# The Effects of Module Temperature on the Energy Yield of Bifacial Photovoltaics: Data and Model

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## Abstract

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_{sc}), open-circuit voltage (V

_{oc}), power at the maximum power point (P

_{mpp}), and the energy yield of a bifacial and a monofacial minimodule. Such minimodules, realised with the same geometry, cell technology, and module lamination, were tested under the same clear sky outdoor conditions, from morning to afternoon, for three days. The bifacial system experimentally shows higher module temperatures under operation, about 10 °C on a daily average of about 40 °C. Nevertheless, its energy yield is about 15% larger than the monofacial one. We propose a physical quantitative model that fits the experimental data of module temperature, I

_{sc}, V

_{oc}, P

_{mpp,}and energy yield. The model was then applied to predict the annual energy yield of PV module strings. The effect of different PV module temperature coefficients on the energy yield is also discussed.

## 1. Introduction

_{sc}), open-circuit voltage (V

_{oc}), and BF, and for their low temperature coefficient [4] compared with the most common p-type cells [5].

_{sc}, V

_{oc}, power at the maximum power point (P

_{mpp}), and energy yield. By comparing minimodules realised by the same PV technology, the differences in module temperature can only be ascribed to the differences in the mode in which the solar radiation impinges on the modules.

## 2. Experimental

_{oc}of 730 mV, an I

_{sc}of 9.3 A, a BF of 90%, and a power conversion cell efficiency (PCCE) of 22.7%. We realised our minimodules by connecting 3 cells in series with copper strips and laminating them in a double transparent polyethylene substrate with EVA backing. One of the modules was covered with white cardboard on the back to completely prevent the albedo light collection. In this way, the module operated similarly to a monofacial module with a white back sheet. In fact, the white cardboard here used has a low transmittance in the infrared range while, in some cases, the infrared white back sheets transmittance can be quite large [15], which would likely imply a better thermal behaviour of the module.

_{front}) and back (T

_{back}) surfaces of the module over time during one day of measurements, on both bifacial and monofacial minimodule.

_{Front}is larger than T

_{Back}. This is most likely mainly due to the different amounts of solar radiation impinging on the front and back surfaces of the PV minimodules, evidenced by the very different short circuit current levels measured in bifacial and monofacial systems at all times, as shown in the next section.

_{module}) is the average of the temperatures measured on the front and on the back, that is,

_{sc}, V

_{oc}, and P

_{mpp}. All these parameters were reliably measured from the experimental I–V curves such as those of Figure 3. Each I–V trace was repeatedly taken on each 90 s, obtaining 250 data sets on average during each day. With this setup, we could follow the daily evolution of the PV system characteristics with high time resolution and an accuracy in the measurements of current and voltage of about 0.5% and 0.1%, respectively. Finally, the ambient temperature data were collected from an in situ weather station.

## 3. Results and Discussion

#### 3.1. Module Temperature

_{amb}), averaged over the three days of measurements. As expected, temperatures are lower in the morning, reach their maximum at midday, and decrease in the afternoon. Module temperatures are much higher than the ambient temperature since solar irradiation warms up the modules. In particular, it is evident that the bifacial module is up to about 12 °C warmer than the monofacial module. This behaviour, systematically observed and quite remarkable, was quantitatively modelled, as discussed in Section 3.3 of this paper, by using Equations (2) and (3). In fact, Figure 4 also shows the module temperature profiles, calculated according to the proposed model, which reproduces quite well the experimental trends: this is true for the average values as well as for the temperatures measured on a single specific day (17 February 2021) with an RMSE of 7.3% of experimental values for the bifacial minimodule and 11.7% for the monofacial minimodule.

#### 3.2. Module Electrical Parameters

_{sc}, V

_{oc}, and electrical energy yield at the maximum power point as a function of time averaged in the 3 days of measurements. For this experiment, we define the energy yield as the cumulative energy produced by the minimodule at its maximum power point since the start of the measuring period (about 9 a.m.). The figures also report the calculated curves of the best fit of the model to the experimental data. In particular, Figure 5 also reports the calculated contribution to the bifacial PV module I

_{sc}due to the albedo light collection by the back of the PV cell (green continuous line). The I

_{sc}difference in bifacial and monofacial modules is due to the contribution of the current collected by the back of the PV module. The latter, compared with the monofacial module I

_{sc}corrected by the PV cell BF, provides an estimate of the ratio of the solar radiation flux collected by the back surface (A

_{bot}) with respect to the one collected by the front A

_{top}. A

_{bot}/A

_{top}was measured by using two photodetectors oriented similarly to the PV minimodules, but one facing up and the other facing down towards the ground (data not shown), which results in the order of 17–20%; that is, the radiation impinging on the back is about 17–20% of the radiation incident on the front. The proposed model captures this feature quite well since, from Figure 5, it is evident that the model and data are in good agreement. The model fits both the average and the chosen day data, with an RMSE of 4.7% and 1.5% for bifacial and monofacial minimodules, respectively.

_{oc}, attributed to the larger module temperature, and a remarkably larger energy yield at the maximum power point.

_{oc}value, we obtained an RMSE of 0.8% for the bifacial minimodule and 0.9% for the monofacial minimodule, while for the energy yield, we obtained an RMSE of 2.4% and 2.1% for bifacial and monofacial minimodules, respectively. In the next section, we describe the proposed model and report its evaluations of bifacial PV annual energy yields as a function of the PV module’s temperature coefficients.

#### 3.3. Model of Bifacial PV and Data Fitting

_{sc}component due to the solar radiation impinging on the front I

_{sc,front}, and the I

_{sc}component due to the albedo radiation diffused by the ground, I

_{sc,back}. I

_{sc,front}was calculated by considering only the direct and the diffused radiation incident on the front, exactly in the same way as in the case of the monofacial solar cells. Vice versa, I

_{sc,back}was calculated only in the case of bifacial modules, and it was obtained by integrating over all the elements of the ground on which the PV system was installed, which all act as isotropic light sources diffusing light proportionally to the global horizontal radiation and to the ground albedo. More specifically, I

_{sc,front}was calculated as the convolution of the front side external quantum efficiency (EQE) with the spectrum of the solar radiation incident to the front, while I

_{sc,back}was calculated as the integral over all the underlying ground elements of the radiation diffused by each element, proportional to the solid angle under which it sees the solar cell back. Further details of the model are reported in [11]. In the calculation, we took into account the wavelength dependence of ground albedo, back-side EQE, and the spectrum of the horizontal component of the solar spectrum. A larger ground area was considered to correctly evaluate the back-side irradiance of outermost modules. The model also took into account when the incident radiation has a large incidence angle on the receiving PV surface element, to correct for the increasing reflectivity which reduces the actually collected radiation.

_{sc}was calculated as the sum of I

_{sc,front}and I

_{sc,back}, as reported in more detail in [10], the cell current–voltage (I–V) characteristics were calculated according to the well-known current source/single-diode lumped element circuit model of the PV cell [23]. The I–V curve of the PV module or of the PV string was then numerically calculated by considering the series of all the PV cells. In the present case, this corresponded to numerically calculating the series of 3 cells in the case of the minimodule and of 432 cells in the case of the string of 6 PV modules; then, the V

_{oc}was obtained as the PV system voltage corresponding to a current equal to 0 A, while the P

_{mpp}was evaluated as the maximum of the power produced by the system.

_{front}is the intensity of the solar radiation impinging on the PV cell front, to be expressed in W/m

^{2}, while NOCT

_{mono}is the nominal operating condition temperature to be expressed in °C.

_{bif}is the NOCT of the bifacial PV module. As far as the radiation impinging on the back surface is concerned, rather than simply adding such radiation to E

_{front}, we believed that it is more accurate to account for this additional term by calculating the ratio between I

_{sc,back}and I

_{sc,front}, as each factor already considers the radiation that is actually absorbed by the respective side of the cell. In fact, as stated above, one of the factors in the calculation of I

_{sc}is the EQE, which is different for each side and excludes from the calculation the fraction of irradiance that is reflected or transmitted which does not contribute to cell heating.

_{bif}, NOCT

_{mono}, the power temperature coefficient α

_{T}, the STC PV cell I

_{sc}, V

_{oc}, and the series resistance R

_{s}. All best-fit values are very close to the average values measured for unencapsulated cells in STC [27]. Slight changes of the order of 10% around the STC values were allowed for V

_{oc}and I

_{sc}. On the contrary, for the R

_{s}parameter, an increase up to a factor 3 of the STC value was allowed. The R

_{s}best-fit value (2× the STC value) found is likely due to the bus bar and lamination processes which can produce some worsening of the series resistance. The best-fit values used for the curves calculated in Figure 4, Figure 5, Figure 6 and Figure 7 are reported in Table 1.

_{oc}, I

_{sc}).

_{bif}is larger than that of NOCT

_{mono}. This result can be explained by considering the definition of NOCT, which is the operating condition temperature of the module when irradiated at 800 W/m

^{2}, at 45° inclination, at an ambient temperature of 20 °C, and with a wind flowing at 1 m/s. Given the definition, it appears realistic that NOCT

_{bif}would be larger than NOCT

_{mono}since, under solar irradiation, the bifacial module collects the albedo light from the ground. This is, on the contrary, mostly reflected away by the monofacial module which has a white back sheet. Therefore, more solar power is collected by the bifacial module, producing a larger temperature.

#### 3.4. Model Extrapolations to Annual PV Energy Yield and Effect of α_{T}

_{sc}will dominate the energy yield. This effect becomes much stronger for a large string of 6 modules with 432 cells; therefore, the PV relative bifacial gain is clearly lower. Nevertheless, the relative bifacial gain is still quite remarkable, calculated to be always above 10%, with a clear and remarkable advantage of energy yield. Such results are in good agreement with the experimental data reported in refs. [29,30,31] and with the calculated values reported in refs. [32,33]. We also note that, according to our model, the maximum difference in temperature between bifacial and monofacial modules is between 9 °C and 12 °C at the latitude of Catania throughout the year.

_{T}parameter of the solar cells for the application in the bifacial mode. In general, it is well known that PV technologies with low α

_{T}in absolute value or even positive temperature coefficients are preferable for application in warm climates. This feature is also very useful in the case of bifacial systems. In fact, as we showed here, the temperature of a bifacial module tends to be higher, compared with that of the same module used in monofacial mode with a white surface on the back. Hence, one expects that the relative bifacial gain will be better in technologies with low α

_{T}in absolute value. To quantify the advantage, we performed calculations using the model here proposed.

_{T}, which is varied from −0.26%/°C to −0.45%/°C, that is, in the range of the most important silicon PV technologies currently available. As expected, as α

_{T}increases in absolute value the relative bifacial gain decreases. From the best to the worst case, the change is noticeable, of about −20%. In all cases, however, the bifacial systems show a strong advantage in terms of energy yield.

_{T}in absolute value provide more advantage when used in bifacial mode. This is, for example, the case of the HJT technology used in the experiments here reported, with an α

_{T}of −0.26%/°C.

## 4. Conclusions

_{oc}, maximum power point, I

_{sc}, and module temperature. Using this approach, we directly compared monofacial and bifacial operations within the same Si PV technology, evaluating the quantitative correlation between PV electrical performance, solar irradiance on the PV module front and back, and the module temperature.

_{oc}, I

_{sc}, maximum power point, and energy yield, both in monofacial and in bifacial operations. Hence, we used the model to evaluate the annual energy yields and the effect of varying the power temperature coefficient. From such analysis, the n-type HJT technology appears to be particularly suitable for bifacial photovoltaics given its very low temperature coefficient.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- International Technology Roadmap for Photovoltaics, 12th ed. 2021. Available online: https://itrpv.vdma.org/en/ (accessed on 20 February 2021).
- Liang, T.S.; Pravettoni, M.; Deline, C.; Stein, J.S.; Kopecek, R.; Singh, J.P.; Luo, W.; Wang, Y.; Aberle, A.G.; Khoo, Y.S. A review of crystalline silicon bifacial photovoltaic performance characterisation and simulation. Energy Environ. Sci.
**2019**, 12, 116–148. [Google Scholar] [CrossRef] - Gu, W.; Ma, T.; Ahmed, S.; Zhang, Y.; Peng, J. A comprehensive review and outlook of bifacial photovoltaic (bPV) technology. Energy Convers. Manag.
**2020**, 223, 113283. [Google Scholar] [CrossRef] - Patel, M.T.; Vijayan, R.A.; Asadpour, R.; Varadharajaperumal, M.; Khan, M.R.; Alam, M.A. Temperature-dependent energy gain of bifacial PV farms: A global perspective. Appl. Energy
**2020**, 276, 115405. [Google Scholar] [CrossRef] - Yu, B.; Song, D.; Sun, Z.; Liu, K.; Zhang, Y.; Rong, D.; Liu, L. A study on electrical performance of N-type bifacial PV modules. Sol. Energy
**2016**, 137, 129–133. [Google Scholar] [CrossRef] - Yusufoglu, U.A.; Lee, T.H.; Pletzer, T.M.; Halm, A.; Koduvelikulathu, L.J.; Comparotto, C.; Kopecek, R.; Kurz, H. Simulation of Energy Production by Bifacial Modules with Revision of Ground Reflection. Energy Procedia
**2014**, 55, 389–395. [Google Scholar] [CrossRef] [Green Version] - Yusufoglu, U.A.; Pletzer, T.M.; Koduvelikulathu, L.J.; Comparotto, C.; Kopecek, R.; Kurz, H. Analysis of the Annual Performance of Bifacial Modules and Optimization Methods. IEEE J. Photovolt.
**2015**, 5, 320–328. [Google Scholar] [CrossRef] - Shoukry, I.; Libal, J.; Kopecek, R.; Wefringhaus, E.; Werner, J. Modelling of Bifacial Gain for Stand-alone and in-field Installed Bifacial PV Modules. Energy Procedia
**2016**, 92, 600–608. [Google Scholar] [CrossRef] [Green Version] - Sun, X.; Khan, M.R.; Deline, C.; Alam, M.A. Optimization and performance of bifacial solar modules: A global perspective. Appl. Energy
**2018**, 212, 1601–1610. [Google Scholar] [CrossRef] [Green Version] - Galluzzo, F.R.; Canino, A.; Gerardi, C.; Lombardo, S.A. A new model for predicting bifacial PV modules performance: First validation results. In Proceedings of the 2019 IEEE 46th Photovoltaic Specialists Conference (PVSC), Chicago, IL, USA, 16–21 June 2019; pp. 1293–1297. [Google Scholar] [CrossRef]
- Galluzzo, F.R.; Zani, P.E.; Foti, M.; Canino, A.; Gerardi, C.; Lombardo, S. Numerical Modeling of Bifacial PV String Performance: Perimeter Effect and Influence of Uniaxial Solar Trackers. Energies
**2020**, 13, 869. [Google Scholar] [CrossRef] [Green Version] - Lamers, M.W.P.E.; Özkalay, E.; Gali, R.S.R.; Janssen, G.J.M.; Weeber, A.W.; Romijn, I.G.; Van Aken, B.B. Temperature effects of bifacial modules: Hotter or cooler? Sol. Energy Mater. Sol. Cells
**2018**, 185, 192–197. [Google Scholar] [CrossRef] - Zhang, Z.; Wu, M.; Lu, Y.; Xu, C.; Wang, L.; Hu, Y.; Zhang, F. The mathematical and experimental analysis on the steady-state operating temperature of bifacial photovoltaic modules. Renew. Energy
**2020**, 155, 658–668. [Google Scholar] [CrossRef] - Rodríguez-Gallegos, C.D.; Bieri, M.; Gandhi, O.; Singh, J.P.; Reindl, T.; Panda, S.K. Monofacial vs. bifacial Si-based PV modules: Which one is more cost-effective? Sol. Energy
**2018**, 176, 412–438. [Google Scholar] [CrossRef] - McIntosh, K.R.; Jung, J.; Abbott, M.D.; Sudbury, B.A. Determination and evaluation of a backsheet’s intrinsic reflectance. AIP Conf. Proc.
**2018**, 1999, 020018. [Google Scholar] [CrossRef] - Privitera, S.; Muller, M.; Zwaygardt, W.; Carmo, M.; Milazzo, R.; Zani, P.; Leonardi, M.; Maita, F.; Canino, A.; Foti, M.; et al. Highly efficient solar hydrogen production through the use of bifacial photovoltaics and membrane electrolysis. J. Power Sources
**2020**, 473, 228619. [Google Scholar] [CrossRef] - Notton, G.; Cristofari, C.; Mattei, M.; Poggi, P. Modelling of a double-glass photovoltaic module using finite differences. Appl. Therm. Eng.
**2005**, 25, 2854–2877. [Google Scholar] [CrossRef] - Marion, B.; MacAlpine, S.; Deline, C.; Asgharzadeh, A.; Toor, F.; Riley, D.; Stein, J.; Hansen, C. A Practical Irradiance Model for Bifacial PV Modules. In Proceedings of the 2017 IEEE 44th Photovoltaic Specialist Conference (PVSC), Washington, DC, USA, 25–30 June 2017; pp. 1537–1542. [Google Scholar] [CrossRef]
- American Society of Heating, Refrigerating and Air-Conditioning Engineers. ASHRAE Handbook, 1985 Fundamentals: An Instrument of Service Prepared for the Profession Containing Technical Information; The Society: Atlanta, GA, USA, 1985. [Google Scholar]
- Global Solar Atlas. Available online: https://globalsolaratlas.info/ (accessed on 20 February 2021).
- Liu, B.; Jordan, R. Daily insolation on surfaces tilted towards equator. ASHRAE J.
**1961**, 10, 53–59. [Google Scholar] - Ross, R.G., Jr. Interface design considerations for terrestrial solar cell modules. In Proceedings of the 12th Photovoltaic Specialists Conference, Baton Rouge, LA, USA, 15–18 November 1976; pp. 801–806. [Google Scholar]
- Xiao, W.; Dunford, W.G.; Capel, A. A novel modeling method for photovoltaic cells. In Proceedings of the 2004 IEEE 35th Annual Power Electronics Specialists Conference (IEEE Cat. No.04CH37551), Aachen, Germany, 20–25 June 2004; pp. 1950–1956. [Google Scholar]
- Santiago, I.; Trillo-Montero, D.; Moreno-Garcia, I.; Pallarés-López, V.; Luna-Rodríguez, J. Modeling of photovoltaic cell temperature losses: A review and a practice case in South Spain. Renew. Sustain. Energy Rev.
**2018**, 90, 70–89. [Google Scholar] [CrossRef] - Weather Underground. 2020. Available online: https://www.wunderground.com/ (accessed on 20 February 2021).
- Zouine, M.; Akhsassi, M.; Erraissi, N.; Aarich, N.; Bennouna, A.; Raoufi, M.; Outzourhit, A. Mathematical Models Calculating PV Module Temperature Using Weather Data: Experimental Study BT. In Proceedings of the 1st International Conference on Electronic Engineering and Renewable Energy, Saidia, Morocco, 15–17 April 2018; pp. 630–639. [Google Scholar]
- Foti, M.; Galiazzo, M.; Cerasti, L.; Sovernigo, E.; Gerardi, C.; Guglielmino, A.; Litrico, G.; Sciuto, M.; Spampinato, A.; Ragonesi, A.; et al. Silicon Heterojunction Solar Module using Shingle interconnection. In Proceedings of the 2021 IEEE 48th Photovoltaic Specialists Conference (PVSC), Fort Lauderdale, FL, USA, 20–25 June 2021; pp. 1092–1095. [Google Scholar] [CrossRef]
- Green, M.A.; Dunlop, E.D.; Hohl-Ebinger, J.; Yoshita, M.; Kopidakis, N.; Hao, X. Solar cell efficiency tables (Version 58). Prog. Photovolt. Res. Appl.
**2021**, 29, 657–667. [Google Scholar] [CrossRef] - Park, H.; Chang, S.; Park, S.; Kim, W.K. Outdoor Performance Test of Bifacial n-Type Silicon Photovoltaic Modules. Sustainability
**2019**, 11, 6234. [Google Scholar] [CrossRef] [Green Version] - Molin, E.; Stridh, B.; Molin, A.; Wackelgard, E. Experimental Yield Study of Bifacial PV Modules in Nordic Conditions. IEEE J. Photovolt.
**2018**, 8, 1457–1463. [Google Scholar] [CrossRef] - Jang, J.; Lee, K. Practical Performance Analysis of a Bifacial PV Module and System. Energies
**2020**, 13, 4389. [Google Scholar] [CrossRef] - Gu, W.; Li, S.; Liu, X.; Chen, Z.; Zhang, X.; Ma, T. Experimental investigation of the bifacial photovoltaic module under real conditions. Renew. Energy
**2020**, 173, 1111–1122. [Google Scholar] [CrossRef] - Abotaleb, A.; Abdallah, A. Performance of bifacial-silicon heterojunction modules under desert environment. Renew. Energy
**2018**, 127, 94–101. [Google Scholar] [CrossRef]

**Figure 1.**Image of the experimental setup: front view of the two minimodules, with the bifacial on the left and the monofacial on the right.

**Figure 2.**Example of measured temperatures of the minimodule on the front and back surfaces as a function of time for bifacial (

**a**) and monofacial (

**b**) minimodule measured in one of the days of measurement.

**Figure 3.**Experimental I–V curves collected from the bifacial minimodule in one of the days of measurements.

**Figure 4.**Data of a single day of module temperature compared with the values predicted by the model (

**a**) and average values compared with the model (

**b**). Ambient temperature is also reported as reference.

**Figure 5.**Data of a single day of module I

_{SC}compared with the values predicted by the model (

**a**) and average values compared with the model (

**b**). The model allows also to separately calculate the current generated by the back surface of the module.

**Figure 6.**Data of a single day of module V

_{OC}compared with the values predicted by the model (

**a**) and average values compared with the model (

**b**).

**Figure 7.**Data of a single day of module energy yield compared with the values predicted by the model (

**a**) and average values compared with the model (

**b**).

**Figure 8.**Modelled relative bifacial gain over the course of the year for a minimodule (blue) and a string of six modules (red).

**Figure 9.**Modelled percent increase in relative bifacial gain over the course of the year of a six-module string for different values of the power temperature coefficient.

Parameter | Best-Fit Value | Measured STC Value |
---|---|---|

PV cell I_{sc} | 9.15 A | 9.30 A |

PV cell V_{oc} | 720 mV | 730 mV |

PV cell R_{s} | 6 mΩ | 3 mΩ |

PCCE at maximum power point | 21.1% | 22.7% |

α_{T} | −0.26%/°C | −0.26%/°C |

Mini-module NOCT_{mono} | 42 °C | - |

Mini-module NOCT_{bif} | 47 °C | - |

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**MDPI and ACS Style**

Leonardi, M.; Corso, R.; Milazzo, R.G.; Connelli, C.; Foti, M.; Gerardi, C.; Bizzarri, F.; Privitera, S.M.S.; Lombardo, S.A.
The Effects of Module Temperature on the Energy Yield of Bifacial Photovoltaics: Data and Model. *Energies* **2022**, *15*, 22.
https://doi.org/10.3390/en15010022

**AMA Style**

Leonardi M, Corso R, Milazzo RG, Connelli C, Foti M, Gerardi C, Bizzarri F, Privitera SMS, Lombardo SA.
The Effects of Module Temperature on the Energy Yield of Bifacial Photovoltaics: Data and Model. *Energies*. 2022; 15(1):22.
https://doi.org/10.3390/en15010022

**Chicago/Turabian Style**

Leonardi, Marco, Roberto Corso, Rachela G. Milazzo, Carmelo Connelli, Marina Foti, Cosimo Gerardi, Fabrizio Bizzarri, Stefania M. S. Privitera, and Salvatore A. Lombardo.
2022. "The Effects of Module Temperature on the Energy Yield of Bifacial Photovoltaics: Data and Model" *Energies* 15, no. 1: 22.
https://doi.org/10.3390/en15010022