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An approach to reduce the effect of partial shading on photovoltaic modules Chaw, Cheng Long 2015

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AN APPROACH TO REDUCE THE EFFECT OF PARTIAL SHADING ON PHOTOVOLTAIC MODULES  by Cheng Long Chaw   B.A.Sc., The University of British Columbia, 2012  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF  THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES  (Electrical and Computer Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA  (Vancouver)  August 2015  © Cheng Long Chaw, 2015   ii  ABSTRACT Partial shading (PS) losses occur when some photovoltaic (PV) cells in a PV array, panel, or module are shaded from the illuminating light source. Such a phenomenon causes a substantial reduction in power generation, and it is seen to be an inevitable problem in maximizing the efficiency of the entire PV system, especially in the case of small-scale urban implementations, where the location choices are often suboptimal and shading obstacles are commonly encountered. Therefore, this thesis proposes a robust technique to reconfigure a PV module’s connection pattern in order to passively reduce the effect of PS by dispersing the shade to other parts of the module without either intensely modifying the circuitry or requiring the introduction of additional electronic devices. An ideal single-diode model of the PV cell is used to simulate and compare the performance of PV modules using different connecting methodologies, including the proposed strategy under extensive PS conditions. The proposed configuration is able to obtain improved maximum power points (MPP(s)), while displaying fewer significant disadvantages that the other shade dispersion methods have exhibited. It also shows fewer scalability limitations after ensuring the PV module is reasonably sufficient in size, as there is no requirement on the scale and the parity combination from its numbers of rows and columns. Moreover, under the placement rules of the proposed strategy, only alternating, and therefore no more than half of the columns in the configuration, are required to be changed, thus making the process modularizable, and reducing the total implementation costs. Furthermore, the resulting PV characteristic curves are shown to have more distinct MPP after utilizing the shade dispersion strategy, which become more convenient for following MPP tracking controls if desired. Finally, a PV module prototype, consisting of 6 x 6 PV cells, is implemented, and the experimental results validate the effectiveness of the proposed shade dispersion approach. The achieved MPP improvements are found to be better than the other tested shade dispersion method if the shade comes with an angle, and significantly better than the typical series-parallel or the total-cross-tied configuration when the shade is substantial in size.   iii  PREFACE This dissertation is original, unpublished, and represents independent work performed by the author, C. L. Chaw.   iv  TABLE OF CONTENTS Abstract ............................................................................................................................... ii Preface................................................................................................................................ iii Table of Contents ............................................................................................................... iv List of Tables .................................................................................................................... vii List of Figures .................................................................................................................. viii List of Symbols ................................................................................................................. xii Acknowledgements .......................................................................................................... xiii Dedication ........................................................................................................................ xiv 1 Introduction ................................................................................................................. 1 1.1 Background .......................................................................................................... 1 1.2 Motivation and Objectives ................................................................................... 3 1.3 Thesis Overview ................................................................................................... 4 2 Literature Review ........................................................................................................ 6 2.1 Photovoltaic Effect ............................................................................................... 6 2.2 Types of Photovoltaic Cell ................................................................................... 6 2.3 Solar Spectrum ..................................................................................................... 7 2.4 Partial Shading ..................................................................................................... 7 2.5 Shade Dispersion Techniques .............................................................................. 9 3 Photovoltaic Cell Modelling ...................................................................................... 11 3.1 Photovoltaic Cell Models ................................................................................... 11 3.1.1 The Single-Diode Model............................................................................. 11 3.1.2 The Double-Diode Model ........................................................................... 13 3.2 Software Implementation ................................................................................... 14 3.2.1 Photocurrent Equation ................................................................................ 14 v  3.2.2 Reverse Saturation Current Equation.......................................................... 15 3.2.3 Shunt Current Equation............................................................................... 15 3.2.4 Load Current and Thermal Voltage Equations ........................................... 15 3.2.5 Diode Current Equation .............................................................................. 16 3.3 Simulations and Performance Results ................................................................ 16 3.3.1 Change of Cell Number in Series or in Parallel .......................................... 17 3.3.2 Change of Solar Irradiation ......................................................................... 19 3.3.3 Change of Operating Temperature .............................................................. 20 3.4 Chapter Summary ............................................................................................... 21 4 Shade Dispersion Technique ..................................................................................... 22 4.1 Partial Shading Conditions ................................................................................. 22 4.1.1 Shadow Shape ............................................................................................. 22 4.1.2 Shading Factor ............................................................................................ 24 4.1.3 Rearranged PS patterns ............................................................................... 25 4.2 The Proposed Strategy ....................................................................................... 26 4.3 Simulations and Performance Results ................................................................ 29 4.3.1 6 x 6 PV Modules Comparisons ................................................................. 29 4.3.2 6 x 7, 7 x 6, and 7 x 7 PV Modules Comparisons....................................... 32 4.4 Chapter Summary ............................................................................................... 43 5 Experimental Validation ............................................................................................ 44 5.1 Equipment Used ................................................................................................. 44 5.2 Short Circuit Current vs. Shade Displacement................................................... 45 5.3 Experimental Results.......................................................................................... 47 5.3.1 No Shade and Long-Narrow Shade ............................................................ 47 5.3.2 Long-Wide Shade ....................................................................................... 49 vi  5.3.3 Short-Narrow Shade.................................................................................... 53 5.3.4 Short-Wide Shade ....................................................................................... 57 5.3.5 Diagonal Shade ........................................................................................... 61 5.4 Results Evaluation .............................................................................................. 65 5.5 Chapter Summary ............................................................................................... 66 6 Conclusions ............................................................................................................... 67 6.1 Advantages and Limitations ............................................................................... 67 6.2 Possible Future Work ......................................................................................... 67 References ......................................................................................................................... 68 Appendices ........................................................................................................................ 78 Appendix A: Block Diagrams of SDM ......................................................................... 78 Appendix B: Simulated Configurations ........................................................................ 82 Appendix C: Code for Figure Plotting .......................................................................... 84    vii  LIST OF TABLES Table 3-1 Electrical parameters used in the simulation. ................................................... 17 Table 4-1 Summary of each configuration’s MPP under simulated PS conditions. ......... 43 Table 5-1 Experimental data for PV panel under no shade, and long-narrow shade. ....... 47 Table 5-2 Experimental data for PV panel under long-wide shade. ................................. 52 Table 5-3 Experimental data for PV panel under short-narrow shade. ............................. 56 Table 5-4 Experimental data for PV panel under short-wide shade. ................................ 60 Table 5-5 Experimental data for PV panel under diagonal shade. ................................... 64 Table 5-6 Summary of the maximum power point achieved in % comparison. ............... 65   viii  LIST OF FIGURES Figure 2.1 Before and after the Su-Do-Ku reconfiguration. ............................................. 10 Figure 2.2 Before, after, and weakness of stepwise reconfiguration. ............................... 10 Figure 3.1 Equivalent circuits: ISDM; SSDM; SDM; DDM (from left to right). ............ 11 Figure 3.2 Top-level overview of the single-diode model implementation...................... 16 Figure 3.3 Effect of changing the PV cell number in series. ............................................ 17 Figure 3.4 Effect of changing the PV cell number in parallel. ......................................... 18 Figure 3.5 Effect of changing the solar irradiation strength. ............................................ 19 Figure 3.6 Effect of changing the PV cell temperature. ................................................... 20 Figure 4.1 Four different PS conditions. ........................................................................... 22 Figure 4.2 Shade (original): long-narrow (6 x 6). ............................................................. 23 Figure 4.3 Shade (original): long-wide (6 x 6). ................................................................ 23 Figure 4.4 Shade (original): short-narrow (6 x 6). ............................................................ 23 Figure 4.5 Shade (original): short-wide (6 x 6). ............................................................... 23 Figure 4.6 Shade (original): diagonal (6 x 6). ................................................................... 23 Figure 4.7 Shade (shading factor): long-narrow (6 x 6). .................................................. 24 Figure 4.8 Shade (shading factor): long-wide (6 x 6). ...................................................... 24 Figure 4.9 Shade (original): short-narrow (6 x 6). ............................................................ 24 Figure 4.10 Shade (shading factor): short-wide (6 x 6). ................................................... 24 Figure 4.11 Shade (shading factor): diagonal (6 x 6). ...................................................... 25 Figure 4.12 Shade (stepwise): long-narrow (6 x 6). ......................................................... 25 Figure 4.13 Shade (stepwise): long-wide (6 x 6). ............................................................. 25 Figure 4.14 Shade (stepwise): short-narrow (6 x 6). ........................................................ 25 Figure 4.15 Shade (stepwise): short-wide (6 x 6). ............................................................ 26 Figure 4.16 Shade (stepwise): diagonal (6 x 6). ............................................................... 26 Figure 4.17 Solar panel 6x6 cell matrix using the proposed rearrangement. ................... 27 Figure 4.18 Proposed rearrangement: even (left); odd (right) number of rows and columns. ............................................................................................................................ 27 Figure 4.19 Mathematical generalization of the proposed strategy. ................................. 28 Figure 4.20 Shade (proposed): long-narrow (6 x 6). ........................................................ 28 ix  Figure 4.21 Shade (proposed): long-wide (6 x 6). ............................................................ 28 Figure 4.22 Shade (proposed): short-narrow (6 x 6). ........................................................ 28 Figure 4.23 Shade (proposed): short-wide (6 x 6). ........................................................... 29 Figure 4.24 Shade (proposed): diagonal (6 x 6). .............................................................. 29 Figure 4.25 Curves under long-narrow shade (6 x 6). ...................................................... 30 Figure 4.26 Curves under long-wide shade (6 x 6). .......................................................... 30 Figure 4.27 Curves under short-narrow shade (6 x 6). ..................................................... 31 Figure 4.28 Curves under short-wide shade (6 x 6). ......................................................... 31 Figure 4.29 Curves under diagonal shade (6 x 6). ............................................................ 32 Figure 4.30 Shade (stepwise): long-wide (6 x 7). ............................................................. 32 Figure 4.31 Shade (stepwise): long-wide (7 x 6). ............................................................. 32 Figure 4.32 Shade (stepwise): long-wide (7 x 7). ............................................................. 33 Figure 4.33 Shade (proposed): long-wide (6 x 7). ............................................................ 33 Figure 4.34 Shade (proposed): long-wide (7 x 6). ............................................................ 33 Figure 4.35 Shade (proposed): long-wide (7 x 7). ............................................................ 33 Figure 4.36 Shade (stepwise): diagonal (6 x 7). ............................................................... 33 Figure 4.37 Shade (stepwise): diagonal (7 x 6). ............................................................... 34 Figure 4.38 Shade (stepwise): diagonal (7 x 7). ............................................................... 34 Figure 4.39 Shade (proposed): diagonal (6 x 7). .............................................................. 34 Figure 4.40 Shade (proposed): diagonal (7 x 6). .............................................................. 34 Figure 4.41 Shade (proposed): diagonal (7 x 7). .............................................................. 34 Figure 4.42 Curves under long-narrow shade (6 x 7). ...................................................... 35 Figure 4.43 Curves under long-wide shade (6 x 7). .......................................................... 35 Figure 4.44 Curves under short-narrow shade (6 x 7). ..................................................... 36 Figure 4.45 Curves under short-wide shade (6 x 7). ......................................................... 36 Figure 4.46 Curves under diagonal shade (6 x 7). ............................................................ 37 Figure 4.47 Curves under long-narrow shade (7 x 6). ...................................................... 37 Figure 4.48 Curves under long-wide shade (7 x 6). .......................................................... 38 Figure 4.49 Curves under short-narrow shade (7 x 6). ..................................................... 38 Figure 4.50 Curves under short-wide shade (7 x 6). ......................................................... 39 Figure 4.51 Curves under diagonal shade (7 x 6). ............................................................ 39 x  Figure 4.52 Curves under long-narrow shade (7 x 7). ...................................................... 40 Figure 4.53 Curves under long-wide shade (7 x 7). .......................................................... 40 Figure 4.54 Curves under short-narrow shade (7 x 7). ..................................................... 41 Figure 4.55 Curves under short-wide shade (7 x 7). ......................................................... 41 Figure 4.56 Curves under diagonal shade (7 x 7). ............................................................ 42 Figure 5.1 Hardware set-up overview. .............................................................................. 44 Figure 5.2 Panel of cells in TCT configuration. ............................................................... 44 Figure 5.3 Light source ratings. ........................................................................................ 45 Figure 5.4 A single multi-crystalline silicon cell. ............................................................. 46 Figure 5.5 A shade obstacle with some interval measurements. ...................................... 46 Figure 5.6 Short circuit current vs. displacement (width). ............................................... 46 Figure 5.7 Short circuit current vs. displacement (length). ............................................... 46 Figure 5.8 PV panel under long-narrow shade. ................................................................ 47 Figure 5.9 Curves under no shade (experimental vs simulated). ...................................... 48 Figure 5.10 Curves under long-narrow shade (experimental vs simulated). .................... 48 Figure 5.11 PV panel under long-wide shade as TCT. ..................................................... 49 Figure 5.12 PV panel under rearranged long-wide shade as stepwise. ............................. 49 Figure 5.13 PV panel under rearranged long-wide shade as proposed. ............................ 49 Figure 5.14 Curves under long-wide shade as TCT (experimental vs simulated). ........... 50 Figure 5.15 Curves under long-wide shade as stepwise (experimental vs simulated). ..... 50 Figure 5.16 Curves under long-wide shade as proposed (experimental vs simulated). .... 51 Figure 5.17 Experimental curves under long-wide shade (TCT vs stepwise vs proposed)............................................................................................................................................ 52 Figure 5.18 PV panel under short-narrow shade as TCT.................................................. 53 Figure 5.19 PV panel under rearranged short-narrow shade as stepwise. ........................ 53 Figure 5.20 PV panel under rearranged short-narrow shade as proposed. ....................... 53 Figure 5.21 Curves under short-narrow shade as TCT (experimental vs simulated). ...... 54 Figure 5.22 Curves under short-narrow shade as stepwise (experimental vs simulated). 54 Figure 5.23 Curves under short-narrow shade as proposed (experimental vs simulated). 55 Figure 5.24 Experimental curves under short-narrow shade (TCT vs stepwise vs proposed)........................................................................................................................... 56 xi  Figure 5.25 PV panel under short-wide shade as TCT. .................................................... 57 Figure 5.26 PV panel under rearranged short-wide shade as stepwise. ............................ 57 Figure 5.27 PV panel under rearranged short-wide shade as proposed. ........................... 57 Figure 5.28 Curves under short-wide shade as TCT (experimental vs simulated). .......... 58 Figure 5.29 Curves under short-wide shade as stepwise (experimental vs simulated). .... 58 Figure 5.30 Curves under short-wide shade as proposed (experimental vs simulated). ... 59 Figure 5.31 Experimental curves under short-wide shade (TCT vs stepwise vs proposed)............................................................................................................................................ 60 Figure 5.32 PV panel under diagonal shade as TCT. ....................................................... 61 Figure 5.33 PV panel under rearranged diagonal shade as stepwise. ............................... 61 Figure 5.34 PV panel under rearranged diagonal shade as proposed. .............................. 61 Figure 5.35 Curves under diagonal shade as TCT (experimental vs simulated). ............. 62 Figure 5.36 Curves under diagonal shade as stepwise (experimental vs simulated). ....... 62 Figure 5.37 Curves under diagonal shade as proposed (experimental vs simulated). ...... 63 Figure 5.38 Experimental curves under diagonal shade (TCT vs stepwise vs proposed). 64   xii  LIST OF SYMBOLS PV  Photovoltaic PS  Partial Shading MPPs  Maximum Power Points MPPT  Maximum Power Point Tracking Irr  Solar irradiation, insolation AM  Air Mass SDM  Single-diode Model ISDM  Ideal Single-diode Model SSDM  Simplified Single-diode Model DDM  Double-diode Model I  Current V  Voltage P  Power R  Resistance RS  Series Resistance RP / RSH  Shunt Resistance IPH  Photon (Sun) Current ID  Diode Current SP  Series-Parallel TCT  Total-Cross-Tied NS  No Shade LN  Long-Narrow Shade LW  Long-Wide Shade SN  Short-Narrow Shade SW  Short-Wide Shade DI  Diagonal Shade   xiii  ACKNOWLEDGEMENTS My sincere thanks to my supervisor, Dr. William G. Dunford, for his professional guidance, ideas that motivated me to research into this thesis, and his efforts to ensure me succeeding in my graduate studies.  My sincere thanks to my co-supervisor, Dr. Stephen O’Leary, for his constructive suggestions, feedback, and reviews of my thesis. Special thanks to the Kaiser 3075 Lab coordinator, Dr. Martin Ordonez, for allocating the required bench space and equipment to conduct my hardware implementations and experiments. Special thanks to all the colleagues and friends in Kaiser 3085 Lab, it is a pleasure to share the same office with them. Lastly, my utmost gratitude to the encouragement and support from my dearest family.   xiv  DEDICATION           To my father John, my mother Alice, and my sister Sophie          1  1 INTRODUCTION 1.1 BACKGROUND One of the ways to categorize energy resources is based on a consideration of their sustainability and renewability [1, 2]. Fossil fuels, such as coal, oil, and natural gas, are examples of conventional energy resources that are not sustainable and non-renewable [2]. On the other hand, biomass and biofuels, geothermal energy, hydropower, wave and tidal power, solar and wind power are types of sustainable and renewable energy sources [2]. Then, there is also nuclear power, which is technically not renewable because it uses nuclear fuel, such as uranium, as a consumable during generation, and it is also hardly sustainable concerning the radioactive waste it creates. However, it is considered as one of the low-carbon power generation sources [3], similar to hydropower, solar, and wind power, hence it is sometimes still classified as a clean alternative energy source in spite of its arguable sustainability.  It is a well-known fact that the world’s demand for electricity has been growing over the past few decades and that this trend shows no sign of diminishing for the foreseeable future. The demand for electrical energy will remain strong, and with technological advancements, in addition to increased public awareness, it is not surprising to see that the usage of renewable energy sources has increased over the time [4]. According to a 2014 energy statistics publication from the International Energy Agency (IEA), in 1973, the distribution of the fuel supply for electricity generation was 38.3% coal, 24.8% oil, 20.9% hydro, 12.1% natural gas, 3.3% nuclear, and 0.6% other sources; in 2012, the distribution was 40.4% coal, 22.5% natural gas, 16.2% hydro, 10.9% nuclear, 5.0% oil and 5.0% other sources [4]. It is clear that there has been a significant drop in oil consumption for electricity generation, and part of the demand for electricity is being replaced by the increasing supplies from renewable energy sources, which have increased by more than five times over the past few decades. This might be mostly due to various economic reasons, but the role of technological improvements driven from academic researchers in many fields, have also played an important role in this worldwide change over the years.  2  One of the motivations to research better technology in the energy field is to create more effective solutions in meeting the present energy demands without compromising the capability of future generations in meeting theirs. As a matter of fact, most human activities rely heavily on the consumption of energy and during the process, part of the energy is wasted, usually in the form of pollution. To recover and reuse this otherwise wasted energy, researchers have developed more efficient and cost effective technologies with reduced environmental impact. For example, new household appliances, such as refrigerators, use substantially less energy than their older counterparts. According to a study from McKinsey & Company, the increased installation of new energy efficient household appliances is one of the best global solutions to reduce greenhouse gas emissions [5]. Another example is the creation of energy-efficient vehicles, these vehicles utilizing better aerodynamics and reduced weight in order to further improve fuel economy [6]. Hybrid vehicles can also use regenerative braking in order to recapture energy that would otherwise be wasted in conventional vehicles [7, 8]. In addition, environmentally friendly laws and habits have been designed and established through public education or monetary incentives [9] in order to increase the efficiency of energy usage. For instance, the public can be rewarded with cheaper electricity if the consumption is to occur during off-peak periods when the overall energy demand is low. Affordable energy costs are one of the prime foundations for a healthy economy and a politically stable society. Unfortunately, different distributions of energy resources throughout the world have created boundless energy competitions between countries, especially those that rely heavily on energy imports. Hence, the degree of vulnerabilities of a country’s energy reserve is its energy security, and it can be effectively improved with more national renewable energy sources that have no dependence on imports [2]. Renewable energy is generally seen as energy that comes from naturally replenishable resources, and based on the definition of renewable energy technology from the IEA, technologies utilizing renewable energy can be classified into three generations [10]. The first generation technologies can be traced back to the 19th Century industrial revolution, including biomass, geothermal, and hydro, which are still widely in use today [10]. Second generation technologies are modern forms of biomass, solar, and wind power. Most of them are currently in the market with government incentives to ensure cost 3  reduction as a result of market learning, which provides complementary improvements as manufacturers refine products and manufacturing processes [10]. Third generation technologies are those which are still under development and are not yet widely commercialized, these newest technologies including advanced biomass gasification, bio-refinery technologies, concentrating solar power, hot rock geothermal power, ocean energy, and advances in nanotechnology [10]. On the whole, the significance of renewable energy technologies are that they are essential contributors to energy security by reducing dependence on imported resources and ensure independent energy supplies. Most importantly, they also lower the climatological effects of conventional energy sources, such as global warming.  Numerous studies into renewable energy technologies have been conducted, most for the environmental reasons and economic benefits explained in this section. This thesis will share the same inspiration, and solar power will be the technology being investigated. Being one of the well-established second generation renewable technologies, solar power is reliable using the Sun as the energy source. It also has a low maintenance cost due to its static nature and is highly modular because of its scalable panel design [11, 12, 13, 14, 15]. However, its output can be severely hindered from undesirable environmental factors, such as partial shading (PS) causing low power generation efficiency [16, 17]. To elaborate more, the physical operation of a photovoltaic (PV) cell, the effect of PS, and some of the solutions researchers have developed to tackle this problem, will be briefly explained in the literature review in the following chapter. Furthermore, a detailed motivation of this thesis and the objectives it tries to achieve are explained in the coming section. 1.2 MOTIVATION AND OBJECTIVES In this thesis, the motivation is to contribute to the energy development of solar power by providing a solution to tackle the problem of PS. An alternative passive PS reduction strategy, that utilizes the shade dispersion technique, is proposed and explored, this strategy involving rearranging the photovoltaic (PV) cell pattern in the module using an unique set of placement rules to distribute the effect of the shaded area over the entire 4  board, thus reducing the overall effect of PS and improving the power generation efficiency by increasing the attainable maximum power point (MPP). The objectives can be divided into three main parts: first, to create a simulation model of the PV cell using the equations derived, and to confirm that it can match the expected basic properties of a real cell. Second, using the verified model to simulate against different PS conditions in different module configurations, including the proposed rearrangement, then to compare their performance using their respective current-voltage (I-V) and power-voltage (P-V) characteristics curves, and to see if the proposed strategy can offer improved results. Third, to implement a validation experiment, and to see if the experimental data acquired are similar to the simulation results, so as to practically confirm the effectiveness of the proposed strategy.  1.3 THESIS OVERVIEW Chapter 1 gives an overview of energy resources and the technology advancements that have occurred in the utilization of these resources over the years. The background of renewable energy technologies is also briefly explained, leading to the establishment of the thesis motivation on solar power. Then, the main objectives of this thesis are explained, which is to propose and experiment the effectiveness of a new reconfiguration strategy that utilizes the idea of shade dispersion in order to reduce the impact of the PS effect. Chapter 2 is a literature review. It introduces basic the physical operation of a PV cell, difference between the mono-crystalline and multi-crystalline structures, general background of the solar spectrum, definition of the standard testing conditions, and the problem of PS with its negative effect on the performance of PV modules as well as the strategies presently used in order to reduce such an effect. It then further reviews an alternative PS reduction technique of shade dispersion that the proposed rearrangement is built on and improved upon.  Chapter 3 introduces the types of models that can be used to simulate a PV cell. Equations of the single-diode model and double-diode model are presented, and a simplified version of the single-diode model is chosen and modeled for simulations using 5  parameters from a real solar panel (BP-350). PV characteristics curves are acquired and evaluated under different physical and environmental conditions, such as changing the number of cells in series or parallel, the operating temperature, and the solar irradiation strength in order to demonstrate the validity of the simulation model used.  Chapter 4 presents the proposed strategy and the placement rules used to obtain the reconfiguration. Then it compares the simulations results under different PS conditions between the configurations, including those presently used or introduced from other literature, this being used to demonstrate the performance difference and the effectiveness of using the proposed shade dispersion method. It is important to note that a rearranged version of the PS patterns is used for the shade dispersion rearrangement, so that the same structure of the simulation model can be re-used for more configurations. The results are shown with their respective I-V and P-V curves, evaluations and summary are also provided at the end. Chapter 5 provides the experimental validation of the proposed strategy. A prototype 6 x 6 PV module is implemented in order to experiment the performance difference between the older configurations, and the newly proposed strategy in a practical perspective. Information on the testing conditions, such as the solar irradiation strength, the type of PV cell used, and the measuring tools used, is also presented. Additionally, an experiment is conducted to measure the performance of a single PV cell against a series of fixed intervals of shade, this being to investigate if the metal grid on the cell surface will play a role in PS. The experimental results are then compared to the simulation ones, and between each configuration, with their respective I-V and P-V curves under each PS pattern. Chapter 6 presents the conclusions, and a summary of results deduced from the simulations and experiments is presented. Advantages and limitations of the proposed shade dispersion approach are discussed. Possible future work and practical applications of solar modules, using the proposed strategy, are also suggested.   6  2 LITERATURE REVIEW 2.1 PHOTOVOLTAIC EFFECT A PV cell is an electronic device that converts sunlight into direct current electricity through the PV effect. In order for this energy conversion to be possible, silicon-based semiconductors are widely-used to form a p-n junction in the PV cell. This junction is created by connecting n-type and p-type semiconductors, which are usually produced through ‘doping’: doping is a technique used to vary the number of electrons and holes in semiconductors so as to modify their electrical properties through the addition of impurities [18]. Through the connection, excess electrons diffuse to the p-type semiconductor from the n-type semiconductor, and conversely excess holes diffuse to the n-type semiconductor from the p-type semiconductor, such a movement creating a positively charged area at the n-type side and a negatively charged area at the p-type side, hence forming an electric field at the junction [19]. When the photovoltaic cell is illuminated, electrons in the semiconductor material will be knocked loose from their atoms when light photons hit the cell, assuming that the energy of these photons is greater than the energy band gap of the material, multiple electron-hole pairs will be formed and electrons will start to flow through the material and the external circuit in the direction dictated by the electric field at the junction. After completing all the traveling, the electrons will then return and recombine with the holes back in the semiconductor to close the circuit, and therefore direct current electricity is generated as the result. On the other hand, an inverter can be used to convert direct current into alternating current if required. 2.2 TYPES OF PHOTOVOLTAIC CELL Mono-crystalline and multi-crystalline cells are the two most basic comparable silicon-based types of PV cell that are widely-used for traditional solar panels. Mono-crystalline cells offer better efficiency but the ordered crystal structure is more expensive to manufacture [20]. On the other hand, multi-crystalline cell has lower quality due to the presence of grain boundaries, reducing the cell performance by introducing more 7  recombination losses at the boundaries [21]. In this thesis, the main focus is the effectiveness of the proposed PS mitigation strategy, thus the efficiency of the implemented solar panel for hardware validation is sacrificed, and the multi-crystalline cells are used in order to be more cost effective. 2.3 SOLAR SPECTRUM As a matter of fact, the solar irradiation at the Earth’s surface is different from the one incident on the Earth’s atmosphere. Such changes in the spectra and intensity are caused by many factors, for example: atmospheric effects, such as absorption and scattering, variations in the atmosphere composition, such as weather and pollution levels, the geographic locations of the surface with different altitude and latitude magnitudes, the time of day, and also the day of the year [22, 23]. In order to standardize the measurement referencing conditions, the American Society for Testing and Materials (ASTM) has issued a widely-accepted standard of air mass (AM) coefficient in order to help characterize the solar spectrum after solar irradiation has travelled through the atmosphere. The coefficient is defined as a ratio: the real sunlight path length from the atmosphere to the surface, relative to the virtual normalized path length at the zenith. Hence, if the Sun is directly overhead, the coefficient is 1 and it is expressed as AM1. That being said, AM1.5 is the most common standard to represent the overall yearly average performance of PV cells as most parts of the world population lie within the mid- or temperate latitudes. As a result, this thesis also adopts the AM1.5 standard testing conditions (STCs) with 1000 W/m2 as the input sunlight power density and 25 oC as the room temperature.  2.4 PARTIAL SHADING General speaking, PS is a phenomenon that occurs when the sunlight on a certain part of a PV array, panel, or module is blocked by obstacles, such as passing clouds, buildings, or trees [24, 25]. This reduces the power generation of the affected PV unit causing PS losses, through affecting the cell temperature and the irradiation level. So with the non-optimal output voltage and current, the maximum power point (MPP) of the affected PV array, which is the maximum power that the array can generate will be different from that 8  of the unaffected ones in series or in parallel causing a MPP mismatch, thus reducing the efficiency of the whole PV system [26, 27, 28, 29]. PS will also trigger on the by-pass diode across each shaded cell in order to maintain power generation from the other cells in series, thus creating thermal resistive losses which leads to the problem of a hot-spot. Lastly, some extreme cases of PS can also mislead the implemented maximum power point tracking (MPPT) control to operate at a local maxima instead of the global maxima resulting in an inefficient operation [30, 31, 32, 33]. A number of strategies can be used to reduce PS losses, and generally they are separated into either active or passive techniques. The most common and simplest passive technique involves the use of a by-pass diode [30, 34]. It can be implemented across one or a number of PV cells in order to prevent the formation of extreme local heating from the reverse bias of the shaded PV cell(s) and enables power generation from a series array that will otherwise be open-circuited. Another passive technique is to manufacture PV units in a certain pre-defined pattern [35, 36, 37]. There are a number of different patterns that each performs differently under similar PS conditions, such as the typical series-parallel (SP) configuration, and also the bridge linked (BL) and total-cross-tied (TCT) configurations, which offer more resistivity against PS. The structure of these interconnections can be found in Appendix C, and it was found that TCT is the most efficient at reducing PS losses amongst the three aforementioned configurations [38, 39, 40, 41, 42]. On the other hand, one of the widely-used active techniques is the installation of MPPT in order to avoid MPP mismatch between PV units. Its effectiveness will be largely dependent on how sophisticated the implemented MPPT algorithm is [43, 44, 45]. Another common solution is to implement a fully reconfigurable PV unit [46] that has the ability to sense the given PS condition and then automatically reforms the connection of the PV cells, arrays, panels, or even modules, accordingly to lower the PS loss [47, 48, 49, 50, 51, 52]. Theoretically, these active techniques are able to achieve the maximum attainable power generation under PS, however, the disadvantages are that more electronic components and complex control algorithms are required, hence increasing the bulkiness and the total cost of the final design [53, 54]. 9  2.5 SHADE DISPERSION TECHNIQUES From the past literature, it can be seen that efforts have been made to create more innovative, specially designed configurations in order to tackle the problem of PS through the use of shade dispersion, such as the Su-Do-Ku [55] and the ‘stepwise’ [56] patterns, which both have demonstrated improved power generation under PS than the regular TCT. To elaborate, the idea of the shade dispersion technique is to rearrange the physical locations of the PV cells in the modified module to a certain pattern, so that the effect caused by the shade on the affected cells is transferred to the other unshaded parts of the module from the perspective view of electrical circuitry. However, these older configurations unfortunately either contain a degree of scalability limitation or do not perform as well against certain type of PS condition. Take the Su-Do-Ku configuration as an example. The pattern itself is created from the popular Su-Du-Ku ‘Number Place’ puzzle that is made with a 9 x 9 number matrix. With how the rules used to create a Su-Do-Ku puzzle, the numbers in each possible combination are seen as evenly distributed over the whole matrix and are used as a guide to construct a PV module pattern that can effectively disperse different PS conditions. In Figure 2.1, an example of a Su-Do-Ku reconfiguration, is shown. To clarify, the number in each cell represents its position in the configuration: the first digit is the row number and the second digit is column number. The first digit also represents the location of the cell after the rearrangement according to a properly finished Su-Do-Ku puzzle. Unfortunately, even though PV modules employing such ‘random’ configurations did provide better efficiency, as shown in the literature, the wiring rearrangement is costly, difficult, and is arguably more than necessary. Most importantly, such a configuration will also be limited in the scale of a 9 x 9 matrix and will not be possible if the number of rows and columns in the PV panel are not the same. 10   Figure 2.1 Before and after the Su-Do-Ku reconfiguration. On the other hand, there is the ‘stepwise’ pattern, the name is used in this thesis as the configuration that is created by moving the columns of the PV panel into a TCT configuration down by a cell relative to their left counterpart. It is introduced from the literature as an improved strategy to the Su-Do-Ku configuration. An example of this reconfiguration is shown in Figure 2.2. Similar to the Su-Do-Ku pattern, the number in each cell represents its position in the configuration. However, even this configuration has shown improved efficiency and has no limitations on the number of rows or columns for the PV panel, there is an unavoidable weakness with this pattern: imagine a simple shade of a pole diagonal to the PV panel, the performance of this pattern will be worse when such a type of shade is aligned closely to the movement of the columns as the shaded cells will be moved to the same rows. A graphic explanation of this problem is also shown in Figure 2.2, and it is also demonstrated with the simulations in Chapter 4. Moreover, the implementing costs and manufacturing difficulties also preserve this rearrangement as a full modification is required for the whole module.   Figure 2.2 Before, after, and weakness of stepwise reconfiguration.    11  3 PHOTOVOLTAIC CELL MODELLING 3.1 PHOTOVOLTAIC CELL MODELS PV cell simulation models are essential in conducting PV-related studies since the information acquired from the manufacturing datasheet is usually limited and the consistency of the provided results also varies from one unit to another. It is widely recognized that a programmable user-defined simulation model will be beneficial in creating more accurate and reliable designs under different types of situations [57, 58]. This is certainly the case for this thesis. As shown in Figure 3.1, a PV cell can generally be expressed into two major types of equivalent circuit: the single-diode model (SDM) and the double-diode model (DDM), which can be distinguished by the number of electronic diode(s) used to model the electrical properties of a PV cell. The addition of series and shunt resistances are used in order to account for the parasitic power losses. The SDM is a more commonly used model in the industry as it offers a more reasonable trade-off between accuracy and complexity [59, 60, 61]. It also has the advantage that it can be easily parameterized based on typical datasheet information [62, 63, 64]. On the other hand, the DDM offers higher accuracy [65, 66, 67, 68] but suffers longer computation times because of its additional complexity [69, 70].  Figure 3.1 Equivalent circuits: ISDM; SSDM; SDM; DDM (from left to right). 3.1.1 The Single-Diode Model In general, there are three main types of equivalent circuit commonly used for SDM: the ideal single-diode model (ISDM), the simplified single-diode model (SSDM), and the regular single-diode model (SDM), as shown in Figure 3.1. The ISDM is the least complex among all three models because it only requires three parameters to set up its I-V characteristic equation [71], but it does not always promise good simulation results, especially in practical situations [72]. The SDM is a more popular option in the industry, 12  as it provides better accuracy. However, with the addition of the parameters from the shunt and series resistors, as opposed to the ISDM, this model requires solving five non-linear equations in order to set up its I-V characteristic equation [73], thus requiring the use of a non-linear numerical solver which adds complexity to the system and leads to longer computation times [74]. The SSDM is an alternative approach to reduce the complexity of the SDM by eliminating the shunt resistance [75], but the model will then have less accurate simulation results against some environmental changes, such as temperature variations, and it will still require a non-linear numerical solver for the remaining four parameters [76]. Using the SDM, as an example, based on the equivalent circuit from Figure 3.1, the I-V characteristics of a single PV cell can be derived as follows: Using Kirchhoff’s Current Law:   =  −  − , (2.1) where I is the output current, Iph is the photocurrent, ID is the diode current, Ish is the shunt current. Using Kirchhoff’s Voltage Law and Ohm’s law:   =  +  × , (2.2) where VD is the diode voltage, V is the output voltage, Rs is the series resistor. Using Ohm’s Law, it may be seen that:   =  × , (2.3) where Rsh is the shunt resistor. Substituting Eq. (2.3) into Eq. (2.2), we have:   =  =  . (2.4) From the Shockley’s diode equation, we have:   =  	  − 1 (2.5) where Is is the diode reverse saturation current, n is the emission coefficient/ideality factor, and VT is the thermal voltage. 13   The thermal voltage can be expressed as:   =  , (2.6) where kB is the Boltzmann’s constant, T is the temperature of the PV cell, and q is the magnitude of the electron charge constant. Finally, substituting Eq. (2.4) to (2.6) into Eq. (2.1), we will have the final form of the I-V characteristics equation for a single PV cell using the SDM:    =  −  	  − 1 −  . (2.7) 3.1.2 The Double-Diode Model The DDM, as shown back in Figure 3.1, is a more accurate yet extra complicated representation of a PV cell than the SDM, since it does not ignore the recombination losses within the depletion region [77]. To elaborate more, the SDM assumes a constant value for the ideality factor, but in reality it should be a variable between 1 and 2 as a function of voltage across the diode. This extra feature is modeled using one additional diode and hence in total seven parameters will be required in order to set up the I-V characteristics equation [77]. Using the equivalent circuit of the DDM from Figure 3.1, the I-V characteristics equation can be derived similarly as in the previous section for the SDM, the results being shown in Eq. (2.8). Using Kirchhoff’s Current Law and Eq. (2.4):   =  −  −  −  , (2.8) where the diode currents can be expressed as follows:   =  	  − 1,    =  	  − 1.  Efforts are made to reduce the complexity of this approach, and one of the strategies is to assume reasonable fixed values to some of the parameters. Some widely used 14  assumptions are n1 = 1, and n2 = 2 [78]. Even though these approximations are able to decrease the computation time by reducing the number of variable parameters to five, they obviously will not be always true and the computation time will still be long [79]. As a result, the marginal gain in accuracy of using the double-diode model usually does not outweigh its cost of complexity and longer computation time, so the simulations in this thesis are conducted using a simplified version of the SDM which is already adequate in terms of accuracy and demonstrating effectiveness of the proposed strategy. 3.2 SOFTWARE IMPLEMENTATION After the derivation of the I-V characteristics equation using the SDM, the next step is to implement it in the computer for further simulations. Since the output power of a single PV cell is minimal, it is more practical to have the model set up for a PV array. A PV array is a group of PV cells connected in series and/or parallel in order to generate a required output voltage and current. The equation for a PV array, that consists of Ns series PV cells and Np parallel PV cells, can be derived similarly as in Eq. (2.7), and is shown in Eq. (2.9), i.e.,   =  −   	  − 1 −  . (2.9) In addition to Eq. (2.9), several more equations will be needed in order to fully set up the PV model, and they are presented as follows: 3.2.1 Photocurrent Equation This equation is to calculate the photocurrent generate by the PV cell(s) based on the solar radiation it absorbs and the operating temperature of the device.   =  + − 298 , (2.10) where ISC is the short circuit current, Ki is the short circuit temperature coefficient and Irr is the solar irradiation. 15  3.2.2 Reverse Saturation Current Equation This equation is combined with two parts: the reverse saturation current of the diode at the reference temperature, as shown in Eq. (2.11), and the current at the operating temperature, as shown in Eq. (2.12), i.e.,   =  , (2.11) where Voc is the open-circuit voltage.   =     , (2.12) where Eg is the band-gap energy of the semiconductor used in the PV cell and Tr is the reference temperature. 3.2.3 Shunt Current Equation From Eq. (2.4), we have the equation to model the shunt current. In the case of a PV array with Ns series cells and Np parallel cells, it becomes:    = . (2.13)  However, the ISDM is chosen in the context of this thesis to further reduce the complexity, hence the parasitic power losses are neglected with the assumptions of infinitely small series resistance and infinitely large shunt resistance. 3.2.4 Load Current and Thermal Voltage Equations The equations to model the thermal voltage and the load current have already been introduced and shown in Eq. (2.1) and Eq. (2.6) respectively.   =  −  −  (2.1)   =   (2.6) 16  3.2.5 Diode Current Equation From Eq. (2.5), we have the equation to model the diode current. In a PV array with Ns series cells and Np parallel cells, it becomes:     	   1	. (2.14) After implementing the sub-system corresponding to each equation, they are then connected to each other, as shown in Figure 3.2, to form the required SDM. The model is verified by connecting to a resistor which acts as a variable load to produce the necessary simulation results. The circuit also includes a bypass diode for future PS simulations. A STOP Simulation block is used to end the simulation when the current value is negligibly small in order to reduce the total run time. Additional figures of the testing circuit and the block diagrams for each part of the simulation system are included in Appendix A.  Figure 3.2 Top-level overview of the single-diode model implementation. 3.3 SIMULATIONS AND PERFORMANCE RESULTS In this section, the derived ISDM is validated in simulations by parameterizing a PV module of BP 350U from BP Solar, which is made with 36 PV cells connected in series. The other used parameters are provided in Table 3-1. 17  Table 3-1 Electrical parameters used in the simulation. Parameters VOC (V) ISC (A) n Eg (eV) k (JK-1) q (C) KV (V/oC) KI (1/oC) Values 21.8 3.17 1.38 1.12 1.38x10-23 1.6x10-19 80x10-3 6.5x10-4  Simulations for different testing conditions are conducted to verify this ISDM, each is presented with I-V and P-V characteristics curves of the model in the following figures, and the results are shown matching to the expectations in all tested cases. Note that the abbreviations used in the figures, NS and NP are the number of modules (BP 350U panel) in series and in parallel respectively, Irr is the solar irradiation, and TOP is the operating temperature used in the simulations. 3.3.1 Change of Cell Number in Series or in Parallel The first simulation varies the number of PV cells in series. It is expected that the output voltage will increase proportionally with more cells in series.  Figure 3.3 Effect of changing the PV cell number in series. The second simulation varies the number of PV cells in parallel. Similar to the first simulation, it is expected that the output current will increase proportionally with the number of cells in parallel. 0 10 20 30 40 50 60 7001234I-V CurvesVoltage (V)Current (A)  Ns = 1Ns = 2Ns = 30 10 20 30 40 50 60 70050100150200P-V CurvesVoltage (V)Power (W)  Ns = 1Ns = 2Ns = 318   Figure 3.4 Effect of changing the PV cell number in parallel. Using basic engineering electric circuit analysis, it is understandable to recognize that all of the elements in a series circuit carry the same current, and the total voltage is the sum of each of the individual voltage sources. Conversely, the voltages across the ends of the elements connected in parallel are the same, and the total current is the sum of the currents passing through each of the individual elements. Hence, from Figure 3.3, with an increasing number of PV cells in series, the voltage is increased proportionally and the current is kept constant in the simulation. On the other hand, from Figure 3.4, with an increasing number of PV cells in parallel, the voltage is kept constant instead and the current is increased proportionally in the simulation.   0 5 10 15 20 250246810I-V CurvesVoltage (V)Current (A)  Np = 1Np = 2Np = 30 5 10 15 20 25050100150200P-V CurvesVoltage (V)Power (W)  Np = 1Np = 2Np = 319  3.3.2 Change of Solar Irradiation The third simulation varies the strength of the solar irradiation. It is expected that both the output current and voltage will increase with stronger solar irradiation.  Figure 3.5 Effect of changing the solar irradiation strength. As mentioned previously, a PV cell essentially is a device that coverts light energy into electricity, hence, as shown in Figure 3.5, the change of solar irradiation affects the degree of input photon energy thus changing both the voltage and current outputs of the solar module. The influence on current is significantly larger than that of the voltage, this being due to the fact that the current is more greatly affected by the change as demonstrated by the practical direct proportionality in the photocurrent equation, whereas the voltage is only related to the current with a small short-circuit temperature coefficient.   0 5 10 15 20 2501234I-V CurvesVoltage (V)Current (A)  0 5 10 15 20 25020406080P-V CurvesVoltage (V)Power (W)  Irr = 800 W/m2Irr = 1000 W/m2Irr = 1200 W/m2Irr = 800 W/m2Irr = 1000 W/m2Irr = 1200 W/m220  3.3.3 Change of Operating Temperature The fourth simulation varies the PV cell temperature. It is expected that the voltage will decrease with higher temperature and the corresponding current will increase slightly.  Figure 3.6 Effect of changing the PV cell temperature. Since the PV cell is made of semiconductors that temperature change will alter its excitation energy band-gap. Hence, increasing the operating temperature will increase the energy of the electrons in the cell which means a decreasing band gap as lower energy will be required to break the chemical bonds, causing a lower open-circuit voltage, as shown in Figure 3.6. The increase in the temperature also causes a weak increase in the current, this being due to the shifting of the irradiation spectrum under different temperature. Though the effect is minor, the change in irradiation alters the current correspondingly similar to the previous section as demonstrated by the photocurrent equation.   0 2 4 6 8 10 12 14 16 18 2033.053.13.153.23.25Zoomed I-V CurvesVoltage (V)Current (A)  0 5 10 15 20 250102030405060P-V CurvesVoltage (V)Power (W)  Top = 25 oCTop = 50 oCTop = 75 oCTop = 25 oCTop = 50 oCTop = 75 oC21  3.4 CHAPTER SUMMARY This chapter started with an introduction to SDM and DDM that can be used to simulate the performance of a PV cell, equations are derived for both models and their respective advantages and disadvantages are discussed further. As the purpose of this thesis is to investigate a new PV rearrangement pattern using the proposed strategy and compare it to the existing configurations, individual cell accuracy is not the main emphasis, hence it is more convenient to use ISDM for the simulations.  The mathematical model of ISDM is recreated in the computer using the derived equations. Block diagrams of the whole implementation are shown in Appendix A. Moreover, the model is also made with real electrical input and output so that each block of PV cells can be interconnected with each other to form a panel physically. The electrical parameters used in the model is obtained from BP-350, a solar panel from BP Solar, and its electrical ratings is included in Appendix B. Since the PV panel is made with 36 PV cells in series, the simulation model is then reformed correspondingly to exam its validity.  From Figure 3.3, we can see from the I-V curve that the current and voltage were approximately 3.2 A and 22 V for the case of one PV module, which are the same as the given data and curve provided in the Appendix B. Furthermore, the remaining simulation results are also able to validate important PV cell performance properties, such as: doubling the cell number in series doubles the voltage, doubling the cell number in parallel doubles the current, increasing the solar insolation improves the overall performance, and decreased performance when the module becomes hotter with increasing temperature. To summarize, the derived ISDM is verified to be a good simulation model of the actual PV unit.   22  4 SHADE DISPERSION TECHNIQUE 4.1 PARTIAL SHADING CONDITIONS  4.1.1 Shadow Shape As suggested from the literature [55, 56, 80], in order to scientifically model the simulated PS conditions to compare the performance difference between different connecting methodologies, a series of PS patterns, using the chart shown in Figure 4.1, is chosen and used similarly in this thesis.   Figure 4.1 Four different PS conditions. Furthermore, in addition to the short-wide (SW), short-narrow (SN), long-wide (LW), and long-narrow (LN) PS conditions, as shown from Figures 4.2 to 4.5, a special case of diagonal shade (DI), as shown in Figure 4.6, is also included in the simulations of this thesis in order to further distinguish the performance between the ‘stepwise’ configuration and the proposed strategy. Matrices of 6 x 6 PV unit are used to demonstrate each simulated PS condition, with ON indicating the cell is under full available irradiation and OFF indicating the cell is shaded.   23  OFF OFF ON ON ON ON OFF OFF ON ON ON ON OFF OFF ON ON ON ON OFF OFF ON ON ON ON OFF OFF ON ON ON ON OFF OFF ON ON ON ON Figure 4.2 Shade (original): long-narrow (6 x 6). OFF OFF OFF OFF OFF OFF OFF OFF OFF OFF OFF OFF OFF OFF ON ON ON ON OFF OFF ON ON ON ON OFF OFF ON ON ON ON OFF OFF ON ON ON ON Figure 4.3 Shade (original): long-wide (6 x 6). OFF OFF ON ON ON ON OFF OFF ON ON ON ON OFF OFF ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON Figure 4.4 Shade (original): short-narrow (6 x 6). OFF OFF OFF OFF OFF OFF OFF OFF OFF OFF OFF OFF ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON Figure 4.5 Shade (original): short-wide (6 x 6). OFF OFF ON ON ON ON OFF OFF OFF ON ON ON ON OFF OFF OFF ON ON ON ON OFF OFF OFF ON ON ON ON OFF OFF OFF ON ON ON ON OFF OFF Figure 4.6 Shade (original): diagonal (6 x 6).   24  4.1.2 Shading Factor Another characteristic to model PS conditions is to consider the intensity of the shade, which is what degree of the irradiation is filtered and shined over the PV cell [80]. As suggested from the literature, this effect is named, shading factor, and ranges from 0 (no shadow) to 1 (full shadow) [80]. Hence, the light intensity on the LN, LW, SN, SW, and DI shade patterns are modified accordingly and shown below, in order to better simulate the performance under each type of PS condition.  1 1 ON ON ON ON 0.9 0.9 ON ON ON ON 0.8 0.8 ON ON ON ON 0.7 0.7 ON ON ON ON 0.6 0.6 ON ON ON ON 0.5 0.5 ON ON ON ON Figure 4.7 Shade (shading factor): long-narrow (6 x 6). 1 0.9 0.8 0.7 0.6 0.5 0.9 0.9 0.8 0.7 0.6 0.5 0.8 0.8 ON ON ON ON 0.7 0.7 ON ON ON ON 0.6 0.6 ON ON ON ON 0.5 0.5 ON ON ON ON Figure 4.8 Shade (shading factor): long-wide (6 x 6). 1 0.8 ON ON ON ON 0.8 0.6 ON ON ON ON 0.6 0.4 ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON Figure 4.9 Shade (original): short-narrow (6 x 6). 1 0.9 0.8 0.7 0.6 0.5 1 0.9 0.8 0.7 0.6 0.5 ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON Figure 4.10 Shade (shading factor): short-wide (6 x 6).   25  1 0.9 ON ON ON ON 1 0.9 0.8 ON ON ON ON 0.9 0.8 0.7 ON ON ON ON 0.8 0.7 0.6 ON ON ON ON 0.7 0.6 0.5 ON ON ON ON 0.6 0.5 Figure 4.11 Shade (shading factor): diagonal (6 x 6). 4.1.3 Rearranged PS patterns As mentioned in the literature review, the Su-Do-Ku configuration is not applicable for PV modules that have different numbers of rows and columns. It is also limited to a scale of 9 x 9 PV array as it is created using the Su-Do-Ku puzzle pattern. The lack of its viability makes it reasonable not to be taken into consideration in this thesis. Hence, the stepwise configuration, which is a relatively improved shade dispersion method, is used in addition to the typical SP and TCT configurations to demonstrate the effectiveness of the proposed strategy. The PS conditions for a stepwise reconfiguration are rearranged into the following patterns, as described in the literature review. 1 0.9 ON ON ON ON 0.9 0.8 ON ON ON ON 0.8 0.7 ON ON ON ON 0.7 0.6 ON ON ON ON 0.6 0.5 ON ON ON ON 0.5 1 ON ON ON ON Figure 4.12 Shade (stepwise): long-narrow (6 x 6). 1 0.9 ON ON ON ON 0.9 0.8 ON ON ON 0.5 0.8 0.7 ON ON 0.6 0.5 0.7 0.6 ON 0.7 0.6 ON 0.6 0.5 0.8 0.7 ON ON 0.5 0.9 0.8 ON ON ON Figure 4.13 Shade (stepwise): long-wide (6 x 6). 1 0.6 ON ON ON ON 0.8 0.4 ON ON ON ON 0.6 ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON 0.8 ON ON ON ON Figure 4.14 Shade (stepwise): short-narrow (6 x 6).   26  1 0.9 ON ON ON ON 1 ON ON ON ON 0.5 ON ON ON ON 0.6 0.5 ON ON ON 0.7 0.6 ON ON ON 0.8 0.7 ON ON ON 0.9 0.8 ON ON ON Figure 4.15 Shade (stepwise): short-wide (6 x 6). 1 0.9 0.8 0.7 0.6 0.5 1 0.9 0.8 0.7 0.6 ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON 0.9 0.8 0.7 0.6 0.5 Figure 4.16 Shade (stepwise): diagonal (6 x 6). 4.2 THE PROPOSED STRATEGY The proposed shade dispersion approach is described in this section using an example of a 6 x 6 PV module configuration employing such strategy, as shown in Figure 4.17. The rearrangement is scalable with even or odd number of rows and columns, and also potentially reduces half of the work and cost in the implementation as opposed to the other reconfiguration methods as no more than half of the columns within the PV module are required to modify, as explained in the following placement rules with the figure shown in Figure 4.18. A mathematical generalization of the strategy is also shown in Figure 4.19. The hypothesis is that by rearranging half of the PV cells, the remaining half is also rearranged relatively thus ensuring the least necessary amount of effort in order to disperse the shade. In doing so, (1) the columns of the configuration should be modified alternatively; (2) the relocated PV cells should not stay next to the former adjacent ones (for example, PV cell 2 should not have the PV cells 1 and 3 located at the top or bottom of it after the relocation); (3) the PV cells should be relocated in a way such that the configuration could disperse the shade evenly at the rearranged columns, that is, from the top to the middle or bottom, from the bottom to the top or middle, and from the middle to the top or bottom of the PV module. Another advantage of the proposed configuration is that there is no additional rearrangement or rotation of the PV module necessary against ‘irregular’ patterns, such as the diagonal shade, since it is already been dispersed. 27   Figure 4.17 Solar panel 6x6 cell matrix using the proposed rearrangement.  Figure 4.18 Proposed rearrangement: even (left); odd (right) number of rows and columns. 28   Figure 4.19 Mathematical generalization of the proposed strategy. Similar to the rearranged PS patterns for the stepwise configuration in the previous section, the PS patterns for the proposed configuration are also rearranged accordingly. 1 0.8 ON ON ON ON 0.9 0.6 ON ON ON ON 0.8 0.9 ON ON ON ON 0.7 0.5 ON ON ON ON 0.6 0.9 ON ON ON ON 0.5 0.7 ON ON ON ON Figure 4.20 Shade (proposed): long-narrow (6 x 6).  1 0.8 0.8 ON 0.6 ON 0.9 0.6 0.8 ON 0.6 ON 0.8 0.9 ON 0.7 ON 0.5 0.7 0.5 ON ON ON ON 0.6 0.9 ON 0.7 ON 0.5 0.5 0.7 ON ON ON ON Figure 4.21 Shade (proposed): long-wide (6 x 6). 1 0.4 ON ON ON ON 0.8 ON ON ON ON ON 0.6 0.8 ON ON ON ON ON ON ON ON ON ON ON 0.6 ON ON ON ON ON ON ON ON ON ON Figure 4.22 Shade (proposed): short-narrow (6 x 6). 29  1 ON 0.8 ON 0.6 ON 1 ON 0.8 ON 0.6 ON ON 0.9 ON 0.7 ON 0.5 ON ON ON ON ON ON ON 0.9 ON 0.7 ON 0.5 ON ON ON ON ON ON Figure 4.23 Shade (proposed): short-wide (6 x 6). 1 0.9 ON 0.7 ON ON 1 ON 0.8 0.7 ON 0.5 ON 0.9 0.8 ON ON ON ON ON 0.8 ON 0.6 0.5 ON 0.9 ON ON 0.6 ON ON ON ON 0.7 0.6 ON Figure 4.24 Shade (proposed): diagonal (6 x 6). 4.3 SIMULATIONS AND PERFORMANCE RESULTS The performance of each configuration, namely series-parallel (the most widely-used one in the industry), total-cross-tied (said to be the most efficient against PS before applying any shade dispersion), stepwise (the other tested shade dispersion configuration), and the proposed strategy, are simulated and compared in this section with their respective I-V and P-V curves under each PS condition (LN, LW, SN, SW, DI). The structure models used for the simulated configurations and the code for figure plotting are provided in Appendix C and E. Note that each PV unit is simulated using the PV module BP-350 from Chapter 3. 4.3.1 6 x 6 PV Modules Comparisons The PS patterns used in this matrix size has already been presented in the previous sections. Based on the acquired figures, the performance of the proposed configuration is observed to have a slightly better MPP than the SP, TCT and stepwise configurations under the LN and SN shade patterns. However, under LW and SW shade patterns, while the proposed configuration is able to maintain comparable MPP, its performance is not as significantly improved as the stepwise configuration, this being due, in large measure, to the trade-off from the proposed placement rules in order to avoid modifying the whole structure of the PV module. As a result, the improvement is not as significant in these cases, yet it prevents the same disadvantage that the stepwise configuration suffers in the case of DI shade. 30   Figure 4.25 Curves under long-narrow shade (6 x 6).  Figure 4.26 Curves under long-wide shade (6 x 6). 0 20 40 60 80 100 120 14005101520I-V Curves (LN)Voltage (V)Current (A)  0 20 40 60 80 100 120 140050010001500P-V Curves (LN)Voltage (V)Power (W)  SPTCTstepwiseproposedSPTCTstepwiseproposed0 20 40 60 80 100 120 14005101520I-V Curves (LW)Voltage (V)Current (A)  0 20 40 60 80 100 120 140020040060080010001200P-V Curves (LW)Voltage (V)Power (W)  SPTCTstepwiseproposedSPTCTstepwiseproposed31   Figure 4.27 Curves under short-narrow shade (6 x 6).  Figure 4.28 Curves under short-wide shade (6 x 6). 0 20 40 60 80 100 120 14005101520I-V Curves (SN)Voltage (V)Current (A)  0 20 40 60 80 100 120 1400500100015002000P-V Curves (SN)Voltage (V)Power (W)  SPTCTstepwiseproposedSPTCTstepwiseproposed0 20 40 60 80 100 120 14005101520I-V Curves (SW)Voltage (V)Current (A)  0 20 40 60 80 100 120 140050010001500P-V Curves (SW)Voltage (V)Power (W)  SPTCTstepwiseproposedSPTCTstepwiseproposed32   Figure 4.29 Curves under diagonal shade (6 x 6). 4.3.2 6 x 7, 7 x 6, and 7 x 7 PV Modules Comparisons In addition to the simulations done using a PV module of 6 x 6 PV units, the comparisons are also carried out using PV modules with combinations of 6 x 7, 7 x 6, and 7 x 7 PV units in order to demonstrate the scalability of the proposed strategy and its effectiveness under different parity combinations. The new rearranged PS shade patterns are very similar to the ones used for 6 x 6 PV modules, hence only the LW and DI versions for the stepwise and the proposed configurations are shown below at each matrix sizes. 1 0.9 ON ON ON ON 0.4 0.9 0.8 ON ON ON 0.5 0.4 0.8 0.7 ON ON 0.6 0.5 0.5 0.7 0.6 ON 0.7 0.6 ON ON 0.6 0.5 0.8 0.7 ON ON ON 0.5 0.9 0.8 ON ON ON ON Figure 4.30 Shade (stepwise): long-wide (6 x 7). 1 0.9 ON ON ON ON 0.9 0.8 ON ON ON ON 0.8 0.7 ON ON ON 0.5 0.7 0.6 ON ON 0.6 0.5 0.6 0.5 ON 0.7 0.6 ON 0.5 0.4 0.8 0.7 ON ON 0.4 0.9 0.8 ON ON ON Figure 4.31 Shade (stepwise): long-wide (7 x 6). 0 20 40 60 80 100 120 14005101520I-V Curves (DI)Voltage (V)Current (A)  0 20 40 60 80 100 120 140020040060080010001200P-V Curves (DI)Voltage (V)Power (W)  SPTCTstepwiseproposedSPTCTstepwiseproposed33  1 0.9 ON ON ON ON ON 0.9 0.8 ON ON ON ON 0.4 0.8 0.7 ON ON ON 0.5 0.4 0.7 0.6 ON ON 0.6 0.5 0.5 0.6 0.5 ON 0.7 0.6 ON ON 0.5 0.4 0.8 0.7 ON ON ON 0.4 0.9 0.8 ON ON ON ON Figure 4.32 Shade (stepwise): long-wide (7 x 7).  1 0.8 0.8 ON 0.6 ON 0.4 0.9 0.6 0.8 ON 0.6 ON 0.4 0.8 0.9 ON 0.7 ON 0.5 ON 0.7 0.5 ON ON ON ON ON 0.6 0.9 ON 0.7 ON 0.5 ON 0.5 0.7 ON ON ON ON ON Figure 4.33 Shade (proposed): long-wide (6 x 7).  1 0.4 0.8 ON 0.6 ON 0.9 0.8 0.8 ON 0.6 ON 0.8 0.6 ON ON ON ON 0.7 0.9 ON 0.7 ON 0.5 0.6 0.5 ON ON ON ON 0.5 0.9 ON 0.7 ON 0.5 0.4 0.7 ON ON ON ON Figure 4.34 Shade (proposed): long-wide (7 x 6).  1 0.4 0.8 ON 0.6 ON 0.4 0.9 0.8 0.8 ON 0.6 ON 0.4 0.8 0.6 ON ON ON ON ON 0.7 0.9 ON 0.7 ON 0.5 ON 0.6 0.5 ON ON ON ON ON 0.5 0.9 ON 0.7 ON 0.5 ON 0.4 0.7 ON ON ON ON ON Figure 4.35 Shade (proposed): long-wide (7 x 7). 1 0.9 0.8 0.7 0.6 0.5 ON 1 0.9 0.8 0.7 0.6 ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON 0.9 0.8 0.7 0.6 0.5 0.4 Figure 4.36 Shade (stepwise): diagonal (6 x 7).   34  1 0.9 0.8 0.7 0.6 0.5 1 0.9 0.8 0.7 0.6 0.5 ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON 0.9 0.8 0.7 0.6 0.5 Figure 4.37 Shade (stepwise): diagonal (7 x 6). 1 0.9 0.8 0.7 0.6 0.5 ON 1 0.9 0.8 0.7 0.6 ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON 0.9 0.8 0.7 0.6 0.5 0.4 Figure 4.38 Shade (stepwise): diagonal (7 x 7). 1 0.9 ON 0.7 ON ON ON 1 ON 0.8 0.7 ON 0.5 ON ON 0.9 0.8 ON ON ON ON ON ON 0.8 ON 0.6 0.5 ON ON 0.9 ON ON 0.6 ON ON ON ON ON 0.7 0.6 ON 0.4 Figure 4.39 Shade (proposed): diagonal (6 x 7). 1 ON ON ON ON 0.5 1 0.9 0.8 0.7 ON ON ON ON 0.8 0.7 ON 0.5 ON 0.9 0.8 ON 0.6 ON ON ON ON ON 0.6 0.5 ON 0.9 ON ON 0.6 ON ON ON ON 0.7 ON ON Figure 4.40 Shade (proposed): diagonal (7 x 6). 1 ON ON ON ON 0.5 ON 1 0.9 0.8 0.7 ON ON ON ON ON 0.8 0.7 ON 0.5 ON ON 0.9 0.8 ON 0.6 ON ON ON ON ON ON 0.6 0.5 ON ON 0.9 ON ON 0.6 ON 0.4 ON ON ON 0.7 ON ON 0.4 Figure 4.41 Shade (proposed): diagonal (7 x 7). 35   Figure 4.42 Curves under long-narrow shade (6 x 7).  Figure 4.43 Curves under long-wide shade (6 x 7). 0 20 40 60 80 100 120 14005101520I-V Curves (LN)Voltage (V)Current (A)  SPTCTstepwiseproposed0 20 40 60 80 100 120 1400500100015002000P-V Curves (LN)Voltage (V)Power (W)  SPTCTstepwiseproposed0 20 40 60 80 100 120 14005101520I-V Curves (LW)Voltage (V)Current (A)  SPTCTstepwiseproposed0 20 40 60 80 100 120 140050010001500P-V Curves (LW)Voltage (V)Power (W)  SPTCTstepwiseproposed36   Figure 4.44 Curves under short-narrow shade (6 x 7).  Figure 4.45 Curves under short-wide shade (6 x 7). 0 20 40 60 80 100 120 1400510152025I-V Curves (SN)Voltage (V)Current (A)  SPTCTstepwiseproposed0 20 40 60 80 100 120 1400500100015002000P-V Curves (SN)Voltage (V)Power (W)  SPTCTstepwiseproposed0 20 40 60 80 100 120 1400510152025I-V Curves (SW)Voltage (V)Current (A)  SPTCTstepwiseproposed0 20 40 60 80 100 120 1400500100015002000P-V Curves (SW)Voltage (V)Power (W)  SPTCTstepwiseproposed37   Figure 4.46 Curves under diagonal shade (6 x 7).  Figure 4.47 Curves under long-narrow shade (7 x 6). 0 20 40 60 80 100 120 1400510152025I-V Curves (DI)Voltage (V)Current (A)  SPTCTstepwiseproposed0 20 40 60 80 100 120 140050010001500P-V Curves (DI)Voltage (V)Power (W)  SPTCTstepwiseproposed0 20 40 60 80 100 120 140 16005101520I-V Curves (LN)Voltage (V)Current (A)  SPTCTstepwiseproposed0 20 40 60 80 100 120 140 1600500100015002000P-V Curves (LN)Voltage (V)Power (W)  SPTCTstepwiseproposed38   Figure 4.48 Curves under long-wide shade (7 x 6).  Figure 4.49 Curves under short-narrow shade (7 x 6). 0 50 100 15005101520I-V Curves (LW)Voltage (V)Current (A)  SPTCTstepwiseproposed0 50 100 150050010001500P-V Curves (LW)Voltage (V)Power (W)  SPTCTstepwiseproposed0 20 40 60 80 100 120 140 16005101520I-V Curves (SN)Voltage (V)Current (A)  SPTCTstepwiseproposed0 20 40 60 80 100 120 140 1600500100015002000P-V Curves (SN)Voltage (V)Power (W)  SPTCTstepwiseproposed39   Figure 4.50 Curves under short-wide shade (7 x 6).  Figure 4.51 Curves under diagonal shade (7 x 6). 0 20 40 60 80 100 120 140 16005101520I-V Curves (SW)Voltage (V)Current (A)  SPTCTstepwiseproposed0 20 40 60 80 100 120 140 1600500100015002000P-V Curves (SW)Voltage (V)Power (W)  SPTCTstepwiseproposed0 50 100 15005101520I-V Curves (DI)Voltage (V)Current (A)  SPTCTstepwiseproposed0 50 100 150050010001500P-V Curves (DI)Voltage (V)Power (W)  SPTCTstepwiseproposed40   Figure 4.52 Curves under long-narrow shade (7 x 7).  Figure 4.53 Curves under long-wide shade (7 x 7). 0 20 40 60 80 100 120 140 16005101520I-V Curves (LN)Voltage (V)Current (A)  SPTCTstepwiseproposed0 20 40 60 80 100 120 140 16005001000150020002500P-V Curves (LN)Voltage (V)Power (W)  SPTCTstepwiseproposed0 50 100 15005101520I-V Curves (LW)Voltage (V)Current (A)  SPTCTstepwiseproposed0 50 100 1500500100015002000P-V Curves (LW)Voltage (V)Power (W)  SPTCTstepwiseproposed41   Figure 4.54 Curves under short-narrow shade (7 x 7).  Figure 4.55 Curves under short-wide shade (7 x 7). 0 20 40 60 80 100 120 140 1600510152025I-V Curves (SN)Voltage (V)Current (A)  SPTCTstepwiseproposed0 20 40 60 80 100 120 140 16005001000150020002500P-V Curves (SN)Voltage (V)Power (W)  SPTCTstepwiseproposed0 20 40 60 80 100 120 140 1600510152025I-V Curves (SW)Voltage (V)Current (A)  SPTCTstepwiseproposed0 20 40 60 80 100 120 140 16005001000150020002500P-V Curves (SW)Voltage (V)Power (W)  SPTCTstepwiseproposed42   Figure 4.56 Curves under diagonal shade (7 x 7). According to the PV characteristics curves shown in this section, similar to the case of 6 x 6 PV module, the proposed strategy is to be able to deliver enhanced MPP under the LN and SN shade patterns, while maintaining a comparable MPP under the LW and SW shade patterns. It also offers better MPP than the stepwise shade dispersion approach in the case of DI shade pattern. The table in the chapter summary outlines their performance quantitatively.   0 50 100 1500510152025I-V Curves (DI)Voltage (V)Current (A)  SPTCTstepwiseproposed0 50 100 1500500100015002000P-V Curves (DI)Voltage (V)Power (W)  SPTCTstepwiseproposed43  4.4 CHAPTER SUMMARY Table 4-1 Summary of each configuration’s MPP under simulated PS conditions. MPP (W) LN LW SN SW DI SP 6 x 6 1306 941.2 1426 1279 964.2 6 x 7 1667 1154 1740 1492 1137 7 x 6 1524 1183 1711 1606 1280 7 x 7 1905 1451 2085 1874 1507 TCT 6 x 6 1381 967.7 1508 1279 1154 6 x 7 1715 1183 1854 1492 1491 7 x 6 1628 1231 1776 1606 1366 7 x 7 2022 1504 2183 1874 1761 stepwise 6 x 6 1406 1117 1567 1403 937.8 6 x 7 1739 1420 1912 1638 1094 7 x 6 1657 1392 1845 1670 1264 7 x 7 2050 1748 2249 2048 1475 proposed 6 x 6 1419 976.2 1599 1237 1069 6 x 7 1750 1198 1935 1462 1413 7 x 6 1700 1195 1958 1467 1296 7 x 7 2022 1456 2350 1732 1619  In this chapter, the performance of SP, TCT, stepwise, and the proposed configurations are simulated and compared using their respective I-V and P-V curves. The modeled PS conditions and their rearranged patterns are also presented. The simulations are carried out using different matrix sizes, including the 6 x 6, 6 x 7, 7 x 6, and 7 x 7 PV modules, this is to demonstrate the scalability of the proposed shade dispersion strategy while validating its effectiveness in PS loss reduction. Based on the evaluation of the simulation results, it is found that the proposed rearrangement has the best overall MPP performance under LN and SN shades. Additionally, its acquired MPPs are also very close to those of the stepwise configuration in the case of LW and SW shades. All in all, both rearrangements are able to outperform the typical SP and TCT configurations under the four general PS conditions, validating the effect of shade dispersion methods. On the other hand, when under the special case of diagonal PS condition, the proposed strategy is able to achieve significantly better MPP than the stepwise reconfiguration, demonstrating its ability to overcome the limitation of the old shade dispersion method, as explained before in the literature review.   44  5 EXPERIMENTAL VALIDATION A prototype of a 6 x 6 PV module is implemented and presented in this chapter to experimentally evaluate the effectiveness of the proposed strategy and compare it to the performance of TCT and stepwise configurations, a graphical overview of the set-up is shown below in Figure 5.1. The set-up consists a flood lamp as the light source, a panel of hand-made PV cells in TCT configuration, as shown in Figure 5.2, a rheostat as the variable load, and an oscilloscope to measure the required voltage and current values with a current sensor.  Figure 5.1 Hardware set-up overview.   Figure 5.2 Panel of cells in TCT configuration.  5.1 EQUIPMENT USED The light source used in the experiment is a flood lamp with the power rating of 700W, as shown in Figure 5.3, the light intensity it produces is approximately 1000 w/m2 given that the size of the solar panel is around 0.65 meter square: the length is 1.3 m and the width is 0.5 m.  ℎ   !" = 700#1.3$ × 0.5$ = 1077 #/$  ≈ 1000 #/$ 45   Figure 5.3 Light source ratings. The type of PV cell used in this hardware implementation is multi-crystalline silicon cell, as shown in the figure below. They are less expensive and more commonly-used. Though less efficient, they are good enough for the purpose of this thesis. A rheostat, as shown before in the overview figure, is an electrical device that has an adjustable resistance. It is a convenient way to vary the current and the voltage across the circuit, so that I-V and P-V characteristics curves can be traced. It has some power loss and the response is less linear, but the effects are insignificant enough to be neglected for the comparisons. An oscilloscope is used to measure the current and voltage outputs, in addition to the regular voltage probe, a current sensor, utilizing the Hall Effect, is used to acquire quick and accurate current measurements. 5.2 SHORT CIRCUIT CURRENT VS. SHADE DISPLACEMENT One of the PV cells, as shown in Figure 5.4, is put to test against a shifting PS to see how its performance varies with a fixed incremental interval of shade. The width and length of the cell are measured to be 8 cm and 15 cm respectively, and so a shade obstacle of the same size as shown in Figure 5.5, is made and used. The resulting figures show of linear relationship between the short circuit current and the shade displacement, there being no observable discontinuity indicating that the PV cell performance is inversely proportional to the area of PS in spite of its location on the cell. Additionally, the role of the metal grid structure is also insignificant in the study of PS loss as the results have shown no visible change with how the grids are shaded. Note that the current value is not totally zero at 8 46  cm and 15 cm, this being due to the fact that the sides of the cell are not completely shaded with some residual light coming from the surrounding environment.   Figure 5.4 A single multi-crystalline silicon cell.   Figure 5.5 A shade obstacle with some interval measurements.   Figure 5.6 Short circuit current vs. displacement (width).   Figure 5.7 Short circuit current vs. displacement (length).     0 1 2 3 4 5 6 7 800.20.40.60.811.21.41.61.8Short Circuit Current vs. Displacement (Width)Displacement (cm)Current (A)0 5 10 1500.20.40.60.811.21.41.61.8Short Circuit Current vs. Displacement (Length)Displacement (cm)Current (A)47  5.3 EXPERIMENTAL RESULTS The voltage and current measurements for each tested configuration under different PS conditions are listed below in their respective tables, and figures of I-V and P-V curves are also presented to compare their performance. In addition, photos of the original and rearranged PS patterns are also provided. 5.3.1 No Shade and Long-Narrow Shade The shading factor is not considered in the hardware validation in order to reduce the workload. It is also not entirely required to verify the effectiveness of the proposed strategy, as it is able to do so with the use of different PS conditions. Note that the PS patterns in the cases of LN and obviously NS are the same for every tested configurations, therefore only the comparisons between the simulated and the experimental results are considered. Table 5-1 Experimental data for PV panel under no shade, and long-narrow shade.   Figure 5.8 PV panel under long-narrow shade.  No Shade Long-Narrow Shade Voltage (V) Current (A) Voltage (V) Current (A) Voltage (V) Current (A) Voltage (V) Current (A) 0.27 3.68 2.83 1.74 0.21 3.18 2.81 1.41 1.10 3.54 2.90 1.29 1.10 3.06 2.83 1.12 1.58 3.35 2.94 1.05 2.17 2.86 2.89 0.826 2.10 3.32 2.97 0.80 2.55 2.60 2.91 0.64 2.70 2.65 2.99 0.55 2.69 2.00 2.94 0.25 2.75 2.25 3.00 0.24 48   Figure 5.9 Curves under no shade (experimental vs simulated).  Figure 5.10 Curves under long-narrow shade (experimental vs simulated).   0 0.5 1 1.5 2 2.5 301234I-V Curves (No Shade)Voltage (V)Current (A)  Exp.Sim.0 0.5 1 1.5 2 2.5 302468P-V Curves (No Shade)Voltage (V)Power (W)  Exp.Sim.0 0.5 1 1.5 2 2.5 301234I-V Curves (Long Narrow Shade)Voltage (V)Current (A)  Exp.Sim.0 0.5 1 1.5 2 2.5 302468P-V Curves (Long Narrow Shade)Voltage (V)Power (W)  Exp.Sim.49  5.3.2 Long-Wide Shade   Figure 5.11 PV panel under long-wide shade as TCT.  Figure 5.12 PV panel under rearranged long-wide shade as stepwise.  Figure 5.13 PV panel under rearranged long-wide shade as proposed.  50   Figure 5.14 Curves under long-wide shade as TCT (experimental vs simulated).  Figure 5.15 Curves under long-wide shade as stepwise (experimental vs simulated). 0 0.5 1 1.5 2 2.5 300.511.5I-V Curves (Long Wide Shade) (TCT)Voltage (V)Current (A)  0 0.5 1 1.5 2 2.5 300.511.522.5P-V Curves (Long Wide Shade) (TCT)Voltage (V)Power (W)  Exp.Sim.Exp.Sim.0 0.5 1 1.5 2 2.5 300.511.522.5I-V Curves (Long Wide Shade) (Stepwise)Voltage (V)Current (A)  0 0.5 1 1.5 2 2.5 3012345P-V Curves (Long Wide Shade) (Stepwise)Voltage (V)Power (W)  Exp.Sim.Exp.Sim.51   Figure 5.16 Curves under long-wide shade as proposed (experimental vs simulated).   0 0.5 1 1.5 2 2.5 300.511.522.5I-V Curves (Long Wide Shade) (Proposed)Voltage (V)Current (A)  0 0.5 1 1.5 2 2.5 3012345P-V Curves (Long Wide Shade) (Proposed)Voltage (V)Power (W)  Exp.Sim.Exp.Sim.52  Table 5-2 Experimental data for PV panel under long-wide shade. Long-Wide Shade TCT stepwise proposed V I V I V I V I V I V I 0.16 1.18 2.78 0.52 0.17 2.40 2.83 0.53 0.16 2.12 2.81 0.53 1.05 1.07 2.82 0.38 1.04 2.28 2.85 2.89 1.07 2.08 2.84 0.32 1.40 1.04 2.85 0.22 1.49 2.23 2.87 2.24 1.45 1.96 2.85 0.20 1.86 0.99   2.11 2.12   1.91 1.91   2.11 0.97   2.51 1.87   2.32 1.83   2.55 0.93   2.67 1.34   2.67 1.18   2.68 0.80   2.73 1.09   2.74 0.93   2.74 0.66   2.78 0.80   2.78 0.74     Figure 5.17 Experimental curves under long-wide shade (TCT vs stepwise vs proposed).   0 0.5 1 1.5 2 2.5 300.511.522.5I-V Curves (Long Wide Shade)Voltage (V)Current (A)  TCTStepwiseProposed0 0.5 1 1.5 2 2.5 3012345P-V Curves (Long Wide Shade)Voltage (V)Power (W)  TCTStepwiseProposed53  5.3.3 Short-Narrow Shade   Figure 5.18 PV panel under short-narrow shade as TCT.  Figure 5.19 PV panel under rearranged short-narrow shade as stepwise.  Figure 5.20 PV panel under rearranged short-narrow shade as proposed. 54   Figure 5.21 Curves under short-narrow shade as TCT (experimental vs simulated).  Figure 5.22 Curves under short-narrow shade as stepwise (experimental vs simulated). 0 0.5 1 1.5 2 2.5 301234I-V Curves (Short Narrow Shade) (TCT)Voltage (V)Current (A)  0 0.5 1 1.5 2 2.5 302468P-V Curves (Short Narrow Shade) (TCT)Voltage (V)Power (W)  Exp.Sim.Exp.Sim.0 0.5 1 1.5 2 2.5 301234I-V Curves (Short Narrow Shade) (Stepwise)Voltage (V)Current (A)  0 0.5 1 1.5 2 2.5 302468P-V Curves (Short Narrow Shade) (Stepwise)Voltage (V)Power (W)  Exp.Sim.Exp.Sim.55   Figure 5.23 Curves under short-narrow shade as proposed (experimental vs simulated).   0 0.5 1 1.5 2 2.5 301234I-V Curves (Short Narrow Shade) (Proposed)Voltage (V)Current (A)  0 0.5 1 1.5 2 2.5 302468P-V Curves (Short Narrow Shade) (Proposed)Voltage (V)Power (W)  Exp.Sim.Exp.Sim.56  Table 5-3 Experimental data for PV panel under short-narrow shade. Short-Narrow Shade TCT stepwise proposed V I V I V I V I V I V I 0.35 3.23 2.78 1.15 0.15 3.13 2.74 1.21 0.17 3.22 2.69 1.61 1.03 3.06 2.82 0.89 1.27 3.12 2.82 0.86 1.06 3.18 2.73 1.36 1.49 3.06 2.88 0.38 1.89 3.06 2.86 0.42 1.68 3.04 2.77 1.05 2.13 2.98 2.90 0.26 2.31 2.88 2.90 0.24 2.26 2.98 2.81 0.82 2.36 2.90   2.49 2.53   2.45 2.68 2.83 0.57 2.53 2.48   2.55 2.37   2.51 2.57 2.85 0.46 2.58 2.28   2.61 2.12   2.58 2.24 2.88 0.23 2.73 1.50   2.71 1.52   2.60 2.11     Figure 5.24 Experimental curves under short-narrow shade (TCT vs stepwise vs proposed).   0 0.5 1 1.5 2 2.5 301234I-V Curves (Short Narrow Shade)Voltage (V)Current (A)  TCTStepwiseProposed0 0.5 1 1.5 2 2.5 302468P-V Curves (Short Narrow Shade)Voltage (V)Power (W)  TCTStepwiseProposed57  5.3.4 Short-Wide Shade   Figure 5.25 PV panel under short-wide shade as TCT.  Figure 5.26 PV panel under rearranged short-wide shade as stepwise.  Figure 5.27 PV panel under rearranged short-wide shade as proposed. 58   Figure 5.28 Curves under short-wide shade as TCT (experimental vs simulated).  Figure 5.29 Curves under short-wide shade as stepwise (experimental vs simulated). 0 0.5 1 1.5 2 2.5 300.511.5I-V Curves (Short Wide Shade) (TCT)Voltage (V)Current (A)  0 0.5 1 1.5 2 2.5 300.511.522.5P-V Curves (Short Wide Shade) (TCT)Voltage (V)Power (W)  Exp.Sim.Exp.Sim.0 0.5 1 1.5 2 2.5 300.511.522.53I-V Curves (Short Wide Shade) (Stepwise)Voltage (V)Current (A)  0 0.5 1 1.5 2 2.5 30123456P-V Curves (Short Wide Shade) (Stepwise)Voltage (V)Power (W)  Exp.Sim.Exp.Sim.59   Figure 5.30 Curves under short-wide shade as proposed (experimental vs simulated).   0 0.5 1 1.5 2 2.5 300.511.522.5I-V Curves (Short Wide Shade) (Proposed)Voltage (V)Current (A)  0 0.5 1 1.5 2 2.5 30123456P-V Curves (Short Wide Shade) (Proposed)Voltage (V)Power (W)  Exp.Sim.Exp.Sim.60  Table 5-4 Experimental data for PV panel under short-wide shade. Short-Wide Shade TCT stepwise proposed V I V I V I V I V I V I 0.07 1.18 2.74 0.55 0.14 2.94 2.66 1.43 0.17 2.47 2.63 1.43 1.02 1.10 2.78 0.35 1.22 2.82 2.71 1.17 1.06 2.35 2.69 1.19 1.50 1.01 2.80 0.29 1.75 2.73 2.76 0.87 1.55 2.27 2.73 1.00 1.92 0.96 2.81 0.23 2.14 2.66 2.80 0.67 2.07 2.19 2.78 0.70 2.30 0.94   2.38 2.46 2.82 0.45 2.38 2.12 2.81 0.51 2.53 0.90   2.50 2.13 2.85 0.26 2.44 2.08 2.82 0.39 2.67 0.71   2.57 1.88 2.86 0.22 2.58 1.78 2.86 0.24 2.70 0.66   2.62 1.61   2.59 1.64     Figure 5.31 Experimental curves under short-wide shade (TCT vs stepwise vs proposed).   0 0.5 1 1.5 2 2.5 300.511.522.53I-V Curves (Short Wide Shade)Voltage (V)Current (A)  TCTStepwiseProposed0 0.5 1 1.5 2 2.5 30123456P-V Curves (Short Wide Shade)Voltage (V)Power (W)  TCTStepwiseProposed61  5.3.5 Diagonal Shade   Figure 5.32 PV panel under diagonal shade as TCT.  Figure 5.33 PV panel under rearranged diagonal shade as stepwise.  Figure 5.34 PV panel under rearranged diagonal shade as proposed. 62   Figure 5.35 Curves under diagonal shade as TCT (experimental vs simulated).  Figure 5.36 Curves under diagonal shade as stepwise (experimental vs simulated). 0 0.5 1 1.5 2 2.5 300.511.522.53I-V Curves (Diagonal Shade) (TCT)Voltage (V)Current (A)  Exp.Sim.0 0.5 1 1.5 2 2.5 30123456P-V Curves (Diagonal Shade) (TCT)Voltage (V)Power (W)  Exp.Sim.0 0.5 1 1.5 2 2.5 300.511.5I-V Curves (Diagonal Shade) (Stepwise)Voltage (V)Current (A)  Exp.Sim.0 0.5 1 1.5 2 2.5 300.511.522.5P-V Curves (Diagonal Shade) (Stepwise)Voltage (V)Power (W)  Exp.Sim.63   Figure 5.37 Curves under diagonal shade as proposed (experimental vs simulated).   0 0.5 1 1.5 2 2.5 300.511.52I-V Curves (Diagonal Shade) (Proposed)Voltage (V)Current (A)  Exp.Sim.0 0.5 1 1.5 2 2.5 3012345P-V Curves (Diagonal Shade) (Proposed)Voltage (V)Power (W)  Exp.Sim.64  Table 5-5 Experimental data for PV panel under diagonal shade. Diagonal Shade TCT stepwise proposed V I V I V I V I V I V I 0.17 2.92 2.65 1.38 0.06 1.16 2.54 0.82 0.10 1.94 2.74 0.81 0.57 2.84 2.70 1.10 0.40 1.11 2.63 0.70 1.10 1.90 2.75 0.59 1.22 2.79 2.74 0.81 1.09 1.05 2.67 0.64 1.63 1.84 2.81 0.39 1.72 2.71 2.78 0.70 1.39 1.00 2.71 0.49 2.20 1.83 2.82 0.31 2.17 2.53 2.8 0.52 1.71 0.97 2.75 0.36 2.36 1.70 2.82 0.23 2.42 2.18 2.83 2.56 1.88 0.97 2.78 0.21 2.55 1.47   2.49 1.90 2.84 0.22 2.10 0.93   2.59 1.29   2.59 1.63   2.41 0.92   2.66 1.07     Figure 5.38 Experimental curves under diagonal shade (TCT vs stepwise vs proposed).   0 0.5 1 1.5 2 2.5 300.511.522.53I-V Curves (Diagonal Shade)Voltage (V)Current (A)  TCTStepwiseProposed0 0.5 1 1.5 2 2.5 30123456P-V Curves (Diagonal Shade)Voltage (V)Power (W)  TCTStepwiseProposed65  5.4 RESULTS EVALUATION Table 5-6 Summary of the maximum power point achieved in % comparison. Shade Patterns Maximum Power Point (W) TCT stepwise proposed Values % vs TCT Values % vs TCT % vs Stepwise NS Same LN Same LW 2.36 4.69 +98.73 4.25 +80.08 -9.38 SN 6.84 6.65 -2.78 6.73 -1.61 +1.2 SW 2.26 5.85 +158.85 5.08 +124.78 -13.16 DI 5.49 2.21 -59.74 4.03 -26.59 +82.35  Table 5-6 above summarizes how the performance of the proposed rearrangement compares to the regular TCT and the stepwise configurations in terms of their acquired MPPs. The configurations obviously have the same performance when there is no shade or under the LN shading patterns because the rearranged shades are the same as the original ones. The experimental results achieved are very close to the simulated ones, the differences only being caused by the series and shunt resistive effects from the real PV cell which have been neglected in the simplified single-diode model used in the simulations. They also have similar performance with less than 3% difference when under the short-narrow shading condition. This may be due to the limitations of the experiment, as it is carried out at lower electric ratings, thus making the discrepancy insignificant. On the other hand, when under the LW and SW shades, both the stepwise and the currently proposed rearrangement offer enormous improvement for their MPP with an increase of at least 80% to 160% when comparing to the TCT configuration. Even though the proposed rearrangement has around 9% to 13% less enhancement compared with the stepwise reconfiguration in these two shade sceneries, it outperforms the latter by 82% and is only 27% lower than the TCT configuration in the case of DI shade. It is expected that with a larger scale experiment, the performance will be even better.   66  5.5 CHAPTER SUMMARY In this chapter, a hardware validation is carried out to experiment and compare the performance of TCT, stepwise, and the proposed configurations under different PS conditions. An overview of the equipment used in the experimental set-up is given in Section 5.1. There is also an experiment included to investigate the effect of metal grid structure and the location of the shade on a single PV cell under a series of fixed incremental shade intervals. After that, I-V and P-V characteristic curves of each configuration are plotted against each other using the experimental data, as provided in the tables. Based on an evaluation of the experimental results, no observable difference can be seen in the case of NS and LN as the shade is the same for every tested configurations. For LW, SN, and SW PS conditions, similar performances with 13.16 % difference at most are detected between the stepwise and proposed configurations, while outperforming the original TCT configuration with as high as 124.78 % better MPP in the case of SW. On the other hand, when under the special case of diagonal PS, the proposed rearrangement has an 82.37 % better MPP than the stepwise reconfiguration. All in all, similar to the simulation results, the experimental results verified the effectiveness of the proposed rearrangement strategy at improving the performance under PS: while achieving a higher MPP than the TCT in shades such as LW and SW, it is also able to maintain a satisfactory MPP under DI shade that the other dispersion method is not able to do.   67  6 CONCLUSIONS  The proposed shade dispersion approach is presented and has demonstrated its effectiveness at reducing PS losses on PV modules in this thesis. Simulations and experimental validations of this approach have shown efficiency improvement with better MPP under several tested PS conditions. 6.1 ADVANTAGES AND LIMITATIONS As opposed to the configurations introduced from the literature, the proposed strategy has the ability to provide improved MPP like the other shade dispersion methods but without exhibiting similar limitations. It is also scalable with any parity number combination of columns or rows, and the unique placement rules of this strategy also ensures a lower manufacturing cost as only the alternating columns of PV cell in the module are required to be rearranged. Hence, the whole PV panel is essentially being separated into two types of PV array, which can then be manufactured independently into two different modules and combined alternatingly together as one at the end.  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Saga, "Advances in crystalline silicon solar cell technology for industrial mass production," NPG Asia Materials, vol. 2, no. 3, pp. 96-102, 2010.  [82] P. Wurfel and U. Wurfel, "The Solar Spectrum," in Physics of Solar Cells: From Basic Principles to Advanced Concepts, Weinheim, Wiley-VCH Verlag GmbH & Co. KGaA, 2009, p. 27. [83] P. Hersch and Z. Kenneth, "The Typical Single-Crystal Silicon Solar Cell," in Basic Photovoltaic Principles and Methods, Colorado, Technical Information Office, Solar Energy Research Institute, 1982, p. 24.     78  APPENDICES APPENDIX A: BLOCK DIAGRAMS OF SDM  Figure A.1 Modeling of the photocurrent equation.  Figure A.2 Modeling of the rev. sat. current eqn. at reference temperature.   79   Figure A.3 Modeling of the rev. sat. current eqn. at operating temperature.  Figure A.4 Modeling of the shunt current equation.   80   Figure A.5 Modeling of the load current equation.  Figure A.6 Modeling of the thermal voltage equation.   81   Figure A.7 Modeling of the diode current equation.  Figure A.8 Testing circuit for the single-diode model.   82  APPENDIX B: SIMULATED CONFIGURATIONS  Figure B.1 Series-parallel (SP) configuration.  Figure B.2 Bridge-linked (BL) configuration. 83   Figure B.3 Total-cross-tied (TCT) configuration.   84  APPENDIX C: CODE FOR FIGURE PLOTTING Chapter 3 %**************************************************** % Curves for varying cell number in series %****************************************************   figure (1)   subplot(2,1,1) plot(Vout1.signals.values, Iout1.signals.values,'k', Vout2.signals.values, Iout2.signals.values,'--k', Vout3.signals.values, Iout3.signals.values,':k') title('I-V Curves', 'fontsize', 14) xlabel('Voltage (V)') ylabel('Current (A)') legend({'Ns = 1', 'Ns = 2', 'Ns = 3'},'location','southwest')   subplot(2,1,2) plot(Vout1.signals.values, Pout1.signals.values,'k', Vout2.signals.values, Pout2.signals.values,'--k', Vout3.signals.values, Pout3.signals.values,':k') title('P-V Curves', 'fontsize', 14) xlabel('Voltage (V)') ylabel('Power (W)') legend({'Ns = 1', 'Ns = 2', 'Ns = 3'},'location','northwest')   %**************************************************** % Curves for varying cell number in parallel %****************************************************   figure (2)   subplot(2,1,1) plot(VoutMp1.signals.values, IoutMp1.signals.values,'k', VoutMp2.signals.values, IoutMp2.signals.values,'--k', VoutMp3.signals.values, IoutMp3.signals.values,':k') title('I-V Curves', 'fontsize', 14) xlabel('Voltage (V)') ylabel('Current (A)') legend({'Np = 1', 'Np = 2', 'Np = 3'},'location','southwest')   subplot(2,1,2) plot(VoutMp1.signals.values, PoutMp1.signals.values,'k', VoutMp2.signals.values, PoutMp2.signals.values,'--k', VoutMp3.signals.values, PoutMp3.signals.values,':k') title('P-V Curves', 'fontsize', 14) xlabel('Voltage (V)') ylabel('Power (W)') legend({'Np = 1', 'Np = 2', 'Np = 3'},'location','northwest')   %**************************************************** % Curves for varying solar irradiation strength %****************************************************   figure (3)   subplot(2,1,1) plot(Voutr2.signals.values, Ioutr2.signals.values,'k', Voutr1.signals.values, Ioutr1.signals.values,'--k', Voutr3.signals.values, Ioutr3.signals.values,':k') title('I-V Curves', 'fontsize', 14) xlabel('Voltage (V)') ylabel('Current (A)') 85  legend({'Irr = 800 W/m^2', 'Irr = 1000 W/m^2', 'Irr = 1200 W/m^2'},'location','southwest')   subplot(2,1,2) plot(Voutr2.signals.values, Poutr2.signals.values,'k', Voutr1.signals.values, Poutr1.signals.values,'--k', Voutr3.signals.values, Poutr3.signals.values,':k') title('P-V Curves', 'fontsize', 14) xlabel('Voltage (V)') ylabel('Power (W)') legend({'Irr = 800 W/m^2', 'Irr = 1000 W/m^2', 'Irr = 1200 W/m^2'},'location','northwest')   %**************************************************** % Curves for varying the PV cell temperature %****************************************************   figure (4)   subplot(2,1,1) plot(Voutt1.signals.values, Ioutt1.signals.values,'k', Voutt2.signals.values, Ioutt2.signals.values,'--k', Voutt3.signals.values, Ioutt3.signals.values,':k') title('Zoomed I-V Curves', 'fontsize', 14) xlabel('Voltage (V)') ylabel('Current (A)') legend({'Top = 25 ^oC', 'Top = 50 ^oC', 'Top = 75 ^oC'},'location','southwest') ylim([3 3.25])   subplot(2,1,2) plot(Voutt1.signals.values, Poutt1.signals.values,'k', Voutt2.signals.values, Poutt2.signals.values,'--k', Voutt3.signals.values, Poutt3.signals.values,':k') title('P-V Curves', 'fontsize', 14) xlabel('Voltage (V)') ylabel('Power (W)') legend({'Top = 25 ^oC', 'Top = 50 ^oC', 'Top = 75 ^oC'},'location','northwest')  Chapter 4 %**************************************************** % 6 x 6 - Long Narrow %****************************************************   figure (1)   subplot(2,1,1)   plot(vsp6x6ln.signals.values,isp6x6ln.signals.values,':k'); hold all plot(vtct6x6ln.signals.values,itct6x6ln.signals.values,'-.k'); plot(vstpws6x6ln.signals.values,istpws6x6ln.signals.values,'--k'); plot(vprpsd6x6ln.signals.values,iprpsd6x6ln.signals.values,'-k'); hold off   title('I-V Curves (LN)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp6x6ln.signals.values,psp6x6ln.signals.values,':k'); hold all 86  plot(vtct6x6ln.signals.values,ptct6x6ln.signals.values,'-.k'); plot(vstpws6x6ln.signals.values,pstpws6x6ln.signals.values,'--k'); plot(vprpsd6x6ln.signals.values,pprpsd6x6ln.signals.values,'-k'); hold off   title('P-V Curves (LN)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')   %**************************************************** % 6 x 6 - Long Wide %****************************************************   figure (2)   subplot(2,1,1)   plot(vsp6x6lw.signals.values,isp6x6lw.signals.values,':k'); hold all plot(vtct6x6lw.signals.values,itct6x6lw.signals.values,'-.k'); plot(vstpws6x6lw.signals.values,istpws6x6lw.signals.values,'--k'); plot(vprpsd6x6lw.signals.values,iprpsd6x6lw.signals.values,'-k'); hold off   title('I-V Curves (LW)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp6x6lw.signals.values,psp6x6lw.signals.values,':k'); hold all plot(vtct6x6lw.signals.values,ptct6x6lw.signals.values,'-.k'); plot(vstpws6x6lw.signals.values,pstpws6x6lw.signals.values,'--k'); plot(vprpsd6x6lw.signals.values,pprpsd6x6lw.signals.values,'-k'); hold off   title('P-V Curves (LW)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')   %**************************************************** % 6 x 6 - Short Narrow %****************************************************   figure (3)   subplot(2,1,1)   plot(vsp6x6sn.signals.values,isp6x6sn.signals.values,':k'); hold all plot(vtct6x6sn.signals.values,itct6x6sn.signals.values,'-.k'); plot(vstpws6x6sn.signals.values,istpws6x6sn.signals.values,'--k'); plot(vprpsd6x6sn.signals.values,iprpsd6x6sn.signals.values,'-k'); hold off   title('I-V Curves (SN)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest') 87    subplot(2,1,2)   plot(vsp6x6sn.signals.values,psp6x6sn.signals.values,':k'); hold all plot(vtct6x6sn.signals.values,ptct6x6sn.signals.values,'-.k'); plot(vstpws6x6sn.signals.values,pstpws6x6sn.signals.values,'--k'); plot(vprpsd6x6sn.signals.values,pprpsd6x6sn.signals.values,'-k'); hold off   title('P-V Curves (SN)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')   %**************************************************** % 6 x 6 - Short Wide %****************************************************   figure (4)   subplot(2,1,1)   plot(vsp6x6sw.signals.values,isp6x6sw.signals.values,':k'); hold all plot(vtct6x6sw.signals.values,itct6x6sw.signals.values,'-.k'); plot(vstpws6x6sw.signals.values,istpws6x6sw.signals.values,'--k'); plot(vprpsd6x6sw.signals.values,iprpsd6x6sw.signals.values,'-k'); hold off   title('I-V Curves (SW)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp6x6sw.signals.values,psp6x6sw.signals.values,':k'); hold all plot(vtct6x6sw.signals.values,ptct6x6sw.signals.values,'-.k'); plot(vstpws6x6sw.signals.values,pstpws6x6sw.signals.values,'--k'); plot(vprpsd6x6sw.signals.values,pprpsd6x6sw.signals.values,'-k'); hold off   title('P-V Curves (SW)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')   %**************************************************** % 6 x 6 - Diagonal %****************************************************   figure (5)   subplot(2,1,1)   plot(vsp6x6di.signals.values,isp6x6di.signals.values,':k'); hold all plot(vtct6x6di.signals.values,itct6x6di.signals.values,'-.k'); plot(vstpws6x6di.signals.values,istpws6x6di.signals.values,'--k'); plot(vprpsd6x6di.signals.values,iprpsd6x6di.signals.values,'-k'); hold off 88    title('I-V Curves (DI)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp6x6di.signals.values,psp6x6di.signals.values,':k'); hold all plot(vtct6x6di.signals.values,ptct6x6di.signals.values,'-.k'); plot(vstpws6x6di.signals.values,pstpws6x6di.signals.values,'--k'); plot(vprpsd6x6di.signals.values,pprpsd6x6di.signals.values,'-k'); hold off   title('P-V Curves (DI)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')  %**************************************************** % 6 x 7 - Long Narrow %****************************************************   figure (1)   subplot(2,1,1)   plot(vsp6x7ln.signals.values,isp6x7ln.signals.values,':k'); hold all plot(vtct6x7ln.signals.values,itct6x7ln.signals.values,'-.k'); plot(vstpws6x7ln.signals.values,istpws6x7ln.signals.values,'--k'); plot(vprpsd6x7ln.signals.values,iprpsd6x7ln.signals.values,'-k'); hold off   title('I-V Curves (LN)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp6x7ln.signals.values,psp6x7ln.signals.values,':k'); hold all plot(vtct6x7ln.signals.values,ptct6x7ln.signals.values,'-.k'); plot(vstpws6x7ln.signals.values,pstpws6x7ln.signals.values,'--k'); plot(vprpsd6x7ln.signals.values,pprpsd6x7ln.signals.values,'-k'); hold off   title('P-V Curves (LN)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')   %**************************************************** % 6 x 7 - Long Wide %****************************************************   figure (2)   subplot(2,1,1)   plot(vsp6x7lw.signals.values,isp6x7lw.signals.values,':k'); 89  hold all plot(vtct6x7lw.signals.values,itct6x7lw.signals.values,'-.k'); plot(vstpws6x7lw.signals.values,istpws6x7lw.signals.values,'--k'); plot(vprpsd6x7lw.signals.values,iprpsd6x7lw.signals.values,'-k'); hold off   title('I-V Curves (LW)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp6x7lw.signals.values,psp6x7lw.signals.values,':k'); hold all plot(vtct6x7lw.signals.values,ptct6x7lw.signals.values,'-.k'); plot(vstpws6x7lw.signals.values,pstpws6x7lw.signals.values,'--k'); plot(vprpsd6x7lw.signals.values,pprpsd6x7lw.signals.values,'-k'); hold off   title('P-V Curves (LW)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')   %**************************************************** % 6 x 7 - Short Narrow %****************************************************   figure (3)   subplot(2,1,1)   plot(vsp6x7sn.signals.values,isp6x7sn.signals.values,':k'); hold all plot(vtct6x7sn.signals.values,itct6x7sn.signals.values,'-.k'); plot(vstpws6x7sn.signals.values,istpws6x7sn.signals.values,'--k'); plot(vprpsd6x7sn.signals.values,iprpsd6x7sn.signals.values,'-k'); hold off   title('I-V Curves (SN)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp6x7sn.signals.values,psp6x7sn.signals.values,':k'); hold all plot(vtct6x7sn.signals.values,ptct6x7sn.signals.values,'-.k'); plot(vstpws6x7sn.signals.values,pstpws6x7sn.signals.values,'--k'); plot(vprpsd6x7sn.signals.values,pprpsd6x7sn.signals.values,'-k'); hold off   title('P-V Curves (SN)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')      90  %**************************************************** % 6 x 7 - Short Wide %****************************************************   figure (4)   subplot(2,1,1)   plot(vsp6x7sw.signals.values,isp6x7sw.signals.values,':k'); hold all plot(vtct6x7sw.signals.values,itct6x7sw.signals.values,'-.k'); plot(vstpws6x7sw.signals.values,istpws6x7sw.signals.values,'--k'); plot(vprpsd6x7sw.signals.values,iprpsd6x7sw.signals.values,'-k'); hold off   title('I-V Curves (SW)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp6x7sw.signals.values,psp6x7sw.signals.values,':k'); hold all plot(vtct6x7sw.signals.values,ptct6x7sw.signals.values,'-.k'); plot(vstpws6x7sw.signals.values,pstpws6x7sw.signals.values,'--k'); plot(vprpsd6x7sw.signals.values,pprpsd6x7sw.signals.values,'-k'); hold off   title('P-V Curves (SW)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')   %**************************************************** % 6 x 7 - Diagonal %****************************************************   figure (5)   subplot(2,1,1)   plot(vsp6x7di.signals.values,isp6x7di.signals.values,':k'); hold all plot(vtct6x7di.signals.values,itct6x7di.signals.values,'-.k'); plot(vstpws6x7di.signals.values,istpws6x7di.signals.values,'--k'); plot(vprpsd6x7di.signals.values,iprpsd6x7di.signals.values,'-k'); hold off   title('I-V Curves (DI)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp6x7di.signals.values,psp6x7di.signals.values,':k'); hold all plot(vtct6x7di.signals.values,ptct6x7di.signals.values,'-.k'); plot(vstpws6x7di.signals.values,pstpws6x7di.signals.values,'--k'); plot(vprpsd6x7di.signals.values,pprpsd6x7di.signals.values,'-k'); hold off   91  title('P-V Curves (DI)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')  %**************************************************** % 7 x 6 - Long Narrow %****************************************************   figure (1)   subplot(2,1,1)   plot(vsp7x6ln.signals.values,isp7x6ln.signals.values,':k'); hold all plot(vtct7x6ln.signals.values,itct7x6ln.signals.values,'-.k'); plot(vstpws7x6ln.signals.values,istpws7x6ln.signals.values,'--k'); plot(vprpsd7x6ln.signals.values,iprpsd7x6ln.signals.values,'-k'); hold off   title('I-V Curves (LN)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp7x6ln.signals.values,psp7x6ln.signals.values,':k'); hold all plot(vtct7x6ln.signals.values,ptct7x6ln.signals.values,'-.k'); plot(vstpws7x6ln.signals.values,pstpws7x6ln.signals.values,'--k'); plot(vprpsd7x6ln.signals.values,pprpsd7x6ln.signals.values,'-k'); hold off   title('P-V Curves (LN)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')   %**************************************************** % 7 x 6 - Long Wide %****************************************************   figure (2)   subplot(2,1,1)   plot(vsp7x6lw.signals.values,isp7x6lw.signals.values,':k'); hold all plot(vtct7x6lw.signals.values,itct7x6lw.signals.values,'-.k'); plot(vstpws7x6lw.signals.values,istpws7x6lw.signals.values,'--k'); plot(vprpsd7x6lw.signals.values,iprpsd7x6lw.signals.values,'-k'); hold off   title('I-V Curves (LW)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp7x6lw.signals.values,psp7x6lw.signals.values,':k'); hold all 92  plot(vtct7x6lw.signals.values,ptct7x6lw.signals.values,'-.k'); plot(vstpws7x6lw.signals.values,pstpws7x6lw.signals.values,'--k'); plot(vprpsd7x6lw.signals.values,pprpsd7x6lw.signals.values,'-k'); hold off   title('P-V Curves (LW)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')   %**************************************************** % 7 x 6 - Short Narrow %****************************************************   figure (3)   subplot(2,1,1)   plot(vsp7x6sn.signals.values,isp7x6sn.signals.values,':k'); hold all plot(vtct7x6sn.signals.values,itct7x6sn.signals.values,'-.k'); plot(vstpws7x6sn.signals.values,istpws7x6sn.signals.values,'--k'); plot(vprpsd7x6sn.signals.values,iprpsd7x6sn.signals.values,'-k'); hold off   title('I-V Curves (SN)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp7x6sn.signals.values,psp7x6sn.signals.values,':k'); hold all plot(vtct7x6sn.signals.values,ptct7x6sn.signals.values,'-.k'); plot(vstpws7x6sn.signals.values,pstpws7x6sn.signals.values,'--k'); plot(vprpsd7x6sn.signals.values,pprpsd7x6sn.signals.values,'-k'); hold off   title('P-V Curves (SN)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')   %**************************************************** % 7 x 6 - Short Wide %****************************************************   figure (4)   subplot(2,1,1)   plot(vsp7x6sw.signals.values,isp7x6sw.signals.values,':k'); hold all plot(vtct7x6sw.signals.values,itct7x6sw.signals.values,'-.k'); plot(vstpws7x6sw.signals.values,istpws7x6sw.signals.values,'--k'); plot(vprpsd7x6sw.signals.values,iprpsd7x6sw.signals.values,'-k'); hold off   title('I-V Curves (SW)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest') 93    subplot(2,1,2)   plot(vsp7x6sw.signals.values,psp7x6sw.signals.values,':k'); hold all plot(vtct7x6sw.signals.values,ptct7x6sw.signals.values,'-.k'); plot(vstpws7x6sw.signals.values,pstpws7x6sw.signals.values,'--k'); plot(vprpsd7x6sw.signals.values,pprpsd7x6sw.signals.values,'-k'); hold off   title('P-V Curves (SW)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')   %**************************************************** % 7 x 6 - Diagonal %****************************************************   figure (5)   subplot(2,1,1)   plot(vsp7x6di.signals.values,isp7x6di.signals.values,':k'); hold all plot(vtct7x6di.signals.values,itct7x6di.signals.values,'-.k'); plot(vstpws7x6di.signals.values,istpws7x6di.signals.values,'--k'); plot(vprpsd7x6di.signals.values,iprpsd7x6di.signals.values,'-k'); hold off   title('I-V Curves (DI)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp7x6di.signals.values,psp7x6di.signals.values,':k'); hold all plot(vtct7x6di.signals.values,ptct7x6di.signals.values,'-.k'); plot(vstpws7x6di.signals.values,pstpws7x6di.signals.values,'--k'); plot(vprpsd7x6di.signals.values,pprpsd7x6di.signals.values,'-k'); hold off   title('P-V Curves (DI)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')  %**************************************************** % 7 x 7 - Long Narrow %****************************************************   figure (1)   subplot(2,1,1)   plot(vsp7x7ln.signals.values,isp7x7ln.signals.values,':k'); hold all plot(vtct7x7ln.signals.values,itct7x7ln.signals.values,'-.k'); plot(vstpws7x7ln.signals.values,istpws7x7ln.signals.values,'--k'); plot(vprpsd7x7ln.signals.values,iprpsd7x7ln.signals.values,'-k'); hold off 94    title('I-V Curves (LN)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp7x7ln.signals.values,psp7x7ln.signals.values,':k'); hold all plot(vtct7x7ln.signals.values,ptct7x7ln.signals.values,'-.k'); plot(vstpws7x7ln.signals.values,pstpws7x7ln.signals.values,'--k'); plot(vprpsd7x7ln.signals.values,pprpsd7x7ln.signals.values,'-k'); hold off   title('P-V Curves (LN)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')   %**************************************************** % 7 x 7 - Long Wide %****************************************************   figure (2)   subplot(2,1,1)   plot(vsp7x7lw.signals.values,isp7x7lw.signals.values,':k'); hold all plot(vtct7x7lw.signals.values,itct7x7lw.signals.values,'-.k'); plot(vstpws7x7lw.signals.values,istpws7x7lw.signals.values,'--k'); plot(vprpsd7x7lw.signals.values,iprpsd7x7lw.signals.values,'-k'); hold off   title('I-V Curves (LW)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp7x7lw.signals.values,psp7x7lw.signals.values,':k'); hold all plot(vtct7x7lw.signals.values,ptct7x7lw.signals.values,'-.k'); plot(vstpws7x7lw.signals.values,pstpws7x7lw.signals.values,'--k'); plot(vprpsd7x7lw.signals.values,pprpsd7x7lw.signals.values,'-k'); hold off   title('P-V Curves (LW)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')   %**************************************************** % 7 x 7 - Short Narrow %****************************************************   figure (3)   subplot(2,1,1)   plot(vsp7x7sn.signals.values,isp7x7sn.signals.values,':k'); 95  hold all plot(vtct7x7sn.signals.values,itct7x7sn.signals.values,'-.k'); plot(vstpws7x7sn.signals.values,istpws7x7sn.signals.values,'--k'); plot(vprpsd7x7sn.signals.values,iprpsd7x7sn.signals.values,'-k'); hold off   title('I-V Curves (SN)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp7x7sn.signals.values,psp7x7sn.signals.values,':k'); hold all plot(vtct7x7sn.signals.values,ptct7x7sn.signals.values,'-.k'); plot(vstpws7x7sn.signals.values,pstpws7x7sn.signals.values,'--k'); plot(vprpsd7x7sn.signals.values,pprpsd7x7sn.signals.values,'-k'); hold off   title('P-V Curves (SN)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')   %**************************************************** % 7 x 7 - Short Wide %****************************************************   figure (4)   subplot(2,1,1)   plot(vsp7x7sw.signals.values,isp7x7sw.signals.values,':k'); hold all plot(vtct7x7sw.signals.values,itct7x7sw.signals.values,'-.k'); plot(vstpws7x7sw.signals.values,istpws7x7sw.signals.values,'--k'); plot(vprpsd7x7sw.signals.values,iprpsd7x7sw.signals.values,'-k'); hold off   title('I-V Curves (SW)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp7x7sw.signals.values,psp7x7sw.signals.values,':k'); hold all plot(vtct7x7sw.signals.values,ptct7x7sw.signals.values,'-.k'); plot(vstpws7x7sw.signals.values,pstpws7x7sw.signals.values,'--k'); plot(vprpsd7x7sw.signals.values,pprpsd7x7sw.signals.values,'-k'); hold off   title('P-V Curves (SW)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')       96  %**************************************************** % 7 x 7 - Diagonal %****************************************************   figure (5)   subplot(2,1,1)   plot(vsp7x7di.signals.values,isp7x7di.signals.values,':k'); hold all plot(vtct7x7di.signals.values,itct7x7di.signals.values,'-.k'); plot(vstpws7x7di.signals.values,istpws7x7di.signals.values,'--k'); plot(vprpsd7x7di.signals.values,iprpsd7x7di.signals.values,'-k'); hold off   title('I-V Curves (DI)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('SP','TCT','stepwise','proposed','location','southwest')   subplot(2,1,2)   plot(vsp7x7di.signals.values,psp7x7di.signals.values,':k'); hold all plot(vtct7x7di.signals.values,ptct7x7di.signals.values,'-.k'); plot(vstpws7x7di.signals.values,pstpws7x7di.signals.values,'--k'); plot(vprpsd7x7di.signals.values,pprpsd7x7di.signals.values,'-k'); hold off   title('P-V Curves (DI)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('SP','TCT','stepwise','proposed','location','northwest')  Chapter 5 %**************************************************** % Shade effects on a single cell (Isc vs. d) %****************************************************   x_w_1pv = [0 1 2 3 4 5 6 7 8]; i_w_1pv = [1.18 1.06 0.935 0.809 0.655 0.511 0.347 0.192 0.048]./1.18.*1.76;   x_l_1pv = [0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15]; i_l_1pv = [1.76 1.67 1.54 1.43 1.29 1.17 1.03 0.921 0.803 0.667 0.563 0.430 0.350 0.227 0.138 0.0298];   figure(1) plot(x_w_1pv,i_w_1pv,'k-') title('Short Circuit Current vs. Displacement (Width)','fontsize',14) xlabel('Displacement (cm)') ylabel('Current (A)')   figure(2) plot(x_l_1pv,i_l_1pv,'-k') title('Short Circuit Current vs. Displacement (Length)','fontsize',14) xlabel('Displacement (cm)') ylabel('Current (A)')    97  %**************************************************** % No shade - Exp. vs Sim. %****************************************************   v_NS = [0.27 1.1 1.58 2.1 2.7 2.75 2.83 2.9 2.94 2.97 2.99 3]; i_NS = [3.68 3.54 3.35 3.32 2.65 2.25 1.74 1.29 1.05 0.801 0.55 0.24]; p_NS = v_NS.*i_NS;   figure subplot(2,1,1) plot(v_NS,i_NS,'-k',Vout_TCT_NS.signals.values/max(Vout_TCT_NS.signals.values)*max(v_NS),Iout_TCT_NS.signals.values/max(Iout_TCT_NS.signals.values)*max(i_NS),'--k') title('I-V Curves (No Shade)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('Exp.','Sim.','location','southwest')   subplot(2,1,2) plot(v_NS,p_NS,'-k',Vout_TCT_NS.signals.values/max(Vout_TCT_NS.signals.values)*max(v_NS),Pout_TCT_NS.signals.values/max(Pout_TCT_NS.signals.values)*max(p_NS),'--k') title('P-V Curves (No Shade)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('Exp.','Sim.','location','northwest')  %**************************************************** % Long Narrow - Exp. vs Sim. %****************************************************   v_LN = [0.214 1.1 2.17 2.55 2.69 2.81 2.83 2.89 2.91 2.94]; i_LN = [3.18 3.06 2.86 2.6 2 1.41 1.12 0.826 0.636 0.245]; p_LN = v_LN.*i_LN;   figure subplot(2,1,1) plot(v_LN,i_LN,'-k',Vout_TCT_LN.signals.values/max(Vout_TCT_LN.signals.values)*max(v_LN),Iout_TCT_LN.signals.values/max(Iout_TCT_LN.signals.values)*max(i_LN),'--k') title('I-V Curves (Long Narrow Shade)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('Exp.','Sim.','location','southwest')   subplot(2,1,2) plot(v_LN,p_LN,'-k',Vout_TCT_LN.signals.values/max(Vout_TCT_LN.signals.values)*max(v_LN),Pout_TCT_LN.signals.values/max(Pout_TCT_LN.signals.values)*max(p_LN),'--k') title('P-V Curves (Long Narrow Shade)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('Exp.','Sim.','location','northwest')  %**************************************************** % Exp vs. Sim - Long Wide %****************************************************   % TCT figure(1) subplot(2,1,1) plot(v_tct_LW,i_tct_LW,'-k',Vout_TCT_LW.signals.values./max(Vout_TCT_LW.signals.values).*max(v_tct_LW),I98  out_TCT_LW.signals.values./max(Iout_TCT_LW.signals.values).*max(i_tct_LW),'--k') title('I-V Curves (Long Wide Shade) (TCT)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('Exp.','Sim.','location','southwest') subplot(2,1,2) plot(v_tct_LW,p_tct_LW,'-k',Vout_TCT_LW.signals.values./max(Vout_TCT_LW.signals.values).*max(v_tct_LW),Pout_TCT_LW.signals.values./max(Pout_TCT_LW.signals.values).*max(p_tct_LW),'--k') title('P-V Curves (Long Wide Shade) (TCT)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('Exp.','Sim.','location','northwest')   % Stepwise figure(2) subplot(2,1,1) plot(v_sw_LW,i_sw_LW,'-k',Vout_SW_LW.signals.values./max(Vout_SW_LW.signals.values).*max(v_sw_LW),Iout_SW_LW.signals.values./max(Iout_SW_LW.signals.values).*max(i_sw_LW),'--k') title('I-V Curves (Long Wide Shade) (Stepwise)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('Exp.','Sim.','location','southwest') subplot(2,1,2) plot(v_sw_LW,p_sw_LW,'-k',Vout_SW_LW.signals.values./max(Vout_SW_LW.signals.values).*max(v_sw_LW),Pout_SW_LW.signals.values./max(Pout_SW_LW.signals.values).*max(p_sw_LW),'--k') title('P-V Curves (Long Wide Shade) (Stepwise)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('Exp.','Sim.','location','northwest')   % Proposed figure(3) subplot(2,1,1) plot(v_p_LW,i_p_LW,'-k',Vout_P_LW.signals.values./max(Vout_P_LW.signals.values).*max(v_p_LW),Iout_P_LW.signals.values./max(Iout_P_LW.signals.values).*max(i_p_LW),'--k') title('I-V Curves (Long Wide Shade) (Proposed)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('Exp.','Sim.','location','southwest') subplot(2,1,2) plot(v_p_LW,p_p_LW,'-k',Vout_P_LW.signals.values./max(Vout_P_LW.signals.values).*max(v_p_LW),Pout_P_LW.signals.values./max(Pout_P_LW.signals.values).*max(p_p_LW),'--k') title('P-V Curves (Long Wide Shade) (Proposed)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('Exp.','Sim.','location','northwest')  %**************************************************** % Long Wide - Exp. - TCT vs Stepwise vs Proposed %****************************************************   v_tct_LW = [0.162 1.05 1.4 1.86 2.11 2.55 2.68 2.74 2.78 2.82 2.85]; i_tct_LW = [1.18 1.07 1.04 0.989 0.967 0.925 0.804 0.659 0.522 0.378 0.22]; p_tct_LW = v_tct_LW.*i_tct_LW;   v_sw_LW = [0.172 1.04 1.49 2.11 2.51 2.67 2.73 2.78 2.83 2.85 2.87]; 99  i_sw_LW = [2.4 2.28 2.23 2.12 1.87 1.34 1.09 0.8 0.527 0.288 0.235]; p_sw_LW = v_sw_LW.*i_sw_LW;   v_p_LW = [0.162 1.07 1.45 1.91 2.32 2.67 2.74 2.78 2.81 2.84 2.85]; i_p_LW = [2.12 2.08 1.96 1.91 1.83 1.18 0.934 0.737 0.527 0.315 0.196]; p_p_LW = v_p_LW.*i_p_LW;   figure subplot(2,1,1) plot(v_tct_LW,i_tct_LW,'--k') hold on plot(v_sw_LW,i_sw_LW,'-.k') plot(v_p_LW,i_p_LW,'-k') hold off title('I-V Curves (Long Wide Shade)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('TCT','Stepwise','Proposed','location','southwest')   subplot(2,1,2) plot(v_tct_LW,p_tct_LW,'--k') hold on plot(v_sw_LW,p_sw_LW,'-.k') plot(v_p_LW,p_p_LW,'-k') hold off title('P-V Curves (Long Wide Shade)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('TCT','Stepwise','Proposed','location','northwest')  %**************************************************** % Exp vs. Sim - Short Narrow %****************************************************   % TCT figure(1) subplot(2,1,1) plot(v_tct_SN,i_tct_SN,'-k',Vout_TCT_SN.signals.values./max(Vout_TCT_SN.signals.values).*max(v_tct_SN),Iout_TCT_SN.signals.values./max(Iout_TCT_SN.signals.values).*max(i_tct_SN),'--k') title('I-V Curves (Short Narrow Shade) (TCT)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('Exp.','Sim.','location','southwest') subplot(2,1,2) plot(v_tct_SN,p_tct_SN,'-k',Vout_TCT_SN.signals.values./max(Vout_TCT_SN.signals.values).*max(v_tct_SN),Pout_TCT_SN.signals.values./max(Pout_TCT_SN.signals.values).*max(p_tct_SN),'--k') title('P-V Curves (Short Narrow Shade) (TCT)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('Exp.','Sim.','location','northwest')   % Stepwise figure(2) subplot(2,1,1) plot(v_sw_SN,i_sw_SN,'-k',Vout_SW_SN.signals.values./max(Vout_SW_SN.signals.values).*max(v_sw_SN),Iout_SW_SN.signals.values./max(Iout_SW_SN.signals.values).*max(i_sw_SN),'--k') title('I-V Curves (Short Narrow Shade) (Stepwise)','fontsize',14) xlabel('Voltage (V)') 100  ylabel('Current (A)') legend('Exp.','Sim.','location','southwest') subplot(2,1,2) plot(v_sw_SN,p_sw_SN,'-k',Vout_SW_SN.signals.values./max(Vout_SW_SN.signals.values).*max(v_sw_SN),Pout_SW_SN.signals.values./max(Pout_SW_SN.signals.values).*max(p_sw_SN),'--k') title('P-V Curves (Short Narrow Shade) (Stepwise)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('Exp.','Sim.','location','northwest')   % Proposed figure(3) subplot(2,1,1) plot(v_p_SN,i_p_SN,'-k',Vout_P_SN.signals.values./max(Vout_P_SN.signals.values).*max(v_p_SN),Iout_P_SN.signals.values./max(Iout_P_SN.signals.values).*max(i_p_SN),'--k') title('I-V Curves (Short Narrow Shade) (Proposed)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('Exp.','Sim.','location','southwest') subplot(2,1,2) plot(v_p_SN,p_p_SN,'-k',Vout_P_SN.signals.values./max(Vout_P_SN.signals.values).*max(v_p_SN),Pout_P_SN.signals.values./max(Pout_P_SN.signals.values).*max(p_p_SN),'--k') title('P-V Curves (Short Narrow Shade) (Proposed)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('Exp.','Sim.','location','northwest')   %**************************************************** % Short Narrow - Exp. - TCT vs Stepwise vs Proposed %****************************************************   v_tct_SN = [0.349 1.031 1.49 2.13 2.36 2.53 2.58 2.73 2.78 2.82 2.88 2.90]; i_tct_SN = [3.23 3.06 3.06 2.98 2.9 2.48 2.28 1.5 1.15 0.892 0.378 0.258]; p_tct_SN = v_tct_SN.*i_tct_SN;   v_sw_SN = [0.147 1.27 1.89 2.31 2.49 2.55 2.61 2.71 2.74 2.82 2.86 2.9]; i_sw_SN = [3.13 3.12 3.06 2.88 2.53 2.37 2.12 1.52 1.21 0.857 0.42 0.239]; p_sw_SN = v_sw_SN.*i_sw_SN;   v_p_SN = [0.17 1.06 1.68 2.26 2.45 2.51 2.58 2.6 2.69 2.73 2.77 2.81 2.83 2.85 2.88]; i_p_SN = [3.22 3.18 3.04 2.98 2.68 2.57 2.24 2.11 1.61 1.36 1.05 0.817 0.573 0.456 0.234]; p_p_SN = v_p_SN.*i_p_SN;   figure subplot(2,1,1) plot(v_tct_SN,i_tct_SN,'--k') hold on plot(v_sw_SN,i_sw_SN,'-.k') plot(v_p_SN,i_p_SN,'-k') hold off title('I-V Curves (Short Narrow Shade)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('TCT','Stepwise','Proposed','location','southwest')   subplot(2,1,2) plot(v_tct_SN,p_tct_SN,'--k') hold on 101  plot(v_sw_SN,p_sw_SN,'-.k') plot(v_p_SN,p_p_SN,'-k') hold off title('P-V Curves (Short Narrow Shade)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('TCT','Stepwise','Proposed','location','northwest')  %**************************************************** % Exp vs. Sim - Short Wide %****************************************************   % TCT figure(1) subplot(2,1,1) plot(v_tct_SW,i_tct_SW,'-k',Vout_TCT_SW.signals.values./max(Vout_TCT_SW.signals.values).*max(v_tct_SW),Iout_TCT_SW.signals.values./max(Iout_TCT_SW.signals.values).*max(i_tct_SW),'--k') title('I-V Curves (Short Wide Shade) (TCT)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('Exp.','Sim.','location','southwest') subplot(2,1,2) plot(v_tct_SW,p_tct_SW,'-k',Vout_TCT_SW.signals.values./max(Vout_TCT_SW.signals.values).*max(v_tct_SW),Pout_TCT_SW.signals.values./max(Pout_TCT_SW.signals.values).*max(p_tct_SW),'--k') title('P-V Curves (Short Wide Shade) (TCT)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('Exp.','Sim.','location','northwest')   % Stepwise figure(2) subplot(2,1,1) plot(v_sw_SW,i_sw_SW,'-k',Vout_SW_SW.signals.values./max(Vout_SW_SW.signals.values).*max(v_sw_SW),Iout_SW_SW.signals.values./max(Iout_SW_SW.signals.values).*max(i_sw_SW),'--k') title('I-V Curves (Short Wide Shade) (Stepwise)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('Exp.','Sim.','location','southwest') subplot(2,1,2) plot(v_sw_SW,p_sw_SW,'-k',Vout_SW_SW.signals.values./max(Vout_SW_SW.signals.values).*max(v_sw_SW),Pout_SW_SW.signals.values./max(Pout_SW_SW.signals.values).*max(p_sw_SW),'--k') title('P-V Curves (Short Wide Shade) (Stepwise)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('Exp.','Sim.','location','northwest')   % Proposed figure(3) subplot(2,1,1) plot(v_p_SW,i_p_SW,'-k',Vout_P_SW.signals.values./max(Vout_P_SW.signals.values).*max(v_p_SW),Iout_P_SW.signals.values./max(Iout_P_SW.signals.values).*max(i_p_SW),'--k') title('I-V Curves (Short Wide Shade) (Proposed)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('Exp.','Sim.','location','southwest') subplot(2,1,2) 102  plot(v_p_SW,p_p_SW,'-k',Vout_P_SW.signals.values./max(Vout_P_SW.signals.values).*max(v_p_SW),Pout_P_SW.signals.values./max(Pout_P_SW.signals.values).*max(p_p_SW),'--k') title('P-V Curves (Short Wide Shade) (Proposed)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('Exp.','Sim.','location','northwest')  %**************************************************** % Short Wide - Exp. - TCT vs Stepwise vs Proposed %****************************************************   v_tct_SW = [0.0694 1.02 1.5 1.92 2.3 2.53 2.67 2.7 2.74 2.78 2.8 2.81]; i_tct_SW = [1.18 1.1 1.01 0.964 0.944 0.895 0.712 0.662 0.545 0.345 0.287 0.232]; p_tct_SW = v_tct_SW.*i_tct_SW;   v_sw_SW = [0.144 1.22 1.75 2.14 2.38 2.5 2.57 2.62 2.66 2.71 2.76 2.8 2.82 2.85 2.86]; i_sw_SW = [2.94 2.82 2.73 2.66 2.46 2.13 1.88 1.61 1.43 1.17 0.872 0.673 0.452 0.263 0.223]; p_sw_SW = v_sw_SW.*i_sw_SW;   v_p_SW = [0.169 1.06 1.55 2.07 2.38 2.44 2.58 2.59 2.63 2.69 2.73 2.78 2.81 2.82 2.86]; i_p_SW = [2.47 2.35 2.27 2.19 2.12 2.08 1.78 1.64 1.43 1.19 0.996 0.702 0.506 0.386 0.238]; p_p_SW = v_p_SW.*i_p_SW;   figure subplot(2,1,1) plot(v_tct_SW,i_tct_SW,'--k') hold on plot(v_sw_SW,i_sw_SW,'-.k') plot(v_p_SW,i_p_SW,'-k') hold off title('I-V Curves (Short Wide Shade)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('TCT','Stepwise','Proposed','location','southwest')   subplot(2,1,2) plot(v_tct_SW,p_tct_SW,'--k') hold on plot(v_sw_SW,p_sw_SW,'-.k') plot(v_p_SW,p_p_SW,'-k') hold off title('P-V Curves (Short Wide Shade)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('TCT','Stepwise','Proposed','location','northwest')  %**************************************************** % Exp vs. Sim - Diagonal %****************************************************   % TCT figure(1) subplot(2,1,1) plot(v_tct_DI,i_tct_DI,'-k',Vout_TCT_DI.signals.values./max(Vout_TCT_DI.signals.values).*max(v_tct_DI),Iout_TCT_DI.signals.values./max(Iout_TCT_DI.signals.values).*max(i_tct_DI),'--k') 103  title('I-V Curves (Diagonal Shade) (TCT)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('Exp.','Sim.','location','southwest') subplot(2,1,2) plot(v_tct_DI,p_tct_DI,'-k',Vout_TCT_DI.signals.values./max(Vout_TCT_DI.signals.values).*max(v_tct_DI),Pout_TCT_DI.signals.values./max(Pout_TCT_DI.signals.values).*max(p_tct_DI),'--k') title('P-V Curves (Diagonal Shade) (TCT)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('Exp.','Sim.','location','northwest')   % Stepwise figure(2) subplot(2,1,1) plot(v_sw_DI,i_sw_DI,'-k',Vout_SW_DI.signals.values./max(Vout_SW_DI.signals.values).*max(v_sw_DI),Iout_SW_DI.signals.values./max(Iout_SW_DI.signals.values).*max(i_sw_DI),'--k') title('I-V Curves (Diagonal Shade) (Stepwise)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('Exp.','Sim.','location','southwest') subplot(2,1,2) plot(v_sw_DI,p_sw_DI,'-k',Vout_SW_DI.signals.values./max(Vout_SW_DI.signals.values).*max(v_sw_DI),Pout_SW_DI.signals.values./max(Pout_SW_DI.signals.values).*max(p_sw_DI),'--k') title('P-V Curves (Diagonal Shade) (Stepwise)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('Exp.','Sim.','location','northwest')   % Proposed figure(3) subplot(2,1,1) plot(v_p_DI,i_p_DI,'-k',Vout_P_DI.signals.values./max(Vout_P_DI.signals.values).*max(v_p_DI),Iout_P_DI.signals.values./max(Iout_P_DI.signals.values).*max(i_p_DI),'--k') title('I-V Curves (Diagonal Shade) (Proposed)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('Exp.','Sim.','location','southwest') subplot(2,1,2) plot(v_p_DI,p_p_DI,'-k',Vout_P_DI.signals.values./max(Vout_P_DI.signals.values).*max(v_p_DI),Pout_P_DI.signals.values./max(Pout_P_DI.signals.values).*max(p_p_DI),'--k') title('P-V Curves (Diagonal Shade) (Proposed)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('Exp.','Sim.','location','northwest')  %**************************************************** % Diagonal - Exp. - TCT vs Stepwise vs Proposed %****************************************************   v_tct_DI = [0.173 0.566 1.22 1.72 2.17 2.42 2.49 2.59 2.65 2.7 2.74 2.78 2.8 2.83 2.84]; i_tct_DI = [2.92 2.84 2.79 2.71 2.53 2.18 1.9 1.63 1.38 1.1 0.813 0.697 0.519 0.255 0.224]; p_tct_DI = v_tct_DI.*i_tct_DI;   104  v_sw_DI = [0.0625 0.395 1.09 1.39 1.71 1.88 2.1 2.41 2.54 2.63 2.67 2.71 2.75 2.78]; i_sw_DI = [1.16 1.11 1.05 1 0.971 0.965 0.933 0.918 0.817 0.698 0.638 0.487 0.357 0.209]; p_sw_DI = v_sw_DI.*i_sw_DI;   v_p_DI = [0.102 1.09 1.63 2.2 2.36 2.55 2.59 2.66 2.74 2.75 2.81 2.82 2.82]; i_p_DI = [1.94 1.9 1.84 1.83 1.7 1.47 1.29 1.07 0.806 0.59 0.389 0.308 0.229]; p_p_DI = v_p_DI.*i_p_DI;   figure subplot(2,1,1) plot(v_tct_DI,i_tct_DI,'--k') hold on plot(v_sw_DI,i_sw_DI,'-.k') plot(v_p_DI,i_p_DI,'-k') hold off title('I-V Curves (Diagonal Shade)','fontsize',14) xlabel('Voltage (V)') ylabel('Current (A)') legend('TCT','Stepwise','Proposed','location','southwest')   subplot(2,1,2) plot(v_tct_DI,p_tct_DI,'--k') hold on plot(v_sw_DI,p_sw_DI,'-.k') plot(v_p_DI,p_p_DI,'-k') hold off title('P-V Curves (Diagonal Shade)','fontsize',14) xlabel('Voltage (V)') ylabel('Power (W)') legend('TCT','Stepwise','Proposed','location','northwest')    

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