HÖGSKOLAN I GÄVLE Characterization of Stationary Concentrating Photovoltaic-Thermal Solar Collectors Prototypes [REESBE – Resource-Efficient Energy Systems in the Built Environment] João Gomes 2/2/2018 [Type the abstract of the document here


Characterization of Stationary Concentrating Photovoltaic-Thermal Solar Collectors Prototypes

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REESBE – Resource-Efficient Energy Systems in the Built Environment

João Gomes


Type the abstract of the document here. The abstract is typically a short summary of the contents of the document. Type the abstract of the document here. The abstract is typically a short summary of the contents of the document.


To Sara, my baby girl, so that she has the opportunity to discover this wonderful world, like I have had.



Background and motivation for this work
This thesis is part of an Industrial PhD done within REESBE (Resource-Efficient Energy Systems in the Built Environment). This thesis was performed at the company Solarus Sunpower Sweden AB in Gävle, Sweden.
This work was aimed at detailing the scientific principles behind the Solarus concentrating photovoltaic-thermal (C-PVT) solar collector, which is a design with unique features. A better understanding of its own product will help the company to improve its product while, at the same, the knowledge generated will increase the scientific understanding on the issues around C-PVT panels and hopefully support future researchers in this topic.
Aims and Research Questions
The research questions include both broader solar aspects and very specific questions about C-PVT solar collectors:
1. How is the annual energy output ratio between PV and T collector varying around the world?
2. What are the most important parameters that define a concentrating PVT collector?
3. What type of reflector geometry is the most adequate for a stationary low concentration factor C-PVT?
4. What type of cell string layout is most adequate for a stationary low concentration factor C-PVT?
5. Is there good agreement between the results of the outdoor testing with the simulations in LTSPICE and raytracing Tonatiuh?
6. Which combination of materials and production processes allows silicone solar cells to resist the expansion of aluminum at stagnation temperatures of 200C?

List of appended papers and author´s contribution

7 papers were selected for the thesis.

Paper I: Gomes J., Junge J., Lehmann T. et Karlsson B. Defining An Annual Energy Output Ratio Between Solar Thermal Collectors And Photovoltaic Modules. Presented at IAHS Conference, 2016. Conference proceeding. Planned to be deepened and submitted to a journal in 2018.
Key Message: A new tool for comparison of T and PV technologies and market overview.
Author contribution: 90%. The author wrote the paper and did most of the work. The world maps, part of the market survey and some of the simulations were performed by Ms Junge and Ms Lehmann.

Paper II: Gomes J., Diwan L., Bernardo R. et Karlsson B. Minimizing the Impact of Shading at Oblique Solar Angles in a Fully Enclosed Asymmetric Concentrating PVT Collector. Presented at ISES Solar Conference 2013. Published in peer review Energy Procedia, Volume 57, 2014, p. 2176-2185 (Impact factor 1.16). Available at https://doi.org/10.1016/j.egypro.2014.10.184
Key Message: Analysis of the impact of shading in an asymmetric low concentration stationary PVT which including collector testing at two universities.
Author contribution: 85%. The author wrote the paper and did the majority of the work. Part of the collector testing work was conducted at Dalarna University by Mr Diwan with support from the author. The rest of the collector testing was done by the author at Gävle University.

Paper III: Gomes J., Bonfiglio ., Giovinazzo C., Fernandes C., Torres J., Olsson O., Branco P. et Nashih S. Analysis of C-PVT reflector geometries. Presented at the 17th international conference on power electronics and motion control. Available at DOI: 10.1109/EPEPEMC.2016.7752175. Submitted in April 2017 to a journal of IEEE: Transaction of Industrial Applications (Impact factor of 1.9).
Key Message: Analysis of the raytracing results of different reflector geometries including costs/output balance.
Author contribution: 85%. The author wrote the paper and did the majority of the work.

Paper IV: Giovinazzo C., Bonfiglio L., Gomes J. et Karlsson B. Ray Tracing Modelling of an Asymmetric Concentrating PVT. Presented at Eurosun 2014 and published in the conference proceedings (p.67). Available at DOI: 10.18086/eurosun.2014.21.01
Key Message: The Solarus C-PVT collector has been modelled using Tonaituh to extract a 3D map of the effective solar radiation that reaches both top and bottom sides of the receiver.
Author contribution: 65%. The author wrote the paper and supported Ms Giovinazzo and Mr Bonfiglio that performed the ray tracing simulations.

Paper V: Nashih S., Fernandes C. , Torres J., Gomes J. et Branco P. Validation of a Simulation Model for Analysis of Shading Effects on Photovoltaic Panels. Published on Journal of Solar Energy Engineering: Including Wind Energy and Building Energy Conservation, Volume 138, Issue, 14th June 2016 (Impact Factor 1.19). Available at DOI: 10.1115/1.4033646.
Key Message: Validation of the LTSpice model.
Author contribution: 50%. The author wrote part of the paper, did the experimental testing and supported both the theoretical and simulation work.

Paper VI: Fernandes C., Torres J., Branco P., Fernandes J. et Gomes J. Cell string layout in photovoltaic collectors. Published in Energy Conversion and Management journal, Volume 149, 1st October 2017, Pages 997-1009 (Impact Factor: 5.589). Available at DOI: 10.1016/j.enconman.2017.04.060.
Key Message: Simulations using an LTSPICE to predict the shading impact on a C-PVT.
Author contribution: 40%. The author wrote part of the paper, did the experimental testing and supported both the theoretical and simulation work.

Paper VII: Bernardo R., Davidsson H., Gentile N., Gomes J., Gruffman C., Chea L., Mumba C. et Karlsson B. Measurements of the Electrical Incidence Angle Modifiers of an Asymmetrical Photovoltaic/Thermal Compound Parabolic Concentrating-Collector. Presented at PEEC 2013. Published in Engineering, Vol. 5 No. 1B, 2013, pp. 37-43 (Impact Factor: 0.72). Available at DOI: 10.4236/eng.2013.51B007.
Key Message: Characterization of the IAM of an early C-PVT prototype.
Author contribution: 40%. The team did the measurements and wrote part of the paper.

List of all papers from the author relevant to this thesis
In total, the author of this thesis has produced 22 papers in both conferences and journals. The list below shows all papers produced by the author of this thesis and categorizes them. Some of these papers were selected to be an integral part of this thesis as shown on the previous chapter while others were only used partially.

Paper VIII: Gomes J, Bastos S., Henriques M., Diwan L. et Olsson O. Evaluation of the Impact of Stagnation in Different Prototypes of Low Concentration PVT Solar Panels. Presented at the ISES world congress 2015 and published in the proceedings (p1025-1036). Available at DOI: 10.18086/swc.2015.10.14.
Key Message: Analysis on the impact of stagnation on solar cells encapsulated by silicone and different methods for mitigation of the impact.

Paper IX: Mantei F., Henriques M., Gomes J., Olsson O. et Karlsson B. The Night Cooling Effect on a C-PVT Solar Collector. Presented at the ISES world congress 2015 and published in the proceedings (p1199-1207). Available at DOI: 10.18086/swc.2015.10.33.
Key Message: Night cooling using glazed PVT´s collectors will work only under very few circumstances.

Paper X: Davidsson H., Bernardo R., Gomes J., Chea L., Gentile N. et Karlsson B. Construction of laboratories for solar energy research in developing countries. Presented at ISES Solar Conference 2013 and published at peer review Energy Proceedia, Volume 57, 2014, Pages 982-988 (Impact Factor: 1.16). DOI: 10.1016/j.egypro.2014.10.081.
Key Message: Study on the design and components for a solar lab for research and education in developing countries.

Paper XI: Gomes J., Gruffman C., Davidsson H., Maston S. et Karlsson B. Testing bifacial PV cells in symmetric and asymmetric concentrating CPC collectors. Presented at PEEC 2013. Published in Engineering, Vol. 5 No. 1B, 2013, PP. 185-190 (Impact Factor: 0.72). DOI: 10.4236/eng.2013.51B034.
Key Message: Different low concentration bi-facial PV collector prototypes were built and tested.

Paper XII: Gentile N., Davidsson H., Bernardo R., Gomes J., Gruffman C., Chea L., Mumba C. et Karlsson B. Construction of a small scale laboratory for solar collectors and solar cells in a developing country. Presented at PEEC 2013. Published in Engineering, Vol. 5 No. 1B, 2013, PP. PP. 75-80 (Impact Factor: 0.72). DOI: 10.4236/eng.2013.51B014.
Key Message: Developing and reducing the cost of components of solar collector testing labs while maintaining the necessary accuracy.

Paper XIII: Contero F., Gomes J., Mattias G. et Karlsson B. The impact of shading in the performance of three different solar PV systems. Presented at Eurosun 2016 and published in the proceedings. DOI: 10.18086/eurosun.2016.08.25.
Key Message: Evaluation of the electrical shading at HiG´s installation. Comparison between different shading mitigation devices.

Paper XIV: Gomes J. et Karlsson B. Analysis of the Incentives for Small Scale Photovoltaic Electricity Production in Portugal. Presented at Eurosun 2010 and published in the proceedings. DOI: 10.18086/eurosun.2010.08.05.
Key Message: Analysis of the impact of the incentive schemes in PV penetration.

Paper XV: Gomes J. et Karlsson B. Analysis of Reflector Geometries for Flat Collectors. Presented at Renewable Energy Conference, Yokohama, Japan, 2010.
Key Message: Analysis on the best point for truncation for reflectors in concentrating solar thermal collectors.

Paper XVI: Diogo Cabral, Paul-Antoine Dostie-Guindon, João Gomes et Björn Karlsson. Ray Tracing Simulations of a Novel Low Concentrator PVT Solar Collector for Low Latitudes. Presented at ISES solar world congress 2017 and will be published in the conference proceedings.
Key Message: Comparison between different reflector geometries for a low concentrating PVT using Tonatiuh ray tracing.

Paper XVII: Alves P., Fernandes J., Torres J., Branco P., Fernandes C., Gomes J. Energy Efficiency of a PV/T Collector for Domestic Water Heating Installed in Sweden or in Portugal: The Impact of Heat Pipe Cross-Section Geometry and Water Flowing Speed. Presented at the 12th SDEWES conference in 2017 and published in the proceedings.
Key Message: Simulations were conducted to verify the influence of the flow, losses in electric efficiency, temperature variation, shading effect in the back receiver of electrical efficiency in Portugal and Sweden.

Paper XVIII: Fernandes C., Torres J., Nashih S., Gomes J. et Branco P. Effect of reflector geometry in the annual received radiation of low concentration PV systems. Submitted on Dez 2017 to IEEE Transactions on Industry Applications (TIA)
Key Message: Soltrace simulations.

Paper XIX: Fernandes C., Torres J., Nashih S., Gomes J. et Branco P. Cell string layout in a stationary solar concentrating solar photovoltaic collectors. Published in Power Electronics and Motion Control Conference (PEMC), 2016 IEEE. DOI: 10.1109/EPEPEMC.2016.7752179
Key Message: Simulations using an LTSPICE to predict the shading influence in a C-PVT.

Paper XX: Torres J., Nashih S., Fernandes C. et Gomes J. The effect of shading on photovoltaic solar panels. Published October 2016 in Energy Systems, page 1-14 (Impact Factor 0.912). DOI: 10.1007/s12667-016-0225-5
Key Message: LTSPICE study on the shading impact in a PVT.

Paper XXI: Fernandes C., Torres J., Nashih S., Gomes J. et Branco P. Shading Effects on Photovoltaic Panels. Presented at Conftele conference at Aveiro University 2015. Conference proceeding.
Key Message: Early shading study with LTSPICE.

Paper XXII: Kurdia A., Gomes J., Olsson O., Ollas P. et Karlsson B. Quasi-dynamic testing of a novel concentrating solar collector according to ISO 9806:2013. Submitted to Eurosun 2018.
Key Message: Comparison of the testing results between the Solarus C-PVT and a standard flat plate

Paper XXIII: Torres J., Fernandes C., Gomes J., Olsson O., Bonfiglio L., Giovinazzo C. et Branco P. Effect of Reflector Geometry in the Annual Received Radiation of Low Concentration Photovoltaic Systems. Published in Energy 2018, 11(7), 1878 (Impact Factor 3.05); DOI: 10.3390/en11071878
Key Message: Analysis of different reflector geometries using the soltrace software.

Note: References to the above papers will be marked as, for example, XXIII. ?
Literature review
Climate change
“Today, like always before, society faces its gravest challenge.”
Although, current challenges always appear to be the most pressing as the above quote somewhat cynically postulates, it is nevertheless an objective and undeniable reality that mankind today has an unprecedented capacity to alter the planet which supports its life.
And, in its quest to improve its life quality, mankind as created environmental problems that today threaten its very survival. Climate change is a reality and must be tackled, if humans are to continue to exist.
Figure 1 shows the temperature data from four reputable international science institutions. All show rapid warming in the past few decades and that the last decade has been the warmest on record 1.
Figure 2 clearly shows not only how large the atmospheric CO2 increase since the Industrial Revolution has been, but also how drastically fast the planetary balance of the last 400000 years has been disrupted. This figure was made based on the comparison of atmospheric samples contained in ice cores and more recent direct measurements 2.

Figure 2: Variation of atmospheric carbon dioxide levels over 400.000 years
(Source: Vostok ice core data/J.R. Petit et al.; NOAA Mauna Loa CO2 record)
Lüthi et all, plotted CO2 levels during 800000 years and the cycles still remain between 160 and 300 3. As a time reference for comparison, Homo sapiens, the first modern humans have evolved from their early hominid predecessors about 250000 years ago, language was developed about 50000 years ago and the great migration from Africa started about 70000 years ago 4. Mankind has existed always within this range of atmospheric CO2. Climate change impacts are multiple from acidification of the oceans to melting of the polar caps. Furthermore, the greenhouse effect may make planetary and regional temperatures spiral out of control. And while, there is no crystal ball to accurately predict the future, we know that the climate balance that allowed humans to thrive will be greatly disturbed. At a planetary level, this would be just one of many climate changes, and it is even likely that a percentage of the current species would adapt to survive a major climate change. However, it is likely that humans are too dependent on the global ecosystem to survive such changes. And this is definitely a risk that is not worth taking.
Overview of the Energy Sector
Energy use is one of the most important cause of climate change. As a result, mankind needs to convert to low CO2 emitting energy sources, preferably renewable which are sustainable in the long run.
Energy is used in two forms: Heat and electricity. The graph below illustrates the shares of the different energy sources in the world´s final energy consumption.

Figure 3: Estimated Renewable Energy Share of Global Final Energy Consumption in 2014 5

According to the REN21, renewable energy reports, in 2009, the share of renewable energy in the total energy usage of the world was 16% 6. In 2014, the same share was 19.2%, up 3,2% in 5 years 5.
In the same period, modern renewables accounted for the bulk of the increase, from 6% to 10.3% of the world´s energy usage. Traditional biomass relevance has decreased by 1.1%, from 10% to 8.9% 6.
Regarding renewable electricity, the year of 2015 saw the largest increase ever of 147 GW of total capacity added. This represented an increase of almost 9% to a total installed capacity of 1849 GW 5.
Both Wind and Solar PV made record additions and together they made up 77% of all renewable power capacity added in 2015 5.
A landmark change is the fact that today the world adds more renewable power capacity annually than what it adds in net capacity from all fossil fuels combined! This way, in 2015, renewables have accounted for 60% of all net additions to global power generating capacity 5.
By the end of 2015, renewables represent 29% of the world’s power generating capacity, which supplied 23.7% of global electricity, with hydropower representing 16.6%.

Figure 4: Estimated share of Renewable Energy in Global Electricity Production in 2015 5

By 2040, it is expected that the cumulative growth of RE will contribute to a total primary energy consumption to 50% 7 8.
Solar Energy: PV and Thermal collectors
Energy from solar radiation can be collected in two forms:
Solar Electricity
Solar Heat

1) Solar Electricity
Solar Electricity is either produced by the photovoltaic (PV) effect or by the conversion of solar radiation into heat which is then used to drive a turbine that generates electricity. The latest process can only be achieved in large centralized power plants and is called Concentrated Solar Power (CSP).
In 2015, CSP had a total installed capacity of 5 GW which compares to 227 GW of PV. In the same year, 50 GW of PV have been installed 5. Although only 10 years ago, CSP was expected to become the mainstream of solar electricity production method, PV has managed to greatly surpass CSP having today a total installed capacity that is 45 times higher. This is probably due to the simplicity and modularity of PV installations which overall has much lower capital requirements than CSP. However, thermal storage can help CSP to gain momentum, as it allows CSP to do baseload. In 2016, all CSP plants where built with storage 9.
The growth in PV has been so fast that capacity installed in the world in 2015 is nearly 10 times higher than the cumulative installed capacity of 2005 8.
The figure below shows the top 10 countries in total installed capacity of PV. Germany has been the installed capacity leader for the last decade however, in 2015, China took the lead 5. In 2016, Japan became second 9. A major shift has also happened in PV production in the world. According to the REN21 2014 report: “Less than 10 years ago, almost all solar panels were produce Europe, Japan and the USA. In 2013, Asia accounted for 87% of global production (up from 85% in 2012) with China producing 67% of the world total (62% in 2012). Europe´s share continue to fall to 9% while Japan remained at 5% and the US at only 2.6%”. 10

Figure 5: Installed capacity and new additions of PV in 2016 for the top 10 countries 9

Moreover, it is important to note that several PV technologies exist with very different efficiencies and development stages. However, silicone solar cells are today the dominating PV technology with about 90% of the PV market. Within this, monocrystalline silicone cells represent about 25% of the world panel production in 2015 11 12 13 14.
It is also important to note that “Solar PV saw record additions and, for the first time, accounted for more additional power capacity (net of decommissioned capacity) than any other renewable technology. Solar PV represented about 47% of newly installed renewable power capacity in 2016, while wind and hydropower accounted for most of the remainder, contributing about 34% and 15.5%, respectively”. 9

2) Solar Heat
Solar Heat or Solar Thermal (ST) is the process of converting solar radiation into heat. A large number of different technologies exists ranging from uncovered flat plate collectors, to vacuum tube collectors or large tracking concentrating solar collectors. These technologies produce heat at different temperatures and therefore have multiple applications in residential and industrial sectors.
The figure below shows the total installed capacity in 2016 of solar heating in the world at 456 GWth. As a referential, one can compare to the 303 GWe of installed capacity PV 9, although it is fundamental to keep in mind that PV and ST have different capacity factors and that they produce energy with different values. The 456 GWth of ST are estimated to have produced 375 TWh of heat at different temperatures. At the same time, the 303 GW of PV produced about 375 TWh 9.
In 2017, China alone has accounted for 75% of the total new additions. The Chinese market has been undergoing a change from small residential to large installations such has hotels or the public sector 9. In 2015, the installed capacity of ST collectors grew by 6,3% (26 GWth) which is a significant growth reduction from previous years. As a comparison point, the installed capacity of PV is breaking record as it grew by 28% which corresponds to 50 GW 5.
As shown in the figures 5 and 6, over the last 10 years, ST total installed capacity has roughly quadrupled while PV has been multiplied a factor 45. However, although there is a difference of an order of magnitude between these two numbers, it is important to point out that PV started with a much lower base number from which it was easier to increase. Both figures show how China is currently dominating the solar market.

Figure 7: Installed capacity of ST in the top 20 countries in 2015 15
Finally, it is important to refer that the heat produced by ST can serve different purposes, as show in the figure below. In the world, domestic hot water production either for single or multi family houses is the main application for ST, although some economic regions install ST for different purposes.
Figure 8: Solar Thermal Applications by economic region in 2015 15

Basics of Solar Energy: Differences between PV and ST
The effect of solar radiation in PV and ST collectors
The Figure 9 shows the effect of solar radiation on both power and efficiency for photovoltaics panels and solar thermal collectors, which is calculated according to a simplified model using the following formulas:
Photovoltaic panels: P=I?? (eq. 1)
Solar thermal collectors: P=?_0?I-((U_1+U_2? ?T)? ?T) (eq. 2)

where P is the power from the collector, I is the irradiance on the plane, ? is the efficiency of the collector, ?_0 is the optical efficiency of the thermal collector, U1 is the first order heat losses and U2 is the second order heat losses.

In equation 2, the heat loss value (U) is already including both components U1 and U2. Figure 1 shows a graphical representation of the above formulae.

Figure 9: The impact of solar radiation on power (A) and efficiency (B) for PV and T collectors at a ?T of 50°C I

The collector values used to plot the above graphs were taken from a market survey which is shown in the result section. These efficiencies values represent standard thermal collector calculated based on the aperture area of collectors working a ?T = (Tmed – Tambient) = 50°C, where Tmed = (Tin + Tout) / 2. In this model, only the most relevant factors are taken in consideration. In reality, there are other factors to consider, such as the fact the efficiency of a crystalline solar cell is reduced at lower radiation levels 16 or that an increase in the temperature of the solar cells will lead to a decrease in solar cell efficiency of around -0,44 %/ºK for mono crystalline solar cells 17. However, the point that is made by the above figure is that, at a constant temperature, the efficiency of a PV-system is almost independent of the solar irradiance, while the efficiency of solar thermal-systems is strongly dependent. The efficiency of a thermal collector is often zero at low solar radiation intensities.
System losses such as inverters, cabling, or piping were not considered neither for ST nor for PV.

The effect of temperature in PV and T collectors
Figure 10 shows the effect of operating temperature on the efficiency of the solar panels which was calculated using the formulas 1 and 2. For the PV panels, the cell temperature dependency was taken into account as described below.

Figure 10: The impact of temperature in efficiency of PV ; ST panels at a constant solar radiation of 1000W/m2 I

As mentioned in the author´s paper I, the operational temperature of a PV panel varies according to how much solar radiation is received and how much heat the panel is able to lose, which is greatly influenced by factors like panel construction or type of installation (building integrated vs free standing). The operating temperature of a PV panel is defined by the nominal operating cell temperature (NOCT). For this graph, it was accepted that 120ºC was the maximum temperature for the PV panel since many panels break after that temperature 18. Just like for PV panels, the operational temperature of an ST collector is also a function of solar radiation and heat losses although in ST systems a fluid is extracting heat from collector. This fluid can be water, glycol or a special type of oil for collectors that work at very high temperatures. The amount of heat that is carried away by the fluid temperature depends on factors such as the temperature difference between the fluid and the collector, the ambient temperature, the characteristics of the fluid and the speed and type of flow 19.
A major difference between PV and ST panels is that, in ST panels, the heat is carried from the collector to the tank, while in standard PV panels the built up of heat is passively dissipated. A similarity of both types of panels is that the efficiency goes up when the operating temperature is decreased.
Influencing factors: local climate
Weather conditions widely vary around the globe. An example from paper I shows the variation of beam radiation around the world while figure 2 shows the annual average temperature. Many other parameters, such as the median daily variation of temperature or the air humidity could be shown to illustrate these large variations. The numbers in figure 11 show the percentage of beam radiation in the total solar radiation normal to the ground, while the color shows the total amount of solar radiation. As recognizable in the figure, the beam fraction is not dependent on the latitude although the total amount of solar radiation generally increases at lower latitudes. The main influence on the beam fraction is the local climate 20.

Figure 11: Percentage of beam in the total solar radiation (number) and total solar radiation in different locations (color) I
The percentage of beam radiation in the total radiation ranges from 43% in Singapore to 77% in El Paso and Tamanrasset. Singapore, Naha, Chon Buri, Manaus and Bergen are the only five cities where the diffuse radiation represents more than 50% of the annual solar radiation received in the ground. The main reason for this effect is the presence of clouds 5. Cities in Southeast Asia are affected by the monsoon, twice a year. Bergen has 200 rainy days over the year and a moderate climate 10. Manaus, located close to the equator, is affected by a long rainy season which leads to the 48% of beam in the total solar radiation. Whereas in desert areas like El Paso or Tamanrasset, the climate is dry and the ratio reaches up to 77%. As expected, the countries closer to the equator show the warmest average temperatures around the world which go up to 30°C. However, there are exceptions like La Paz with 8,2ºC which owes its low annual temperature to the high altitude. At high altitudes, the layer of atmosphere is less dense which leads to both higher temperature variations (the atmosphere has less capacity of retaining the heat) and higher solar radiation (the atmosphere is less dense and absorbs less solar radiation). The main cause of low temperatures at higher latitudes is the angle at which the incoming rays hit the ground. Although, the normal solar radiation in a perfect sunny day is close to 1000W/m2 anywhere in the world at sea level, if the sunlight has a lower angle, that sunlight will be spread over a larger area. This effect is also known as the cosine effect 21.

Figure 12: Annual average temperature of 66 cities around the globe

Locations with the same annual temperature may present very different temperature profiles. For example, Lisbon and El Paso have similar annual temperatures around 17ºC but when comparing the daily profile, it can be found that the temperature is steady in Lisbon, a coastal city with a Subtropical-Mediterranean climate while El Paso has large variations over 24 hours and a hot desert climate. Another example is the climate on the West Coast of Europe is much milder than the climate in the interior of Europe at the same latitude. This is due to the effect of the Gulf Stream that not only warms up the air but also stabilizes its temperature 22.
Basics of Concentration in Solar Collectors
Concentrating collectors have the ability to re-direct solar radiation that passes through an aperture into the receiver or absorber. The goal is to reach a better ratio of €/kWh of heat and/or electricity produced. These collectors sometimes include also a tracking system in order to maximize the energy yield 23.
Concentration designs vary greatly from low concentration non tracking design to large concentrated solar power (CSP) plants with extremely high concentration factors. Depending on the type of concentration, concentrating collectors are often categorized in two types: high or low concentration.
The low concentration can be subdivided into three different types: (i) Booster reflector; (ii) Compound Parabolic Concentrator (CPC); (iii) Luminescent Concentrator 24 23 25 26. The following figure shows the high concentration technologies currently available.

Figure 13: Four technologies for high concentration solar energy. Linear concentrators: Trough (a) and Fresnel (b). Punctual concentrators: Tower (c) and Dish (d) 27
Concentration factor

The concentration factor (Ci) is one of the most important parameters for concentrators. It is defined as the ratio between the effective area of the aperture and the area of the receiver.
“Ci = ” “Aperture Area” /”Receiver Area” (e.q. 7)

A collector with no concentration is said to have a concentration factor of 1, while a collector that has an aperture (Aa) that is twice the receiver area (Ar) is said to have a concentration factor of 2 25. Designs with higher concentrations require tracking the sun, while low concentration designs may dispense tracking. Tracking increases the amount of solar irradiation that reaches the receiver but also increases cost, complexity and may not suitable all locations.
Ideal two-dimensional (linear) non-truncated CPC with an acceptance half angle ?c has a maximum concentration factor that is given by the following equation 28 19:
“Ci = ” “1” /(“Sin” ?_((?c))?” sin ” ) (2.6)

Compound Parabolic Collectors

This thesis work will focus on CPC´s, which is a non-imaging type of concentrators that does not necessarily require a tracking system due to the ability of reflecting both beam and diffuse radiation to the receiver. The incidence angle for these concentrators makes them very attractive from the point of view of system simplicity, flexibility and cost effectiveness 28 29 30. CPC concentrators are combining two parabolic reflectors that can be symmetric or asymmetric. Each reflector has its own focus length (F) at the lower edge of the other parabola, as shown in the figure on the right side.

The angle between the axis of the collector and the line connecting the focus of one of the parabolas with the opposite edge of the aperture is called acceptance half-angle (?c). The relationship between the size of the aperture (2a), the size of the receiver (2a’) and the acceptance half-angle is expressed through the following equation 19:
?”2″ “a” ^”‘” ” = 2a sin?” ?_”c” (eq. 3)

Knowing the concentration ratio, it is possible to obtain the acceptance half-angle 15:
“C” _”i” ” = ” “2a” /”2a'” “=” “1” /?”sin?” ?_”c” (eq. 4)

The following equations establish the relation between the focal distance of the side parabola and the acceptance half-angle (?c), receiver size, and height of the CPC (h) 19:
?”f = a'(1 + sin?” ?_”c” ) (eq. 5) Add to Nomenclature!
“h = ” ?”f cos?” ?_”c” /(?”sin” ?^”2″ “?” _”c” ) (eq. 6) Add to Nomenclature!

CPC concentrators are made, so that each ray that comes into the aperture with an angle smaller than ?c is reflected onto the receiver at the base. However when the angle of the ray is greater than ?c, the ray will be reflected back to the atmosphere. The figure below shows this effect:

Figure 15: Reflection of the light rays directed to the CPC concentrator at different angles 19.

Maximum Reflector Concentration Design
The Maximum Reflector Concentration (MaReCo) is a patented design that originated from research done at Vatenfall. It is based on an asymmetric truncated CPC-collector with a bi-facial flat receiver that is specially adapted for the asymmetric annual solar radiation profiles of high latitudes. A solar thermal collector with this reflector design will be able to better match the asymmetric heat production profile existent at high latitudes to the nearly constant annual demand profile of a Domestic Hot Water (DHW) consumer and thus, be able to prevent stagnation damage 31.
The general design of the MaReCo reflector trough consists of two parabolic reflectors with their individual optical axis tilted 20° and 65° from the horizon, collecting all the incoming irradiation between a solar altitude of 20° and 65° as shown in figure 9 32 33.

Figure 16: Sketch of the basic MaReCo design 32 31

The optical axis from the parabola defines the lower and upper acceptance angles. The reflector is divided in sections A, B and C. Section A comprises a lower side parabola that goes from point 1 to 4. The optical axis is placed along the upper acceptance angle and its focal point on point 5, the upper part of the receiver. Section B is characterized by the circular section between points 1 and 2. Solar radiation that reaches this reflector is directed towards the backside of the reflector which in this case is between point 1 and 5 in this case. However, the receiver could be located anywhere in section B, for example a receiver between points 2 and 5 (the dotted line) would also be possible and have the same theoretical performance. Section C is an upper parabolic reflector that reaches between points 2 and 3, with an optical axis along the lower acceptance angle and focus at point 5.
The dotted line that goes between points 3 and 4 defines a truncation point for both parabolas. However, several other truncations points are possible with an considerable impact on the annual performance of the solar collector.
Additional MaReCo design configurations were created for different situations such as stand-alone, the roof integrated and the wall 29. These configurations are described below in more detail.

The stand-alone MaReCo

The figure on the right shows the stand-alone MaReCo design. This design has a concentration factor (Ci) of 2.2, an upper acceptance angle of 65°, a lower acceptance angle of 20° and an aperture tilt of 30°29.

Figure 17: Section of the stand-alone MaReCo for Stockholm conditions, a stationary asymmetrically truncated wedge CPC with acceptance angles between 20° and 65°. Aperture tilt 30° 31 32.
The roof integrated MaReCo

The roof integrated MaReCo designed features a cover glass start that starts immediately where the circular section of the MaReCo ends, as shown by the following figure. This MaReCo design has a concentration factor (Ci) of 1.5 and is meant for a roof with a tilt of 30° 29. All the radiation normal to the cover glass is accepted.

Figure 18: Section of the roof integrated MaReCo design for
a tilt of 30o and optical axis 90° from the cover glass 31
Other roof integrated MaReCo designs were developed, such as the roof MaReCo for east/west and the spring/fall MaReCo. The roof MaReCo for east/west is shown below. It has a Ci = 2.0 and was designed for roof facing west. It accepts radiation between 20° and 90°, meaning that the optical axis is 70° from the cover glass 29.

Figure 19: Section of the east/west roof MaReCo 26

The roof spring/fall MaReCo has been designed for a roof tilted 30° and it has an optical axis at 45° from the horizon. Direct radiation that hits the reflector at an angle smaller than 15° from the aperture normal will be reflected out of the collector which prevents overheating. This design has a concentration factor (Ci) of 1.8 29.

Figure 20: Section of the spring/fall MaReCo 26.

The wall MaReCo

This design was developed for a south facing wall, in order to be an alternative to standard installations. The figure below shows the design which has a Ci = 2.2, an optical axis at 25° from the horizon and an acceptance angle between 25° and 90° from the horizon 29.

Figure 21: Section of the wall MaReCo 26.

PVT collectors: Advantages and Disadvantages
As mentioned in the author´s papers IV and I, photovoltaic/thermal (PVT) collectors produce both heat and electricity. The main benefits of PVT collectors when compared to standard thermal and photovoltaic (PV) solar collectors are:
• The possibility of increasing cell efficiency by reducing the cell operational temperature when the hot water is extracted at low temperatures. In order for this to be achieved, it is fundamental that the panel design is able to transfer the heat from the cells to the cooling liquid efficiently as well as homogeneously.
• The production of one unit of PVT uses fewer raw materials than an equivalent area of thermal and photovoltaic panels. This is expected to enable a lower production cost per kWh of annual produced combined power.
• Reduction of the installation area, which enables the deployment of more installed capacity per roof area and should also lower the installation costs.

The main disadvantages for PVT´s are the higher complexity in both for collector production and installation and the reduced market share since it requires customers that need both the heat and the electricity.

Table 1: Advantages and disadvantages of PVT collectors (Vs T and PV)
Topic Advantage Disadvantage
Efficiency Higher energy output/m2 compared to PV and T. Possibility to increase electrical efficiency by cooling. Heat has more value at high temperatures but this reduces electrical output.
Collector Cost Fewer raw materials needed to obtain the same energy output Early in the Technology curve. Cell Price has greatly decreased making PVT (and T) less attractive.
Production Cost – Increased complexity at production level
Installation Cost/ Reliability Lower installation cost can be achieved due to smaller area for the same output Increased complexity at installation level
Market – Nice Market (require need for heat and electricity)

C-PVT collector: Advantages and Disadvantages
As mentioned in the author´s papers IV and I, some PVT manufacturers combine the concept with concentration to reduce the usage of PV cells and thermal absorber material. Concentration carries the penalty due to extra reflection losses from the reflector and a lower Incident Angle Modifier (IAM) profile but at the same time, it reduces the amount of expensive components (solar cells, receiver and/or selective surface) 23. In the end, it is a trade between the positive effect of lowering the collector cost and the negative effect of lower output per square meter. The steep decrease in the price of silicone solar cell made C-PV concepts less popular. However, in PVT collectors, the receiver becomes again more expensive since it features both the thermal absorber and the PV cells.
Concentration also helps to reduce the heat losses, though conduction and convection losses. This way, concentration also allows achieving higher temperatures, although higher temperatures will reduce the efficiency of the solar cells in PVT collectors 23.
Some of the disadvantages concentration are Aesthetics (bulkier), higher stagnation temperatures which lead to more expensive components and lower power density 23.
A number of factors are important such as simplicity or aesthetic are important for solar costumers, however, in the end, the most important number in solar remains the cost per kWh of heat and electricity produced, including the installation cost 34. This way, the table below shows a list of the factors but does not quantify their importance.

Table 2: Advantages and disadvantages of C-PVT collectors (Vs PVT)
Topic Advantage Disadvantage
Electrical Output/Cost Concentration reduces costs Concentration also reduces output/m2
Thermal Output/Cost Concentration reduces heat losses and increases range of possible working temperatures Higher stagnation temperatures
Product complexity – Concentration increases complexity
Aesthetics – Concentration can reduce aesthetics

The impact of shading and concentration in PV panels and solar thermal collectors
Shading can be caused by many factors, such as building, trees or other solar panels. As mentioned in the author´s papers IV and I, shading has a considerably different impact on PV panels than on thermal collectors. In PV modules, the solar cells are commonly connected in series, thus one completely shaded solar cell will reduce the output of the whole string. Bypass diodes can be used to mitigate this effect by allowing current to flow in a different path at the expense of a minor fraction of the total power. However, the introduction of diodes increases both assembly time and material cost which leads to increased costs. On the other hand, diodes also prevent hotspots that can destroy PV panels 35 36. In thermal collectors, the decrease in power produced due to shading is approximately proportional to the shaded area. Thus, shading clearly has a much bigger impact on PV panels than thermal collectors I.
Non-uniform concentration is a feature of all compound parabolic concentrators (CPC) 19 28 37 XV. Its effects are similar to partial shading. For a PV panel, differential illumination levels in the cells increases the series resistance losses. However, the most significant losses are at a string level when at least one of the series connected cells has a lower illumination level which reduces the current in the whole string 37 I IV. This lower illumination level is often cause by shading from the collectors´ box frame or the lack of reflector. In other words, in a stationary CPC, the transversal shading impacts all cells in a string and does not cause one cell to have more current than another which means that the losses are almost proportional to the shaded area. On the other hand, the longitudinal shading causes the edge cells to receive a lower illumination than the rest of the series connected cells greatly amplifying the effect of shading.
This way, non uniform illumination is considerably more critical for PV panels than for solar thermal.
The analyzed PVT design includes a CPC concentrator. For this reason, the study on shading was mainly focused on the electrical part of an asymmetric compound parabolic concentrating (CPC) photovoltaic/thermal hybrid (PVT).
First Look at the Solarus C-PVT
Over time, Solarus has developed several versions of its C-PVT, many of which have been analyzed during this thesis. For simplicity, this section will only detail the latest version of the Solarus collector which called Power Collector (PC) 38. The figure below shows the PC:

Figure 22: The latest version of the Solarus C-PVT, the Power Collector

However, all versions of the Solarus C-PVT solar collector can be divided into two defining main components: The collector box and the PVT receiver, both of which are presented in the next chapters.

The Collector Box
The figure below shows a breakdown of all components of the collector.

Figure 23: Solarus C-PVT PC components profile.

The collector box has four main components:
A black plastic solid frame that provide structural support to the reflector;
A gable with a reported 90% of transparency and that is made from Polymethylmethacrylate (commonly known as PPMA) that seals the collector sides as shown on the picture below;

Figure 24: Profile view of the Solarus C-PVT showing the transparent gable and the black plastic frame.

A 4mm tempered solar glass with anti-reflective treatment (on both sides) to reach a 1.5% absorptance and 2% of reflectance per side;
A 0.4mm aluminium reflector with a reflectance is 92 % of reflectance at an air mass of 1.5, according to the standard. The reflector geometry is a variation of the roof integrated Maximum Reflector Concentration (MaReCo). As shown in the figure below. The concentration factor is 1.7.

Figure 25: Cross section of the MaReCo collector 29

Receiver core
The receiver core is the heart of the Solarus C-PVT. It has 2321 mm long, 165 mm wide and 14.5 mm thickness. As shown below, there are solar cells on both sides of the aluminum receiver. These solar cells are encapsulated by a highly transparent silicone with a reported transparency of 97%.

Figure 26: Solarus bifacial receiver
The receiver consists on an aluminum receiver with 8 elliptical channels as shown in the figure above. The cooling fluid flows through the 8 channels in order to extract heat from the collector. The core is made of extruded aluminum.

Figure 27: Side view of the receiver core showing the 8 elliptical channels. Dimensions in mm.

The collector uses standard monocrystalline solar silicon cells with and efficiency of 19.7%. The cell string layout consists in 4 cells strings in the bottom and 4 in the top side of the receiver. This is shown in the figure below:

Figure 28: Receiver, showing 4 cell strings and its distribution in the receiver.

Each side of the receiver has 38 cells, and each receiver has 76 cells. Each collector has 152 cells. The dimension of each cell is 52 mm length, 156 mm height and 0.2 mm of thickness, with a nominal efficiency of 19.7%. The manufacturer obtains these cells by cutting standard size cells (156mm*156mm) into three pieces with the same size. The reasons for this is to reduce the current in the strings, which reduces the resistance losses, being that the losses in ribbons that connect the cells is particularly important for the performance.

Figure 29: Two images showing general aspects of the Solarus C-PVT technology 38

Systems Integration of the Solarus C-PVT
Solarus produces heat and electricity as therefore requires costumers that have a need for both. The simplest system in which a Solarus collector can be utilized is for example in a hotel using the heat to cover the DHW demand and feeding the electricity to the grid for a fee. Solarus is today focusing mainly in this market. However, other systems are possible. The figure below shows a system that can produce heat, cooling and electricity.

Figure 30: Sketch of a possible Solarus system proving heat, cooling and electricity to a household 38

Besides these three applications, the manufacturer is looking into options to provide three other applications: (i) steam; (ii) desalination; (iii) water purification.

Figure 31: Possible applications for the PC 38
PVT Market Overview

Consider to Include also large picture with comparison simulation done or exclude this table
This table could contain a summary of the information from the two large papers on PVT
Method Overview

A combination of complementary methods was used in order to answer the research questions.
The main method utilized was performance testing on a large array of different C-PVT collector prototypes that were built for this thesis. The collector testing results was complemented with three types of simulations:
Winsun in order to obtain the annual output;
Raytracing with Tonatiuh for characterizing the current reflector and comparing different reflector geometries;
LTSpice for analyzing the impact of different string layouts.

Additionally a market survey was conducted and a new ratio was defined as a way to compare different collectors.
Definition of the ratio between ST and PV
Although PV and ST produce different types of energy, they are often competing among themselves. This is not just because the investment capacity is limited as but also because of limitations in other factors such as the energy demand and roof space. Additionally, as mentioned in paper 1, “electricity can be converted into heat and vice-versa. However, electricity can be converted into heat at an efficiency of almost 100% while heat conversion into electricity has a much lower efficiency and requires more complex equipment”.
The previously described large climate variations around the world lead to significant differences in the performance of solar systems around the globe. Moreover, each type of solar system has a different response to these variations.
Therefore, it makes sense to develop a ratio that quantifies the difference in annual energy output between standard solar thermal collectors and PV panels for different locations. This ratio is useful, for example, to support the decision between installing ST or PV, when combined with other local specific information such as the value of heat and electricity for a specific location and application, the system complexity and efficiency, and even factors such as the knowledge of local installers knowledge or the available offer. This ratio was defined, as following:

Ratio Between ST and PV=(Annual Energy Output per m2 of ST collector)/(Annual Energy Output per m2 of PV panel) (eq. 3)

This ratio was calculated for the different solar systems based on the results obtained from a market analysis. Two types of PV panels were considered: average monocrystalline and polycrystalline panels. Two main types of ST panels were considered: Flat Plate and Vacuum Tube. Additionally, for ST collectors, the following collector average temperatures were investigated: 30ºC, 50ºC and 80ºC.
The annual energy outputs in the above ratio were obtained through Winsun simulations.
This ratio was then calculated and plotted on the world map for a clear visualization. The three above mentioned temperatures were plotted but only the middle temperature (50ºC) is shown since it was found to be the most relevant one.
Market survey
A detailed market survey was carried out to investigate the prices and standard panel characteristics for both PV and ST in January of 2014. The ST survey included a total of 90 collectors of 3 types: flat plate, vacuum tube with flat absorber, vacuum tube with round absorber. This survey comprised 43 companies in 16 countries. All collectors were tested according to the standard EN 12975 11 and an average was made.
The PV survey looked into 150 different PV panels from 35 companies of 9 countries.

Winsun Simulations
Winsun is a TRNSYS based solar simulation software that was developed by Bengt Perers and Björn Karlsson at Lund University. Winsun can simulate both the annual performance of an ST or PV panel. The inputs and outputs of the program are described in the figure below. A new collector file was made for Winsun based on the market survey findings regarding the standard collector characteristics per aperture area. The values for efficiency and heat losses were taken from the market study and are presented in the results. For all performed simulations, the collector was stationary at a tilt equal to the latitude of the selected city. Simulations were performed for 66 cities around the world in a range of different latitudes and climatic regions in order to obtain a good visualization of the variation of the ratio in the world map.

Figure 32: Winsun’s inputs and outputs 39 I

Winsun was used to simulate the performance of PV and ST panels over the year and provide the annual output per m2 of aperture area.

The following formulas are used by the winsun to calculate the annual output:
Q=?_0b?K_b (?)?G_b+?_0b?K_diffuse?G_d-U_1 (T_m-T_a )-U_2 (T_m-T_a )² (eq. 4)
K_b (?)=1-b_0?1/cos??(?)-1? (eq. 5)
Market Survey
The market studied, conducted in the first four months of the thesis in 2013, obtained the average performance values for solar thermal as described in the table below.

Table 3: Values for different T collectors expressed per absorber area, aperture area and gross area I
?0 (%) U1 (W/m²K) U2 (W/m²K) ?0 (%) U1 (W/m²K) U2 (W/m²K) ?0 (%) U1 (W/m²K) U2 (W/m²K)
Flat Plate 80,3 3,967 0,009 78,6 3,877 0,008 71,3 3,526 0,008
Vacuum with round absorber 74,1 2,088 0,009 64,4 1,809 0,008 39,9 1,117 0,005
Vacuum with flat absorber 82,0 1,626 0,004 74,0 1,468 0,003 54,9 1,085 0,003

A standard average efficiency was found for both polycrystalline and monocrystalline panels and is shown in the table below.
Table 4: Average efficiency for monocrystalline and polycrystalline modules I
Type of PV panel Efficiency
Monocrystalline 16,5%
Polycrystalline 14,6%

Finding out the price of the panels proved to be a more complex process than expected and some uncertainty lingered, as the price variations that were found were considerable large. The prices that our market survey found for PV were 15% lower than mentioned in the sites like PVXchange. ST prices were also found to vary substantially so a similar error margin exists. The following tables describe the prices that were found in the market study.

Table 5: Price of a ST collector in € per gross and aperture area I
Type of ST panel Flat Plate Vacuum Tube (Flat absorber) Relative difference
FP to VT
Sale with VAT (consumer) in €/m² gross 158 166 5%
Sale with VAT (consumer) in €/m² aperture 187 275 32%
Relative difference gross to aperture area 15% 40% –

Table 6: PV Price from cell to panel in €/Wp I
Type of PV panel Poly Mono Unit
Cell price 0,27 0,31 €/Wp
Panel sale price with VAT (consumer) 0,52 0,56 €/Wp
Price increase from cell to panel 1,93 1,81 –

Table 7: Price comparison PV to ST (including VAT) at consumer level in EU (custom cleared) I
Type of Solar panel Price €/m² aperture Comparison to Poly Comparison to VT
ST Flat Plate 187 179% 68%
ST Vacuum Tube with flat absorber 275 263% 100%
PV Polycrystalline 104 100% 38%
PV Monocrystalline 127 122% 46%

Winsun Simulations
The annual energy output ratio between PV and ST was calculated for the 66 cities.
For all locations and for a working temperature of 50ºC, the ST panel always produces more energy than PV. As expected, this is also true for a ST operating temperature of 30ºC but at an operating temperature of 80ºC, there were two locations of this study (in Russia and Norway) where the flat plates were performing worse than PV. Unlike flat plates, vacuum tube performed better than PV in all simulated locations and temperatures due to a lower heat loss factor. Additionally, around the world, vacuum tubes normally outperform flat plate collector per aperture area for temperatures of 50ºC and 80ºC. However, for a temperature of 30ºC, the flat plate is sometimes outperforming the vacuum tube with flat absorber, especially in warm locations. This is due to the fact that flat plates have 5% higher peak efficiency.

The ration between PV and ST ratio was then plotted on the world map for a clear visualization. Since the most commonly used ST temperature is 50ºC, only this temperature was plotted. This way, four world maps were created. All maps show how much more energy the ST produces comparing to PV. In general, the ratio increases when the latitude decreases. Some examples of this ratio are shown below for 3 cities at 3 different latitudes: close to the Equator, Tropic of Capricorn and Arctic Circle line.

Table 8: Irradiance (kWh/m2), panel outputs (kWh/m2) and ratios ST/PV I

As shown in the above table, the ratio between a flat plate working at 50ºC and a polycrystalline PV panels varies considerably around the world. In Nairobi, a flat plate will produce 3.7 times more energy than a PV panel with 14.6% efficiency while for Rio de Janeiro this ratio is 3.8. These two cities are an example that the ratio does not always increase when moving towards the equator. In Umea, the ratio is considerably lower at 2.6.

Each legend in the map has the same scale for the next four maps. The scale goes from green (stronger ST location) to blue (weaker ST location). The black color is an extreme case which only happens in very specific situations.

Figure 33: Ratio Flat plate 50°C to PV 14.6% polycrystalline I

The figure above shows the ratio between a flat plate collector working at an average temperature of 50°C and a polycrystalline module with an efficiency of 14.6%. The lowest ratio of 1.36 is found in figure 34 the coldest place with the highest latitude. On the opposite end, the city of Dijbouti at latitude of 12° reaches a ratio of 4.46 signaling a high over-performance of ST facing PV.
Singapore is an exception, since it has a considerably lower ratio than the other cities at similar latitudes. This is mostly caused by a long duration of a cloudy rain season, which also lowers the ratio of beam to total radiation as shown previously. All four maps show that for locations with high diffuse radiation or low ambient temperature, the ratio goes down which means that ST is producing less energy in comparison to the PV.

Figure 34: Ratio Flat plate 50°C to PV 16.4% monocrystalline I

Figure 34 shows the annual energy output ratio between a flat plate working at 50ºC and a monocrystalline PV with 16.4% of efficiency. The ratios above figure 34 are lower than in figure 33, since monocrystalline modules have a higher efficiency than the polycrystalline. The ratio from ST to mono is always around 88% of the ratio of ST to poly. This happens for both vacuum tubes and flat plates collectors.

Figure 35: Ratio Vacuum tube with flat absorber 50°C to PV 14.6% polycrystalline I

As expected, the ratio between vacuum tube with flat absorber and the poly modules show the highest ratio values in all four maps. For a ST working temperature of 50ºC, the highest ratio value was found to be 4.76 in Dijbouti, a city located close to the equator with a warm average temperature of 30°C.
The lowest ratio in Figure 35 is 3.06 which is considerably higher than the lowest ratio found in figure 33 that shows the ratio between flat plate and polycrystalline PV which is 1.54. This is mainly explained by the extremely low temperatures in this location combined with the fact that vacuum tubes have lower heat losses than standard flat plates. In between latitudes of 40ºN and 40ºS, all ratios on the map are above 4.2.

Figure 36: Ratio Vacuum tube with flat absorber 50°C to PV 16.4% monocrystalline I

From the four maps shown in the paper, figure 36 has the smallest variation between the highest and lowest ratio. This variation is 1.5. The highest ratio found was 4.21 which is lower than the highest ratio between flat plate to poly which is 4.46. In all maps, the lowest ratio is always Cape Zhelaniya (Russia) while the highest ratio of the graph is in Dijbouti.
A market survey was conducted that determined the average performance and price values for a few types of ST and PV panels. These performance values were then used to simulate the annual energy output of each type of panel. This was the basis for establishing a qualitative comparison between ST and PV panels, the annual energy output ratio. In order to facilitate the interpretation of those results, several world maps were drawn to graphically show the differences in annual energy production of the different solar technologies in different locations.
On a world scale, this ratio tends to increase at lower latitudes which is clearly visible in the four previous figures. This happens despite large variation being introduced by local climate. The higher ratios at low latitudes mean that ST panels are performing comparatively better than PV and the inverse for higher latitudes. Two main factors are responsible for this:
The efficiency of a PV panel is reduced with the increase of air temperature while in solar thermal the opposite effect takes place.
Under low intensity solar irradiance, the efficiency of a PV panel is maintained while a solar thermal collector might not reach the required operating temperatures and have an output of zero.
The ratio maps allow reaching the following conclusions:
For all locations and for a working temperature of 50ºC, the ST panel always produces more energy than PV.
Around the world, vacuum tubes with flat absorber normally outperform flat plate collectors per aperture area for temperatures of 50ºC and 80ºC. However, the price per aperture area of vacuum tube with flat absorber is also 32% higher than flat plate. This means that, assuming that the installation cost is the same for both ST technologies, vacuum tubes should be preferred only, if its annual output is higher than a flat plate annual output by 32%.
For a temperature of 30ºC, the flat plate is sometimes outperforming the vacuum tube with flat absorber, namely in warm locations.
All four maps show that for locations with high diffuse radiation or low ambient temperature, the ratio goes down meaning that ST is producing less energy in relation to the PV.
For latitudes lower than 66º, the ratio flat plate at 50ºC to PV is ranging from 1,85 to 4,46 while in the ration between vacuum tube at 50ºC and PV from 3,05 to 4,76. These numbers can be an important tool when making the decision of going for PV or ST. However, it is important not to forget that dimensioning ST installations so that all the energy is utilized is key in generating good revenue from projects.
The ratio was also calculated for ST operating temperatures of 30ºC and 80ºC. As expected, the ratio goes up for 30ºC (meaning that it is more favorable to ST) and goes down for 80ºC (meaning that it is less favorable for ST).
The ratio for ST to monocrystalline is always around 88% of the ratio of ST to poly. This happens for both vacuum tubes and flat plate collectors.
Collector testing
Testing is an essential step in order to be able to evaluate solar collectors. This section describes the different collector prototypes that were tested as well as the equipment at the different locations where the collectors were tested and the tests that were conducted at each location.
Collector Testing Method
Key thermal parameters to test in a low concentration C-PVT
Solar collector characterization relies on two main testing methodologies: Quasi Dynamic Testing (QDT) and Steady State (SS). During this thesis, both methods were used to characterize the different prototypes that were tested.
According to Petterson et al 40, QDT method offers the following advantages over SS:
“It allows for accurate characterization of a wide range of collector types;
It allows for testing under a wide range of operating and ambient conditions;
It gives a more complete characterization of the collector through an extended parameter set as compared to steady state testing.”

However according to Afonso el al 41, “applying QDT can be difficult in other locations where the weather is very stable or where diffuse fractions are constantly very low”.
Other sources such as Fisher et al 42 or Carvalho et al 43 et al concur with the above statements.

In the QDT method some of the boundary conditions parameters are kept strictly steady (flow rate and inlet temperature), while other parameters are left freely dynamic with only minor limit constraints. Paper XXII utilizes QDT to characterize a standard flat plate thermal collector and the Solarus C-PVT. The equation utilized was adapted from the ISO 9806:2013 and is detailed below:
Q ?/A=F^’ (??) K_?b (?_L,?_T ) G_b+F^’ (??) K_?d G_d-C_1 (t_m-t_a )-C_2 (t_m-t_a )^2 (eq. 1)
-C_3 u(t_m-t_a )+C_4 (E_L-?T_a^4 )-C_5 (dt_m)/dt-C_6 uG

The required input parameters for a successful characterization using the above formula are:
Total irradiation; beam irradiation fraction; diffuse irradiation fraction; mean temperature of the collector; ambient temperature; wind speed; long wave irradiation; mean collector temperature change over time; and the power output of the collector.
For the case of glazed collectors, however, it is often recommended that the wind speed and the long wave radiation are omitted since their impact on the absolute losses and gains is negligible. In paper XXII, two of the input parameters have been kept steady throughout the testing, the flow rate and the inlet fluid temperature, while the rest were allowed to change freely.
The tool used for the parameter identification is the Multiple Liner Regression (MLR), this statistical model identifies the equation factors that best describe the collector based on how closely the produced equation can reproduce the collector power output accurately.

The following list summarizes the main terms commonly used to define a solar thermal collector:
F´(??): zero loss efficiency of the collector for beam radiation, at normal incidence angle;
K?b(?L,?T): incidence angle modifier for beam solar radiation. K?b varies with the incidence angles ?L, and ?T;
K?d: incidence angle modifier for diffuse solar radiation;
c1 : heat loss coefficient at (tm – ta) = 0 (also mentioned as U1 in literature) ;
c2 : temperature dependence in the heat loss coefficient (also mentioned as U2 in literature);
c3 : wind speed dependence of the heat losses;
c4 : long wave irradiance dependence of the heat losses;
c5 : effective thermal capacitance;
c6 : wind dependence of the collector zero loss efficiency;

SS testing, on the other hand, keeps all parameters in steady state under a narrow range. The Elforsk report 44 utilizes the SS method to characterize the first C-PVT prototype built by Solarus which was tested by the author at Lund University. The following formula was used to obtain the thermal power from the measured collector:

P = (Tout – Tin) * Specific heat of water (Cp) * Density of water (?) * Flow / Area of collector (eq. 2)

An important number for collectors is the stagnation temperature. Stagnation temperature is often defined, as the temperature reached by the solar thermal collector under no flow, 1000W/m2 of solar radiation and ambient temperature of 40°C. At stagnation, all incoming solar radiation becomes heat losses from the collector. This number is often used to define the heat resistance properties that the solar collector must possess in order to survive stagnation. Stagnation commonly occurs after the malfunctioning of a pump or controller in a solar thermal system during a sunny day.

Key electrical parameters to test in a low concentration C-PVT
The most important electrical parameter to describe a PV panel are peak power (Pmp). Cell temperature dependence is usually given by the manufacturers but it can also be measured. Parameters such as short circuit current (Isc), maximum power current (Imp), maximum power voltage (Vmp) or open current voltage (Voc) are also important. As of 2018, common peak power of a silicone module range between 200 to 350W for an area of 1.6m2. The cell temperature dependence characterizes the variation in power, efficiency, current or voltage that a solar cell or PV panel undergoes with the change of temperature. For efficiency, in a silicone solar cell, this coefficient often ranges +0.3 to 0.5%/°K 18.
Both the standard for flat PV panels (IEC 61215) and the standard for concentrated panels (IEC 62108), specify that peak power of a PV panel must be measured at Standard Test Conditions (STC) which are defined as ambient temperature of 25°C, 1000W/m2 of solar radiation, air mass of 1.5 and no wind speed.
These tests are generally performed outside but they can also be done in a solar simulator. However, it is difficult to accurately simulate the solar spectrum since the sun is a very distant mass at a very high temperature.

Incidence angle modifier
The incidence angle modifier (IAM) is a key parameter to define for any stationary collector but it is especially important for concentrating collectors and even more relevant for stationary asymmetric concentrating collectors, as the Solarus Power Collector.
According to Carvalho et al 43, for standard flat plate solar thermal collector, the IAM is commonly defined by the following equation:

K?b(?) = 1 – b0 ((1/cos ?i) – 1) (eq. 2)

As mentioned above, other collectors such as vacuum tubers or stationary concentrating collectors have more complex IAM profiles that need to be characterized with additional detail. A common resolution for IAM testing is 5° steps. Namely, the Solarus C-PVT has specific characteristics that are important to considering when measuring the IAM.
The IAM can be electrical or thermal. In order to measure the IAM, the collector´s electrical or thermal power is measured at different incidence angle, while making sure that the irradiation and the cell temperature remain constant. For the thermal IAM, the measurements must be spaced out in time to account for the thermal mass.
Further details on the measuring methods of the IAM are given in chapter 5.3.2 and in paper VII.
Calculation of the theoretical maximum electrical power

This chapter presents a theoretical calculation of the maximum electrical power of the collector. The calculations below represent an improvement over the calculations done in paper VII by adding further information like the transparency of silicone or the average number of bounces:
P_(electric_max)=P_(electric_top_max)+P_(electric_bottom_max) (eq. 2)
P_(electric_max)=110.5+159= 269.5 W

P_(electric_top_max)=A_(cells_top)×?_silicone×?_glass×?_(cells_(25°C))×G_max (eq. 2)
P_(electric_top_max)=110.5 W

P_(electric_bottom_max)=P_(electric_bottom_beam)+P_(electric_bottom_diffuse) (eq. 2)
P_(electric_max)=149.2+9.8=159 W

P_(el_bot_beam)=C× A_(cells_bot)×?_silicone×?_glass×(r_ref ×avg_(bounce)) ×?_(cells_(25°C))×G_b (eq. 2)
P_(electric_bottom_beam)=149.2 W

P_(el_bot_dif)=C ×1/C × A_(cells_bot)×?_silicone×?_glass×(r_ref ×avg_(bounce)) ×?_(cells_(25°C))×G_dif
(eq. 2)
P_(electric_bottom_diffuse)=1.7× 1/1.7 × 0.617×0.97×0.945×0.883×0.197×100
P_(electric_bottom_diffuse)=9.8 W

List of the different versions that have been tested

Within this thesis, a large number of prototype was tested. The table below lists the most relevant prototypes that were tested and gives a description of the key differences between them.


Table 9: Collectors tested during this thesis

Testing at Lund University
This section summarizes the testing of the first ever version of the Solarus C-PVT as well as a comparison to a stationary concentrating thermal collector also from Solarus. A full description can be found on the Elforsk report 44. Throughout this thesis, this prototype version will be named as V1.

Description of the prototype collector
The figure below describes the V1 prototype C-PVT collector that was tested.

Figure 37: Side and front views of the first Solarus C-PVT Prototype (V0) installed at Lund University

The glazed area of this prototype was 2.3 m2, which is a significant difference to the current version (PC). Effective solar thermal area was 2.18 m2.
Each receiver had 26 solar cell on each side. Each cell had the dimensions of 0.07 * 0.145 mm. This means that a string of 26 cells has 0.264 m2. The total cell area of the two receivers in the above figure totals: 4 * 0.264 = 1.06 m2. The effective glass area for electricity production equals 2 * 3 * 0.264 = 1.58 m2. The cells were soldered manually. Manual soldering causes more micro cracks than machine soldering.
The backside and the front side PV cells were connected in parallel. The top and the bottom receiver sides were also connected between themselves in parallel.
The geometric concentration factor of this reflector design is 3, however since there are solar cells on the front and back of the absorber the real concentration factor was 1.5. Concentration ratio for the front is 1, while the cells on the back receive 2 suns.

Figure 38: Four Solarus stationary concentrating thermal collectors installed at Lund University

Four Solarus stationary concentrating thermal collectors were utilized as a comparison point to the C-PVT prototype and are thus named reference collectors. Both the reference and the C-PVT collector have the same of the box with the same reflector geometry as well as glazed area. The absorber of the reference collector has selective surface on both side and was produced by the company Sunstrip.


Testing was conducted at the solar laboratory of Lund University. The main testing period was between 7th of May to 30th of May. Collector tilt was set 30° for both C-PVT and reference thermal collectors.

Thermal Testing:
The thermal testing method was SS, which was described in the previous chapter. The flow was set to 11 l/6m = 3.12 * 10-5 m3/s and kept constant throughout the full duration of the tests.

In order to produce the thermal efficiency curves, it was necessary to select two periods that are fully sunny days without any clouds so that the solar radiation remains constant. Additionally, these two periods have to be large enough to ensure that a thermal equilibrium point has been reached.
In each of these two days, the collector was supplied with pure water at a steady temperature with a variation no larger than 0.5°C. On the 20th of May, the collector was stable at low temperature (25°C) while, on the 26th of May, at a higher temperature (45°C). The following two graphs show that the global radiation remained very stable for the periods utilized for the thermal efficiency graphs.

Figure 39: Global Solar Irradiance for the two measurement points of the thermal efficiency

Furthermore, an extra measurement was taken which was the night values for power at high and low inlet water temperatures. These measurement is a common technique for estimating the U-value of a collector, since the U-value is equal to the slope of the curve.

Electrical Testing:
The C-PVT V1 has two receivers as shown in the previous figure. On the bottom receiver, the measured values were for both the back side and the front side simultaneously. On the top receiver, the cables were reconnected in order to allowed performing individual measurements to just the backside or just the front side.
IV curves were continuously measured and recorded in a CR1000 logger. With each IV curve, Pmax, Isc, Imp, FF, Vmp and Voc were stored. These values were averaged for every 6 minute period.


Thermal efficiency curves:
Using the two best periods, it was possible to obtain the following thermal efficiency graphs. These results are displayed in the figures below.

Figure 40: Thermal Efficiency for the Solarus C-PVT V1 and reference thermal at I>900W/m2

Night heat loss measurements:

The following figures were made based on all available night values and they allow estimating the U-value.
Figure 41: Heat loss measurement during night time for the C-PVT V1 and for the reference thermal

From the above figures, it is possible to extract the optical efficiency of both collectors and the global heat loss coefficient (U-value). As expected, the optical efficiencies of both collectors were identical but there was a large difference in heat losses, which are particularly visible at higher temperatures.
It is relevant to note again that the only difference between both collectors is the receiver. However while, V1 C-PVT possesses a non-selective string of PV cells encapsulated on a reflective aluminum receiver, the reference collector has a black selective absorber that greatly reduces the radiation heat losses. This is the reason for the reference collector about half of the U-value of the C-PVT V1.

Table 10: Optical efficiency and measured heat losses of tested collectors
Reference Thermal Collector V1 of C-PVT
Optical Efficiency (%) 59.1 58.7
Global (day) U-value (W/m2, K) 2.92 5.19
Night U-value (W/m2, K) 2.25 4.22

Daily Thermal Power Curves:
The figure below shows the daily output and the mean fluid temperature of the reference thermal collector and the Solarus C-PVT V1 as well the global radiation.

Figure 42: Global Radiation and average collector temperature plus power output for the Reference and V1 collector on 17th and 26th of May

Daily Electrical Power Curve:

A large number of electrical measurements have been performed and analyzed.

Figure 43: Electrical power from the front and back side of the V1 collector during a clear day with high fraction of beam irradiance.

The IV-curves in the figure above show that the front cells are working as expected at midday:
? = 45 / (1000 * 0.264) = 17.1%
The output of the backside is low at solar noon and decreases rapidly outside of this period. The efficiency in the middle of the day is:
? = 32.5 / (2 * 1000 * 0.264) = 6.2%
In order to calculate the efficiency of the backside cells, it is important to take into account the backside concentration of 2. The low efficiency at solar noon is due to optical losses in the reflector and uneven lighting. Outside of solar noon, falls rapidly outside of the side gables cast a shadow on the outermost cells which causes the whole string to stop working since the cells are series connected between themselves.
An analysis of the IV curves of the front cells results in a fill factor of 75%. This indicates that the absorber is able to successfully cool the cells. However the IV-curve for the backside cells at 12:24 when there is no shading due to the side gables results in a fill factor of 60%. The lower fill factor should be a result of uneven illumination of the cells. The focus line of an ideal reflector creates a varying irradiation over the cells but with the same overall irradiation on each cells. However, in reality, reflectors are not ideal and, thus, create different overall irradiation of the cells. Both these effects reduce the fill factor. The varying total irradiation between the cells has the greatest negative ie pact on the fill factor and performance. In addition, it is likely that the current capacity of the backside cells is reducing the backside output due to resistivity losses.

Solarus C-PVT V1 has been tested. Thermal performance has been quantified and compared to a reference thermal collector. Overall optical efficiency of both collectors are relatively low however the heat loss factor is also low. As expected, the optical efficiencies of both collectors are similar but the heat losses have a significant difference due to the lack of selective surface on the C-PVT V1. The higher heat losses will lead to a lower stagnation temperature, which in turn improves survivability and reduces material requirements. Due to the heat losses, the V1 collector is best suited for low to medium temperature applications. The V1 receiver also seems to have a higher inertia since its thermal power output tends to drop slower during the afternoon. Electrical measurements show the front side cells are working well which indicates that the receiver is able to successfully cool down the cells. Reflector losses and high current in the cells dictates a low peak power for the backside cells. Furthermore, the side shade from the gable has a very large impact on the daily power collector and needs to be prevented. Either some cells are removed for the edge of the strings or diodes are placed to bypass these cells outside of peak sun.
Lastly, the packing density should be increased to maximize the total electricity output.

Paper VII: Testing at Eduardo Mondlane University
Together with colleagues from Lund University, the author has built from scratch a solar laboratory at Eduardo Mondlane University, in Maputo the capital of Mozambique. The construction of this solar laboratory is described in full detail in papers X and XII. The testing results from this laboratory are described in its fullest extent in paper VII and in report 45.
Description of the prototype collector and laboratory set-up
As a part of a project funded by the Swedish International Development Agency (SIDA) and the Gulbenkian foundation of Portugal, a small solar laboratory was constructed. The equipment installed at this laboratory is described in detail in paper XII and summarized below:
1) Data Loggers:
a) Campbell CR1000 DataLogger. Analog, digital and pulse inputs are suitable for the adopted scientific data logger. For the mean voltage input range ±2.5V, maxi-mum resolution is 0.67 mV and measurable through up to 16 single-ended ports. High accuracy, versatility and reliability allowed this product to be spread worldwide for scientific application. The price is approximately 1500 USD.
b) MELACS®. It enables stand alone data logging and remote collection through the built in web server. Connection of multiple loggers (e.g. to increase the number of ports) is possible through the Ethernet port. Voltage input range is fixed to ±3.3V, corresponding to 0.8 mV of resolution and measurable through 8 channels. Pulse and digital channels are also available. It works with open source GPL software. Current price is about 260 USD.
2) Water temperature sensors:
a) PT100 Class A. High precision temperature measurements were carried out through a PT100 sensor with immersed insert. The Class A definition guarantees the accuracy of ?T=±(0.15+0.002·|T|), where |T| is the absolute temperature in °C. Pentronic AB was the chosen manufacturer, which supplied and tested 30 sensors according to EN10204. In order to have similar offset in measurements, the two PT100 with closer response during the test were chosen for the ?T measurements. Despite the benefit of fluid immersed measurement, appropriate plumbing adaptation is required as show in the figure below. Adaptors are rather expensive, approximately 60 USD.
b) LM35CZ. LM35CZ are precision integrated-circuit temperature sensors produced by National Semiconduc-tor Corporation. Voltage output is linearly proportional to Celsius temperature with 0 mV as set point for 0°C and +10.0 mV/°C scale factor; nonlinearity typically below ±1.4°C is guaranteed over the full range of 55-150°C. Accuracy is ±0.4°C, hence ±4 mV, at 25°C, up to a typical value of ±0.8°C in extreme conditions. The price is of approximately 5 USD each. Copper paste on the surface and good insulation around the pipe must be carefully provided to have good thermal contact and low heat losses. Indeed, the sensor could record the air temperature in the proximity of the pipe instead of the pipe surface temperature as shown the figure below. Since the device is not specifically designed for water temperature measurements, it can be successfully used for other applications.

Figure 44: Sensor positioning for PT100 (left) and LM35 (right)

3) Solar radiation:
a) Kipp&Zonen CMP 11. Scientific pyranometer calibrated after purchase according to the technical regulations of World Meteorological Institute. Estimated combined expanded uncertainty for the used device is ±1.4%, corresponding to 8.67 ?V/W/m2 of sensitivity at normal incidence on horizontal pyranometer. Commercial price is about 4,000 USD.
b) Finsun SRS1000. Basic pyranometer with sensing element made of single crystal Si-cell. The output voltage is 100 mV when exposed to 1000 W/m2 solar radiation. Sensitivity, offset and ageing tests were performed. Commercial price is approximately 115 USD.
4) Flow meter.
Kamstrup 10EVL-MP110 energy and flow meter was adopted. No cheaper flow meter was tested.
5) Concentrating thermal (reference) and C-PVT collectors. It is important to mention that this version of the C-PVT solar collector is named V1 in this thesis.
6) Solar tracker. A horizontal single axis tracker (HSAT) was installed. The tracker is based on an engine driven by Melacs® logger. The software controls the position of solar panels using time and location as input. This solution allows a correct positioning without the use of additional photodiodes-based trackers, thus cutting costs and maintenance.
7) IV tracer. The IV tracer used had the capacity to perform IV curves with the limits of 30V and 10A.

The following figures show several aspects of the equipment of the solar lab such as the solar tracker, the two installed collectors, the tank, the pump, the logger, the flowmeter, the MELACS loggers, and more, as well as the set-up for both the longitudinal and transversal IAM measurements:

Figure 45: The C-T and C-PVT solar collectors installed in the solar tracker (left) and the some of the installation equipment such as computers, CR1000, two MELACS units,flowmeter, expansion valve, pump and tank.
Figure 46: The collectors installed for the transversal IAM measurements (left) and the team celebrating the success of the longitudinal IAM measurements (right)

Figure 47: Detailed view of the C-PVT V1 and the pyranometers

The figure below describes the electrical arrangement of the solar cells PVT V1:

Figure 48: Electrical diagram of the PVT V1

The below shows the areas used to calculate the efficiency of the collector.
Table 10: Different areas used to calculate the efficiency of PVT V1
Acells of one receiver (m2) 0.577
Aeffective reflector electrical (m2) 0.869
Effective Concentration Factor (-) 1.506

As discussed previously in chapter 5.1, there are a number of factors that influence the performance of a C-PVT solar collector. Due to this, performance measurements should be conducted in a specific order. The first step was to determine the efficiency of the solar cells and its relation to the temperature of the working fluid. This test was performed in an incidence angle that maximizes the electrical output, i.e. close to normal incidence, but not normal, due to the asymmetric curvature of the reflector. Once the temperature dependence was determined, the angular dependence or, more accurately, the incidence angle modifier could be measured.
Normally, it is expected that an electric load is permanently connected to the PV cells and electric power is continuously extracted at maximum power point. However, the presented method of instantaneous IV curve measurements simplifies the whole test procedure. These results are less expensive and less time consuming to achieve while still maintaining a good level of accuracy. If an electric load were continuously connected, the absorber would be colder since a part of the incoming radiation would be converted to electricity. This would mean lower temperatures and thus slightly lower thermal losses. This difference is however small and has little impact on the results 46. Since the cell is encapsulated in silicone, it was not possible to measure the cell temperature directly. Instead, the temperature of the outlet water was measured. In a series connected string, the cell producing the lowest output will be limiting the string output. In general, the warmest cell tends to be the cell with the lowest output, however, this may not always be the case, as there are efficiency differences between each cell due to the production process.

Incidence Angle Modifier testing method:
As mentioned previously, the transverse incidence angle modifier (IAMt) is defined by the reduction in electrical efficiency for a given irradiation caused by the increase of the incidence angle between the sun and the normal to the collector in the transverse direction (?t). This is exemplified in figure below. From 0° to +90° the sun’s direction is inside the acceptance angle of the reflector and outside from 0° to -90°. However, the front part of the receiver accepts light coming in from-90° to 90°. The IAM measurements are a combination of all angular effects such as decrease of transmission in the glazing for high incidence angles and shading effects by edges, etc.

Figure 49: Transversal incidence angle to the left and longitudinal incidence angle to the right

To be able to measure IAMt for different transverse angles the longitudinal angle had to be kept equal to zero. This was measured by facing the collector towards the solar azimuth for various tilt angles. This is illustrated below:
Figure 50: Tilting the collector to achieve different transverse incidence angles

The incidence angle modifier is applied for the direct radiation only. However, even during clear days, there is always a percentage of diffuse light that contributes to the measured power output, and while, in a clear day, this percentage can be around 10%, in less sunny days, this percentage can reach 100%. This way, the diffuse contribution becomes relevant for low concentrating collectors such as this one.
The fraction of useful diffuse radiation for a concentrating collector, relative to the total diffuse radiation on the glazed cover of the collector is described in the figure below. The pyranometer, labelled as (A), will see ((1+cos?(?)))?2 of the full sky. This is the same as for the front side of the receiver which is labelled (B). They thus see the same part of the diffuse sky and it would be a correct assumption when a non-concentrating collector is tested. This is however not the case for the backside of the receiver. The acceptance angle for the reflector blocks a substantial part of the sky. This part is indicated with red arrows. The radiation that will reach the backside of the receiver is labelled (C), and is equal to the radiation measured by the pyranometer minus half the sky due to the acceptance angle. This is true for a positive tilt, i.e. the left collector shown in the figure below. The collector on the right hand side of the figure shows the case for tilting the reflector backwards. The pyranometer (D) and the front side (E) of the receiver are unaffected. However, the backside radiation (F) will be half of the sky as long as the tilt ? is less than 90°. This happens since the part outside the acceptance angle is now facing the ground. Thus, the part of the diffuse radiation inside the acceptance angle is always half of the sky.

Figure 51: Fraction of useful diffuse radiation for different transverse incidence angles

The fraction, f, of the diffuse radiation that is useful for the collector can be calculated by summing the contributions from the front side and the backside of the receiver and dividing this by the diffuse radiation measured by the diffuse pyranometer. The front side of the receiver accounts for one third of the total glazed area while the backside, via the reflector, accounts for two thirds of the total glazed area. If the collector is rotated as in the left side of the above figure f will be:
f=(1/3 ((1+cos?(?))/2)+2/3((1+cos?(?))/2-1/2))/(((1+cos?(?))/2) ) (eq 1)
If the collector is rotated as in the right side of the above figure f will be:
f=(1/3 ((1+cos?(?))/2)+2/3(1/2))/(((1+cos?(?))/2) ) (eq 2)
However, this is true for an infinitely long trough without any shading from the edges. This is not the case for the investigated collector. The front side of the receiver will be only slightly affected by shading and the shading effect is thus omitted. The shading of the backside will be more relevant. This is illustrated to the right in Figure 51.

Figure 52: Shading of the PV cells due to the gables of the collector

The black arrows hit the edge cells while the red arrows miss the cell. The arrow labelled 1, close to normal incidence will be reflected to the outermost PV cell. So will all rays coming from an even lower angle, e.g. rays labelled 2 and 3. For radiation with a higher incidence angle, the rays will be either reflected to hit another cell or will be stopped by the edges. This means that the outermost cell can only see roughly half of the diffuse sky. The problem is identical for the left side of the collector. This will reduce the contribution from radiation to the backside of the receiver, i.e. (C) and (F) in Figure 50 by approximately 50%. This will change equation (1) and equation (2) to:
f=(1/3 ((1+cos?(?))/2) (+2/3((1+cos?(?))/2-1/2))?2)/(((1+cos?(?))/2) )=(1+2cos?(?))/(3(1+cos?(?))) (eq 3) (3)
f=(1/3 ((1+cos?(?))/2)+(2/3(1/2))?2)/(((1+cos?(?))/2) )=(2+cos?(?))/(3(1+cos?(?))) (eq 4)

Measurements of the IAMt were carried out by varying the tilt ? from -30° to +30° as shown in Figure 49 and Figure 50. Figure 52 shows a plot of equation (3) and equation (4). The variation in the fraction of the useful diffuse radiation is small for this tilt interval. Hence, the fraction of useful diffuse radiation was set to be the average of its value and equal to 50%.

Figure 53: The fraction of useful diffuse radiation as a function of the collector tilt

The longitudinal incidence angle modifier (IAMl.) was measured while keeping a constant ?t which corresponds to the measured maximum value of IAMt.
The figure below shows the measured electrical efficiency per cell area for the V1 PVT collector at 25°C, which is 20.9%. Expressed per active glazed area this efficiency is 13.9%. This means that the maximum electrical power for a collector is 241 W or 139 W/m2 active glazed area. As expected, this number is 11% lower than the optimum output of 269.5 W for a perfect optical efficiency.
The dependence of electrical efficiency on temperature (KT) is -0.41%/K, which in good agreement with values commonly described in literature 18.

Figure 54: Dependence of the electrical efficiency on temperature

The next figure shows the electrical transverse and longitudinal incidence angle modifiers for the beam radiation, IAMt in blue and IAMl in red. The measured values are adjusted for temperature variations. The sharp increase/decrease around 0° for the IAMt is due to the radiation shifting from outside to inside of the acceptance angle. The IAMl for the front side and backside receivers is shown in yellow and green respectively. The figure shows that the front side receiver behaves very similarly to a flat plate solar panel. The backside receiver is the main responsible for the efficiency drop during low incidence angles in the longitudinal direction due to the series connection of the cells.

Figure 55: Electrical transverse incidence angle modifier (IAMt) for beam radiation in blue and the longitudinal incidence angle modifier (IAMl) in red. The IAMl for the backside and the front side of the receiver are shown in yellow and green respectively.

By examining the figure, it is possible to conclude that, if the collector was tracking the sun around an axis aligned in the East-West direction, it should maintain the projected solar height over the day close to 10° in order to maximize the annual output. The drop in the longitudinal incidence angle modifier is due to the shading caused by the reflector edges. When 0°