**2. Methodology**

The input dataset used in this study is composed of one-minute output of 12 solar collectors (Figure 1) installed for three years (2016–2018) on the roof of the Institute for Meteorology and Climatology (IMUK) of the Leibniz Universität Hannover (Hannover, Germany; 52.23◦ N, 9.42◦ E and 50 m above sea level). Measurements have been made, using crystalline silicon PV devices with individual temperature sensors (Mencke and Tegtmeyer GmbH, Hameln, Germany). The PV devices have been calibrated by the manufacturer in November 2013 and they are cleaned regularly to prevent the accumulation of dirt and dust. In addition, all devices are compared after one year of measurements by placing them side by side horizontally. These comparisons were performed under different weather conditions and have showed an agreement within ±3%.

**Figure 1.** Set of solar PV devices based on silicon sensors mounted in several different tilt angles and orientations, operational at the IMUK (Institute for Meteorology and Climatology) [IMUK, 2017].

Two groups of identical devices are considered here: The first group consist of devices with 45◦ tilt, oriented to S, E, W, SE, and SW; the second group consists of vertical devices, oriented to S, E, W, SE, SW, and N. The tilt angle for the first group (45◦) is chosen to represent the large number of roof pitches, where most residential houses in Germany were built with a tilted roof angle between 40◦ and 45◦ [29]. According to the initial design of the measurement system, the S measurements are conducted at tilt angles of 40◦ and 50◦, therefore we take the average of both sensors (40◦ and 50◦) to represent the PV outputs at 45◦ tilt; the uncertainty resulting from this procedure and other orientation uncertainties are less than 1% according to PVGIS calculations. Table 1 shows an overview about the inclination

uncertainty, according to a Photovoltaic Geographical Information System (PVGIS) calculation [30] for Hannover.


**Table 1.** Annual PV energy produced in Hannover with respect to the optimal inclination [%] according to PVGIS.
