Simulation and experimental study of power losses due to shading
and soiling on photovoltaic (PV) module
Norwegian University of Life Sciences Faculty of Environmental Science and Technology
Department of Mathematical Sciences and Technology
Master Thesis 2015 30 credits
Anna Derås Pettersen
Preface
This thesis is a result of an initiative take by Institute for Energy Technology (IFE) and was carried out to determine the power losses due to shading and soiling accumulation on a photovoltaic (PV) module.
A simulation tool was used to construct a model that can handle complex shading profiles. An experimental basis was established for quantifying the transmission losses due to the natural accumulation of soiling in Norway in the period of October-‐
November 2014. The simulation model was used for predicting power losses from a partial snow cover on PV modules at a PV-‐plant located at Evenstad, and was verified by production data.
The development of the solar industry in Norway is at an early stage. This thesis provides a basis of knowledge on the power losses directly related to the natural
accumulation of soiling, due to the Norwegian/Scandinavian climate. Simulation studies provide an understanding of how partial snow accumulation on PV modules can cause major power losses.
I would like to thank my supervisors at IFE, Erik Stensrud Marstein and Josefine Helene Selj for their huge engagement and for always taking the time to help me. I would also like to thank my supervisor at Norwegian University of Life Sciences (NMBU) Dr. Ing.
Espen Olsen for valuable advices. Thanks to Statsbygg for login in permission, access to all the production data and information about the PV-‐plant at Evenstad.
I would like to thank my cousin Ola Kristoffer Derås Verlo for one of our last
conversations together, involving the future of renewable energy. This thesis is written in memory of you.
Ås, February 2nd 2015
Anna Derås Pettersen
Abstract
A model for predicting and quantifying the effects of complex partial shading profiles on a PV-‐module has been constructed by using the simulation tool LTspice IV. The model is constructed according to the two-‐diode model equivalent circuit for solar cells.
Technical specifications from REC255PE were implemented in the model, and partial shade was simulated by applying shade normal to the strings, and along the strings on the module.
An experimental basis has been established for quantifying the transmission losses due to the natural accumulation of soiling in Norway. The soiling accumulation is caused by several typical Norwegian weather conditions in the period of 10.25.14-‐11.23.14.
Results show that the transmission is reduced by up to 0.92% and 1.1% during one week for a standard module glass and an anti-‐soiling coated glass respectively. The results show no positive effect of the anti-‐soiling coated glass relative to a standard module glass, which is opposing to other previous studies. A longer measurement series is required in order to make a significant conclusion. This experimental basis was also established for measuring the transmittance through snow covers at various depths and implement snow as soft shade in the LTspice model to predict power losses due to snow accumulation. Due to the heat dissipated by the light source on the experimental setup, and the fact that the setup was located indoors, this experimental setup was not
sufficient for measurements on snow.
The simulation model was used to predict power losses due to partial snow cover on a PV module at a PV plant located at Evenstad, Norway. The simulation results were verified by inverter data at Evenstad. Simulation results showed that if one PV module, where 5 of 10 rows were snow covered, the power output was reduced by 40% for the entire inverter-‐string, assuming snow depth of less than 10 cm. For thick snow depths, assumingly higher than 10 cm, the power produced from a module string is assumed to be close to zero due to very low transmittance through the snow and the fact that the modules are installed in upraised position.
Simulation results show that, for this particular scenario, installing the modules in laying position would increase the power produced by each module with about 19%.
Sammendrag
I denne masteroppgaven er en simuleringsmodell konstruert for å predikere og
kvantifisere effekten av delvis skygge på solcellemoduler. Modellen ble konstruert etter to-‐diode ekvivalentkrets-‐modellen for solceller. REC 255PE ble modellert i
simuleringsverktøyet LTspice IV, basert på tekniske spesifikasjoner tilgjengelig fra produsenten. Skyggeprofiler på tvers og på langs av modulstrengene ble simulert.
En eksperimentell metode er utviklet for å utføre systematiske transmisjonsmålinger på modulglass. Måledataene ble brukt til å beregne transmisjonstap gjennom to typer modulglass som følge av naturlig tilsmussing. Resultatene viser at transmisjonen gjennom et standard modulglass og et glass med anti-‐soiling belegg ble redusert med opptil henholdsvis 0,92 % og 1,1 % ukentlig i måleperioden 25.10.14-‐23.11.14.
Resultatene fra disse målingene viser ingen effekt av anti-‐soiling glass relativt til standard modulglass, som er motstridende med andre tidligere studier. En lengre måleserie er derfor påkrevd for å kunne foreta en signifikant konklusjon. Det eksperimentelle oppsettet er ikke tilstrekkelig for målinger av snø og is, og krever videre utvikling. Dette på grunn av varmen som avgis av lyskilden, og at målingene utføres innendørs.
Simuleringsmodellen ble brukt til å predikere effekttapet som følge av et delvis
snødekke på en modul på solcelle anlegget på Evenstad i Norge. Simuleringsresultatene, verifisert ved produksjonsdata fra Evenstad, viser at et delvis snødekke kan få store konsekvenser for produksjonen. Dette skyldes at modulene er koblet i serie, 11 og 12 moduler til hver inverter. Modulen med mest skygge eller dekke, vil påvirke de andre modulene i samme streng, og nedjustere effekten levert fra de ikke-‐skyggede modulene til samme effekt som den skyggede modulen. I dette tilfellet tilsvarer det et predikert effekttap på 40 % for hele inverter strengen.
Ved å installere moduler i liggende posisjon, kan effekten som leveres av en skygget modul økes på grunn av bypass diodenes plassering. Simuleringsresultater viser at det for det undersøkte snødekket vil øke effekten fra modulen med ca. 19 %.
List of Figures
Figure 1.1: Plot showing the predicted PV market (cumulative) development in Europe.
Figure is taken from (EPIA 2014) p.32. ... 8
Figure 1.2: Mean values of insolation (W/m2) measured at Evenstad by tilted pyranometer (Sunny Portal). ... 10
Figure 2.1: Intensity of sunlight (W/m2nm) as a function of wavelength, representing the AM1.5 spectra (International ISO 9845-‐1 AM1.5G spectra 1992). ... 14
Figure 2.3: Sketch of a 6’’ multi-‐crystalline Si-‐solar cell, with contact grid and fingers, size and the approximate thickness of a cell. Picture from (IFE Department for Solar Energy). ... 17
Figure 2.4: The two-‐diode model equivalent circuit to a solar cell. ... 18
Figure 2.5: Simulated I(V)-‐ and P(V)-‐plot for a single solar cell under STC. ... 20
Figure 2.6: Simulated I(V)-‐plot for various series resistances Rs (Ω) at STC. ... 21
Figure 2.7: Simulated I(V)-‐plot for various values for the shunt resistance RSH (Ω) at STC. ... 22
Figure 2.8: Simulated I(V)-‐plot for various saturation current densities for diode 2. ... 23
Figure 2.9: Simulated I(V)-‐plot for various saturation current densities for diode 1. ... 24
Figure 2.10: Simulated I(V)-‐plot for various cell temperatures. ... 25
Figure 2.11: Cross section to illustrate the layers of a standard PV module. ... 26
Figure 2.12: Basic illustration of how hard shade (left), and soft shade (right) affects the transmitted sunlight through a surface. ... 27
Figure 2.13: Simulated I(V)-‐ plots of a single solar cell for irradiances 200, 400, 600, 800 and 1000W/m2 at temperature 25°C. ... 28
Figure 2.14: Sketch of shade applied along (left) the module strings, and along the module strings (right). ... 30
Figure 2.15: Uniform fresh snowfall coverage of PV modules, at Kjeller, Skedsmo (left), and Evenstad (right). ... 34
Figure 3.1: Numbered cells and placement of the bypass diodes of 60 cell PV module. .. 41
Figure 3.2: Sub-‐circuit for the solar cell defining two-‐diode model. ... 42
Figure 3.3: An extract of the syntax used for series connecting cells and implementing parameter values. ... 43
Figure 3.4: Solar simulator sketch (IFE Department for Solar Energy). ... 47
Figure 3.5: Glass samples placed on a rooftop located at IFE. The samples has equal tilt angle as the adjacent PV modules. ... 52
Figure 3.6: Schematic of the transmittance measurement setup (IFE Department for Solar Energy). ... 53
Figure 3.8: Sketch of PV plant at Evenstad, Hedmark, Norway. Picture provided by (Statsbygg). ... 59
Figure 3.9: Screenshot of live view at Evenstad, where one module in string 1.2 has 5/10 rows covered with snow (login required, permission given by Statsbygg). ... 60
Figure 3.10: Sketch of REC255PE whereas 5/10 rows are covered with snow. ... 61
Figure 3.11: Mean values of the mean insolation measured by a pyranometer at Evenstad, Hedmark, Norway (Sunny Portal). ... 62
Figure 3.12: Module temperature (mean values), and wind speed (mean values) measured at Evenstad, Hedmark, Norway (Sunny Portal). ... 63
Figure 3.13: Sketch of laying module position, whereas 5/6 rows are covered with snow. ... 66
Figure 4.1: Plot of table 4.1, ISC plotted as a function of number of fingers shaded, with corresponding linear trend line. ... 69 Figure 4.2: Modeled I(V)-‐plot (blue) and P(V)-‐plot (red) from LTspice model at STC. .... 70 Figure 4.3: Sketch of hard shade applied across all strings of PV module, 50% cell area (left) and 100% cell area (right) ... 72 Figure 4.4: Simulated I(V)-‐ and P(V)-‐plot of hard shade across strings applied to 50% of the cell area of all bottom cells. ... 73 Figure 4.5: Simulated I(V) and P(V)-‐plot of hard shade across all the strings applied to 100% of cell area of all bottom cells. ... 74 Figure 4.6: Sketch of hard shade applied along one string on a PV module, 50% of cell area (left), and 100% cell area (right). ... 75 Figure 4.7: Simulated I(V) and P(V)-‐plot of hard shade along one string applied to 50%
of the cell area. ... 76 Figure 4.8: Simulated I(V) and P(V)-‐plot of hard shade along one string applied to 100%
of the cell area. ... 77 Figure 4.9: Sketch of soft shade applied across all strings, and along one string on the modeled PV module. ... 78 Figure 4.10: Simulated I(V)-‐ and P(V)-‐plot of soft shade with t=20% to t=100% applied across all strings, 100% cell area. ... 79 Figure 4.11 Simulated I(V)-‐ and P(V)-‐plot of soft shade with t=20% to t=100% applied along one string, 100% cell area. ... 80 Figure 4.12: Plot of Pmax for various transmission t, from Figure 4.10 and Figure 4.11. .. 81 Figure 4.13: Precipitation measured at Skedsmo, Norway, the closest weather station to Kjeller, at the given period of the experiment. Data downloaded from (eKlima). ... 83 Figure 4.14: Simulated I(V) and P(V)-‐plot for PV module without snow coverage. ... 92 Figure 4.15: Simulated I(V) and P(V) for PV module with 5/10 rows snow covered. ... 93 Figure 4.16: Production data for inverter 1 at Evenstad from 1/8/2015 (Sunny Portal).
... 94 Figure 4.17: Simulated I(V) and P(V) for PV module with 5/6 rows snow covered, with t=20% through snow in laying position ... 96
Table of contents
Preface ... 1
Abstract ... 2
Sammendrag ... 3
List of Figures ... 4
1 Introduction ... 8
1.1 Background ... 8
1.2 Thesis statement ... 11
1.3 Thesis structure ... 11
2 Theoretical background ... 13
2.1 Definitions related to solar radiation ... 13
2.1.1 Reference solar spectra ... 13
2.1.2 Absorptance, reflectance and transmittance ... 15
2.2 Physics of solar cells ... 16
2.2.1 Semiconductors ... 16
2.2.2 Solar cell ... 16
2.3 The two diode model ... 18
2.3.1 Parameters of the two-‐diode model ... 19
2.4 PV module ... 26
2.5 Shading ... 27
2.5.1 Partial shade ... 28
2.5.2 Shading of single solar cell ... 29
2.5.3 Shading of PV module ... 30
2.6 Soiling ... 32
2.6.1 Dust and pollution ... 32
2.6.2 Snow ... 33
2.6.3 Soiling accumulation due to Norwegian climate ... 35
2.6.4 Anti-‐soiling coatings ... 36
3 Experimental methodology ... 38
3.1 Modeling a PV module ... 39
3.1.1 Introduction to modeling software: LTspice IV ... 39
3.1.2 60-‐cell PV module ... 39
3.1.3 REC 255PE ... 43
3.1.4 Shade simulation ... 46
3.2 Validation of simulation model ... 46
3.2.1 Shading of solar cell ... 47
3.2.2 Shading of PV module ... 48
3.3 Soiling ... 51
3.3.1 Field-‐test location and experimental setup ... 51
3.3.2 Transmission measurement setup ... 53
3.3.3 Five-‐week transmission loss ... 57
3.3.4 Weekly transmission losses ... 58
3.3.5 Observations of glass samples ... 58
3.4 Predicted power losses due to snow accumulation on PV module ... 59
3.4.1 Location ... 59
3.4.2 Snow accumulation ... 60
3.4.3 Data availability ... 62
4 Results and discussion ... 68
4.1 Validation of simulation model ... 68
4.1.1 Shading of solar cell ... 68
4.1.2 Shading of PV module ... 70
4.1.3 Section summary ... 81
4.2 Soiling ... 82
4.2.1 Reference transmission measurements ... 84
4.2.2 Five week transmission loss ... 85
4.2.3 Effect of washing glass samples ... 87
4.2.4 Weekly transmission loss ... 88
4.2.5 Observations of glass samples ... 90
4.2.6 Section summary ... 91
4.3 Predicted power losses due to snow accumulation on PV module ... 91
4.3.1 Section summary ... 97
5 Conclusions ... 98
Further work ... 99
References ... 100
Appendix ... 105
A.1: REC255PE model ... 105
A.2 Transmission plots ... 113
A.3 Images of glass samples ... 118
1 Introduction
1.1 Background
According to a report predicting the global market outlook for 2014-‐2018, published by European Photovoltaic Interest Organization (EPIA), the PV-‐industry represents a growing market. This is despite of economic recessions such as the financial crisis between 2007 and 2010. In the same report it is suggested that for a high scenario future prediction, the European PV-‐marked is to increase up to an installed capacity of 156 GW in 2018, compared to about 81 GW in 2013 (see Figure 1.1). It is also predicted that, without major changes of policy, the PV technology will contribute with about 7-‐
11% of the total European electricity demand in 2030 (EPIA 2014).
Figure 1.1: Plot showing the predicted PV market (cumulative) development in Europe. Figure is taken from (EPIA 2014) p.32.
The total capacity in Norway is about 11 MW, whereas 0.6 MW was installed in 2013 (IEA 2013).
The sun is an unlimited resource. Still, typical cell efficiencies are 16-‐24%. The
efficiency is measured as the percentage of sunlight that can be converted to electricity by a solar cell under ideal standardized illuminating conditions.
Since 1990, a combination of increased solar cell efficiencies and cost reduction due to decreased wafer thickness and decreasing silicon prices has reduced the price of solar cells (ISE 2014).
Even though the sun is an unlimited resource, there are several external factors, such as shade caused by environmental factors, and shade from the surrounding objects that might interfere with sunlight interacting with PV systems.
Environmentally caused shade due to snow, ice, frost, dust, pollution, sand, pollen, leafs and bird droppings that accumulate on module glasses are to a large extent difficult to predict. In the PV industry, the word soiling is used to describe this broad term. Due to different climate and topographies around the world, the power losses caused by soiling vary to a large extent. Studies on soiling accumulation have mainly been carried out in the Middle East and California.
In Norway, the development of the solar industry is at an early stage, and there is little knowledge about the power losses directly related to the soiling accumulation due to the Norwegian/Scandinavian climate. In countries like Norway, snowfall is assumed to cause the highest annual power loss, due to the frequency of the snowfall and the duration of the winter. Little knowledge about how snow accumulates on tilted PV modules and how this, often partial, shading affects the power output on modules results in uncertain expected power productions.
Figure 1.2 shows mean values of insolation measured at a PV-‐plant at Evenstad in Norway, by a pyranometer tilted on rooftop (Sunny Portal). As it appears, the insolation level is low during winter months such as October-‐February and is significantly higher in March-‐September.
Figure 1.2: Mean values of insolation (W/m2) measured at Evenstad by tilted pyranometer (Sunny Portal).
The electricity needs are at its highest during winter months in Norway, and in these months the power produced from PV-‐plants will be low. During winters with frequent snowfall, the power production can at times be close to zero. Thus in the absence of power production from the PV-‐plant, the demand of external power supply increases.
There is little knowledge whether snow removal is cost effective compared with the cost of additional electricity during the winter. Little knowledge and experience on this subject of matter might lead to great economic loss for installers and investors. This particularly applies in periods from March to April, because of relatively high insolation levels, and periods of snowmelt, where snow may partially cover PV-‐modules and cause large power losses.
In order to limit, or predict these power losses it is necessary to understand the behavior of a PV system under these conditions. Field-‐testing can be expensive, and requires supervision, and the results do not necessarily apply to other locations. A simulation model is therefore an important tool to understand the behavior of a PV system, and also to predict the power losses due to the effects of shading.
1.2 Thesis statement
The thesis addresses two goals.
The first goal is to construct a simulation model to predict the effects of shading on a PV module, which can also handle complex partial shading conditions. The simulation results are compared with experimental results to verify the model accuracy. The term shading can be divided into two parts; shading in terms of hard and soft shade. The soft shade represents the case of some degree of transmission through the shaded area, and the hard shade represents the case of no transmission through the shaded area.
The second goal of this thesis is establish an experimental basis for quantifying the transmission losses due to the natural accumulation of soiling in Norway. The soiling accumulation is caused by several typical Norwegian weather conditions in the period of October-‐November. The simulation model will also be used to apply soft shade due to snow coverage on PV modules, and to predict the power losses this leads to.
1.3 Thesis structure
The structure of this thesis is as follows:
Chapter 1: In this chapter the thesis statement is defined, thereby the goals for this project. A motivational background is presented.
Chapter 2: In this chapter, the theoretical background that is required to understand the methodology and experiments that are set up in this thesis. Physics of solar cells, and definitions related soiling and shading are presented. Previous work and studies of relevance to this thesis are presented.
Chapter 3: In this chapter the experimental methodology is presented. The simulation program LTspice is introduced and shade implementation in the mode is defined.
The experimental setup for the experiments carried out to quantify the transmission losses due to soiling accumulation is presented. In this chapter the procedure for using the simulation model to predict power losses due to snow accumulation is presented, and how this is applied to a specific scenario at a PV-‐plant at Evenstad is presented.
Chapter 4: Simulation results, and experimental results, carried out according to the methodology described in Chapter 3 are presented and discussed.
Chapter 5: An overall conclusion for this thesis is given.
Further work: Suggested further work is presented
Appendix: All relevant appendixes is included is this section.
2 Theoretical background
In this chapter, the theory required to understand the methodology and the
experiments in this thesis is given. There are many theoretical aspects related to the PV technology, and in this chapter some brief introductions are given to some of these theoretical aspects, with references to further literature. In order to understand the effect of shading on PV modules, and the theoretical assumptions made to construct the simulation model, electronics related to solar cells and PV modules are presented. Some subjects within optics are presented in order to understand how soiling accumulates on a module glass, and how this affects the transmission through the glass. All the I(V)-‐ and P(V)-‐ plots in this chapter are modeled using the simulation tool LTspice. The I(V)-‐plot expresses the current I as a function of the voltage V, and P(V) is the power output P as a function of V. For further information on LTspice, see chapter 3.1.
2.1 Definitions related to solar radiation
2.1.1 Reference solar spectra
The optical path length light travels through the Earth's atmosphere can be defined as the irradiance per unit area (W/m2). With no atmosphere to pass through, the Air Mass is defined as 0 (AM0). This defines the spectra just outside the atmosphere (Chen 2011).
AM is in general a measurement of the atmospheric length the light travels when the sun is at zenith angle 𝜃, the angle given by the position of the sun relative to the perpendicular position of the sun (Chen 2011). A standardized measure for
representing the mid-‐latitudes, in the case of 1.5 atmosphere thickness, is the AM1.5G spectra. This is used by the solar energy industry as a reference spectrum. The
corresponding zenith angle to this atmospheric length can be expressed by
𝐴𝑀= 1
cos (𝜃). 2.1
By inserting 1.5 as the value of AM, and solving the equation for 𝜃, AM1.5G corresponds to a zenith angle of 48.2 degrees.
Global radiation is defined as the sum of diffuse and direct radiation (Markvart 2000).
The G in AM1.5G specifies that the spectrum is for global radiation. Using a
pyranometer, which measures the incoming radiation per unit area, on a horizontal or tilted surface, global radiation can be measured. These measurements are locally
dependent on the solar altitude, and weather conditions limiting the incoming radiation, such as cloud formation and the presence of aerosols in the air.
The intensity of sunlight as a function of wavelength is shown in Figure 2.1 for the AM1.5G spectrum.
Figure 2.1: Intensity of sunlight (W/m2nm) as a function of wavelength, representing the AM1.5 spectra (International ISO 9845-‐1 AM1.5G spectra 1992).
The AM1.5G spectra includes several atmospheric effects, see Chen (2011) further literature. The integrated power of the AM1.5G spectra is about 1000 W/m2 according to the ASTM G-‐173-‐03 (International ISO 9845-‐1 AM1.5G spectra 1992), and is often referred to as 1 sun.
0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8
0 500 1000 1500 2000 2500 3000 3500 4000
Intensity (W/m2nm)
Wavelenght (nm)
AM1.5G
The intensity of light can also be expressed by the intensity of photons (#photons/m2s) the sun emits per wavelength. Since the energy of the photons is wavelength dependent, the spectra will look different than the spectra for the intensity of light (W/m2). The AM1.5 spectra with the intensity of sunlight in W/m2nm will be used further in this thesis.
2.1.2 Absorptance, reflectance and transmittance
Sunlight interacts with matter by reflecting, absorbing and transmitting the incident light. The reflectance (r) absorptance (a) and transmittance (t) are wavelength dependent fractions. Assuming that all incoming radiation from the sun at a specified wavelength will interact with matter, the energy is conserved. Thus the fractions will equal to 1 (Chen 2011), and can be expressed according the following equation
𝑎 𝜆 +𝑟 𝜆 +𝑡 𝜆 = 1. 2.2
Figure 2.2 illustrates how incoming radiation perpendicular to a surface transmits a larger fraction of the incoming radiation, and reflects and absorbs a smaller fraction:
Figure 2.2: Sketch of how incoming radiation is reflected, absorbed and transmitted on surfaces such as glass.
Examples of matter that interacts in a similar manner as the above figure are glass and other transparent surfaces. It is for this thesis important to distinguish between the terms transmittance and transmission. Transmission is defined as an overall
measurement of how much incident light that passes through a surface. Transmittance can be defined as the fraction of incident light with a defined wavelength that passes through a surface.
2.2 Physics of solar cells
Solar radiation can be converted to electricity by the photovoltaic effect, using a solar cell as an electrical device. In this subsection provides an overview of the structure and property of the solar cell and the PV module consisting of several series connected solar cells.
2.2.1 Semiconductors
A semiconductor is the main component in a solar cell. Semiconductors have the property of having a narrow energy gap (Green 1982). There are several types of
semiconductors that are suitable as solar cells, as they have material characteristics that fit the spectra of available sunlight. Examples of materials are crystalline silicon, and thin film materials like CdTe, CIGS, a-‐Si and GaAs. In 2014, silicon based solar cells represent about 90% of the total market (ISE 2014).
2.2.2 Solar cell
The energy of the electrons in the crystal structure of the semiconductor material is aligned in defined bands; the valence band and the conduction band. The band-‐gap between these two bands represents an energy state the electrons cannot occupy. The band gap for crystalline-‐Si is about 1.11 eV which represents the minimum energy required to excite an electron from the covalent band to the conduction band (Chen 2011). The valence band represents the band of energy states containing valence electrons. The next higher energy state is the conduction band, where the electron has the energy level required to move freely.
A full valence band prevents the electrons from being able to move. Thus, a pure
semiconductor is really an insulator (Markvart 2000). To make semiconductors able to conduct, the material can be infused with impurities. Silicon has four outer electrons, bonded within covalent bonds in the crystal structure. As the most common appliance, group IV atoms such as phosphorus are added to silicone as the phosphorous atoms contributes fill the rest of the valence band and leaves one electron to the conduction band. This result in a surplus of electrons, thus an n-‐type material is created. Adding group III atoms like boron to silicon creates the p-‐type material, with a surplus of holes, as four electrons are required to fill the valence band but boron only has three (Green 1982). When the p-‐type and the n-‐type material are brought together, excess electrons from the surface of the material diffuse from the n-‐type material to the p-‐type material.
This results in a layer of phosphorus ions, which are positive charged. The excess holes from the surface of the p-‐type material diffuse into the n-‐type material, leaving a layer of negatively charges boron ions (Markvart 2000). This build in potential makes the pn-‐
junction work as a diode. The pn-‐junction is the main element of a solar cell.
Further and more detailed literature on this subject can be found in chapter 2 in (Green 1982).
A standard Si-‐solar cell is made from a wafer, based on materials like mono-‐ or multi-‐
crystalline silicon with contact grids (most commonly two to three vertical lines) made from busbars, and fingers (several horizontal lines). The thickness of the solar cells are continuously decreasing, and is today about 180-‐200 µm thick, see Figure 2.3.
Figure 2.3: Sketch of a 6’’ multi-‐crystalline Si-‐solar cell, with contact grid and fingers, size and the approximate thickness of a cell. Picture from (IFE Department for Solar Energy).
2.3 The two diode model
The solar cell is a complex device that converts sunlight into electricity. By treating the solar cell as an electrical circuit, the behavior of a solar cell can be further examined. An accurate model is to treat the solar cell as an equivalent circuit consisting of two diodes, one representing current losses due to diffusion (diode 1) and the second diode
represents current losses due to charge recombination losses (diode 2). Further and more detailed literature on these losses can be found in Markvart (2000). This model is known as the two-‐diode model. The electrical circuit for this model is illustrated in Figure 2.4:
Figure 2.4: The two-‐diode model equivalent circuit to a solar cell.
The series resistance Rs and the shunt resistance RSH, represent resistances related to certain power losses, which will be further described in the upcoming subchapter.
Based on Kirchhoff’s law, the current generated a solar cell can according to the two-‐
diode model be expressed by the following equation:
𝐼 =𝐼!"−𝐼!"(𝑒!!!!!! !" −1)−𝐼!"(𝑒!!!!!! !!" −1)−!!!!! !
!" . 2.3
In the above equation, V is the voltage, I is the current generated by the solar cell, ISC is the short circuit current, T is the cell temperature, and q is the electron charge and k is the Boltzmann constant. I0 and I02 is the diode saturation current of diode 1 and 2 respectively.
The relationship between current and current density is
𝐼=𝑗𝐴, 2.4
where j is the current density (A/m2) and A is the total area of the solar cell.
From equation 2.3 it is clear that the currents through the two diodes are expressed by exponential factors, which are dependent on V, I, Rs, and T. For diode 1, the ideal diode factor n equals to 1. For diode 2, the ideal diode factor n equals to 2. These factors are expressed as the factors next to the kT expression under the fraction line. Equation 2.3 is implicit and numerical methods are needed to solve it.
The short circuit current is the highest possible current generated by a solar cell and will for an ideal solar cell equal the light generated current IL. This is at the scenario when RS=0 and I02=0, at V=0 (Castaner & Silvestre 2003):
𝐼! =𝐼!"−𝐼!"(𝑒!!!! !" −1)−0(𝑒!!!!! !!" −1)−0+𝐼0
𝑅!" = 𝐼!". 2.5
In exception from ISC, the parameters in equation 2.4 are usually not available on commercial datasheets for PV modules or solar cells.
2.3.1 Parameters of the two-‐diode model
In this sub-‐chapter the parameters in the two-‐diode model will be further examined. All the following plots presented are simulation results from the model constructed in LTspice IV, as described further in chapter 3.1.
By plotting the output current as a function of the voltage, solar cells characteristics can be determined. This plot is known as an I(V)-‐plot for a solar cell. As a reference,
manufacturers provide technical data under standard test conditions (STC). STC is a condition defined as an irradiance of 1000W/m2 (AM1.5G) and cell temperature 25°C.
The most common characterizing parameters related to electricity production from a solar cell is the open-‐circuit voltage VOC, the short circuit-‐current ISC and the maximum
power point Pmax. The open circuit voltage is the highest voltage across the cell terminals, and occurs when the net current generated equals to zero. These
characteristic points on an I(V)-‐ and P(V) plot of a solar cell under STC is shown in Figure 2.5:
Figure 2.5: Simulated I(V)-‐ and P(V)-‐plot for a single solar cell under STC.
The power produced from a solar cell is the product between the output current and the voltage.
𝑃= 𝐼𝑉 2.6
The maximum output power from a solar cell is expressed in peak watts, Pmax, and is located at the point where the product between I and V as at its highest:
𝑃!"# =𝐼!"#𝑉!"# 2.7
Pmax is located at the peak of the P(V)-‐plot, as seen Figure 2.5.
According to the two-‐diode model, there are several parameters that cause losses in both current and voltage. All the following plots presented in this section are simulation results in terms of I(V)-‐plots from LTspice model for various parameter values at STC unless otherwise is stated. These simulation results provide an understanding of how the parameters affect both the current and voltage. As a manufacturer does not
commercially provide these data, the results from these plots are used to determine the values of the parameters in the two-‐diode model so they fit the other provided technical data at STC for a given module that will be further described in chapter 3.1.
The series resistance is resistances from contributions such as busbars and the contact between metal grids and silicon (Castaner & Silvestre 2003). The impact of the series resistance is illustrated by the I(V)-‐plots for various series resistances in Figure 2.6.
Figure 2.6: Simulated I(V)-‐plot for various series resistances Rs (Ω) at STC.
It appears from the above figure that values for RS in the range of 0.0001Ω ≤ Rs ≤ 0.001Ω does not cause any drastically impacts on the I(V)-‐plot. For Rs higher than 0.1, the slope is drastically changed. Thus RS is assumed to be less than 0.1 for modern solar cells.
0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00 10,00
0,000 0,100 0,200 0,300 0,400 0,500 0,600 0,700
Current (A)
Voltage (V)
Effect of the series resistance R
SRs=0.0001 Rs=0.001 Rs=0.01 Rs=0.1 Rs=1
Resistance contributions from manufacturing defects are parameterized as a shunt resistance (Castaner & Silvestre 2003). For solar cells with low shunt resistance, the light might be provided an alternative path, thus a high RSH is preferred.
The effect of various shunt resistances on a single solar cell is illustrated by the I(V)-‐
plots presented in Figure 2.7:
Figure 2.7: Simulated I(V)-‐plot for various values for the shunt resistance RSH (Ω) at STC.
The above figure shows that the plots will be close to identical for values for RSH between 100Ω and 10 000Ω, thus RSH is assumed to be higher than 100Ω for modern solar cells. Values within this range will cause little impact on the I(V)-‐plot.
0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00 10,00
0,000 0,100 0,200 0,300 0,400 0,500 0,600 0,700
Current (A)
Voltage (V)
Effect of the shunt resistance R
SHRsh=10 000 Rsh=1000 Rsh=100 Rsh=10 Rsh=1 Rsh=0.1
The effect of the diode saturation current density parameter j02 in the two-‐diode model, which represents charge recombination losses, is illustrated in Figure 2.8:
Figure 2.8: Simulated I(V)-‐plot for various saturation current densities for diode 2.
0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00 10,00
0,000 0,100 0,200 0,300 0,400 0,500 0,600 0,700
Current (A)
Voltage (V)
Effect of j
02I(V):1E-‐10 A/cm2 I(V):1E-‐7 A/cm2 I(V):1E-‐5 A/cm2 I(V):1E-‐3 A/cm2
The effect of the diode saturation current density parameter j0 in the two-‐diode model, which represents the effect of diffusion losses, is illustrated in Figure 2.9:
Figure 2.9: Simulated I(V)-‐plot for various saturation current densities for diode 1.
It appears in Figure 2.8 and Figure 2.9 that by decreasing the diode saturation current density, the voltage generated by the solar cell will increase. Due to the fact that the diode factor n of diode 2 equals 2, and n of diode 1 equals 1, they will have a different impact on the I(V)-‐plot. As it appears, diode 2, representing recombination losses will cause a higher impact on the voltage generated by the solar cell than the losses due to diffusion. These parameter values should be chosen so that the I(V)-‐plot fit VOC provided by the manufacturer.
The voltage generated by a solar cell is also temperature dependent. The cell temperature does not equal to the ambient air temperature, as solar cells is heated when illuminated. NOTC (Normal Operating Test Conditions) is the electrical data provided at irradiance 800W/m² and ambient temperature 20°C, wind speed 1m/s and AM1.5 (PVeducation).
0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00 10,00
0,000 0,100 0,200 0,300 0,400 0,500 0,600 0,700
Current (A)
Voltage (V)
Effect of j
oI(V): 1E-‐12 A/cm2
I(V): 1E-‐10 A/cm2
I(V): 1E-‐7 A/cm2
I(V): 1E-‐5 A/cm2
The linear relationship between the cell and ambient temperature can be described as
𝑇!"## = 𝑇!"# 𝑇!"#$ −20°𝐶
800𝑊/𝑚² 𝐺,
2.8
where 𝑇!"#$ is the cell temperature given at NOTC and 𝑇!"## is the cell temperature, and G is the irradiance and 𝑇!"# is the ambient temperature for the condition the cell
temperature corresponds to.
The I(V)-‐plots for a solar cell at various cell temperatures is shown in Figure 2.10:
Figure 2.10: Simulated I(V)-‐plot for various cell temperatures.
As seen in Figure 2.10, VOC decreases for increasing cell temperature, thus Pmax decreases for increasing temperature.
0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00 10,00
0,000 0,100 0,200 0,300 0,400 0,500 0,600 0,700
Current (A)
Voltage (V)
Temperature effects
I(V): 0°C I(V): 10°C I(V): 20°C I(V): 30°C I(V): 40°C
2.4 PV module
The voltage from one solar cell alone is not enough for common appliances. By
connecting several solar cells in series, the terminal voltage is multiplied by the number of cells that are connected. Due to the series connection, the total current will be the same regardless of how many cells connected.
Solar cells are sensitive, and the materials are easily affected by the surroundings.
Therefore, the connected cells are covered with glass surrounded by a metal frame. The cells are most commonly encapsulated by ethylene-‐vinyl acetate plastic (EVA)
(Markvart 2000). Silicon has a reflectance coefficient at approximately 0.34 (Chen 2011), and an anti-‐reflection coating (ARC) is necessary to reduce the reflectance on the surface. For further physics of ARC see chapter 9 in (Chen 2011).
For most common applications, the backside of the PV module consists of a second layer of EVA and a back sheet layer. See Figure 2.11 for a basic illustration of the layers:
Figure 2.11: Cross section to illustrate the layers of a standard PV module.
The current output by a PV module is direct current (DC), and by connecting an inverter to a PV module, the current can be converted into alternating current (AC), to be
compatible with the power grid. The inverter also has a maximum power point tracker (MPPT). The MPPT detects the voltage and current that provides the maximum power output.
Several solar cells connected together are referred to as a string. A PV module usually consists of several strings connected in series and with bypass diodes connected in parallel to each string. The most common application is one bypass diode connected to each string.
The purpose of connecting bypass diodes to a PV module is to reduce damages and power losses due to shading, which will be further described in the next sub-‐chapter.
2.5 Shading
The definition of shade needs to be divided into two terms, as the two terms have different impacts on a solar cell, or PV module. Soft shade is defined as a shade causing a transmission drop through a defined area. Hard shade is defined as an object completely blocking the incoming light, resulting in no transmission through a defined area.
A basic illustration of how sunlight is transmitted, reflected and absorbed by a surface such as glass covered with hard and soft shade is shown in Figure 2.12:
Figure 2.12: Basic illustration of how hard shade (left), and soft shade (right) affects the transmitted sunlight through a surface.
Soft shade might cover a solar cell or PV module uniformly, with the same overall reduced transmission over the entire module area. If a solar cell or module is shaded partly, a defined area of the module has reduced transmission.
I(V)-‐plots of a single solar cell at various uniform irradiance G, with cell temperature 25°C is shown in Figure 2.13:
Figure 2.13: Simulated I(V)-‐ plots of a single solar cell for irradiances 200, 400, 600, 800 and 1000W/m2 at temperature 25°C.
As it appears in the above figure, the short circuit current is proportional to the irradiance. Hence, this relationship can to a good approximation be expressed as
𝐼!" 𝐺 = 𝐼!",!"#
1000 ∗𝐺
2.9
The irradiance will also affect the VOC, but not to the same extent as the ISC. VOC is a logarithmic function of irradiance. See Castaner and Silvestre (2003) for derivation.
2.5.1 Partial shade
Partial shade is defined as shade partially covering a defined area of a solar cell or PV module. Partial shade applied to PV modules might result in complex I(V)-‐ and P(V)-‐
0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00 10,00
0,000 0,100 0,200 0,300 0,400 0,500 0,600 0,700
Current (A)
Voltage
Irradiance effects
I(V):200W/m2 I(V):400W/m2 I(V):600W/m2 I(V):800W/m2 I(V):1000W/m2
