

C (

%)

Current

SOC

d)Current & SOC of battery

Fig. 5.10. Simulation results of

the control scheme in Section

5.3.1

5 10 15 200

15

30

45

60

Cur

rent

(A

)

5 10 15 2069.5

70

70.5

Time (s)

SO

C(%

)

Current

SOC




5.3.2

5 10 15 200

15

30

45

60

Time (s)

Cur

rent

(A

)

5 10 15 2069.5

70

70.5

SO

C(%

)

Current

SOC




5.3.3

100

5 10 15 20

0.8

0.9

1

Time (s)Ir

radi

atio

n

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

Power balancing between supply and demand is the most critical task in the system. To

check the demand-following services, the initial grid reference active power is given as 15kW,

which has a positive value when gird power inflow to the dc-link direction (Fig. 5.1).Then grid

demand changes to -35 kW and 5kW separately at t=8s and t=15s. The reactive power reference

is set at 0kVar practically. The simulation results of three control schemes include: PV and grid-

side generated power and grid-side reactive power (Figs. 5.10a, 5.11a and 5.12a), dc-link voltage

(Figs. 5.10b, 5.11b and 5.12b), battery and SC voltage profiles (Figs. 5.10c, 5.11c and 5.12c),

and battery SOC and current profiles (Figs. 5.10d, 5.11d and 5.12d).

The simulation shows that by using any of the coordinated control schemes, the active

and reactive power can follow the reference well with no error at steady state (Figs. 5.10a, 5.11a

and 5.12a). However, the methods described in Section 5.3.1 and 5.3.2 present a power

overshoot of tens of kilowatts when a change of reference active power occurs at t=8s and t=15s,

which causes voltage fluctuations, distribution losses, power quality and power balancing

reduction, and increase wear and tear on grid hardware. The proposed coordinated control has

the ability to provide the grid with the desire power at both transient and steady state

environments. PV generation maximum power point can be achieved in this situation due to the

roundness and fast response of applied adaptive MPPT control scheme (Section 3.3.2). The

101

reactive power generated in the grid side keeps at 0Var as designed through GCC direct-current

vector control.

Compared the dc-link voltage results (Figs. 5.10b, 5.11b and 5.12b), the proposed control

method which controls dc-link voltage using direct current control has the most accurate

response to the dc-link voltage. This is due to the reason that direct-current vector control

strategy is applied to the dc/ac inverter. Dc-link Voltage control through ESUs will have a delay

on the dc-link voltage performance because the chemical storage process needs a certain period

of time. Additionally, dc-link voltage control through power-balancing control of ESUs has a

delay response not only due to chemical storage process but also a result from calculation error

of the variation of system parameters and the neglect of power loss in the system.

The charging and discharging-voltage profiles present how battery and SC respond to

power regulations. The charging voltage in SC is continuously increasing because power inflows

to ESU in the whole process. However, the low frequency component in the surplus power

decides the discontinuousness of battery charging voltage and current. In Figs 5.10d, 5.11d and

5.12d, there is a point where SOC is larger than 70%, the charging current is switched to

constant-voltage control which is regulated at 335V. The charging current is smooth because the

initial value is set to be same as constant-current control reference current for the constant-

voltage controller.

The three-phase current waveforms on the grid side are shown in Fig. 5.14. Reactive

power is regulated at 0Var, which indicates that iq =0, therefore, the amplitude of three-phase

current is proportional to the value of id, which is decided by the grid-side power (Fig. 5.14a and

5.12a). A zoomed-in of three-phase currents (Fig. 5.14b) shows that the currents are balanced

and smooth in Opal-RT simulator. This is because RT-Event allows multiple events in a single

102

simulation time-step, and it is used to generate fast and accurate PWM pulses for high-frequency

switches.

3 8 13 18 22-50

-25

0

25

50

Time (s)

Grid

Cur

rent

(A

)

a) Three-phase currents in grid side

12.95 12.975 13 13.025 13.05-50

-25

0

25

50

Time (s)

Grid

Cur

rent

(A

)

b) A zoomed in three-phase currents

Fig. 5.14. Three-phase grid-side currents

So far, this chapter studies the configuration and detailed components of the grid-

connected PV system with energy storage units. It also investigates and compares three

coordinated control designs. In general, the PV array is controlled for MPPT, the battery is used

for slow charging or discharging control, and the suppercapacitor is used for fast charge or

discharge control. However, there are differences in detailed ESU control design depending on

whether the GCC is used for dc-link voltage control or not. If the GCC is used for dc-link

voltage control, the ESUs must be controlled in such a way to meet grid power control demand.

103

If the GCC is used for active power control, the ESUs must provide dc-link voltage control either

directly or through a power balance control mechanism. The simulation results using three

different control schemes shows that when the GCC is used for dc-link voltage and grid reactive

power control, a stable dc-link voltage can be obtained and the integrated PV system can follow

the grid reference power properly.

5.5 Other Applications of Coordinated Control

This dissertation also discusses other applications of coordinated control including the

coordinated control of single-phase system and considering about the ramp rate limit.

5.5.1 Coordinated Control in Single-phase System

With the increasing need for electric power, small distributed generation (DG) systems

are becoming more common. Small DG systems are usually built close to the end-users and they

take advantage of using different energy sources such as wind and solar [105-108]. A few

examples are hybrid cars, solar houses, data centers, or hospitals in remote areas where providing

clean, efficient and reliable electric power is critical to the loads [105-108]. The configuration of

above mentioned systems are similar to Fig.5.8, and the only difference is that there is a single-

phase inverter, which is the only interface between sources connected to DC bus and loads

connected to an AC bus. By using the control method proposed in Section 5.3.3 to the single-

phase grid-connected PV system, the single-phase inverter is responsible for the control of dc-

bus voltage and the AC bus reactive power. AC bus active power management is achieved by

charging and discharging ESUs.

104

The DQ rotating frame transformation used in the direct-current vector control of GCC

makes all time-varying state variables become DC variables, thus making the analysis easier

because the GCC can be treated as a dc-dc converter. Because of the limitation of only one

available phase in single-phase converters, this transformation cannot be realized unless a second

phase is created for every state variable in the circuit. Therefore, based on the real circuit model

of the inverter, an imaginary orthogonal circuit is created [105, 107]. Assuming the steady state

real circuit variable is expressed as

cosR MX X t (5.13)

where, XR is the peak value of sinusoidal waveform which may represent either the voltage or the

current in the rotating frame, φ is the initial phase and ω is the fundamental frequency. Ideally

the corresponding imaginary orthogonal circuit variable would be:

sinI MX X t (5.14)

Equation (5.15) defines the transformation from stationary to rotating frame and from

rotating frame to stationary frame

1d dM M

q qI I

X XX XT and T

X XX X

(5.15)

where,

cos( ) sin( )

sin( ) cos( )

t tT

t t

(5.16)

1 cos( ) sin( )

sin( ) cos( )

t tT

t t

(5.17)

It is important to notice that the variables in the rotating frame become constants (DC

values), as shown in (5.15). Those DC values define the DC operating point of the single-phase

105

converters in the rotating DQ frame. All of the control methods developed for DC/DC converters

can be applied.

Fig. 5.15. Single-phase grid connected solar PV generator under the control of a dc/dc power

converter using SimPowerSystems and Opal-RT RT-LAB

A computational experiment platform of the single-phase grid-connected PV system with

ESUs has also been developed using SimPowerSystems and Opal-RT RT-LAB. Both the real

and imaginary signals are implemented in GCC direct-current vector control (Fig. 5.4) with real

circuit electrical signals as d-axis components and imaginary orthogonal circuit electrical signals

as q-axis components. In this low-voltage DG system, the PV array has a series-parallel

connection configuration having 10 parallel strings with each string consisting of 3 series panels

and the dc bus voltage is initialized and expected to be at 440V. Assuming the solar irradiation is

constant at 750kW/m2 and the ac load changes from -10kW to -2 kW at t=1.5min, and then

changes to -6kW at t=3 min. The reactive power reference is set to be 0kVar practically.

106

0.5 1 1.5 2 2.5 3 3.5 4-12

-8

-4

0

4

Time (min)

P(k

W)a

nd Q

(kV

ar)

PV Load Q

a) Active power of PV system and single-phase load active power and reactive power

0.5 1 1.5 2 2.5 3 3.5 4400

450

500

Time (min)

Dc-

link

Vol

tage

(V)

b) DC-bus voltage

-400

-200

0

200

400

Vol

tage

(V

)

0.5 1 1.5 2 2.5 3 3.5 4-150

-50

50

150

Time (min)

Cur

rent

(A

)

c) Single-phase voltage and current

1.55 1.5505 1.551 1.5515 1.5521.552-400

-200

0

200

400

Vol

tage

(V

)

1.55 1.5505 1.551 1.5515 1.552-150

-50

50

150

Time (min)

Cur

rent

(A

)

d) A zoomed in single-phase voltage and current

Fig. 5.16. Simulation results of the proposed method applications in single-phase inverter

107

Simulation results of the proposed coordinated control method applications in single-

phase inverter and ESUs are shown in Fig. 5.16. In fig. 5.16a, it is shown that the proposed

control method can provide the ac-bus load with the demanded active power when the PV

system outputs a same value of generated power. This is achieved by charging and discharging

battery and SC.

Also, it shows that the GCC vector control effectively maintains the reactive power of

system at 0kVar and regulates the dc-bus voltage at 440V steadily as requested (Fig. 5.16b).

With the steady performance of the DC-link voltage, MPPT enables the system to capture the

maximum power of the PV array, which stays the same value because of the same solar radiation

during this period of time.

Ac-bus load single-phase voltage and current are shown in Fig. 5.16c. The amplitude of

voltage is 220 V and it is noted that the amplitude of current is proportional to the amplitude of

active power. The reason is that the regulated reactive power is 0kVar, which determines that the

q-axis component of current is zero (Eq. 5.6), and then according to Eq. 5.5, the d-axis

component of current is proportional to the active power. Figure 5.16d is a zoomed-in of Fig.

5.16c, where a balanced and smooth profile of single-phase current is presented to demonstrate

the effective real-time simulation of OPAL-RT. As it can be seen from simulation results, the

proposed decoupled vector control can control power feeding into the grid, maintain reactive

power of grid and dc-link voltage.

In conclusion, Section 5.5.1 demonstrates that the proposed coordinated control method

presents its effectiveness in controlling load demand and maintaining dc-bus voltage in a single-

phase system. The control method allows the single-phase inverter for reactive power and dc-link

voltage control, and makes use of ESUs to control the active power flow. The method uses the

108

DQ synchronous reference frame transformation for a single-phase inverter. Therefore, it is

important to create an imaginary orthogonal circuit for control. To validate the control method, a

grid-tied PV system with ESUs model has been built for simulation. Simulation results present

that the synchronous rotating frame current control for the single-phase inverter can fulfill

control objectives of following active and reactive power from the DMS, maintaining the

stability of the dc link voltage of the PV and energy storage system. Therefore, the coordinated

control scheme prosed in Section 5.3.3 can also be applied in single-phase grid-connected PV

system with ESUs.

5.5.2 Coordinated Control Considering about Ramp Rate Limit

Mitigation of the variability in output power of renewable generators such as solar

photovoltaic (PV) systems is a growing concern as these generators reach higher penetrations on

electric grids [109]. Solar resource short-term variability where the PV system is installed may

be high from the standpoint that most days are partly cloudy. The irradiance patterns from a

plane of array (POA) at the Tennessee plant is presented in Ill. 5.1.

It can been seen that some weather events in Ill. 5.1 can increase PV generation from

negligible levels to maximum output in a very short period of time, therefore, PV can have very

volatile real power flows. The resulting output fluctuations can adversely affect the grid in the

form and voltage sags if steps are not taken to quickly counteract the change in generation. In

small power systems, frequency can also be adversely affected by sudden changes in renewable

energy generation. ESUs, whether located at the PV generation system or distributed along a

feeder, can provide power quickly in such scenarios so as to minimize disturbances. With the

proper control schemes, ESUs can mitigate the above challenges while improving system

109

reliability and improving the effectiveness of the renewable resource, thus providing a solution to

the integration of distributed renewable energy sources to the electric grid.

Ill. 5.1 Measured solar irradiance profiles (blue areas) for each day in August 2012 [109]

One-min average data are shown from a POA at the Tennessee plant

In this application, the hybrid system of battery and SC are used to smooth the output

power of a PV array. The proposed control is designed to provide active power support with

power smoothing and power ramp control by charging and discharging ESUs (Fig. 5.17) while

maintaining dc-link voltage by GCC direct vector control shown in Section 5.3.3.

In the control structure for ESUs, the difference between the desired and the actual PV

output power can be either injected or drawn from ESUs. Therefore, this energy becomes the

reference generated/ absorbed power from storage units, Psto_ref.. Reference charging or

110

discharging power of battery Pb_ref is obtained after applying a low-pass filter on Psto_ref , and

then the reference current of battery ib_ref is calculated. The rest is used as the SC reference power

Psc_ref and to calculate reference current of SC, isc_ref.

pvp _sto refp_b refp

_sc refppvv

pvibv

scv

_b refi

_sc refi

bi

1/ dcv

sci1/ dcv

Fig. 5.17. Energy storage units connected converters control structure

ESU control strategy shown in Fig. 5.17 is implemented in the computational experiment

platform (Fig. 5.8) for simulation. To evaluate the control schemes, solar radiation data of two

random days in Adair Casey [54] is used as two simulation scenarios (Fig. 5.18). Because the

data is provided in minute-scale, a linear interpolation is used for prediction of data between

minutes.

0 4 8 12 16 20 240

0.5

1

1.5

Time (h)

Sol

ar R

adia

tion

(kW

/m2)

0 4 8 12 16 20 24

0

0.5

1

1.5

Time (h)

Sol

ar R

adia

tion

(kW

/m2)

a) Scenario 1 b) Scenario 2

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

111

4 6 8 10 12 14 16 18 200

10

20

30

40

50

Time (h)

P(k

W)a

nd Q

(kV

ar)

PPV

PPV

+PESU

Grid Q

a) PV generated power, smooth power

after ESU and grid reactive power

4 6 8 10 12 14 16 18 200

5

10

15

20

Time (h)

P(k

W)a

nd Q

(kV

ar)

P

PV

PPV

+PESU

Grid Q

a) PV generated power, smooth power

after ESU and grid reactive power

13 13.5 14 14.5 15 15.5 16 16.5

10

20

30

40

50

Time (h)

P(k

W)a

nd Q

(kV

ar)

PPV

PPV

+PESU

b) Zoomed-in PV and ESU power of a)

7.5 8 8.5 9 9.5 10 10.5

5

10

15

Time (h)

P(k

W)a

nd Q

(kV

ar)

P

PV

PPV

+PESU

b) Zoomed-in PV and ESU power of a)

4 6 8 10 12 14 16 18 20

-20

0

20

Time (h)

P(k

W)

Battery

SC

c) ESU Charging and discharging power

4 6 8 10 12 14 16 18 20-5

-2.5

0

2.5

5

Time (h)

P(k

W)

Battery

SC

c) ESU Charging and discharging power

4 6 8 10 12 14 16 18 20-30

-15

0

15

30

Time (h)

P(k

W/m

in)

Original

Controlled

d) Comparison of min-to-min ramp rates

Fig. 5.19 Simulation results of scenario 1

4 6 8 10 12 14 16 18 20-10

-5

0

5

10

Time (h)

P(k

W/m

in)

Original

Controlled

d) Comparison of min-to-min ramp rates

Fig. 5.20 Simulation results of scenario 2

112

Figures 5.19 and 5.20 present simulation results in both solar irradiation scenarios, based

on which the following conclusions are obtained:

1) Figures. 5. 19a and 5.20a present the PV generated power, active power injected to

grid and grid reactive power. The reactive power reference can follow the reference at 0kVar.

The power injected to gird consists of PV generated power and ESUs charging and discharging

power. It is noted that the ramp rate refers only to real power, and that the reactive power

capabilities of the ESUs can be dispatched simultaneously and independently to achieve other

power system goals. According to Fig 5.19a, 5.20a and their corresponding zoomed-in in Fig.

5.19b and 5.20b, the power captured by PV array is nearly proportional to the solar irradiation.

Therefore, large amount of solar irradiation fluctuations produce relatively large changes in the

captured PV power. Also, it is observed that the proposed ramp rate control can smooth real

power fluctuations from an associated POA, following the moving average of trend of the PV

output. Therefore, the solar PV system with ESUs inject less fluctuated power into the network.

Different low-pass filter parameters are used in these two scenarios for desired performance.

Therefore, two necessary considerations for the control design are indicated: 1) using dynamic

ramp control instead of fix ramp control; and 2) predicting solar radiation profile.

2) Figure 19c and 20c are the charging and discharging power profiles for two scenarios,

the power profile of SC has a much larger frequency than that of battery. The power output of a

POA does not necessarily consist of an equal number of upward and downward deviations, so

the ESUs could have a tendency to discharge or charge outside of its desired operating range.

Therefore, it is observed that one important factor that needs to be considered when

implementing a ramp rate control, is keeping the battery at an appropriate level of charge. The

historical solar irradiation and its probabilities should be applied to design an economic ESU

113

systems associated with the PV generation. Actually, in this real-time simulation, it is remarked

that those factors that can limit the real power output, including the maximum power generation/

absorption of the ESUs, ESUs current limit, battery state of charge, which are satisfied and

simplified in this dissertation for testing the effectiveness of the proposed control method.

3) 1-min ramp rate of original PV generated power and power after ramp rate control are

presented in Fig. 19d and 20d. 1-minute ramp rate is defined as the absolute value of the

difference between the instantaneous power at the beginning and at the end of a 1-minute period

[111]. It should be noted that ramp rate values are highly dependent on the time range used to

determine the scalar ramp rate value. The 1-second ramp rates are far different than the 10-

minute ramp rate. Formally, ramp rates over different time scales (∆t) can be calculated using the

equation [111]

0 0( ) ( )P t P t t

Ramp Ratet

(5.18)

where, P(t0) and P(to+∆t) are the instantaneous power at t0 and after ∆t. Both comparisons of 1-

minute ramp rate in Fig. 19d and 20d depict the operation of ramp rate control smooth the

volatile ramp rate of PV array under different irradiation profiles. This behavior translates to a

significant reduction in wear and tear on the electrical grid, and helps to maintain system

electrical frequency.

In order to see the performance of ramp rate control, Table 5.2 shows a comparison of

mean and maximum values of ramp rate before and after ramp rate control in two scenarios. In

the table, ramp rate under scenario 1, which has more severe variations in the solar irradiation,

presents a larger improvement in controlled ramp rate value. It is concluded that integration of

ESUs into the grid to manage the real power variability of PV generation by providing ramp rate

114

control can optimize the benefits of PV resources because of the evident reduction of ramp rate

under both scenarios.

Figure 5.21 is profiles of dc-link voltage for two scenarios, which proves that GCC vector

control effectively regulates and maintains the dc-bus voltage at 1500V steadily as desired.

Table 5.2. Comparison of ramp rate value before and after designed

ramp rate control in two scenarios

Study Case

Ramp Rate Scenario 1 (kW/min) Scenario 2 (kW/min)

Mean value before control 3.00 0.12

Mean value after control 0.72 0.07

Maximum value before control 27.47 4.95

Maximum value after control 6.67 1.28

4 6 8 10 12 14 16 18 201480

1490

1500

1510

1520

Time (h)

Dc-

link

Vol

tage

(V)

4 6 8 10 12 14 16 18 201480

1490

1500

1510

1520

Time (h)

Dc-

link

Vol

tage

(V)

a) Scenario 1 b) Scenario 2

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

115

In conclusion, the proposed coordinated control scheme is effective to provide active

power support with power smoothing, power ramp control, and dc-link voltage support.

Coupling PV generation and energy storage devices will drastically increase reliability of the

grid, enables more effective grid management. The rapid-response characteristic of the ESUs

makes storage especially valuable as a regulation resource and enables it to compensate for the

variability of PV generation. It is indicated that both dynamic ramp rate control and solar

radiation profile prediction are necessary for the control design, also, factors that can limit the

real power output include: the maximum power generation/absorption of the ESUs, ESUs current

limit, battery state of charge should be consider for ramp rate control effectively and

economically.

5.6 Conclusion

Energy storage systems are a promising solution regarding the integration of fluctuating

renewable energy into grids. This chapter focuses on control designs of grid-connected

photovoltaic system with ESUs and how to coordinate all the electrical devices in the whole

system by the control of power electronics. In the proposed method, GCC is operated at VQ

mode to maintain a stable dc-link voltage and adapt to the reactive power command, PVCC is

designed to implement the MPPT of PV array, and ESUs connected converters control are

conceived to achieve the power balance of the whole system. A comprehensive computational

simulation study demonstrates that the proposed control structure can effectively supply the

desired reactive and active power to the grid and achieve the stability of dc link voltage through

power electronic converters coordination.

116

The proposed coordinated control has also been modified and tested in other applications

considering single-phase DQ control and ramp rate control. In single-phase grid-connected PV

system with ESUs, it is demonstrated that the proposed method allows inverter for active and dc-

link voltage control with active power buffered through ESUs. An imaginary orthogonal circuit

has been successfully created and applied into the DQ control. In ramp rate control, the proposed

system control scheme can be used to provide active power support with power smoothing,

power ramp control, and dc-link voltage support. Coupling PV generation and storage devices

will drastically increase reliability of the grid, enabling more effective grid management. It is

indicated that parameters of ESUs and desired level of smooth should be taken into consideration

to make control economical.

117

CHAPTER 6

CONCLUSIONS AND FUTURE WORK

6.1 Contributions of the Dissertation

This dissertation demonstrates solar photovoltaic energy generation and conversion from

devices to grid integration.

Firstly, this dissertation investigates solar PV system performance under uneven shading

and dissimilar conditions, especially using both simulation tools and Newton-Raphson algorithm

to study and cross-verify the I-V and P-V characteristics of shaded and unshade cells. It is found

that a traditional PV module with one single shaded cell is the most hazardous condition to affect

proper function of a PV module. It is observed that, with bypass diodes, the performance of PV

device is more complicated and different from the traditional understanding of the PV I-V and P-

V characteristics and each PV cell with a bypass diode will have the most significant

improvement in the performance of a PV module/array under uneven shading.

Secondly, this dissertation provides a fast and robust MPPT technique and compares it

with typical conventional MPPT algorithms used in solar PV industry. Through both software

and hardware simulation, it is concluded that the proposed MPPT approach has the least

oscillation and the highest stability. Both the sampling rate affects and variable solar irradiance

levels are considered in the comparison. The comparison between the traditional and proposed

adaptive methods shows that the hyperbolic processing of the derivation is important for high

performance of a solar PV system.

118

Thirdly, this dissertation compares the energy extraction characteristics of a solar PV

system for different converter schemes, including central, string and micro converter

configurations especially uneven shadings. It is concluded that the central converter based PV

system with properly built-in bypass diodes is an effective and economic approach to improve

efficiency, performance, and reliability of a PV system.

Last but not least, this dissertation discusses control designs of grid-connected

photovoltaic system with ESUs and how to coordinate all the electrical devices in the whole

system by the control of power electronics. In the proposed method, GCC is operated at VQ

mode to maintain a stable dc-link voltage and adapt to the reactive power command, PVCC is

designed to implement the MPPT of PV array, and ESUs connected converters control are

conceived to achieve the power balance of the whole system. A comprehensive computational

simulation study demonstrates that the proposed control structure can effectively supply the

desired reactive and active power to the grid and achieve the stability of dc-link voltage through

power electronic converters coordination. Additionally, the proposed coordinated control has

also been modified and tested in other applications considering single-phase DQ control and

ramp rate control. The simulation results present an effective performance in these two

applications.

6.2 Limitations and Future Work

In ramp rate control of gird-connected PV system with ESUs, it is noted that a dynamic

ramp control design instead of fix ramp is necessary for a practical control in the future work

because of volatile solar radiation.

119

Also, it is not yet considered how to keep ESUs at an appropriate level of charging/

discharging when implementing ramp rate control.

The parameters of ESUs in this dissertation are given ideally to verify the effectiveness of

ramp rate control without optimizing the cost. It is important to design economically considering

factors that can limit the real power output including the maximum power generation/ absorption

of the ESUs, ESUs current limit, ESUs state of charge. With great certainty, we can say that the

demand for development and improvement of grid-integrated renewable energy will remain.

120

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