1960, H. Mori pointed out the role of the second pn-junction at the rear side to ... According to the term coined by Mandelkorn and Lamneck [18], âBifacial solar cells ...... Beckmann, Solar Engineering of Thermal processes, 2nd ed., John Wiley.
Albert Ludwigs University of Freiburg Faculty of Forest and Environmental Sciences In cooperation with
ZEE- Centre for Renewable Energy
Automated Data Evaluation and Performance Modelling of Bifacial Solar Modules
Master thesis submitted in partial fulfillment of the requirements for the Degree of Master of Science in Renewable Energy Engineering and Management By
Akshayaa Pandiyan Matriculation No. 3957482 Compiled at Reliability of Solar Modules and Systems Division Fraunhofer Centre for Silicon Photovoltaics
First Examiner:
Prof. Dr. Ralf B. Wehrspohn
Second Examiner:
Prof. Dr. Leonard Reindl
Scientific Supervisors: Dr. Matthias Ebert Mr. David Daßler Mrs. Stephanie Malik Dr. Martin Heinrich Freiburg im Breisgau, Germany Date of Submission: 01.June.2017
Declaration I, Akshayaa Pandiyan, declare that this master thesis titled “Automated Data Evaluation and Performance Modelling of Bifacial Solar Modules” has not been submitted elsewhere and was produced without external aid and is entirely my own work. I have duly acknowledged all the sources of information which have been used in the thesis.
Date, Place
Akshayaa Pandiyan
Acknowledgment Firstly, my sincere thanks to my supervisors Prof. Dr. Ralf B. Wehrspohn and Prof. Dr. Leonard Reindl for accepting to oversee my work and their cooperation. I am indebted to the ‘Reliability of solar modules and systems’ group of Fraunhofer CSP and its team head Dr. Matthias Ebert for entrusting me in such an ambitious topic and his cooperation and extensive support every time it was needed. I would also like to express my heartfelt gratitude to Mr David Daßler and Mrs. Stephanie Malik, my scientific supervisors from Fraunhofer CSP, for their weekly supervision and valuable feedback on my research progress and results. I deeply appreciate their guidance, patience, support and dedication which kept me motivated throughout the work period and made this thesis possible. I would also like to thank Dr. Martin Heinrich, my external scientific supervisor, for spending his valuable time with me for discussions and comments about my work. I would like to thank Mr. Jens Fröbel, Mr. Hamed Hanifi and Mr. Matthias Pander for their scientific expertise and helping me optimise my simulation experiments. I honestly thank all of my colleagues from Fraunhofer CSP for their interesting exchange of ideas and creative discussions, thus making a positive atmosphere to work in. For the whole master degree duration, I would like to thank my supportive friends and professors from Freiburg, Munich, and Halle who have accompanied me, making this journey amazing. My special thanks to my friends from Chennai, especially Kavya, Asif, Yuvaraj, Ashwin, Shilpa, Niveadhitha and Poorvaja for always being there for me through hardships. Lastly but most importantly, I would like to thank my parents, brother and grandparents for their endless love, encouragement and blessings throughout my life. Thank you all for this wonderful experience!
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Abstract Bifacial Modules, unlike the standard Photovoltaic modules, have the advantage of capturing solar insolation from both the front and the rear surfaces. They therefore have a higher yield than conventional monofacial PV modules in relation to the ground area. And, the yield of a bifacial module depends on several parameters like the albedo, module installation configuration and environmental irradiance. However, a standard system to model the outdoor performance of bifacial modules is not available. In this thesis, a detail research on modelling bifacial modules will be implemented based on its electrical and thermal characteristics. The main objective of this thesis would be to develop an accurate mathematical model of the performance of a bifacial module, and to simulate and validate the model using the C++ programming language. In addition to this, an interest to program an application in OriginPro 2016 which can assist in automated analytical monitoring of PV modules was also developed. A total of 9 different types of thermal modelling methods were analysed and validated to accurately define the module temperature of a bifacial module as a function of ambient temperature, irradiance and wind velocity. Out of which, the method with the lowest RMSE (
) was preferred
and was integrated with the electric model. For electrical modelling of bifacial modules, a hybrid two diode model was adopted where and
and
are deduced through analytical solving and
are computed through differential evolution DE algorithm. Furthermore, other
optimization solutions to improve the IV Curve prediction of the model were realized based on comprehensive research on existing models. To validate the accuracy of the proposed model, it was tested against real time measured parameters from bifacial modules installed at two different sites in Saxony Anhalt, Germany - in one of the sites the module was installed on a fixed mount and in the other, on a two axis tracker. The proposed model exhibited good accuracy for both testing sites for a wide range of irradiance and temperature. In particular, the accuracy is superior at lower irradiance when compared to high irradiance conditions. The relative mean error between the measured and the simulated IV parameters were found to be in-between 0.7% to 1.9% and are consistent within this range. In addition, since this model is independent of previously measured on-site module parameters and relies only on the STC measured parameters of the front and rear surface along with the material properties of the PV module, it can be contemplated and adapted for studying the performance of any bifacial module and thus, making it a useful tool for PV simulation.
ii
Table of Contents Acknowledgment...................................................................................................................................... i Abstract ................................................................................................................................................... ii Index of Figures....................................................................................................................................... v Index of Tables ...................................................................................................................................... vii Nomenclature ....................................................................................................................................... viii 1.
2.
Introduction ..................................................................................................................................... 1 1.1.
Problem statement ................................................................................................................... 1
1.2.
Thesis objective ....................................................................................................................... 2
State of the Art Bifacial Technology ............................................................................................... 3 2.1.
2.1.1.
Types of bifacial cell design ............................................................................................ 3
2.1.2.
Bifacial Modules ............................................................................................................. 5
2.1.3.
Potential of bifacial modules ........................................................................................... 6
2.2.
3.
Basic module characterization ................................................................................................. 7
2.2.1.
Current-Voltage (IV) Curves ........................................................................................... 7
2.2.2.
Cell efficiency ................................................................................................................. 8
2.2.3.
Spectral response ............................................................................................................. 9
2.2.4.
Bifaciality ...................................................................................................................... 11
Photovoltaic Modelling ................................................................................................................. 12 3.1.
Theory of PV Modelling ....................................................................................................... 13
3.1.1.
Irradiance and weather .................................................................................................. 13
3.1.2.
Incident irradiation and losses ....................................................................................... 13
3.1.3.
Module temperature....................................................................................................... 16
3.1.4.
Module output ............................................................................................................... 17
3.2.
4.
Bifacial photovoltaics .............................................................................................................. 3
Field measurements ............................................................................................................... 19
3.2.1.
Weather data measurement............................................................................................ 20
3.2.2.
Module installation profile ............................................................................................ 21
Bifacial PV Modelling ................................................................................................................... 23 4.1.
Thermal model ...................................................................................................................... 23
4.1.1.
Approach 1: Parameter fitting ....................................................................................... 24
4.1.2.
Approach 2: Thermal energy balance modelling .......................................................... 25
Input Flux .................................................................................................................................. 27 Thermal capacitance .................................................................................................................. 28 Conductive heat transfer ............................................................................................................ 28
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Convective heat transfer ............................................................................................................ 28 Radiative heat transfer ............................................................................................................... 30 Method of solving ..................................................................................................................... 31 4.2.
Electrical model ..................................................................................................................... 33
4.2.1.
Analytical solving.......................................................................................................... 33
Calculation of IPV,bi and IMPP,bi .................................................................................................... 35 Calculation of VOC,bi .................................................................................................................. 35 Calculation of VMPP,bi ................................................................................................................. 36 4.2.2.
Soft computing .............................................................................................................. 37
Mutation .................................................................................................................................... 39 Crossover ................................................................................................................................... 40 Selection .................................................................................................................................... 41 4.2.3.
Hybrid electrical model ................................................................................................. 41
Fitness function ......................................................................................................................... 41 Hybrid algorithm ....................................................................................................................... 42 5.
Automated Data Evaluation........................................................................................................... 45
6.
Results and Optimization of Individual Models ............................................................................ 48 6.1.
6.1.1.
Approach 1: Parameter fitting ....................................................................................... 48
6.1.2.
Approach 2: Thermal energy balance modelling .......................................................... 50
6.2. 7.
Annual power modelling results ............................................................................................ 62
Conclusion ..................................................................................................................................... 64 8.1.
9.
Electrical model ..................................................................................................................... 54
Validation and Discussion of the Integrated Model ...................................................................... 60 7.1.
8.
Thermal Model ...................................................................................................................... 48
Future improvements ............................................................................................................. 65
References ..................................................................................................................................... 67
Appendix A: Simulated Parameters ...................................................................................................... 76
iv
Index of Figures Figure 1: n – type Si bifacial double junction cells [17]. ........................................................................ 4 Figure 2: BSF bifacial solar cell [17]. ..................................................................................................... 4 Figure 3: Single junction bifacial cell with dielectric passivation [17]. .................................................. 5 Figure 4: BOSCO cell structure. [28] ...................................................................................................... 5 Figure 5: Dark and illuminated I-V Curve of a solar cell. ....................................................................... 7 Figure 6: IV curve and Power curve of a solar cell [39]. ........................................................................ 8 Figure 7: Effective albedo for various PV technologies (a) Solar farm Materials (b) Commercial Materials [46]. ....................................................................................................................................... 10 Figure 8: Process flow for performance modelling. .............................................................................. 12 Figure 9: PV modelling steps [50]......................................................................................................... 13 Figure 10: Types of irradiance reaching the front surface [52]. ............................................................ 14 Figure 11: Visual representation of Parameters [33]....................................................................... 16 Figure 12: Two diode equivalent model. ............................................................................................... 18 Figure 13: Model validation steps [88] ................................................................................................. 19 Figure 14: Environment conditions measuring system at Site 1. (a) Rooftop weather data acquisition system. (b) Irradiance measurement system for GHI, DNI, DHI. ......................................................... 20 Figure 15: Irradiation sensor. ................................................................................................................ 21 Figure 16: Bifacial photovoltaic modules installed at Site 1 (Fraunhofer CSP, Germany). (a) Front view (b) Rear view. ............................................................................................................................... 21 Figure 17: Reference cell for rear side irradiance calculation. .............................................................. 21 Figure 18: Bifacial and monofacial modules installed on a two-axis solar tracker in Site 2. (a) Front view (b) Rear view. ............................................................................................................................... 22 Figure 19: Schematic of bifacial modelling [12]. .................................................................................. 23 Figure 20: Configuration of standard bifacial PV module [93]............................................................. 25 Figure 21: Thermal equivalent circuit for a bifacial photovoltaic module using electrical analogy. .... 26 Figure 22: Hybrid model flow chart. ..................................................................................................... 44 Figure 23: Measurement system database connection with Origin2016 Pro Software. ........................ 45 Figure 24: Plausibility test feature for module measurement data from PV Analysis app in Origin. ... 46 Figure 25: Additional graphing features of the automated data evaluation application suggested by the IEA. ....................................................................................................................................................... 47 Figure 26: PV Analysis Graphing Toolbar from the app. ..................................................................... 47 Figure 27: Measured and simulated module temperature for Clear sky conditions (data from site 1 on 15.Sept.2016)......................................................................................................................................... 51 Figure 28: Measured and simulated module temperature for Clear sky conditions (data from site 2 on 06.May.2016). ....................................................................................................................................... 51 Figure 29: Measured and simulated module temperature for Cloudy sky condition (data from site 2 on 09.July.2016). ........................................................................................................................................ 52 Figure 30: Measured and simulated module temperature for Cloudy sky condition (data from site 2 on 02.June.2016). ....................................................................................................................................... 52 Figure 31: Monofacial IV curves for bifacial module. (a) Front and back side measured at STC. (b) Front side measured at 750,450,250 Wm-2 ............................................................................................ 54
v
Figure 32: Comparing the hybrid electrical model for different constant parameter assumptions. ...... 55 Figure 33: Comparison of IV curves at varying irradiance and temperatures from site 1 (Fixed modules). ............................................................................................................................................... 55 Figure 34: Comparison of the various IV parameters at varying irradiances from site 1 (Fixed modules). (a) ISC (b)VOC (c) IMPP (d) VMPP ............................................................................................. 56 Figure 35: Comparison of IV curves at varying irradiance and temperatures from site 2 without considering the effects of shading of the rear surface (Two axis tracked modules).............................. 57 Figure 36: Comparison of IV curves at varying irradiance and temperatures from site 2 after considering the effects of shading of the rear surface (Two axis tracked modules). ............................. 58 Figure 37: Comparison of the various IV parameters at varying irradiances from site 2 (Two axis tracked modules with scaled GR’). (a) ISC (b) VOC (c) IMPP (d) VMPP ...................................................... 59 Figure 38: Temperature trends in different layers of the module (simulation results based at site 2 on 06 May 2016). ....................................................................................................................................... 60 Figure 39: IV parameter validation for integrated bifacial model using the measured data from site 1 on 05 May 2016..................................................................................................................................... 61 Figure 40: IV parameter validation for integrated bifacial model using the measured data from site 2 on 05 May 2016..................................................................................................................................... 62 Figure 41: Monthly yield prediction and validation against measured yield for bifacial module Bifa1 and Bifa2 installed at site 1. .................................................................................................................. 63
vi
Index of Tables Table 1: Solar tracker properties. .......................................................................................................... 22 Table 2: Thermal modelling tools. ........................................................................................................ 24 Table 3: Optical properties of PV materials. ......................................................................................... 27 Table 4: Heat capacitance of different layers. ....................................................................................... 28 Table 5: Energy balance equation at each node. ................................................................................... 31 Table 6: Manufacture data sheet and Flash test result for BiFacial B270 Mono model [92]. ............... 35 Table 7: DE variants mutation strategy. ................................................................................................ 39 Table 8: Thermal modelling tools with fitted parameters for site 1 (Fixed modules). .......................... 48 Table 9: Thermal modelling tools with fitted parameters for site 2 (Two axis tracked module). ......... 48 Table 10: RMSE comparison table of thermal modelling tools for site 1 (Fixed Modules). ................ 49 Table 11: RMSE comparison table of thermal modelling tools for site 2 (Two Axis Tracked Modules). ............................................................................................................................................................... 50 Table 12: RMSE comparison table of Approach 2................................................................................ 53 Table 13: RMSE comparison table for different approaches at constant temperature, T =25°C. ......... 55 Table 14: Integrated model validation for site 1 (Fixed modules). ....................................................... 60 Table 15: Integrated model validation for site 2 (Two axis tracked modules). ..................................... 61 Table 16: Parameters obtained from monofacial simulations using various methods under different irradiance at 25ºC. ................................................................................................................................. 76 Table 17: Paramters obtained form bifacial simulation at site 1 under various irradiance and temperature. ........................................................................................................................................... 77 Table 18: Paramters obtained form bifacial simulation at site 2 under various irradiance and temperature. ........................................................................................................................................... 77
vii
Nomenclature Label AI
ANN
Al-BSF BOSCO BSF CoO
DB DE DHI DNI EA ECN
FL FSR
GA GHI
Description [Unit] Area [m2] Artificial Intelligence Module area [m2] Annual Energy Yield [kWh] Artificial Neural Networks Ideality Factor for Diode1 Ideality Factor for Diode2 Aluminium Back Surface Field Both Sides Collecting and Contacted Back Surface Field Cost Of Ownership Specific heat capacity [JKg-1K-1] Heat capacitance [JK-1] Heat capacitance of air [JK-1] Crossover Ratio Number of DE parameters DataBase Differential Evolutionary algorithm Diffuse Horizontal Irradiance [Wm-2] Direct Normal Irradiance [Wm-2] Evolutionary Algorithms Energy research Centre of the Netherlands Spectral irradiance [Wm-3] Mutation factor Fill factor Fuzzy Logic Full Scale Range Standard gravity [9.8ms-2] Irradiance [Wm-2] Thermal conductivity [Ω-1] Generic Algorithms Global Horizontal Irradiance [Wm-2] Grashof number Conductive heat transfer coefficient [Wm-2K-1] Convective heat transfer coefficient [Wm-2K-1] Free convective heat transfer coefficient [Wm-2K-1] Forced convective heat transfer coefficient [Wm-2K-1] Radiative heat transfer coefficient [Wm-2K-1]
Label HALE IAM IEA
MPPT
NREL
ODBC
PERC PERT
PSO PV
viii
Description [Unit] Hale Altitude Long Endurance Incidence Angle Modifier International Energy Agency Current Gain Saturation current [A] Schottkey diode saturation current [A] Recombination diode saturation current [A] Diode current [A] Photocurrent [A] Spectral short circuit current [Am-1] Short circuit current [A] Boltzmann constant [1.3806e-23 JK-1] Short circuit current temperature coefficient [A K-1] Power temperature coefficient [%K-1] Open circuit voltage temperature coefficient [VK-1] Length of module [m] Characteristic length [m] Ratio between the saturation currents Maximum Power Point Tracking No. of excited electrons No. of photons National Renewable Energy Laboratory Number of population No. of cells in series Nusselt number Open DataBase Connectivity Pseudo-Fill factor Power [W] Bifacial power [W] Passivated Emitter Rear Contact Passivated Emitter, Rear Totally Diffused Prandtl number Particle Swarm Optimization Photovoltaic Charge of an Electron [1.6021e-19 C] Heat loss [W] External quantum efficiencies [%]
Label
RMSE SPA
STC
UAV
Description [Unit] Internal quantum efficiencies [%] Reflectance Resistance [Ω] Shunt resistance [Ω] Series resistance [Ω] Rayleigh number Reynolds number Root Mean Square Error Transmittance Sun Position Algorithm External spectral response [AW-1] Internal spectral response [AW-1] Standard Test Condition Time [s] Temperature [K] Donor vector Unmanned Air Vehicle Wind velocity [ms-1] Voltage [V] Open circuit voltage [V] Thermal Voltage [V] Trial vector View factor Dynamic viscosity [m2s] Kinetic viscosity [m2s] Power density [Wm-3] Optical thickness Target vector Irradiance ratio Thickness [m] Absorptivity of glass Absorptivity of PV cell Thermal expansion of air [K-1]
Label
Description [Unit] Azimuth angle [Degrees] Angle of elevation [Degrees] Angle of incidence [Degrees] Tilt angle [Degrees] Array tilt angle [Degrees] Zenith angle [Degrees] Flux per unit area [Wm-2] Thermal tool modelling parameter [K-1] [K-1]
Subscripts
MPP
Packing factor Reflectivity Emissivity of glass Efficiency [%] Bifacial efficiency [%] Density [Kgm-3] Wavelength [m] Thermal conductivity [Wm-1K-1] Thermal conductivity of air [Wm-1K-1] Stefan–Boltzmann constant [5.67e-8 Wm-1K-1] Reflectivity Transmissivity of glass Transmissivity of PV cell Albedo
ix
Ambient condition Bifacial Back glass Conduction Convection Electrical EVA Front surface of bifacial module Front glass Index of current generation Index of candidate solution Module Maximum Power Point Index of parameter PV cell Radiation Rear surface of bifacial module Non shaded region Shaded region Standard Test Conditions
Chapter 1 | Introduction
1. Introduction Growth of clean and green energy source has realised an exponential growth in the past decade as more people recognise the limitation of fossil fuels. Among the various renewable energy sources, solar energy remains one of the most accepted alternatives due to its abundance and versatility. Solar energy can be adapted in any scale of application, from a residential scale application like solar thermal water heating systems to large industrial applications like solar photovoltaic (PV) plants. For meeting the mankind’s electrical demand in the increasing global energy needs, whilst reducing the adverse effects of fossil fuels, adapting PV technology seems to be a good solution [1]. In addition, solar PV technology provides an advantageous solution for powering remote locations where the electrical grid cannot be easily accessed. This has introduced and encouraged a wide field of research for PV technology development and deployment. Solar panels are generally manufactured using semiconductor materials such as silicon, but organic solar cells are also currently a developing technology. Solar panels are commonly produced with monofaciality, that is, they are capable of capturing solar insolation only on one side. In monofacial modules, aluminium paste is used for contact which usually covers most of the rear side of the PV cell structure in a homogeneous manner. Consequently, due to the opacity of the back cover, light cannot enter from this side. On the contrary, bifacial cells are capable of generating electricity through light incident on both sides of the cell. Therefore, the generated current is higher as compared with monofacial cells when placed in a flat panel with transparent covers [2]. Most photovoltaic cells are actually intrinsically bifacial, but the rear contacts and the back sheet prevent the light from reaching the cells from the rear side. Even though bifacial modules have limited triumph in the market, the very last years have shown a new and particularly strong research interest in this technology. It has been shown that the gain in terms of yield for a bifacial module in comparison to a monofacial module can be as high as 54% by capturing the indirect light from the rear [3]. Therefore, precise modelling of bifacial modules can immensely improve the annual energy gain of a solar farm, which is a major interest when the project land is limited.
1.1.
Problem statement
Bifacial solar cells were devised as early as the 1960s [4] and has been initially presented at the First European Photovoltaic Solar Energy Conference in Luxembourg by two research groups, from Mexico [5] and Spain [6]. Since the 1970s abundant research has been dedicated to improving the efficiency of the bifacial solar cells by optimising numerous parameters. To accurately evaluate the outdoor performance of any PV module installation, a proper modelling and characterisation is required at the cell and module level. From the solar cell point of view, in-depth characterisation of solar cells improves their performance. In case of monofacial cells, a set of defined measurements under standard test conditions (STC) * are well established, which are used to characterise them. *
STC refers to indoor measurement under A.M. 1.5, 1000 W/m2 and 25°C.
Page | 1
Chapter 1 | Introduction However, there is no widely adopted characterisation method for bifacial cells or modules. Nevertheless, many authors [7, 8, 9] proposed the idea of measuring the front and rear electrical parameters (open circuit voltage (
), short circuit current (
), fill factor (
) and efficiency ( ))
separately covering the other side with an opaque black sheet and characterising the bifacial module based on these measurements and others suggested with front side electrical parameters and rear-tofront
ratio [10]. However, this way of separately defining the front and the rear side efficiency do
not correspond to the actual bifacial behaviour as bifacial characteristics are not a linear combination of monofacial properties. Singh et al. in [11] introduced two new parameters to characterise the bifacial performance based on STC measurements of each side of the module. Also, at the Energy research Centre of the Netherlands (ECN) a model is under development to correlate the STC measurements of bifacial module with the outdoor measurements [12]. An accurate PV model provides superiority in predicting the annual energy yield using the STC measurements and installation conditions (location, weather etc.). Therefore, this can provide an advantage in calculating the Cost-Of-Ownership (CoO) costs more precisely, also for testing the measuring system of the PV system.
1.2.
Thesis objective
The purposes of this thesis is to present an accurate and fast evaluating model for the calculation of the performance of a bifacial panel in arbitrary surroundings as well as to verify the model experimentally. Detailed theoretical analysis of two configurations of bifacial module (Fixed and Two-Axis tracking) was carried out to study the physical intricate relations between the thermal and the electrical behaviour, eventually aiming to use it finally as a basis for controlling further outdoor measurements. The first objective is to develop a mathematical model of the bifacial module performance (Power and bifacial gain) in relation to its thermal and electrical characteristics. Simultaneously, various real time measured parameters from the installed bifacial modules and meteorological data by Fraunhofer CSP, Saxony-Anhalt, Germany are collected. Secondly, the developed mathematical relations are modelled in C++ programming and verified with the collected field data to obtain the initial model. This will be adjusted and remodelled if suitable optimization conditions are available. Another interest of the thesis is to obtain a tool to generate performance graphs of the installed PV modules based on the measured field data by directly interfacing OriginPro with the online database. The purpose of this tool should be to visualize the simulated performance (see first objective) with the measured performance of bifacial modules. To summarize, this research will briefly analyse the key thermal and electrical parameters which influence the performance of a bifacial module and their consequences. And the results of the thesis would be to provide a discussion on the accuracy of the developed model in comparison with the existing bifacial models. Page | 2
Chapter 2 | State of the Art Bifacial Technology
2. State of the Art Bifacial Technology 2.1.
Bifacial photovoltaics
Research interests for bifacial solar cells have increased recently, the determination being to reduce the cost of PV electricity. An initial approach for a bifacial cell was to create two pn-junction on each surface of a silicon wafer to increase the conversion efficiency of silicon solar cells [13]. “In 1960, H. Mori pointed out the role of the second pn-junction at the rear side to improve the collection efficiency for long-wavelength photons”. His patent proposed an idea to use mirrors to resemble the property of double-sided illumination with p+np+ structure. Since then many researchers have contributed various structural designs and models to improve the efficiency of a bifacial PV cell. Standard bifacial solar cells are similar to the conventional Aluminium Back Surface Field (AlBSF) cell, except the back layer is replaced by a transparent layer such that light could incident from both sides of the cell. Both the front and the rear surface are fabricated with contact grids in similar patterns, therefore, capable of generating higher current compared to monofacial cells. Other than these changes, the working principle of bifacial and monofacial cells are similar. The first experimental model of PV showing only 7% efficiency was presented by A. Luque et al. [6] in Luxemburg Conference in 1977. However, in recent advancements, a bifacial n-PERT (Passivated Emitter, Rear Totally Diffused) cell can reach conversion efficiencies up to 20% [14]. Various n-type and p- type silicon substrates favouring bifaciality (Section 2.2.4) are under development and p-type bifacial cells are researched in ECN and in Fraunhofer ISE [15]. Recently, Imec have claimed to have developed a bifacial cell of 26% effective efficiency by achieving 80-90 bifaciality with n-PERT cells [16]. Overall, bifacial cells have demonstrated an improved efficiency and yield per sq. m over the standard monofacial cells under STC. This chapter provides a brief literature review of bifacial cell structures, module fabrication, benefits over monofacial cells, and bifacial applications. 2.1.1.
Types of bifacial cell design
A wide variety of bifacial cells are investigated and available in the market, depending on the materials and processes used in their fabrication, among which a few examples are discussed in this section. Bifacial solar cells can be classified based on the number of junctions they form: Bifacial double junction cells Monofacial solar cells prominently have only one pn junction where photons can be harnessed into flowing current. This constricts the cells to limited conversion efficiency. When bifaciality research was established in the early 60’s, H. Mori a Japanese researcher, proposed a bifacial solar cell with a possibility of double-sided illumination by vertical – horizontal dihedron mirror arrangement, forming a second pn-junction consequently improving the conversion efficiency. This advanced bifaciality research and many researchers were leaning towards transistor-like solar cells, in most Page | 3
Chapter 2 | State of the Art Bifacial Technology cases with p+np+ (Figure 1). In 2000, Hitachi researchers engineered high efficiency transistor structure bifacial cells featuring complex triode structure fabrication, which showed a 21.3% front and 19.8% rear efficiency [8].
Figure 1: n – type Si bifacial double junction cells [17].
Bifacial BSF solar cells According to the term coined by Mandelkorn and Lamneck [18], “Bifacial solar cells having homopolar pp+ or nn+ junction on the opposite surface to where the heteropolar pn junction is, are known as bifacial Back Surface Field (BSF) cells”, as shown in Figure 2. High efficiency BSF cells brought a revolutionary origin to current prevalent cells.
Figure 2: BSF bifacial solar cell [17].
In 1975, Russians [19] initially patented the first theoretical explanation supported by experimental results regarding BSF in suppressing surface recombination, later repeated in Spain [20] and France [21]. Many concepts like producing a drift field from heavy recombination [22], gettering effect [23], surface passivation [24] and optimising phosphorous emitter have helped evolve the BSF technology to find relevance in space applications [25, 26]. Another cell structure similar to the BSF cell structure, but fabricated with Czochralski Silicon (Cz) wafers and alkaline etching, are the n-Pasha bifacial cells. ECN modified n-Pasha cells (2014) with ‘baseline’ processing, including the new chemical pre- treatment for Boron-diffusion now results in efficiencies up to 20.5% [27]. Bifacial cells with dielectric passivation As mentioned in previous sections, the back sheet restricts a conventional solar cell to single side illumination. However, it is possible to make a bifacial cell with a single pn-junction by replacing the rear metal contact with high quality contact grid fabrication and passivating the inner-metallic space with dielectric (Figure 3). The presented structure was proposed by Chevalier and Chambouleyron [5, 21] consisting of a simple n+p structure, with tin oxide (SnO2) rear passivation, which has a measured bifaciality of 63%.
Page | 4
Chapter 2 | State of the Art Bifacial Technology
Figure 3: Single junction bifacial cell with dielectric passivation [17].
This proposal of using direct contacts with the p-substrate in a restricted area, while passivating the rear surface, conceived the innovation of Passivated Emitter Rear Contact (PERC) cells. BOSCO solar cells The recently introduced Both Sides Collecting and Contacted (BOSCO) solar cells exhibits a double sided emitter connected by diffused vias and a grid on both sides as shown in Figure 4. However, the emitter is disconnected from rear contact grid. This consequently allows bifacial operation while supporting standard module interconnection and double-sided collection of carriers in the base. Investigations of the BOSCO cells in Fraunhofer ISE (2014), Germany have reported that, “Since the BOSCO cell’s rear side exhibits p-doped as well as highly n+-doped surfaces the dielectric used as rear-side passivation needs to be suitable to passivate both polarities.” [28]. This supports the use of lower diffusion length material such as multicrystalline silicon (mc-Si). The article has experimentally justified an improved efficiency of BOSCO cells by optimising rear-side passivation.
Figure 4: BOSCO cell structure. [28]
2.1.2.
Bifacial Modules
Intrinsically all solar cells are bifacial in production, but in monofacial configuration due to full area aluminium back surface field passivation they lose their ability to harness the rear side irradiation due to the opaque back plate. Upon using dielectric passivation, these high efficiency cells can be made responsive from both sides. This is known as the bifacial configuration. When cells are encapsulated in bifacial configuration the optical losses have increased to 5.3% when compared to the 4.8% in monofacial arrangement (white backsheet) [29], however this becomes irrelevant as power is harnessed from the rear surface also. Recent researches about bifacial configuration state that [29- 33]: 1. The elevation angle of the module mounting highly influences the rear side contribution. Under non-uniform irradiance conditions when the diffused irradiation contribution is dominating, the gain of the module at maximum power is limited by the cells which receive merest irradiance. The margin of influence of this non-uniformity is inversely proportional to the elevation angle of the module. Page | 5
Chapter 2 | State of the Art Bifacial Technology 2. Module elevation has a logarithmic relation to the power gain of the module. However, an ideal parity should be achieved between elevation and power as these effects the installation costs of the module. 3. To avoid the self-shadowing or partial-shadowing effects of bifacial photovoltaic systems, increasing the tilt angle of modules is necessary. However, in areas with high albedo lower elevation angles are preferred as the inhomogeneity in the rear irradiation is supressed which allows higher energy yield from the module. Therefore, the installation of the bifacial module has an intricate relationship between many parameters and choosing the optimum is obligatory to minimise gain losses. 2.1.3.
Potential of bifacial modules
Bifacial solar cells are expected to realize low-cost photovoltaic solar systems, with respect to the reduced usage of land space and silicon material, and better overall efficiency. The development of application systems that can utilise the advantages of bifacial modules are researched in broad perspective, of which vertically installed flat modules and bifacial space applications will be discussed in brief in this section. South facing – optimised tilt mount maximises the yearly output of both monofacial and bifacial modules. However, this arrangement imposes costly and severe restrictions on module installations. Taking advantage of the ability to produce additional power by the irradiance due to albedo in bifacial modules, vertical installation has lots of advantages, including reduced cost installation. In 2000, T. Joge et. al. conducted field tests to experimentally analyse the applications of vertically installed bifacial modules and demonstrated the possibilities of Fence-integrated and pole-mounted systems [34]. Real time research plant for fence-integrated was then demonstrated in Aichi Airport, Japan, which concluded commendable results [35]. In 2016, these applications were adapted by Portugal researchers, S. Freitas and M. C. Brito, who proposed a method of using bifacial modules in solar buildings as balconies with reflecting mirror doors/sidewalls acting as an albedo surface [36]. In a summary, vertical mounting is more advantageous in urban areas, but the diffuse fraction data and albedo should be thoroughly assessed for that location and type of use. The benefit of bifacial solar cells is also prominently deployed in space applications. “In space, bifacial cells offer a lower solar absorbance, reduced operating temperature, high power/weight ratio, and increased sunlight collection from the Earth’s albedo” [13]. This predicts an increased power generation of 10-20 % as exhibited by 10kW bifacial space arrays at the International Space Station [37]. Also, to boost rear side power of bifacial arrays in space stations during moderate irradiation, ground-based laser beaming is a considered solution. However, due to reduced minority carrier diffusion length in the base region, bifacial cells have limited applications in space vehicles [29]. They are also employed in automated aerial vehicles, using the albedo reflected from clouds and other water bodies for added power boost. These are known as High Altitude Long Endurance (HALE) solar Page | 6
Chapter 2 | State of the Art Bifacial Technology electric Unmanned Air Vehicle (UAV), where the cells are specially manufactured using flexible crystalline silicon such that the power-weight ratio of 396W/Kg is achieved and are sustainable at lowest cell temperatures of 264K [38]. Bifacial PV with other orientations and performance enhancers like reflectors, concentrators and trackers has also been evaluated for matching power demand. Conjointly, bifacial photovoltaics have also commenced strong competition in the fields of space heating, PV sun-shading and PV-T systems.
2.2.
Basic module characterization
Photovoltaic manufactures worldwide handle various measurement procedures to comprehend the PV characteristics in pursuit of an accurate performance prediction and warranted annual yield from a photovoltaic module. This being achieved can potentially reduce the band in which the tolerance of a module is specified. Current-Voltage (IV) curves, cell efficiencies and spectral response of cells are the most common tools which can formulate the characteristics of a solar cell. This will be discussed in the current section. 2.2.1.
Current-Voltage (IV) Curves
IV Curve is the fundamental tool used to characterise a solar cell by collecting data sets of current and voltage pairs through direct indoor measurements without any knowledge of the internal device structure. The subsequent plot of the measured current-voltage pairs results the IV Curve from which the important operation points called ‘IV parameters’ at open circuit, short circuit and maximum power conditions can be obtained. Under dark conditions (Irradiance,
= 0), the solar cell will act as a
normal diode and its corresponding IV characteristics is known as the ‘dark IV curve’ (first quadrant of Figure 5). The shown figure corresponds to a silicon solar cell, where a small forward threshold voltage can lead to a sharp increase in current. However, when the solar cell is illuminated ( > 0) the IV curve shifts downwards (fourth quadrant of Figure 5) and current starts flowing from the cell. Since power gets delivered, to follow electrical conventions, the current axis is reversed such that the product of current and voltage is positive.
Figure 5: Dark and illuminated I-V Curve of a solar cell.
Page | 7
Chapter 2 | State of the Art Bifacial Technology While measuring solar cells, it is important that the light source closely matches the sunlight not only in terms of intensity, but also the spectrum. A common approach for indoor measurements is to replicate the STC conditions. However, continuous one sun illumination produces an excess heat effect in the cell which can result erroneous
measurements. To avoid imprecision, a common
method used to measure solar cells is flash testing them using short span flashes and quick measurements. This ensures cell temperature controlling, and synchronised measurements; therefore flasher is widely used in bulk manufacturing industries making strict large scale quality production possible.
Figure 6: IV curve and Power curve of a solar cell [39].
By utilizing the measured IV dataset, the power curve of the cell or module can also be plotted as shown in Figure 6. From this plot the IV parameters can be easily determined from the measured internal environment. For bifacial modules, the manufacturer usually provide a data sheet of measured IV parameters for the front side alone after covering the rear with a non-reflecting surface and double side illumination for various imitated albedos at STC. Another approach would be to measure the front and rear side separately using a flasher. The later approach is adopted in this research as it ensures precision and can contribute to the accuracy of modelling. 2.2.2.
Cell efficiency
Efficiency essentially describes the percentage of the input energy that can be converted into useful output energy. The efficiency of a solar module can be represented in terms of cell efficiency or module efficiency; and both depend on various factors like substrate material, rear passivation, manufacturing process, number of junctions and contact profile etc. On a cell level, “Single junction silicon cells have a theoretical efficiency of 29.4% limited by Shockley-Queisser limit” [40]. Whereas, double junction monofacial cells can reach efficiency limit up to 42.5%. Bifacial efficiency of a solar cell depends on the chosen irradiance level on each side. However, due to the bilateral property of bifacial solar cells, a standard set of characteristics defining its property is yet to be defined. One approach to measure efficiency of a bifacial cell is to measure these devices with a non-reflective setup for each surface separately [41]. Consequently, this would give an absolute value for one side Page | 8
Chapter 2 | State of the Art Bifacial Technology illumination (front and rear surface under one or several suns), which can then be used for calculating the ‘Equivalent Efficiency’. Equivalent efficiency is the sum of front and rear efficiencies scaled by a factor of irradiance on each side of the bifacial solar cell [42]. Also, this term can be used to represent the energy generation ability of a bifacial cell equal to the efficiency of a regular monofacial cell to generate the same power per unit area at similar test conditions [43]. Another common parameter known as the ‘Bifaciality Factor’ is also used for bifacial cells and is defined as the ratio between the front surface efficiency
and the rear surface efficiency
at STC conditions as
represented in Eq. 1 [29]. (Eq. 1) On the other hand, module efficiency relates to the entire module surface and is therefore always lower than the cell efficiency, for example due to the unused spaces between the arrays of cells. 2.2.3.
Spectral response
The spectral response of solar cells is the process of examining the association of short circuit current with respect to photons of different wavelength. In addition, spectral response of a cell is further classified into internal and external spectral response. The external spectral response (
)
can be defined as: (Eq. 2) and the internal spectral response (
) as [44]: (Eq. 3)
where,
Wavelength [m] Charge of an electron (=1.60217 x10-19 C). Cell area [m2] Spectral short circuit current [A/m] Spectral irradiance [W/m3]
Transmittance Reflectance Parasitic absorptance Optical thickness
Usually the external spectral response is measured experimentally and the internal spectral response, from the knowledge of the grid shadowing, reflectance, and optical thickness. Evaluating the internal response of solar cells can comprehend the sources of recombination, which are affecting the cell performance. It also has implications on the requirements for the cover and encapsulation materials. Another approach for defining the spectral response of solar cells is through external and internal quantum efficiencies. “The external quantum efficiency as the ratio of the number of excited electrons photons
of a solar cell is defined
reaching the cell contacts to the number of
incident on the cell area within a finite wavelength
centred on ” [45] (Eq. 4). (Eq. 4)
Page | 9
Chapter 2 | State of the Art Bifacial Technology An ideal solar cell would show a near 100% quantum efficiency in the infrared wavelength range. However, when the performance of a cell moves away from the ideal performance due to surface recombination, efficiency
reflectance,
transmittance
and
absorptance
losses,
the
internal
quantum
is used to define the performance of the cell as shown in Eq. 5. (Eq. 5)
Albedo is defined as the fraction of radiation that is reflected by Earth’s surface back to the atmosphere which is utilized by the rear side of the module for energy yield. Albedo also has spectral and directional properties and consequently, affects the spectral response of a bifacial module from the rear side. Recently M.P. Brennan et al. conducted experimental procedures to evaluate seven solar cell materials (GaAs, c-Si, mc-Si, CdTe, a-Si:H, CZTSS and organic) installed in 22 commonly occurring surface in rooftop, residential and solar farm configurations [46]. The effect of spectral albedo can be deciphered from the experimental results for solar farm and rooftop installations shown in Figure 7.
(a)
(b) Figure 7: Effective albedo for various PV technologies (a) Solar farm Materials (b) Commercial Materials [46].
Page | 10
Chapter 2 | State of the Art Bifacial Technology 2.2.4.
Bifaciality
As discussed in the previous sections, a standard and widely accepted method of characterisation for bifacial modules is not available. Currently, bifacial module manufacturers quote the price per watts of the bifacial devices based on their front side monofacial illumination or tabulating the front and rear efficiency with linear relationship. Many authors have reported different methods to define the bifaciality of the module by characterising the front and rear side separately and then summing those values [7, 9]. However, linear combination of monofacial characteristics does not enclose the whole information about bifacial behaviour. In actuality both the front and rear surfaces absorb irradiation simultaneously. Thus, this approach lacks to account for the end-use gain of bifacial modules which primarily defines devices of this type. In 2001, H. Ohtsuka et. al. proposed a simulation system that simultaneously illuminates and measures both surfaces of the cell [47]. This method was further improvised by A. Edler et al. in 2012 using a flasher setup with accessories [48]. But both these approaches require specialised equipment arrangements along with the flasher which makes it expensive and being a time consuming process, questions its applicability. Recently J.P. Singh et al. published a new approach for defining the IV parameters of bifacial modules by utilizing only single-sided measurements under STC [11]. The paper derives the bifacial short circuit current
, open circuit voltage (
) and the fill factor (
) of a bifacial module
considering a one-diode model. Sequentially the simulated data are compared with the indoor measured data for validation. In this research, the Singh et al. method is improvised using a two diode model and successively validating the results with measurements from outdoor installed modules. To estimate the IV parameters of a bifacial module, the author defined a new parameter called irradiance ratio
which can be defined as the ratio between the rear
and front
irradiance (Eq. 6).
This, however, should not be confused with albedo which is defined as the faction of the solar global irradiance which is reflected from the ground. (Eq. 6) To define the IV parameters the irradiance ratio is used as the scaling factor. Since, the photons from the absorbed irradiation is responsible for exciting the charge carriers, it is assumed that the short circuit current of the bifacial module differs linearly with the front and rear irradiance. The energizing of the charge carriers is independent of the side from which the photon is absorbed [49]. The aggregate current of the module is the sum of the short circuit currents of the respected surfaces scaled by . Observably, for different irradiance cases the IV parameters also vary. For a bifacial module of cell area
, the power
and efficiency
of the module is defined as: (Eq. 7) (Eq. 8)
The derivations of bifacial IV parameter are explained in detail in section 4.2.1. Page | 11
Chapter 3 | Photovoltaic Modelling
3. Photovoltaic Modelling Performance modelling is a tool to analyse system aspects and outputs. Modelling and simulations are methods which are commonly used by performance analysis to respect constraints and optimise performance. A proper model of any system should consider available resources, key influencing parameters affecting the performance, their interrelationships, and possible trade-offs among different parameters to obtain optimum output. Consequently the outcome reveals the achievability of the system, in this instance, the annual yield of the photovoltaic system. The expected flow of a modelling process is as shown in Figure 8.
Figure 8: Process flow for performance modelling.
In brief, the initial step for performance modelling of a PV system would be to draft an agenda summarising the critical scenarios (Eg. weather conditions, module installation) and the significant scenarios (Eg. wind, shading, soiling) that have a direct influence on the system output. The subsequent step would be to derive a function based on the drafted scenarios, which best illustrates the performance of the installed system. This is known as Photovoltaic (PV) Modelling. PV Modelling and analysis is a great practical and theoretical importance in research, design, development and optimization of PV Performance. A model that correctly predicts the module performance using module characteristics, received irradiation and climate data is the basis of a reliable prediction of annual energy production of the installed PV system. For a monofacial module, a discrete set of parameters has already been defined to interpret the performance of the module. Many simulation tools like MatLAB toolbox (PVLib), PVGrid Toolbox, INSEL and PVSyst has also been developed for monofacial modules. This lacking for the bifacial modules, the modelling becomes more complex. Figure 9 systematically explains the steps that are involved in modelling a PV plant. However, this research is focused up to the modelling of a single PV module, therefore limiting the thesis for steps 1, 4 and 5. The concluding steps after designing the model would be to review its compatibility based on speed and precision through simulations and comparing results with field measured data. Page | 12
Chapter 3 | Photovoltaic Modelling
Figure 9: PV modelling steps [50].
3.1.
Theory of PV Modelling 3.1.1.
Irradiance and weather
Obtaining the meteorological data of the field is the most essential part of modelling and testing PV. This includes the sun position, available irradiance, ambient temperature, wind speed and other weather conditions (including cloudy conditions, rain, snow etc.). The Sun Position Algorithm (SPA) developed by the National Renewable Energy Laboratory (NREL) to calculate solar zenith azimuth angle
and
, has the least uncertainties (≤0.0003°) in the period from year -2000 to 6000 [51].
This algorithm has been developed in C language (by NREL) and as library tools (by Sandia) which makes it easily available. The intensity of the sun at the top of the earth’s atmosphere on a plane normal to the sun and parallel to the horizontal plane of installed PV can be estimated from the sun’s position and module installation parameters. Also, many online databases like PVGIS, NSRDB, INSELDB, offer a wide library of weather data which could be utilized for simulation of the model. For this research, irradiance and weather database is achieved by measuring each parameter in the outdoor PV laboratories. 3.1.2.
Incident irradiation and losses
Studying the optical behaviour of any PV module and evaluating its net incident irradiation on the plane of the module is known as optical modelling. However, in this work, an optical model for bifacial photovoltaics is neither mathematically designed nor soft programmed. Optical behaviour of bifacial PV modules has an intricate association with wide set of parameters, starting from plant area, module installation profile and also the varying optical behaviour of the module materials with respect to different wavelengths. These relationships have to be studied in detail both theoretically and experimentally to obtain an accurate model. However, this becomes beyond the scope of this research in terms of time and resources. Since familiarity of optical properties is essential to evaluate the operation for PV modules, an intensive literature study was accomplished before starting the thermal
Page | 13
Chapter 3 | Photovoltaic Modelling and electrical modelling. This broad study of the optical modelling and the existing modelling tools which are available for bifacial module are discussed in brief in this section.
Figure 10: Types of irradiance reaching the front surface [52].
The module power output depends on three types of insolation: 1. Direct Normal Irradiation from the sun (DNI). 2. Diffuse irradiation due to scattering of light from clouds, aerosols and molecules in the atmosphere, called Diffuse Horizontal Irradiance (DHI) 3. Reflected light from the ground. (Albedo). Knowing the total measured Global Horizontal Irradiance (GHI) and the sun position obtained from weather database and algorithms respectively, the total DHI can be determined by applying any sky diffuse model, for example Perez et al. model [53], Erbs model [54]. And the difference between GHI and DHI is equal to horizontal beam irradiance or DNI. However, the irradiance reaching the surface of the PV module will vary from the evaluated irradiance model depending on the array orientation. An array orientation can be characterised by: 1. Array tilt angle
: It is the angle between the plane of array and the horizontal plane where
the PV is installed. 2. Array azimuth angle
: It is the angle at which the front surface of the plane is facing
with respect to the geographical North. For instance, for a south facing module
=180°.
A PV array can be either in a fixed or a tracked array orientation. At fixed array orientation the array is stationary, therefore tilt and array azimuth angle remains the same throughout panel operation. Whereas, in tracked array orientation the array is traced along the position of the sun such that the angle of incidence
of irradiance (the angle between the irradiance and a perpendicular to the
surface at the point of incidence) is always zero. The order of rotation can be one or two, depending on the complexity of the tracking system. Therefore, the irradiance is translated to the plane of array using
and
to obtain a more realistic value of the received irradiation. Apart from the
inplane beam and diffuse irradiation, the reflected irradiation from the ground is also essential, especially for bifacial modules. The calculation of the ground-reflected irradiation requires a more sophisticated procedure based on the implementation of view factor ( Page | 14
) known from heat transfer
Chapter 3 | Photovoltaic Modelling fundamentals. This is a geometric entity that ranges from 0 to 1 that defines the fraction of radiation that is received by a surface due to emission of radiation from another surface [55]. The summation of the direct, diffuse and albedo results in the total irradiation incident on the respective surfaces. In addition, this net incident irradiance on the array is further reduced due to irradiance losses by reflection, soiling and/or shading. 1. Reflection losses: Reflection losses are optical effects corresponding to the weakening of the incident irradiation on the PV module surface when the angle of incidence is greater than zero. The Incidence Angle Modifier (IAM) is defined as the loss factor due to the angle of incidence. 2. Soiling: Soiling is the accumulation of dust on solar panels that decreases the panel efficiency. Soiling can have large effects on dry land, which consistently occurs with a large solar resource. Sea salt, pollen, and particulate matter originating from air pollution, agricultural activity, construction and other anthropogenic and natural sources accumulates on the panels until it is removed either by rain or washing [56]. 3. Shading: Shading can be internal by an adjacent array (Self-shading) or external due to a tree branch, building, dust or any opaque objects. Since the cells in a module are connected in series, shading of a single cell can cause a steep decrease in the overall current. In [12], Gaby et al. proposed an equation based on these principles for module.
and
of the bifacial
can be calculated as:
(Eq. 9) where
is the albedo of the ground,
is a designated fraction for circumsolar irradiation,
is the
view factor of the front surface and, (Eq. 10) where, replacing
is the sun’s zenith angle. Similarly, he suggested that Eq. 9 can be translated for and
by its supplements and an appropriate
relatable to
by
in reference to [57].
However, this approach assumes the shading is uniform throughout the module and this contradicts with practical cases. Later, Yusufoglu et al. modified this simplification by analysing the effects of self-shading of bifacial modules and adapting
for shaded (subscripted by
) and non-shaded (
)
regions for every cell of the PV module based on their spatial distribution ( ) with respect to the ground [33]. The deductions made by the authors to calculate
can be deciphnered from Figure 11,
and the resulting net rear reflected irradiance is calculated as: (Eq. 11)
Page | 15
Chapter 3 | Photovoltaic Modelling where,
is the view factor calculated from the shaded region and
is the view factor
calculated from the non-shaded region to the module. In addition, this research also investigated the influence of varying module elevation, tilt angles and reflecting surfaces on bifacial annual energy yield. In future, the results from [33] can be integrated as an efficient tool to model the optical behaviour of bifacial modules with thermal and electrical models proposed in this work.
Figure 11: Visual representation of
Parameters [33].
Furthermore, modelling reflection and soiling losses on the PV array is a tedious process mainly because it is a function of the place at which the array is installed. However, existing IAM models like Physical IAM model [58], ASHRAE IAM model [59] and Sandia IAM model [60] are available which could be fitted into the evaluated model from the previous steps. 3.1.3.
Module temperature
Measuring or predicting module temperature is the first step in estimating cell temperature, which is also needed to predict the module IV curve. The instantaneous temperature of a cell depends upon the amount of irradiance received, electrical properties, installation profile and its heat exchange with the environment. Many researchers have depicted that in a massive structure like a PV module “the effective cell temperature may be higher than the corresponding temperature of the rear glass surface where one would normally try to measure the module temperature” [61]. Also, the cell temperatures within a module could also vary from the corners to the centre, depending on the conductivities of the frame and the plastic casing. Accordingly, a thermal model is necessary in order to understand the behaviour of a PV module in varying temperatures. Various authors have modelled the module temperature of monofacial photovoltaics as a function of heat exchange through radiation, convection, conduction and the power generated. Wilshaw et al. conducted a linear regression fit relating the difference between module and ambient temperature with the irradiance and the efficiency of the module between 21 °C and 27 °C considering that all the layers of the PV module is at the same steady state temperature [62]. This evaluation was based on real time data from a large demonstration array of south faced PV mounting in the Northumberland building at the University of Northumbria, Newcastle. A.D. Jones et al., in 2001, derived a non-steady state model for module temperature with respect to the theoretical description from Schott (1985) and adapted the same methodology with the data from Northumberland Building array characteristics [63]. Many authors have adapted fitting methods where an equation defining the thermodynamics of a module is Page | 16
Chapter 3 | Photovoltaic Modelling derived. Then, the measured data are fitted for this equation to obtain a thermal modelling tool [60], [64-69]. A. Tuomiranta in [70] analysed a group of 16 thermal modelling tools for monofacial modules in arid climates, among which 6 modelling tools with low RMSE were adapted and evaluated for bifacial modules in this work. In addition, D. Faiman in [69] studied the steady state Whillier–Bliss equation [71, 72], that is used for thermal analysis of flat plate solar thermal collectors, and modified it to assess PV module temperature. This will be the 7th modelling tool which will be evaluated for bifacial modules in this work. Other authors have exercised methods to thermodynamically evaluate the heat flow, gain and losses across the different layers of a PV module and its heat exchange with the surroundings. Therefore, this approach is independent of past outdoor module measurements. Because the heat flow across the different layers of a module is a function of their respective thermal and optical properties, this can be adapted for any type of module provided the thermal and optical properties of the different layers are known. The properties of bifacial module layers are usually standardised, and in this work, thermal models which are proposed for Building Integrated Glass-Glass PV modules [73, 74] are reconditioned for bifacial modules by introducing slight changes. The main objective of thermal modelling in this thesis would be to predict the module temperature to a degree of precision that is meaningful under the given outdoor conditions. This will be the prerequisite for the calculating the IV parameters in electrical modelling. In total, 9 different thermal models are discussed in this work and they are compared with real time measure data and tested for accuracy. Consequently, the most accurate model is integrated with the electrical model to obtain the resulting IV curves. However, the variation of PV cell based on spatial orientation was not considered in these models. The stepwise module temperature dependencies and thermal modelling followed in this research is briefly explained in Section 4.1. 3.1.4.
Module output
This step covers the electrical modelling of the PV modules, integrating the previously mentioned thermal modelling. The module output is the generated power from the PV module which is a function of voltage and current. Electrical characteristics of a solar cell can be represented as mathematical interpolation of current and voltage [75, 76] or by its equivalent circuit [77]. The latter provides a convenience of seamlessly simulating the PV electrical circuit model using standard software such as MATLAB, INSEL and PVsyst. Moreover, the luxury of integrating the model into larger PV systems comprising of power electronics can also be achieved. A PV cell consists two layers of differently doped semiconductor materials forming a p-n junction, which in the absence of irradiation behaves as a simple p-n junction diode and its characteristics are governed by the Schokley diode [78]. When exposed to sunlight, however, results in carrier recombination across the junction, thus building up a potential difference. Consequently, free moving charge carriers start flowing through the external circuit. This photovoltaic effect results to an Page | 17
Chapter 3 | Photovoltaic Modelling electric current known as photocurrent
which is dependent on temperature and the irradiance
flux of the PV cell. The simplest approach to design an equivalent circuit is the single diode ideal model where a current source is connected parallel to a diode. This helps to rudimentarily interpret the relationship between the PV cell construction and the incident light. In this work, the two diode model (Figure 12) is used for deriving the output current
. This
model is realistic as it incorporates the practical operation of PV cells considering losses due to contact resistance, current flow resistance and resistance due to electrodes, junction recombination and the influence of temperature on the open circuit voltage (
) [79-82].
Figure 12: Two diode equivalent model.
There are seven modelling parameters for this model, namely and
for diode D1 and D2 respectively, shunt resistance
factors
and
, reverse saturation currents
, series resistance
and the ideality
. (Eq. 12)
where, k is the Boltzmann constant (=1.380653 x 10-23 J/K). This results in an intricate current equation as shown in Eq. 12. Even though more complex models like Breitenstein-Rißland model [83] or 3-diode model with resistance [84, 85] were discussed for implementation, two-diode model have a perfect balance between accuracy and speed. This accounts for adopting this model for this thesis. Therefore, output power can be defined by the IV Curve of a module that is obtained by this equivalent circuit. To utilize this model for predicting the annual yield of a PV module the model parameters should be determined. Analytically solving for all the parameters would be problematic and time consuming. The most feasible approach would be to extract the important points of an IV curve from the given manufacturer datasheet, for instance
and
determined by calculating the reciprocal of the slopes near
and from this and
and
Can be
respectively. Some authors
have proposed different methods to simplify this evaluation by constant parameter modelling [86], where it is assumed that the resistances and the ideality factors are constant and only the photocurrent and saturation currents are subject to change with
and . However, the accuracy of the result is
dependent on the selected points in the given IV curves and keeping majority of the modelling Page | 18
Chapter 3 | Photovoltaic Modelling parameters as constant is too idealistic considering that
and
have a substantial effect on all the
parameters. In other cases, several authors have proposed to assume the saturation currents of the two diodes to be equal. This is highly erroneous because the recombination saturation current than
in orders of magnitude. In [87], V. J. Chin et al. introduced a new parameter
is greater , which is
defined by the ratio between the saturation currents. This can be represented by Eq. 13. (Eq. 13) Therefore, without the compensation of accuracy, assumptions of quantitative values are avoided and all the seven unknown parameters of the two-diode model, namely
and
are
computed in this work. For any model, the electrical parameters can be calculated using either analytical solutions or soft computing method which is thoroughly analysed in section 4.2.1 and 4.2.2 respectively. Some authors have also adopted a hybrid approach which will bring together the accuracy of analytical calculations and the speed of soft computing [87]. However, these models are only proposed for monofacial modules. The method exercised in this research would be a hybrid approach that is modified for bifacial modules by utilizing the results of earlier researches done for bifacial characterisation (Section 4.2.3). The accuracy of this model is estimated based on the margin of error between the modelled output and the measured output from the system at similar conditions (Section 3.2). Once an accurate model is achieved, it can be further implemented in other installations to check the outdoor measuring system.
3.2.
Field measurements
Model validation is the decisive step of the modelling process which defines closeness of the model with the actual data. The requirements to evaluate a performance model are (Figure 13): 1. Measured output: Continuous measurement of the system output and environment under realtime conditions which are concurrent to the simulated situations. 2. Modelled output: The designed performance model inputs with the measured system environment data to obtain the modelled output, which is then evaluated.
Figure 13: Model validation steps [88].
Page | 19
Chapter 3 | Photovoltaic Modelling To obtain proper model validation it is essential for the environmental, and the measured data to be easily retrievable, consistent, and most importantly, flawless. The fidelity of measured data varies depending on the objectives of the validation effort and the detail contained in the model to be evaluated. Therefore, data used for validation itself should be checked for plausibility. In this work, an automated data evaluation system was implemented using OriginPro software. 3.2.1.
Weather data measurement
Time resolved meteorological data are essential for evaluating the annual energy yield of the module. Therefore the Fraunhofer CSP performs outdoor measurements of different module technologies on the “PV Outdoor Lab Halle”, an outdoor test area (Site 1) where the modules and the environmental conditions are measured continuously and synchronously. The data required for the validation are collected over a period of one year beginning from mid-January 2016 to 2017. The environmental conditions are measured via a weather data acquisition system (Figure 14.a). This system includes an analog weather transmitter installed in the test area which can measure the wind profile, precipitation, humidity, pressure and the ambient temperature over a wide scale. The measurements taken by the weather transmitter are averaged and stored at 60-seconds interval. An irradiance sensor is also installed, that measures the Global Horizontal Irradiance (GHI), Direct Normal Irradiance (DNI) and Diffuse Horizontal Irradiance (DHI) averaged over every minute near by the installed module (Figure 14.b). Also, independent pyranometers are placed in the plane of array of the module to measure the total front irradiance. Through these measurements the module can be compared under the same conditions and indicates the energy yield depending on these conditions.
(a) (b) Figure 14: Environment conditions measuring system at Site 1. (a) Rooftop weather data acquisition system. (b) Irradiance measurement system for GHI, DNI, DHI.
In addition, 3 bifacial modules supported on a two-axis tracker are installed at another site, in Rödgen, 30 km away from the PV outdoor lab (Site 2). The weather data acquisition system installed on the tracker includes Si-crystalline irradiance sensors on the module plane (2 on the front side & 1 on the backside of the tracker) and a pyranometer (Figure 15). The global horizontal irradiance is measured with an additional pyranometer. Wind direction and speed as well as ambient temperature, are logged using a combined device [89, 90]. Page | 20
Chapter 3 | Photovoltaic Modelling
Figure 15: Irradiation sensor.
3.2.2.
Module installation profile
Module measurement includes the installation profile of the module and instantaneous electrical measurements. The modules in the PV outdoor lab (Site 1) are ground installed at an elevation angle of 30° and are fixed facing 180°S (Figure 16). Unfortunately, the albedo of the ground was not measured but can be deciphered from the measured front and rear irradiance. A reference cell is installed in the rear side of the PV profile which measures the back irradiance (Figure 17).
(a) (b) Figure 16: Bifacial photovoltaic modules installed at Site 1 (Fraunhofer CSP, Germany). (a) Front view (b) Rear view.
Figure 17: Reference cell for rear side irradiance calculation.
The modules under measurement installed on the other site are on an individual driven two-axis tracking system in Saxony-Anhalt, Germany (Site 2). The tracker supports 3 bifacial modules (one of which is completely covered with a black sheet on the back side) and a monofacial module from the same manufacturer (Figure 18). This helps in comparing the performance of monofacial and bifacial modules under similar conditions. Consequently, the algorithm can be inclusive of the effect of the Page | 21
Chapter 3 | Photovoltaic Modelling front and rear side of the bifacial modules. The solar tracker properties are discussed in Table 1. However, measurements utilized from this site are restricted to two-axis tracking condition on specific days and are not continuous. The albedo of the concrete ground wasn’t measured. Since the optical model is not designed in this work, this reflects a negligible effect in thermal and electrical modelling of the bifacial modules. Table 1: Solar tracker properties.
Properties
Values
Mast height
3.6 m
Module mounting area
12 m2
Azimuth range
35° – 325°
Elevation Range
0° – 90°
In both sites, each module is operated at its maximum power point. The measuring device has a current-full scale range (FSR) of 10.24 A as well as 12.5 A (dependent on the measuring place) with a resolution of 1 mA. The FSR of the voltage is 259 V with a resolution of 10 mV.
(a) (b) Figure 18: Bifacial and monofacial modules installed on a two-axis solar tracker in Site 2. (a) Front view (b) Rear view.
Page | 22
Chapter 4 | Bifacial PV Modelling
4. Bifacial PV Modelling Modelling the yield of bifacial module necessarily depends on many factors like weather data, installation parameters of the panel, reflectivity of the ground, wind conditions etc. These parameters act as the input variables for the modelling. The output variables are usually the output power ( ), but in certain cases
and
are also considered. The number of unknown parameters, which the PV
performance depends on, increases when the equivalent circuit of the chosen model becomes more sophisticated and far from being the ideal form [91]. To facilitate the PV modelling, various input parameters which influence the module power are categorised into 3 different models (namely optical, thermal and electrical). Subsequently, these models are interrelated with each other to develop a performance model for a bifacial module. A schematic of the integration of these models is shown in Figure 19. However, as mentioned before in section 3.1.2, the optical modelling for bifacial modules is skipped as it is beyond the scope of this thesis. The methods employed for defining the thermal and electrical behaviour of a bifacial module are demonstrated in this chapter.
Figure 19: Schematic of bifacial modelling [12].
4.1.
Thermal model
Solar cells, being a semiconductor, are very sensitive to temperature. Open-circuit voltage decreases significantly with the increasing module temperature (-0.45 %/K for the used module) and the short circuit current increases with increasing temperature (0.04%/K) [92]. The instantaneous module temperature is a function of air temperature, wind speed, incident irradiance, module material, mounting and module heat exchange with the surroundings. There are two different approaches used in this research to predict the module temperature at a given ambient condition. In both approaches, the difference in temperatures with respect to the special arrangement in the module (near or away from the frame) and the received irradiation is ignored and the entire module is assumed to be at the same temperature by taking an average. Page | 23
Chapter 4 | Bifacial PV Modelling 4.1.1.
Approach 1: Parameter fitting
In approach 1, some commonly used, existing modelling methods are analysed with respect to bifacial modules. However, these models assume steady state condition and all the parameters related to the thermo-physical properties of the module material are combined together as one or more modelling parameters,
(where =1,2,3,4). Therefore, these tools do not require any material specific
parameter for odelling. The module temperature (
) derived from these tools are exclusively
dependant on the measured ambient temperature ( ), incident irradiance (
and
) and wind speed
( ). The time resolved data collected at Site 1 and Site 2 (Section 3.2) are utilized for obtaining the modelling parameter for the 7 thermal modelling tools shown in Table 2. Table 2: Thermal modelling tools.
Equation No.
Referred from
Modelling Tool
Eq. 14
[64]
Eq. 15
[65]
Eq. 16
[66]
Eq. 17
[67]
Eq. 18
[60]
Eq. 19
[68]
Eq. 20
[69]
The measured data collected for a month in June 2016 was used for deriving the modelling parameter for the tools through various methods of fitting for site 1. And, the measured data on specific days in March 2016 and April 2016 when two-axis tracking was performed was used for site 2. For Eq. 14 and Eq. 15, the parameters of (
against (
fitting of the plot between
(where =1 to 4) are obtained by linear fitting of the plot
, whereas the parameters for Eq. 16 - Eq. 19 are obtained by non-linear and
considering
and
as independent variables. The
modelling parameters for Eq. 20 are obtained from the linear fitting of the plot against the wind speed . Furthermore, for Eq. 19 and Eq. 20 the measured data used for plotting is filtered between the timestamp 10 am and 3 pm. This is to reduce the noise caused by low irradiance and wind speeds early during the day and after late evening. The fitting is achieved using OriginPro 2016 which uses linear regression and Levenberg-Marquardt algorithm for linear and nonlinear fitting respectively The main drawback of using these tools for thermal modelling is that sufficiently large database (2 - 4 week) of measured values of Page | 24
and
are required for obtaining good modelling
Chapter 4 | Bifacial PV Modelling parameters. The process of collecting large data for modelling and different sets of data for validating the results is a tedious process, especially if a thermal model of unknown installation profile is needed. Also, the modelling parameters are constricted to steady state conditions. This was the motive for adopting another approach to predict the module temperature independent excessive database and relies only on instantaneously measured environment conditions. The most adaptable modelling tool is concluded through cross validation among the different demostrated models with respect to their RMSE (Root Mean Square Error) over different irradiance ranges evaluated for a different measured dataset of values and also analysing the margin of error from Approach 2. 4.1.2.
Approach 2: Thermal energy balance modelling
In this method, the operating temperature of the module is determined based on the heat energy balance between the different layers of the module by evaluating the heat transfer processes both internal and external to the cell layer. In this approach, a nearly bi-dimensional model is followed based on nodal discretisation of a photovoltaic model. A standard bifacial photovoltaic module can be segregated into 5 regions as shown in Figure 20. The nodes considered in this simulation (from top to bottom) are the front glass cover ( (
), the EVA layers on the two sides of the PV cell layer
), PV cells along with the glass fibre (
) and the back glass cover (
).
Figure 20: Configuration of standard bifacial PV module [93].
The irradiance absorbed by the PV module is not entirely converted into electricity, but a part of it is dissipated as thermal heat. This internal heating process depends on the efficiency of the individual module, and results in a higher operating temperature for the module when compared to stable ambient conditions. The heat dissipated from the module is transferred to the environment as heat loss through three main heat transfer mechanisms: Conduction ( radiation (
), convection (
) and
). (Eq. 21) Page | 25
Chapter 4 | Bifacial PV Modelling Eq. 21 represents the general non-steady state thermal balance of a PV module, where heat loss due to different thermal mechanisms,
is the
is the input flux acting as the heat source, and
is
the electrical power generated by the module. When decomposed to different layers, this equation can be adapted by studying the possible heat exchange of each layer with its adjacent layer(s). For a better interpretation of the heat flow, the thermal balance equation of each node can be translated into electrical analogy where the temperatures, heat flow, heat source and imposed temperatures are correspondingly assimilated to potentials, current, current source and voltage generators [93]. The electrical resistance and capacitance are analogous to thermal resistance ( thermal capacitance (
) and
). Therefore the equivalent thermal circuit of the bifacial layer can be
represented as shown in Figure 21 and
at each node can be evaluated using Kirchoff’s law [94].
Figure 21: Thermal equivalent circuit for a bifacial photovoltaic module using electrical analogy.
The following assumptions were followed in this approach: 1. Conductive heat exchange between the module frame and the module are negligible. 2. All the material properties (Eg. absorptivity, transmissivity, emissivity etc.) are assumed independent of temperature and the wavelength of insolation. 3. The solar irradiation absorbed by the PV cells is partly converted into electrical energy and the trace is converted into thermal energy. 4. The internal reflections and transmissions among the different layers of the module are considered negligible. Page | 26
Chapter 4 | Bifacial PV Modelling 5. The ambient temperature and wind speed with respect to the front and the back glass surface are presumed to be the same. 6. The variation of temperature from cell to cell is neglected and the entire module is presumed to be in uniform temperature The methods for calculating the heat transfer coefficients
) for the different mechanisms and
the heat flux in each ( ) layer are discussed in the next sections. Input Flux In the formulated thermal model (Figure 21), there are 3 input fluxes (Front glass, PV and the Back glass) due to the incident irradiance. These act as heat sources to the circuit. Since the thermal contribution of EVA layer is insignificant (
), it is neglected as a heat source. Studying the
fundamental optical properties, a material can absorb, reflect or transmit the incident radiation in different ratios which is controlled by its absorptivity ( ), reflectivity ( ) and transmissivity ( ) respectively. The absorptivity of EVA is negligibly small and have high transmittance, thus both the EVA layers are overlooked in all optical calculations further in this work. Table 3 summarizes the optical properties of glass and Silicon, where both the front and the rear glass have the same optical properties. Table 3: Optical properties of PV materials.
Material
Absorptivity ( )
Transmissivity ( )
Reflectivity ( )
Glass [57]
0.054
0.81
0.136
Silicon [61]
0.902
0.08
0.018
Based on these principles, for the front glass, the total incident irradiation is the sum of the net
and
after deduction of all absorptions and transmissions from the bottom 4 layers of the PV
modules. Since all the absorbed irradiation of glass is converted into heat, the input flux per unit area can be deduced as: (Eq. 22) where,
and
are absorptivity of glass and
is the transmissivity of glass. Similar to Eq. 22, the
input heat flux per unit area of the back glass layer can be deduced as: (Eq. 23) For the PV layer, a share of the incident irradiation is converted into electrical energy and the trace into heat energy, which acts as the third heat source. Therefore the flux per unit area in the PV layer is depicted by Eq. 24. (Eq. 24)
Page | 27
Chapter 4 | Bifacial PV Modelling The power generated by the PV layer is estimated using coefficient (
and its respective temperature
). This is usually specified by the module manufacturer. Knowing the STC parameters,
the efficiency of the module at the given temperature can be easily calculated by Eq. 25 [61]. (Eq. 25) Accordingly, the electrical power generated per unit by PV cell is: (Eq. 26) where,
is the packing factor defined by the ratio between the area of the cell to the area of the
entire module. Thermal capacitance “Thermal capacitance refers to the ability of a material to absorb and store heat.” [95]. It is defined as: (Eq. 27) where,
is density,
is specific heat capacitance and
is the thickness of each layer. Given these
values the heat capacitance per unit area of each layer can be calculated as shown in Table 4. Table 4: Heat capacitance of different layers.
Layer
Thickness , [m]
Density
Specific heat capacity -3
-1·
-1
, [Kg·m ]
, [J·Kg K ]
Heat capacitance , [J·K-1·m-2]
Glass
0.002 [92]
3000 [61, 95]
500 [61, 95, 96]
3000
EVA
0.00045 [96]
960 [95]
2090 [96]
902.87
Silicon
0.00018 [96]
2330 [61, 95]
836 [61]
217.12
Conductive heat transfer The conductive heat transfer coefficient
can be represented as: (Eq. 28)
where,
is the thermal conductivity of different layers. In this work the thermal conductivity of
silicon is taken as 130 W m-1 K-1 [61, 96] and 1 W m-1 K-1 for glass [61]. The thermal conductivity of EVA is assumed 0.35 W m-1 K-1 as suggested by Armstrong et al. in [95]. Convective heat transfer The convective heat loss per unit area is: (Eq. 29) where, calculating Page | 28
is the convective heat transfer coefficient. Even though many condensed equations for have been proposed by different authors [97, 98], in this work
is evaluated by
Chapter 4 | Bifacial PV Modelling considering the glass plates of the module as an inclined isothermal entity and investigating the forced convective heat transfer,
(which is caused due to the wind flowing over the surface of the PV
panel) and the free convective heat transfer
, both based on fundamental heat transfer theory [99].
During forced convection due to external wind, there are two possibilities for the characterisation of flow of the wind: Laminar flow or turbulent flow. This solely depends upon the characteristic length ( ) of the glass layer and can be established by calculating the Reynolds number ( Nusselt number (
) corresponding to the instantaneous speed of the wind [100].
) and
is calculated
using Eq. 30. (Eq. 30) where,
(Eq. 31)
(Eq. 32) and,
(Eq. 33) (Eq. 34)
in which,
and
heat capacity of air,
are dynamic and kinetic viscosities of air respectively, is the corresponding heat conductance,
is the specific
is Prandtl number and L is the
characteristic length which is calculated by Eq. 35. (Eq. 35) When there is little or no wind ( < 2m/s), the free convection becomes dominant. This is prominently observed in cold climatic conditions when the difference between large [101]. The estimation of
is based on calculating
and
is noticeably
which is in turn correlated with
and the orientation of the surface under consideration. For a flat plane inclined at an angle respect to the ground,
is calculated by evaluating
and with
for the same plane in horizontal and
vertical configurations and then adapting it to the inclined plane. For a vertical configuration of a flat plate, When
is defined as:
(Eq. 36)
(Eq. 37)
Page | 29
Chapter 4 | Bifacial PV Modelling
where,
(Eq. 38) (Eq. 39)
in which, (=9.8ms-2),
is the Rayleigh number, is Grashof number, represents the standard gravity is the module length and is the thermal expansion of air that can be approximated by
Eq. 40. (Eq. 40) At horizontal configuration, the calculation of
depends on the difference between
and
.
When the upper surface (front glass) is at a higher temperature than the ambient or the lower surface (back glass) is at a cooler temperature than the ambient the following equations are used: When
(Eq. 42)
and when the front glass is at a lower temperature than the ambient or the back glass is at a higher temperature than the ambient: (Eq. 43) where,
is calculated at the characteristic length (Eq. 35) instead of
.
(Eq. 44) After computing
and
,
can be calculated by Eq. 45.
+ where,
is the tilt angle of the installed module and the overall
(Eq. 45) is represented by: (Eq. 46)
Radiative heat transfer The rate of longwave radiative heat loss from a surface to the ambient per unit area, according to Stefan–Boltzmann law is given by [63]: (Eq. 47) where,
is the emissivity of the glass,
is the Stefan–Boltzmann constant (=5.67E-8 Wm-1K-1),
is
the temperature of the surface (front glass or back glass). For the purpose of solving the thermal Page | 30
Chapter 4 | Bifacial PV Modelling balance equation, Eq. 47 is linearized to Eq. 48 and evaluate the heat transfer coefficient of radiation (
) to solve the equation [102]. (Eq. 48)
where,
(Eq. 49)
and,
.
for both front and back glass is set to a value of 0.91 as suggested by [95].
Method of solving For each node, the thermal balance equation considering the heat exchanges with its adjacent layers is fabricated based on the equivalent thermal circuit shown in Figure 21. Since all the terms in the left and right hand side have the area of the module (
) in common, the heat exchange per unit
area is computed. Table 5 summaries the energy balance equation at each node, where heat exchange coefficient for various thermal mechanisms and
represents the
is the input flux at each node.
Table 5: Energy balance equation at each node.
Layer
Thermal Balance Equation
Front Glass ( )
(Eq. 50)
EVA(
)
(Eq. 51)
PV cell (
)
(Eq. 52)
EVA(
)
(Eq. 53)
Back Glass ( )
(Eq. 54)
The simplest method to solve the first order differential equations represented above for a given
, is to adapt the Euler method of integration. The Euler’s method of calculation of
temperature at each node,
at time step
temperatures at step and the calculated rate of change of temperature
, given the nodal using Table 5, is by: (Eq. 55)
where,
is defined by the difference between
initial value method for which the values of actual data, a measured starting value of
and . However, the Euler method is an
at time is required. For testing the model against will be used for all nodal temperatures (
) (Section
6.1.2). The accuracy of the solution depends upon the known initial nodal temperatures, and caution should be taken as to not choose a measured value at increased irradiation or wind speed levels [63]. Clearly, without measured
and substituting measured
instead yielded unsatisfactory results and
a new technique for solving the equations was considered. Page | 31
Chapter 4 | Bifacial PV Modelling Based on fundamental thermodynamic principles another approach was adapted in Fraunhofer CSP for solving the ordinary differential equation defining the linear heat flow for BIPV by assuming a constant power density
[103]. This
for each layer can be calculated by: (Eq. 56)
where,
is the before calculated net heat flow per unit area (
)
for each layer and is the thickness of their respective layer. As a part of this project, a computing Scilab code was designed in order to deduce the temperature of the different layers in BIPV. In this method, the heat distribution among the layers of PV module can be condensed to one dimensional thermally conductive material with heat sources and, these sources depend not only on the nodal temperatures but also the position coordinates. This implies that the nodal temperatures
are further
derived as a function of thicknesses of the different PV module layers. Assuming the thermal heat conductivities
of all the materials are constant with respect to temperature, the heat
conduction equation is represented as a function of layer thickness ( ) in Eq. 57 [104]: (Eq. 57) can be solved into: (Eq. 58) using the boundary and transition conditions for each layer, 1. Heat transfer condition for front glass, (Eq. 59) 2. Heat transfer condition for back glass (Eq. 60) 3. Identical temperatures at the interface, (Eq. 61) 4. Heat currents are identical to the interface, (Eq. 62) Therefore, the temperature of each layer is deduced interpolating between the nodes by calculating the solution coefficients
and
through iterative algorithms. This algorithm was adapted
in C++ for solving the thermal boundary equations Eq. 59 to Eq. 62, while the heat transfer coefficients and the heat flow of the different layers are evaluated in the similar method discussed previously in this section. The observations will be discussed in detail in Section 6.1.2. Page | 32
Chapter 4 | Bifacial PV Modelling
4.2.
Electrical model
The electrical model of a PV module is principally the equivalent circuit which defines the IV curve of a cell, module or an array of modules as a continuous function for a given set of constraints. The shape and amplitude of the curve in turn depend on the model parameters. These parameters can be estimated from the key information like open circuit voltage current
and maximum power point voltage and current (
, short circuit and
correspondingly). However, these data are measured at STC conditions and, as mentioned before, the field conditions vary a lot from STC. Also, the physical behaviour of any PV module is a function mainly dependent on irradiance and temperature, therefore it is compulsory to determine all modelling parameters simultaneously for the given G and T. However, a complex model such as a two diode model with seven unknown parameters can be tedious to solve by depending only on analytical equations. On the other hand, approximations and assumptions of parameter values for model manageability could compromise the accuracy of the solution [79]. In recent years, many authors have adopted the methods of soft computing algorithms to solve this problem and have achieved to gain accurate results. However, the speed of convergence of the algorithm towards the optimised solution is inversely proportional to the dimension of the search space and therefore the number of unknown parameters. Therefore, in this thesis, to simplify and speed up the algorithm, some parameters like
,
and
are calculated algebraically and the others by soft computing using DE, therefore
developing a hybrid model. In this section, the procedure of analytical methods and the soft computing method are individually comprehended in section 4.2.1 and 4.2.2 respectively, and the strategy adapted to combine them as a hybrid approach is discussed in section 4.2.3. As a result, an accurate electrical model is developed which can attribute to superiority in precisely predicting the IV characteristics over a wide range of irradiance and temperature variations. 4.2.1.
Analytical solving
Analytical solving involves numerical iterations and algebraic manipulations to solve the equivalent circuit current equation to result in accurate modelling parameters. Therefore, this method requires information on the certain key points of the IV parameters. Usually, the circuit is analysed in three important conditions: Short circuit condition, Open circuit condition and Maximum power point condition. The governing equations for the two diode model of PV module are discussed in this section, mostly in reference with [78]. is the photo-generated current inside the solar cell which is one of the modelling parameters. Under short circuit conditions,
is the externally measured and the cell or module exhibits very high
shunt, and low series resistivity. Therefore, for simplicity, it is reasonable to assume that almost all of the generated current reaches the output in this condition and the terms
and
are
Page | 33
Chapter 4 | Bifacial PV Modelling interchangeable. The effect of temperature and irradiance on
can be related to the individual side
of a bifacial module as: (Eq. 63) where,
is temperature co-efficient of current and
representing front and rear side
respectively. Similarly, the current and voltage at maximum power point can be related as a function of irradiance and temperature as: (Eq. 64) (Eq. 65) where,
and
are the temperature co-efficient of current and voltage at maximum
power point respectively The open circuit voltage of PV modules, however, varies logarithmically with irradiance as represented in Eq. 66. (Eq. 66) in which,
is temperature co-efficient of voltage, and
in the module. And
is the number of cells connected in series
can be derived as:
(Eq. 67)
Similarly, the relation for
canbe derived at maximum power point condition as:
(Eq. 68) To evaluate the performance of the front and rear side of the bifacial module at a given temperature and irradiance, standard monofacial measurements are essential as mentioned in section 2.2.1. An indoor AAA module flasher at STC was used during this research for measurements. While measuring the bifacial module, it is necessary to shield the opposite side from reflected irradiance by covering it with an opaque black sheet. The used black sheet was ensured to have very low reflectivity to avoid erroneous reading due to reflected light passing through the active area of the module. Table 6 summarizes the flash test results for the front and back side of the bifacial module used for this thesis along with its manufacturer data sheet for comparison. This module was later installed in Site 1 and Site 2 for outdoor monitoring. Page | 34
Chapter 4 | Bifacial PV Modelling Table 6: Manufacture data sheet and Flash test result for BiFacial B270 Mono model [92].
I-V Parameters
Manufacture Data Sheet Front STC
Ground 10.01 38.80 292 9.35 31.18 >74
9.1 38.7 270 8.6 31.6 >74
Short Circuit Current, Open Circuit Voltage, Max. Power, Current at MPP, Voltage at MPP, Fill Factor,
Bifacial STC Grass 12.01 38.95 324 11.35 28.54 >74
Flash Test Snow 11.83 39.00 351 11.18 31.40 >74
Front STC
Rear STC
9.64 38.82 279.69 9.02 31.00 74.75
7.98 38.53 224.12 6.86 32.69 72.91
Now, to evaluate the integrated performance of the bifacial module under bifacial illumination, we assume that the currents (
) have a linear relationship with the irradiance and the bifacial
module acts as a monofacial module operating at a current which is the summation of both the front side and rear side currents scaled by the irradiation ratio . The corresponding bifacial parameters can be calculated as explained in the following subsections. Calculation of IPV,bi and IMPP,bi Adapting for the results achieved by Singh et al. from [105], for a given front radiance rear irradiance
, equivalent bifacial short circuit current (
and
) can be calculated as given in Eq. 69. (Eq. 69)
where,
is the irradiation ratio (
) and is the gain in short circuit relative to the monofacial
front side current. This can be expressed as: (Eq. 70) The bifacial current at MPP can also be scaled similarly as represented in Eq. 71: (Eq. 71) where,
is the current gain at the maximum power point represented as: (Eq. 72)
Calculation of VOC,bi As mentioned in section 3.1.4, the two diode approximation is adopted for this research. On a module level, the current (
) equation for a bifacial module is written as: (Eq. 73)
where, resistance
is the thermal voltage of a PV module. During high irradiance, the shunt can be neglected from Eq. 73 can be neglected and can be written as follows: Page | 35
Chapter 4 | Bifacial PV Modelling
(Eq. 74) For deriving the relationship between open circuit conditions (when
(bifacial open circuit voltage) and
, equations at
) is considered. Therefore Eq. 74 can be altered as: (Eq. 75)
Similarly, considering only front and rear surfaces of a bifacial module individually, the short circuit currents of the respective surfaces are derived as: (Eq. 76) (Eq. 77) Substituting equations Eq. 13, Eq. 75, Eq. 76 and Eq. 77 in Eq. 69,
can be derived as:
(Eq. 78) where,
and
. Knowing all the parameters from preious calculations, it can be
assumed as a constant . Therefore Eq. 78 can be condensed to: (Eq. 79) Analytically solving
from Eq. 79 can be inconvenient, considering the unknown value for
Therefore, it is computed using Newton’s method after obtaining the value of
.
through soft
computing. This is explained in Section 4.2.3. Calculation of VMPP,bi At MPP condition the power from the module will be the product of .Therefore,
can be calculated dividing the power by the calculated
and . This is
represented in (Eq. 80) The bifacial fill factor (
) is calculated by considering the relative resistive losses first by
Ohm’s law and then by considering the change in power loss. Then, both of the derived power loss equations are evaluated together [11]. Adapting the derivations from [105] and [11], the relation of with
and
is represented as: (Eq. 81)
Page | 36
Chapter 4 | Bifacial PV Modelling where,
is the fill factor of the front surface for the given irradiance and temperature and
is
the pseudo-Fill factor which is derived by assuming that there is no series resistance loss [105]. It is represented by Eq. 82.
(Eq. 82)
where
and
is the fill factors of the respective front and rear surface and can be
evaluated from the STC measurements. Assuming that the effect of the shunt resistance negligible, the fill factor can be expressed as a function of
on
is
as shown in Eq. 83 [106, 107]. (Eq. 83)
and knowing the values of the other parameters, 4.2.2.
can be easily calculated.
Soft computing
Soft computing is a modelling approach by using Artificial Intelligence (AI) techniques such as Fuzzy Logic (FL) [108], Artificial Neural Networks (ANN) [109, 110], or Evolutionary Algorithms (EA) [87]. In the recent years EA have taken a hike of interest in the field of photovoltaic modelling. Many EA methods like Generic Algorithms (GA) [111, 112], Particle Swarm Optimization (PSO) [113], etc. have been adapted for PV modelling. In this thesis, we will concentrate on adapting the Differential Evolutionary (DE) algorithm [81, 87] for bifacial PV modelling. GAs are stochastic optimization algorithms, structured by studying biological processes such as evolution, genetic inheritance and dominant genetic pooling. DE is a variant of GA which is a simple and yet powerful tool to compute global optimised point introduced by Prince and Storn [114]. Due to its good convergence properties and easy interpretation, DE algorithm has been used in many practical applications. The objective of a DE algorithm would be to find a best solution for group of unknown parameters. Comparable to any EA, DE also works with populations or vectors of candidate solutions, where each candidate solution denotes a unique set of values for each unknown parameter. Therefore, the dimension of the search space for the DE algorithm will be equal to the number of unknown parameters ( ). As mentioned before
and
are considered as unknown parameters for the
adapted DE algorithm in this work, and therefore = 4. Principally, DE algorithms initialize a candidate solution with a known population size followed by the process of mutation of these candidates, crossover of parameters among them and the selection of the best candidate among a population. When using a DE algorithm, it is also necessary to define a fitness function which helps the algorithm to converge towards an optimal point. Therefore, upon each Page | 37
Chapter 4 | Bifacial PV Modelling iteration the candidate solution is compared with a derived solution population for better ‘closeness’ towards the optimal point and is feed backed to the algorithm as the candidate solution for the next iteration. The iterations are repeated until the (near-) optimal point is reached. To determine the quality of the solution and the efficiency of the search, a set of algorithm control parameters is initialised before implementation. The control parameters suggested for a DE algorithm [114, 115] is as listed below and their respective role within the algorithm will be explained briefly later in this section: 1. Number of Population
: This parameter defines the number of candidates allowed per
solution or population. A proper NP value considers the speed of the algorithm without compromising the quality of the solution. 2. Mutation scaling factor
: It is a value chosen between the range [0, 1] which defines the
weight of mutation during a DE algorithm and deals with population diversity. Hence, smaller values of 3. Crossover Rate
results in premature convergence [116]. : It is also a user determined value in the range [0, 1] that decides the
crossover probability. This, in turn, influences the inheritance among the different populations and algorithm convergence speed. Choosing these parameter values, despite its crucial importance, is a problem-dependant task and there is no standardised procedure to evaluate the same. Concluding a proper parameter value requires previous experience and complete understanding of the optimisation problem. An initial population of candidate solutions of dimensions
is randomly generated in
precedence to the optimisation process. This acts as the target vector for the first iteration of the DE algorithm. By literature, a target vector is known as the parent vector from the current generation which is represented as
where
is the index of unknown the parameter,
is the index of the candidate solution and the generation. Initial population of the algorithm (i.e. distribution generator bounded between the interval and
is the index of ) are randomly selected using a uniform where
are the lower and upper limits of the different parameters in the
search space, respectively. The initialised target vector can be represented as: (Eq. 84) Eq. 85 represents the matrix representation for target vector of DE for a particular generation for better understanding.
(Eq. 85)
Page | 38
Chapter 4 | Bifacial PV Modelling Following the initialisation of the target vector, the DE algorithm searches for the optimum solution based on the fitness function in the search space bounded by the upper and lower limits of the unknown parameters. For this, the algorithm iterates three stages, namely mutation, crossover, and selection, until the optimum solution or the maximum number of generations is reached. Based on the strategy used for mutation process, number of pairs of vectors chosen for mutation, and the type of crossover, there are 10 strategies of DE algorithm. These are known as DE variants. The general convention followed to represent a DE variant is DE/p/q/r, where ‘p’ is the method of mutation, ‘q’ represents the number of pairs of vectors selected during the mutation process, and ‘r’ being the method of crossover [116]. A total number of 10 DE variants were coded in C++ for this work, so that the user has freedom to choose the desired variant for deriving the module parameters. The operation of each step and its variants are as explained below: Mutation Mutation is the process of changing the structure of a candidate by insertion or alteration of attributes with another random element(s). Accordingly, mutation process requires a target vector which acts as the parent and undergoes various mutation processes to produce a mutant vector called the donor vector ( range
). For a given parameter, a number of random samples are selected in the
and from distinct candidate solutions. For example, for mutation strategy DE/rand/1 and
for the first unknown parameter ( and
, 3 random samples are needed. Therefore, samples
are chosen randomly such that
each other. The weight of mutation is restricted by the control parameter
and
are not equal to
and the different mutation
strategies are as discussed in Table 7. Table 7: DE variants mutation strategy.
Variants
Mutation Strategy
DE/rand/1
(Eq. 86)
DE/rand/2
(Eq. 87)
DE/best/1
(Eq. 88)
DE/best/2
(Eq. 89)
DE/rand-tobest/1
(Eq. 90)
In DE/best/1, DE/best/2, and DE/rand-to-best/1 mutation strategies,
represents the
candidate solution that has the near-optimised cost of the fitness function in the given generation.
Page | 39
Chapter 4 | Bifacial PV Modelling Also, it should be noted that index of all randomly generated samples is distinct (i.e. ). Eq. 91 denotes the matrix representation of donor vector.
(Eq. 91)
Crossover Crossover is the process of inserting attributes of the donor vector into the target vector. Therefore, the target and donor vector are recombined to form the offspring vector called the trial vector (
), which is the result of the crossover process. As mentioned previously, this process is
overseen by the control parameter
. Among the DE variants, there are two possible ways to
implement the crossover process. 1. Binomial Crossover: This is the most commonly implemented crossover strategy which is defined by Eq. 92, where
denotes a uniformly selected random number from [0, 1), and
is the decision variable index that ranges from
and uniformly randomly selected.
The value of CR is chosen such that there is a probability of at least one parameter to crossover from the donor to the target vector. (Eq. 92) 2. Exponential Crossover: This is implemented as shown in Algorithm 1. Exponential crossover is similar to the 1 or 2 point crossover in GA [115, 117], where the attributes of the donor vector are passed to the trial vector continously once the crossover condition is met. Algorithm 1: Exponential crossover 1
Initialise
2
Randomly select
3
Repeat
. from
3.a 3.b 3.c
until The matrix representation of a trial vector is as shown in Eq. 93.
(Eq. 93)
Page | 40
Chapter 4 | Bifacial PV Modelling In the standard DE algorithm, some values of the trial vector tend to exceed the physical limits of the parameter that it represents. To avoid this, a penalty function (Eq. 94) is introduced [81, 87]. The values of the trial vectors which exceed the limits of the parameters are replaced with random generated values, ensuring that all the values are well within the allowable range. (Eq. 94) Selection Different selection strategies can be adapted based on the demands of the problem. The most commonly adapted is the tournament selection or greedy selection process as explained in Eq. 95 is used for this work. The selection process compares the cost of the fitness function for every candidate from the trial and the target vectors, then choses the candidate having the lowest cost. Hence, the generation gets better or stays the same, but never deteriorates. The result of the selection process will act as the trial vector for the next iteration until the optimised solution is reached or maximum iterations are completed. (Eq. 95) where,
is the fitness function that should be minimised. The matrix representation of the
selection process is explained in Eq. 96.
(Eq. 96)
4.2.3.
Hybrid electrical model
The aim of the hybrid electrical model would be to integrate the accuracy of the analytical equation with the speed of DE algorithm. Eq. 63 – Eq. 68 define the relationship of the PV module parameters with respect to T and G. After the modelling parameters like through random generation from the DE algorithm
and
and
are obtained
can be easily detrmined by
using Eq. 69, Eq. 67 and Eq. 68 respectively. As mentioned before, the DE algorithm is a search based algorithm which requires a fitness function to converge at global optimal point. In this section, the fitness function and the algorithm used for the hybrid model is comprehended in detail. Fitness function The fitness function can be defined as the objective function that can be used to determine the closeness of a given solution set with respect to the desired output [118]. Since the slope of the PV curve of a photovoltaic module is zero at MPP condition, this can be utilized as the ideal fitness function. The derivative of
with respect to
is: Page | 41
Chapter 4 | Bifacial PV Modelling
(Eq. 97) The fitness function
defined from the derivative
at MPP can be represented by Eq.
98 as follows: (Eq. 98) where,
and
can be evaluated by using Eq. 71 and Eq. 80 respectively. The term
is obtained by deriving Eq. 73 with respect to
at MPP condition. The result is as
represented by Eq. 99.
(Eq. 99) Hybrid algorithm For easy understanding of the working of the hybrid scheme, it is important to realise the required inputs for the algorithm. The different parameters which are prompted from the user and the automatically initialized parameters by the C++ are discussed below: 1. User required inputs: The IV parameters such as and
for both front and back surfaces
coefficients
and
, along with bifacial temperature
are mandatory inputs from the user. These data can be
easily found in the datasheet provided by the module manufacturer. In this work, the former s obtained from the indoor flash test of the module is taken as the input (Table 6) and the latter from manufacturer’s datasheet. 2. Default DE control parameters: Based on the suggestions from V.J. Chin et al. in [87], the DE control parameters
and
are set to 50, 0.8, 0.8 respectively and DE\rand\2\bin
strategy is used by default. However, all these parameters are changeable to the desired values during the input prompt from the program. 3. Setting the limits for modelling parameters: Other than the number of parameters, the range in which the unknown parameters are searched using the DE algorithm also plays an important role for swift deduction. Based on broad research and prior knowledge, the search boundaries for the four DE generated parameters are set as follows: and
. Also, certain sets of DE generated parameters can result in non-
physical (negative) values for which is set to
[119]. Therefore, it is necessary to assign limits to .
4. Initializing the target vector at Gen = 1: Before the actual execution of the DE algorithm an initial target vector is randomly generated using the mentioned limits (4.2.2) which is also considered as an input to DE. Page | 42
Chapter 4 | Bifacial PV Modelling The algorithm of the hybrid model is briefed in Algorithm 2 and for simpler understanding a flow chart with the outputs of each step is shown in Figure 22. Algorithm 2: Hybrid model 1
Set the limits for
2
Set the DE control parameters
3
Get Inputs: STC parameters of the module,
4
Initialize the target vector at gen =1 (
5
Calculate
6
Repeat
6.a
Mutate
6.b
Crossover
6.c
Calculate
6.d
Evaluate
6.e
If
and
and
. and
and
and
using Eq. 69 and Eq. 71.
(DE Crossover). using Eq. 78 and Eq. 80 for all
(Eq. 67 and Eq. 68) for all : Set the corresponding
Else: Calculate the corresponding 6.f
for both front and rear surface.
(DE Mutation).
to obtain and
and
).
for the given to obtain
.
Perform DE selection between
and
and .
= 1e20
using Eq. 99 and
to obtain
6.g
until:
7
Output the parameters corresponding to the population with the closest
to 0.
The algorithm is coded using C++ language, utilizing individual classes for the DE algorithm and PV characteristics. This enables to easily study the interactions between them, thus assuring proper execution. The prime reason for choosing the C++ programming language is that it is a general purpose programming language which can be interfaced with external programs with ease. This extends the applicability of the proposed model and therefore can be incorporated with other tools of a PV simulator, for example, MPPT algorithm, grid, etc. It is also possible to design user-defined standalone blocks in INSEL using C++ programming language for PV designing and development. In addition, C++ have object-oriented, imperitive and generic programming features, thus expediting the computational speed of the algorithm rather than implementing it in Matlab.
Page | 43
Chapter 4 | Bifacial PV Modelling
Figure 22: Hybrid model flow chart.
Page | 44
Chapter 5 | Automated Data Evaluation
5. Automated Data Evaluation The analysis of qualitative validation of the proposed models utilizes a substantially large database (Section 3.2) from two fields of measurement (Site 1 and 2). Handling such large data would be cumbersome, especially when dealing with sensors with different measuring intervals, redundant calculations for a specific data set, grouping, analysis of bad data and template graphing. In this work Origin2016 Pro was the prime software tool used for graphing and data handling and the measured data from both sites is stored in specific databases using MySQL server. To ease the process of data handling, a standalone app called “PV Analysis” was designed in Origin2016 Pro using LabTalk programming language. This app connects the software directly to the online database, allowing it to download the measured data within the user define timestamps and have the luxury to perform pre-defined functions. The data downloaded was constrained to specific formatted worksheets to follow uniformity and ease of communication between Origin and MySQL. The data flow and the interfaces between the operating software are as depicted in Figure 23 for better understanding.
Figure 23: Measurement system database connection with Origin2016 Pro Software.
The following data manipulations and features were integrated into the app designed in Origin: 1. The installed ambient temperature and the wind velocity sensor in both sites have the measurement averaged over an interval of 60s, whereas the other measurements are taken at an interval of 10s. Thus, the missing data points are assumed NULL values by the MySQL server and analysing these data in Origin results in data type errors. This was avoided by employing the averaged values of
and
for the preceding 5 timestamps, therefore
resulting in 10s interval measured data points for all sensors. 2. The quality of the model validation is directly dependant on the quality of the comparing measured data. It is unavoidable in an outdoor installed measuring system to be affected by noise leading to sets of bad data. These data, when used for fitting parameters or when deduced for RMSE margins could conclude with misleading results. Therefore, it was programmed in Origin that data values exceeding the predefined physical limits of their respective variable are sequentially masked and ignored for computation. The masked data can also be realised graphically by plotting a plausibility test, which is one of the feature designed in the app. Page | 45
Chapter 5 | Automated Data Evaluation
Figure 24: Plausibility test feature for module measurement data from PV Analysis app in Origin. Showing sample graphs for the measured- Left top: ; Right top: ; Left bottom: ; Right bottom:
.
3. Redundant calculations, specifically for obtaining the modelling parameters for different equations in thermal model - Approach 1(Section 4.1.1) that requires a same set of data fitted linearly or non-linearly depending on the order of the equation, were made uncomplicated using template graphing. During the installation of the app on the user system, the templates necessary for proper operation of the various features are loaded into the Origin workspace. Therefore, when the icon for thermal modelling is clicked, Origin prompts the user for the timestamps between which the data is downloaded, tested for plausibility and fitted for various equations (Table 2) to get the modelling parameters automatically. Also, since Eq. 19 and Eq. 20 requires dataset only in the time interval 10 am to 3 pm, this is also integrated in the application to filter the data before fitting for these equations. 4. Also, for detailed analysis of the competence of the different thermal modelling techniques followed in this work, the RMSE between the deduced and the measured values over different bounds of irradiance and velocity are considered (Section 6.1.1). This is automated using LabTalk commands in Origin, which otherwise would be a tedious process if done manually. 5. Additional graphing tools for analytical PV monitoring suggested by the International Energy Agency (IEA) based on the IEA-PVPS report [120] are also apprehended to this app as additional features (Figure 25). These are not necessarily specific to bifacial modelling, but for PV analysis in general.
Page | 46
Chapter 5 | Automated Data Evaluation
Criteria
Plot
Current Vs. Irradiance: To study the current as a function of irradiance and possibly the effect of sky conditions on current.
Yield plot: Per week plot between the final yield and the reference yield measured from the site and to test its linear relationship
Reference yield Vs. Temperature: To study the effects of temperature with respect to the reference yield of the module.
Figure 25: Additional graphing features of the automated data evaluation application suggested by the IEA.
6. For user friendly interface, all the features defined in the app are segregated into lucid icons and arranged into a toolbar (Figure 26). Additional tool help is also appended for user convenience.
Figure 26: PV Analysis Graphing Toolbar from the app.
Page | 47
Chapter 6 | Results and Optimization of Individual Models
6. Results and Optimization of Individual Models After interpreting the methods discussed in Chapter 4 in C++, each model and their approaches were individually designed, executed and the simulated results obtained for the given ambient conditions were analysed against measured data. The results and their deviations will be the prime point of discussion in this chapter.
6.1.
Thermal Model
A total of 9 thermal modelling techniques was analysed in this work, comprehensively 7 modelling tools in approach 1 and two methods of solving from approach 2 (Section 4.1). Among which, one method will be implemented in the integrated model. The verification of these 9 modelling techniques against measured data is presented in this section. 6.1.1.
Approach 1: Parameter fitting
For approach 1, after fitting the equations in Origin by implementing the procedures discussed before, the modelling tools from Table 2 can be updated as shown in Table 8 and Table 9 for site 1 and 2 respectively. Table 8: Thermal modelling tools with fitted parameters for site 1 (Fixed modules).
Modelling Tool
Equation No. Eq. 100 Eq. 101 Eq. 102 Eq. 103 Eq. 104 Eq. 105 Eq. 106
Table 9: Thermal modelling tools with fitted parameters for site 2 (Two axis tracked module).
Modelling Tool
Equation No. Eq. 107 Eq. 108 Eq. 109 Eq. 110 Eq. 111 Eq. 112 Eq. 113
Page | 48
Chapter 6 | Results and Optimization of Individual Models Knowing the modelling parameters, conditions (
can be calculated for a given set of measured ambient
and ). This was done using the PV Analysis app in Origin and the results of the
simulated values were studied against measured values from a dataset different from the one used for obtaining the modelling parameters itself. This ensures versatility of the modelled tool over a wider range of input data, and the precision of the modelling tool can be studied discreetly. Therefore, for site 1 the modelling tools were validated against the measured data from September 2016 and for site 2 the measured data from different dates in May and June 2016 when two axis tracking was done. The overall RMSE for each modelling tool and the RMSE for respective irradiation ranges are discussed in Table 10 and Table 11 for site 1 and site 2 respectively. The RMSE was examined over different ranges of irradiation to observe the consistency of the modelling tool over the entire irradiation spectrum. The colour conditioning scale used in the following tables is as depicted below:
Table 10: RMSE comparison table of thermal modelling tools for site 1 (Fixed Modules).
Irradiation range [Wm-2] [0,100) [100,200) [200,300) [300,400) [400,500) [500,600) [600,700) [700,800) [800,900) [900,1000) [1000,1100) [1100,1200) [1200,1300) [1300,1400)
Eq. 100 1.832 2.173 3.430 3.896 3.501 3.418 3.218 3.504 3.641 3.594 4.870 6.122 10.168 7.156
Eq. 101 1.589 2.231 3.498 3.948 3.534 3.427 3.219 3.498 3.623 3.582 4.913 6.265 10.404 7.455
Eq. 102 1.485 2.328 3.607 4.007 3.590 3.435 3.168 3.465 3.738 3.578 4.537 5.429 9.038 6.114
Mean
2.536
2.444
2.472
RMSE [°C] Eq. 103 1.851 2.172 3.395 3.813 3.357 3.262 2.951 3.240 3.292 3.295 4.900 6.210 9.957 11.119 2.470
Eq. 104 1.831 2.192 3.430 3.894 3.497 3.414 3.217 3.503 3.632 3.594 4.870 6.122 10.168 7.156
Eq. 105 1.848 2.163 3.377 3.803 3.355 3.256 2.963 3.230 3.266 3.259 4.854 6.216 10.032 10.121
Eq. 106 1.863 2.141 3.302 3.698 3.254 3.282 3.043 3.326 3.282 3.427 5.366 7.327 8.502 12.370
2.536
2.462
2.419
It was observed that all the modelling tools for the fixed modules give at least an average RMSE of 2°C when compared with the measured module temperatures. It is also noticeable that at very high irradiance (
), the RMSE values also increases manifold. This is due to the high diffused
irradiance conditions. During cloudy sky conditions, the diffused irradiance dominates over the direct irradiance received by the module and is subject to high margins of fluctuations. The quick reaction time of the modelling tool towards the measured value results in high noise in the simulated results. However, in reality, the temperature does not react to irradiance or velocity instantly, but takes a moderate amount of time for even an 1°C increase in module temperature. This is also the reason for not depicting the simulated temperatures from the modelling tools graphically, because of its high Page | 49
Chapter 6 | Results and Optimization of Individual Models margin of fluctuations. To minimize this noise effect the wind speed data input for the modelling tools were averaged over a 60s interval. Comparing the overall results from parameter fitting thermal modelling approach for fixed modules, Eq. 100 and Eq. 104 gives the least favourable fit and Eq. 106 gives the most favourable fit. Table 11: RMSE comparison table of thermal modelling tools for site 2 (Two Axis Tracked Modules).
Irradiation Range [Wm-2] [0,100) [100,200) [200,300) [300,400) [400,500) [500,600) [600,700) [700,800) [800,900) [900,1000) [1000,1100) [1100,1200) [1200,1300) [1300,1400) [1400,1500)
Eq. 107 1.217 2.281 3.969 4.371 5.046 4.291 4.033 3.981 3.908 5.502 5.821 6.215 6.559 4.966 5.686
Eq. 108 1.065 2.405 4.082 4.460 5.118 4.326 4.043 3.983 3.907 5.500 5.833 6.274 6.617 5.017 5.827
Eq. 109 3.875 2.491 2.947 3.319 3.989 4.571 5.198 5.398 5.655 7.050 7.690 8.894 8.779 6.319 7.667
Mean
3.973
3.985
5.611
RMSE [°C] Eq. 110 1.225 1.894 3.446 4.480 5.618 8.198 11.202 13.649 16.450 18.710 22.052 28.754 26.568 21.058 23.244 14.540
Eq. 111 1.217 2.067 3.661 3.779 4.185 3.815 3.592 3.527 2.999 4.206 5.061 6.244 8.025 8.595 11.653
Eq. 112 1.265 2.120 3.888 4.694 5.252 4.752 4.749 4.591 4.599 5.802 6.287 5.359 4.902 6.643 7.735
Eq. 113 1.215 2.300 4.129 4.384 4.944 4.300 3.848 3.552 3.393 4.462 4.620 4.539 5.472 5.884 7.523
3.641
3.540
3.335
For the two-axis tracked modules, the average RMSE value was over 3°C and Eq. 110 had the worst fit. In both cases, the modelling tool proposed by Faimann. D. [69] shows promising results and the best fit. The initial reasoning made after reaching this outcome, was to assume that the best fit of this equation was maybe due to the filtration of the fitting data between 10 am and 3 pm to avoid low irradiance and velocity noise, whereas the first 5 modelling tools used all-day data. Therefore, to test this hypothesis fitting for the other 5 modelling tools was done using the filtered data too. However, fitting these tools using filtered data only increased the RMSE value rather than improving the fit. In summary, out of the 7 modelling tools that were analysed Faimann. D. model will be the preferred tool to be compared with the results from Approach 2. 6.1.2.
Approach 2: Thermal energy balance modelling
To compare the performance of the two solving methods used in this approach, two types of irradiance conditions are identified: clear sky and cloudy sky. The measured and the simulated data are plotted for specific days relevant to these irradiation conditions. Evaluation based on irradiation types is done for the same reasons stated above for different irradiation ranges. In this section, the Euler’s method of solving will be regarded as Method 1 and the method of solving adapted from Fraunhofer CSP [103] will be regarded as Method 2 for convenience. Page | 50
Chapter 6 | Results and Optimization of Individual Models For clear sky condition, Figure 27 shows the measured and simulated module temperature values at site 1. For the fixed modules on site 1, the module temperature follows a pseudo-smooth curve which is predominantly affected by the irradiation. Figure 28 shows the change of module temperature for measured and simulated values for a clear sky condition in site 2. The measured values correspond to a two axis tracked bifacial module on 06.May.2016.
Figure 27: Measured and simulated module temperature for Clear sky conditions (data from site 1 on 15.Sept.2016).
Figure 28: Measured and simulated module temperature for Clear sky conditions (data from site 2 on 06.May.2016).
Since the initial module temperature is assumed equal to the ambient in case of Method 1, this simulation constantly predicts temperature lower than expected values. It can also be noticed that the early morning temperatures are predicted to be slightly higher than the measured data in both cases. This is may be due to the low insolation at this hour, which is not strong enough to warm the modules completely above their night-time sub ambient temperatures. But on the whole, method 2 is seen to be in reasonable agreement with the measured values and therefore can be accepted as a good model. Page | 51
Chapter 6 | Results and Optimization of Individual Models Figure 29 and Figure 30 depict the measured and simulated module temperature for a cloudy sky condition in site 1 and 2 respectively.
Figure 29: Measured and simulated module temperature for Cloudy sky condition (data from site 2 on 09.July.2016).
The irradiance varies strongly during the cloudy sky conditions, consequently resulting in a fluctuating module temperature. Since method 2 is highly sensitive to the incident irradiance, oscillation of its simulated
is also high. This is, however, not apparent in method 1. Furthermore,
the high degree scattering of the deduced module temperature in case of method 2 could be probably caused by gusting winds producing non-symmetric module temperature fluctuations.
Figure 30: Measured and simulated module temperature for Cloudy sky condition (data from site 2 on 02.June.2016).
Page | 52
Chapter 6 | Results and Optimization of Individual Models Graphically analysing the results of the two methods of solving over different sites and irradiance condition could help picturize their behaviour in an efficient way. However, for a fair comparison with the modelling tools from Approach 1, both methods of solving from approach 2 are simulated for module temperature using the same set of climate data selected the modelling tools to obtain Table 10 and Table 11. The resultant RMSE error using Approach 2 for site 1 and 2 is summarized in Table 12. Table 12: RMSE comparison table of Approach 2.
Irradiation range [Wm-2] [0,100) [100,200) [200,300) [300,400) [400,500) [500,600) [600,700) [700,800) [800,900) [900,1000) [1000,1100) [1100,1200) [1200,1300) [1300,1400) [1400,1500) Mean
Eq. 106 1.863 2.141 3.302 3.698 3.254 3.282 3.043 3.326 3.282 3.427 5.366 7.327 8.502 12.37 --
Site 1 [°C] Method 1 2.856 2.502 2.764 3.372 3.908 4.511 5.839 6.106 7.263 6.779 6.736 10.49 7.353 6.410 --
Method 2 1.998 2.643 3.666 3.704 3.663 4.177 3.858 4.815 3.966 4.447 8.308 10.493 10.315 10.523 --
2.419
3.632
2.856
Eq. 113 1.215 2.3 4.129 4.384 4.944 4.3 3.848 3.552 3.393 4.462 4.62 4.539 5.472 5.884 7.523
Site 2 [°C] Method 1 1.942 1.647 2.346 3.198 4.467 4.986 5.702 6.323 6.334 7.005 6.244 6.199 6.069 6.208 7.670
Method 2 1.284 1.816 3.333 3.932 4.128 4.291 4.360 3.894 3.273 3.885 4.565 4.639 8.133 10.539 12.112
3.335
3.881
3.047
It can be deciphered from Table 12 that both methods show promising results with a mean RMSE below 4°C. However, it should be noted that input data for method 1 should be continuous and if otherwise, the initial nodal temperatures should reset again to the measured
for that instance. For
example, in case of site 1, since the modules were continuously measured it was easy to simulate
.
But, in case of site 2 where the measurements were constrained to specific days where the tracker was set to two axis tracking, the drafted code of the model was adapted to understand interruptions in the input data. Also, in method 1, a deceitful assumption of assuming all the initial nodal temperatures to be equal to the previously measured
was made, which resulted in some erroneous simulations.
Furthermore, the RMSE between the thermal model tool from [69] and method 2 were not far apart from each other (< 0.5°C). Thus, considering the advantage of method 2 being independent from previously measured
data, it was selected as the preferred thermal model for integrating with the
electrical model. Adapting method 2 for thermal modelling also helps in studying the different nodal temperatures for the module layers and how they vary with respect to the ambient condition. This relation and the interactions of the thermal model with the electrical model will be comprehended in the next chapter (Chapter 7). Page | 53
Chapter 6 | Results and Optimization of Individual Models
6.2.
Electrical model
The hybrid algorithm for bifacial modules discussed in section 4.2 will be validated against outdoor measured data from site 1 and site 2 in this section. However, to ensure proper working of the algorithm, it was initially tested with indoor monofacial measurements of the bifacial modules, that is, one side of the module is covered with a non-reflective black sheet while measuring the other side. Figure 31 (a) shows the comparison between the simulated and the measured IV curves of the front and back side of a bifacial module at STC. The measurements were done using AAA flasher. The small steps seen in the rear side measured curve is due to shading of the junction box which is attached on the back side of the module. The simulated IV curves are obtained by setting and
for front side
for rear side. In conclusion, the STC simulations showed promising results and further
indoor monofacial simulations were done where while keeping
at 25°C and
was set at 750 Wm-2, 450 Wm-2 and 250 Wm-2
. The results can be deciphered from Figure 31 (b), which shows
a good fit with the measured values.
(a) (b) Figure 31: Monofacial IV curves for bifacial module. (a) Front and back side measured at STC. (b) Front side measured at 750,450,250 Wm-2
It was also an area of interest to compare the results of the proposed algorithm if some parameters were considered constant instead of random generation. Therefore, three particular cases were considered for comparison. Firstly, all four algorithm. Secondly, while
and
and
were generated randomly through the DE
was obtained from the IV curve measured at STC and is assumed constant,
are assumed values 1 and 2 respectively, and
algorithm as before. The third case is that
and
is generated through the DE
are generated through DE algorithm, and
is
determined at STC and is kept constant. The results of these simulations when compared with the measured indoor values can be deciphered from Figure 32. All three methods show good general agreement with the measured values, but under close inspection, the RMSE with respect to measured and simulated current was the least when all the parameters were simulated in most cases (Table 13). The parameters obtained from each method are shown in Appendix A. Page | 54
Chapter 6 | Results and Optimization of Individual Models
Figure 32: Comparing the hybrid electrical model for different constant parameter assumptions. Table 13: RMSE comparison table for different approaches at constant temperature, T =25°C.
Irradiance [Wm-2] 750 450 250
All variable simulated [A] 0.1652 0.1214 0.0414
and constant [A] 0.2039 0.0568 0.0749
constant [A] 0.199 0.1363 0.0442
For bifacial model simulations, the simulated results were validated against the measured data from both sites on 5.May.2016. Figure 33 and Figure 34 summarizes the simulation results for site 1.
Figure 33: Comparison of IV curves at varying irradiance and temperatures from site 1 (Fixed modules).
The solid circles in the Figure 33 represent the measured points of the IV curves for the bifacial module, whereas the solid lines represent the simulated IV curves from the developed model. 4 Page | 55
Chapter 6 | Results and Optimization of Individual Models different curves at varying irradiance and temperatures measured at different times of the day on 05.May.2016 were taken into account to predict the model behaviour over the day. It is understood from the plot that the model prediction is in good agreement with the measured curves. It should be noted that the rear irradiance sensor at site 1 is installed at the bottom edge of the module mount, which measures the well shaded region of the module. Due to the inclination angle and height, the insolation reaching the backside is more inhomogeneous than the tracker from site 2, and the lowest illuminated cells determine the output current in a series-connected cellular module design. However, it is also noticeable that because the
at increased irradiance is predicted higher that measured values. It is
decreases in a non-linear fashion at higher irradiances [105]. This is probably due to
the assumed evaluation of
as an independent parameter from
, however in practice
plays a
significant role at high irradiance.
(a)
(b)
(c) (d) Figure 34: Comparison of the various IV parameters at varying irradiances from site 1 (Fixed modules). (a) I SC (b)VOC (c) IMPP (d) VMPP
To further investigate the closeness of the electrical model, the different simulated IV parameters were compared with the measured values from the same day. Figure 34 summaries the trend of and Page | 56
for bifacial illumination with respect to the irradiance varying from 0
Chapter 6 | Results and Optimization of Individual Models to 1100 Wm-2. It can be seen that all the simulated parameters agree well with the measured values. The high scattering of the simulated whereby the RMSE of the simulated
is mainly due to its dependency on the fluctuant
,
is 0.49 V from the measured values (1.12% relative
error). The deviation of the currents are approximately 0.2 A for
and 0.09 A for
. Overall,
Figure 34 can certify the effectiveness of the proposed electrical model for bifacial illumination. Figure 35 shows initially simulated IV curves for the bifacial modules installed at site 2 when illuminated on both sides. As can be seen, a high margin of error with respect to the currents
and
was observed, which recedes with decreasing irradiance. Further, it was clear from the analytical part of the electrical model that the irradiation factor
restricts the bifacial currents with
respect to irradiation. And upon a detailed study of the results, it was deduced that the mount of the bifacial module on two axis tracker have a significant shading effect on the rear side of the module (Figure 18). Thus, it was considered mandatory to include a shading factor to accordingly scale
.
Figure 35: Comparison of IV curves at varying irradiance and temperatures from site 2 without considering the effects of shading of the rear surface (Two axis tracked modules).
To calculate an approximate value for the shading factor, IV parameters were measured while the tracker was vertical and the azimuth of the sun could be tracked. This implies that the rear surface of the bifacial module shadowed by the installation frames is made to act as the front surface and vice versa. Since a black covered bifacial module was also installed in the same plane as the bifacial module, it was easy to differentiate the contribution of the front and rear surface respectively. The aim of this process is to determine the ‘Shade-free’ current contributions from the module from the side facing the ground. Finally, assessing the IV curves of the two modules in this special condition an Page | 57
Chapter 6 | Results and Optimization of Individual Models approximate value of 0.31 was computed as the shading factor for the rear surface of the bifacial module. Now, scaling
with the computed shading factor, the bifacial simulation results for site 2 can
be optimized as shown in Figure 36. Different IV curves measured on 05.May.2015 from site 2 at varying irradiance and temperatures were plotted for evaluating the performance of the proposed bifacial electrical model for two axis tracked modules. Since the shading factor is just an approximation and needs more calculations to define a concrete value, slight discrepancy still exists with the simulated currents, chiefly with
simulations.
Figure 36: Comparison of IV curves at varying irradiance and temperatures from site 2 after considering the effects of shading of the rear surface (Two axis tracked modules).
Detailed inspection of the IV parameters can be done by comparing them to the measured parameters directly as shown in Figure 37. The RMSE for
and
0.13 A and 0.09 A respectively. Similar to the results from the site 1,
were calculated to be for the tracked module is
also scattered due to its dependency of
at higher irradiances. The RMSE for
the measured data is 0.17 V and for
it is 0.67 V.
Page | 58
with respect to
Chapter 6 | Results and Optimization of Individual Models
(a)
(b)
(c)
(d)
Figure 37: Comparison of the various IV parameters at varying irradiances from site 2 (Two axis tracked modules with scaled GR’). (a) ISC (b) VOC (c) IMPP (d) VMPP
Page | 59
Chapter 7 | Validation and Discussion of the Integrated Model
7. Validation and Discussion of the Integrated Model After assessing the results of the different proposed models and their respective accuracy with the measured outdoor data, the thermal model and the electrical model were integrated as a standalone code in C++ which depends only on the measured ambient conditions and is capable of predicting its consequent performance of the installed modules at site 1 and 2. As discussed earlier in section 6.1, Approach 2 will be combined with the bifacial electrical model due to its independence of premeasured data. Also, this thermal model approach gives an opportunity to study the evolution of the temperatures of the different layers as shown in Figure 38 plotted for the module installed on site 2. We can note that the temperature gradient among the PV layers is very low, which shows that the temperature is uniform in the PV panel. Hence, we can justify the assumption made in this work as to consider an average temperature of the photovoltaic module and this temperature have been used for the calculations in the electrical model.
Figure 38: Temperature trends in different layers of the module (simulation results based at site 2 on 06 May 2016).
Using the simulated
, and
and
measured from site 1, their corresponding IV parameters
were derived using the hybrid electrical model. The comparison of the simulated and the measured parameters are as shown in Figure 39. As it can be deciphered from the plots, the simulated values are in very good agreement with the measured values, thus ensuring the accuracy of the integrated model itself. Analysing the error of the IV parameters statistically, the results are summarized in Table 14. Table 14: Integrated model validation for site 1 (Fixed modules).
IV Parameters
Page | 60
RMSE
MBE
Relative mean [%]
0.004 A
0.039 A
1.89
0.203 V
-0.227 V
0.791
0.006 A
0.057 A
1.982
0.171 V
-0.073 V
0.901
Chapter 7 | Validation and Discussion of the Integrated Model
(a)
(b)
(c)
(d)
Figure 39: IV parameter validation for integrated bifacial model using the measured data from site 1 on 05 May 2016.
Similar to site 1 validation, the comparison of the measured and the simulated parameters for site 2 using the integrated model is as shown in Figure 40. Unlike the results from site 1, the simulated parameters show a high margin of deviation, especially in case of
and
. This is probably
due to the shading factor that was discussed before in section 6.2. Therefore, proper optical modelling is essential for bifacial modules whose rear side is significantly affected by frame shading. The model accuracy can be understood from the error analysis of the individual IV parameters which is summarised in Table 15. Table 15: Integrated model validation for site 2 (Two axis tracked modules).
IV Parameters
RMSE
MBE
Relative mean [%]
0.0140 A
-0.079 A
1.502
0.118 V
0.006 V
0.708
0.007 A
-0.042 A
1.201
0.493 V
0.570 V
1.982
Page | 61
Chapter 7 | Validation and Discussion of the Integrated Model
(a)
(b)
(c)
(d)
Figure 40: IV parameter validation for integrated bifacial model using the measured data from site 2 on 05 May 2016.
7.1.
Annual power modelling results
Annual power model of bifacial modules infers to the prediction of the annual energy yield ( of an installed module.
)
can be defined as the summation of the calculated power output over a
year’s time resolved meteorological data. For this, the measured meteorological data at site 1 from 01 March 2016 until 01 April 2017 were used as inputs for the integrated modelling tool to deduce and
, from which the
for bifacial modules can be calculated as: [kWh]
It should be noted that, to convert
(Eq. 114)
units to kWh, it is divided by 60,000 as the weather data
(input for the model) is calculated every 60 seconds. For verification and validation of the power modelling the measured annual yield from the site 1 for the mentioned time period was used as comparison data. Since 2 bifacial modules are installed in this site (Figure 16 (b)), the yield from both the modules (Bifa1 and Bifa2) were used. However, due to technical maintenance and other interferences in the outdoor lab the data has short intervals (2-4 Days) at certain points and therefore is Page | 62
Chapter 7 | Validation and Discussion of the Integrated Model not the exact annual yield of the modules. The measured
for Bifa1 is 283.13 kWh and for Bifa2 is
283.933 kWh for the mentioned period and deducing the same using the integrated model gave a yield of 286.695kWh. This has a relative error of 1.25% for Bifa1 and 0.97 % for Bifa2 module. For better understanding of the yield prediction Figure 41 depicts the simulated yield with respect to the measured yield from both modules along with theie received irradiance.
Figure 41: Monthly yield prediction and validation against measured yield for bifacial module Bifa1 and Bifa2 installed at site 1.
Page | 63
Chapter 8 | Conclusion
8. Conclusion In this research, the theory of bifacial PV module technology was briefly discussed and an efficient model which could define the electrical and thermal performance of bifacial modules based on measured ambient conditions is designed. The designed model is later cross-validated using real time measured parameters from two different sites in Saxony-Anhalt, Germany. For variability one site has bifacial modules fixed on immobile mounts and in the other site, bifacial modules were mounted on a two axis tracker. The primary concepts for PV modelling namely, optical, thermal and electrical model is elaborated to highlight their intricate relationship among themselves. Also, their respective existing models for both monofacial and bifacial modules were investigated. Based on the gained fundamental literature background, the modelling tools which could be adopted for thermal and electrical modelling of bifacial modules were selected. For bifacial thermal modelling, two approaches were employed. The first approach is to adapt widely used existing modelling tools. For this, 7 modelling tools from different authors were chosen which were then assessed through cross validation based on measured weather and module temperature from the aforementioned measurement sites. The second approach however is based on comprehending the heat flow across the different layers of the PV modules and it heat exchange with its surroundings. Therefore, devising layer specific heat equations based on fundamental thermodynamics and solving them to obtain the module temperature for the given ambient condition. Finally, the mentioned models were cross validated against measured data and since the second approach was observed with the lowest RMSE value of approximately 3°C for both sites 1 and 2, it will be integrated with the electrical model. Also, this approach was preferred due to its independence of pre-measured module temperatures. For the electrical modelling, an accurate hybrid two diode computational method is developed. In which, the values of parameters, namely,
and and
are calculated analytically and the other 4 modelling are obtained through soft computing. This method was initially
proposed in [87] for monofacial modules. But in this work, the algorithm was fully adapted for bifacial modules by deducing irradiance ratio
and
based on bifacial current gain ( ) and the
proposed for indoor bifacial estimation by Singh et al. in [105]. Therefore, the
resulting electrical model is a full functioning hybrid approach which is capable of predicting the bifacial electrical output for outdoor installed modules under bifacial illumination. All the models are coded and executed in C++ programming language which is a general purpose programming language with low level memory manipulations. Therefore, helps in fast computation of the algorithm and can be easily interfaced with other programs. This comes in handy while incorporating the model with other tools of a PV simulator, for example, MPPT algorithm, grid, etc. As the final step of PV modelling, the designed thermal and electrical models are validated for standPage | 64
Chapter 8 | Conclusion alone and integrated accuracy. The proposed model is observed to be more accurate for site 1 measurements where the measured rear irradiance is inclusive of the shading effects. For site 2, the measured irradiance was scaled with a deduced shading factor due to the shading effects of the installation frames on the rear side of the bifacial module. The mean relative error in the simulated IV parameters with respect to the measured values was consistent within the range of 0.7% to 2%. In conclusion, the simulated IV parameters agree well with the measured values and thus the proposed model is asserted to be a very useful tool for simulation applications where an accurate model for bifacial PV modules is desired. In addition to performance modelling of bifacial modules, a need for quick access tool which can evaluate large database of measured data with ease was mandatory. This was realised during the thermal modelling process where redundant calculations were solved for a sufficiently large amount of measured temperatures to fit and validate the thermal modelling results. The calculations also involved repeated fitting algorithms and graphing. Therefore, an automated data evaluation app in OriginPro 2016 was developed to directly connect the software to the online measurement database and allows the user to perform defined modelling and graphing features.
8.1.
Future improvements
In the view of accurate computation of bifacial yield, the next step to improvise the proposed model would be to integrate the optical behaviour of bifacial modules. From the accomplished literature study of the optical behaviour of bifacial modules during this research, many authors have achieved in designing an approximate estimation of the front and rear irradiation [12, 33]. These can be utilized to develop a mathematical model and correspondingly, designed as a computational C++ code. Furthermore, the bifacial yield also depends on the installation profile of the module and therefore an attempt to define a bifacial module performance as a function of height of installation, installation angles and special shading conditions can also be relevant. Based on these developments, a more elaborate and versatile model that is independent of measured module parameters can be achieved to predict module yield exclusively dependant on location of installation. The RMSE analysis practiced in this work to evaluate the performance of various models, despite being a useful indicator, do not provide useful information regarding their consistency. Due to this, descriptive statistical analysis (Eg. Student’s T-test method) can be incorporated when assessing the results, especially for the electrical model which involves stochastic parameters. In the view of thermal modelling, the layers of the considered module were assumed to be at uniform temperature throughout their area, but in reality, it is not so. The temperature near the module and the installation frame is usually higher due to heat conductivity of metals. Also the incident insolation of each cell varies with respect to its spatial orientation and consequently influences its cell temperature. Therefore, improving the thermal model based on the spatial orientation of the cells could also be a relevant model improvisation. It should also be noted that the electrical model proposed in Page | 65
Chapter 8 | Conclusion this work is based for cases where the cells in a module is connected in series. In cases that the cells are not arranged in series, like in the case of custom made modules, then the electrical modelling should also be narrowed down to the cell level, which implies that each cell would be treated as a basic unit and its IV parameters are calculated individually. Finally the increasing concerns of PV degradation due to ageing and climatic aggressiveness can be modelled as additional parameters. These could be added to the equivalent circuit as special coefficients to represent the effects of cell deterioration as a function of time. This helps to estimate the module performance on a longer run and their payback time for customers. Also, in case of meticulous detailing of PV modelling, the spectral response of PV and presenting its optical and thermal parameters as a function of wavelength can be adapted into the proposed model.
Page | 66
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Chapter 9 | References [88] Sandia corporation, “Data Requirements for Model Validation,” Sandia PVPMC blog, [Online]. Available: https://pvpmc.sandia.gov/applications/data-requirements-for-model-validation/. [Accessed 6 Febraury 2017]. [89] S. Malik, D. Dassler, J. Froebel, A. Pandiyan and M. Ebert, “Angular-dependent outdoor investigation of bifacial modules,” in PVSECT 16, Munich, Germany, 2016. [90] S. Malik, D. Dassler, J.Fröbel, J. Schneider and M. Ebert, “Outdoor data evaluation of half-/fullcell-modules with regard to measurement uncertainties and the application of statistical methods,” in European Photovoltaic Solar Energy Conference and Exhibition, Amsterdam, The Netherlands, 2014. [91] H. Bellia, R. Youcef and M. Fatima, “A detailed modelling of photovoltaic module using MATLAB,” NRIAG Journal of Astronomy and Geophysics, no. 3, pp. 53-61, 2014. [92] SI Module GmbH, “SI-ENDURO: B265/305 – B270/310 Bifacial Datasheet,” Freiburg, 2014. [93] G. Notton, C. Cristofari, M. Mattei, P. Poggi, “Modelling of a double-glass photovoltaic module using finite differences,” Applied Thermal Engineering, vol. 25, pp. 2854-77, 2005. [94] W. P. Wah, Y. Shimoda, M. Nonaka, M. Inoue and M. Mizuno, “Field study and modeling of semi-transperent PV in power, thermal and optical aspects,” JAABE, vol. 4, no. 2, pp. 549-56, 2005. [95] S. Armstrong and W. Hurley, “A thermal model for photovoltaic panels under varying atmospheric conditions,” Applied Thermal Engineering, vol. 30, pp. 1488-95, 2010. [96] C. Bernsdorf, S. Voswinckel and M. Pander, Entwicklung eines Berechnungsmodells für die thermische Charakterisierung von gebäudeintegrierten Solarmodulen, Halle, Germany, 2012. [97] F. Kreith and J. Kreider, Principles of Solar Engineering, McGraw-Hill, 1978. [98] J. Holman, Heat Transfer, McGraw-Hill, 1992. [99] F. Incropera and D. DeWitt, Fundamentals of Heat and Mass Transfer, 2002: John Wiley & Sons. [100] S. W. Churchill and H. H. S. Chu, “Correlating equations for laminar and turbulent free convection from a vertical plate,” International Journal of Heat and Mass Transfer, vol. 18, no. 11, pp. 1323-9, Nov 1975. [101] O. Turgut and N. Onur, “Three dimensional numerical and experimental study of forced convection heat transfer on solar collector surface.,” International Communications in Heat and Mass Transfer, vol. 36, pp. 274-9, 2009. [102] A. C. COGLEY, S. E. GILLES and W. G. VINCENTI, “Differential approximation for radiative transfer in a nongrey gas near equilibrium.,” AIAA Journal, vol. 6, no. 3, pp. 551-3, 1968. [103] Fraunhofer CSP, “Untersuchung und Optimierung der mechanischen Eigenschaften von Gebäudeintegrierten PV-Modulen: Schlussbericht,” PV-Gebäude- und elektrische Page | 73
Chapter 9 | References Systemintegration (BIPV) im Rahmen des Spitzenclusters "Solarvalley Mitteldeutschland", Halle, 2010-13. [104] H. D. Baehr and K. Stephan, “Heat conduction and mass diffusion,” in Heat and Mass Transfer, New york, Springer, 1998, pp. 105-253. [105] J. P. Singh, A. Aberle and T. Walsh, “Electrical characterization method for bifacial photovoltaic modules,” Solar Energy Materials & Solar Cells, vol. 127, pp. 136-142, 2014. [106] M. A. Green, “Solar cell fill factors: general graph and empirical expressions,” Solid state electronics, vol. 24, no. 8, pp. 788-789, 1981. [107] Mitesh D Parmar,R. J. Parmar, V. R. Solanki, R. J. Pathak and V. M. Pathak, “The Effect of Global Solar Irradiance on the Electrical Parameters of Multicrystalline Silicon Solar Cell,” International Journal of Emerging Technology and Advanced Engineering, vol. 5, no. 4, pp. 152-161, 2015. [108] MT, Elhagry; AAT, Elkousy; MB, Saleh; TF, Elshatter; EM., Abou-Elzahab, “Fuzzy modelling of photovoltaic panel equivalent circuit,” in 40th Midwest symposium on circuits and systems, 1997. [109] A, Mellit; M, Benghanem; AH, Arab; A., Guessoum, “An adaptive artificial neural network model for sizing stand-alone photovoltaic systems: application for isolated sites in Algeria.,” Renewable Energy, vol. 30, pp. 1501-1524, 2005. [110] A, Mellit; M, Benghanem; SA., Kalogirou, “Modeling and simulation of a standalone photovoltaic system using an adaptive artificial neural network: proposition for a new sizing procedure,” Renewable Energy, vol. 32, pp. 285-313, 2007. [111] Moldovan N; Picos R; Garcia-Moreno E;, “Parameter extraction of a solar cell compact model using genetic algorithms,” in Spanish conference on electron devices, 2009. [112] Zagrouba M, Sellami A, Bouaïcha M, Ksouri M, “Identification of PV solar cells and modules parameters using the genetic algorithmss: application to maximum power extraction,” Solar Energy, vol. 84, pp. 860-6, 2010. [113] J. J. Soon and K.-S. Low, “Photovoltaic Model Identification Using Particle Swarm Optimization with Inverse Barrier Constraint,” IEEE transactions on power electronics, vol. 27, no. 9, pp. 3975-82, 2012. [114] R. Storn and K. Price, “Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces,” J. Global Optimiz., vol. 11, pp. 341-359, 1997. [115] R. Storn and K. Price, “Differential Evolution—A Simple and efficient adaptive scheme for global optimization over continuous spaces.,” International Computer Science Institute, Berkeley, CA, 1995. [116] Aswani, V. V. Praveen and S. Thangavelu, “Performance Analysis of Variants of Differential Evolution on Multi-Objective Optimization Problems,” Indian Journal of Science and Page | 74
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Appendix A: Simulated Parameters Table 16: Parameters obtained from monofacial simulations using various methods under different irradiance at 25ºC.
Model Parameters
and constant
All variable simulated
constant
= 750Wm-2
= 450Wm
= 250Wm
Page | 76
7.23 A
7.23 A
7.23 A
2.26771e-010 A
9.60647e-011 A
1.04403e-009 A
3.2353e-007 A
3.89544e-006 A
7.2116e-007 A
1.02958
1
1.09797
3.79089
2
3.51848
0.39883 Ω
0.362216 Ω
0.362216 Ω
375.724 Ω
3000 Ω
499.354 Ω
4.338 A
4.338 A
4.338 A
2.91298e-010 A
1.09477e-010 A
1.49757e-009 A
8.18901e-007 A
3.26642e-008 A
3.89257e-007 A
1.0403
1
1.11558
3.68351
2
3.78995
0.444931 Ω
0.362216 Ω
0.362216 Ω
559.991 Ω
503.006 Ω
725.365 Ω
2.41 A
2.41 A
2.41 A
3.08777e-009 A
1.09247e-010 A
3.02719e-010 A
1.01556e-005 A
2.5988e-008 A
7.77445e-008 A
1.15264
1
1.04204
3.78752
2
3.41776
0.0935299
0.362216 Ω
0.362216 Ω
1265.4
793.538 Ω
866.604 Ω
-2
-2
Table 17: Paramters obtained form bifacial simulation at site 1 under various irradiance and temperature.
Model Parameters
G = 1006 Wm-2 T= 35.5ºC 9.72878 A
G = 772 Wm-2 T= 33.6ºC 7.45823 A
G = 503 Wm-2 T= 27.8ºC 4.84531 A
G = 310 Wm-2 T= 22.9ºC 2.97714 A
8.50191e-010 A
3.06959e-009 A
2.46363e-009 A
6.13322e-010 A
3.27369e-007 A
7.46892e-006 A
3.12296e-007 AA
6.5379e-008 A
1.01409
1.08752
1.11899
1.0877
3.73099
3.23809
2.56872
2.79026
0.444424 Ω
0.457598 Ω
0.47896 Ω
957.527 Ω
1925.92 Ω
1012.5 Ω
0.499232 Ω 932.189 Ω
Table 18: Paramters obtained form bifacial simulation at site 2 under various irradiance and temperature.
Model Parameters
G = 1109 Wm-2 T= 31.8 ºC 9.96677 A
G = 930 Wm-2 T= 29.9ºC 8.44296 A
G = 600 Wm-2 T= 27ºC 5.49374 A
G = 334 Wm-2 T= 23.7ºC 3.06721 A
1.22994e-009 A
5.60981e-010 A
3.67748e-010 A
1.45633e-009 A
6.71762e-006 A
6.5781e-006 A
2.35276e-007 A
3.26401e-007 A
1.00027
1.03354
1.03635
1.12297
3.67684
3.26601
2.39037
3.54939
0.439179 Ω
0.454719 Ω
0.479172 Ω
2262.16 Ω
667.519 Ω
565.708 Ω
0.495015 Ω 1146.04 Ω
Page | 77
