SOLAR PHOTOVOLTAIC ENERGY GENERATION AND CONVERSION FROM DEVICES TO GRID INTEGRATION HUIYING ZHENG SHUHUI LI, COMMITTEE CHAIR

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1 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

2 Copyright Huiying Zheng 2013 ALL RIGHTS RESERVED

3 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, ii

4 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. iii

5 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. iv

6 LIST OF ABBREVIATIONS AND SYMBOLS I D I S I L R p R s I 0 m q T k I c P s V d V c P c N D N A K Diffusion current Drift current Photogenerated current Parallel resistance accounting for current leakage through the solar cell Series resistance which causes an extra voltage drop between the junction voltage and the terminal voltage of the solar cell Diode reverse saturation current Diode ideality factor Elementary charge Absolute temperature Boltzmann's constant Output current of a solar device Shading factor that the shaded cell is relevant to the unshaded cell P-n junction diode voltages Output voltage of a solar device Generated power of a solar device Net doping concentration in n-type region Net doping concentration in p-type region Approximate constant with respect to temperature v

7 E g Band-gap energy of the semiconductor (ev) S Ratio of the present solar irradiation over the nominal irradiation of 1000W/m 2 I MPP I SC k sc V MPP V OC K oc Current at the maximum power point Short-circuit current of a PV array Ratio of current at the maximum power point to the short-circuit current Voltage at the maximum power point Open-circuit voltage of a PV array Ratio of voltage at the maximum power point to the open-circuit voltage I V Instant conductance a a I V Incremental conductance a a tanh( ) Hyperbolic function SOC i b_ref i sc_ref V dc_ref p sto_ref p dc_ref p g_ref p pv p f i d i q R f State of charge of battery Battery reference current Supercapacitor reference current Dc-link capacitor reference voltage Storage units reference power Dc-link capacitor reference power Grid reference power PV system generated power Power losses in grid filter Grid d-axis current Grid q-axis current Resistance of grid filter vi

8 X R Peak value of sinusoidal waveform X I φ ω T T -1 P(t) Corresponding imaginary orthogonal of X R Initial phase Fundamental frequency Transformation matrix from stationary frame to rotating frame Transformation matrix from rotating frame to stationary frame Instantaneous reactive power vii

9 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 viii

10 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. ix

11 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 Semiconductor Characteristics and Equivalent Model of a Solar Cell Silicon Solar Cell Photogenerated Current and Voltage Equivalent Model of a Solar Cell Energy Extraction Characteristics of PV cells under Uneven Shading Conditions Two Series PV Cells under Uneven Shading Condition PV Module under Uneven Shading Condition Model Validation Bypassing Diode Impact to the Characteristics of Solar PV Cells...22 x

12 2.4 Energy Extraction Characteristics of PV Arrays under Uneven Shading Virtual Transient Experiment Conclusions...33 CHAPTER 3 - A FAST AND RELIABLE APPROACH FOR MAXIMUM POWER POINT TRACKING Extracted Power Characteristics of a PV System The Effect of Temperature The Effect of Illumination Intensity Conventional Fixed-step MPPT Methods Short-Circuit Current Method Open-Circuit Voltage Method Perturb & Observe Method Incremental Conductance Method Adaptive MPPT Strategies Traditional Adaptive MPPT Methods Proposed Hyperbolic -PI (H-PI) Adaptive MPPT Method Computational Experiment MPPT under Step and Ramp Changes of Solar Irradiation Sampling Rate Impact MPPT under Variable Solar Irradiation Condition Hardware Experiment and Comparison Laboratory Setup and Design Experiment Analysis and Comparison Conclusions...61 xi

13 CHAPTER 4 - PV ENERGY EXTRACTION CHARACTERISTICS STUDY UNDER SHADING CONDITIONS FOR DIFFERENT CONVERTER CONFIGURATIONS Configurations of Grid-connected Solar PV Systems Power Converters Architecture of PV Arrays Central Dc/ac and Dc/dc Converters Central Dc/ac Inverter and String Dc/dc Converters Dc/dc Optimizers Detached Microinverters Central and String Inverters PV Array Models for Different Converter Configurations PV System Energy Extraction Characteristics without Bypass Diodes Central Converter Configuration String Converter Configuration Micro-inverter Configuration PV System Energy Extraction Characteristics with Bypass Diodes Central Converter Configuration String Converter Configuration Comparison of Maximum Power Using Central, String and Micro Converter Configuration Conclusion...83 CHAPTER 5 - COORDINATED CONTROL FOR GRID INTEGRATION OF PV ARRAY, BATTERY STORAGE, AND SUPERCAPACITOR WITH RELATED ISSUES Grid-connected PV and Energy Storage System Photovoltaic Arrays...86 xii

14 5.1.2 Rechargeable battery Supercapacitor Grid-Connected Converter Integrated Control System Coordinate PV Array, ESU and GCC Control Control of Bi-directional Dc/dc Converters for ESUs Direct-Current Vector Control of GCC Coordinated Control Mechanisms for Grid Integration Dc-link Voltage Control through ESUs Power Balancing Control of ESUs Dc-link Voltage Control through GCC Coordinated Control Evaluation and Comparison Other Applications of Coordinated Control Coordinated Control in Single-phase System Coordinated Control Considering about Ramp Rate Limit Conclusion CHAPTER 6 - CONCLUSIONS AND FUTURE WORK Contributions of the Dissertation Limitations and Future Work REFERENCES xiii

15 LIST OF TABLES 3.1 Comparison of MPPT methods Comparison of maximum power extraction without bypass diodes for different converter configurations Comparison of maximum power extraction under 50% shading factor Comparison of maximum power extraction under 100% shading factor Parameters of electrical components in grid-integrated PV system Comparison of ramp rate value before and after designed ramp rate control in two scenarios xiv

16 LIST OF FIGURES 2.1. Diffusion current, drift current, and depletion zone of a p-n junction Illustration of drift current as well as photogenerated current and voltage Solar cell equivalent circuit model Solar cell I-V and P-V characteristics Two series PV cells with uneven shading Characteristics of two series solar cells A PV module connected to an external circuit Characteristics of PV module (one cell shaded) Characteristics of PV module (18 cells shaded) Schematics of a PV module connected with bypassing diodes, created by NI Multisim Characteristics of a PV module (3 cells with a bypass diode) Characteristics of a PV module (9 cells with a bypass diode) Characteristics of a PV module (18 cells with a bypass diode) Bypass and blocking diodes in a solar PV generator PV array characteristics (without bypass diode) PV array characteristics (one module with a diode) PV array characteristics (each cell with a bypass diode) Solar PV generator under an open-loop controlled dc/dc power converter.. 31 xv

17 2.19. Transient simulation results of a PV array relevant to the 100% shading condition applied in Fig Configuration of grid-connected solar PV system Typical daily temperature and irradiation plots P-V characteristics of a PV array vs. temperature and voltage Derivative of power over terminal voltage under different temperatures P-V characteristics of a PV array vs. irradiation and voltage Derivative of power over terminal voltage under different irradiations Graphic relation of I MPP over I SC and V MPP over V OC Conventional MPPT methods of SCC and OCV Flowchart of the fixed step P&O algorithm Flowchart of the incremental conductance algorithm PI based MPPT control loop diagram of the PV system A tangent sigmoid function for adaptive MPPT Control loop diagram of proposed adaptive MPPT Solar PV generator with the MPPT and grid-integration using SPS and Opal-RT RT-LAB MPPT digital control module Step and ramp changes of irradiation Comparison of MPPT under step and ramp changes of solar irradiation levels Dc-link voltage Three-phase grid-side currents Dc/ac inverter power at the grid side MPPT comparison under different sampling rates...56 xvi

18 3.22. MPPT comparison of under variable solar irradiation condition Hardware experiment setup for evaluation of MPPT algorithms Hardware experiment of captured maximum power using conventional and proposed MPPT algorithms PV array with central dc/ac and dc/dc converter structure PV array with central dc/ac inverter and string dc/dc converters Dc/dc optimizers per module and a central inverter Detached microinverter PV system PV array with central and string inverters Characteristics of PV array with central converter Characteristics of series PV strings with shaded cells Characteristics of PV module under shading conditions Characteristics of PV array under shading conditions Characteristics of PV array for different bypass diode schemes Characteristics of series PV strings Configuration of grid-connected PV system with ESUs Block diagram of nested-loop battery control strategy GCC converter schematic GCC direct-current vector control structure Control of dc-link voltage through ESUs Power balance control structure of ESUs Energy storage units connected converters control structure Solar PV generator under the control of a dc/dc power converter using SPS and Oparl-RT RT-LAB Solar PV array characteristics used in simulation...98 xvii

19 5.10. Simulation results of the control scheme in Section Simulation results of the control scheme in Section Simulation results of the control scheme in Section Solar irradiation over the nominal irradiation of 1000W/m Three-phase grid-side currents Single-phase grid connected solar PV generator under the control of a dc/dc power converter using SPS and Opal-RT RT-LAB Simulation result of the proposed method applications in single-phase inverter Energy storage units connected converters control structure Hourly solar radiation data of two random days in Adair Casey Simulation results of scenario Simulation results of scenario Dc-link voltages of two solar irradiation scenarios xviii

20 LIST OF ILLUSTRATIONS 4.1 Configuration of grid-connected solar PV system Measured solar irradiance profiles for each day in August xix

21 CHAPTER 1 INTRODUCTION Investment in solar photovoltaic (PV) energy is rapidly increasing worldwide [1]. A gridconnected 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 1

22 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 2

23 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 3

24 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 4

25 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 gridconnected 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. 5

26 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 photogenerated charge carries. Therefore, semiconductor layers are the most important parts of a solar cell 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 6

27 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 I D from the p side to the n side (Fig. 2.1a). When the electrons diffuse across the p-n junction, they recombine with holes on the p-type side. The diffusion of 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 I S, that opposes and eventually balances out the diffusion current I D. The region where electrons and holes have diffused across the junction is called the depletion zone (Fig.2.1b). (a) Diffusion current I D from the p side to the n side (b) Drift current I S from the n side to the p side and the depletion zone Fig Diffusion current, drift current, and depletion zone of a p-n junction 7

28 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 I D balancing out the drift current I S until a new equilibrium state is reached inside a solar cell. Fig Illustration of drift current as well as photogenerated current and voltage 8

29 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 so that the net output current of the solar cell is reduced. Fig 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 I L, in parallel with a diode, representing the p-n junction of a solar cell. In a real solar cell, there exist other effects, not accounted for by the ideal model. 9

30 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 R p 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 R s, 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 qv d V mkt d I I I0 e 1, V V I R Rp c L c d c s (2.1) where I L is proportional to the sunlight illumination intensity, m is the diode ideality factor (1 for an ideal diode), the diode reverse saturation current I 0 depends on temperature, q is the elementary charge, k is the Boltzmann's constant, and T is the absolute temperature [22]. For all the studies presented in this dissertation, I L =6A, I 0 = A, R P =6.6Ω, R S =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 I c and power P c versus output voltage V c characteristics. Figure 2.4 shows typical I-V and P-V characteristics of a solar cell under ideal condition and with the consideration 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 10

31 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 Solar cell I-V and P-V characteristics (T = 25 C, I 0 = A, I L = 6A, R p =6.6 and R s = ) 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] 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 11

32 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. Rs1 IL1 IL2 Rp1 Rp2 Rs2 Vs Fig 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 12

33 I I I e V V V I R qv d 1 c mkt d1 L 0 1, c1 d1 c Rp s (2.2) I p I I e V V V I R qv d 2 c mkt d 2 (1 s) L 0 1, c2 d2 c Rp s (2.3) V V V (2.4) s c1 c2 where p s stands for the shading factor that the shaded cell is relevant to the unshaded cell, and I L represents the photogenerated current of unshaded cell under the full sun condition, V d1 and V d2 and V c1 and V c2 represent p-n junction diode voltages and output voltages of the unshaded and shaded cells, respectively. Based on (2.2) to (2.4), a system of nonlinear equations can be developed as f V, V 0 f V, V 0 (2.5) 1 d1 d2 2 d1 d2 Then, for a given voltage applied to the PV cells, voltage V d1 and V d2 can be solved numerically by using Newton-Raphson algorithm in the following steps: a) Initial estimation: b) Compute Jacobian matrix: Vd d1, d2 V V (2.6) k k f1 Vd1 f1 V d2 J k k (2.7) f2 Vd1 f2 Vd2 c) Compute correction k V d and update PV cell voltage V : k 1 d V V V (2.8) k 1 k k d d d d) Error calculation: k 1 k 1 Vd Vd err f f (2.9) 13

34 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 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 14

35 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 I 0 and I L 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 15

36 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 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 16

37 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 p i. Then, the mathematical model of a PV module under a shading condition is described by: I p I I e V V V I R qv di mkt di c (1 i) L 0 1, ci di c s Rp (2.10) V V V V V (2.11) s c1 c2 c( n 1) cn where p i stands for the shading factor of the ith cell relevant to the full sun condition, I L represents the full sun photogenerated current, and V di and V ci are the p-n junction diode voltages and output voltages of the ith PV cell. Similar to Section 2.2.1, a system of N nonlinear equations can be developed as shown by (2.12). f V,, V 0 f V,, V 0 (2.12) 1 d1 dn N d1 dn Then, for a given voltage applied to a PV module, voltage V d1, V d2, V dn 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 V d1, V d2, V dn 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 17

38 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]. Shade Vs Fig 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 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. 18

39 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 e) Shaded cell terminal voltage characteristics f) Shaded cell P-V characteristics Fig 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 19

40 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 e) Shaded cell terminal voltage characteristics f) Shaded cell P-V characteristics Fig Characteristics of PV module (18 cells shaded) 20

41 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 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 R p and R s, must be identified first. These can be obtained through parameter extraction, such as the procedure shown in [29, 30]. The parameter 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 21

42 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 22

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