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By a careful study of data collected from seven varieties of photovoltaic (PV) module it is demonstrated that a simple modified form of the Hottel–Whillier–Bliss (HWB) equation, familiar from the analysis of flat-plate solar–thermal collectors, can be employed to predict module temperatures within an accuracy comparable to the cell-to-cell temperature differences typically encountered within a module. Furthermore, for modules within the range of construction parameters employed in this study, the actual values of the two modified HWB constants do not appear to depend upon module type. The implication of these results for the accuracy of outdoor module characterization is discussed. Copyright © 2008 John Wiley & Sons, Ltd.

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... Effective irradiance The initial simulation model estimates the effective irradiance on the module plane by using the SAPM model as explained in [7]. Optical losses are aspired to be partly considered by the usage of the corresponding modifying factors stated in the Martin and Ruiz model. ...

... Optical losses are aspired to be partly considered by the usage of the corresponding modifying factors stated in the Martin and Ruiz model. The basic formula for the effective irradiance (Ee) by SAPM [7] is shown below: ...

... Due to the assumption of clean modules, a soiling factor (SF) as an indicator for the module pollution of 1 is assumed. [7] The estimation of the incident modifier (IAM) as a designation for the angular losses in dependency of the AOI is shown in (5). The model contains the angular losses coefficient (ar), an empirically estimated parameter which describes the reflectance of different module types with regards to their configuration [8,9]. ...

In this work a simulation model for a novel air-based BIPVT roof tile system with rear ventilation is presented. This work contributes to closing the research gap concerning the performance estimation of the electrical and thermal system of such BIPVT systems, also under real operating conditions. Therefore, a simulation model which enables a holistic evaluation of a BIPVT system energy yield and performance is set up and refined. To achieve this, the initial simulation model is adapted to state-of-the-art PV modelling and expanded by still required simulation approaches for system components not investigated yet. Additionally, besides the coupling of insights from previous research, influencing parameters are derived specifically for installed components on site. The calculation results for the installed test site indicate electrical system yields within the range of conventional PV systems and above average performance ratios. Due to the consideration of the solar cooling effect, an efficiency gain for the electric energy yield of 2.0 % is achieved. An increase of the annual performance of the heat pump of 6.0 % at best case is identified by using the solar roof tiles waste heat. In this context, a low mass flow rate of the base-fluid appears to be the operating condition leading to the highest benefits for the overall system yield. A model validation performed with the use of infield measurement data shows an overestimation of 1.3 % concerning the actual electrical yield. Overall, the final model predicts the electric power output before inverter losses with an accuracy of 4.7 % in relative RMSE. It can be concluded that the developed simulation model enables a realistic overall energy yield prediction for the novel BIPVT solar roof tile.

... By correcting the Mean Bias Error (MBE) of the testing dataset (using it as a fixed radiation loss component), the thermal models are further improved. The filtering -EWM -MBE correction (FEM) methodology is applied on five thermal models and 24 datasets of varying time resolution: two thermal model variants we introduce (WM1 and WM2), which are compared against those of Ross [7], King et al [8] and Faiman [9]. We then evaluate the thermal models along various dimensions and timescales, contextualising the model results against measured data. ...

... Barry et al [18] proposed an extended form of Faiman's model [9] as part of their dynamic modelling approach on 1 min data, using a coefficient u 3 to multiply against the sky-ambient temperature difference. The determination of u 3 itself is not clear, yet it appears to depend on the sky temperature T sky , which is obtained through measured data, using long-wave downward welling irradiance measured by a pyrgeometer. ...

... Fundamentally, we start by taking the (residual) RC-equivalent thermal network of a PV module shown in Figure 2, similar to Armstrong et al [19], to re-evaluate and re-examine equationbased thermal model "families" 1 that have seen high uptake in the literature, namely those by Ross (Equation (2)) [7], King et al [8] (also known as the Sandia model: Equation (3)) and Faiman [9] (Equation (4)). In practice, Faiman's model is typically used in its simplified form (Equation (5)) [23], as determining the optical efficiency η o requires additional effort, while the electrical efficiency η e varies as a function of the module's temperature. ...

This paper presents a range of methods to improve the accuracy of equation-based thermal models of PV modules at second-to-minute timescales. We present an RC-equivalent conceptual model for PV modules, where wind effects are captured. We show how the thermal time constant $\tau$ of PV modules can be determined from measured data, and subsequently used to make static thermal models dynamic by applying the Exponential Weighted Mean (EWM) approach to irradiance and wind signals. On average, $\tau$ is $6.3 \pm 1~$min for fixed-mount PV systems. Based on this conceptual model, the Filter- EWM - Mean Bias Error correction (FEM) methodology is developed. We propose two thermal models, WM1 and WM2, and compare these against the models of Ross, Sandia, and Faiman on twenty-four datasets of fifteen sites, with time resolutions ranging from 1$~$s to 1$~$h, the majority of these at 1$~$min resolution. The FEM methodology is shown to reduce model errors (RMSE and MAE) on average for all sites and models versus the standard steady-state equivalent by -1.1$~$K and -0.75$~$K respectively.

... Faiman D. [19] proposed a modified form of the Hottel-Whillier-Bliss equation, usually used for solar thermal collectors, in order to predict PV temperatures. Mattei M. et al. [20] proposed different simple models to estimate the PV temperature. ...

... The overall RMSE obtained for temperature is 1.84 °C. This result is lower than that of other works in the literature, such as Mavromatakis et al. [19] (∼2.1-2.2 °C) and Mattei et al. [21] (2.24 °C). The error is greater when compared to more complex methods. ...

... The overall RMSE obtained for temperature is 1.84 • C. This result is lower than that of other works in the literature, such as Mavromatakis et al. [19] (∼2.1-2.2 • C) and Mattei et al. [21] (2.24 • C). The error is greater when compared to more complex methods. ...

The production of electricity from photovoltaic panels has experienced significant developments. To manage the energy flows introduced into the electricity grid, it is necessary to estimate the productivity of PV panels under the climatic conditions. In this study, a photovoltaic panel is modelled from thermal and electrical points of view to evaluate electrical performance and identify the temperature distribution in the layers. The analysis performed is time dependent and the problem is solved using the finite difference technique. A methodology is introduced to estimate the cloudiness of the sky, which affects radiative heat exchange. The calculation method is validated using experimental data recorded in a laboratory of the University of Calabria. Temperature and electrical power are predicted with RMSE of 1.5–2.0 °C and NRMSE of 1.2–2.1%, respectively. The evaluation of the temperature profile inside the panel is essential to understand how heat is dissipated. The results show that the top surface (glass) is almost always colder than the back of the panel, despite being exposed to radiation. In addition, the upper surface dissipates more heat power than the lower one. Cooling systems, such as spray cooling, work better if they are installed on the back of the panel.

... As shown in Figure 8.3a, the power output model [113] also performs well (NRMSE = 3.3%) under partial illumination, since the bifacial flat plate PV cells in the EyeCon module only receive diffuse light. Moreover, the temperature of the flat plate c-Si PV cells (TPV) is calculated using the model in the PV energy rating standard (IEC 61853-2 [126]) which is described in [86]. However, the measured temperature of the Si cell array inside the EyeCon module was calculated with its VOC and temperature coefficient using the method described in the IEC 60904-5 standard [103]. ...

... As given in Equation 8.5, the inputs of the cell temperature model [86] are Tamb, Vwind and the absorbed irradiance (Gabs), ...

... For a conventional flat plate PV module, Gabs = GTI + BTI, whereas for the bifacial PV array of the hybrid EyeCon module Gabs = DNI + DTI + BTI, because the Si cells also dissipate the DNI absorbed by the CPV cells. Therefore, we chose to use both of these models [86,113] in our worldwide calculation because they reproduce our measurements with sufficient accuracy. In addition, they address the main irradiance, temperature and spectral effects that affect the performance of single-junction flat plate PV technology. ...

In this cumulative thesis, a novel hybrid photovoltaic module combining the concentrator and flat plate approach (CPV/PV), named EyeCon, is developed and characterized. Conventional concentrator photovoltaic (CPV) modules use highest efficiency III-V multi-junction solar cells and convert up to 38.9% of the direct sunlight. Nevertheless, the use of concentrating optics prevents them from absorbing the diffuse part of the solar spectrum. On the other hand, flat plate silicon (Si) photovoltaic (PV) modules convert light from all angles of incidence with efficiencies around 20%. This work focuses on the enhancement of a multi-junction CPV module by the integration of bifacial Si PV cells to obtain the highest power output per unit area through the conversion of direct, diffuse and rear side irradiance.
The development and manufacturing of the EyeCon module consisted of the design of the 4-terminal circuit of the CPV and flat plate PV cells, the optimization of the metallization grid of the bifacial Si PV cells under partial illumination, the thermal validation of using the Si PV cells as heat spreaders for the CPV cells and the development of a seamless process that integrates the flat plate PV cells into a CPV module with minimum additional steps and materials.
The main optical, thermal and electrical characterizations include the quantification of the effective amount of irradiance absorbed by the Si PV cells under the concentrating optics, the effect of tracker misalignment on power output when the focal spot moves from the CPV receivers onto the flat plate PV cells, the definition of hybrid reference standard conditions and filtering criteria and the development of a power rating procedure for hybrid CPV/PV bifacial modules.
The analysis of the EyeCon module performance under different meteorological and spectral conditions comprises the power output under a hypothetical voltage-matched interconnection between the CPV and the bifacial PV cells, the extensive worldwide energy yield modeling and the techno-economic comparison with CPV and single-junction flat plate PV modules.
Under the scope of this research, a world record efficiency of 34.2% and a bifacial power output beyond 350 W/m2 at standard test conditions were reached using III-V four-junction CPV and flat plate bifacial Si PV cells. Furthermore, hybrid CPV/PV technology is expected to generate up to 1150 kWh/m2 in subtropical arid regions, whereas in places like Europe, China, central Africa and Latin America a 25 - 35% higher yield than its closest contender is expected. Thus, hybridization is a promising path towards increasing the competitiveness of conventional CPV technology.

... For the Si PV array of the EyeCon module we used its measured value from [7], i.e. = 0.64. As shown in Figure 3a, the power output model Moreover, the temperature of the flat plate c-Si PV cells (TPV) is calculated using the model in the PV energy rating standard (IEC 61853-2 [32]) which is described in [33]. However, the measured temperature of the Si cell array inside the EyeCon module was calculated with its VOC and temperature coefficient using the method described in the IEC 60904-5 standard [34]. ...

... As we previously showed in [10], this method works well since it yields the effective cell temperature based on electrical characteristics despite the inhomogeneous temperature profile on the Si cells. As given in Equation 5, the inputs of the cell temperature model [33] are Tamb, Vwind and the absorbed irradiance (Gabs), ...

... For a conventional flat plate PV module, Gabs = GTI + BTI, whereas for the bifacial PV array of the hybrid EyeCon module Gabs = DNI + DTI + BTI, because the Si cells also dissipate the DNI absorbed by the CPV cells. Figure 3b shows how the cell temperature model [33] estimates the temperature of the c-Si PV cells with a low RMSE of 2.6 K. ...

Hybridization of multi-junction concentrator photovoltaics with single-junction flat plate solar cells (CPV/PV) can deliver the highest power output per module area of any PV technology. Conversion efficiencies up to 34.2% have been published under the AM1.5g spectrum at standard test conditions for the EyeCon module which combines Fresnel lenses and III-V four-junction solar cells with bifacial c-Si. We investigate here its energy yield and compare it to conventional CPV as well as flat plate PV. The advantage of the hybrid CPV/PV module is that it converts direct sunlight with the most advanced multi-junction cell technology, while accessing diffuse, lens-scattered and back side irradiance with a Si cell that also serves as the heat distributor for the concentrator cells. This article quantifies that hybrid bifacial CPV/PV modules are expected to generate a 25 - 35% higher energy yield with respect to their closest competitor in regions with a diffuse irradiance fraction around 50%. Additionally, the relative cost of electricity generated by hybrid CPV/PV technology was calculated worldwide under certain economic assumptions. Therefore, this article gives clear guidance towards establishing competitive business cases for the technology.

... In IEC61853-2 (IEC, 2018) the Faiman model is recommended as the preferred method to estimate the module temperature (K) in yield assessment analysis. In the model proposed by Faiman (2008) the electrical efficiency, η, is taken into consideration so that the fraction of the incident irradiance being converted to electrical energy is not considered to be contributing to the increase in module temperature, while this is not included in the standard. When the electrical efficiency is taken into consideration the module temperature, T mod (K), is given by. ...

... In this work, the performance ratio and relative yield is used to assess the overall performance of the system and compare the FPV and GPV system, respectively. Additionally, the heat loss coefficient is calculated using the Faiman model (Faiman, 2008). These different analyses will be explained in the following sections, with Table 2 listing the filters and given time period used for each. ...

... W/m 2 K (Ghabuzyan et al., 2021), 31.9 W/m 2 K (Faiman, 2008) and 33-35.8 W/m 2 K (Koehl et al., 2011). ...

Floating photovoltaics (FPV) is a rapidly emerging technology that provides an alternative to ground-mounted PV (GPV), particularly where land is scarce or expensive. Despite an impressive technological development and growth in installed capacity in recent years, studies on the performance and reliability of FPV are scarce. This work provides insight with respect to the performance, reliability, and operational characteristics of a new FPV technology with the aim to identify innovation opportunities, reduce risks, develop improved solutions, and improve bankability of FPV. We have analysed production and weather data from one year of operation for an open FPV system with a small water footprint located on a water body in Kilinochchi, Sri Lanka. The technology is developed by the company Current Solar. Using established filtering routines and algorithms from pvlib, the yield and performance ratio is calculated and compared to a GPV system installed on the shore of the lake. We find that the technology gives a stable overall performance over the one-year period, and that the period of amphibious operation did not impact the continued performance of the system. Calculations of the U-value of the system, based on the production and weather data, gives a median U-value of 33 W/m²K, slightly higher than the default PVsyst value of 29 W/m²K for freestanding GPV systems. The calculated U-values are used in an energy yield analysis in PVsyst to estimate the energy production of the FPV technology and benchmark it against measured data.

... Part 2 also describes the experimental procedures to obtain the uo and u1 thermal coefficients that are required to estimate the module temperature , from in-plane irradiance , , , ambient temperature , and wind speed . The uo and u1 coefficients are from the Faiman model [11], and describe the effect of radiation and wind cooling on module temperature, respectively. IEC 61853 Part 3 "Energy rating of PV modules" describes the calculation steps needed for PV module ratings. ...

... The third step is the calculation of the module temperature Tmod,j, for which the Faiman model is used [11] (eqn. 8). ...

... The Module 1 data set uses the thermal coefficients u0=25 W/(m²×K) and u1=6.84 W/(m³×s×K) taken from literature [11]. All other module parameters are measured at TÜV Rheinland, the results are in Tab. 1 and Fig. 2 in this work. ...

p>The IEC 61853 standard series aims to provide a standardized measure for PV module energy rating, namely the Climate Specific Energy Rating (CSER). For this purpose, it defines procedures for the experimental determination of input data and algorithms for calculating the CSER. However, some steps leave room for interpretation regarding the specific implementation. To analyze the impact of these ambiguities, the comparability of results and the clarity of the algorithm for calculating the CSER in part 3 of the standard, an intercomparison is performed among research organizations with 10 different implementations of the algorithm. We share the same input data, obtained by measurement of a commercial crystalline silicon PV module, among the participating organizations. Each participant then uses their individual implementations of the algorithm to calculate the resulting CSER values. The initial blind comparison reveals differences of 0.133 (14.7%) in CSER. After several comparison phases, a best practice approach is defined, which reduces the difference by a factor of 210 to below 0.001 (0.1%) in CSER for two independent PV modules. The best practice presented in this paper establishes clear guidelines for the numerical treatment of the spectral correction and power matrix extrapolation, where the methods in the standard are not clearly defined. Additionally, we provide input data and results for the PV community to test their implementations of the standard’s algorithm. To identify the source of the deviations, we introduce a climate data diagnostic set. Based on our experiences, we give recommendations for the future development of the standard.</p

... Part 2 also describes the experimental procedures to obtain the uo and u1 thermal coefficients that are required to estimate the module temperature , from in-plane irradiance , , , ambient temperature , and wind speed . The uo and u1 coefficients are from the Faiman model [11], and describe the effect of radiation and wind cooling on module temperature, respectively. IEC 61853 Part 3 "Energy rating of PV modules" describes the calculation steps needed for PV module ratings. ...

... The third step is the calculation of the module temperature Tmod,j, for which the Faiman model is used [11] (eqn. 8). ...

... The Module 1 data set uses the thermal coefficients u0=25 W/(m²×K) and u1=6.84 W/(m³×s×K) taken from literature [11]. All other module parameters are measured at TÜV Rheinland, the results are in Tab. 1 and Fig. 2 in this work. ...

p>The IEC 61853 standard series aims to provide a standardized measure for PV module energy rating, namely the Climate Specific Energy Rating (CSER). For this purpose, it defines procedures for the experimental determination of input data and algorithms for calculating the CSER. However, some steps leave room for interpretation regarding the specific implementation. To analyze the impact of these ambiguities, the comparability of results and the clarity of the algorithm for calculating the CSER in part 3 of the standard, an intercomparison is performed among research organizations with 10 different implementations of the algorithm. We share the same input data, obtained by measurement of a commercial crystalline silicon PV module, among the participating organizations. Each participant then uses their individual implementations of the algorithm to calculate the resulting CSER values. The initial blind comparison reveals differences of 0.133 (14.7%) in CSER. After several comparison phases, a best practice approach is defined, which reduces the difference by a factor of 210 to below 0.001 (0.1%) in CSER for two independent PV modules. The best practice presented in this paper establishes clear guidelines for the numerical treatment of the spectral correction and power matrix extrapolation, where the methods in the standard are not clearly defined. Additionally, we provide input data and results for the PV community to test their implementations of the standard’s algorithm. To identify the source of the deviations, we introduce a climate data diagnostic set. Based on our experiences, we give recommendations for the future development of the standard.</p

... To reach accurately the estimation schemes which is very important for long-term techno-economic analysis (Karaveli et al., 2018;) to find out truthfully the efficiency and yield the software in hand as: HOMER, Helioscope, PVsyst, and PV*SOL (Folsom Labs, 2019; HOMER Software, 2019; PVsyst, 2019; Valentin Software, 2019) are detailly studied. The present work comprehensively achieves to be as an original stand work in PV temperatures with the temperature estimation formulas developed by several authors (Duffie et al., 1985;Faiman, 2008;King et al., 2004;Skoplaki et al., 2008). ...

... U0 and U1 in equation (3) are the thermal coefficients describing the effect of the solar radiation on PV cell temperature, and the cooling effect of the wind, respectively (Koehl et al., 2011). They are taken as 23.09 and 3.11 for the CIS module while for other modules they are taken as 25 and 6.84 (Faiman, 2008;Koehl et al., 2011). ...

The software used today, on the estimation of module temperature of photovoltaic systems, seem very important to be analyzed. These estimates are crucial in future techno-economic and environmentally friendly analyses of the systems to reach better achievements for future generations. This is very important to reach lifetime analyses of long-term feasibility to find out payback time and the levelized cost of energy. The present work is based on this issue, to test the module temperature estimation formulas used by four commonly used software models, and to determine the most suitable software for temperature analyses of five different photovoltaic modules in Middle Anatolia. Outdoor truthful long-term testing is the main realistic approach to reach fundamental contemplations. After an introductory basic knowledge, the main materials and methods are discussed to enlighten the analysis. The main methodology is given and further prospects are enlightened. Four well-known software are analyzed using four years of outdoor testing of five different photovoltaic modules. Measured ambient temperature and solar irradiance are used in the categorization of the software estimation performances. PV*SOL appears to be superior at low irradiance and ambient temperature, whereas Helioscope appears to be superior overall.

... In addition, Tpv itself is considered as an implicit function in the Tpv prediction. The importance of the effect of the above factors as well as the module geometry and mounting configuration in the Tpv prediction is shown theoretically by proposed formulas [1][2][3][4], or by formulas based on ANN [5] or by simulation models [6,7]. Measured Tpv in various conditions and structures have been compared with predicted values obtained from simulation models [8][9][10][11]. ...

... F depends, also, on Tpv through its effect on ηpv and Upv and on β. In addition, vw has an impact on f and Tpv and plays a significant role in the efficiency and power degradation [1,[3][4][5]13,31,32]. F is determined experimentally from eqs.(1,2) by using the measured IT, Tpv or Tb and Ta values or the Tref notion. ...

The PV temperature, Tpv, in a BIPV and BIPV/T structures was studied experimentally and theoretically. For this a
holistic formula was used based on the Ross coefficient prediction under any environmental conditions accounting
additionally for the building thermal parameters. It was shown that the slope of the PV temperature,Tpv, vs the solar
radiation, IT, on the BIPV modules corresponds to a generalized expression of the Ross coefficient, f, which must account
for the BIPV thermal conditions, too. The profiles of the Ross coefficient for BIPV/T, BAPV and free standing PV
operating in the same site were determined, compared and discussed. The theoretical and experimental analysis of a
BIPV/T test cell disclosed that Tpv vs IT is a linear function in all cases from sunrise till solar noon with a practically
constant slope and coefficient of determination, R2
>0.96. Correspondingly, from noon to sunset the linearity still holds
but with a lower slope which depends on the insulation of the building and the increased ambient temperature during
sunset compared to sunrise, which is the usual case. An improved version of a Tpv prediction holistic formula was
developed to take into account the building thermal parameters, the ratio of the PV surface over the building surface, and
the environmental parameters. This new and improved methodology for the f and Tpv prediction for both morning to noon
and noon to sunset periods was tested against measured Tpv vs IT and the predicted results confirmed its validity.
Keywords: BIPV, BIPV/T, BAPV, PV temperature prediction, Ross coefficient

... Due to this effect, temperature is one of the most relevant stressors influencing degradation of modules in operation. PV modules always operate at elevated temperatures, compared to ambient conditions [16] if they are not technically cooled. For the determination of the temperature load, it is important to use the module temperature (microclimate) and not the ambient temperature (macroclimate) since they differ significantly. ...

... The module temperature mainly depends on the ambient temperature, irradiation, module design, wind, and installation. There are models which allow the calculation of module temperatures with adequate accuracy using ambient climatic conditions and type specific parameters as input factors [16,17]. Comparing the situation at one specific location, the type of installation has the biggest influence [18,19]. ...

The market for Photovoltaic systems has experienced an enormous growth worldwide and will further grow over the coming decades. Investments in Photovoltaics became an important financial product with the special feature of very long contract durations. Typically operation of over 20 years is expected, during which generation of electricity and revenues are expected. Due to these long operational times, quality, durability, reliability, and degradation rates become crucial for the investment. PV modules are the dominating components in this regard since they prevail the investment. Accelerated ageing tests are in general used to ensure the quality of photovoltaic components. These tests are partly standardized, for PV mainly by IEC and are used for type approval or safety testing. Accelerated ageing tests are also adapted to specific needs and e g used for Quality Assurance (QA) of manufacturers or Service Life Prediction (SLP) by manufacturers or research institutes. All the efforts are taken to gain knowledge about the behaviour of PV modules in operation and thus the accelerated tests have to be related to normal operation. Since PV is used around the globe, the conditions vary significantly depending on the location of installation. In addition, the installation has severe influence on the operational conditions of PV modules. The papers attempt is to give an overview on the state of the art of accelerated testing and field performance analysis of PV modules with focus on developments over the last five to ten years. Developments are described and the status is analysed regarding the significance of tests including the latest developments and open scientific gaps related to the envisaged correlation of accelerated tests with field performance. The reader is enabled to differenciate between reliability testing and service life prediction. The understanding for a comprehensive approach of reliability testing including field evaluation data is develope

... Suitable heat exchange coefficients must therefore be chosen in the thermal models used to evaluate the temperature of the PV cells. For ground systems, the temperature estimation models from [18] are used, while for FPV systems the models from [11] are used. -Albedo: The albedo of a water body is very low (0.1, which is much lower than the normal value of 0.2 for ground). ...

... Faiman [18] model of equation Eq. (1) is used to estimate the temperature of the modules. In this work, the quantity U 0 and U 1 for the FPV are chosen respectively as follow [11]: ...

Floating photovoltaic systems (FPV) are an innovative technology, in which photovoltaic modules are installed on water surfaces with the aim of reducing land occupation and at the same time increasing its efficiency and creating synergies with aquaculture and hydroelectric plants. The purpose of this study is to evaluate the energy performance on an annual basis of a fixed G/FPV (ground/floating photovoltaic) system, with vertical, horizontal or two-axis tracking, with mono or bifacial modules. The simulated data for FPV (floating PV) systems are compared with those of a GPV (ground PV) system through performance indexes. The analysis of the energy output is carried out depending on the geometric variables of the plant. The energy production of PV systems is highly dependent on the local climate. Therefore, the study was developed for two locations characterised by different components of diffuse solar radiation, one at high latitudes and the other at mid-latitudes. The two locations are: Anapo Dam in Sicily (Italy) and Aar Dam in the Lahn-Dill district (Germany).
As for the gain due to the bifaciality of the systems with bifacial modules, it can be stated that for the analyzed configurations, a gain greater than 3% can be obtained for Anapo Dam in Sicily and greater than 4% for Aar in Germany.
As for the gain due to the natural cooling of the modules, it can be stated that for the analyzed configurations, a gain of more than 5% can be obtained for Anapo Dam in Italy and greater than 4% for Aar in Germany.
If the overall gain due to bifaciality tracking and cooling is considered, the following gains are obtained for the two locations Anapo and Aar respectively: 16.9% and 14.4% for Horizontal E-W system; 27.6% and 23.3% for Horizontal N-S system; 31.3% 27.8% for One Axis Vertical system; 47.4% and 42.5% for Dual axis system.

... Nevertheless, the reason to choose I MPP among the available electric variables was due to its equivalence to the I SC method when soiling is known to be uniform and for its nearly constant response to temperature variations compared to DC power, which is influenced by the typical higher temperature dependency of the voltage (Seapan et al., 2020). Although the cleaned and the non-cleaned PV modules are theoretically identical, temperature differences exist even among PV cells with average values higher than 2 K (Faiman, 2008;Martín-Chivelet et al., 2022), which may cause power determination errors above 1% (for a typical temperature coefficient of 0.5%/K). Since soiling loss values can be in the same order, the method based on I MPP measurement was considered as the best option. ...

... Five different simplified thermal balances found in literature (see Table IV) have been compared and the temperatures variations as a function of incident solar radiation intensity are shown in Fig. 3. It is observed that models [5,6,7,8,9] ...

... where T a is the ambient temperature [46], W s is the wind speed, and coefficients U 0 = 26.9 and U 1 = 6.2 are determined in [47]. Lastly, generic system loss L = 14.0%, as recommended by PVGIS, was considered. ...

The implementation of the energy transition and the building of energy communities are driving forward the exploitation of the potential for rooftop photovoltaic power generation. Estimating rooftop PV generation potential requires the processing of different types of data, such as the cadastral information of buildings, a detailed description of available rooftop areas, and solar irradiance data. High-resolution estimation based on GIS data is normally limited to small survey areas. Instead, by using an algorithm for the efficient calculation of shadows over rooftops, and the integration of solar irradiance over time, we developed a procedure that allows for the rapid full census assessment of rooftop photovoltaic potential with a spatial resolution of 1 m, applicable at the regional scale and requiring minimal computational resources. We applied this approach to the rooftops of buildings in Sardinia, an island and region of Italy of particular interest for the energy transition. In addition to estimating the geographic potential, we carried out a preliminary assessment of the technical and economic potential, yielding a maximal photovoltaic rooftop generation potential of 22 TWh for the entire region.

... A key to increasing electricity output of PV panels is lowering their temperature. A widely used correlation for estimating panel temperature (T m ) in different environmental conditions [4], which was derived from empirical data at a desert test site in Israel, is given in Eq. 1, ...

The effect of vegetation on solar PV panel efficiency was tested in a commercial solar farm in the Negev Desert of Israel. Panel temperature of mono-facial modules in two test sites of 0.22 hectares each with different plant treatments was up to 3.5°C lower at midday compared to the panel temperature in an adjacent reference plot with bare loess soil. The temperature difference was not uniform, being greatest for the upper panels in a ground-mounted array (average reduction 2.2°C), and lowest for panels closest to the ground (1.0°C reduction). The temperature reduction is attributed primarily to smaller fluxes of solar radiation reflected from the plants, which have a lower albedo than the bare soil, and to less infrared radiation emitted from the plants, which are cooler. A small reduction in air temperature due to evapotranspiration also contributed to this outcome. Electricity production measured in the test plots was approximately 1% higher over the summer test period. The Land Equivalent Ratio (LER) of the test plots was 1.67, reflecting the combined contribution of the increased electricity production, the value of the crops, and the reduction in site maintenance costs.

... For example, the Faiman model is one of the most basic methods, in which PV convection is related linearly to only external wind speed. 24,25 While this model predicts cooling well for PV modules in individual farms, it has significant limitations in moderate temperatures and when comparing separate geographical locations. 26 More elaborate methods consider additional variables to assess productivity, including textbook Nusselt number (Nu ¼ hL=k) correlations for turbulent, forced convection, as input calculations for cooling potential. ...

Heat mitigation for large-scale solar photovoltaic (PV) arrays is crucial to extend lifetime and energy harvesting capacity. PV module temperature is dependent on site-specific farm geometry, yet common predictions consider panel-scale and environmental factors only. Here, we characterize convective cooling in diverse PV array designs, capturing combined effects of spatial and atmospheric variation on panel temperature and production. Parameters, including row spacing, panel inclination, module height, and wind velocity, are explored through wind tunnel experiments, high-resolution numerical simulations, and operating field data. A length scale based on fractal lacunarity encapsulates all aspects of arrangement (angle, height, etc.) in a single value. When applied to the Reynolds number Re within the canonical Nusselt number heat transfer correlation, lacunarity reveals a relationship between convection and farm-specific geometry. This correlation can be applied to existing and forthcoming array designs to optimize convective cooling, ultimately increasing production and PV cell life.

... This thermal model is used in the commercial software PVsyst and is derived from the Faiman model Equation (28) [65]: ...

Bifacial technology is attracting the attention of the photovoltaic community. Although considered premature, research and development activities still need to be carried out to improve bPV performance. In addition, the need for a standard test reference will aid bankability and increase confidence in this technology. This article describes the state of the art of bifacial technology, going through the bPV cell and its difference compared to conventional monofacial cells and listing the different sources of limitations, with an identification of different parameters that characterize the performance of the bifacial. Then, the paper reviews the different modeling methods that allow predicting the performance of bPV systems, and ends with the most important applications, whether for dual use of land to produce energy and food (agrivoltaic) or for placing bPV modules on water bodies instead of on the ground (aquavoltaics), or for vertical use as solar fences, acoustic barriers, or building-integrated photovoltaic modules.

... These two models have the disadvantage that the proposed environmental conditions rarely coincide with the actual operating conditions of the PV systems. [25][26][27]; while others do not consider it, such as Akhsassi et al. [28]; but all agree that irradiance is the main cause that causes an increase in temperature of the PV cell. Statistical models can be subdivided into two groups: Artificial Intelligence (AI) methods and linear models. ...

The efficiency of photovoltaic modules depends on the operating temperature of the cells. Currently it is difficult to choose a suitable model to estimate the temperature of the modules, due to the variety of proposed models. In this research, ten temperature estimation models of the modules were evaluated, based on three input variables: ambient temperature, irradiance and wind speed. For the modeling, in situ measurements were used, recorded for six months, by the 7.5 kWp monocrystalline silicon photovoltaic system and a climatological station of the Solar Energy Research Center of Santiago de Cuba. King et al (2004) was the model with the best accuracy criteria, with squared error, mean absolute error and coefficient of determination equal to 3.482 ºC, 2.698 ºC and 0.912, respectively. Finally, the effect of the operating temperature of the modules on the efficiency was simulated, obtaining useful information for future projects of photovoltaic systems in Cuba.

... There are many models that predict the module temperature Tm of PV systems: the NOCT [1], Sandia [2], and Faiman [3] models are the best known, and there are other more sophisticated models (e.g., [4]- [10]) that distinguish between radiative, convective and conductive heat flow, and incorporate transient effects. All effectively treat convection with one or two parameters, Uc and Uv × w, where Uc and Uv are constants and w is wind speed. ...

... The performance of a PV module decreases with an increase in its temperature, which is affected by ambient temperature, light intensity and local wind speed [103][104][105]. This study assumes that measured global horizontal irradiance is available but not a complementary dataset of temperature or wind speeds. ...

Small island developing states (SIDS) are the lowest emitters of greenhouse gases yet are the most vulnerable to the impacts of global climate warming. Many islands, such as the Caribbean islands, identified solar photovoltaics as a technology for reducing greenhouse gas emissions from their electricity sector. However, prefeasibility economic studies for photovoltaics are challenging as operational photovoltaic system data are nonexistent, and the measured solar radiation datasets are limited. Thus, a prefeasibility PV tool that uses ground-measured global horizontal irradiation and a supplementary photovoltaic derating factor model is proposed for use in tropical SIDS. In addition, the bias of a modelled irradiation dataset was quantified with limited solar radiation data for a tropical Caribbean SIDS, Trinidad and Tobago. For this SIDS, the tool estimates the annual energy output of a 50 MW photovoltaic system to be 57,890 MWh and the levelized cost of electricity to be USD 0.12/kWh. The performance of the proposed tool was comparable with two existing prefeasibility models, RETScreen and SAM, which use past ground measurements and modelled data, respectively. The biases in the annual irradiation data for RETScreen and SAM were determined to be 6% and 25%, respectively, against the solar irradiance dataset used. The proposed tool may be useful for first approximation prefeasibility photovoltaic studies in similar regions with limited climatic data.

... (8)), the Faiman model (Eq. (9)) [17] ...

The rapid growth in grid penetration of photovoltaic (PV) calls for more accurate methods to forecast the performance and reliability of PV. Several methods have been proposed to forecast the PV power generation at different temporal horizons. In this chapter the different methods used in PV power forecasting are described with an example on their applications and related uncertainty. The methods discussed include physical, heuristic, statistical and machine learning methods. When benchmarked, it is shown that physical method showed the highest uncertainties compared to other methods. In the chapter, the effect of degradation on lifetime PV power and energy forecast is also assessed using linear and non-linear degradation scenarios. It is shown that the relative difference in lifetime yield prediction is over 5% between linear and non-linear scenarios.

... The latest work based on first-principle calculations shows that disorder by itself has low influence on device performance, but it reduces the formation energy of detrimental deep Sn Zn and Sn Cu defects [77], thus having an important role during the synthesis of kesterite absorbers. Nevertheless, all the latest studies on soft PDTs in CdS/kesterite based devices (in the temperature limits 100-200 • C), including the present investigation, show a quite low thermal stability of this absorber and of the absorber/buffer interface (with several positive and/or negative effects taking place), and this should be taken into account not only at the final stages of the device preparation (deposition of window layer or device encapsulation), but even during the device operation (the working temperature of solar modules can exceed 100 • C during operation) [78,79]. ...

The thermal stability of the Cu2ZnSnSe4 (CZTSe) absorber and CdS buffer layers in SLG/Mo/CZTSe/CdS/i-ZnO/ITO devices is explored by performing a series of soft (∼200 °C) post deposition treatments (PDTs). A comprehensive analysis of a sample comprised by 56 individual devices by means of Raman and photoluminescence spectroscopies coupled with optoelectronic characterization is performed at different PDT steps. This allows isolating the effects of the PDT on the CZTSe absorber and CdS buffer layer separately and reveals clear evidences of: i) a degradation of the absorber due to Cu/Zn disorder that hinders device performance, and ii) an improvement of the buffer layer by the recrystallization of the CdS nanolayer that is the main responsible for the PDT-induced efficiency improvement. As such, it is concluded that CZTSe/CdS based PV devices present a low thermal stability under relatively low temperatures (in the 100–200 °C range), comparable to the temperatures employed at the final production stages of thin film PV devices or even during device operation, that leads to significant changes in solar cell performance and needs to be taken into consideration for the further development of the kesterite PV technology. These results are supported by a novel methodology for easily discerning between changes in Cu/Zn disorder and in point defects concentration in kesterites based on solely on Raman spectroscopy that is proposed in this work and developed through the analysis of a set of CZTSe powder samples with strong variation of the order parameter Q.

... The steady-state thermal models most commonly used in simulation software for yield assessment and energy rating are one-dimensional, linear, lumped-parameter models with empirically determined coefficients: Faiman [1], SAPM [2], PVsyst [3], SAM-NOCT [4]. This means they use just a few parameters to represent all the complexities of the heat exchange between the module and its environment, and indeed also of the heat generation and transfer within the module. ...

PV module operating temperature is the second-most important factor influencing PV system yield—after irradiance—and a substantial contributor to uncertainty in energy system yield predictions. Models commonly used to predict operating temperature in system simulations are based on a simplified energy balance that lumps together different heat loss mechanisms—including radiation—and assumes an overall linear behavior. Radiative heat loss to the sky is usually substantial, but modeling it accurately requires additional information about down-welling long-wave radiation or sky temperature and increases the complexity of temperature model equations.
In this work we show how radiative losses to the sky can be separated into two parts to improve the accuracy of modeling without additional complexity. We also predict and demonstrate the variation of these losses at different tilt angles and show that the effective view factor is reduced by the non-isotropic distribution of down-welling long-wave radiation. Finally, we demonstrate substantial reduction in bias (MBE) and scatter (RMSE) when the new radiative loss term is added to the Faiman model using one year of measurements at Sandia National Labs.

... This does not include temperature losses in PV modules and PV inverter clipping losses which are separately taken into account. Temperature losses due to PV module heating are modelled in python pvlib package using the Faiman empirical heat loss model [33], which calculates PV module temperature by considering the POA global irradiance, air temperature, and wind speed at the PV module height. Air temperature measurements are taken from the pyranometer, while wind speed at the module height is calculated from available wind speed measurements from one of the WTGs at the nacelle, using the well-known Hellmann exponential law: ...

Curtailment losses for large-scale hybrid wind–solar photovoltaic (PV) plants with a single grid connection point are often calculated in 1 h time resolution, underestimating the actual curtailment losses due to the flattening of power peaks occurring in shorter time frames. This paper analyses the curtailment losses in hybrid wind–PV plants by utilising different time resolutions of wind and PV production while varying the grid cut-off power, wind/solar PV farm sizes, and shares of wind/PV capacity. Highly resolved 1 s measurements from the operational wind farm and pyranometer are used as an input to specialized wind and PV farm power production models that consider the smoothing effect. The results show that 15 min resolution is preferred over 1 h resolution for large-scale hybrid wind–PV plants if more accurate assessment of curtailment losses is required. Although 1 min resolution additionally increases the estimation accuracy over 15 min resolution, the improvement is not significant for wind and PV plants with capacity above approx. 10 MW/10 MWp. The resolutions shorter than 1 min do not additionally increase the estimation accuracy for large-scale wind and PV plants. More attention is required when estimating curtailment losses in wind/PV plants with capacity below approx. 10 MW/10 MWp, where higher underestimation can be expected if lower time resolutions are used.

... The higher its value, the better the thermal exchange of the PV module with the environment, and, therefore, the lower its operating temperature. In its original formulation (Faiman, 2008), the U-value is split into a constant and a convective components, and this last one is multiplied by the wind speed. However, PVSyst recommends using the heat loss coefficient U without wind dependency. ...

In floating photovoltaics, modules are mounted on or above water surfaces in order to limit the land occupancy, an issue arising with the growing deployment of photovoltaics. The floating structures are also expected to lower the capital expenditures required by traditional in-land systems, thanks to the lack of major site preparation needs and to the hybridization with hydropower plants. This work estimates the yield potential and the cost effectiveness of floating photovoltaics across suitable water bodies in Europe compared to optimally tilted land-based photovoltaics. Energy and economic outputs are modelled using referenced models, field-measured parameters and considering weather and economic conditions specific to each location and each country. The results show that, despite the lower tilts, floating photovoltaics with improved heat transfer capabilities can achieve energy yields up to 2 % greater than land-based photovoltaics. This is especially true in the Mediterranean region, where the average position of the Sun and the temperatures are higher. However, in some configurations, floating photovoltaics might not achieve lower temperatures than land-based photovoltaics, leading to lower energy yields. Despite that, it is found that, even when underperforming, floating photovoltaics can be cost competitive with land-based photovoltaics if the installation costs are reduced by less than 12 %. Last, this study estimates that each additional degree of tilt angle in floating photovoltaic installations is worth between 2.5 and 7.5 €/kW.

... Based on the above nominal model, many scholars have carried out many studies. Many photovoltaic module temperature prediction models such as those by Skoplaki et al. [25], Mattei et al. [26], Sandia et al. [27], Faiman [28], and Muzathik et al. [29,30] have been proposed. The multiple linear regression equation model proposed by Muzathik is shown in Equation (3): ...

Studying the temperature field of photovoltaic modules is important for improving their power generation efficiency. To solve the problem of traditional sensors being unsuitable for measuring the spatial temperature field, we designed a real-time detection scheme of the photovoltaic module temperature field based on a fiber Bragg grating (FBG) sensor array. In this scheme, wavelength division multiplexing and space division multiplexing technologies were applied. The multi-channel FBG sensor strings were arranged on the surface and in the near field of the photovoltaic module. Different FBG strings were selected through optical switches, and the wavelength of the FBG string was addressed and demodulated using the tunable laser method and a peak-seeking algorithm. A measurement experiment of the photovoltaic module temperature field was carried out in an outdoor environment. The experimental results showed that the fluctuation law of the photovoltaic module surface and near-field temperature is basically consistent with that of solar radiation power. The temperature of the photovoltaic module decayed from the surface to space. Within 6 mm of the photovoltaic module surface, the temperature sharply dropped, and then the downward trend became flat. The lower the solar radiation power and the higher the wind speed, the faster the temperature decay. This method provides technical support for measuring the temperature field of a photovoltaic module and other heat source equipment.

... the ambient temperature (T a ), and one of three module temperature models: the nominal operating cell temperature (NOCT) [55], Faiman [56], or Sandia [57] models. The latter two models are empirically derived functions of G c , T a , and wind speed. ...

Bifacial photovoltaic (PV) performance models strive to accurately quantify rear-incident irradiance. While ray tracing models are optically rigorous, they require significant computational resources; faster view factor (VF) models are widely adopted but require user-defined loss factors to approximate rear shading and irradiance nonuniformity, introducing uncertainty in energy yield predictions. This article describes DUET—a bifacial PV performance model that calculates optical and electrical performance based on a physically representative array geometry. DUET's novel shading algorithm pairs a 3-D VF model with deterministic ray-object intersections to capture 2-D shade-inclusive irradiance profiles while minimizing computational cost. Series and parallel combination of current–voltage curves capture irradiance nonuniformity throughout the module and array. This article provides validation against open-access system measurements from a test site in Roskilde, Denmark, and comparison to other software tested there [1]. DUET's modeled bifacial energy yield agrees with measured data within −1.56% for fixed-tilt and −0.65% for horizontal single-axis tracked (HSAT) systems. Mean absolute error (MAE) in hourly bifacial power is 14.2–15.0 mW/Wp for fixed-tilt and 17.3–18.3 mW/Wp for HSAT, depending on the module temperature model applied. Comparing modeled and measured rear irradiance of two rear-facing pyranometers, DUET's MAE values of 2.8 W/m $^{2}$ for fixed-tilt and 3.7 W/m $^{2}$ for HSAT are among the lowest errors reported for other software tested at this site. DUET provides computationally efficient bifacial performance modeling with geographic, temporal, and structural specificity to determine loss factors for use in other performance models or to be used directly in system design optimization.

... Additionally, in (6) authors have assumed that the orthogonal disposition of 46 polarizations components implies the non-interference between them (Y. Soler-Castillo et al., 2022) [13], for which the mean of spec-47 tral reflectance described by (6) would be the average of both reflectance polarizations components as represented by (7), regarding the 48 unpolarized light (50% p-polarized, 50% s-polarized As it is described by (6), the spectral reflectance largely, it is a function of the inte-49 grated irradiance in the spectral range of the sensor that performs its measurement, and its modulation by the coefficient of the reflec-50 tion and geometry spatial losses, here proposed by authors. In Fig.1 is plotted the spectral reflectance behavior as function of the irradi-51 ...

Empirical models for the mean spectral reflectance and the fill factor.

... Temperature effects on PV module efficiency are well-documented [1] and many models exist for calculating module temperature [2]. Module temperature models vary in complexity, from three-dimensional finite element analysis [3] to simpler and more practical empirical approaches in one dimension [4]- [7]. Although three-dimensions and finite element analysis may be more accurate with respect to modeling the heat transfer behavior of a PV module, it is computationally prohibitive when it comes to long-term, fine resolution energy yield analyses and/or real-time monitoring. ...

PV module operating temperature is the second most important factor influencing system yield, after irradiance. A variety of temperature models are used within yield simulation software to predict module operating temperature, which then determines operating efficiency. Four temperature models are frequently used: PVsyst, Faiman, SAPM and SAM NOCT. Although these models are similar, their parameter values are not directly interchangeable. In this work we demonstrate the equivalence or near-equivalence of these four temperature models, and from there we develop equations to convert their parameter values back and forth. This is more than a convenience for users of simulation software. We use this capability, for example, to compare and analyze the typical and default values preset for different model/software combinations. The functions to perform the parameter conversions are made available as open-source software in pvlib-python.

... However, the actual operating conditions of PV devices in the field often significantly deviate from STC [119]. With increasing temperature, parameters such as VOC, FF, and maximum power output decrease [120]. ...

... The drawback of this method is that only solar irradiance is included in the determination of q PV . In contrast, the models of Faiman [30] and King et al. [31] also consider the wind speed. ...

The cooling of PV has been shown to increase electricity production. Among passive techniques, evaporative cooling has one of the greatest potentials. In this work, the efficiency and sustainability of this technique have been investigated for various climatic conditions. In-situ experiments were conducted to develop parametric models for PV cell temperatures and back surface convective heat transfer coefficient. Experiments have revealed an up to 20.1 °C lower peak PV temperature and up to 9.6% increased electric power. Year-round analysis was made for eight cities to determine the required roof size to capture precipitation and the volume of rainwater storage for sustainable evaporative cooling. The study shows that sustainable PV evaporative cooling is possible in cities with temperate and continental climates, where 1–3 m² of roof area and 50–150 l of rainwater storage are needed for 1 m² of PV. The annual electricity production can increase by 5.9–9.4 kWh/m²a, which is a 3.6–4.6% increase. In the semi-arid climate of Lampedusa, a roof above 4 m² and a storage of up to 500 l per m² of PV are required. In the desert climate of Almeria and Athens, sustainable evaporative cooling is not feasible.

... The annual climate change related evolution of solar irradiation, module temperature, and total degradation rate are shown in Figure 9. Note that the module temperature is estimated from ambient temperature, solar irradiation, and wind speed using the Faiman model [31]. ...

The environmental footprint of photovoltaic electricity is usually assessed using nominated power or life cycle energy output. If performance degradation is considered, a linear reduction in lifetime energy output is assumed. However, research has shown that the decrease in energy output over time does not necessarily follow a linear degradation pattern but can vary at different points in the module’s lifetime. Further, photovoltaic modules follow different degradation patterns in different climate zones. In this study, we address the influence of different degradation aspects on the greenhouse gas (GHG) emissions of PV electricity. Firstly, we apply different non-linear degradation scenarios to evaluate the GHG emissions and show that the differences in GHG emissions in comparison to a linear degradation can be up to 6.0%. Secondly, we use the ERA5 dataset generated by the ECMWF to calculate location-dependent degradation rates and apply them to estimate the location-specific GHG emissions. Due to the reduction in lifetime energy output, there is a direct correlation between the calculated degradation rate and GHG emissions. Thirdly, we assess the impact of climate change on degradation rates and on the respective GHG emissions of photovoltaic electricity using different climate change scenarios. In a best-case scenario, the GHG emissions are estimated to increase by around 5% until the year 2100 and by around 105% by 2100 for a worst-case scenario.

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. “Developing an energy rating for bifacial photovoltaic (PV) modules” demonstrates how the IEC 61853 standard could be extended to bifacial modules, which are becoming the most common PV module type. The authors develop an irradiance model that calculates the rear irradiance on the PV module. Furthermore, they extend the energy yield calculation algorithm IEC 61853‐3 to include bifacial modules, discuss first results, and make it available to the PV community.

Under the two-step framework of photovoltaic (PV) power forecasting, that is, forecasting first the irradiance and then converting it to PV power, there are two chief ways in which one can account for the uncertainty embedded in the final PV power forecast. One of those is to produce probabilistic irradiance forecast through, for example, ensemble numerical weather prediction (NWP), and the other is to pass the irradiance forecast through a collection of different irradiance-to-power conversion sequences, which are known as model chains. This work investigates, for the first time, into the question: Whether pairing ensemble NWP with ensemble model chain is better than leveraging any individual method alone? Using data from 14 utility-scale ground-mounted PV plants in Hungary and the state-of-the-art global mesoscale NWP model of the European Centre for Medium-Range Weather Forecasts, it is herein demonstrated that the best probabilistic PV power forecast needs to consider both ensemble NWP and ensemble model chain. Furthermore, owing to the higher-quality probabilistic forecasts, the point forecast accuracy is also improved substantially through pairing. Overall, the recommended paring strategy achieves a mean-normalized continuous ranked probability score and a root mean square error of 18.4% and 42.1%, respectively.

Nowadays, surveillance and protection systems are standard equipment at many airports. However, their use can be quite restrictive in the case of their relatively short-term use in an area that does not normally extend to their perimeter of protection. The limiting factor in such situations is mainly their low mobility and dependence on external galvanic lines, especially if the individual sensors require mutually different power requirements. In consequence, this article is devoted to the analytical estimation of the energy provided by the photovoltaic power supply for a mobile monitoring unit, intended to monitor a surrounding area and inform about a possible unauthorized intrusion into perimeter protection. The essence of the analysis was to estimate the time of the one discharging cycle during which the designed battery-based photovoltaic system power supply can continuously provide sufficient energy to keep the mobile monitoring unit in its full operational mode.

The current study developed an analytical model to predict the PV module's operating temperature based on an experimental database, which considers cell temperature, local meteorological data (irradiance, ambient temperature, wind velocity, and humidity), voltage, and current generated by the photovoltaic system associated with the purely resistive load. Based on the analysis of the 172-day database, it was possible to compare the most used correlations in the literature with the analytical model developed in the current work. For all conditions, the model showed a better response to climate variation-with 100% of the data within an error band of ± 20% and an absolute mean percentage error of 3.1%-predicting well the PV module's operating temperature for both sky conditions (clear or cloudy) and demonstrated that the thermal capacity of the PV module to climatic variations should not be neglected. Moreover, the new model considered the PV module's thermal response capacity to include the variations in the incident solar irradiance caused by the presence of clouds (shading effect). By considering a global heat capacity as a mean value of the heat capacities of the layers of the PV module, the term transient-generally neglected in several works-is considered in the energy equation in the current work, which gives a better response to the variations in the incident radiation.

In spite of a continuous decrease of the cost of photovoltaic cells and modules over the last decades, the PV industry keeps on trying to be more innovative in terms of implementing new cell concepts to improve the efficiency and the productivity. This boosted the development of the bifacial technology while maintaining a low cost of implementation in production lines, previously dedicated to monofacial modules only. Given the ability to produce energy from both sides and a lower thermal coefficient due to the utilization of new topologies for solar cells structure, the implementation of this technology has become bankable and has achieved market prices similar to their monofacial counterparts and is expected to have a significant impact on reducing the cost of solar energy. A bifacial module allows to increase the energy produced normalized to an equivalent monofacial power system by 10 to 20% depending on the configuration.The bifacial gain is provided by the backside irradiance, whose magnitude depends on many system installation factors unlike monofacial systems. Therefore, in the last years there has been a great interest in developing models to simulate the performance of bifacial systems. However, unlike the well-established models for monofacial modules, the validation of bifacial models remains an ongoing task for the research centers collaborating with the PV industry in order to reduce the uncertainty and increase the reliability of the predictions. Increased uncertainty in the reliability of performance predictions indeed leads to reduced investor confidence in the profitability of the bifacial PV technology, making it difficult to finance and deploy large-scale bifacial PV systems. For this reason, further validation of these simulation models based on long-term field data acquired by monitoring systems in different geographical locations and with different geometrical configurations are necessary to overcome the aforementioned challenges.The present work proposes the implementation of a comprehensive and proven simulation methodology for the prediction of the energy yield of bifacial photovoltaic systems. As the simulation of a photovoltaic system requires a combination of optical, thermal and electrical modelings, the methodology chains sub models based on the recent literature review and related aspects for an accurate prediction of the energy yield of bifacial PV systems. Two main approaches, ray tracing and view factor, are evaluated for modeling the front and back irradiance on bifacial photovoltaic modules. Coupled to the thermal and electrical model results, a calculation of the energy production and the bifacial gain is achieved.For the validation of the simulation following this methodology, the results are compared with experimental data acquired on 4 PV systems comprising small and large-scale systems with different mounting configurations, at different locations and based on different bifacial technologies.The results show an overestimation in the energy yield prediction for an 8-module system of between 3 and 4 percent, and between 2 and 3 percent in the case of a large-scale system.The results thus demonstrate that the energy yield of bifacial can be modeled with similar accuracy to the monofacial PV systems. Finally, this simulation method is applied to the exploration of fault detection and the diagnosis of a photovoltaic system through the application of neural networks for fault classification by training from a synthetic database. An accurate simulation helps the identification of faults and their location in large photovoltaic systems; this is a key issue to improve the maintenance and the operation of such plants.

Ensuring single-phase growth during evaporation of perovskite absorbers for solar cells is a critical step towards industrialization, since the mechanisms of δ-phase suppression need to be fully understood.

Curved photovoltaics (PV) is gaining widespread application in modern energy-efficient infrastructure, wearable electronics, and vehicles. Due to the different orientations of the solar cells in curved PV modules, current mismatch between solar cells is more prevalent in curved PV than conventional flat PV. In this article, we investigated the effect of shunt resistances, which can mitigate current mismatches in series-connected solar cells, on the performance of curved thin-film PV modules. A flexible 85 × 80 mm
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mini-module composed of 17 series-connected solar cells on a curved surface was characterized experimentally and theoretically. We found that the short-circuit current of the curved PV module is affected by all the solar cells connected in series and is not simply determined by the current-limiting solar cell. The current-voltage characteristics of a curved PV module are well described by a simple model that includes low shunt resistance. The power generated from normal irradiance decreases with shunt resistance; however, the power for tilted illumination is higher than that of a module without shunt resistance. This indicates that the low shunt resistance can suppress the power loss due to current mismatch. In addition, curved PV modules cause self-shading under highly tilted illumination but curved PV modules with low shunt resistances provide power even when some solar cells are not illuminated. Furthermore, sudden current mismatches in solar cells, which generate detrimentally high reverse biases can be eliminated by the shunt resistance. This confirms the protective effect of the shunt resistance to enhance the durability of curved PV modules.

Physical model chain is a step-by-step modeling framework for the conversion of irradiance to photovoltaic (PV) power. When a model chain is fed with irradiance forecasts, it provides the corresponding PV power forecasts. Despite its advantages, forecasting with model chains has yet to receive the attention that it deserves. In several recent works, however, the idea of model-chain-based solar forecasting has been formally modernized, though the framework was restricted to deterministic forecasting. In this work, the model-chain-based forecasting framework is extended to the probability space, in that, a calibrated ensemble of model chains is used to generate probabilistic PV power forecasts. Using two-year data from eight PV plants in Hungary, alongside professional weather forecasts issued by the Hungarian Meteorological Services, it is empirically shown that the raw model-chain ensemble forecasts tend to be underdispered, but adequate post-processing is able to improve calibration and reduce the continuous ranked probability score of raw ensembles by 20%. Given the fact that uncertainty quantification has a cardinal importance to grid integration, this probabilistic extension of the model-chain-based solar forecasting framework is thought beneficial.

In floating photovoltaics (FPV), modules are installed on water to alleviate the land requirement of this energy source. In addition, FPV installations are expected to work at lower operating temperatures compared to land based photovoltaic (LPV) systems, thanks to the cooling effect of water. If confirmed, these lower temperatures would (i) increase the energy yield and (ii) reduce degradation and performance losses, boosting the cost-competitiveness of FPV. However, some recent works have reported cases of FPV systems working at higher temperatures than co-located LPV systems. The present review gathers the literature on the thermal behaviour of FPV, outlining the models and discussing the currently available experimental results. It is found that FPVs of different configurations can experience different thermal behaviours, not always necessarily better than LPV. In particular, air- and water-cooled FPV systems should be always distinguished, considering their diverse cooling mechanisms. Initial comparative analyses make it possible to identify designs and conditions that can favour the heat transfer in FPV compared to LPV. The role of additional factors on the FPV temperature, such as the PV material or the more frequent biofouling, is also discussed. Last, estimations of the economic impact of the thermal behaviour on the FPV costs and competitiveness are presented.

Irradiance-to-power conversion is an essential step of state-of-the-art photovoltaic (PV) power forecasting, regardless of the source and post-processing of irradiance forecasts. The two distinct approaches for mapping the irradiance forecasts to PV power are physical and data-driven, which can also be hybridized. The contribution of this paper is twofold; first, it proposes a concept and identifies the best implementation of a hybrid physical and machine learning irradiance-to-power conversion method. Second, a head-to-head comparison of the physical, data-driven, and hybrid methods is performed for the operational day-ahead power forecasting of 14 PV plants in Hungary based on numerical weather prediction (NWP). To respect the rule of consistency but still obtain as complete picture as possible, two directives are set, namely minimizing the mean absolute error (MAE) and minimizing the root mean square error (RMSE), and separate sets of forecasts are optimized for both directives. The results reveal that for two years of training data, the hybrid method that involves the most physically-calculated predictors can reduce the MAE by 5.2% and 10.4% compared, respectively, to the optimized physical model chains and the machine learning without any physical considerations. The two most important physical modeling steps are separation and transposition modeling, and the rest of the physical PV simulation can be left to machine learning in hybrid models without a significant increase in the errors. The optimization of the physical model chains is found to be important even in the case of hybrid modeling; therefore, it should become a standard procedure in practical applications. Finally, the hybrid method is only beneficial for at least one year of training data, while in the initial period of the operation of a PV plant, it is advised to stay with optimized physical modeling. The guidelines and recommendations of this paper can help both researchers and practitioners design and optimize their power conversion model to increase the accuracy of the PV power forecasts.

The operating temperature has a critical impact on the electrical performance of solar cells. It has been shown that the temperature coefficient is not uniform across devices and often varies between different regions due to the inhomogeneous distributions of defects. In this study, temperature‐dependent photoluminescence imaging measurements are used to assess the influence of different processes such as gettering, firing and advanced hydrogenation on the temperature‐dependent electrical performance of cast‐mono silicon wafers. It is found that the height of the wafer within the ingot impacts the response of the temperature coefficient to different fabrication processes. Advanced hydrogenation is found to reduce the temperature sensitivity, more than expected solely from the improvement in implied open‐circuit voltage. Crystallographic defects are found to be the least temperature sensitive regions, indicating that their detrimental impact is reduced at higher operating temperatures. The interesting low temperature sensitivity in the defective regions is further investigated using hyperspectral photoluminescence imaging measurements and atom probe tomography. It is suggested that the reduced sensitivity is due to impurities decorating crystallographic defects. This study assesses the influence of gettering, firing and advanced hydrogenation on the spatially resolved temperature coefficient of cast‐mono silicon wafers. Most regions containing crystallographic defects are characterised by low temperature sensitivity and are further investigated using hyperspectral photoluminescence (PL) imaging and atom probe tomography. The combination of three advanced characterisation methods, from the nanoscale to the milliscale, provides an in‐depth understanding of the temperature‐dependent electrical properties of cast‐mono silicon.

To predict and evaluate better the thermal behavior of photovoltaic arrays, a study has been initiated to predict the operating cell temperatures of various systems existing today. This effort has been completed for five prototypes at the Southwest Residential Experiment Station (SW RES), encompassing the widest range of residential photovoltaic designs, and their temperature responses have been modeled to near the tolerance error of the measuring instruments. The arrays include a direct mount, rack mount, integral mount, and two standoff mounts designs. It is concluded that the thermal response of the integral, standoff, and rack mount designs of the Tri-Solar, BDM, and TEA prototypes are thermally equivalent. The direct mount design of the GE prototype operates 14 degree C to 18 degree C hotter than the others. The remaining thermal differences among the prototypes is a result of the different module designs.

A simulation model of finite differences describing a double-glass multi-crystalline photovoltaic module has been developed and validated using experimental data from such a photovoltaic module. This simulation model is based on various thermal hypotheses, particularly concerning the convective transfer coefficients: thus, various hypotheses found in the literature have been tested and the best one has been accepted. Using this modelling procedure, the cell temperature is estimated with a root mean square error of 1.3°C.

The well known Hottel-Whillier model for thermal analysis of flat plate
collectors is extended to the analysis of combined photovoltaic/thermal
collectors in a manner, such that, with simple modification of the
conventional parameters of the original model, all of the existing
relations and supporting information available in the literature still
apply. Beyond the basic assumptions of the original model, it is only
necessary to assume that the local electrical conversion efficiency of
the solar cell array (absorber) is a linear decreasing function of the
local absorber temperature over its operating temperature range. Based
on the extended model, examples of both thermal and electrical
performance of a combined collector as a function of collector design
parameters are presented and discussed.

We present the results of experiments which demonstrate that a sinusoidal variation in the long-term, STC-corrected, outdoor performance of PV modules is caused by seasonal spectral changes in the received sunlight. This variation may be factored out to increase the precision of outdoor studies. We use this result (a) to quantify the rate of EVA degradation observed in the Negev desert under natural 1-sun conditions and (b) to identify a principal source of the “summer recovery” observed in modules of amorphous silicon cells.

All variables influencing the efficiency of a flat-plate solar heat collector as a heat exchanger can be combined into a single “efficiency factor.” These efficiency factors are more or less design constants of the particular collector design, and are only slightly influenced by operating conditions. Consequently they are extremely convenient for use in accurate design and performance calculations. The full mathematical derivations are presented for several of these efficiency factors for various types of collectors, together with graphical data and examples of their use.

The nominal operating cell temperature (NOCT), an effective way to characterize the thermal performance of a photovoltaic module in natural sunlight, is developed. NOCT measurements for more than twenty different modules are presented. Changes in NOCT reflect changes in module design, residential roof mounting, and dirt accumulation. Other test results show that electrical performance is improved by cooling modules with water and by use of a phase change wax. Electrical degradation resulting from the marriage of photovoltaic and solar water heating modules is demonstrated. Cost-effectiveness of each of these techniques is evaluated.

Evaluation of flat plate collector performance. Transactions of the Conference on the Use of Solar Energy

- Hottel Hc
- Whillier

Hottel HC, Whillier A. Evaluation of flat plate collector performance. Transactions of the Conference on the Use of Solar Energy, Vol. 2, Part 1, University of Arizona Press, 1958; p. 74.

Solar Energy Engineering

- F Kreith
- Kreider
- Jf

Kreith F, Kreider JF. Solar Energy Engineering. McGraw-Hill: New York, 1978.