The solar radiation that reaches a surface in space varies by 63.3% because of the variation in the distance of the sun to Earth. The amount of extra-terrestrial solar radiation incident on a surface in space at any time of the year can be determined from [37]:

where I₀ is the extraterrestrial radiation for a specific day while I_S is the solar constant (1367 W/m²), N is the day’s number in the year with 1st January as 1,θ_z is the sun’s zenith angle.

The extra-terrestrial solar radiation on a horizontal surface per hour was calculated from:

where ∅ is the latitude of the location, δ is declination, H₁ and H₂ are the hour-angle at 30 minutes before and after the hour under consideration.

The angle of incidence of beam radiation on a horizontal surface, or zenith angle θ_z, can be expressed as [38]:

The geometric relationship for the cosine of the angle of incidence of beam radiation on a tilted surface with respect to the horizontal plane can be derived as [39]:

Eq. (4) is the cosine effect formula for solar irradiance on a tilted surface. θ is the angle of incidence, the angle between the incoming solar beam (direct normal irradiance) and the normal (perpendicular) to the surface of the bifacial PV panel, H is the hour-angle, γ is the altitude, and β is the slope.

Global horizontal irradiance (GHI) at a given site can be obtained from satellite information, from a weather station positioned in the study site, or from a clear sky model. To find the maximum solar radiation for a given site, the clear sky models are applied to calculate the clearness index [40]. The Kasten-Czeplak (KC) clear sky model for the global horizontal irradiance (W/m²) is given as [41]:

In this work, decomposition models are used to provide accurate estimates of the components [42]:

The model used to calculate irradiance on an inclined plane is the transposition model array. The direct plane of array irradiance can be expressed as [43]:

where α is the angle of incidence between direct normal irradiance (DNI) and the front/rear side of the solar module. Irradiance transposition was performed using the Perez model, which considers all three diffuse components: isotropic, circumsolar, and horizon diffuse. The reflected irradiance at the ground is described as [43]:

ρ is the albedo, θ is the tilt angle. Albedo refers to the solar radiation that is reflected from a certain surface and is usually expressed in percentages or in a decimal number where 1 is an excellent reflector, like snow or any white surface, while 0 is a surfaces that absorb all incident radiation, like black painted surfaces. Total irradiance on the array plane is expressed as [43]:

where G_s is the sum of all the in-plane irradiance, G_bs is the direct normal irradiance, G_ds is the sum of the sky diffuse irradiance, and G_gs is the sum of the ground reflected irradiance due to the influence of albedo on the plane of an array.

Global Irradiance on the Plane of Array (G_POA) as a percentage of Global Horizontal Irradiance (GHI) at each tilt angle provides additional information on the performance of a tilted solar panel as opposed to a horizontal surface, which depends on the tilting angle and orientation. The derived percentage reflects how much irradiance is either gained or lost as a result of the tilt, which can also be useful to determine the effect of the cosine effect and possibly maximize energy yield by adjusting the panels accordingly. To calculate the percentage of G_POA relative to GHI for each tilt angle, it can be expressed as:

The effect of albedo is considerably different for concrete, sand, and grass surfaces, as concrete reflects the most radiation, sand is intermediate, and grass reflects the least. These differences in surface reflectivity have important implications in local as well as global radiative forcing with respect to climate and the Earth’s energy balance. The total irradiance received by the plane can be expressed as [44]:

where G_POA is the incident radiation received on the panel, BF is the bifaciality factor (0.8), and G_rear is the reflected irradiance.

For a more rigorous quantitative comparison between the simulation outputs and field measurements, three statistical performance indicators were employed: Mean Absolute Relative Error (MARE), Mean Percent Error (MPE), Mean Absolute Error (MAE), and correlation (r). The MARE expresses prediction errors as a percentage of absolute values between simulated and experimental values, thereby providing a normalized measure of overall accuracy. It is useful for applications involving data with varying scales [45]:

X_Exp is the experimental result, X_Sim is the simulated value, n is the number of data point.

The MPE quantified the bias in the simulation results, indicating whether the model systematically overestimated or underestimated the experimental values. This quantification is essential for improving model accuracy and predictive capability, as it allows for the identification of systematic errors:

Mean Absolute Error (MAE) measures the average magnitude of errors between simulation and experimental values, without considering the direction (positive or negative). MAE shows the typical size of the errors in the same units as the measurement [45]:

During comparison, we identified a reporting mismatch between the simulated and measured datasets. The field experiment recorded DC energy aggregated over the array (the summed DC output from the modules), whereas the simulation output files reported AC energy per simulation unit. To ensure a consistent comparison, the simulated AC values were converted to comparable DC totals by accounting for the inverter conversion of 95% as used in the simulation and the photovoltaic panel size used in the experiment. Specifically, simulated AC energy was converted to DC equivalent energy:

N_Mod is the number of modules represented and η_Inv is the inverter efficiency used in the simulation setup.

Eq. (17) is a standard approximation used in solar PV performance modelling. It's a key part of the process for adjusting a simulated solar irradiance value to account for real-world losses that are not typically included in the raw simulation:

where GPOA_Adj is the adjusted GPOA, S ¯ is the average spectral mismatch factor, I A ¯ M is the average incidence angle modifier, (1−f_soiling) is the soiling loss factor, and GPOA_Sim is the simulated GPOA.

The simulation for the bifacial photovoltaic (PV) system was conducted using PVsyst 8.0.5. The system was modelled for the IEET Building at Jomo Kenyatta University of Agriculture and Technology (JKUAT), Kenya, using synthetic meteorological data from Meteonorm 8.1 (1991–2007). The geographical parameters included a latitude of 1.03°S, a longitude of 36.98°E, and an altitude of 1571 m. The PV system design consisted of an unlimited shed configuration with a tilt and azimuth of 180° South, a height above ground of 1 m, 1.5 m, 2 m, and 2.5 m, and a ground coverage ratio (GCR) of 30.4 %. A single bifacial module (JAM72-D40-575-BP-Bifacial) with a nominal power of 575 W_p was connected to a single-phase inverter (AS-IR02-700, 0.7 kW, 1 MPPT), resulting in a DC/AC ratio of 0.82. The bifacial model employed was the 2D unlimited sheds configuration, incorporating a bifaciality factor of 80%, a ground albedo of 0.23 for concrete, 0.21 for sand, and 0.19 for grass. The rear-side shading and mismatch losses are 5% and 10%, respectively. The simulation was modelled for the period from February to March. The average ambient temperature was 21.27 °C. The energy production was based on the orientation of the panel and the height above the ground. The result from the simulation is presented in Figure 3.

The field setup was designed to be a direct replica of the simulation environment, ensuring the accurate validation of the modelled results. Three types of ground surfaces: concrete, sand, and grass, were prepared, ensuring uniform and even surfaces to minimize variability in measurement. As shown in Figure 2, metallic mounting frames were subsequently mounted on each of the prepared surfaces. As for the orientation, the panels were installed in the north/south direction, as this is the ideal orientation for the location of the study. The mounts were adjustable for tilt angles and had a locking mechanism. More specifically, they were designed to allow for four discrete angles of inclination: 0°, 5°, 10°, and 15°, and performance could thus be measured under varied incline conditions. The mounting structure heights were 1 m, 1.5 m, 2 m, and 2.5 m. A Suunto inclinometer was used for all installations and adjustments in incline angle to ensure that each panel's experimental tilt angle was set accurately.

Figure 2.

Image of the bifacial panel mounted on different surfaces

Thermocouples were installed on the front (top) as well as the back sides of the panels to measure the actual cell temperatures during the tests. Ambient temperature was also recorded throughout the testing period to evaluate environmental influence on panel performance. Each panel configuration was separately connected to one of three MPPT charge controllers, which directed the power into the 24 V 40 Ah battery configuration (two 12 V 40 Ah batteries connected in series). The system load consisted of a 24 V 10 A DC water pump, which was connected across the terminals of the battery. A data logger was used to log energy generation and energy consumption at 20-second intervals for six hours daily to record the energy performance of the system. Incident and reflected solar irradiance were measured with a TM-208 solar power meter to evaluate the contribution of rear-side gains from bifacial panels. The results of all experimental data are summarized in Table 4, which illustrates system performance.

In line with the objective of this study, the data collected from the field experiments encompassed key parameters essential for evaluating the performance of bifacial photovoltaic panels under varying tilt angles and mounting heights. Specifically, measurements included the energy harvested from each panel, which served as a direct indicator of system output across different configurations, as shown in Table 4. Solar irradiance data, both incident and reflected, were captured using a solar power meter to assess the total radiation received by the panel surfaces.

Table 5 presents experimental results showing how varying tilt angles (0°, 5°, 10°, and 15°) affect the Global Horizontal Irradiance (GHI) and Global Plane of Array Irradiance (G_POA), along with the percentage of irradiance captured on the panel surface. When the tilt angle of the bifacial solar panels increases, the incident radiation received on the panel surface progressively declines. While the tilt angle varied from 0° to 5°, 10°, and 15°, the incident radiation decreased by approximately 5 %, 7 %, and 10 %, respectively. This decrease in G_POA is due to the Cosine effect. Overall, the data suggest that tilt angles between 0° and 5° are optimal for maximizing irradiance capture in fixed PV installations, especially in regions with high sun angles, while larger tilt angles lead to reduced energy captured. The 5° tilt offers practical benefits such as improved self-cleaning. The optimal tilt angle for bifacial PV panels in tropical regions typically ranges from 0° to 15°, showing improved energy output [2], [46], [47]. In tropical regions where the sun is generally high in the sky, flatter orientations (lower tilt angles) align more directly with the sun's position throughout the day, resulting in greater solar exposure and subsequently higher energy yield [48].

The corresponding beam irradiance from the simulated result is shown in Table 6.

The GHI represents the total solar radiation received per unit area on a horizontal surface and serves as a baseline for estimating available solar energy at a site. However, what the panel absorbs depends heavily on its tilt and orientation. The irradiance on the plane of the bifacial panel (G_POA) declined with increasing tilt, despite GHI values remaining stable or only slightly fluctuating. This discrepancy can be attributed to the angular mismatch between the solar beam and the tilted surface.

The simulated GPOA values were adjusted to a real-world equivalent for accurate comparison with experimental data, a standard procedure in solar energy research to account for optical losses not captured in raw simulation outputs. This methodology is based on a conceptual framework that incorporates key loss mechanisms. The incidence angle modifier (IAM) was applied to account for the reduction in performance as sunlight strikes the panel at a non-normal angle, a principle well-established by Duffie and Beckman [49]. Soiling losses, a significant real-world factor, were modeled using a soiling factor derived from the [50] model. The spectral mismatch factor, which accounts for the difference between the simulated and real-world solar spectrum, was also applied, consistent with research and datasets provided by institutions like Sandia National Laboratories [51]. By integrating these validated loss models, the simulated data were converted into a realistic representation, allowing for a robust and meaningful comparison with the experimental field measurements.

To calculate the percentage of G_POA relative to GHI for each tilt angle, as shown in Table 5 and Table 6, eq. (11) was used.

Figure 3.

A plot of Simulated value against Experimental value

In this analysis, the performance of a simulation model against experimental data was visually and quantitatively evaluated. As shown in Figure 3, a strong positive linear relationship is evident between the simulated and experimental values, with data points clustering closely around the line of best fit. This visual observation is corroborated by the calculated Pearson correlation coefficient (r = 0.806), which, being very close to the ideal value of 1, indicates that the two datasets change in a highly consistent and predictable manner. While the correlation is strong, a more detailed understanding of the model's accuracy is provided by the error metrics. The Mean Absolute Relative Error (MARE) of 8.23% indicates that, on average, the simulated values deviate by about 8% from the actual experimental values, which is below the 10% threshold commonly cited in photovoltaic performance validation [52]. The Mean Percentage Error (MPE) of 1.74%, indicates that the simulation slightly underestimates the experimental GPOA values by less than 2% on average, which is within the ±5 % tolerance defined in ASHRAE Guideline 14 [53]. The Mean Absolute Error (MAE) was found to be 62.5 W/m², corresponding to approximately 6 ‒ 8% of typical tropical irradiance values (800 ‒ 1000 W/m²), which is acceptable given natural sensor uncertainties and environmental variability. Collectively, these results demonstrate that the simulation model provides a highly reliable representation of the experimental trends, with only modest deviations at the individual data-point level.

Figure 4 shows that energy harvested and irradiance (GHI and G_POA) vary with tilt angle and installation height across different surfaces in both experimental and simulated setups. Figure 4a, 4b, 4c and 4d are the results from the experimental results, while the corresponding Figure 4a′, 4b′, 4c′ and 4d′ are from the simulated results at varying heights. At 1m, concrete yields slightly more energy than grass and sand, with high GHI but fluctuating G_POA. At 1.5 m, both energy and irradiance increased, indicating minimal shading. The highest energy output occurs at 2 m with 0° to 5° tilt, beyond 5°, both GHI and energy declined. Radwan et al. [54] reveals that increasing the tilt angle beyond 5° results in reduced GHI and energy output due to less effective rear-side irradiance capture. At 2.5 m, energy decreases notably at higher tilts despite good irradiance at lower angles.

Results from the field were in accordance with predictions derived from simulation models, thus confirming the theoretical basis of the analysis. Based on the simulation outputs, higher tilt angles would imply a lower total irradiance on the panel’s plane because of an apparent misalignment with the sun’s trajectory [33]. This prediction was confirmed in the field test, where actual energy harvested decreased with the decrease in incident radiation. These findings highlight that while some tilt can enhance rear side irradiance capture (due to improved reflectance geometry), this gain is overshadowed by the loss in front side irradiance at higher tilt angles [9]. Thus, the field data support the argument that smaller tilt angles are preferred for equatorial climates when maximizing energy capture is the main goal.

The tilt angle of the bifacial solar panels is a determining factor of the energy yield for this current study. Given that solar radiation is time and location-dependent, it is important to improve the tilt angle of the bifacial panels to achieve the most efficient capture of solar energy [27], [28]. Although the use of dynamic sun tracking systems represents the possibility of constantly optimizing the orientation of the panels throughout the day, these have the disadvantage of typically being quite expensive and the complexity to the system. Considering these constraints, the present study looks into another alternative of applying a more practical and feasible solution for actual installations and optimal fixed tilt angle.

Figure 4.

The graph of energy harvested, GHI, and G_POA against the varying tilt angle and height

Figure 4 is a comparison of simulated and experimental daily energy yield (kWh) of the bifacial PV array under three different ground surfaces (Concrete, Sand, Grass). The dataset of the simulated result shows an apparent discrepancy of approximately 14. This was due to two issues: (i) The simulation results were reported in AC terms (including inverter efficiency ~95%) while the experimental values were logged in DC. The data was converted to DC using Equation 16 for proper comparison. (ii) the experimental setup was constrained by a fixed resistive load of 24 V × 10 A (≈240 W), corresponding to ~14% of the 1.725 kW array’s potential capacity. After harmonizing both datasets to the same DC basis and array scaling, the simulation (~12.8 kWh/day) and experimental (~13 kWh/day) values show close agreement, with residual deviations attributable to wiring/mismatch losses, sensor tolerances, and environmental variability.

Figure 5 shows that the reflected irradiance from different surfaces (concrete, sand, and grass) varies with the tilt angles and height. Among the surfaces, the concrete surface (R_Con) consistently reflects more irradiance than sand (R_Sand) and grass (R_Grass) across all tilt angles. The highest reflected irradiance from all surfaces is observed at a tilt angle of 5°, where R_Con is slightly above 200 W/m², followed by R_Sand and R_Grass. The lowest values of reflected irradiance occur at a tilt angle of 15°, where all surfaces drop to approximately 97 W/m². This pattern indicates that surface material significantly affects the reflected irradiance, with concrete being the most reflective under the same solar conditions. This aligns with findings from [44] and [16], who reported that high-albedo surfaces such as concrete and white-painted ground substantially increase rear-side contribution. The results further suggest that adjusting the tilt angle can moderately affect how much irradiance is reflected by different ground surfaces [17].

Figure 5.

Reflected irradiance

Figure 6.

Total Irradiance received

In Figure 6, the total irradiance received (G_con, G_san, and G_grass) follows a similar trend across all surface types, indicating minimal variation due to surface material. The maximum total irradiance occurs at a 0° tilt angle, 2 m height, with the total irradiance from all surfaces exceeding 1000 W/m². The total irradiance is the combination of both incident and reflected irradiance. Optimizing the tilt angle enhances the solar irradiance captured. The minimum irradiance received is approximately 581 W/m². The total irradiance profiles seem to be similar regardless of surface type, indicating that, although the nature of the surface has an effect on reflected irradiance, it exerts a limited effect on total irradiance absorbed by the panels.

Various surfaces, such as concrete, sand, and grass, have different albedo values that directly affect how much solar radiation is reflected. Albedo is the ratio of solar energy that is reflected from the ground surface back to the atmosphere and is an important factor in the local and global balance of energy [44]. In this study, concrete has an average albedo of 0.23, meaning it reflects 23% of the incoming solar radiation. This characteristic of concrete means it has a very high reflectance compared to the other surface types analysed. The high albedo of concrete can thus increase the rear-side irradiance of bifacial solar panels, allowing for a larger portion of energy to be harvested.

Moderate albedo values are associated with dry and bright sand surfaces. In this experiment, the mean reflectance of sand was 0.21. While sand is less reflective than concrete, it does reflect a considerable amount of sunlight, so it is considered an “intermediate” surface for bifacial solar use, as shown in Figure 6. In contrast, grass and other similar types of vegetation have much lower albedo values. Grass surfaces had an average albedo of 0.19, meaning that grass absorbs more solar radiation and reflects less than concrete and sand. Grass surfaces, with a lower albedo, offered the least reflectance, confirming earlier observations in Malaysian [17] and Philippine [10] studies where vegetation-covered sites underperformed compared to high-reflectivity grounds. Although the disparity between sand and grass is minimal, grass tends to be more sand-like than concrete when it comes to reflectivity.

The total irradiation received by a bifacial solar panel is the combined contribution of front-side and rear-side irradiation. While the front side captures direct sunlight and diffuse sky radiation, the rear side primarily absorbs reflected radiation (albedo) from the ground and surrounding surfaces [32]. The total irradiance G_T received by the plane, as shown in Figure 6, can be expressed as using eq. (12).

As shown in Table 7, panel elevation has a strong effect on energy production from bifacial solar panels according to the experimental data. Regardless of the type of surface, the energy production increased when the panels were elevated from 1 m to 2 m. This trend is attributable to enhanced rear-side irradiance capture at higher elevations, where self-shading is reduced and the rear surface maintains a larger, unobstructed view factor to reflective ground areas. Similar gains have been reported in tropical and subtropical settings by [16] and [31], who observed performance improvements of 10–20% when elevating panels above 1.5 m, due to improved light collection and reduced ground shadowing.

Figure 7.

Energy harvested at different heights

From Figure 7, at 1m, all three surfaces recorded the lowest energy production, likely due to limited rear-side irradiance caused by proximity to the ground and increased shading. As height increased to 1.5 m, a moderate rise in energy output was noted, indicating improved irradiance exposure [11]. The experimental results showed that the highest energy output occurred at a height of 2 m. At this height, bifacial panels could capture the highest energy because there was little or no self-shading and also a larger angle of incidence for reflected light. As Table 7 shows, in concrete, the energy generated at a height of 1m was 12.2 kWh and 14.2 kWh at a height of 2 m, which represents an increase of around 16.8%. This aligns closely with findings from [32] in tropical freshwater systems, where 2 m mounting maximized bifacial gain without incurring substantial structural complexity. When the height of the panel was increased to 2.5 m, the energy estimation slightly decreased. This indicates the beginning of the saturation effect, possibly due to higher exposure to wind or thermal losses that compensate more positively than the advantages of irradiance when the height increases, as also noted by [33].

These findings highlight that the installation height as well as the type of the installation surface should be carefully chosen in order to optimally exploit the energy harvesting potential of bifacial PV systems [9]. The mounting height of 2 m is identified as the most favourable mounting height for tropical regions, balancing irradiance capture with minimal performance losses. This height is where exposure to reflected and diffuse irradiance is optimal, and therefore, bifacial solar systems will be most productive.

From a deployment perspective, the findings have direct implications for utility-scale PV design in tropical regions. Adopting low tilt angles (around 5°) on high-albedo surfaces, combined with mounting heights of 2 m, can maximize bifacial energy yield while minimizing land use, installation complexity, and soiling issues. For large-scale projects, such configurations could reduce the levelized cost of electricity (LCOE) by increasing annual energy output without the added capital and maintenance costs of tracking systems.