Predicting the Potential Energy Yield of Bifacial Solar PV Systems in Low-Latitude Region

: The validation of the potential energy yield of bifacial PV systems of various conﬁgurations at low latitudes under West African climatic conditions is critical for evaluating performance and for promoting market expansion of the technology since validation has mostly occurred in high-latitude regions. In this paper, the potential energy yield from an inclined south-facing bifacial PV module and a vertically mounted east–west bifacial PV module are compared to an inclined south-facing monofacial PV module using an analytical model, ﬁeld-measured data, and simulations. For measured/modelled and PVsyst/modelled monofacial systems, the model predicts RMSE values of 1.49 and 9.02, respectively. An inclined bifacial PV system has RMSEs of 1.88 and 7.97 for measured/modelled and PVsyst/modelled, respectively, and a vertically installed system has RMSEs of 10.03 for measured/modelled and 3.76 for PVsyst/modelled. Monthly energy yield is predicted by the model, with deviations from measured data ranging from 0.08% to 1.41% for monofacial systems, from 0.05% to 4.06% for inclined bifacial systems, and from 4.63% to 9.61% for vertical bifacial systems. The average bifacial gains from the modelled, measured, and simulated data of an inclined south-facing stand-alone bifacial PV system over an inclined south-facing stand-alone monofacial system are 9.05%, 10.15%, and 5.65%. Finally, at 0.25 albedo, the inclined monofacial PV system outperforms and yields more energy than the vertically installed bifacial PV system.


Introduction
A viable technology for the future growth of photovoltaics (PVs) is the bifacial solar photovoltaic module. This is because bifacial solar cells absorb incident solar radiation from the sun on the front side while also collecting light falling on the backside, making use of direct, diffuse, and albedo radiation from the ground to generate more power per area than the conventional (monofacial) modules [1][2][3][4][5]. When compared to the conventional modules, bifacial PV can significantly increase energy yield while lowering the levelized cost of energy (LCOE) of photovoltaic modules [6][7][8].The following articles reiterated that the use of bifacial PV modules can reduce the levelized cost of energy. For places with high land costs, such as Seattle, optimizing the bifacial system can significantly decrease the LCOE by 23% [9]. While for high latitudes with high module costs, optimizing the tilt angle between 10-15% higher is required, which can result in a 2-6% reduction in LCOE [10]. Depending on the location for latitudes below 40 • , a bifacial PV system with an albedo range of 0.12-0.30 can become more cost-effective than a monofacial system [11]. Extensive research is being conducted to evaluate the technology's performance from a stand-alone system [12] to a solar farm [10,13] as the manufacturing cost difference between bifacial monofacial PV modules under West African climatic conditions. The findings of this study provide an understanding of the performance of bifacial PV modules of various deployments in low latitudes under West African climatic conditions not only to the PV research communities but also to PV installation companies and governments interested in expanding solar energy projects in the region.
The paper is laid out as follows. Section 1 introduces bifacial PV technology and the reasons for the paradigm shift toward the technology, followed by a literature review that includes the methods used to examine performance, variables influencing energy yield, and bifacial gain reported across various regions, research gaps, and contributions. Section 2 then presents the mathematical equation for the analytical model of the location's global horizontal radiation, incident irradiance on the modules, energy yield, bifacial gain, field data to validate the model, and simulated data. In Section 3, we present the results of the modelled and measured single-day in-plane irradiance and compared the predicted potential energy yield, bifacial gain, deviation, and root mean squared error for various configurations, and finally, in Section 4, we summarize the results and highlight the impact of the research.

Materials and Methods
The analytical model used in this study is developed to validate the performance of three solar PV configurations in a Microsoft Excel environment: i.
An inclined stand-alone monofacial PV system oriented towards the south; ii. An inclined bifacial PV system oriented towards the south; iii. A vertically installed east-west stand-alone bifacial PV system.

Theoretical Framework
To model the output of a bifacial solar photovoltaic module for the various stand-alone PV systems, the irradiance, which is the power of the sunlight per area (W/m 2 ), for the location on any particular day must be determined. Then, the plane of array of irradiance incident on the modules, and lastly, through the physics-based model, the power output of the insolation is calculated.
To begin with, the solar path and intensity of sunlight are required to calculate a location's temporal solar irradiance data [40]. At any particular time during the day, the extraterrestrial irradiance and solar path, which are functions of zenith θ Z and azimuth α S angle, and elevation angle [24] are determined for the geographical location [22], in this case, Navrongo (10.89 • N, 1.09 • W). To calculate the global horizontal irradiance (GHI), the sun position data were fed into five clear sky models, namely the Haurwitz model, the Berger-Duffie (BD) model, the Robledo-Soler (RS) model, the Adnot-Bourges-Campana-Gicquel (ABCG) model, and the Kasten-Czeplak (KC) model from [40,41]. The hourly global horizontal irradiance (GHI) generated was compared, and the Kasten-Czeplak (KC) clear sky model was chosen because its values are the closest to those obtained from the ground weather station data at Navrongo.
where z is the zenith angle of the sun.

GHI Decomposition into DNI and DHI
The global horizontal irradiance (GHI) is composed of two components: direct normal irradiance (DNI) and diffuse horizontal irradiance (DHI). Their relationship is expressed as follows: GHI must be decomposed from the equation into the variables that make up the value. The diffuse fraction (K D ) is determined using the hourly sky clearness index (K T ) when implemented in the Reindle model [42,43], and the clearness index is the ratio of GHI to extraterrestrial irradiance. The DHI is then estimated through the relationship between diffuse fraction and GHI. Finally, from Equation (1), DNI can then be calculated. Since GHI is already determined, based on the day of the year, I 0 . I can be computed analytically.
In the literature, there are various empirical models for decomposing GHI. On average, a reasonable agreement has been established amongst these models [31]. The Hay and Davies model [44,45] is used for DHI transposition on the plane of the array. The diffuse circumsolar irradiance surrounding the DNI is accounted for using the model. This ensures that the anisotropic nature of the diffuse irradiance is properly considered as the circumsolar diffuse irradiance is superimposed on the isotropic model, lowering the model's overestimation of energy yield PV modules. The angle of incidence (AOI) at the front/back surface of the two oriented panels must be determined to assess the contribution of direct normal irradiance (DNI) for both stand-alone optimally inclined north-south and vertically installed east-west orientation. The angle of incidence (AOI) is a function of the zenith angle θ Z , tilt angle τ, the azimuth angle of the sun, and the module expressed as α S and α M . The angle of incidence (AOI) for the north-south-oriented inclined panel can be expressed as follows [10,32,46]: cos AOI rear = cos θ Z cos 180 − τ f ront + sin θ Z sin 180 − τ f ront cos α s − α M f + 180 The angle of Incidence (AOI) for the vertically installed east-west orientation is given as follows [31]: cos AOI back = sin θ Z cos(α S + π/2) (7)

Optical Collection Model on the Panel
Based on the orientation of the module, the amount of irradiance incident on the surface of a panel can be estimated. This may be divided into irradiance hitting the front surface E f W/m 2 and irradiance at the rear surface E r W/m 2 for the monofacial and bifacial module configurations. The total irradiance at the front side of the module is given as follows [17]: These are the direct, the diffuse, and the reflected irradiances in W/m 2 .

Direct Irradiance
The equation for the proportion of direct normal irradiance (DNI) incident on the module is as follows [11,32]: AL is the angular losses in PV modules, the angle of incidence (AOI) influences the angular losses of direct normal irradiance to the module surface [47], and the model proposed to compute these losses is as follows: where ar is the angular loss coefficient considered to be 0.16 in this study. This value falls between the normal ar values for commercial C-si modules [47].

Diffuse Irradiance
Because of the anisotropic nature of the diffuse radiation, accounting for diffuse radiation on a tilted module is challenging when compared to direct irradiance. The transposition model performance analysis of diffuse irradiance has been conducted by Yang et al. and Xie et al. [45,48]. The author of [45] concluded that there is no universal model after analyzing the performance of 26 transposition models against 18 datasets throughout the world. The author identified the Hay and Davies transposition model, which includes two components, as one of the best with two components. The model is used for the hourly in-plane diffuse irradiance. The isotropic component of diffuse radiation is thought to be homogeneous across the sky globe. The circumsolar component radiates from the Sun's immediate surroundings [24]. Each of these components has a unique method for estimating the optical plane of array radiation on the solar module. This is given as follows: where sv f is the sky view factor from the module to the sky, AL di f f is the diffuse angular loss [24,47,49], and the angle of incidence of circumsolar AOI cir is the same as that of the direct irradiance [32]. The integration of the two components gives the total radiation on the front and the rear side of the module.

Ground Albedo Irradiance
The methodology for calculating the front and back sides of the reflected ground is divided into two parts. The ground reflected irradiance for the front surface is calculated assuming that global radiation is isotropic; that is, the radiation is uniform and independent of the direction and it is given as follows [11,24,50]: where gv f = 1−cos τ 2 is the ground view factor, AL gre f is the ground angular losses [47,49], and GH I is the global horizontal irradiance in W/m 2 . For the calculation of the rear-side ground reflected irradiance, the radiation attenuation caused by the module's resulting shadow on the ground is accounted for using the equation from [51]. Only diffuse radiation is received by the shaded area, whereas ground horizontal radiation is received by the unshaded area. Thus, the method used by Shoukry et al. [12], Sun et al. [32], and Appelbaum [50] for the rear-side plane of module radiation was adopted.
F rsgrd and F rnsgrd represent the shaded area and the non-shaded area of the rear side. The total irradiance at the rear side of the module is given as follows: Note that the height of the panel is 1 m and the elevation of the panel from the ground is 1 m; a low ground albedo of 0.25 is considered as it corresponds to vegetation/soil ground, as reported by [15,32].

Power Conversion Efficiency Model
A single-point power model is used to convert the light incident on the modules to electrical power output [32,52], which is written as follows: where the E f and E r are the sum of the front-and rear-side in-plane irradiance on the panel, A is the area of the PV module, η f and η r are the efficiencies of the front and rear sides of the PV module, and P PV is total power output. The bifaciality is given as η rear(STC) /η f ront(STC) [32]. The rear-side efficiency is determined as the bifaciality, and the front side efficiency is given by the module manufacturer. The potential energy is given as follows: where Y bi f acial represents the energy yield in the bifacial PV module and Y mono f acial is the monofacial energy yield.

Field Data Methodology for Validation of the Model with Field Data
The model results were validated against the field data for Navrongo (10.89 • N, 1.09 • W) in Ghana. The site installation includes a reference inclined monofacial PV module, as well as two stand-alone bifacial PV modules, one inclined and oriented south and the other vertically mounted and oriented east-west (see Figure 1). Hourly on-site global horizontal irradiance (GHI), front in-plane irradiance, and rear-side in-plane irradiance measurements are available for November 2020 to June 2021. The instrumentation for measuring and recording field data consisted of Campbell CMP-1 and SP-421 Apogee Pyranometer for measuring the global horizontal irradiance and the in-plane irradiance, a Microstep BIM205 intelligent solar charger, 12 V DC battery, load, and a Campbell CR300 logger. Each of the modules was connected to a single solar charger with MPPT function, which in turn is connected to the battery, load, and data logger. Tables 1 and 2 show the electrical properties of the PV modules (JA Solar JAM72S09-385/PR and LG NeoN2 Bifacial LG335N1T-V5) as well as the system parameters installed at the location. To obtain the optimum performance on the yield, the inclined south-facing PV system is tilted at an optimum angle of 14 • while the vertically mounted east-west is at 90 • .

Simulation Data
To determine the energy yield for each configuration, the stand-alone system was simulated in PVsyst version 7.2 with a Jinkosolar product (JKM335M-60H-BDVP-BIFACIAL and JKM335M-60H-TV) under the same system parameter conditions. The electrical characteristics of the module are presented in Table 3.

Results and Discussions
The radiation received by each configuration can be calculated using the model presented in Section 2. Figure 2 depicts the in-plane radiation received by each configuration on the 21st of March, June, and December. The model output result is compared to the measured data from the field (Navrongo, 10.89 • N, 1.09 • W). The south-facing bifacial PV module tilted at 14 • receives the most in-plane radiation in a single day, as shown in Table 4. The model in-plane irradiance values are higher than the experimental values. Though models are ideal, the disparity in value with the measured can be due to the inaccuracy in the orientation of the module, daily diurnal variation, and site climatic conditions. The in-plane radiation of monofacial and bifacial PV modules oriented towards the south has one peak period at noon. A bifacial PV module oriented east-west and tilted at 90 • has two peak periods during which the in-plane radiation received by the module is at its highest: morning and evening. In the global analysis of a vertically installed bifacial PV module by Guo et al. [22], a similar pattern of in-plane irradiance received by the module was reported. The output power curve for vertically mounted bifacial PV modules shown by Sun et al. [32] and Thomas et al. [53] has the same pattern of two peak periods. These dual peak periods have been discovered to be advantageous in network integration because they aid in improving power network efficiency as well as matching the daily power generated and the load profile [54][55][56].

Estimation of Energy Yield by Different Solar PV Configurations
The accuracy of the model for each PV module configuration is examined in this section. The analysis is based on the potential energy yield from the previous year's field data (November 2020-June 2021) and energy output simulated with PVsyst 7.2. Figures 3-5 represent the potential monthly energy yield from various solar PV configurations. The calculated values are compared to the measured results and PVsyst simulation values. Tables 5 and 6 show the deviation between the measured data, PVsyst data, and modelled data and the root mean square error of the systems. This aids in determining how well the model can predict the energy yield of the systems. In Figures 3 and 4, the potential energy yield predicted by PVsyst is greater than both the modelled and measured energy yield for inclined monofacial and bifacial PV systems. The modelled and measured potential energy yields for the two systems are in more agreement, with deviation ranges of 0.08-1.41% for the monofacial system and 0.05-4.06% for the inclined bifacial PV system. The two systems' average deviation values are 0.75% and 1.01%, and the root mean square errors for the modelled and the measured potential yield are 1.49 and 1.88, respectively. This indicates that the proposed model for estimating monthly energy yield is suitable for the system [57].
As shown in Figure 5, the potential energy yield for the PVsyst simulation results and the modelled data in a vertically installed system are in more agreement and are higher than that of the measured data. While the model assumed equal radiation intensity before and afternoon (morning and evening), resulting in an overestimation of potential energy yield, there is a variation in radiation intensity, with in-plane radiation being slightly lower toward in the evening period [53]. The average deviation between the modelled and measured potential energy yields is 6.86%, while the deviation between the PVsyst and the modelled potential energy yield is 2.47%. It is worth noting that the PVsyst software for the simulation adopted the Perez model that accounts for the horizon diffusion which was not considered by the model. The variation in a system's model, measured, and simulated potential energy output can be linked to uncertainties in the measuring equipment, local weather interannual variation, and simulation software inefficiency [58,59].

Comparison of the Model Energy Output of the Two Bifacial PV Systems
Based on the model data, the annual energy output of both bifacial PV systems (tilted south-facing and vertically mounted east-west) is compared. The tilted bifacial PV module system, as shown in Figure 6, generated more energy throughout the year. The annual average relative difference between the two configurations in energy output is 18.09%.

Inclined Bifacial Energy Gain over the Monofacial System (Bifacial Gain)
The monthly bifacial gain from the measured, modelled, and PVsyst simulated energy output of an inclined bifacial system over a monofacial system is shown in Figure 7 and Table 7. From the field data (November 2020-June 2021), the bifacial gain from monthly measured data of an inclined bifacial system over a monofacial system ranges between 7.08 and 10.27%; however, a higher bifacial gain of 6.64-12.44% is observed in the modelled system. Meanwhile, the PVSyst simulated gain observed is less than the measured and modelled bifacial gains. Interestingly, the average bifacial gain under vegetation or soil (albedo: 0.20-0.25) of an inclined bifacial system over a monofacial system from measured, modelled, and simulated data aligns with what other authors have reported for latitudes below 30 • [12,32].     Table 8 shows the performance of a vertically installed bifacial PV system on natural vegetation with an albedo of 0.25. Regardless of the method adopted to determine the energy yield, the monofacial PV system outperforms the vertically installed bifacial system at Navrongo. Though a vertically installed bifacial PV system has the advantage of shifting peak power generation to dawn and dusk, system optimization is required to improve the energy yield. Khan et al. [31] reported that globally, the albedo of a vertically installed bifacial PV module should be increased to 0.5 to outperform a monofacial system. Guo et al. [22] reported that the performance of a vertically installed bifacial PV system over a monofacial PV system is dependent on albedo and that it varies from location to location. This viewpoint is supported by research conducted by Shoukry et al. [12], who discovered that at an albedo of 0.2 at El Gouna (Egypt) and Constance (Germany), a monofacial system outperforms a vertically installed bifacial system. Increasing the albedo to 0.5 at both locations resulted in an annual energy gain of 15.77% at Constance and a loss of −5.99% at El Gouna. Hence, for an installation of a vertically mounted east-west bifacial PV system in this location, the albedo will have to be optimized to boost the energy yield over the monofacial PV system.

Conclusions
An analytical model was used in this study to determine the potential energy yield of a south-facing bifacial PV stand-alone system and a vertically installed east-west bifacial PV stand-alone system in comparison to a monofacial system at low latitude in Navrongo, northern Ghana. The model considers important system parameters such as albedo, module elevation, and module self-shading, all of which can influence the potential energy yield. The model was validated using in-plane field irradiance data (Navrongo, Ghana) from November 2020 to June 2021, as well as PVsyst.
The results from  show that the proposed model has a higher accuracy in predicting the output of the potential energy yield for a south-facing-inclined bifacial PV system than for a vertically installed east-west bifacial PV system. The model predicts RMSE values of 1.49 and 9.02 for measured/modelled and PVsyst/modelled monofacial systems. For an inclined bifacial PV system, RMSE values of 1.88 and 7.97 are obtained for measured/modelled and PVsyst/modelled, and lastly, for a vertically installed system, RMSE values of 10.03 for measured/modelled and 3.76 for PVsyst/modelled were predicted. The model predicts monthly energy yield, with a deviation from measured data ranging from 0.08% to 1.41% for monofacial systems, from 0.05% to 4.06% for inclined bifacial systems, and from 4.63% to 9.61% for inclined bifacial systems. Taking this into consideration, this model is useful in predicting the potential energy yield for various configurations at this location, and depending on the system configuration and parameters, the model can be applied anywhere in the world in the absence of measured data to determine the energy yield. The technical assessment of a bifacial PV module under West African climatic conditions revealed an average bifacial gain of between 5.65% and 10.15%. Conducting a technoeconomic assessment to determine financial viability will make scaling up the system easier.  financial support of the EnPe project for the establishment of the experimental facilities used in this study. Additionally, the authors appreciate the support from the Faculty of Environmental Sciences and Natural Resources Management, Norwegian University of Life Sciences, Ås, Norway.

Conflicts of Interest:
The authors declare no conflict of interest.