1. Introduction
Solar energy plays a crucial role in the deployment of renewable energies. Today, one of the most common technologies for using solar energy is photovoltaics (PV), which, thanks to their modularity, technological improvement and decreasing cost, have evolved and reached maturity at many scales of installed capacity, ranging from solar farms of several megawatt peak (MW
p) to small systems of some kilowatt peak (kW
p) distributed along urban environments where the PV modules can be added, or integrated as a building material into the skin of the buildings. The architectural integration of PV into building (known as building integrated photovoltaics, BIPV) can offer an attractive solution to the promotion of sustainable energy supply [
1] as it does not compete with land with other uses, such as agriculture, as utility scale PV plants do. Moreover, BIPV is in line with European Directives (2010/31/EU, 2018/844/EU) and a keystone of the nearly zero energy buildings (nZEB) concept.
However, PV systems integrated in urban structures usually do not follow classical PV system design practices, where, in order to maximise the production, both tilt and orientation angles are optimised. The tilt angle is approximately equal to the latitude and the orientation is facing towards the Equator. For a more integrated system, adapted to the building architectural design, non-optimal inclinations and orientations should be considered as defined by the orientation and tilt of the façades and roofs.
In major urban areas, PV façades have a significant impact on the solar energy potential because of their large surface area compared to roofs where structures and appliances, such as air-conditioning units, ventilation systems or elevator engines, are commonly placed. In a four-storey building, for example, the area of the façades is about four times the area of the roof [
2]. PV façades can produce, compared to rooftop systems, relatively more power in winter and less in summer, and more in the early and late hours of the day, when the Sun is lower, due to the more favourable inclination. In addition to this, the different façades of a building can produce electricity during different times of the day widening the peak of production and allowing a closer match to the consumption profile. Despite that the annual irradiation on vertical surfaces is lower than on horizontal surface in most regions of the word, several studies have shown that the solar potential of façades is relevant. When quantifying the solar potential of façades, it is also important to take into account the existence of windows that are normally considered for passive uses only. However, they may be used as solar active area by the integration of semi-transparent PV modules whose average efficiencies could be half of opaque standard PV modules [
2]. Díez-Mediavilla et al. [
3] analysed the potential of vertical façades using experimental data from Burgos (Spain) and concluded that the energy collected by four vertical façades facing the cardinal points are almost double the collected by the horizontal plane over the year, and it would be almost three times compared to a horizontal surface in winter. Redweik et al. [
4] applied a digital surface model to a case study of the campus of the University of Lisbon and found that adding the potential of the façades to the roof area (with a potential of 34 GWh/year), the production increases and almost doubles with a total of 53 GWh/year. Vulkan et al. [
5] estimate the solar potential using three-dimensional (3D) modelling in an urban area in Rishon LeZion, Israel. Their results remark the substantial contribution of high-rise apartments blocks (eight to 13 floors) with south and east façades.
The potential of vertical PV arrays has been studied in the literature from different points of view. For instance, analysing the energy yield losses caused by dust deposition at different tilt angles [
6,
7], Lu and Yang [
8] addressed this work from an environmental point of view, and Suri et al. [
9] showed the seasonal variability of the solar resource in Europe is lower for vertically mounted PV modules than at optimal angles.
Whatever approach is chosen, reliable solar radiation data at a given orientation and tilt are essential to estimate the real potential of the considered system. Modelling the potential for BIPV systems depends on the exposure to solar radiation and weather conditions, which vary with the location. However, solar resource at vertical surfaces is rarely measured, while the most common solar radiation data measured is the global horizontal irradiance (GHI, G
h). Over large geographical areas, solar radiation data are available from different sources, with the most common ones the satellite-based datasets and the ground measurements from stations distributed across different locations. In general, ground stations are used to validate satellite-based methods that have reached a high degree of maturity with global coverage and resolutions up to 15 min and a few kilometres [
10]. For this reason, these databases are integrated in some of the most popular online PV simulation tools such as the photovoltaic geographical information system (PVGIS) [
11] or the tool developed by the National Renewable Energy Laboratory, PVWATTS [
12]. Additionally, there are approaches based on estimating solar radiation by correlating it with available meteorological parameters. Many models have been proposed and developed on this basis [
13,
14]. Boca et al. [
15] proposed a multi-regression model to estimate the yearly solar radiation, only taking into account geographical factors (latitude and elevation of the site) and average temperature as input parameters. However, these approaches have some limitations since they do not consider, for instance, the horizon height profile or the daily variability. Moreover, they are commonly used to estimate monthly average daily or daily and hourly global radiation since they are less accurate on smaller time intervals [
14]. Therefore, for precise estimations, real-time measurements will be needed and, thus, a reliable monitoring system to gather long-term time series.
Photovoltaic and weather system monitoring are useful site-level analysis tools that provide information about the performance of a PV module subjected to a wide range of real operation conditions. Solar radiation is one of the most important parameters to be monitored since it can be used to determinate the optimal system size (installed capacity) and the best location of the PV installation, at the time that it can contribute to monitor the correct performance of a PV system. Location and climate can affect the energy output of a PV system, and thus, affect future investment decisions. Furthermore, adding other meteorological, thermal and electrical parameters, such as ambient temperature, wind speed, PV module temperature and I–V curves, gives an indication of the change of system efficiency and performance ratio which are directly related to lifetime and reliability of the installation, helping to monitor the proper performance of the installation.
However, due to cost and the difficulties of maintaining, calibrating and operating monitoring systems, data regarding global solar radiation received by each face (in-plane global irradiance, Gc) are not usually available as measured data. It is therefore necessary to use estimated values using as input available data in the most accurate possible way. For this purpose, it is necessary to validate the models used to calculate the solar radiation at different orientations and inclination from the measured data at a given orientation and tilt. The models should provide reliable solar radiation estimates, which can be then used in simulations of energy production. Architects and engineers will use these results of solar radiation estimation from the point of view of passive architecture, providing flexibility for the structural design of the building, and at the same time promoting the use of BIPV systems.
In this sense, transposition models, which take horizontal irradiance components as input, are frequently used, because measurements at this plane are commonly taken or can be retrieved for a specific location from satellite-based datasets (such as those available at PVGIS). Many attempts have been made to validate and compare transposition models [
16,
17,
18]. However, no universal model has been found yet. There are cases where a specific model performs better than others. Yang [
17] inter-compared different transposition models and established four clusters based on the predictive accuracy of each model being the first two clusters those expected to provide better results. The first one, includes all Perez family models [
19,
20,
21,
22] and the second groups well-known models such as Muneer [
23,
24], Gueymard [
25] or Hay [
26,
27]. Gracia and Huld [
28] analysed different anisotropic models for the validation of the transposition procedure used in PVGIS tool [
11]. Muneer’s model [
23] was applied to estimate the in-plane global irradiance in PVGIS, and it was compared with two component [
25,
29,
30,
31,
32] and three component [
19,
33,
34,
35] anisotropic models. The report concluded that there is not one particular model that outperforms the others in terms of mean bias difference (MBD) and root mean square difference (RMSD). It is interesting to note that both studies agree on most transposition models struggling to perform in vertical planes, which means a barrier to provide the most accurate solar radiation estimates when these are used for architecture purposes.
The objective of this work is to evaluate the most representative transposition models for their suitability in passive energy management and BIPV systems. For that purpose, two well-known and widely used transposition models, Perez [
19] and Muneer [
24], are compared and their performance is analysed for different sky conditions considering vertical surfaces oriented east, west, south and north. Experimental data measured in Murcia (southeast Spain) and datasets collected by the Joint Research Centre (EC-JRC) and National Renewable Energy Laboratory (USA-NREL) [
36] have been used for the validation of the estimates. PVGIS, developed by JRC, is a free online tool widely used due to its simplicity to use and coverage (the latest version contains different solar radiation database covering land territory of Europe, Africa, Asia to 115°E and America between 60°N and 20°S). It provides hourly values of satellite-based solar irradiance (global, beam and diffuse) for horizontal and tilted planes for several years, as well as other variables such as ambient temperature or wind speed. Similarly, the NREL database provides measured data of irradiance at vertical planes. For this study, one year of irradiance data has been used and compared to the irradiance data measured at a ground station located on the roof of a three-storey building in Murcia (Spain). In this way, a climatic dataset (combination of in-plane irradiance and ambient temperature) can be generated to provide statistics of the performance environment that each façade is exposed to under real operation conditions.
The article is organised as follows. The transposition models under consideration are presented in
Section 2. The experimental design describing the testing ground station, the dataset quality control applied, the error metrics used and the sky conditions considered are present in
Section 3, while the results and discussion are presented in
Section 4. Finally, the main results and conclusions of this study are summarised in
Section 5.
5. Conclusions
Two well-known and widely representative two and three component transposition models to estimate the in-plane irradiance on tilted surfaces were analysed in order to evaluate their performance on architectural practice and building integrated photovoltaic systems. Both use as input data the global and diffuse horizontal irradiance, which are commonly measured or can be retrieved from satellite-based estimates such as the datasets available at PVGIS tool. Estimated tilted irradiances were compared with experimental measurements recorded in Spain, NREL data measured at United States and with data obtained from PVGIS, paying special attention to the performance of the presented methodologies on vertical surfaces.
The results showed that both models present low performance at north (non-equator) facing surface, where diffuse fraction is predominant. A model which works well at any sky condition and orientation is not identified. However, both methodologies are easy, accurate enough and reliable to use for architectural designs and BIPV systems.
Regardless what methodology is chosen, there are some aspects which must be considered when it comes to urban environments, such as the contribution of ground-reflected solar irradiance, which is considered isotropic. It should be considered a key point in façade elements close to the ground since a high proportion of the incident irradiance will be due to ground reflections. Therefore, it is recommended to quantify the ground albedo coefficient by empirical evidence at the place of interest to obtain more accurate results.
Depending on the surrounding environment, it may be necessary to dismiss times with low solar elevation angles. It should be considered that under realistic conditions, there are potentially stringent limitations on applying correctly both models in an urban environment due to exposed surfaces are not commonly under completely visible sky. It should be necessary to include additional tools (3D models) that enable the user to define and position object creating a geometry for each study case and obtaining the view factor. However, the results show in this study are useful to demonstrate the upper limit of the possible solar irradiation collected by the façades facing different orientations.
Even with non-optimal orientations and tilt angles, the solar potential of PV façades reveals that the equator-facing one could receive twice as much of the solar energy that is collected by the horizontal one in winter time at the considered latitude. The sum of solar radiation received by all faces exceeds the energy collected by the horizontal one.
Finally, the operating condition for vertical surfaces under a full-year real working environment reveals high probability of combination of low irradiance and medium temperature, which are far from the standard test conditions (STC) commonly used to characterise PV modules.