Performance Ratio Estimation for Building-Integrated Photovoltaics—Thermal and Angular Characterisation

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This work proposes a methodology to help determine the performance ratio of BIPV systems, improving their energy simulation and helping in the decision-making process of BIPV system design.

Abstract

Building-integrated photovoltaics (BIPV) requires tools that improve and facilitate simulating and predicting the system’s output energy. The efficiency of a photovoltaic (PV) system can be determined by the performance ratio (PR), which relates the actual system’s output energy to the theoretical output according to the installed power and the solar irradiation, thus accounting for the power losses the PV system undergoes. Among the different parameters affecting PR, module temperature and the angle of incidence of irradiance are the most dependent on the BIPV application due to the varied module positioning. This paper assesses the suitability of several BIPV temperature models and determines the angular losses for any possible module positioning. The proposed methodology is easy to replicate and results in polar heatmap graphs to estimate PR at the desired location as a function of the tilt and azimuth angles of the modules. The calculations require irradiance, ambient temperature, and wind speed data, which can easily be obtained worldwide. Dynamic sky conditions are addressed through filters that smooth out quickly changing input data to avoid high and low peaks. The developed graphs are helpful in the decision-making process for BIPV designs by allowing the designer to estimate the expected PR of the BIPV system for any possible position of the modules on the building envelope, reducing the effect of uncertainties and resulting in more accurate and better predictions of the system’s output energy. The method applied to a BIPV façade in Madrid showed a deviation of less than 3% between the estimated and monitored PRs; the PR values ranged between 0.74 and 0.82, depending on the BIPV application and module position.

1. Introduction

Predicting the electric energy that a photovoltaic (PV) system can produce over a certain period has always been key to PV designers and promoters for ensuring the supply stability and surveillance of PV plants. Meanwhile, forecasting the performance of PV modules in an urban context, particularly building-integrated photovoltaic (BIPV) systems, which entail additional difficulties compared to standard PV plants, has gained attention in the last few years in the framework of net-zero energy buildings to ensure functional system designs that work under suboptimal conditions [1,2]. New developments in BIPV modules are increasingly demanding tools to determine the best option for each case to balance design and PV production [3,4,5,6]. Boundary conditions that need to be considered in an accurate performance analysis of a BIPV system are, e.g., highly probable occurrence of partial shading, reduced or no backside ventilation of BIPV modules, higher angular losses due to the position of the generators, or soiling in non-accessible building areas.

PV in buildings is key in the transition towards improved energy efficiency and decarbonisation, as it can aid in compensating for global energy consumption and emissions associated with buildings. Moreover, BIPV is the option that best combines on-site PV generation with building architecture by replacing conventional construction materials with BIPV elements, which helps achieve more sustainable and resilient buildings [7,8]. All this aligns with the European Union’s strategies on energy efficiency and the use of renewable energies to achieve net-zero greenhouse gas emissions in 2050, resulting in Europe becoming the first climate-neutral continent [9].

BIPV applications can be classified into several groups based on the location and position of the modules within the building envelope, as well as the accessibility from within the building [10,11]. A summary of the most common BIPV applications is presented in Figure 1.

The constructive system for BIPV installations directly affects PV performance. Factors such as rear-side ventilation or thermal insulation deeply impact the module’s temperature [12]. The mounting structure and position of the module (vertical, horizontal or tilted) influence back airflow for the system’s ventilation. A main concern in BIPV designs is predicting the system’s actual output energy after accounting for all possible limiting factors and losses under operating conditions. The energy generated by a PV system, measured in kWh, is mainly a linear function of the solar irradiation received by the PV generator, also modified by secondary factors that affect PV power and cause losses in the system’s output energy. The coefficient for the system’s efficiency that accounts for second-order corrections due to non-ideal boundary conditions is defined as the performance ratio (PR).

The performance ratio has been widely used to assess the performance of PV systems, and it is usually included in the monitoring schemes of operation and maintenance plans to check systems’ performance evolution and health [13]. The PR can be interpreted as the index that accounts for the impact of all losses in the system’s output. These losses include temperature, angular, solar spectrum mismatch, or soiling effects, among others, plus system component inefficiencies or failures, named the balance of system losses, mainly due to the inverter, wiring, and junction boxes, as indicated in the IEC 61724-1 Standard [14]. This IEC Standard describes how to obtain the PR for an existing PV system with experimentally measured data for a given period (day, month, year).

Several studies have analysed the performance ratio of different PV systems and technologies for existing monitored installations worldwide, as summarised in [15], with annual PR values increasing from around 0.6 for older systems to over 0.9 in recent cases. An example is the study of the performance ratio of residential PV systems in Belgium and France, with annual values of 0.78 and 0.76, respectively [16,17]. The effect of electrical losses on PR was studied regarding inverter and microinverter setups and tilt and orientation angles in 200 installations in France, with an average value of 0.79 [18]. A 2014 IEA report analysed the long-term performance ratio of PV systems, showing an average PR of 0.78 ± 0.14 [19].

PR analysis at several Indian sites was performed for free-standing PV and BIPV systems by modelling output power with PVGIS for specific tilts and orientations; PR estimations ranged between 0.68 and 0.79 [20]. Aslam et al. included an evaluation of the PR in PV plants worldwide from 1994 to 2022, with the PR showing a tendency to improve as years go by [21]. Several other works have used simulation tools such as PVWatts, PVGIS, PVSyst, and PV*SOL for the performance ratio determination of BIPV or BAPV systems with different tilt angles and PV technologies, some of them comparing the results with experimental data [22,23,24], revealing significant performance differences depending on the software tool selection [25]. However, none of these studies analysed the modelling of loss factors.

Besides the PR defined in the IEC 61724-1 Standard [14], which has an experimental approach, an additional interest could be developing an analytical approach to estimate PR in advance for reliably predicting the output energy of a BIPV system during the design and sizing stages [26,27]. Following this strategy, the present paper takes a different approach to PR by estimating system losses, primarily in terms of temperature and angular reflection impacts, from different available models to facilitate the modelling of BIPV systems.

Known causes of power losses include module temperature, the effect of the angle of incidence (AOI) of irradiance on the module’s reflection, solar spectrum, soiling, shading, snow, mismatch, wiring, connections, module light-induced degradation (LID), module ageing, and grid availability [28]. These losses are mostly caused by factors external to the PV system (e.g., ambient temperature, solar irradiance), although some contributions come from intrinsic factors and could be minimised through proper design, maintenance, and management. The effect of shading on the final system’s performance depends on local conditions, especially the topology of the surrounding elements. Different methods have been proposed to compute the impact of shading, usually requiring a 3D model of the urban elements in the domain [27,29,30]. Geographic Information Systems (GISs) are frequently used to evaluate the solar potential on rooftops and building façades using 3D models to compute both the shading and the sky view factor [31,32]. However, this approach requires both information about the performance ratio and the solar irradiation under an urban complex topology to compute solar potential and PV generation [33,34,35].

Over the last few decades, research supported by experimental campaigns has progressed in power loss factor modelling. In particular, module temperature [12,36,37,38] and angle of incidence [39,40,41] performance analysis have been the subject of different studies [42]. Regarding temperature, BIPV designers do not have access to easy-to-use tools that help them determine how design decisions may affect such losses. Concerning optical losses related to the AOI (angular losses), they have not yet been systematically analysed for different BIPV applications and all usable building surfaces. Both temperature and angular losses can become critical for BIPV modules due to their structure, their mounting support, and the operating boundary conditions they are subjected to when integrated into a building [43].

The present work aims to contribute to filling these gaps by providing tools to estimate the performance ratio of BIPV systems through a methodology that can be universally applied to any location where irradiation, ambient temperature, and wind speed values are available from in situ experimental measurements or online databases and sources. This methodology analyses the dependence of the performance ratio on BIPV module temperature and the angle of incidence of solar irradiance as the two main factors affecting system losses and their sensitivity to all the possible tilt angles and orientations. In addition, this dependence is determined with state-of-the-art models to compute temperature and angular losses. This leads to tools and graphical information that provide PR estimations as a function of the tilt and azimuth angles of the PV modules. The developed graphs can be used as guidelines during the design stage to assess a PV system’s performance based on the modules’ positioning in the building’s envelope.

Therefore, the main novelty of the work is to provide direct information on the impact of meteorological conditions on the BIPV performance from available data retrievals (satellite-derived information) and assess it with experimental data on a specific building, which can be extrapolated to different emplacements. The proposed methodology constitutes the first step in evaluating potential BIPV solutions in buildings. Additional analysis of shading in the specific emplacement would complement this information afterwards. The methodology has been applied to a case study in Madrid (Spain), since monitoring data for three in situ BIPV systems are available for a whole year and can be compared to modelled values to assess the results.

This paper aims to aid the decision-making process of justifying BIPV envelopes by taking an important step towards better assessing the behaviour of BIPV systems during the design stages of a project, especially regarding the output energy that should be expected from the installation. Contrary to regular PV plants, where PV modules are placed in certain optimal positions, BIPV modules can have any positioning in the building envelope, leading to boundary conditions that are specific to each system. The proposed methodology provides heatmap graphs that can be developed for any desired site to help assess the expected performance ratio for any desired timeframe based on the tilt and azimuth angle of the BIPV system. In addition, the methodology uses free tools and information, meaning that it can easily be replicated by other users for any desired location where the required input data are available.

2. Materials and Methods

2.1. General Approach

The methodology approach for this work consists of determining the performance ratio of BIPV systems by evaluating module temperature models and applying an analytical AOI loss model to any possible BIPV module position. Temperature models are assessed by comparing predicted temperatures with experimental data from a monitored BIPV ventilated façade. Accuracy, simplicity, and ease of use are the criteria considered to select the most suitable temperature model in our case. Concerning angular losses, they are estimated for the different irradiance components (beam, diffuse, and ground-reflected). Other losses that usually have a lower impact on PR are estimated using tabulated values and parameters. All these losses combined lead to the estimation of the PR of a BIPV system based on the tilt and azimuth angles of the modules, which is represented through polar heatmap graphs. The proposed methodology is applied to a case study located in the headquarters of CIEMAT, in Madrid (Spain), with geographic coordinates 40.45° N, −3.74° E. Building 42 includes BIPV arrays on the east, south, and west ventilated façades (Figure 2). The monitoring system records the PV power and the main meteorological parameters measured on the rooftop near the arrays on a minutely basis [44]. For the validation of the work, this paper focuses on the south façade, which includes twenty-eight 305 W monocrystalline silicon modules (adding up to an installed nominal power of 8.54 kW) with an azimuth of 172.65 degrees from the north and a 90-degree tilt (vertical position). Modules are installed in two rows of 14 each at an approximate height varying from 8 m to 10 m above ground.

2.2. Determination of the Performance Ratio

The performance ratio is commonly calculated from the ratio of the final system yield (Y_f) over the reference yield (Y_r). The final system yield is the net output energy of the PV system per unit of installed PV array power; the reference yield is the ratio of the total irradiation to the reference irradiance (Equation (1)):

$$PR={\displaystyle \frac{Y_{\mathrm{f}}}{Y_{\mathrm{r}}}}={\displaystyle \frac{E_{\mathrm{o}\mathrm{u}\mathrm{t}}/P_0}{H_{\mathrm{P}\mathrm{O}\mathrm{A}}/G_{\mathrm{S}\mathrm{T}\mathrm{C}}}}={\displaystyle \frac{E_{\mathrm{o}\mathrm{u}\mathrm{t}}·G_{\mathrm{S}\mathrm{T}\mathrm{C}}}{P_0·H_{\mathrm{P}\mathrm{O}\mathrm{A}}}}$$

(1)

where G_STC stands for irradiance under standard test conditions (STCs), which are 1 kW/m² for plane-of-array irradiance (G_POA), 25 °C for PV cell junction temperature, and 1.5 G for air mass solar spectrum, as defined in the IEC 60904-7 Standard [45]. E_out is the output energy of the PV system; P₀ is the PV array nominal power (maximum power under STCs), and H_POA is the plane-of-array (POA) irradiation.

Measured or estimated PV power and irradiance values over a specific period allow for the determination of PV energy and solar irradiation by time integration, commonly approximated by summation. The output energy can be estimated from G_POA data (either experimental or simulated) and performance ratio estimations (Equation (2)):

$$E_{\mathrm{o}\mathrm{u}\mathrm{t}}={\sum }_{\mathrm{i}}{\displaystyle \frac{P_0}{G_{\mathrm{S}\mathrm{T}\mathrm{C}}}}·G_{{\mathrm{P}\mathrm{O}\mathrm{A}}_{\mathrm{i}}}·∆t·{PR}_{\mathrm{i}}$$

(2)

where index i represents the iteration number for each time interval ∆t. The main challenge is accurately determining the value of the performance ratio at any time. Analytically, PR can be expressed as the product of different power loss factors, each one complementary to the corresponding power loss L_k (Equation (3)) [14]. The expression applies to any time interval:

$$PR=\left(1-L_{\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}}\right)·\left(1-L_{\mathrm{A}\mathrm{O}\mathrm{I}}\right)·\left(1-L_{\mathrm{s}\mathrm{o}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g}}\right)\cdots \left(1-L_{\mathrm{k}}\right)=\prod {(1-L}_{\mathrm{k}})$$

(3)

The power losses and performance ratio can be expressed as a fraction or percentage, with PR equal to 1 (or 100%) being the ideal situation with all L_k = 0. This paper will handle fractional values unless otherwise specified. Power losses related to factors such as, e.g., soiling, snow, and the balance of the system can be found tabulated in the literature [46]. However, losses such as temperature, angular, soiling, and spectral losses rely on environmental and design factors and require further analysis.

In the present work, on the one hand, experimental PR calculations were performed for the year 2019 on an hourly basis using Equation (1). On the other hand, estimated PRs were obtained using CAMS data for irradiance values and PVGIS for ambient temperature and wind speed data using Equation (3). Calculating system losses for the estimated PR can pose different challenges depending on the type of PV system and installation, as well as the availability and quality of input data. This paper has attempted to address these challenges and provide a means to apply the methodology to other PV systems with different boundary conditions.

2.3. Case Study: Building 42

Two different PR determination approaches are considered in this paper: the experimental PR obtained from local meteorological data and output energy measurements and the estimated PR based on irradiance and power loss estimations. The experimental site was the south ventilated façade of Building 42 in the CIEMAT’s facilities in Madrid (Spain), and monitored data were acquired approximately every minute and resampled to hourly mean values. Equation (1) was applied to obtain the experimental PR for every period (day, month, and year).

Regarding the estimated PR, Equations (3), (2), and (1) (in this order) were applied to calculate the PR in the different periods of interest, with monthly and yearly PRs being the most useful to assess the system’s efficiency over time. It is worth noting that the PR over a period (Equation (1)) is not the result of averaging the PR_i values associated with each interval covering that period.

2.4. Input Data for System Loss Calculations

Calculating angular and temperature losses requires input data of irradiance, ambient temperature, and, eventually, wind speed. These data can be obtained from online databases and resources, ideally from experimental measurements conducted under operating conditions as close as possible to those of the intended BIPV system.

If experimental data are unavailable, which is generally the case, the necessary meteorological information must be obtained from alternative sources. The PVGIS and Copernicus Atmosphere Monitoring Service (CAMS) are monitoring services that provide time data series of the required variables. CAMS solar radiation services obtain the solar irradiance components—global horizontal irradiance (GHI), direct normal irradiance (DNI) and diffuse horizontal irradiance (DHI)—from Meteosat satellite imagery [47,48,49,50,51,52,53]. They are based on the Heliosat model for deriving solar irradiance from satellite imagery from Meteosat platform satellites (covering Europe, Africa, the Atlantic Ocean, and the Middle East). CAMS assessment studies using Baseline Surface Radiation Network (BSRN) ground stations have provided high quality and low uncertainty in solar radiation components [54]. POA irradiance calculations for all possible tilt and azimuth angles were performed using the pvlib python library v0.11.0 [55], which includes specific functions for applying the Perez transposition model [56,57] and retrieving CAMS radiation data.

2.5. Temperature Loss Modelling

Module temperature may significantly affect PV systems’ efficiency, especially BIPV ones due to the more limited ventilation of the modules. Temperature loss is directly proportional to the cell’s temperature increase, with a higher temperature difference resulting in higher losses and, therefore, lower PV output power (Equation (4)):

$$L_{\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}}=\gamma ·∆T_{\mathrm{c}}=\gamma ·\left(T_{\mathrm{c}}-T_{\mathrm{c},0}\right)$$

(4)

where γ (%/°C) is the PV technology-dependent temperature power loss coefficient and ∆T_c is the cell temperature difference between operating (T_c) and reference (T_c,0 = 25 °C) conditions. The IEC 60891-3 Standard [58] indicates how to determine γ experimentally, while the IEC 61853-2 [59] includes the procedure to determine the nominal module operating temperature (NMOT).

Calculating temperature losses requires knowing the cell temperature T_c (usually inferred from the module temperature), as seen in Equation (4). While this can be measured in PV installations to account for losses under real operating conditions, when designing a PV system module, temperature needs to be calculated based on one of the different available models. The PV sector has developed different analytical expressions over the years to determine cell temperature, usually assuming steady-state conditions. Temperature models have been mainly applied to modules in ground-level PV plants, where their boundary conditions, such as ventilation, stand-off, and position (tilt angle), differ from those in buildings. As PV in buildings progressively gains weight in the global PV market and BIPV designs become more sophisticated, efforts are being made to adapt these existing NOCT models to better describe the temperature of BIPV modules.

Five temperature models commonly used by the industry were chosen in this study, Ross, King, Faiman, PVsyst, and SAPM, as well as a novel approach proposed by Driesse [60]. PV cell and module temperatures were calculated with each temperature model’s formula and parameters and compared with experimental temperature data through statistical indicators to assess the suitability of each model. The variables used in the temperature models are cell temperature (T_c), module temperature (T_m), ambient temperature (T_a), plane-of-array irradiance (G_POA), and wind speed (Ws) measured at a standard height of 10 m.

2.5.1. Ross Model

The Ross model [61] is simple in its assumptions, as it considers that the difference between cell temperature and ambient temperature only depends on the plane-of-array irradiance through an empirically determined coefficient k (Equation (5)). This model was adopted in the IEC 61215-2 Standard [62] with NOCT as the parameter to fit, which represents the temperature of the PV cells under open-circuit conditions at 800 W/m² irradiance, 20 °C ambient air temperature, 1 m/s wind speed, a tilt angle of 37°, and open-air ventilation. Typical NOCT values for crystalline silicon (c-Si) modules are around 45 °C.

However, in BIPV systems, modules do not undergo such boundary conditions; thus, we will refer to the effective NOCT_eff obtained under the specific tilt angle and limited ventilation conditions of a particular BIPV application. In the case that experimental data to fit the effective nominal temperature are not available, there are some recommendations in the literature, such as [63] from the National Renewable Energy Laboratory (NREL), which suggests increasing the NOCT by 2 to 18 degrees depending on the air gap thickness behind the modules, although not differentiating by mounting configuration or module structure.

$$T_c=T_a+k·G_{POA}=T_a+{\displaystyle \frac{NOCT-20}{800}}·G_{POA}$$

(5)

2.5.2. King Model

King et al. developed a thermal model, currently included in the Sandia Array Performance Model (SAPM) [64,65], which considers the irradiance and wind speed (Ws) effects by means of two empirical parameters a and b (Equation (6)). Their values are dependent on the module construction and mounting configuration, as well as the location and height of wind measurements. Typical experimental values of a and b and corrections to obtain the cell temperature from the module temperature have been suggested by the model’s developers, although no configuration applies to ventilated façades.

$$T_c=T_a+G_{POA}·\mathit{exp}\left(a+b·Ws\right)$$

(6)

2.5.3. Faiman Model

The Faiman [66] model also includes two parameters to account for irradiance (u₀) and wind (u₁) effects on module temperature (Equation (7)). As in the other cases, the parameters are determined by fitting the model to the experimental data. The Faiman model was adopted in the 2016 IEC 61853-2 Standard [59] to determine the nominal module operating temperature (NMOT), which replaced the NOCT established in 2005 [67,68,69]. The main difference is that the NMOT is determined with the module operating at maximum power instead of under open-circuit conditions.

$$T_m=T_a+{\displaystyle \frac{G_{POA}}{u_0+u_{1 }·Ws}}$$

(7)

2.5.4. PVsyst Variation in Faiman Model

PVsyst v. 8.0 software includes a model based on the Faiman model that adds two new parameters: the optical absorption coefficient of solar irradiance α and the PV efficiency related to the module area ηm (Equation (8)) to account for the electrical energy removed from the module.

$$T_c=T_a+{\displaystyle \frac{\alpha ·G_{POA}·\left(1-{\eta }_m\right)}{u_c+u_{v }·Ws}}$$

(8)

2.5.5. Driesse’s Dynamic Approach

Driesse [70] presented a methodology to address the dynamic thermal conditions of weather variables such as irradiance, temperature, and wind speed, as opposed to steady-state temperature models, by including the effect of thermal capacitance and processing G_POA input data with low-pass or moving average filters to smooth out the effect of quickly changing data that cause high and low peaks. These filters dampen and offset the data curve to account for thermal capacitance through optimisation loops to find the time span that minimises the error in modelled temperature calculations. This methodology can be applied to any of the models described above.

2.6. Angular Loss Modelling

Angular reflection losses describe power losses due to the deviation of the irradiance angle of incidence from the surface’s perpendicular (normal incidence). The orientation and tilt of BIPV modules often differ from the optimal module positions typically found in PV plants, which leads to angular losses playing a significant role in the performance of BIPV systems. While STCs consider normal incidence, AOI variations continuously occur under module operation. In addition, module characteristics (surface, materials, and thicknesses) have different influences on reflectance and absorptance, which means that each PV system has a particular angular response.

To account for the angular losses, the PV output power, P, is obtained by correcting the nominal PV power, P₀, with three angular power loss factors that are applied to the three corresponding components of irradiance −direct (beam, B), diffuse (D), and ground-reflected (albedo, A)—following Equation (9):

$$L_{\mathrm{A}\mathrm{O}\mathrm{I}}=1-{\displaystyle \frac{B·{(1-F}_{\mathrm{B}})+D·{(1-F}_{\mathrm{D}})+A·{(1-F}_{\mathrm{A}})}{B+D+A}}$$

(9)

2.6.1. Martín and Ruiz Model

Direct irradiance angular losses, F_B, can be obtained with the expression of the incidence angle modifier (IAM) developed by Martín and Ruiz [71,72] and adopted by the IEC 61853-2 Standard [59] to interpolate the IAM data obtained after following the standard testing procedures. The model expresses IAM as a function of the angle of incidence (θ) and includes a dimensionless fitting parameter, a_r (Equation (10)):

$$F_{\mathrm{B}}=IAM=1-\left[{\displaystyle \frac{1-\mathrm{e}\mathrm{x}\mathrm{p}\left[\frac{-(\cos \theta )}{a_{\mathrm{r}}}\right]}{1-\exp \left(\frac{-1}{a_{\mathrm{r}}}\right)}}\right]$$

(10)

The fitting parameter a_r relates the angular reflectance curve to the angle of incidence, with higher values implying a larger angular dependence of the module’s reflection losses. Typical values for a_r for modules with clean flat front glass were experimentally found to range from 0.20 to 0.23 [39], depending on the PV cell technology, which has a small influence on angular losses compared to the ‘air/glass’ interface. Modules with anti-reflecting coatings show a better angular response for high angles of incidence, i.e., above 40°. In addition, it should be considered that surface soiling might increase a_r by several hundredths (e.g., from 0.17 to 0.20 or 0.27, depending on the type and degree of soiling).

Expressions accounting for diffuse, F_D, and ground-reflected, F_A, irradiance losses were developed by Martín and Ruiz from the IAM expression (Equations (11) and (12)):

$$F_{\mathrm{D}}=1-\mathrm{e}\mathrm{x}\mathrm{p}\left[-{\displaystyle \frac{1}{a_{\mathrm{r}}}}\left(c_1\left(\sin \beta +{\displaystyle \frac{\beta -\sin \beta }{1-\cos \beta }} \right)+c_2{\left(\sin \beta +{\displaystyle \frac{\beta -\sin \beta }{1-\cos \beta }}\right)}^2\right)\right]$$

(11)

$$F_{\mathrm{A}}=1-\mathrm{e}\mathrm{x}\mathrm{p}\left[-{\displaystyle \frac{1}{a_{\mathrm{r}}}}\left(c_1\left(\sin \beta +{\displaystyle \frac{\pi -\beta -\sin \beta }{1+\cos \beta }} \right)+c_2{\left(\sin \beta +{\displaystyle \frac{\pi -\beta -\sin \beta }{1+\cos \beta }}\right)}^2\right)\right]$$

(12)

where β is the tilt angle of the module, c₁ has an adjusted value of 4⁄3π [71], and c₂ is a parameter which is a linear function of a_r (values of c₂ and a_r [71,72] can be used to determine c₂ by linear extrapolation).

2.6.2. ASHRAE Model

A former approach to estimating the incidence angle modifier was developed by Souka and Safat [73] and later adopted by the American Society of Heating, Refrigeration and Air Conditioning Engineers (ASHRAE). The IAM expression only needs a fitting parameter but suffers from discontinuity at a 90° angle of incidence (Equation (13)).

$$IAM=1-b_0\left({\displaystyle \frac{1}{\cos \left(\theta \right)}}-1\right)$$

(13)

2.6.3. Sandia Model

Sandia suggested using a 5th-order polynomial function for the IAM expression [62,63]. The main objection to this is that 5th-order polynomial fitting causes a slight concave-up shape at low angles of incidence.

The authors have used and recommend the Martín and Ruiz model to determine the angular losses of any BIPV system for its simplicity and good fitting results, while also considering soiling conditions. The pvlib python library v0.11.0 includes the functions required to implement any of these models [55].

3. Results and Discussion

Regarding temperature losses, all temperature models include one or more parameters that need to be empirically fitted to each PV system’s data so that the model’s formula can be applied to calculate cell or module temperature properly. Ideally, these parameters should be fitted using experimental data measured in situ for each specific PV system. As Building 42 at CIEMAT has been monitored since 2017 its renovation, experimental data are available on a minutely basis, which can be used to adjust the parameters for all temperature models.

When using experimental data, dynamic conditions involve sudden changes in weather variables, such as clouds or rain, which can lead to irradiance peaks and fluctuations. In addition, low wind speed and gusts can also affect the representativeness of the operating conditions. These issues have been addressed in regulations such as IEC 61853-2 [59] by using filters to reject undesired data (e.g., irradiance below 400 W/m²) [68]. A promising approach to addressing data management was recently developed by Driesse [70], who suggests pre-processing field measurements by delaying and smoothing their fluctuations through a low-pass filter or a moving average filter based on the effect of the thermal mass of the module on module temperature. This procedure uses rolling window calculations to obtain the average data value over several timeframes measured in minutes (e.g., 0–25 min) and performs linear regression analysis to temperature models to find the best-fitting solution, leading to a certain time in minutes to offset and smooth the data curve. Figure 3 shows the effect of this filtering technique applied to local plane-of-array irradiance data, where the delaying value was calculated to be ten minutes. The filtering strategy is applied to irradiance, temperature, and wind speed data, which are then used to fit the parameters of the desired temperature model.

Table 1. The application of temperature models to Building 42’s south ventilated façade, including the experimentally fitted parameters and the statistical error analysis.

Temperature Model	Data Filtering Criteria	Fitted Parameters	MBE (°C)	RMSE (°C)	R2	MBE (°C)	RMSE (°C)	R2
			2020 Minutely			2020 Hourly
Ross	GPOA > 400 W/m2	NOCTeff = 53.3 °C	0.3	4.1	0.72	1.2	2.3	0.97
Ross	moving average	NOCTeff = 55.3 °C	−0.6	2.6	0.96	−0.6	2.2	0.97
King	GPOA > 400 W/m2	a = −3.118 b = −0.042	0	3.8	0.76	1.2	2.1	0.98
King	moving average	a = −3.063 b = −0.048	−0.7	2.4	0.97	−0.7	2.0	0.98
Faiman	GPOA > 400 W/m2	u0 = 22.75 u1 = 1.20	0.4	3.8	0.76	1.3	2.2	0.97
Faiman	moving average	u0 = 21.35 u1 = 1.13	−0.7	2.4	0.97	−0.7	2.0	0.98
PVsyst	GPOA > 400 W/m2	u0 = 17.61 u1 = 0.93	0.4	3.8	0.76	1.3	2.2	0.97
PVsyst	moving average	u0 = 16.33 u1 = 0.86	−0.7	2.4	0.97	−0.7	2.0	0.98

summarises the results of applying regression to fit all temperature models to the experimental data. Two data processing strategies were used: filtering data with G_POA above 400 W/m², as indicated in the IEC 61853-2 [59] and prior standards, and Driesse’s optimised moving average. Parameters were obtained using minutely data for 2020 and then applied to the temperature models using minutely and hourly data, which were in turn compared to experimental data through mean bias error (MBE), root-mean squared error (RMSE), and the coefficient of determination (R²).

From Table 1, it can be concluded that all temperature models predict module temperature with a similar degree of accuracy when applying the same data filtering criteria, regardless of the complexity of the model. This may be due to the limited effect of wind on the BIPV façade analysed in this paper (a ventilated façade, three stories high, with limited rear-side ventilation). Although wind speed may be crucial in PV plants, where modules have their backsides exposed to the air, its effect on certain BIPV configurations could be minimal, reducing the need to include it in the calculations.

Additionally, the moving average strategy proposed by Driesse had a significantly positive impact when using minutely data for all models, consistently reducing the error and improving the module temperature prediction when compared to G_POA above a 400 W/m² threshold filter, with lower improvement due to Driesse’s approach when using hourly data. The main advantage of the moving average method is the possibility of using highly detailed data and minute-based intervals instead of hourly ones.

The conclusion is that, for the case study analysed and presumably for equivalent BIPV systems, the optimal approach for fitting parameters for the south ventilated façade of Building 42 was to combine the Ross model, which only depends on irradiance and ambient temperature, with Driesse’s data processing strategy. This model, with a fitted NOCT_eff of 55.3 °C, was used to calculate cell temperature and estimate temperature losses in the PV system (Equation (4)).

Concerning angular losses, they were calculated for any possible combination of the module’s tilt angle and azimuth at different sites to cover any positioning in BIPV systems. The convenience of considering the Martín and Ruiz IAM model and the derived expressions for each irradiance component, which are dependent on one fitting parameter, a_r (a function of the module’s structure and materials and its soiling degree), lies in their suitability and simplicity. It is recommended to fit this parameter to each particular case by measuring the angular variation in the PV current as stated in the 61853-2 IAM testing procedure. Otherwise, a_r values reported in the literature for similar types of modules can be adopted. Based on the available literature, this paper assumed an a_r value of 0.2. In order to assess the effect of a_r values on angular losses, a sensitivity comparison was developed, where a variation in a_r of the order of ±0.05 (e.g., to account for other angular responses) caused an impact of ±1.1% for the total PR of the system.

Additional losses are caused by modules’ mismatch, wiring, connections, light-induced degradation (LID), nameplate rating, ageing, and grid availability. Characteristic values for these losses can be obtained from the NREL’s PVWatts manual [46], which adapted the system losses obtained by Marion et al. [74] into more realistic values by attending to the current inverter efficiency values.

Table 2. Assumed values for additional losses in PR calculations.

Loss Type	Value
Grid availability	0.03
Connections	0.005
LID	0.0145
Mismatch	0.02
Rating	0.01
Wiring	0.02
Snow	0
Ageing	0
Shading	0

summarises the selected tabulated values for the PR calculations.

Efforts have been made to estimate snow losses [75,76,77]. System Advisor Model software [78] includes a model based on Marion et al.’s model [77], which requires modules’ tilt angle and local data such as daily snow depth measurements, hourly plane-of-array irradiance, and temperature values. These losses are significantly affected by snow removal processes, including sliding, melting, and removal by wind. Snow losses can be neglected for the case of vertical BIPV façades.

Losses due to the progressive degradation of the modules (ageing) are generally expressed as a yearly percentage that can vary over time, usually ranging between 0.5% and 0.7%, but this can increase based on the system and the location [79,80]. The ageing loss was set to zero since the modules were new when the data were taken.

No significant shading occurs in the considered case study. Only shading associated with the sun’s position relative to the surface orientation and tilt angle is included in the calculations. Therefore, only the additional shading cast by obstacles is obviated, but it should be considered in each particular case. However, shading losses depend on the local topology, even for the same geographical coordinates. These losses can be analysed with Geographic Information System tools and data to provide estimations on the effect of shading on the incoming irradiance, as suggested in [81].

The proposed methodology can be refined by delving into additional PR factors such as soiling and solar spectrum effects. Regarding soiling, the more horizontal the surface of the modules, the higher the impact on the losses, and vice versa. Some attempts have led to systematic characterisation studies of soiling losses under different climates and boundary conditions, which help not only in predicting the influence of this variable in PV production but also in decision-making regarding the cleaning schedule of such PV systems [82,83]. Soiling losses highly depend on in situ factors such as rainfall or wind, making it difficult to develop a priori estimations and meaning it is necessary to perform experimental testing for the desired tilt and azimuth of the BIPV system. Nevertheless, soiling losses can be minimised through proper maintenance of the PV modules.

Spectral behaviour, which is highly dependent on the location, has been extensively addressed for decades [84,85]. Commonly used models for estimating the spectral impact on PV performance [86,87,88,89] depend on the air mass, aerosol optical depth, and precipitable water and do not consider the different components of solar radiation separately. This makes them unsuitable for exploring the spectral influence as a function of the module’s surface azimuth and tilt angles. Especially relevant is the case of vertical façades, where the spectral distribution of the incoming solar irradiance might differ notably from the standard. Specific spectral models for façades that depend on the angle of incidence would be needed to account for the spectral impact of different façade orientations. In addition, because vertical or nearly vertical modules face the ground as well as the sky, the albedo of the surrounding topology and ground surfaces may have an additional impact [90]. Karalasingham et al. [91] developed a deep learning model trained with remote sensing and ground station observations for surface albedo forecasting applications, which is particularly useful for bifacial PV modules and façade PV systems.

The contribution of the spectral behaviour to the PR is difficult to generalise. On the one hand, the impact of the incident spectrum can change significantly for very high tilt angles (as in the case of façades), since the influence of the incident angle (which includes the surface orientation and Sun elevation) is remarkable; in this cases, the proposed spectral models, which depend on the air mass, are not valid to model the spectral effects. This fact has been analysed in depth by authors who proposed specific models for spectral effects in facades [92]. In addition, the boundary atmospheric conditions (aerosol optical depth and water vapour content) have to be taken into account. In future works, we aim to explore the range of surface tilt angles for which air mass-based spectral models are valid and when specific spectral models similar to those developed for facades in the mentioned reference need to be applied. In consequence, the spectral impact on the PR was not considered in this paper.

Applying the proposed methodology to Building 42 leads to an estimated PR of 0.78 for 2019, which results in a deviation of less than 3% from the experimental PR. The methodology was then applied to similar BIPV systems, but allowing for any possible tilt angle and orientation of the modules. Polar graphs for yearly irradiation and PR in Madrid were developed to aid in designing BIPV systems. To obtain more representative results for the case site, G_POA estimations were based on a Typical Meteorological Year (TMY) from Meteonorm (https://meteonorm.com/en/, accessed on 5 March 2025), a global climatological database widely used as meteorological input for the simulation of solar applications and buildings (Figure 4).

Figure 5 and Figure 6 show the effects of temperature and angular losses, respectively. Losses related to temperature shift southwestward due to solar heat accumulation in the modules throughout the day. The lowest temperature power loss factor of 0.89 corresponds to temperature losses of 0.11, obtained at the optimal tilt angle for photovoltaic conversion and southwest orientation.

On the other hand, angular losses are symmetrical with respect to the north–south direction, given that the sun’s trajectory is similar before and after solar noon (i.e., the sun’s zenith). Lower angular power loss factors occur at vertical positions and azimuths far from the south orientation. The maximum value of 0.97, which means minimum annual angular losses of 0.003, is obtained at a 35-degree tilt towards the Equator.

The combination of temperature and angular losses with the other power loss factors (Table 2) leads to the total performance ratio of the system, shown in Figure 7. This heatmap represents the final performance ratio for Madrid using data from 2019, though it can be calculated for any desired timeframe using other input data (e.g., a TMY). As observed, the annual performance ratio in Madrid ranged 2019 between 0.74 and 0.82 as a function of the modules’ positions.

This graph helps evaluate the expected performance losses of a BIPV system depending on the azimuth and tilt angles of the module. The irradiation map (Figure 4), together with the PR map (Figure 7), allow the designer to estimate the PV generation of the BIPV system based on the position of the modules, which is also helpful when renovating buildings, as the PV potential for roofs and façades is assessed based on their orientation and tilt angle.

This methodology can be applied to any other location worldwide. As an example, Figure 8 shows the obtained PR heatmap for an equivalent façade in Stockholm. In this case, the PR varies between 0.79 and 0.85.

4. Conclusions

To better simulate and predict the performance of BIPV systems, this paper takes a step towards improving their performance ratio determination, focusing on the thermal and angular power losses. Among the different parameters affecting the PR, module temperature and the angle of incidence of irradiance are the most dependent on the BIPV application due to the varied module positioning.

After reviewing and assessing the suitability of several models to simulate the temperature and angular performance of BIPV modules, the corresponding power losses were calculated for any module’s positioning. The proposed methodology is easy to replicate and proposes polar heatmap graphs to estimate PR at the desired location for assessing at a glance the sensitivity of the system’s efficiency to the tilt and azimuth angles, aiding in the development of BIPV designs.

The estimated PR for the analysed case study in Madrid ranged between 0.74 for a north-oriented 60-degree-tilted module and 0.82 for a north-oriented vertical module. When considering other orientations, the majority of azimuth and tilt combinations show a PR of 0.77–0.80, with better behaviour towards the southeast than the southwest due to the effect of temperature losses that increase module temperature throughout the day. A comparison of the results of temperature (ranging from 0.89 to 1.00) and angular (0.83 to 0.97) power loss factors reveals that angular losses are more relevant than thermal losses for the analysed BIPV ventilated façade in Madrid.

The same heatmap graphs developed for Stockholm indicate higher PR values overall, reaching 0.85 for vertical modules oriented north and showing values above 0.82 in most cases. These graphs also present a better north–south symmetry, given that the temperature impact is lower in colder locations. As can be expected, climatic conditions, latitude, and the modules’ positions are the most influential parameters when analysing annual PR values.

The methodology was validated by comparing modelled results (estimated PR) with in situ experimental measurements (experimental PR) for the case of a BIPV ventilated façade in Madrid. Future work evaluating this procedure in different locations and BIPV systems is advised to assess and refine the proposed methodology. The assessment of the most used cell temperature models has shown improvement in using dynamic temperature approaches, resulting in a more reliable estimation of the PR. However, all the considered models have shown acceptable results for a BIPV ventilated façade if their fitting coefficients are adjusted with experimental local data.

Power losses due to module temperature can be reduced by improving the backside ventilation of the modules, while surface anti-reflecting coatings and surface finishes can lower angular losses and, at the same time, reduce glare caused by BIPV modules.

The visual information delivered in this paper constitutes a first step towards globally estimating the PR for BIPV applications at a pixel spatial resolution. A second step in the analysis should focus on local topology for specific buildings and the surrounding elements. The proposed methodology can be refined by delving into additional PR factors such as soiling and solar spectrum effects.