Developing an energy rating for bifacial photovoltaic modules

The photovoltaic (PV) module energy rating standard series IEC 61853 does not cover bifacial PV modules. However, the market share of bifacial PV modules has dramatically increased in recent years and is projected to grow. This work demonstrates how Parts 3 and 4 of the IEC 61853 standard could be extended to bifacial modules. First, we develop an irradiance model that uses the data already given in the standard IEC 61853‐4 to calculate the irradiance on the rear side of the module. Second, we propose a way to extend the energy yield calculation algorithm IEC 61853‐3 to include bifacial modules and make it available to the PV community. This rear irradiance and bifacial energy yield calculation procedure is tested using real outdoor measurements for a nine‐month period with a root mean square difference between measured and simulated energy yield of 4.65%. To conclude, we investigate the impact of different climates and normalization on the bifacial module energy rating results.


| INTRODUCTION
Photovoltaic (PV) modules are typically evaluated operating under standard test conditions (STCs) 1 with a fixed operating temperature of 25 C and front side irradiance of 1000 W/m 2 with normal incidence and AM1.5G reference spectrum. 2However, in practice outdoors in nearly all climates, PV modules will never operate at those conditions.Energy ratings are a measure to evaluate PV modules over 1 year full of operating conditions in different climates instead of just one.Consequently, PV module energy ratings include evaluation of module performance under irradiance from various directions, with various spectra and intensities as well as different operating temperatures over one full year.
][5][6][7][8][9][10][11][12][13][14] It is important to distinguish between energy yield prediction and energy rating as they are often confused.The goal of an energy yield prediction is to forecast the energy yield of a given system at a specific location as accurately as possible.Thus, it requires several years of location specific meteorological data.In contrast, the goal of an energy rating is to compare the performance of PV modules in a given climate, thus comparability and reproducibility become a priority therefore typically one-year long reference climates are used instead of site-specific meteorological data.
The IEC 61853 series [15][16][17][18] defines a standard method to calculate PV module energy ratings.Recently, an intercomparison of more than 10 different research organizations demonstrated that they could calculate the energy rating of two modules with less than 0.1% deviation across all climates, 19 highlighting the comparability of IEC 61853.The standard series was completed in 2018 and consists of four parts.Part 1 15 deals with the measurement of the so-called power matrix, which consists of module power values for a range of irradiance G and module temperature values T mod , whereas Part 2 16 defines methods to measure the module's operating temperature, spectral response, and dependency on the incidence angle.The reference climates with hourly irradiation, temperature, wind speed, and angle of incidence data are defined in Part 4. 18 Part 3 17 is at the heart of the standard series tying the measured module and the climate data together in an energy yield and rating calculation algorithm.IEC 61853-3 states that it applies to monofacial PV modules 17 explicitly excluding bifacial PV modules.
A technical report 34 has taken a first step in the development of an energy rating for bifacial modules; however, it is mainly focused on Parts 1 and 2. For Parts 3 and 4, it gives no equations for deriving the rear irradiance or how to deal with the rear irradiance in the energy rating calculation.In this paper, we introduce an alternative detailed approach on how Parts 3 and 4 of the IEC 61853 standard could be extended to bifacial modules to further the scientific discussion.
The main additions of this work are (1) a detailed description of the calculation procedure for rear irradiance including a comprehensive set equations for rear irradiance and bifacial module energy rating calculation.(2) The ground reflected rear irradiance is introduced as a separate climate parameter, which is treated properly in the angular correction step.(3) Our approach is applied to all six climates, and the monthly irradiation distribution is discussed, and the resulting data are downloadable.(4) An initial test of our calculation procedure is conducted by comparison with outdoor measurement data rather than just by calculating energy ratings.(5) Two bifacial energy rating definitions are discussed and compared.(6) The impact of different bifaciality values on the bifacial energy ratings is analyzed.(7) We analyze the differences in the impact of the applied irradiation corrections for both sides of the module.

| REAR IRRADIANCE CALCULATION AND RESULTS
In this section, we introduce the model to calculate the rear irradiance and discuss the results.Note that the rear irradiance calculation would only have to be performed when creating the bifacial module energy rating climate data and not by every user.It extends the climate data from IEC 61853-4 to provide additional rear irradiance components necessary for bifacial modules.To further scientific discussions, we publish Supporting information (Data S1-S6) to this paper containing the hour results of Equations ( 1)-( 5) for each climate for a fixed albedo of 0.2.

| Rear irradiation calculation procedure
To calculate the energy rating of a bifacial PV module, the irradiance incidence on both faces of the module must be available for calculation; however, the current standard contains only front side irradiance.Thus, we develop an irradiance model that uses the data already given in the standard IEC 61853-4 18 to calculate the irradiance on the rear side of the module G r according to We split the rear irradiance (G r ) into three components: beam direct (B r ), sky diffuse (D r ), and ground reflected diffuse (D g ) irradiance, all in-plane of the rear side of the module, given by Equations ( 3)- (5).
The hourly incidence angle on the rear side of the module θ r is calculated as where α s is the hourly solar elevation given in the standard, β is the module tilt angle, A s is the sun azimuth angle, and A mr is the azimuth angle of the module rear side, which is defined as facing away from the equator in the standard.Equation (2) only applies for rear incidence angles smaller than 90 , as the standard does for the front side, we set all other angles to 90 .Note that we use 20 module tilt angle in order to enable a comparison of monofacial and bifacial module energy ratings, as the monofacial standard fixes the angle to 20 for all climates irrespective of what the optimum tilt for the climate might be.Different mounting options such as east-west vertical or tracking would enhance the exploitation of the bifacial aspect but would make comparison with the current monofacial standard challenging, which is a core focus of this work.The hourly values for the sun azimuth angle A s and the direct normal irradiance (DNI) are calculated as described in Appendix A.1 as they are not published in IEC 61853-4. 18The direct in-plane rear irradiance B r is calculated via the following equation: The direct in-plane rear irradiance only applies when the sun is located behind the module resulting in a rear incidence angle θ r < 90 .
We select a view factor approach to model the rear irradiance as it is fast enough to calculate six full years of hourly irradiance scenarios.Note that this approach assumes uniform irradiance on to the module plane.Considering nonuniformity would most certainly require knowledge of the position of each cell and their operating points to calculate the impact on the module power correctly, which would greatly increase the complexity of calculating an energy rating.
Several studies suggest [35][36][37] that the impact of nonuniformity is small for low albedo and tilt angle combinations such as 0.2 and 20 .
The 2D view factor model assumes one infinite row of PV modules with a certain module length and tilt.
Figure 1 shows how the view from the rear side of the module can be divided into three view factors for the purpose of calculating the indirect irradiance on the rear side of the module: i.The view to the sky (V r,sky ), which receives the sky diffuse rear irradiance (D r ).
ii.The view to the unshaded ground (V r,shaded ), where the ground receives the global horizontal irradiance (GHI).
iii.The view to the shaded ground (V r,unshaded ), where the ground receives the diffuse horizontal irradiance (DHI).
Using more view factors with a finer resolution as in Marion et al. 38 would most likely be advantageous in more detailed soundings or if a different angular correction method would be applied in the energy rating calculation.
The diffuse in-plane rear irradiance D r is calculated using the Perez model. 39,40As such where α = max{0, cos (θ r )}; b = max{cos(85 ), cos(90 À α s )}; and F 1 and F 2 are the circumsolar and horizon brightness coefficients, respectively, all as given by Perez et al. 39,40 Our 2D view factor model that considers shading of the ground by the PV module is used to calculate ground reflected irradiance D g , where α g is the ground albedo, and the view factor equations can be found in Appendix A.2.The view factors depend on the exact module mounting conditions.The view factors are derived based on our extension of the work by Appelbaum. 41e hourly rear side in-plane irradiance G r is then given by the sum of all three parts (Equation 1).As only the front side global inplane irradiance is given in spectrally (R λ ð Þ) resolved form in the standard, we also only consider the rear side global in-plane irradiance where G f is the global front side in-plane irradiance given in the standard, thus giving the module rear side irradiance the same spectral distribution as the front side.This choice is made because the direct and diffuse spectra are not published in Part 4, which prevents us from making Equations ( 3)-( 5) fully spectrally resolved.Note that the algorithm in the following section would also work, if the spectra on front and rear side would be different.So, if more information would be made available, it could still be used to calculate bifacial energy ratings.

| Irradiance results for the reference climates
We run rear irradiance model for each climate and hour of the year with an albedo of 0.2, a module mounting height of 1 m defined from the lower edge of the module, a module length of 2 m, and a module tilt angle of 20 to keep consistency with the monofacial standard.
Figure 2a shows the rear irradiation distribution for the temperate coastal climate.The ground reflected light accounts for 88% of the rear irradiation, whereas the direct light accounts for less than 1%.
A monthly irradiation comparison (Figure 2b) reveals that the differences are largest in the summer months.The rear irradiation distribution for the five climates not shown here is in Appendix A. F I G U R E 1 View factors from the rear side of the module to the sky and to shaded and not shaded grounds.

| BIFACIAL ENERGY YIELD CALCULATION ALGORITHM AND TEST
Now that we have the necessary rear irradiance data, we adjust the energy yield calculation algorithm of the standard from monofacial to bifacial modules.Then we test the extended algorithm using data from outdoor measurements of a bifacial PV system. 31

| Calculation flow
In this subsection, we show how the energy yield calculation algorithm defined in IEC 61853 Part 3 17 can be extended to bifacial modules.Figure 3 shows the proposed algorithm for the calculation of the bifacial module energy yield and rating.To be consistent and thus comparable with monofacial IEC 61853-3 standard, we keep the four main calculation steps.We follow the best practice guidelines 19 established for the front side, except where the bifacial nature of the module requires us to make the adjustments discussed in the following.
The first step is the correction for angular losses; like the standard, we use the model of Martin and Ruiz 42,43 for this purpose.In contrast to the standard, we apply it twice once for the front and once for the rear irradiation.The equations for rear beam irradiance use the rear incidence angle θ r and as the equations for rear sky diffuse irradiance both use the angular loss coefficient of the rear side a r,r .Because the rear is dominated by ground reflected irradiance (see Figure 2), we also include the correction for ground reflected irradiance.The corrected ground reflected irradiance D g,corr,j is given by where a r,r is the angular loss coefficient of the rear side of the bifacial PV module and γ ¼ 180 À β.The corrected beam B r,corr,j and diffuse irradiance D r,corr,j are calculated via the same equations as the front side with rear side versions of in-plane beam irradiance B r,j , angle of incidence θ r,j , angular loss coefficient a r,r , in-plane diffuse irradiance D r,j , tilt γ replacing their front side counterparts from the standard, and index j runs through all hours of the year.The three angular corrected rear side irradiance components are summed up to calculate the angular corrected rear side in-plane irradiance The second step is the spectral correction, which we do separately for the front and rear side.The spectral correction follows the best practice guidelines 19   where G r,corr,j is the hourly spectral corrected rear side irradiance; λ s and λ e are the start and end wavelength of 306.8 nm and 3991 nm, respectively; S r λ ð Þ is the spectral response of the PV module rear side; R STC λ ð Þ is the AM1.5G reference spectrum 2 ; and R r,corr,AOI,j λ ð Þ is the multiplication of spectrally resolved in-plane irradiance R r,j λ ð Þ (from Equation 6) with the ratio of angular corrected G r,corr,AOI,j and uncorrected G r,j rear side in-plane irradiance.
Before the module operating temperature is calculated, we sum up the angular corrected front (G f,corr,AOI,j Þ and rear side (G r,corr,AOI,j ) irradiances to calculate the total angular corrected irradiance As in the standard, the Faiman model 44 is used to calculate the module operating temperature (T mod,j ) where T amb,j is the ambient temperature, v j the wind speed, and u 0 and u 1 are the thermal coefficients of the PV module.Note that the Faiman model has not been updated for the use of bifacial modules.
Thus, we adjusted the Faiman model 44 and substituted the front irradiance for the total irradiance.This contains the assumption that the rear side absorption for bifacial modules is much higher for bifacial modules than for monofacial ones, which typically have a white backsheet.Further studies on how to adjust the Faiman temperature model to bifacial modules are strongly recommended, but are too extensive for this work, which focuses on PV module energy ratings.
Prior to calculating the module power output, the effective spectrally corrected irradiance (G eff,corr;j Þ needs to be determined according to where b f is the bifaciality factor of the PV module power.The bifaciality factor is the ratio between the rear side module power, when this side is illuminated under STC whereas the front side is covered, and the front side module power output when the module is flipped.Note that the bifaciality is not used in Equation ( 9), because the irradiance, which the rear side of the module could not convert into electrical power, will in most cases still increase the module temperature.
The module power P mod,j is calculated inter-and extrapolating the so-called module power matrix to the hourly operating temperatures and irradiances.The only change from the best practice guidelines 19 is that we interpolate or extrapolate to the effective spectrally corrected irradiance (G eff,corr;j Þ from Equation ( 11) instead of just the front side component.We see the adaptation from front side to effective irradiance as similar to the equivalent irradiance method for determining power output of a bifacial module under bifacial standard test conditions (BSTCs) 45 , while illuminating only the front side.Finally, the yearly energy yield E tot,year is calculated by summing up the module power P mod,j over all hours of the year according to E tot,year ¼ X Note that we add only relatively simple calculation steps (Equations 7-11) and no new type of PV module parameter.Instead, we add rear side versions of the angular loss coefficient (a r,r ) and the modules spectral response (S r λ ð Þ), because the front side counterparts are already in the current IEC 61853 standard, measuring them for the rear side and the front side only slightly increases the effort.Thus, our bifacial energy yield calculation naturally extends PV module energy ratings algorithm from IEC 61853-3 to bifacial modules.

| Test with energy yield measurement data
We use the bifacial ground based reference system next to the floating system introduced by Ziar et al. 31 to check whether the combination of our rear irradiance model (Section 2) and bifacial energy yield calculation algorithm (Section 3.1) can determine the module power output of a bifacial module.For a nine-month period, the module output power, the ambient temperature, the wind speed, and the GHI were measured at the test site.Our calculation procedure also requires the solar altitude and azimuth as well as DHI and DNI.Therefore, we use the PV_LIB toolbox 46 in Matlab to calculate the sun position and the model by Reindl et al. 47 to decompose GHI into DHI and DNI.We adjust the albedo, module tilt.and module parameters to the ones of the reference system.because only the GHI is measured, we calculated decomposition into direct and diffuse as well as in-plane irradiance, which most likely creates additional deviations as compared to the standard where decomposed in-plane irradiance is given.Nevertheless, the agreement indicates that our algorithm is accurate enough to calculate the bifacial module energy yield for the purpose of creating an energy rating.

| BIFACIAL ENERGY RATING DEFINITION AND RESULTS
After introducing the bifacial energy yield calculation algorithm and testing it, this section deals with two ways to define the energy rating for bifacial modules and discusses the results in the climates.

| How to define the bifacial energy rating?
The climate specific energy rating (CSER) for monofacial is defined as energy efficiency in the reference climate over 1 year divided by power efficiency under standard test conditions given by the following equation. 17 where E f,year is the monofacial energy yield, H f,year is the yearly inplane irradiation of the front side, P f,STC is the module power under STC, and G f,STC is the STC irradiance.Replacing these measurables by their bifacial module counterparts, we derive where E tot,year is the bifacial energy yield, H tot,year is the yearly in-plane irradiation of the front and rear side, P BSTC is the module power under BSTC, and G BSTC is the BSTC irradiance.The disadvantage of this definition is that it is hard to compare bifacial and monofacial modules.
This can be best realized, if we try to calculate the CSER bif1 value for monofacial modules or bifacial modules with bifaciality factor of zero.
To do this, we insert the following into Equation ( 14): which has H f,year the yearly in-plane irradiation of the front replacing the total irradiation.This solves the comparison problem with the monofacial energy rating in the existing standard by giving CSER bif2 ¼ CSER mono , when repeating the same thought experiment of calculating the bifacial energy rating for monofacial modules.

| Bifacial energy rating in reference climates
To analyze the differences between these definitions, we use the open source data for the monofacial c-Si "module 1" as published by Vogt et al. 19 As no such data are available for bifacial modules, we assume for the purpose of calculating the bifacial energy rating that this module has rear side with the same angular loss coefficient and spectral response as the front side.This completes the PV module input data for our calculation procedure.Note that while we assume the same front and rear side module parameters that due to different values in Part 4, we still perform the separate calculations as described in Section 3. Furthermore, we vary the bifaciality factor with values of 0, 0.5, and 1.
Figure 5 shows the CSER values for bifacial modules according to Approach 1 (circles) and Approach 2 ("x") for three different bifaciality factors (1 in blue, 0.5 in green, and 0 in red) and the monofacial energy rating (plus).The second approach gives the same CSER value for a bifaciality of zero as the monofacial module, as the modules have identical front sides.In contrast, the first approach always gives a lower CSER even for a bifaciality equal to one.The fact that the first definition is lower for a bifaciality factor of one shows that the rear side energy efficiency is lower than the front side energy efficiency.As desired, both definitions clearly show the advantage Measured bifacial energy yield at the outdoor test site (blue) and simulated energy yield by the model introduced in this work (orange).Over a nine-month period, the root mean square difference between measured and simulated energy yield is 4.65%.
of a higher bifaciality factor.However, due to better comparability with monofacial standard, we recommend the use of the second definition CSER bif2 and focus our further analysis on this definition.
Comparing the impact different climates for this second definition bifacial energy rating with the monofacial energy rating, we see the largest difference of 17.9% for bifaciality of one and 9% for bifaciality In fact, in the subtropical arid climate, the climate with the lowest AOI correction impact, both front and rear correction are responsible for a reduction of 1.7%.This implies that having a separate angular rear irradiance correction step is paramount for a bifacial energy rating.Note that the angular by Martin and Ruiz 42,43 was developed for monofacial modules and that these results are based on the assumption that it also can be used to model the rear side of bifacial modules.
F I G U R E 5 Climate specific energy rating (CSER) for bifacial modules according to Approach 1 (circle) and Approach 2 ("x") for three different bifaciality factors and the monofacial energy rating (plus).The second approach gives the same CSER value for a bifaciality of zero as the monofacial module, when assuming identical front sides.In contrast, the first approach always gives a lower CSER even for a bifaciality of one.
T A B L E 2 Effect of irradiance correction on energy bifacial energy rating.Having no spectral correction decreases the energy rating by up to 3.2% for a bifacial module with bifaciality factor of one, but only by up to 2.7% for a module with bifaciality factor of zero.Thus, the rear side is only responsible for a 0.5% change, whereas the front side accounts for 2.7% change in spectral correction.The change is similar or smaller in all other climates.The high elevation climate differs as it is the only climate in which the spectral correction decreases the energy yield and rating; however, the rear side impact is 0.2% compared to 1.6% for the front side.Therefore, rear side has no over proportional impact on the spectral correction.Note that this might change if a drastically different spectral distribution of the rear side is used instead of Equation ( 6), which invers the front side distribution to the rear side due to a lack of separate diffuse and direct spectra in IEC 61853-4.Also, having a different PV module with different optical properties for the rear side could change these findings.Therefore, we recommend that this should be investigated further in future work.

| SUMMARY AND CONCLUSION
In this work, we proposed and evaluated an energy rating for bifacial modules.The missing rear side irradiance data are calculated using a view factor model.The energy yield calculation algorithm uses separate calculation steps for front and rear side angular as well as spectral correction.The rear side angular correction is extended by a term for ground reflected irradiance.The temperature and power calculation steps use the combined total and effective irradiance, respectively.
Thus, only relatively simple calculation steps and no measurements, which are not already used for the front side, are added when extending the standard to bifacial modules.This procedure was tested using outdoor measurements over a nine-month period.
We evaluated two different approaches for defining the bifacial CSER and conclude that the second one, using only the front side irradiation for reference, is more advantageous due to better comparability and consistency with the established monofacial standard.Further, we show that the bifacial gain in CSER in a climate is linked to the diffuse fraction of the irradiance.We also provide a first indication that the separate angular correction of rear side irradiance is important for bifacial energy ratings.
with the sun zenith angle θ z = 90 À α s : Next, the sun azimuth angle A s is determined using where ω is the hour angle, Φ is the latitude of the climate data given in Part 4, and δ is the declination angle.To determine the declination angle, we use where B is defined by with n being the day of the year.

A.2 | View factors
Figure 1 shows the geometry of our 2D view factor model consisting of a single row of modules with an infinite row length.It is an extension of Appelbaum's work, 41 which considers also the module mounting height above the ground measured from what we would in reality call the front edge of the module but is a point in the 2D.Looking at the projection of the ground to this height, we can see the Appelbaum unshaded ground is equivalent to our unshaded ground behind the module is defined as where L m is the module length, β is the module tilt, and L s is the shadow length, which we take from eq. 3.11 by Smets et al. 48The shaded ground is defined as where the V r,unshaded,1 view factor unshaded ground in front of the module is subtracted from the view factor of Appelbaum's shaded ground.This view factor unshaded ground in front of the module is defined via where L p is the length of the projection of the unshaded ground in front of the shadow to the module mounting height H g .It is calculated via where ρ is the missing angle in a triangle of the module tilt and σ is the angle for the unshaded ground in front of the shadow.They are define via with L UG being the length of the unshaded ground in from of the module where α s is the hourly solar elevation given in the standard, β is the module tilt angle, A s is the sun azimuth angle, and A mr is the azimuth angle of the module rear side.The side S is define as in which E is the extension of the module towards the ground obtained via The sum of both unshaded ground view factors is used in Equation ( 5) of this work.Finally, as an initial test we see that Our work is organized as follows: In Section 2, we show how the climate data from Part 4 could be expanded to have all the irradiance values to consider bifacial modules.The irradiance results are also provided as Supporting information (Data S1-S6) to this work.Section 3 deals with adjusting energy yield calculation algorithm from Part 3 of IEC 61863 to bifacial modules.It also contains a test of the bifacial module energy yield calculation procedure.The energy rating for bifacial modules is defined and discussed in Section 4, before we conclude in Section 5.
established for the front side.Replacing the front side input variables with their rear side counterparts, we derive the equation G r,corr,j ¼ 1000 Á ð λe λs S r λ ð ÞÁ R r,corr,AOI,j λ ð ÞÁ dλ ð λe λs S r λ ð ÞÁR STC λ ð ÞÁdλ , ð8Þ F I G U R E 2 Results of our rear irradiance model.(a) Distribution of light on the rear of the PV module.(b) Comparison of monthly irradiation for mono-and bifacial modules in the temperate coastal climate.T A B L E 1 Yearly in-plane irradiation on bifacial modules and bifacial irradiation gain compared with monofacial modules.

Figure 4
Figure4shows the comparison between measured (blue) and simulated (orange) energy yield.Over the whole period, the root mean square difference is 4.65% based on comparing hourly values of the measured and simulated energy yield of the bifacial module.Note that year , P BSTC ¼ P STC , and G BSTC =G STC , due to the scaling of BSTC with the bifaciality factor, 29 while H tot,year ¼ H tot,year remains the same because a monofacial module receives rear side irradiance.Consequently, one would then have CSER bif1 <CSER mono for the same module.The reason behind this is ultimately that the mono-and bifacial energy rating definitions have different yearly in-plane irradiation reference points.Thus, we propose a second definition: of 0.5 in the tropical humid climate.While the subtropical arid climate results in the lowest difference in bifacial gains of 14.3% and 7.2% for the bifaciality factors of 1 and 0.5, respectively.The diffuse irradiance fraction in the climates drives this trend.Additionally, we investigate the impact of the irradiance correction step by skipping them and calculating the bifacial energy rating CSER bif2 .Table 2 lists the results as percentage change in CSER bif2 for same modules as in the previous figure.Having no angle of incidence (AOI) correction increases the energy rating by up to 5.3% for a bifacial module with bifaciality factor of one, but only by up to 2.9% for a module with bifaciality factor of zero.This signifies that the AOI correction of the rear irradiance reduces the PV module energy rating by 2.4%, whereas the front side AOI correction reduces it by 2.9%.Interestingly the rear side irradiation is only 18.1% of the front side irradiation yet they have nearly the same impact on the bifacial energy rating.The fact that angular correction of the front and rear side irradiation has similar impacts holds for all climates.

A. 3 |
Figures visualizing the monthly irradiance distribution in the other reference climates We run rear irradiance model for each climate and hour of the year with an albedo of 0.2, a module mounting height of 1 m, a module length of 2 m, and a module tilt angle of 20 to keep consistency with the monofacial standard.In Figures A1-A5, we show the rear irradiation distribution for the five climates not shown in Section 2.2.F I G U R E A 1 Results of our rear irradiance model applied to the temperate continental climate data.(a) Distribution of light on the rear of the PV module.(b) Comparison of monthly irradiation for mono-and bifacial modules.F I G U R E A 2 Results of our rear irradiance model applied to the subtropical costal climate data.(a) Distribution of light on the rear of the PV module.(b) Comparison of monthly irradiation for mono-and bifacial modules.F I G U R E A 3 Results of our rear irradiance model applied to the tropical humid climate data.(a) Distribution of light on the rear of the PV module.(b) Comparison of monthly irradiation for mono-and bifacial modules.

F I G U R E A 4
Results of our rear irradiance model applied to the high elevation climate data.(a) Distribution of light on the rear of the PV module.(b) Comparison of monthly irradiation for mono-and bifacial modules.F I G U R E A 5 Results of our rear irradiance model applied to the subtropical arid climate data.(a) Distribution of light on the rear of the PV module.(b) Comparison of monthly irradiation for mono-and bifacial modules.