Furthermore, the impact of height in system efficiency for the 3DPV is remarkable Aglietti et al. Some of the research carried out on this technology is briefly discussed in this paper. According to the Massachusetts Institute of Technology Myers et al.
The optimum shape of the 3D structures was derived using computer simulations such as genetic algorithms for optimising the generated output energy. These 3D structures include a cubic box open at the top, a funnel-shaped cubic box, a sphere, a parallelepiped, or any other 3D shape that in principle is found capable of doubling the daily energy density.
The 3DPV structures were found to lessen some of the variability inherent in solar PV as they provide a more regular source of solar energy generation at all latitudes. They are found capable of doubling the number of peak power generation hours as they intensely reduce the seasonal, latitude and weather variations of solar energy generation when compared to a flat panel design Bernardi et al. The 3DPV technology by Fibonacci number method involves the arrangement of the individual solar cells of the three-dimensional PV module in a leaf-like manner.
The arrangement revealed that such a modular design has the benefits of having each solar cell receive the reflected light from the other cells, thereby maximising power generation per installation area Myers et al.
Another research group carried out a test on a 3DPV module whose configuration was based on Fibonacci numbers Suzumoto et al. The simulation results revealed that the power generation characteristics of the solar cells depend on the shape and spacing of the solar cells for the most effective use of sunlight energy. Accurate 3D technology was found to enable innovative and improved device design, which can result in overall cost effectiveness, improved material processing and system utilisation Gharghi et al.
Of particular interest is the spherical silicon solar technology, which was found to be attractive, ideal and quite inexpensive. It utilises low-cost silicon feedstock for its fabrication process, which is found to be simple and inexpensive Gharghi et al. In addition, self-supporting 3D shapes are discovered to create new schemes for PV installation and increase energy density that can facilitate the use of inexpensive thin film materials in area-limited applications. Hence, harnessing solar energy in three dimensions can open new avenues towards Terawatt-scale generation Bernardi et al.
In recent years, much progress has been made in developing PV that can potentially be mass deployed Fan et al. An example is 3D nanopillar-based cell modules which were used for the purpose of reducing solar cell cost by utilising novel device structures and materials processing to yield acceptable efficiencies.
In this regard, the highly regular, single-crystalline nanopillar arrays of optically active semiconductors are directly grown on aluminium substrates, which are configured as solar modules. The cadmium sulphide cell CdS and cadmium telluride cell CdTe are chemically different semiconductors with different bandgaps and doping or conductivity type. The prefix n or p attached to each semiconductor indicates the type of doping that is given to it, or it indicates its conductivity type Green, Various experiments and modelling exercises proved the potency arising from the geometric configuration of this approach to enable enhanced carrier collection efficiency on both rigid and flexible substrates of the highly versatile nanopillars solar modules Fan et al.
Effect of height in the Fibonacci method of 3DPV generation. The Fibonacci method of PV module FPM installation utilises numbers to attain the height spacing for volumetric adsorption of solar irradiation to optimise solar power generation in an area Suto and Yachi, , Yuji and Yachi, , Seiji Suzumoto1, The manifestations of the Fibonacci numbers and the golden ratio are apparently endless and can be found throughout nature in the form and designs of many plants and animals Grigas, ; Koshy, The Fibonacci sequence can be perceived in nature in the spirals of a sunflower's seeds and the shape of a snail's shell Grigas, These numbers have also long been used in various manners in architecture, art and music as well as medicine, science and engineering.
In particular, the numbers are widely used in engineering applications including computer data structures and sorting algorithms, financial engineering, audio compression, architectural engineering and solar energy application Zou et al. The numbers highlight the order and mathematical complexity of the natural world Grigas, In a similar fashion, a mass of silicon with an expanded surface can absorb the solar radiation in layers of its crystallised molecules Grigas, Conversely, the leaves are not usually arranged on a flat surface, but spread through the whole volume of a plant.
This is analogous to the reason why trees tend to grow vertically - to access most of the solar rays in a given volume. Solar panels can be arranged in a similar fashion and the solar energy considered in terms of Watt-hours per unit volume. To install PV panels on a tall structure is, however more time-consuming and costly than laying them on the ground Yahyavi et al. However, depending on the price of land, arranging the solar equipment on a raised structure could be more cost-effective.
Another advantage of a vertical arrangement is the possibility of rotating Fibonacci solar panels in order to track the sun for a higher efficiency Aglietti et al. The solar-powered tree of about 0. It is 7 m tall and has 27 leaves, each producing power. Many parameters determine the intensity of solar radiation, including latitude, season, altitude, geographical conditions, atmospheric pressure, humidity, time of day, and some other extra-terrestrial effects such as solar storms. On a clear day, the intensity of solar radiation is at its maximum around noon and decreases towards dusk Bernardi et al.
The thesis of this paper is that the long-range solution to the energy woes of the world does not lie in any one particular approach and that several avenu. Solar Photovoltaic (PV) energy conversion system has drawn the tremendous attention of researchers in the past recent years. This paper present an overview of the research going on in this area, focused on aspects mentioned above.
However, the 3DPV structure was found to nearly double the number of peak hours available for solar energy generation and provide a measured increase in the energy density by a factor of about without the use of sun-tracking in cloudy weather Myers et al. The solar radiation received on the surface of the material is proportional to the power absorbed in the entire volume of the 3DPV structure.
Mathematically, the material surface is two-dimensional, while the physical objects are three-dimensional Yahyavi et al. For energy per unit volume consideration, it is assumed that some solar collectors are effectively arranged within any three dimensional structure such as a cube with arbitrary dimensions f , g , h facing northerly with the x , y , z-axes Myers et al. Hence, the cube volume, V, is also considered as a vector V with three assigned components, as in Equation These components are assumed to be proportional to the cube's three faces on which the solar beams radiate on the top, front and east or west at any given time.
The solar irradiance is considered a vector with variable components proportional to the absolute values of x , y , z components.
Hence, solar power, P , going into the cube as indicated earlier can be extended and interpreted as the scalar product of the volume and irradiance vectors. In order to analyse the energy absorbed by the cube, this investigation considered the cube volume and the vector components of the surfaces as shown in Figure 3 , with dimensions f , g , h standing northwest with the x , y , z - axes.
As stated in section 4, the cube volume, V, was considered a vector V , with three components as given in Equation 1. These components of the volume vector were exposed to the solar beam radiation. It was also considered that the solar irradiance is also a vector, with variable components proportional to the absolute values of x, y, z given by Equation 1. The implication of this would be that the solar power going into the cube of a solar tree can be expressed as a scalar product. Total power is the vectorial sum of the components as shown by Equation The module of irradiance for Durban is assumed here as 0.
This is specified by the three components, including Equation 5. The average value of available solar power obtained within the volume is the scalar product of volume vector V and module of irradiance, M as indicated in Equation Hence, Equation 7 with its associated components and Equation 8 are derived. This was found useful in the optimisation computations carried out on these two different solar panels installation configurations. A solar power system can be more efficient depending on how it collects solar energy.
In order to determine the solar irradiance in volume, it was assumed the solar panel was effectively arranged within a cube as shown in Figure 4. From Equation 4, more energy could enter a volume as compared with entering through a surface such that:. The main concept of measuring energy per unit volume is that solar collectors get more irradiance when elevated from the horizontal position as shown in Figure 5 to the vertical position as shown in Figure 4. The solar cell efficiency depends on the collectivity factor c, defined as the ratio of the collected solar energy to the maximum solar energy available in an effective volume occupied by the solar system installed in an area and at a certain height.
The amount of solar energy generated is a function of the collectivity factor and this was found to be in direct proportion with height. In this investigation, computation of solar energy in 2D and 3D was made with comparison between the results obtained on the power Watts generated with the tree-level arrangement 3D in Figure 4 and power Watts generated by its equivalent coplaner arrangement 2D in Figure 5 and the data was made using Matlab program, version Rb. Analysis of results is presented according to Figures 6 , 7 and 8.
In order to estimate the effect of height, the solar panel was configured in 3D and a 10 kW solar array was assumed for the multilevel fixed structure as shown in Figure 4. The index of the real dimensions of the occupied space by the PV panel n was assumed to be 2. From Equation 5, the modules of irradiance of the solar radiation for the 3D and 2D structures were determined for this location and expressed as Equation These values were used for modules of irradiance in the Matlab computations as in Equation 11 and associated components.
It was assumed that the elevation, for the 2D arrangement is one-third of the height h, for the 3D structure. In the 2D arrangement, not all the sides were present as shown in Figure 5 , hence only the front and the pop would receive the solar radiation.
Consequently, for the 2D arrangement the average total power in Watts was estimated as according to Equation Results and discussion. The variables derived for the solar power in equations 4, 7 and 11 were used to determine generated powers for the 2D and 3D solar structures for height variation of 1 to 6 m. The values are presented in Table 1. The linear appearance of results in Figures , obtained in 2D and 3D cases was caused by the effects of other factors such as weather, while seasonal variations such as cloud and rain and temperature were not considered, for simplification.
Table 1 shows that, at the height of 1 m, the 2D and 3D solar structures generated output power of 2.
Consequently, power generation in 3D installation got improved with increasing height. The existence of a linear relationship between solar generated energy and the generated output power substantiated an increase in solar energy generated with increasing height. A solar farm with multiple trees may, however, give different results because of the shading effect from adjacent trees hindering the absorption of the reflected rays by the PV cells, causing a reduction in the generated output power.
In order to avoid excessive partial shading of the elements, the solar trees would need to be installed with a relatively large spacing. A new set of equations would therefore be required to accommodate these changes Sampatakos, In this investigation, the effects of height on solar generated energy and power were analysed and discussed. All other variable parameters, such as weather conditions and time of the day, were not considered. The concept of energy-per-unit volume for solar energy for solar installation with consideration for height was corroborated by the results.
The Module of Irradiance was found to be a simple and useful tool for establishing the per-unit component for the top, front, and the side surfaces of the irradiance into a unit volume. There was an enhanced power output with the use of the Module of Irradiance. The relationship between generated power by volume for the 3DPV system and the generated power by area for the planar system was found to be linear.
Consequently, the introduction of height to solar power installation increases the performance of the solar device. However, in situations where more than one tree is used, different results might be obtained because of the tendency to experience uneven illumination of solar panels caused by overlapping shades of solar cells. This is a different possible scenario outside this study. Aglietti, G. High altitude electrical power generation.
Harnessing high-altitude solar power. Belegundu, A. Optimization concepts and applications in engineering. Cambridge: Cambridge University Press. Bernardi, M. Solar energy generation in three dimensions. Energy and EnvironmentalSscience 5 5 Boyd, M. Analytical model for solar irradiance near a planar vertical diffuse reflector: Formulation, validation, and simulations.