# Exploring the Benefits of Photovoltaic Non-Optimal Orientations in Buildings
## 2 Materials and Methods
### Simulation with PVSYST Software  
The work presented here uses simulations with this software package, so it will be described in some detail. PVSYST [28] is a reference software widely used in industry and research [29] that reproduces the electrical behavior of a PV module under any conditions (irradiance, temperature of cell, incidence angle, and spectral contents). The simulator is based in the one-diode model for crystalline Si cells and extended to the complete module, described in Equation (1). A complete description of the use in PVSYST can be found in [30]. PVSYT provides an accurate set of parameters for a wide number of PV modules from 2002 to present time. \[I=I_{\Phi}-I_{0}\left[e^{(\frac{V+R_{S}}{8\text{Cs}\cdot\pi R_{C}})}-1\right] -\frac{V+I\cdot R_{S}}{R_{Sh}} \tag{1}\]  
where\(I,\ V\): current and voltage of module;  
\(T_{\rm C}\): temperature of cell;  
\(I_{\Phi}\): photocurrent at measured irradiance \(G_{\rm meas}\);  
\(I_{0}\): diode saturation current;  
\(R_{S}\): series resistance;  
\(R_{Sh}\): shunt resistance;  
\(\gamma\): diode ideality factor;  
\(q\): charge of the electron;  
\(N_{\rm CS}\): number of cells in series in the module. While the accurate simulation of PV modules and systems depends on a good physical model and an accurate set of parameters, a high-quality energy yield prediction depends also on the environmental parameters [31]. The most important one is the incident irradiance on the module, i.e., the output power proportional to it for a wide range of irradiances. Solar cells are very sensitive to temperature, as can be deduced from Equation (1). In fact, the power of a crystalline silicon PV module decreases significantly with the temperature (typically between \(-0.3\) and \(-0.4\) %/K). The cell temperature depends on the incident irradiation, the ambient temperature, and the windspeed. In this way, excellent weather datasets are needed. The most accurate method to obtain irradiance measurements (global horizontal and diffuse) is with ground radiometers, with a sparse coverage. Actual databases are built to integrate data from ground radiometers and satellite-based models [32]. In this work, Meteororm and PVGIS-SARAH databases were used. The Meteororm database [33] uses ground data from the Global Energy Balance Archive data [34], provided from national weather services and data from 5 geostationary satellites where no radiation measurement is available nearer than 30 km (10 km in Europe). The data correspond to the periods 1981-1990 and 1996-2015. The PVGIS-SARAH database [35] uses data from two EUMETSAT geostationary satellites and provides long-term averages calculated from the period 2005-2016. These datasets also include hourly data of ambient temperature and windspeed. The data from the datasets were used to generate a typical meteorological year, containing one year of hourly data that represent median weather over a multiyear period. The irradiation data (global and diffuse) allow a calculation of irradiance on inclined surfaces. If diffuse irradiation is not available, PVSYST uses the Erbs correlation model [36] for calculation. In Figure 1, the irradiances and temperatures of one the PVSCS simulated in this work are shown. It can be noted that the module temperature is only calculated when the irradiance is higher than zero. This software was compared with other software packages (HOMER, RESTereen) and was found to be accurate while also providing conservative energy estimations compared with the aforementioned [37]. Figure 1: Environmental variables in PVSYST: irradiances (global horizontal and in plane of array) and temperatures (ambient and array). Note that the array temperature is not calculated when the irradiance is null. An important feature of PVSYST software is that it includes a 3D design tool for calculating the shading scene according to the sun trajectories along the year.