**1. Introduction**

Decarbonization of our energy supply is an important component to fulfill pledges of the Paris Agreement to keep the global warming below 1.5 ◦C, because 65% of the world's current CO2 emissions are due to burning fossil fuels [1]. Renewable energy is one of the most cost-effective options to replace fossil fuels and to reduce electricity-related emissions. In recent years, many countries have begun a transition to more sustainable energy supply based on renewable energies. Solar energy represents the most abundant natural energy resource on the earth and has the potential to replace fossil fuels to satisfy this clean energy demand of our society in future [2]. This exceptional energy source is the most simple and economic renewable energy technology available that can be easily installed, especially on rooftops of houses. The costs for solar modules, measured in \$/Wp, have reduced by as much as 90% during the last decade and are expected to fall further in the future [3].

Consequently, the evolution of renewable energy over the past decade has surpassed most expectations. By the end of 2018, global total renewable generation capacity reached 2351 GW. PV solar electricity has developed rapidly in minor private systems, as well as in large-scale installations connected to national grids. Solar energy represented around 20.6% of renewable energy generation in 2018, with capacities of 486 GW [4].

The solar irradiance changes with geographical location, season, and time of the day according to sun position in the sky. In addition, it varies by the influence of clouds, aerosols, and ground reflection. The orientation and tilt angle of PV collectors are among the most important parameters that affect the performance of a PV system, as they determine the amount of solar radiation received by the PV collector [5]. The orientation and inclination of a PV installation has two effects on system output: On the one hand, there is a larger or smaller amount of total annual yield; on the other hand, there is an impact on the seasonal or daily timing of peak energy generation [6]. In general, PV systems are divided into fixed and tracking systems. Fixed systems are often small systems installed on the roof of a building, while tracking systems are often large PV systems installed to maximize the solar radiation that reaches them [7]. Module performance is also affected by local factors for individual locations e.g., cloudiness, temperature, shading, dust, precipitation, and bird droppings [8].

Based on Earth-sun geometry, many studies were carried out to find the optimum tilt angle and orientation of PV systems in certain areas worldwide, e.g., Italy [9], Turkey [10], Australia [11], the United States [12], India [13], China [14], and Ghana [15]. Most previous studies show that the optimal fixed tilt angle of PV collectors depends only on geographical latitude (ϕ), if local weather and climatic conditions are not considered. However, because of the diffuse solar radiation, the optimal tilt angles may differ from those in reality. Huld et al. [16] showed that climate characteristics have a huge influence on the optimal tilt angle in Europe. Lave and Kleissl [12] showed that the optimal tilt is reduced by up to 10 degrees when cloudiness is taken into consideration, particularly in the northern United States. European studies [17,18] concluded that the optimum tilt must be reduced by 10◦ to 20◦ between southern and northern Europe because of the same effect. Beringer et al. [19] showed that solar collectors oriented to the South at a tilt angle of 50◦–70◦ in the winter months (October–March) and 0◦–30◦ in the summer months (April–September) would result in the highest monthly yield for the location of Hannover, Germany.

Rooftop PV systems have gained importance in the last decade, especially from the drop in the cost of solar PV modules and the increase of end-consumer electricity tariff. According to recent studies, up to 25% of EU electricity consumption could be potentially produced in small rooftop PV systems installed in the existing EU building [20]. Other authors estimate that all electricity needs can be produced on rooftops [21]. There is increased interest in the self-consumption (SC), i.e., the part of PV power production that is consumed by the house owner. The savings from self-consumed PV-generated electricity are much higher than the profit from selling excess generation at spot prices. It may also have a positive effect on the distribution grid and make the production profiles of PV systems connected to the grid smoother.

The SC depends mainly on the system size: The more PV power installed, the more often the produced electricity exceeds consumption; i.e., it is non-linear with installed power [22]. SC can also be increased by energy storage and by load management; i.e., the influence of temporal resolution becomes less distinct with added a battery storage [23]. In practice, the SC rate can range from a few percent to a theoretical maximum of 100%, depending on the PV system size and load profile. Moreover, estimation of SC depends also on time resolution; i.e., it is overestimated when using hourly data of PV electricity production and household load profiles. Luthander et al. [24] found that for individual buildings, sub-hourly data are needed to capture the behavior of high peak power. Leicester et al. [25] found that SC is overestimated by 71.3% when using hourly data, compared with 54.8% when using one-minute data. Accordingly, high temporal resolution data are required to quantify SC accurately.

There are very limited studies that described simultaneous direct measurements of PV generation and consumption. However, one method to obtain more data with greater variety is to use PV data and separately-obtained load profile data, and estimate the SC fraction [25]. With the present reimbursement for feed-in tariffs that value just the yearly sum fed into the grid, suitability studies focused for rooftop have just concentrated on the yearly yield. Many studies and online web tools concerning the suitability of the orientation of rooftop implicitly take only the yearly sum into account [26]. Calculations for the diurnal variability are lacking.

In this study, we use one-minute data to compare the outputs of 12 solar collectors at various tilt and azimuth angles in order to propose an alternative concept for increasing SC via non-south-oriented PV systems and investigate its potential. The calculations are based on measurements from silicon sensors with different orientations and tilt angles in Hannover (Germany). The SC of all orientations is calculated by using a set of separately measured load profiles in order to evaluate the best and more-economic orientations for rooftop PV systems. The results are also compared with the simulated values of two widely used PV software packages, PVSOL [27] and PVsyst [28] to validate this software. Detailed information about the simulation parameters are listed in Tables.
