Harnessing solar power with aesthetic innovation: An in‐depth study on spherical and hemispherical photovoltaic configurations

In pursuing advancing solar energy systems, this research uniquely occupies a position at the intersection of photovoltaic (PV) efficiency, innovative design and aesthetic integration into urban landscapes. This study explores the potential of thin solar cells applied to spherical and hemispherical surfaces and the influence of temperature variations throughout the day. By conducting a comprehensive analysis of voltage–current diagrams, the study deciphers the intricate interconnections of spherical geometries and their response to external thermal impacts, elucidating their subsequent effects on energy conversion efficiency. Moreover, it delved into the dynamics of connecting multiple spherical modules, unveiling their potential to form artistic and utilitarian constructs such as solar trees and architectural embellishments. The findings indicate that while spherical configurations provide superior aesthetics and a power generation profile comparable to solar tracking systems, hemispherical configurations offer a 32% increase in efficiency compared with the spherical configuration and a notable reduction in land footprint. This research underscores the importance of striking a balance between aesthetic appeal, efficiency and land utilization, providing valuable insights for the future of PV technology integration into urban and agricultural landscapes.

first time. 3Within the realm of alternative energy, solar energy stands as the vanguard, a distinction attributed to many factors. 4These factors encompass the boundless and unremitting nature of solar resources, the inherent simplicity in converting solar irradiance into either thermal or electrical energy and its ubiquity, affording widespread availability throughout the year across numerous nations worldwide. 5The direct conversion of sunlight through photovoltaic (PV) modules into electrical energy, commonly called PV technology, constitutes a paramount technological advancement in harnessing solar energy. 6Over the past decade and a half, there has been a noteworthy advancement in this technology, evidenced by a laboratory efficiency rate of 46%. 7n contrast, silicon-based solar cells maintain a predominant position within the PV market at the present moment. 8,9The practical efficiency of the modules available in the market currently stands at 29%. 10 Presently, commercially deployed silicon-based solar cells exhibit an efficiency proximate to 25%, with silicon-based tandem solar cells achieving efficiencies near or surpassing the 30% threshold.These silicon solar cells demonstrate robust longevity, maintaining reliable performance for approximately three decades, irrespective of prevailing operational conditions encompassing varying moisture and oxygen levels and ultraviolet light exposure.In contrast, the emergent genre of flexible solar cells distinguishes itself by fulfilling the exigencies of portability and bendability, attributes that are increasingly sought after in modern applications. 11These modules exhibit categorization into multiple types, each distinguished by distinct attributes and merits encompassing efficiency, cost-effectiveness, longevity, flexibility, lifespan and chromatic variations.
The trichotomy of predominant solar cell classifications comprises monocrystalline (mono), polycrystalline (poly) and thin film. 12PV materials of a polycrystalline nature present advantageous cost efficiency and exhibit commendable scalability.Nonetheless, it is pertinent to acknowledge that the grain boundaries inherent to these materials constitute extended defects.These extended defects have the potential to significantly amplify the rate of carrier recombination, which is a critical factor to consider in the evaluation of their overall performance and efficiency. 13Among solar cell types, monocrystalline solar cells represent the apex in terms of cost and efficiency. 14onversely, thin-film solar cells emerge as a comparatively economical option, 15 characterized by their flexibility and malleability, enabling versatile application in enveloping curved contours.This unique attribute sets them apart from their counterparts, fostering innovative avenues for shaping and configuring PV technology. 16e efficiency of thin-film cells is less affected by heat than other solar cells, which adds another advantage to generating electricity in the summer season.
This study explores new ways to apply thin solar cells on spherical surfaces, examining their unique attributes and performance in electricity generation throughout the day.The analysis includes voltage-current diagrams to understand the behaviour of these shapes, considering their interconnections and the impact of external temperature variations.This thermal impact, in turn, imparts consequential effects on the overall energy conversion efficiency.Additionally, the interaction dynamics between multiple interconnected spheres were examined, offering insights into their potential amalgamation for creating aesthetically pleasing constructs such as solar arboreal formations or artistic embellishments on architectural facades.Such augmentations contribute to urban aesthetics within cityscapes, gardens and parks, and hold the potential for mitigating ground temperature through shadow projection, yielding agricultural and diverse utilitarian benefits.

| LITERATURE REVIEW
Many researchers are working to improve the performance of PV systems by changing the outer surface of the PV system.Arissetyadhi et al. 17 investigate the performance of PV modules arranged in arch configurations, using data collected in both dry (August 2019) and rainy (January 2020) seasons in Palembang.The findings reveal that the concave setting yielded the highest power (20.27W) and efficiency (13.14%) during the dry season.Compared with a flat arrangement, the convex setting demonstrated superior power and efficiency, highlighting the potential of arch configurations in enhancing solar energy harvest.Elatab et al. 18 offer a spherical solar cell composed of flexible monocrystalline silicon that achieves 19% efficiency without the need for sun tracking.Using a corrugation approach, the 4 cm diameter cell beats standard flat cells in instantaneous power production by 14.8% and 39.7% when exposed to reflecting backdrops such as sand and white paper, respectively.Its downward inclination also results in less dust collection, which has intriguing implications for solar energy applications.Shayan et al. 19 evaluate flexible solar modules supporting a PV system on flat, cylindrical and hemispherical surfaces.Fill factors were lowest on flat surfaces, with values of 0.88 and 0.84 on cylindrical and hemispherical surfaces, respectively.Maximum power output was 59.87 W on cylindrical surfaces, 57.84 W on flat surfaces and 61.14 W on hemispherical surfaces.Under standard conditions, system performance on cylindrical and hemispherical surfaces reached 7.45%.Laboratory power output was 46.7, 55.1 and 57.5 W for hemispherical, cylindrical and flat surfaces, respectively.
Flexible PV technology has experienced a notable surge in demand within contemporary society and this trend is anticipated to continue to escalate across diverse applications in the future. 8,20Flexible and transparent thin-film silicon solar cells have been meticulously engineered and refined, catering specifically to their integration within building structures, as well as for bifacial operational purposes. 21Edmund et al. 22 proposed a newly rooftop building-integrated PV design has the potential to meet 49.27% of a building's energy demands and reduce CO 2 emissions by 20,155.32tones throughout the PV system's lifespan.Flexible floating PV systems were successfully fabricated using commercially available PV modules and closed-cell foams following opensource designs.Three buoyancy-tested floating materials successfully deployed PV systems, resulting in a 10-20°C reduction in operational temperature and a consequent increase in efficiency across various PV absorber materials. 23The limited battery life of popular wearable smart devices can be addressed by developing flexible, self-charging photo capacitors, which concurrently harvest and store energy, extending the device's operational lifespan. 24| METHODOLOGY

| Spherical PV module fabrication
Producing solar PV modules in spherical configurations presents inherent complexities, even for fabricating a spherically enveloped solar cell assembly.This intricacy derives from the market's prevalent availability of solar cells, which generally use rectangular geometries, and the modules that may be produced within dedicated manufacturing facilities, which likewise use rectangular boundaries.As a result, realizing spherical solar cells appears to be a daunting task.However, it is possible to cover known spherical shapes with flexible solar cells that conform to rectangle shapes, whereas some surfaces will remain uncovered.These accessible portions can be quantified by computation.Thin-film PV modules shown in Figure 1 used in this study to cover the spherical shape are from Zhuhai Bro Renewable Energy Technology Co., Ltd and their provider characteristics are shown in Table 1.
The sphere's diameter is 0.3 m.Thirty flexible PV modules covered the hemisphere.Thus, the sphere is covered with 60 flexible solar modules after connecting the two hemispheres.

| Configuration types in the study
Spherical solar modules represent a unique and innovative approach to harnessing solar energy.Different shapes and configurations were studied to understand their characteristics, including single and multiple spherical shapes and single and multiple hemispherical shapes.The aim was to explore how these configurations affect the solar PV module efficiency and overall performance, considering their arrangement, connections and distances.
a. Single spherical shape: A single spherical solar module consists of a single spherical structure designed to capture sunlight from all directions.The spherical shape maximizes exposure to sunlight throughout the day, making it suitable for locations with changing sun angles.b.Three spherical shapes: Incorporating three spherical shapes can further enhance the energy capture potential.Configurations involving three spherical shapes can be studied to determine their impact on energy production.Two spherical PV configurations are aligned along a shared axis with a separation distance of 40 cm.At the same time, the third sphere is positioned on an axis parallel to the first and the separation between the two axes is 55 cm.Notably, the centre of the third sphere is strategically situated midway between the two spheres on the first axis, thereby mitigating the formation of shadows to the greatest extent possible, thus optimizing the collection of solar energy.c.Single hemispherical shape: A single hemispherical shape captures sunlight from a half-sphere, making it particularly suitable for locations with a fixed sun angle, such as along the equator.The shape is also easier to mount on flat surfaces.d.Two hemispherical shapes: Combining two hemispherical shapes can maximize energy capture while allowing for better positioning flexibility.The distance between the two shapes is 40 cm and both are in the same holder.e.Three hemispherical shapes: Combining three hemispherical shapes can offer an increased surface area for solar absorption.The distance between the shapes is 30 cm, all in the same holder.Hemispherical shapes, when aggregated and thoughtfully arranged in urban settings, have the potential to make a significant impact by not only enhancing aesthetics but also by creating striking and artistic configurations.These arrangements, when combined, can be used to create intricate three-dimensional patterns, adding beauty and a sense of sophistication to the urban landscape.This innovative use of hemispherical shapes not only elevates the visual appeal but also plays a vital role in increasing public awareness and education regarding the use of clean energy.Furthermore, these arrangements have the practical benefit of generating electrical energy.Spherical configurations represent distinctive forms employed across various architectural and engineering domains for aesthetic enhancement and efficient space utilization.Certain research endeavours have explored the utilization of spherical shapes for energy generation, with inspiration drawn from the black grape tree.The black colour of these spheres aligns with the colour of PV cells.Consequently, the concept of a solar tree, modelled after a hybrid grape tree, presents an opportunity to integrate an aesthetically pleasing urban structure that concurrently serves as an icon while harnessing solar energy for electrical generation.This innovation is distinctive in its examination of the properties associated with spherical and hemispherical geometries, furnishing essential information and data to comprehend the solar energy generation characteristics within these specific shapes.The critical considerations for these spherical and hemispherical configurations include: a. Distances between solar PV modules: the distances between individual spherical or hemispherical shapes play a crucial role in shading and energy capture.Different spacing can be analysed to find an optimal arrangement.b.Series and parallel connections: connecting these solar modules can significantly impact the voltage, current and power output.Series connections increase voltage, while parallel connections increase current.The choice of connection method depends on the specific application and system design.c.Location and arrangement: The location of the spherical or hemispherical modules concerning other modules and their orientation concerning the sun should be carefully considered.These parameters affect the overall efficiency and energy production throughout the day.d.The efficiency and performance of spherical solar modules can be affected by the materials used, the quality of the PV cells and the temperature. 25A comprehensive study would examine these factors, environmental conditions and geographical location to determine the optimal configuration for a given application.The temperature exerts a pronounced influence on energy generation when it exceeds the permissible threshold within operational parameters.Among the primary categories of PV technology, flexible solar cells demonstrate a relatively minimal susceptibility to temperature-induced variations, with a temperature effect factor of 0.234% for each degree of temperature alteration. 26To investigate the impact of temperature on electrical generation and the influence of solar position relative to spherical geometries, sensors have been strategically positioned at various locations on the outer surface of a spherical object designed for temperature measurement in the surrounding environment.

| Power calculations
The measurement period encompassed the months from March through August.In Hungary, the prevailing weather conditions during this period typically feature a preponderance of cloudy days.Consequently, specific days characterized by clear and unobstructed weather conditions were deliberately selected to elucidate the influence of solar irradiance on energy production from spherical geometries.The following equation can calculate the maximum electrical energy generated by the solar PV module. 27 where P m = maximum power (W), ξ = PV module efficiency, A s = PV module surface area (m 2 ) and G t = solar irradiation (W/m 2 ).This equation finds application within conventional planar PV modules.In assessing the computation methodology for electrical energy yield derived from configurations possessing curvature or sphericity, due consideration must be accorded to solar incidence geometry.This imperative arises due to the Earth's perpetual and uninterrupted rotational motion, engendering alterations in the incident angle of solar radiation upon solar cell surfaces, alongside fluctuations in the effective solar projection area upon the nonplanar geometries.
In the spherical shapes, our projection maintains a consistent circular configuration, encompassing all azimuthal angles, with an unchanging diameter throughout a full 360°.On the other hand, when we apply Equation 1to straight structures in the regular coordinate system (with x, y and z axes), it's simpler.This simplicity comes from these structures receiving direct sunlight across the whole surface during the day.However, when we try using Equation 1 on spherical shapes, things get trickier.This happens because of the changing angles at which sunlight hits due to the curves of the sphere.Different parts of the surface experience both direct and indirect sunlight, making it more challenging to measure electrical energy production accurately.This situation calls for a more detailed analysis.
The incidence angle of solar radiation directly influences the production of electrical energy.As illustrated in Figure 3, we observe a distinct behaviour in the IV characteristic curve for the hemispherical configuration.Consequently, this behaviour diverges appreciably from the IV characteristic curve for an individual flexible module of an identical solar cell type without accounting for losses incurred during the interconnection of solar cells within the hemispherical structure.It is important to note that the IV characteristic curve exhibited a hemispherical configuration when placed horizontally, with a concurrent global solar radiation of 880 W/m 2 .Each PV module receives solar radiation in different amounts since the PV module has a different position on the hemispherical shape.Meanwhile, all PV modules continue to generate electricity at the same time.
The maximum power for the spherical PV module = the power from the direct projection area − the power from the rest of the surface area.The PV modules will consume power from the others if they generate less power than others.The following equation will calculate the power for the spherical configuration: where A c = projection circle area (m 2 ) and G d = diffused solar irradiance (W/m 2 ).The outer surface area of any spherical shape = 4ℼr 2 = 4 circle area, the sunlight will fall on the circular projection area of the spherical shape and the rest of the outer surface continues harvesting the diffused solar irradiance.The diffused radiation can be calculated from the following equation 27 : where τ b is the atmospheric transmittance, which can be calculated as follows 27 : The constants K, a 0 and a 1 can be found by the correction factors r a a r a a r K K = / *, = / * and = / * , according to the climate type 27  (5) where A is the altitude of the PV module in kilometres, The calculated power generated for the spherical PV configurations can be calculated by Equations ( 2) and (3), as shown in Table 2.
To enhance result validity and address the scarcity of research on spherical PV shapes, all experiments in this study were systematically replicated multiple times.The outcomes exhibited a high consistency, with a change rate of <7% observed under similar weather conditions, as depicted in Figure 4.
As hemispherical PV modules mix features of spherical and flat modules, they make an intriguing case study for power output modelling.Similar to the spherical module, the hemispherical design ensures that, based on their direction concerning the sun, various areas of the module will get varying quantities of sunlight.To estimate the power output of a hemispherical PV module, an equation similar to the one suggested for the spherical module could be used with more complexity but modified to account for the fact that only half of a sphere is being dealt with. 28 where G(θ,ϕ) is the solar irradiance (W/m²) at a given point on the hemisphere as a function of the polar (θ) and azimuthal (ϕ) angles; cos(θ) accounts for the angle of incidence of the sunlight; dA is the differential area element on the hemisphere.Integration over the surface of the hemisphere would be performed to account for the varying irradiance across the module.The cos(θ)cos(ϕ) term would ensure that areas of the module that are not directly facing the sun contribute less to the total power output, consistent with how PV cells behave.

| Footprint calculation
The land footprint plays a pivotal role in the context of PV technology deployment, with substantial solar installations conventionally sited in arid terrains or peri-urban regions as a response to the exorbitant costs associated with land acquisition in more densely populated areas.A promising remedy to this quandary is the implementation of solar tree structures, which exhibit a markedly reduced land footprint for PV systems, resulting in an impressive 90% reduction in ground utilization when juxtaposed with conventional counterparts.
The surface area of the hemisphere depicted in Figure 5 is 0.1414 m 2 .The portion occupied by the flexible solar cells, which is the sum of the areas of 30 flexible solar modules, amounts to 0.099 m 2. Consequently, the unoccupied section of the hemispherical shape, not covered by solar cells, measures 0.0424 m 2 .This covered area constitutes 70% of the total surface area of the spherical shape.Therefore, based on this calculation, the surface area of the spherical object is 0.2828 m 2 , with the section covered by the flexible solar modules spanning 0.198 m 2 .
To calculate the land footprint of a single hemisphere, first, find the aggregate area of a single flexible module and then multiply this area by the total number of modules composing the hemispherical structure.This metric can then be compared with standard systems for comparison.As delineated in Table 1, the surface area occupied by a single flexible PV module equals 0.0033 m 2 and the quantity of these modules required to cover the hemispherical configuration entirely amounts to 30.
Consequently, these 30 flexible PV modules' cumulative surface area is up to 0.099 m 2 .The land footprint of an individual hemispherical structure can be calculated as the area of a circle with a diameter of 0.3 m, resulting in a T A B L E 2 The calculated and measured power for the spherical PV configuration.value of 0.07 m 2 .Therefore, the ratio of the land footprint of an individual hemispherical structure compared with conventional systems stands at 0.7, signifying a reduction in footprint area by 30% (excluding the need for a stand to support the hemispherical structure).The spherical configuration comprises 60 flexible PV modules.Calculating the land footprint of these flexible PV modules within conventional flat systems necessitates an area of 0.198 m 2 .In this study, the spherical structures are supported by a wooden pole measuring 10 cm × 10 cm.As a result, the ratio of the land footprint of the spherical structures compared with conventional systems stands at 0.05, offering a substantial 95% reduction in land area usage.The solar tree, composed of three spherical structures mounted on a single wooden stand, requires a mere 1.6% of the land space occupied by traditional arrays, resulting in a remarkable 98.4% land footprint savings.

| RESULTS AND DISCUSSIONS
The spherical PV configurations commence the process of solar energy harvesting from the early morning until late afternoon, as they are not reliant on the peak hours typically associated with generating electrical energy between 10:00 h and 16:00 h, as indicated by literature. 29his is facilitated by adequate spatial resources for energy acquisition afforded by the spherical configurations, constituting a primary point of divergence from established conventional PV technology systems.
Elevated temperatures notably influence solar PV modules' performance. 30However, the flexible PV cells employed in this study exhibit reduced sensitivity to temperature fluctuations compared with monocrystalline and polycrystalline cells.In Hungary, the summer temperatures typically range between 26°C and 28°C, which falls within the range of acceptable operating temperatures for PV systems.Consequently, the impact of temperature on the efficiency of solar modules is minimal in this context.

| Single spherical PV module
Spherical configurations persist in collecting solar energy and generating electrical power, commencing in the early morning and extending throughout the day.Figure 6 illustrates the electrical power curve associated with solar radiation incident upon a spherical structure enveloped by PV modules.This curve shows a behaviour like that of a solar tracking system.This similarity can be attributed to the consistent cross-sectional surface area, which maintains a circular area throughout the day for spherical shapes.
The difference between the measured maximum power (2.02 W) and the calculated power (2.41 W) is ~16%.This difference could be considered acceptable in some contexts, especially given the complexity of measuring and modelling the performance of a spherical PV module.
At 8:00 h, the generation amount was 73.6% of the highest generation recorded for that day, and the generation amount at 18:00 h was 74% of the highest recorded generation amount, which records a generation time of up to 10 h per day in Hungary.
Solar modules on the opposite side of sunlight have a negative effect on the total power generation due to their spherical shape.They depend on reflected and scattered The power generated from a single spherical shape.
sunlight only, and the temperature of these modules is the lowest temperature among other solar modules.
The surface of the sphere has a large variation in temperature, with the highest temperature recorded at 50.2°C for a solar module corresponding to direct sunlight, compared with 27°C for the air temperature.As for the rest of the solar modules, they were variable and there is no equality between any two solar modules at the same time due to the changing angle of incidence of sunlight on the spherical surface.The average temperature was 34.2°C, which is the highest average temperature during the day.
The average temperature experienced by the solar PV modules closely approximates the ambient temperature of the surrounding environment, owing to the thermal equilibration of the spherical shape's surface.Additionally, the consistent presence of wind across the extensive surface area of the spherical configuration provides effective cooling for the solar modules, thereby preventing the occurrence of elevated temperatures, particularly considering the substantial surface area available for heat dissipation.

| Three spherical PV modules
The three spherical configurations collectively form a simplified model resembling a solar tree inspired by a grape structure, facilitating the examination of the influence of interconnected spherical shapes on both the environment and energy production.Solar trees represent a valuable addition to urban landscapes as they draw inspiration from nature, 31 harmoniously blending the principles of nature with technology to generate electrical energy.They leave a positive visual impact while reducing the terrestrial footprint, which is a crucial factor in calculating the cost-effectiveness of solar systems.
By offering an extensive surface area relative to their ground footprint, solar trees effectively contribute to decreasing surface temperatures through enhanced airflow, thereby promoting improved heat dissipation and the sustained efficiency of the solar modules.The output of three spherical configurations yielded a power output of 3.13 W, juxtaposed against a theoretically computed value of 4.09 W, resulting in an appreciable variance of 23%.This noticeable difference can be explained by the existence of shadow resulting from the spherical shapes being superimposed.Figure 7 presents data illustrating the energy production, temperatures and solar radiation for three spherical clusters of solar modules.The power curve takes an almost square shape, which explains the stability of power generation throughout the day if the weather is clear and there is no shadow on the solar tree.It also turns out that the amount of generation is reduced by 50% compared with the single spherical shape due to the formation of the shadow balls on each other.
There is great importance in how to form and assemble the solar balls and calculate the distances between them to avoid forming shadows on each other, as depicted in Figure 8.
The area directly exposed to sunlight experiences more significant temperature increases than the remaining external surface of the spherical structures.This results in the continuous alteration of heat concentration areas in tandem with the sun's movement, aiding in the consistent dispersal of heat and the cooling of solar modules, particularly when complemented by windinduced air movement.
F I G U R E 7 The power generated from three spherical shapes.
The extent of distortion, as a percentage, exhibits an upward trajectory as the inter-ball distances decrease, subsequently leading to a reduction in the energy output of the solar tree configurations.Generating energy from solar trees is one of its main goals, in addition to enhancing aesthetics and increasing environmental awareness within urban areas.Therefore, it requires careful study to decide whether the primary intention is to enhance the visual appeal of urban areas or generate energy.On this basis, priorities can be given.In such cases, solar trees' aesthetic quality and symbolic value may outweigh their energy-generating efficiency.Conversely, if the principal focus is on energy generation, then optimizing the inter-ball distances to maximize solar energy harvest would be paramount, even if it involves some compromise on the aesthetic front.Striking a balance between aesthetics and energy efficiency is essential to effectively align the solar tree's design with its intended purpose.

| Single hemispherical PV module
Hemispherical configurations display a notably reduced land footprint and its implications on electrical power generation, as clarified in Figure 9; this figure illustrates power generation, solar radiation, air temperature and the average temperature of the solar PV modules, showcasing a remarkable degree of stability and consistency in power generation.The hemispherical shape recorded an amount of energy higher than the spherical shape by 32%, compared with a similar number of solar modules used in practical experiments, because of losses in the opposite directions of sunlight.
The behaviour of the generating power curve stability is particularly evident from morning until sunset when the solar radiation curve remains constant and the weather conditions are clear.During these periods, the behaviour of power generation closely parallels that of solar modules employing solar tracking mechanisms.However, one noteworthy challenge lies in effectively addressing solar cells on the side opposite to the incident sunlight, as this arrangement can hinder efficient electrical power generation.To mitigate this challenge, a strategic solution involves the distribution of flexible modules symmetrically across the outer surface of the hemispherical shape around its vertical axis.This arrangement accounts for the observed stability in energy generation throughout the day.Simultaneously, the F I G U R E 8 Solar tree from three spherical shapes.
F I G U R E 9 The power generated from a single hemispherical shape.
spaces between the flexible cells serve the dual purpose of reducing and dissipating the temperature within the solar modules.This temperature control, coupled with the moderate air temperature ranging from 25°C to 30°C during daylight hours, falls within the operational temperature range and constitutes a fundamental factor in maintaining the efficiency of the solar modules utilized in this study.

| Two hemispherical PV modules
The two hemispherical configurations of solar modules were interconnected along a single axis in parallel; the ensuing results are presented in Figure 10.These results encapsulate power generation, solar radiation and temperatures.
The increment in power generation, when compared with a singular hemisphere, transpires at a rate slightly less than twofold.Although substantial, the relative increase in power production is not purely proportional to the addition of a second hemisphere.The observed phenomenon is primarily attributed to the shadow cast by one hemispherical shape onto the other, resulting in an energy loss.This shadowing effect arises because the separation distance between the first and second hemispheres is 40 cm, which proves inadequate to mitigate this form of energy loss effectively.Furthermore, it is noteworthy that the average temperature of the solar modules exhibits a marginal decrease of 1.8°C compared with the single hemispherical configuration, possibly due to improved heat dissipation due to the addition of the second hemisphere.
The surface of the hemisphere has a variation in temperature, with the highest temperature recorded at 46.6°C for a solar module corresponding to direct sunlight, compared with 31°C for the air temperature.As for the rest of the solar modules, they were variable and there is no equality between any two solar modules at the same time due to the changing angle of incidence of sunlight on the spherical surface.The average temperature was 38.2°C, which is the highest average temperature during the day.
Hemispherical configurations can create visually captivating geometric patterns that enhance the aesthetic appeal of urban spaces.These elegant and artistic designs not only contribute to the visual charm of the environment but also serve to heighten public awareness regarding using clean and sustainable energy sources.The single spherical shape generated a higher power than the parallel two hemispheres by 12.5%.This is due to the generation of shadowy areas on the lower hemisphere by the upper hemisphere, which caused these losses.

| Three hemispherical PV modules
The three-dimensional PV system shows similar behaviour to the two hemispherical PV modules as illustrated in Figure 11, the power generation curve, solar radiation levels and temperature.The power generation remains uniform throughout the day, reflecting exceptional stability and efficiency.
The capability to generate an average power of 2.4 W at an incident solar irradiance of 600 W/m 2 is noteworthy.This accomplishment distinguishes these hemispherical configurations by their ability to generate significant electrical energy without heavily relying on F I G U R E 10 The power generated from two hemispherical shapes.
high-intensity direct solar radiation.The key lies in a substantial number of solar cells proficiently harnessing energy from direct sunlight and reflected or scattered solar energy.Leveraging scattered solar radiation contributes to the behaviour of the electrical power generation curve, which closely mirrors the performance of solar tracker systems.This capacity to effectively utilize dispersed sunlight further highlights the adaptability and efficiency of these hemispherical shapes in generating electrical power.
One important characteristic that guarantees all temperatures stay within the permitted operating range is how close the average temperature of the solar modules is the ambient temperature outside.Notably, the region directly exposed to sunlight experiences a temperature differential, typically ranging from 5.3°C to 7.5°C higher than the ambient temperature.However, this variance quickly diminishes as the sun changes position and the direction of direct sunlight shifts.On the other hand, places that are shaded or on the side that faces away from the sun have temperatures that are between 1°C and 2°C colder than the surrounding air.As the direction of the solar projection shifts, so do these temperature fluctuations.This temperature behaviour attests to the dynamic thermal response of the hemispherical configurations, influenced by the sun's movements and the distribution of solar energy.

| Power/land occupancy ratio
The evaluation of energy production relative to land footprint represents a fundamental consideration in the feasibility assessment of PV systems within urban environments.This is particularly crucial due to the elevated cost of land in urban areas, thereby resulting in an escalated expenditure associated with the establishment of power generation stations.An assessment of the new configuration is shown in Table 3; all of them have the same wooden stem and the cross-section area of the stem is 0.01 m 2 .Solar tree technology has the potential to solve the problem of land cost in urban areas, as the results show.All the configurations save more than 90% of the land footprint.

| CONCLUSIONS
This study focuses on the outside design features of PV modules to get a unique spherical architectural arrangement that improves the visual appeal of solar energy systems while also investigating the system's performance qualities in electricity generation.Spherical designs are more visually appealing than planar patterns and have a diurnal power generation profile similar to solar tracking systems.When PV module spheres are interconnected to create solar tree structures, they offer a substantial reduction in land footprint, up to 98% in comparison to conventional PV systems, while simultaneously yielding a 65% reduction in capacity relative to flat PV systems when considering equivalent PV cell surface area.Spherical PV configurations showed a better average surface temperature performance of 5.3°C to 7.5°C compared with flat PV systems.This advantage contributes to preserving a superior level of solar PV module efficiency.
Hemispherical configurations demonstrated a 32% increase in efficiency compared with their spherical counterparts and they exhibited a 2% reduction in land footprint compared with the spherical configurations.The impact of temperature variations closely resembled that observed in spherical configurations.

Figure 2
Figure 2 shows the measured current-voltage (IV) characteristic curve of the flexible PV module at the global solar irradiance of 890 W/m 2 .

F
I G U R E 2 Current-voltage (IV) characteristic curve of a single flexible photovoltaic (PV) module.module

F
I G U R E 3 Current-voltage (IV) characteristic curve of the hemispherical photovoltaic (PV) module.

F
I G U R E 11 The power generated from three hemispherical shapes.T A B L E 3 A comparison of the parameters for the PV configuration. ) Abbreviation: PV, photovoltaic.