*4.1. Production and Consumption under Di*ff*erent Weather Conditions*

Figure 4 shows the PV production profiles for the S and E-W orientations during three days of May 2018 with different weather conditions (clear sky, partly cloudy, and fully cloudy) and correspondent customer load profiles for the same days of the year.

**Figure 4.** PV Production profiles for three days of May 2018 and the correspondent customer load profiles for the same days of the year. The thick (gray) curve represents the 10-minte average consumption.

The load profiles show different peaks over the day according to consumption patterns, while, the PV power production changes according to the movement of the sun and the weather conditions. The influence of orientation is shown clearly in clear sky days, when the energy production depends mainly on the sun's position. The E-W orientation covers more the edges of the day and reduces noon peak. On the other hand, the orientation is irrelevant under cloudy conditions, when the solar irradiance dominated by diffuse component. In general, SC rate is higher under cloudy conditions.

#### *4.2. Annual Insolation*

The annual total solar energy as function of surface azimuth and tilt angles is depicted in Figure 5. The left side histogram shows that the maximum annual total energy is for a south-facing surface with a tilt angle between 30◦ and 40◦, closer to 40◦. The annual total energy is less than the maximum by approximately 0.2% for surface orientation of 30◦ S, and it decreases gradually with higher or lower tilt angles. The annual produced energy for the surfaces oriented at the same tilt angle (45◦) toward E and W are 77.0% and 75.9% of the optimal orientation respectively. For orientations of 45◦ SE or SW, the

annual total energy produced are 94.8% and 93.3% of maximum produced energy. The inequality in total energy for E and W and in SE and SW may denote asymmetric distributions of solar irradiance before and after midday. On the right histogram of Figure 4 we can see that, for a vertical surface with orientation of 90◦ south, the produced energy is 66.2% of the 40◦ tilted surface, whereas it is about 50% for E and W surfaces. The annual total energy of the northern vertical surface is reduced by about 74%.

**Figure 5.** Produced and consumed PV power averaged over all days of the years 2016–2018 for the S, E-W, and SE-SW orientations at 45◦ tilt. The area below the gray curve represents the average load profile. The E-W and SE-SW facing installation produce more electricity in the mornings and evenings with a lower midday peak, so they match the load profile more closely.

In general, the amount of energy produced by a PV collector is proportional to solar radiation received by a surface in a specific orientation. Table 2 shows the annual produced energy and its percentage from the maximum value (at 45◦ S) for different orientations and tilt angles. The table also shows the SC rate and AD for each orientation. For 45◦ tilt surfaces, the lowest SC rate (37.9%) is for the S facing solar installation, while the highest SC rate (51.4%) is for the E-W combination. The high SC rate is because the power output of E-W installation matches the load profile more closely, producing more electric energy at the beginning and at the end of the day, with a lower midday peak (Figure 6). The AD has its maximum at SE-SW combination (40.7%) and its minimum at the E orientation (35.4%). Moreover, the economic efficiency of all studied orientations for the cases with and without FIT is also listed in Table 2. Overall, the E-W and SE-SW combinations have the lowest electricity cost (29.2 Ct/kWh and 29.1 Ct/kWh respectively), while the E orientation has the highest one (30.7 Ct/kWh), both cases for the system without FIT. For PV systems with FIT, the S-facing systems have the lowest electricity price (22.0 Ct/kWh) because of the high PV generation and accordingly the high feed-in amount, while the E-facing systems have the highest price (25.6 Ct/kWh).


**Figure 6.** Average annual total solar energy (2016–2018) measured at IMUK and normalized values (in %) with respect to the annual total maximum energy at 40◦ S. The solar energy decreases for higher or lower tilt angles and for other azimuth angles.

The IRR analysis of PV systems without FIT shows that the SE-SW and E-W orientations tilted at 45◦ is more beneficial with an IRR value of 2.09% and 1.90%, respectively, when compared to the S orientation at the same tilt with 1.59%. For PV systems with FIT, the IRR for the S orientation is higher with a value of 7.05%, compared to the SE-SW and E-W orientations with 6.82% and 5.14%, respectively.

As expected, for the vertical surfaces, the S orientations gives the highest output (66.8% of the maximum), while the lowest energy is produced by N-facing surface (25.8 of the maximum), because of the Earth-sun geometry in the northern hemisphere. In terms of the SC rate, the N surfaces have the highest rate, due to the low energy production in this direction, while the lowest rate (50.0%) is for the SE surface. The AD has its maximum at SW orientation (36.7%) and it is minimum at N orientation (25.4%). Accordingly, the SW orientation has the lowest electricity cost (30.4 Ct/kWh) for the system without FIT, while the S and SW orientations have the lowest electricity cost (27.1 Ct/kWh) for PV systems with FIT. The difference between prices is found to be small and is within ±3%. However, we found that a changing the irradiance of 3% cause only a small change of the price and therefore conclude that the assessed measurement uncertainties do not significantly affect the prices.

Moreover, we examined whether the PV self-consumption will be influenced similarly in all investigated orientations, by changing the system size. For that purpose, we varied the module area by +/−50% in 5% steps (Figure 7). As expected, the SC rate increased by a reduction of the module area (in our specific case the default area was 24.3 m2) for the orientations (S45, E45-W45, SE45-SW45). This increase only slightly depends on the orientation: The E40-W40 increased by 29% while the south orientation increased by 26% with a reduction of the module area of 50%. While it is obvious that the SC rate becomes smaller for larger module areas, an increase in module size will affect all orientations, but the S orientation will be affected slightly less than the other orientations.

**Figure 7.** The change in self-consumption (SC) rate with varying the module area by +/−50% in 5% steps. The change in SC rate depends on the orientations.
