FEDERAL UNIVERSITY OF RIO GRANDE DO NORTE TECHNOLOGY CENTER
POST-GRADUATION PROGRAM IN MECHANICAL ENGINEERING
INFLUENCE OF TEMPERATURE ON POLYCRYSTALLINE SILICON SOLAR CELL TECHNOLOGIES
NÍCOLAS MATHEUS DA FONSECA TINOCO DE SOUZA ARAÚJO NATAL- RN, 2019
FEDERAL UNIVERSITY OF RIO GRANDE DO NORTE TECHNOLOGY CENTER
POST-GRADUATION PROGRAM IN MECHANICAL ENGINEERING
INFLUENCE OF TEMPERATURE ON POLYCRYSTALLINE SILICON SOLAR CELL TECHNOLOGIES
NÍCOLAS MATHEUS DA FONSECA TINOCO DE SOUZA ARAÚJO
Dissertation presented to the Post-Graduation Program in Mechanical Engineering (PPGEM) of the Federal University of Rio Grande do Norte as part of the requirements for obtaining the title of
MASTER IN MECHANICAL
ENGINEERING, supervised by the Prof. Dr. Fábio José Pinheiro Sousa and co- supervised by the Prof. Dr. Flavio Bezerra Costa.
NATAL - RN 2019
Araújo, Nícolas Matheus da Fonseca Tinoco de Souza.
Influence of temperature on polycrystalline silicon solar cell technologies / Nicolas Matheus da Fonseca Tinoco de Souza Araújo. - 2019.
113 f.: il.
Dissertation (master's degree) - Federal University of Rio Grande do Norte, Technology Center, Post-Graduation Program in Mechanical Engineering, Natal, RN, 2019.
Orientador: Prof. Dr. Fábio José Pinheiro Sousa. Coorientador: Prof. Dr. Flavio Bezerra Costa.
1. PV cells - Dissertation. 2. Temperature - Dissertation. 3. Solar simulator Dissertation. 4. Equivalent model
-Dissertation. I. Sousa, Fábio José Pinheiro. II. Costa, Flavio Bezerra. III. Título.
RN/UF/BCZM CDU 620.91
Universidade Federal do Rio Grande do Norte - UFRN Sistema de Bibliotecas - SISBI
Catalogação de Publicação na Fonte. UFRN - Biblioteca Central Zila Mamede
Dedication
I dedicate this work to all those who help make the world a better place for unknowns, but have never had a worthy recognition.
Acknowledgments
A Deus.
As duas pessoas mais importantes da minha vida: meus pais, Sérgio Roberto de Araújo e Juraneide da Fonseca Tinoco de Souza Araújo, os quais, juntos, mostraram-me a importância dos estudos e da perseverança na vida, além de propiciar todos os possíveis e impossíveis meios para que eu pudesse estudar da melhor forma.
Aos meus irmãos, Nickson Sérgio da Fonseca Tinoco de Souza Araújo e Nilberth Roberto da Fonseca Tinoco de Souza Araújo, os quais me deram todo tipo de apoio sempre que necessitei.
Aos meus avôs (Diniz Araújo e Jurandir Fonseca) e às minhas avós (Mirtô Tinoco e Maria das Neves - Sassá) por terem propiciado um ambiente ímpar aos meus pais e, portanto, a mim. Minha eterna gratidão a vocês.
A minha companheira, Lílyan Manásseias Romeiro Dantas, com quem tenho a oportunidade de crescer cada dia mais. Uma mulher que admiro pela inteligência, simplicidade e garra, a qual não permitiu que obstáculos a impedissem de buscar sempre o melhor.
Aos professores Dr. Fábio José Pinheiro Sousa e Dr. Flavio Bezerra Costa por me aceitarem como seu aluno orientado e co-orientado, respectivamente, e por incentivarem a pesquisa científica sempre nivelada por cima. Além de, juntos comigo, terem aceitado a dar início a uma nova empreitada acadêmica, uma nova ramificação na árvore do conhecimento.
Ao Professor Dr. Gabriel Ivan Medina Tapia por ceder espaço físico no Laboratório de Sistemas Térmicos e Energias Alternativas da UFRN para a realização dos ensaios experimentais importantíssimos para o trabalho. Além das incontáveis discussões agregadoras de conhecimento acadêmico e pessoal.
A todos os integrantes do Grupo de Estudos de Tribologia e Integridade Estrutural da UFRN e do Laboratório de Sistemas Térmicos e Energias Alternativas com quem tive a oportunidade de conviver e aprender. Grato em especial aos meus orientadores diretos de Iniciação Científica João Andrade Lopes de Sousa, Gracilene dos Santos Aquino Pontes e Fernando Nunes da Silva, e ao amigo produtivo Felipe Pinheiro Maia. Grato também ao meu orientador indireto de Iniciação Científica o professor Dr. João Telésforo Nóbrega de Medeiros o qual admiro enormemente por seu incentivo às pesquisas científicas, assim como os debates de cunho sociais e pessoais ‘haut niveau’.
Ao Programa de PPGEM-UFRN. E, por fim, à CAPES, pelo apoio financeiro.
“Everything should become as simple as possible, but not simplified.”
ix Araújo, N. M. T. S. Influência da temperatura na tecnologia da célula fotovoltaica policristalina de silício. 2019. 113 p. Dissertação de Mestrado em Engenharia Mecânica (Programa de Pós-Graduação em Engenharia Mecânica) - Universidade Federal do Rio Grande do Norte, Natal-RN, 2019.
Resumo
Ao longo dos anos, a contribuição da energia fotovoltaica para um mundo ambientalmente consciente está continuamente crescendo, enquanto seus custos, reduzindo. Nas tecnologias fotovoltaicas (PV), a temperatura da célula solar e a irradiação solar incidente são os principais fatores os quais afetam seu desempenho. O foco desse trabalho é a análise da influência da temperatura sobre as células fotovoltaicas, tendo em vista seu impacto nos parâmetros físicos desta tecnologia, na capacidade de simulação dos modelos equivalentes existentes e na efetividade dos simuladores solares. Por conseguinte, a fim de compreender esses efeitos, fez-se um estudo acerca do impacto da temperatura nos parâmetros de defez-sempenho de uma célula solar de silício, uma busca por qual o modelo mais adequado para simular células fotovoltaicas com a temperatura de operação variando e uma análise do efeito da temperatura nas condições de simulação ao utilizar um simulador de baixo custo, o SOLSIM. O experimento foi realizado utilizando células fotovoltaicas policristalinas de silício com um intervalo de temperatura de 20 a 60 °C sobre uma intensidade luminosa média de 1.000 W/m², empregando um simulador solar (SOLSIM) desenvolvido pelo INPE e adaptado pelo autor. Neste trabalho, uma breve revisão das diversas relações matemáticas envolvendo a influência da temperatura sobre as células solares foi desenvolvida. Mostrou-se que no intervalo entre 20 e 60 °C os parâmetros da célula solar de silício policristalino variam linearmente com a temperatura, e a potência é reduzida com o aumento da temperatura. Na literatura, identificaram-se sete equações as quais determinam a dependência entre os parâmetros da célula solar e a temperatura. As principais pesquisas acerca do problema de estimação dos parâmetros dos modelos equivalentes de células solares são classificadas de acordo com o número de parâmetros, a forma de extração dos parâmetros, as equações de translação e o material da célula. Uma classificação qualitativa foi realizada e, assim, encontraram-se quatro modelos como sendo os melhores para simular o comportamento de uma célula PV: Boutana et al. (2017), Mahmoud and Xiao (2013), Orioli and Di Gangi (2013) and Ishaque (2011). A temperatura é determinante do valor teórico máximo para a corrente gerada em função do simulador solar utilizado.
x Araújo, N. M. T. S. Influence of temperature on polycrystalline silicon solar cell technologies. 2019. 113 p. Master’s Dissertation in Mechanical Engineering (Post-Graduation Program in Mechanical Engineering) - Federal University of Rio Grande do Norte, Natal-RN, 2019.
Abstract
Over the years, the contribution of photovoltaics energy to an eco-friendly world is continually increasing and its costs reducing. In photovoltaic (PV) technologies, the solar cell temperature and incident solar radiation are the main factors that affect their behaviors. The focus of this work is the analysis of temperature influence over the solar cells, in view of its impact on physical parameters of this technology, on simulation capacity of the existent equivalent models an on effectiveness of solar simulators. Therefore, to comprehend these effects, it was performed a study on the impact of cell temperature on the performance parameters of silicon solar cell, a search for the most suitable model to emulate a solar cell when its operation temperature varies and a analysis of the temperature effect on conditions of simulation while using a low cost solar simulator, the SOLSIM. The experiment was carried out using a polycrystalline silicon solar cell with the temperature in the range 20–60 °C at constant light intensity 1,000 W/m2 employing a solar cell simulator (SOLSIM) developed by the INPE and
adapted by the author. In this work, it was made a brief review of the various existing mathematical relationships involving the influence of temperature over solar cells. In the range 20-60 °C, the polycrystalline solar cell parameters varied linearly with temperature, and the power is reduced with temperature increasing. In literature, it was identified seven equations which determine the dependence between the solar cell parameters and the temperature. The main existing research works on PV cell model parameter estimation problem are classified according to number of parameters, parameters’ extraction, translation equations and PV material technology. A qualitative comparative ranking was made and four models was found to be the best ones to emulating PV cell: Boutana et al. (2017), Mahmoud and Xiao (2013), Orioli and Di Gangi (2013) and Ishaque (2011). The temperature is determinant of the maximum theoretical value to photogenerated current in function of the used solar simulator.
xi
List of figures
Figure 1.1 World energy consumption by energy source (1990-2040). ... 1
Figure 1.2 Estimated US Energy Consumption in 2018: 102.2 Quads. ... 2
Figure 1.3 Learning curve of the PV modules. ... 3
Figure 1.4 Efficiency of solar cells over the years. ... 4
Figure 1.5 Current performance and price of different PV module technologies. ... 4
Figure 2.1 Two band photoconverter. ... 14
Figure 2.2 Power spectrum of a blackbody sun at 5760 K, and power available to its optimum bandgap cell. ... 14
Figure 2.3 Physical structure of PV cell. ... 15
Figure 2.4 Characteristic curve of a PV solar cell. ... 16
Figure 2.5 Environmental influence over the solar cell... 17
Figure 2.6 Spectral distribution of solar radiation for different atmospheric conditions. ... 18
Figure 2.7 Air Mass according to the zenith angle. ... 19
Figure 2.8 IxV curve for different irradiances. ... 20
Figure 2.9 Illuminated J–V characteristics at various temperatures under illumination intensities of (a) 10 suns, (b) 15 suns. ... 21
Figure 2.10 Solar cells efficiency versus temperature for various materials. ... 22
Figure 2.11 Charge carriers’ mobility for silicon doped at two different donor concentrations in relation to temperature. ... 23
Figure 2.12 Temperature effect on the solar cell characteristics. ... 25 Figure 2.13 Evolution of bandgap energy of silicon with temperature. A) Temperature range (0 K to 300 K) according to the limitations of the relations; B) Temperature range (288.15 K to
xii 343.15 K) according to the usual operation temperature of solar cells, out of relations ranges. ... 27 Figure 2.14 Photon flux (AM1.5G) and the integrated short circuit current density as a function of wavelength (bandgap – top x axis). ... 28 Figure 3.1 The low cost solar simulator (SOLSIM) developed by INPE in partnership with the company Orbital Eng. Ltda. ... 40 Figure 3.2 Spectral irradiance curves for AM1.5G standard and SOLSIM. ... 40 Figure 3.3 Instruments used to measure the solar cells temperature. A) K-type Thermocouple and B) NI 9211 module. ... 42 Figure 3.4 Ultra-thermostatic bath... 42 Figure 3.5 SOLSIM light incident area. ... 44 Figure 3.6 Polycrystalline silicon solar cell used in this work. The solar cell is of 15.6 cm length. A) Specimen before cutting process; B) Specimen after cutting process... 44 Figure 3.7 Materials used in the cutting procedure. A) DREMEL 4000 and B) Diamond Wheel. ... 44 Figure 3.8 Instruments used to measure the solar cells voltage and current output. A) NI 9205 module and B) Digital Multimeter model VC8045-II. ... 45 Figure 3.9 Components of the extraction circuit. A) terminal universal connector (5 ways) and resistors, B) Protoboard (EPB 0057) and C) jumpers (20 cm length). ... 45 Figure 3.10 Electrical circuit assembled to enable the extraction of the electrical parameters of the solar cells (current and output voltage). ... 47 Figure 3.11 CompactDAQ Chassis. ... 47 Figure 4.1 Photon flux (SOLSIM) and the integrated short circuit current density as a function of wavelength (bandgap – top x axis) at temperature 298 K. ... 52
xiii Figure 4.2 Maximum theoretical achievable (A) integrated short circuit current density, open-circuit voltage and (B) efficiencies for a single p–n junction solar cell at 298 K as a function of the wavelength for the SOLSIM spectra. ... 53 Figure 4.3 Theoretical variations in solar cell performance parameters: (A) 𝐽𝑠𝑐 and (B) 𝑉𝑜𝑐 for Si, InP, GaAs, CdTe and CdS with temperature for solar cells in the temperature range 298 K– 528 K at SOLSIM spectra. ... 54 Figure 4.4 The theoretical efficiency of solar cells as a function of (A) material, (B) wavelength and temperature for SOLSIM spectra. ... 54 Figure 4.5 Temperature monitoring for all nine conditions. ... 56 Figure 4.6 Temperature controlling using the ultra-thermostatic bath model MA – 185 of Marconi. ... 56 Figure 4.7 Temperature effect on the IxV curve of the solar cell. ... 57 Figure 4.8 Some equivalent models of solar cell... 59
xiv
List of tables
Table 1.1 Advantages and disadvantages of solar photovoltaics during operation. ... 5
Table 2.1 Varshni equation constants for silicon semiconductor material taken from different works. ... 26
Table 2.2 The main goal of 10 different equivalent circuit models for PV cell. ... 34
Table 2.3 Classification of a solar simulator relative to its characteristics. ... 35
Table 2.4 Spectral distribution of the reference radiation, where percentage is relative to the potential share of total radiation. ... 36
Table 3.1 The nine different conditions used in the present work. ... 43
Table 4.1 Load configuration used to extract the whole I x V curve of silicon solar cell. The uncertain is also available. ... 55
Table 4.2 PV operation conditions ranking. ... 60
Table 4.3 Translation Equations' ranking. ... 61
Table 4.4 PV technology ranking. ... 62
xv
List of abbreviations and acronyms
ABNT Brazilian Association of Technical Standards
AM Air Mass
AM0 Solar spectrum incident in outer space (1,353 W/m2)
AM1.5D Solar spectrum incident on the earth (1,000 W/m2; the light is incident directly without any contribution from diffuse rays)
AM1.5G Solar spectrum incident on the earth (1,000 W/m2; includes direct and diffuse rays from the sun)
a-SiC:H Hydrogenated amorphous silicon carbide a-SiGe Amorphous silicon germanium
ASTM American Society for Testing and Materials
CB Conduction band
CdS Cadmium sulfide
CdTe Cadmium telluride
CIGS Copper indium gallium selenide c-Si Crystalline silicon
DCA Diffusion-Current Dominant Area EIA U.S. Energy Information Administration FF Fill Factor
GaAs Gallium arsenide
HIT Heterojunction with intrinsic thin layer IEA International Energy Agency
IEC International Electrotechnical Commission
InP Indium phosphide
INPE National Institute of Space Research (Instituto Nacional de Pesquisas Espaciais - Brazil)
LabMetrol Metrology Laboratory of the Federal University of Rio Grande do Norte LED Light Emitting Diode
mc-Si Mono-crystalline silicon
MPPT Maximum Power Point Tracking NBR ABNT standard designation NI National Instruments
xvi NOCT Normal Operating Cell Temperature
pc-Si Poly-crystalline silicon
PPGEM Post-Graduation Program in Mechanical Engineering
PV Photovoltaic
RCA Recombination-Current Dominant Area SCLC Space-Charge Limited Current
Si Silicon
SOLSIM Solar Simulator developed by INPE STC Standard Test Conditions
TiO2 Titanium dioxide
UFRN Federal University of Rio Grande do Norte
xvii
List of symbols
𝑎 Ideality factor
𝐴 Constant in 𝐽𝑠 expression
𝑐 Velocity of light in vacuum (299 792 458 m/s)
𝐶 Constant in 𝐽𝑠 expression ∆𝜇 Chemical potential (eV) ∆𝑡 Time variation (s)
𝐷𝑛, 𝐷𝑝 Diffusion constants of minority carriers in 𝑛 and 𝑝 region
𝐸𝑐 Conduction band level (eV)
𝐸𝑔 Bandgap (eV)
𝐸𝑔,𝑟𝑒𝑓 Bandgap at STC (eV)
𝐸𝑖 Fermi level in equilibrium 𝐸𝑣 Valence band level
𝐺 Solar irradiation (W/m2) 𝐺0 Solar constant (=1,367 W/m2)
𝐺𝑟𝑒𝑓 Reference solar irradiation (=1,000 W/m2)
ℎ Planck's constant (6.62607004×10−34J∙s) 𝐼 Cell output current (A)
𝐼𝑚𝑝 Maximum power current (A)
𝐼𝑑 Diode current (A)
𝐼𝑠 Cell saturation current (A)
𝐼𝑟𝑠 Cell reverse saturation current (A) 𝐼𝑠𝑐 Short-circuit current (A)
𝐼𝑝𝑣 Light-generated current (A)
𝐼𝑝𝑣,𝑟𝑒𝑓 Light-generated current at STC (A)
𝐽 Cell output current density (A/cm2) 𝐽𝑚𝑝 Maximum power current density (A/cm2) 𝐽𝑑 Diode current density (A/cm2)
𝐽𝑠 Cell saturation current density (A/cm2)
xviii 𝐽𝑠𝑐 Short-circuit current density (A/cm2)
𝐽𝑝𝑣 Light-generated current density (A/cm2)
𝐽𝑝𝑣,𝑟𝑒𝑓 Light-generated current at STC density (A/cm2)
𝑘 Boltzmann’s constant (1.380649 x 10−23𝐽/𝐾)
k Wavevector
𝐿𝑛, 𝐿𝑝 Diffusion lengths of minority carriers in 𝑛 and 𝑝 region
𝜆𝑔 Cut-off wavelength
M Air mass modifier
µ𝑛, µ𝑝 Mobility of the electrons and holes 𝜇𝐼𝑠𝑐 Temperature coefficient of 𝐼𝑠𝑐 (A/K) 𝜇𝑉𝑜𝑐 Temperature coefficient of 𝑉𝑜𝑐 (V/K)
𝑛 Electron density
𝑛𝑖 Intrinsic carrier density
𝜂 Efficiency (%)
𝑁𝐴, 𝑁𝐷 Density of acceptor and donor atoms
𝑝 Hole density
𝑃𝑚𝑝 Maximum power (W)
𝑞 Electron charge (1.602176634×10−19C) 𝑅𝑠 Series resistance (Ω)
𝑅𝑠0 Reciprocal of the slope of the I–V curve for (0, 𝑉𝑜𝑐) (Ω) 𝑅𝑠,𝑟𝑒𝑓 Series resistance at STC (Ω)
𝑅𝑠ℎ Shunt resistance (Ω)
𝑅𝑠ℎ,𝑟𝑒𝑓 Shunt resistance at STC (Ω)
𝑅𝑠ℎ0 Reciprocal of the slope of the I–V curve for (𝐼𝑠𝑐, 0) (Ω) 𝑆 Dimensionless coupling constant
𝜎 Conductivity (𝛺−1𝑐𝑚−1)
𝑇 Cell temperature (K)
𝑇𝑚 Module temperature (K)
𝑇𝑗 Solar cell junction temperature (K) 𝑇𝑟𝑒𝑓 Reference temperature (= 298.15 K)
xix 𝑉𝑚𝑝 Maximum power voltage (V)
𝑉𝑡 Thermal voltage (K/eV)
𝑉𝑛 Ionization energy for electrons (meV)
𝑉𝑝 Ionization energy for holes (meV)
𝑉𝑜𝑐 Open-circuit voltage (V) 〈ћ𝜔〉 Average phonon energy (meV)
Content
RESUMO ... IX
ABSTRACT ... X
LIST OF FIGURES ... XI
LIST OF TABLES ... XIV
LIST OF ABBREVIATIONS AND ACRONYMS ... XV
LIST OF SYMBOLS ... XVII
1. INTRODUCTION ... 1 1.1. PROBLEM FORMULATION... 5 1.2. OBJECTIVES ... 7 1.3. WORK STRUCTURE ... 7 2. LITERATURE REVIEW ... 9 2.1. INTRODUCTION ... 9
2.2. SEMICONDUCTORS AND DOPING ... 9
2.2.1. N TYPE DOPING ... 11
2.2.2. P TYPE DOPING ... 12
2.2.3. EFFECTS OF HEAVY DOPING ... 13
2.3. PHOTOVOLTAIC EFFECT ... 13
2.4. PHOTOVOLTAIC SOLAR CELL ... 14
2.4.1. THE CHARACTERISTIC CURVE ... 15
2.5. PERFORMANCE FACTORS ... 17
2.5.1. SPECTRAL DISTRIBUTION AND MASS OF AIR ... 17
2.5.2. IRRADIANCE ... 19
2.5.3. TEMPERATURE ... 21
xxi
2.6. EQUIVALENT MODELS ... 32
2.7. SOLAR SIMULATORS ... 34
2.8. CALCULATION OF UNCERTAINTIES ... 36
2.8.1. SPREAD OF UNCERTAINTIES ... 37
3. MATERIALS AND METHODS ... 39
3.1. GENERAL CONSIDERATIONS ... 39
3.2. SOLAR CELL CHARACTERIZATION ... 39
3.2.1. IRRADIATION ... 39
3.2.2. TEMPERATURE ... 41
3.2.3. ELECTRICAL PARAMETERS ... 43
3.3. EQUIVALENT MODELS ANALYSIS ... 47
3.3.1. PV OPERATION CONDITIONS ... 48
3.3.2. TRANSLATION EQUATIONS ... 48
3.3.3. PV TECHNOLOGY ... 49
3.3.4. ASSUMPTIONS ... 49
3.3.5. OVERVIEW ... 49
4. RESULTS AND DISCUSSIONS ... 51
4.1. INITIAL CONSIDERATIONS ... 51
4.2. SOLAR CELL CHARACTERIZATION ... 51
4.2.1. SOLSIM ANALYSIS ... 51
4.2.2. RESISTORS ASSOCIATION ... 55
4.2.3. TEMPERATURE ... 55
4.2.4. POLYCRYSTALLINE SILICON SOLAR CELL ANALYSIS ... 57
4.3. EQUIVALENT MODELS ANALYSIS ... 58
4.3.1. PV OPERATION CONDITIONS ... 59
4.3.2. TRANSLATION EQUATIONS ... 61
4.3.3. PV TECHNOLOGY ... 61
4.3.4. ASSUMPTIONS ... 62
xxii
5. CONCLUSIONS ... 66
REFERENCES ... 70
APPENDICES ... 78
APPENDICES A:A BRIEF REVIEW OF EQUIVALENT MODELS ... 79
ANNEXES ... 89
ANNEX A–CALIBRATION CERTIFICATE:THERMOCOUPLE A0 ... 90
ANNEX B–CALIBRATION CERTIFICATE:THERMOCOUPLE A1 ... 91
ANNEX C–CALIBRATION CERTIFICATE:THERMOCOUPLE A2 ... 92
1
1. Introduction
Energy demand is rising due to rapid population growth and rising living standards. Between 2015 and 2040, it was projected that world energy consumption will grow by 28%, according to the latest International Energy Outlook 2017 of the U.S. Energy Information Administration (EIA, 2017; See Figure 1.1). This worldwide increasing energy utilization is one of the greatest challenges that the world is currently dealing with, since there are both the increasing accumulation of greenhouse gases and the decreasing reserves of fossil fuels (Khan et al., 2016).
Figure 1.1 World energy consumption by energy source (1990-2040).
Source: EIA (2017)
From Figure 1.2, the waste of energy is brutal. To produce electricity, 66% is lost (25.3% is lost of a total of 38.2%). There is a lot to do in physics, chemistry, thermodynamics, efficiency, emissions, etc.
As result, there is a vigorous encouragement into eco-friendly energy generation over the years, and critical environmental issues that have increased the awareness to reduce the climate change and global warming. Among the up-to-date energy scenarios, renewable energy is predicted to be a notable part of energy production in the close future (Cuce et al., 2014). There is a vast range of green technologies accessible for clean energy generation, and the utilization of solar energy through photovoltaic (PV) cells has emerged as an auspicious source of green energy since it is one of the most efficient, with large availability, reliable, and eco-friendly solution (Slimani et al., 2017) for satiating the global power demand (Cuce et al., 2015)
Chapter 1. Introduction 2
and for dealing with fossil fuel-oriented environmental concerns. PV systems are free of moving parts and present low noise level (Ishaque et al., 2011) and among renewables, solar PV's provide the highest power density (University of Manitoba, 2017). In this respect, operation and maintenance costs of such systems are notably low in comparison with other clean energy generation technologies (Bianchini et al., 2016). Nowadays, over than 100 countries around the globe are using solar PV's (Green Technology, 2015).
Figure 1.2 Estimated US Energy Consumption in 2018: 102.2 Quads.
Source: Lawrence Livermore National Laboratory (2019).
It is well-known that the PV power research has been progressing on two fronts, in the effort to diminish the cost of solar energy: producing lower cost PV cells/devices and improving their performances. The unceasing research and development in the solar cells area has introduced novel design and concepts, new materials and processing methods, and cost strategies (Yin et al., 2013) to diminish the cost of PV technology.
The economy involving photovoltaic technologies is also in a rapidly growing: during the first 15 years of the century XXI the growth rate of photovoltaic installations was of 41% (Sampaio et al., 2017). Because of intensive attempts to reduce the cost of clean energy generation from PV modules, current production cost of crystalline silicon PV modules is in the range of 0.29–0.35 US$/W as reported by Louwen et al. (2016). The market for photovoltaic
Chapter 1. Introduction 3
systems will probably remain growing in the future as strongly as so far, due to the thrust of subsidies, tax breaks and other financial incentives (Devabhaktuni et al., 2013).
A strategy to reduce costs is to obtain economies of scale. This was evident with the development of crystalline silicon cells and is likely to be true for other technologies when their production volumes increase. In addition to economies of scale a combination of technological innovation, research in this field and improvement in learning are likely to reduce costs significantly. This is shown by the learning curve of the PV modules in Figure 1.3.
According to Figure 1.3, in the last 35 years, the module price decreased by about 19.1% at every duplication of cumulative production modules. Many scientists and engineers familiar with the variety of materials and PV technology concluded that photovoltaic materials of thin film and the third-generation ones are the most likely candidates to continue the 80% price reduction (Sampaio et al., 2017).
Figure 1.3 Learning curve of the PV modules.
Adapted from: Sampaio et al. (2017)
Over the years, the solar cells performance is increasing for the different available technologies. Figure 1.4 presents the growing trend of the PV technologies efficiency. There were already, in the laboratory, multi-junction solar cells with high solar concentration with a 46% efficiency in 2016 (Sampaio et al., 2017).
Chapter 1. Introduction 4 Figure 1.4 Efficiency of solar cells over the years.
Source: Sampaio et al. (2017)
To evaluate the performance and price of different PV module technologies, one can look into the studies conducted by the International Energy Agency (IEA) exemplified in Figure 1.5 which is also presented the market share for each technology.
Figure 1.5 Current performance and price of different PV module technologies.
* is an approximation (%) for the market share.
Source: Sampaio et al. (2017)
Support for research and development, and for implementing photovoltaic technologies, are crucial aspects in accelerating the widespread adoption of photovoltaic
Chapter 1. Introduction 5
systems. These two aspects play a key role in climate policy (Torani et al., 2016). Many countries, such as Germany, Denmark, Spain, China, Taiwan, United States, United Kingdom, Japan, Sweden and South Korea have been using different mechanisms to encourage the renewable energy’s use (Sampaio et al., 2017). According to the reports, the distance between non-renewable and renewable energy resources is narrowed steadily (Cuce et al., 2017), and the task of PV technology in this bias is of significant relevance (Cuce et al., 2014).
Even in the face of all this development in energy costs and efficiency, the feasibility of using a PV plant, however, no mattering the PV technology chosen, depends on the environmental parameters such as irradiance and cell temperature. Sampaio et al. (2017) compiled the main advantages and disadvantages of PV solar energy in Table 1.1.
Table 1.1 Advantages and disadvantages of solar photovoltaics during operation.
Advantages Disadvantages
• Reliable system
• Low cost of operation and maintenance • Low maintenance
• Free energy source • Clean Energy • High Availability
• The generation can be made closer to the consumer
• Does not cause environmental impacts /Environmental friendly
• Potential to mitigate emissions of greenhouse gases
• Noiseless
• Limitations in the availability of systems on the market
• High initial cost
• Needs a relatively large area of installation
• High dependence on technology development
• Geographical conditions (solar irradiation, temperature)
Source: Sampaio et al. (2017)
1.1. Problem formulation
The temperature variation caused by different operational conditions of a PV module was found to affect its electrical efficiency, and to have a considerable value, thus it cannot be neglected (Ayman et al., 2019). In PV technologies, the PV temperature and incident solar radiation are the main factors that affect their behaviors and therefore should be considered during their respective modelling. Others factors, such as ambient temperature, wind speed and direction, dusty, humidity and mounting structure will have a more indirect impact, by modifying how the main ones will behave (Santhakumari and Sagar, 2019).
Chapter 1. Introduction 6
The electrical parameters of PV modules are usually measured by the manufacturers at Standard Test Conditions (STC) – an irradiance level of 1,000 W/m2, a cell temperature of 25 °C and an air mass (AM) = 1.5 spectrum – or at the normal operating cell temperature (NOCT) – this condition is defined by IEC 61215 (2016) standard, which is measured on an open rack-mounted module with an inclination of 45°, an irradiance level of 800 W/m2, an ambient temperature of 20 °C and a wind speed of 1 m/s. However, in view of the interdependent behavior described above, such specifications are not enough to describe all situations that one PV module can operate. In fact, these conditions occur rarely on site since solar radiation of 800-1,000 W/m2 makes it difficult to have a cell temperature of 20-25 °C (DGS, 2017). This leads to the necessity of translation equations that can relate the STC or NOCT to the real ones that are experimented by the PV cell. The focus of this work will be the temperature, in view of the few number of investigations currently available in literature when leading with the interference over the equivalent model selection and solar simulator analysis.
In this work, the analyses will depart from the final behavior of cell temperature after being influenced by its secondary factors (i.e. wind speed, environment temperature, solar cell geometry, etc.). The relation between the main and secondary factors can better understood at the works of Rawat et al. (2017) and Akhsassi et al. (2018).
Aiming to bridge this gap on understanding the temperature influence over the solar cells, a study on the impact of cell temperature on the performance of polycrystalline silicon solar cell is undertaken in this work. The experiment will be carried out using a polycrystalline silicon solar cell with the temperature in the range 20 – 60 °C at constant light intensity 1,000 W/m2 employing a solar simulator.
The silicon photovoltaic cells were chosen based on:
I) They include single crystal, multi-crystalline and the hetero-structure which have more than 80% of the market share (Yeh and Yeh, 2013).
The temperature range was chosen based on:
I) For free-standing modules, in a normal summer day in Germany with an irradiance of 800 W/m2 and an ambient temperature of 20 °C, the common module temperature is around 42 °C (Schwingshackl et al., 2013), while during summer days in Central Europe, it can easily reach 60 °C;
Chapter 1. Introduction 7
1.2. Objectives
The main purpose of this research is identifying and evaluating the temperature influence over the silicon polycrystalline solar cell technology, highlighting the most important physical concepts associated.
The specific objectives of this research are:
I. Evaluate theoretical and empirically the temperature influence over the silicon polycrystalline solar cell technology focusing on the performance parameters (open-circuit voltage, short-(open-circuit current, maximum extracted voltage, maximum extracted current and efficiency);
II. Review the various existing mathematical relationships involving the influence of temperature over solar cells;
III. Identify robust mathematical equivalent electric circuit models that emulate the solar cell parameters (open-circuit voltage, short-circuit current, reverse saturation current and efficiency) as well as its material property (bandgap) against the temperature variation;
1.3. Work structure
As mentioned at the end of the introduction, this work comprises a study on the impact of cell temperature on the performance of polycrystalline silicon solar cell. In this way, all subsequent chapters are divided, at a certain moment, into the study of each performance parameter: as open-circuit voltage, short-circuit current, or efficiency; or material property: bandgap.
Chapter two provides a bibliographical review of the main concepts used throughout the work, starting from the principles of semiconductors and operation of a photovoltaic cell. Shortly thereafter, it is presented the solar cell performance factors, the equivalent electric models and it is discussed about the solar simulators.
Chapter three describes the method adopted for the execution of each stage of this study. The instruments used for simulation and measurement are specified, as well as the assumptions.
The results obtained are presented and discussed in chapter four. This chapter was divided in two fronts: solar cell characterization and the equivalent model analysis.
Chapter 1. Introduction 8
Finally, chapter five presents the conclusions obtained in this work, from the experiments carried out following the methodology defined in chapter three, and presents some directions for future researches in the subject discussed in this dissertation.
9
2. Literature review
2.1. Introduction
Sampaio et al. (2017) made a review on photovoltaic solar energy and showed that its potential is continuously increasing mainly due to efficiency’s increasing and costs’ reducing.
When the center of attention is the efficiency, there is many parameters that have its own influence either direct (temperature and irradiance) or indirect (wind speed and direction, environment temperature, solar cell geometry, mounting structure, plane of the array, transmittance of the glazing-cover, absorbance of the plate and other factors).
This work focuses on a direct influence factor: solar cell temperature.
In this bibliographic review, it will be presented the photovoltaic effect, the basics principles of a solar cell and the main equivalent models for solar cells since it will be used to the extraction of the solar cells performance parameters. It was discussed the importance and some methods for temperature measurements, and finally, the influence of the temperature on the performance parameters of solar cells.
2.2. Semiconductors and doping
When a pair of atoms are brought together into a molecule, their atomic orbitals combine to form pairs of molecular orbitals arranged slightly higher and slightly lower in energy than each original level. It is sad that the energy levels have split. When a very large number of atoms come together in a solid, each atomic orbital split into a very large number of levels, so close together in energy that they effectively form a continuum, or band, of allowed levels. The bands due to different molecular orbitals may or may not overlap. The energy distribution of the bands depends upon the electronic properties of the atoms and the strength of the bonding between them.
Bands are occupied or not depending upon whether the original molecular orbitals were occupied. The highest occupied band, which contains the valence electrons, is normally called the valence band (VB). The lowest unoccupied band is called the conduction band (CB). If the valence band is partly full, or if it overlaps in energy with the lowest unoccupied band, the solid is a metal. In a metal, the availability of empty states at similar energies makes it easy for a valence electron to be excited, or scattered, into a neighboring state. These electrons can readily act as transporters of heat or charge, and so the solid conducts heat and electric current.
Chapter 2. Literature review 10
If the valence band is completely full and separated from the next band by an energy gap, then the solid is a semiconductor or an insulator. The electrons in the valence band are all completely involved in bonding and cannot be easily removed. They require an energy equivalent to the bandgap to be removed to the nearest available unoccupied level. These materials therefore do not conduct heat or electricity easily.
Semiconductors are distinguished, roughly, as the group of materials with the bandgap in the range 0.5 to 3 eV. Semiconductors have a small conductivity in the dark because only a small number of valence electrons will have enough kinetic energy at room temperature to be excited across the bandgap at room temperature. This intrinsic conductivity decreases with increasing bandgap. Insulators are wider bandgap materials whose conductivity is negligible at room temperature. Materials of bandgap < 0.5 eV have reasonably high conductivity and are usually known as semimetals.
When the solid forms a regular crystal, then the energies of the bands, or the band structure can be predicted exactly. Exactly which crystal structure a solid will adopt depends upon the number of valence electrons and other factors. It will prefer a configuration that minimizes the total energy. A bandgap is likely to arise in a crystal structure where all valence electrons are used in bonding.
The semiconductor described so far is intrinsic – it is a perfect crystal containing no impurities. The only energy levels permitted are the levels of well-defined wavevector k which arise from the overlap of the atomic orbitals into crystal bands (See Nelson, 2008). The properties of those bands determine the position of the Fermi level in equilibrium, 𝐸𝑖 , and the intrinsic carrier density, 𝑛𝑖, which have enough thermal energy to cross the bandgap and
conduct electricity. They also determine the conductivity since intrinsic semiconductor has 𝑛 electrons and 𝑝 holes available for conduction and conductivity 𝜎 is given by
𝜎 = 𝑞µ𝑛𝑛 + 𝑞µ𝑝𝑝 (2.1)
where µ𝑛, and µ𝑝are the mobilities of the electrons and holes, respectively, and 𝑞 is the
electronic charge. In equilibrium, 𝑛, electron density, and 𝑝, hole density, are replaced with 𝑛𝑖 in Equation 2.1.
At room temperature, the conductivity of an intrinsic semiconductor is generally very small. For example, for intrinsic silicon, 𝜎 = 3 × 10−6 𝛺−1𝑐𝑚−1, at 300 K. Conductivity increases with increasing temperature, and with decreasing bandgap since 𝑛𝑖 varies as
𝑒𝑥𝑝 (− 𝐸𝑔
Chapter 2. Literature review 11
2 × 10−2 𝛺−1𝑐𝑚−1 while gallium arsenide with a bandgap of 1.42 eV has a conductivity of
𝜎 = 10−8 𝛺−1𝑐𝑚−1, many orders of magnitude smaller.
Now suppose that the crystal is altered by introducing an impurity atom or a structural defect. The impurity or defect introduces bonds of different strength to those which make up the perfect crystal, and therefore changes the local distribution of electronic energy levels. The altered energy levels are localized (unless the density of defects is very high), unlike the extended k states which make up intrinsic conduction and valence band states.
If the impurity energy levels occur within the bandgap they can affect the electronic properties of the semiconductor. Introducing occupied impurity levels above 𝐸𝑖 increases the Fermi level, which increases the density of electrons relative to holes in equilibrium. In the same way, unoccupied levels below 𝐸𝑖 reduce the Fermi level and increase the density of holes relative to electrons. The density and the nature of the carriers in the semiconductor can thus be controlled by adding definite amounts of impurities which energy levels close to the conduction or valence band edge. This is called doping.
2.2.1. n type doping
A semiconductor which has been doped to increase the density of electrons relative to holes is called n type. The principal charge carriers are negative. Occupied levels between 𝐸𝑖
and 𝐸𝑐 are introduced by replacing some of the atoms in the crystal lattice with impurity atoms which possess one too many valence electrons for the number of crystals bonds. Such impurities are called donor atoms because they donate an extra electron to the lattice. An example would be an atom of phosphorus, which has five valence electrons, in the tetravalent silicon lattice. The extra electron is not needed in the strong directional covalent bonds which hold each atom to its neighbors. Therefore, it is much less well bound than the other valence electrons, and is instead held rather loosely in a Coulombic bound state with Phosphorus atom. The donor can be ionized relatively easily, leaving the extra electron free to move and the fixed donor atom positively charged. For typical donors, the ionization energy, 𝑉𝑛, is some meV or tens of meV. If the impurity is chosen so that 𝑉𝑛 is small enough, virtually all the donor atoms will be ionized at room temperature.
In the band picture, the donor electrons have been promoted from a level in the bandgap, 𝑉𝑛 below 𝐸𝑐, into the conduction band. Since the donor states are all filled at 𝑇 = 0, the Fermi level must ow lie between the donor level and 𝐸𝑐.
The density of carriers can be controlled by varying the density of dopants, 𝑁𝐷. If 𝑁𝐷 ≫ 𝑛𝑖 and the donors are fully ionized at room temperature, then
Chapter 2. Literature review 12 𝑛 ≈ 𝑁𝐷 (2.2) and 𝑝 =𝑛𝑖 2 𝑁𝐷 (2.3) since 𝑛𝑝 = 𝑛𝑖2 at equilibrium. The electron density is now greatly increased over its equilibrium value, while the hole density is greatly reduced. The electrons are here called the majority carriers and the holes the minority carriers. Relative to the intrinsic case, the total density of carries is increased, and so therefore is the conductivity. Conductions in n type semiconductors is mainly by electrons.
2.2.2. p type doping
A semiconductor which is doped to increase the density of positive charge carriers relative to negative is called p type. It is produced by replacing some of the atoms in the crystal with acceptor impurity atoms, which contribute too few valence electrons for the bonds they need to form. An example would be the trivalent element boron in silicon. The acceptor becomes ionized by removing a valence electron from another bond to complete the bonding between it and its four neighbors. This releases a hole into the valence band. The energy of this ionized state is higher, by a small amount of energy 𝑉𝑝, than the highest energy of a valence
band electron, and so the acceptor energy level appears in the bandgap close to the valence band edge. The Fermi level now lies between the acceptor level and 𝐸𝑣.
These p type semiconductors contain an excess of positive carriers, holes. For a doping density of 𝑁𝐴 ≫ 𝑛𝑖 ionisable acceptors, it is found
𝑛 ≈ 𝑁𝐴 (2.4)
and 𝑛 =𝑛𝑖
2
𝑁𝐴 (2.5)
Again, the total carrier density and hence the conductivity is greatly increased, but now conduction is mainly by holes, which are the majority carriers in this case.
Notice how the changes in n and p are consistent with the changes in the Fermi level. In an intrinsic (i.e. pure) semiconductor 𝐸𝐹 lies roughly in the middle of the bandgap. The effect of doping is to shift the Fermi level away from the center of the bandgap, towards 𝐸𝑐 in n type
Chapter 2. Literature review 13
Note also that, unlike heating and illumination, doping is a way of increasing the conductivity of the semiconductor at equilibrium without requiring a constant input of energy. 2.2.3. Effects of heavy doping
Heavy doping causes imperfections in the crystal structure which appear as states in the bandgap close to the CB and VB edges. These states have the effect of adding a tail to the CB and VB density of states functions, and so effectively reducing the bandgap. The intrinsic carrier density will increase, because thermal excitation across the bandgap is easier, and this has consequences for solar cell performance. Heavy doping is also likely to increase the density of defect states which act as centers for carrier recombination or trapping.
2.3. Photovoltaic effect
The conversion of solar irradiation into electricity occurs due to the photovoltaic effect, which was observed by the first time by Becquerel in 1839. This effect occurs in materials known as semiconductors, which present two energy bands, in one of them the presence of electrons is allowed (valence bad) and in the other there is no presence of them, i.e., the band in completely “empty” (conduction band).
The function of solar irradiation on the photovoltaic effect is to supply an amount of energy in the form of photons (electromagnetic waves). According to this energy amount, different phenomena will occur: Photons with energy 𝐸 < 𝐸𝑔 cannot promote an electron to the excited state; Photons with 𝐸 ≥ 𝐸𝑔 can raise the electron, thereby creating mobile electron/hole pairs (Sze, 1981) but any excess energy is quickly lost as heat as the carriers relax to the band edges (Figure 2.1), delivering only ∆𝜇(= 𝑞𝑉𝑚) of electrical energy to the load, so only ∆𝜇/𝐸
of their power is available (Nelson, 2008). An absorbed photon with energy 𝐸 ≫ 𝐸𝑔 achieves
the same result as photon with 𝐸 = 𝐸𝑔, all the extra energy becomes heat.
When the available data is the light spectral distribution, it is interesting make a relation between the wavelength and photon energy. The cut-off wavelength of photons of energy useful for carrier generation depends on 𝐸𝑔. The cut-off wavelength is given by (Singh
and Ravindra, 2012) 𝜆𝑔 =
1240 𝐸𝑔(𝑒𝑉)
Chapter 2. Literature review 14 Figure 2.1 Two band photoconverter.
The Figure 2.2 shows how usable energy fraction falls as E increases. Even at 𝐸 = 𝐸𝑔 only a fraction of the incident power is available, since 𝑞𝑉𝑚< 𝐸𝑔. For this reason, it is the
incident photon flux and not the photon energy density which determines the photogeneration. Figure 2.2 Power spectrum of a blackbody sun at 5760 K, and power available to its optimum bandgap
cell.
Adapted from: Nelson (2008) 2.4. Photovoltaic solar cell
Virtually all photovoltaic devices incorporate a p-n junction in a semiconductor, which through a photovoltage is developed. These devices are also known as solar cells or photovoltaic cells. A typical solar cell is shown in Figure 2.3.
The PV solar cell has fundamentally two layers of individually doped semiconductor material with its p-n junction exposed to incident irradiation (Jordehi, 2016; Villalva and Gazoli, 2009). With the purpose of reducing the blockage of incident light, the metal grid on the top side is constructed with thin and discontinuous structure with finger-like metal elements
Chapter 2. Literature review 15
ingrained into the silicon (Ciulla et al., 2014). It is designed to reduce the contact resistances and to maximize the absorbing area (Jordehi, 2016).
Figure 2.3 Physical structure of PV cell.
In the presence of irradiation, as aforementioned, the p-n junction absorbs the photons with energy greater than the bandgap of the semiconductor from incident light and create carriers, namely electron-hole pairs. All the rest of the photons becomes heat.
These carriers are swept away, under the influence of the internal electric fields of the p-n junction and create a current which is proportional to the incident radiation, to opposite sides of a built-in voltage barrier between the dissimilar materials, where the charges are collected at low resistance metallic contacts. The resulting electrical current is named light-generated current and denoted by 𝐼𝑝𝑣. It can be extracted if the two oppositely charged contacts
are then connected through an external load circuit. Desired currents and voltages are obtained by connecting cells in series and parallel to form modules, and by aggregating modules in series and parallel groupings to form arrays, both following the normal electrical aspects. Though the magnitudes of currents and voltages differ, the electrical characteristics are similar for cells, modules, or arrays.
It is important to emphasize that this current, described by Boltzmann Transport equation, can only be achieved in certain configurations, such as a p-n junction. Otherwise, the electron and hole gradients that are similar tend to cancel each other out. The net diffusion currents usually arise only when the electron and hole carrier gradients are very different. In this PV cell’s case, currents are dominated by minority carrier diffusion – See Nelson (2008). 2.4.1. The characteristic curve
The PV solar module are usually described by its characteristic curve (Figure 2.4) which has three remarkable points, the 2-tuple: A - (0, 𝐼𝑠𝑐), B - (𝑉𝑚𝑝, 𝐼𝑚𝑝) and C - (𝑉𝑜𝑐, 0).
Chapter 2. Literature review 16
is the short-circuit current (maximum value achievable); The 2-tuple B is the condition of maximum power extraction, that is, both voltage and current are the ones that produce the maximum power output; The 2-tuple C is the condition of open-circuit, that is, the current is equal to 0 and the voltage is the open-circuit voltage (maximum value achievable).
Figure 2.4 Characteristic curve of a PV solar cell.
Source: Villalva and Gazoli (2009)
In a typical solar cell, it can be concluded from (𝐼, 𝑉) = (𝐼𝑠𝑐, 0) condition that the
Equation 2.7 is valid, i.e., the value of light-generated current (𝐼𝑝𝑣) can be assumed equal to the
value of short-circuit current (𝐼𝑠𝑐). (Mares et al., 2015)
𝐼𝑝𝑣 = 𝐽𝑝𝑣 𝐴 = 𝐼𝑠𝑐 (2.7)
The light-generated current density (𝐽𝑝𝑣) depends on the solar cell material and on the given solar spectral irradiance and it is given by Equation 2.8. Where F(𝜆) represents the incident photon flux in irradiance wavelength 𝜆, q is the electron charge and 𝐴 is the solar cell superficial area.
𝐽𝑝𝑣 = 𝑞 ∫ F(𝜆)
𝜆𝑔
0
𝑑𝜆 (2.8)
The short-circuit current density 𝐽𝑠𝑐, was calculated directly from the irradiance data. These
data are integrated by rectangle rule integration. The photon flux F(𝜆); is calculated from the irradiance 𝐺(𝜆) and the wavelength 𝜆.
F(𝜆) =𝜆 ∙ 𝐺(𝜆) ℎ ∙ 𝑐
(2.9)
The current density at quantum efficiency of unity, when every incident photon creates an electron, can be found by multiplying the photon flux with the electric charge 𝑞
Chapter 2. Literature review 17 𝐽𝑠𝑐 = 𝐹 ∙ 𝑞
The optical absorption is considered to be complete for energies higher than the bandgap. For lower energies, no absorption takes place, no carriers are generated. For smaller quantum efficiencies, a model for the optical absorption must be assumed, respectively.
2.5. Performance factors
Photovoltaic cells can have their operating performance changed according to the current climatic conditions, impacting on their power generation capacity. These magnitudes are directly linked to the geographical location of the operating environment, as well as other local characteristics. These influencer factors can be divide in two groups in terms of how this influence exists: direct and indirectly (Figure 2.5). In this work, as the focus is the temperature influence, the other influencer factors will not be discussed in detail, just a un passant explanation about spectral distribution, mass of air and irradiation since these aspects are indispensable for understand completely the STC Condition.
Figure 2.5 Environmental influence over the solar cell.
Source: Author (2019).
2.5.1. Spectral distribution and mass of air
The atmosphere changes the spectral distribution of light passing through it, attenuating the intensity of its components (Figure 2.6). The spectrum also has a direct impact on the photogenerated current, according to the spectral response of the cell (which depends on the response of the semiconductor material from which it is made). Silicon, for example, has its
Chapter 2. Literature review 18
peak response near to the infrared region (900 nm), reaching red (740 nm) in the region of the visible. The spectral distribution can also be found as spectral irradiance (𝐺λ).
Figure 2.6 Spectral distribution of solar radiation for different atmospheric conditions.
Source: Kininger (2003).
The parameter AM (air mass) is associated with the angle presented by the light beam when crossing a plane normal to the surface of the planet Earth. The AM 0 is the maximum altitude, located above the atmosphere (free space); AM 1.5 is measured in tropical regions - in Ecuador AM 1 is used, while AM 2 and AM 3 are used in regions of high latitudes.
This quantity can be defined by the following equation: 𝐴𝑀 = 𝐿
𝐿0 ≈ 1
cos 𝑧 (2.10)
Where 𝐿 is the path length through the atmosphere, 𝐿0 is the path length at the zenith angle (normal to the earth's surface) and 𝑧 is the zenith angle (in degrees). Figure 2.7 shows the values of Air Mass according to the angle of the light beam relative to the zenith and the position of entry into the Earth's atmosphere.
Chapter 2. Literature review 19 Figure 2.7 Air Mass according to the zenith angle.
Source: Green rhino energy (2013).
2.5.2. Irradiance
It is a unit of magnitude used to describe the incident power per unit of surface area, the integral of the spectral distribution (in λ). As reference, there is the solar constant (𝐺0),
irradiance measured outside the atmosphere (imagining a flat horizontal surface perpendicular to the sun's rays, oriented towards the zenith, at a mean Earth-Sun distance), whose value is equal to 1,367 W/m2. According to the region of the planet, there are several different values of irradiance (the highest values are in the equatorial regions and the lowest are in the poles). The irradiance (𝐺) and temperature (T) is related to the 𝐼𝑠𝑐 of a cell by the approximate relation:
𝐼𝑝𝑣(𝐺) =
𝐺 𝐺𝑟𝑒𝑓
[𝐼𝑝𝑣,𝑟𝑒𝑓+ 𝜇𝐼𝑝𝑣(𝑇 − 𝑇𝑟𝑒𝑓)] (2.11)
Where 𝐼𝑝𝑣,𝑟𝑒𝑓 is the short-circuit current, 𝑇𝑟𝑒𝑓 is the cell temperature, 𝐺𝑟𝑒𝑓 is the
irradiance in the STC condition and 𝜇𝐼𝑝𝑣 is the temperature coefficient of 𝐼𝑝𝑣. This equation try to describe the behaviour presented in Figure 2.8. From a certain value, irradiance increments do not promote the growth of photogenerated current; this threshold value is called the maximum current or saturation current of the cell (Carvalho ALC, 2014).
The air mass is related to the irradiance with the approximate relation (based on Laue's observations):
𝐺(𝑧) = 𝐺0𝑒𝑥𝑝[−𝑐 ∙ (sec 𝑧)𝑠] = 𝐺
Chapter 2. Literature review 20
where 𝐺0 is the radiance outside the atmosphere and 𝑧 is the distance from the zenith. The constants 𝑐 and 𝑠 are empirical and are respectively 0.357 and 0.678.
Figure 2.8 IxV curve for different irradiances.
Source: Kininger (2003).
Concentrated irradiance
Khan et al. (2016) carried out illuminated J–V measurements with temperatures in the 298–353 K interval, under a 𝐺 range of 2–18 suns, for a silicon solar cell. They observed variations in the performance parameters under illumination conditions of up to 6 suns are like those observed under normal illumination conditions. It should be noted that the methods (analytical, curve fitting, and numerical) based on single J–V characteristics sometimes result— at high temperatures—in negative values of 𝑅𝑠 and excessive values of 𝑎, owing to limitations of these methods. The parameter variation trends at 18 suns are like the variation trends at 15 suns (Khan et al., 2016). Therefore, they performed detailed studies only for 𝐺 values of 10 and 15 suns. The experimentally measured illuminated J–V curves of the PV cell at various values
Chapter 2. Literature review 21
of T (298, 308, 318, 333, 343, and 353 K) are shown in Figure 2.9(a) and (b), for 𝐺 values of 10 and 15 suns, respectively.
Figure 2.9 Illuminated J–V characteristics at various temperatures under illumination intensities of (a) 10 suns, (b) 15 suns.
Source: Khan et al. (2016).
2.5.3. Temperature
Solar cells work best at certain temperatures, according to their material properties: Some materials are more appropriate for use in orbit around the earth, some for terrestrial uses, and others for high-temperature applications either under concentrated sunlight or in space near the sun. Figure 2.10 shows how different cell materials lose efficiency with increasing temperature. Note that at normal terrestrial temperatures, 25 °C, silicon's efficiency compares favorably with other materials; but at high temperatures, 200 °C for instance, silicon's efficiency has dropped to 5%, whereas the other materials are near 12%. Silicon is a good material for ambient temperature terrestrial uses; it fails in high-temperature applications.
Although Figure 2.10 does not show it, there is a similar drop-off of efficiency below a certain low temperature for each of the materials. Note that all materials lose efficiency in the range shown.
High-Temperature Losses
The physical effects that determine efficiency's relationship with temperature are quite complex. For the most part, two predominate in causing efficiency to drop as temperature rises: As thermal energy increases, (1) lattice vibrations interfere with the free passage of charge carriers and (2) the junction begins to lose its power to separate charges.
Chapter 2. Literature review 22
The first effect severely degrades silicon's performance even at room temperatures (Figure 2.11). The ability of charge carriers to move without losing their energy is measured by their mobility. Note that silicon is already below its maximum efficiency at room temperature. The high-temperature losses shown here are mostly due to collisions with thermally excited atoms.
Figure 2.10 Solar cells efficiency versus temperature for various materials.
Source: SERI (1982).
The second effect does not occur until temperatures of about 300 °C for silicon are reached. At such temperatures, a huge number of electrons in normal silicon bonds are thermally jostled from their positions; on the n-type side, they join and greatly outnumber the free electrons donated by the n-type dopant. At the same time holes are formed on the n-type side (left behind by the thermally freed electrons); the n-type silicon begins to lose its n-type character as the number of free electrons and holes become similar. The same process is working on the p-type side, which is losing its p-type character. This leads to two effects: (1) The thermally agitated charge carriers have so much energy, they cross over the junction in both directions almost as if the barrier field were not there. (2) Ultimately the junction itself disappears because there is no longer n- and p-type sides to induce it. All of these effects accumulate to erode the activity of the cell, and efficiency diminishes to nearly zero.
Since solar cells are sensitive to temperature increases, and since a PV cell converts a small portion of the irradiance into electrical energy while the remaining is converted into heat (Fouad et al., 2017) which contributes to increase the cell temperature, it is frequently necessary to either match the cell material to the temperature of operation or to continually cool it, removing the extra, unwanted heat. Sometimes this latter method can lead to positive results,
Chapter 2. Literature review 23
raising a solar installation's overall efficiency if the heat is applied to useful purposes. The overheating of the cell mainly occurs due to excessive solar radiation and high ambient temperatures (Abd-Elhady et al., 2016).
Figure 2.11 Charge carriers’ mobility for silicon doped at two different donor concentrations in relation to temperature.
Source: SERI (1982).
Low-Temperature Losses
Low-temperature losses are, if anything, more complex and less understood. They are important, however, only for deep-space PV applications. Two effects are thought to play roles: (1) As temperature falls, thermal energy is less able to free charge carriers from either dopant atoms or intrinsic silicon. Mobility for light-generated charge carriers drops because they collide more frequently with ionized donors or acceptors in n- and p-type regions, respectively. The donors and acceptors are not screened as much by clouds of thermally aroused charge carriers. Also (2) at very low temperature, there is so little thermal energy that even dopants behave as if they were normal silicon atoms. For instance, in the n-type material, donor atoms retain their extra electrons; in the p-type material, holes remain fixed in place because electrons are less likely to pop out of their normal positions to fill them. Since the n- and p-type sides no longer exhibit their doped character, the junction disappears.
Chapter 2. Literature review 24
2.5.4. Relations
There are some proposed correlations in the literature that express the module temperature as a function of variables such as the weather variables (depends on the location) especially the ambient temperature, the local wind speed and direction, mounting structure (Santhakumari and Sagar, 2019), as well as the solar or irradiance incidence on the plane of the array (Fouad et al., 2017). Not only this but also the temperature depends on the material and system-dependent properties such as the transmittance of the glazing-cover, absorbance of the plate and other factors. The effect of different operational conditions on the temperature of a PV module was found not to be negligible and it is also dependent on the actual electrical efficiency due to the solar energy converted to heat (Ayman et al., 2019).
The study of the behavior of solar cells with temperature (𝑇) is important as, in terrestrial applications, they are generally exposed to temperatures ranging from 15 °C (288 K) to 50 °C (323 K) (Singh and Ravindra, 2012) and to even higher temperatures in space and concentrator-systems (Zeitouny et al., 2018).
The cell temperature is the key environmental parameter that has great influence on the behavior of a PV system, as it greatly affects the system efficiency and energy output. It is the key to decide the quality and performance of a solar cell (Chander et al., 2015b).
Earlier studies (Singh and Ravindra, 2012) have pointed out that the performance of solar cells degrades with increase in temperature. The effect of the temperature on the cell performance is mainly reflected in short-circuit current which increase slightly, in open circuit voltage which decrease substantially with temperature (Ayman et al., 2019), and in an overall reduction on the maximum power point. These effects can be visualized in Figure 2.12.
Bandgap
The bandgap energy (𝐸𝑔) of semiconductors is the primordial property that renders them a veritable source of fundamental and technological interest (Bensalem et al., 2017). The gap energy is a fundamental concept, according to the quantum theory, in semiconductor crystals; the lowest point of the conduction band and the highest point of the valence band are separated by a forbidden region called bandgap. The behavior of the gap under external disturbances such as pressure and temperature is a determinant factor of semiconductor-based device performance. In fact, the study of the gap dependence with temperature of
Chapter 2. Literature review 25
semiconductors represents a significant task for eventual technological applications. For silicon, the estimated gap value at the vicinity of the ambient temperature (300 K) is: 1.12 eV for Collings (1980), 1.124 eV for Madelung (1991) and 1.123 eV for Bensalem et al. (2017).
Figure 2.12 Temperature effect on the solar cell characteristics.
Source: Kininger (2003).
Bludau et al. (1974)reevaluated experimentally the 𝐸𝑔 of silicon with good precision between 2 and 300 K through absorption spectroscopy method. Based on the experimental results, the authors performed a quadratic fit using the following approximation:
𝐸𝑔 = 𝐴 + 𝐵𝑇 + 𝐶𝑇2 (2.13) where, 0 𝐾 < 𝑇 ≤ 190 𝐾 150 𝐾 ≤ 𝑇 ≤ 300 𝐾 𝐴 = 1.170 eV 𝐵 = 1.059 × 10−5 eV/𝐾 𝐶 = −6.05 × 10−7 eV/𝐾2 A = 1.1785 eV 𝐵 = −9.025 × 10−5 eV/𝐾 𝐶 = −3.05 × 10−7 eV/𝐾2
