3.1. SCI and SSI
First of all, the SCI and SSI calculated by the measured and calculated production profiles are compared. The calculated production profiles are obtained by using the same technical parameters as described in
Table 2. As the installed power is different for the three installations, the production is normalized following the methodology described in
Section 2.6, with sizing factor
and using the dataset of large consumers. The results are shown in
Figure 7 as a boxplot and in
Table 3. The colored box is delimited by two horizontal lines with the lower representing the 25th percentile (q25) and the upper representing the 75th percentile (q75). The median (q50) is represented by the middle line and the whiskers are representing the boundaries of the dataset. A scatter of points is overlaid on the boxplot for a better visual representation of the distributional differences.
It is clear that the simulation model is able to accurately estimate the SCI and SSI for east-oriented PV. For the south-, west-, and east/west-oriented PV, very small deviations are noticeable. Furthermore, it can be concluded that the east- and west-oriented PV installation has lower SSI compared to a south-oriented PV installation. In addition, the east/west-oriented PV installation has a slightly lower SSI but a significantly higher SCI. This is the case for both simulation and measurement. More important to notice is the fact that the difference of the median of the simulated and measured SCI and SSI between east/west- and south-oriented PV are quite similar:
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SCI: increase of 8.62 percent points for the measured PV and 8.66 for the simulated PV
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SSI: decrease of 0.19 percent points for the measured PV and 0.31 for the simulated PV
Figure 8 shows the sensitivity analysis of SCI and SSI for different sizing factors
c and for different orientations but for the typical roof pitch angle (
). This is done for the three types of consumers, small, medium, and large consumers. As the result of this analysis is in fact a distribution, here only the median of this distribution is considered. The larger the PV installation, the lower the SCI and the higher the SSI. However, these curves are not linear but saturate because of the seasonal behavior. For south-oriented PV with
, the SCI and SSI amounts to almost 30%. When looking at 1D PV installations, oriented to the east or the west, they both have a higher SCI of almost five percent points compared to a south-oriented PV, irrespective of the type of consumer. Although, regarding the SSI, this is for all cases 3 to 4 percent points lower than a south-oriented PV installation. This is mainly due to the fact that an east- or west-oriented PV installation is only able to cover respectively the morning or evening peak while a south-oriented PV installation reaches higher yields and thus can cover the load on a larger extent.
For that reason, it can be interesting to investigate the benefit of 2D PV installations, east- and west-oriented. It is clear from the graphs that the SCI increases significantly for this configuration. The increase amounts to almost 10 percent points for
. This is mainly due to the lower yield rather than a better match between demand and production. For this reason, the SCI could be misleading and is therefore not an ideal parameter to asses the benefit of PV orientation. Nevertheless, the SCI is a good metric to evaluate the amount of the injected energy to the grid. Regarding the SSI, no obvious improvements are noticeable, and the SSI is even worse. When increasing the sizing factor, the SSI for east/west-oriented PV is getting better than for south-oriented PV. However, this increase is marginal. The absolute increase or decrease of the medians of SSI is shown in
Table 4.
It can be noticed that east/west-oriented PV is only getting beneficial from on. This is then only the case for medium and large consumers. For small consumers, the SSI is then equal to that of a south-oriented PV. For , increases further and is the largest for large consumers and the smallest for smaller consumers. However, again, these benefits remain clearly very marginal.
The limited increase of SSI can be further investigated by analyzing the SSI on a monthly basis in order to take the seasonal effects into consideration.
Figure 9 shows the median SSI for east/west- and south-oriented PV and the differences between them using large consumer profiles. It is clear that the benefit is particularly present during the spring and summer months. During these months, the SSI increases up to 5 percent points compared to a south-oriented PV installation. This has two reasons:
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In the northern hemisphere, the autumn and winter sun rises near the southeast and sets near the southwest. Hence, the direct irradiance is limited, while, during the spring and the summer, the sun rises near the east and northeast and sets near the west and northwest. Consequently, the yield increases during the morning and evening and reaches its maximum when the sun crosses the east and the west. The higher zenith angle of the sun during the spring, and especially during the autumn and the winter, causes the south facing panels to have a more optimal angle of incidence during a larger part of the day. This leads, according to Equation (
6), to a higher direct irradiance.
Figure 10 illustrates the solar trajectory during different seasons.
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During the winter months, the winter solstice occurs. The earth’s poles are tilted away from the sun causing shorter daylight. Accordingly, during these months, a south-oriented PV installation is more interesting to cover the day consumption.
Until now, the analysis has been done by considering the median instead of the whole distribution. Moreover, only a number of specific azimuth angles have been investigated. In
Figure 11,
SSI is calculated for 2D PV installations following the methodology described in
Section 2.6. The optimal azimuth angle with regard to the SSI is 90°/270°, irrespective of the type of consumer or the sizing factor. However, the large consumers can benefit more on SSI by orienting their PV installation to east/west than the small consumers. For
, the median of
SSI amounts to one percent point for large consumers and 0.2 percent points for small consumers with outliers going up to 2.4 percent points. For small consumers, the q25 percentile is negative, while, for other types of consumers, only the outliers are negative.
The distributional differences could be explained by analyzing the time of peak occurrence (ToP) of the different types of consumers. The result of this analysis is shown in
Figure 12. Large and medium consumers usually have their peak demand during the evening while small consumers have their peak during the morning. The latter could be explained by the fact that those small consumers are possibly representing retired persons who generally have lower electricity consumption and are doing their activities especially during the middle of the day [
45,
46]. The spread of the ToP for medium consumers is larger than for large consumers. Moreover, only a slight difference can be noticed for the maximum ToP between medium and large consumers. They both have a maximal ToP between 17 h and 18 h. It should be noted that the outliers usually represent the weekends.
As the ToP of small consumers is usually at noon time but with a spread over the whole afternoon, SSI is small and also has a large spread. The median of SSI is slightly higher for large consumers compared to small consumers because of the slightly higher ToP and the smaller spread. Therefore, it can be concluded that east/west-oriented PV is more interesting for medium and especially for large consumers as they typically have a ToP occurring during evening.
In the previous analysis for 2D PV, it is considered that the installed PV capacity is equal for both sides of the roof. From a practical viewpoint, this is not always possible due to e.g., shading obstacles or roof windows. Moreover, it is not yet proven that an equal spread of PV is the most optimal solution. Therefore, a sensitivity analysis is performed for
SSI in a function of the parameter
a for
and for large consumers. The result of this analysis is shown in
Figure 13. The curve shows that the maximal
SSI is achieved for
. This confirms that the previously made consideration leads to the optimal solution.
Until now, only tilt angles of 45° have been considered as they represent a large part of the residential consumers. In
Figure 14, the impact of the tilt angle on the median of the SSI has been investigated for different orientations. For PV installations with
, it has already been investigated that there is rather no benefit compared to a south oriented PV installation. However, for higher tilt angles of 75° or 90°, the benefit increases, especially for E/W- to SE/NW-oriented PV.
For PV installations with
, the benefit is even more visible for high tilt angles, particularly for medium and large consumers. The optimal azimuth angle for small and large consumers is 90°/270° irrespective of the tilt angle, while, for medium consumers, the optimal orientation shifts to SE/NW as the tilt angle increases. In
Table 5, it is shown that 1D PV installations oriented to the east or to the west, considering large consumers, are more strongly influenced by the tilt angle but are in any case not an improvement compared to south-oriented PV. It is remarkable that the SSI increases slightly once the tilt angle is 90°. Two results of this analysis are indicating the potential of building-integrated PV (BIPV). Firstly, the highest SSI could be achieved for
(e.g., transparent solar panels as roof windows). Secondly, the highest benefit in SSI of E/W-oriented PV compared to south-oriented PV is for a vertically installed PV (e.g., facade integrated PV). The authors do suggest for future research to investigate more in detail the benefit of BIPV with regard to self-sufficiency.
3.2. Peak Reduction
In this paragraph, the peak reduction due to oriented PV is assessed by calculating the moving average of the month peaks on an annual basis. Both 1D and 2D PV are considered and only PV systems with
are considered as it is found that only for these sizing factors is a notable improvement achievable. The result of this analysis is shown in
Figure 15. The bar graph can be interpreted as follows. The horizontal axis represents the number of profiles, the vertical axis represents the type of consumers, and the different colored stacks represent the benefit with regard to the moving average month peak.
For 1D configurations, the greatest benefit can be achieved with large consumers as they usually have their ToP in the evening. Almost 45% of the profiles can achieve a saving (which means ) on the peak load and nearly 7% can achieve a savings of more than 2.5%. At the same time, approximately 30% should pay more because of not covering the peak demand appropriately. This part increases further for medium and small consumers, due to the mismatch of the ToP and the PV production.
For east/west-oriented PV, higher benefits could be achieved. Again, this is especially the case for large consumers. More than 60% could achieving a saving in peak load while only 10% should pay more. Nearly 6% would save more than 2.5%. For medium and large consumers, the share of profiles achieving a saving is also higher than for 1D PV. Almost 50% of the medium consumers and 40% of the small consumers could achieve savings. East/west-oriented PV is thus more beneficial as it has a bigger chance to cover the month peak due to the spread yield during the day.
When looking at the impact of the tilt angle on
Figure 16, it can be noticed that the spread increases with increasing tilt angle. This is both the case for west-oriented and east/west-oriented PV. However, for east/west-oriented PV, the median increases also while that is not really the case for west-oriented PV. This increase could be explained by the fact that a higher tilt angle causes the PV installations to produce until later in the evening. For
, the median reduction amounts 0.73 percent points for 2D PV installations with outliers of 4.5 percent points. However, this analysis showed that neither the tilt angle nor the azimuth angle causes a significant reduction of the month peaks.
3.3. Storage
The benefit in terms of energy storage can be analyzed by calculating the needed storage capacity for a certain desired SSI and for the amount of installed PV. This is done for a south- and east/west-oriented PV installation with both the typical tilt angle
and then compared to each other. The analysis is only performed with large consumer profiles as they basically achieve the highest SSI. It should be noted that the storage capacity is here considered as the usable storage capacity, thus excluding all the losses such as self-discharge and converter losses. As the aim of this analysis is to compare two results, these aspects are of little relevance. In order to determine the benefit, the ratio
is defined as the ratio between the needed energy storage system capacity for an east/west-oriented PV installation
and a south-oriented PV installation
:
The result of this analysis is shown in
Figure 17a in the form of a contour plot with on the horizontal axis the desired SSI; on the vertical axis, the installed PV capacity and the contours representing the ratio
. For
, an east/west-oriented PV installation will need a smaller storage capacity to achieve a certain SSI than when having the PV installation south-oriented. The isoline for
is shown as a full black line. When observing the contourplot it can be noticed that a benefit is only achievable for PV installations with
and for
. When wanting to achieve for example a SSI of 60% and having a PV installation with
, 10% of storage capacity could be saved due to orienting the PV to east/west. For higher SSI, east/west-oriented PV is not considered viable; due to lower yield during the winter, a very large storage system would be needed.
When considering residential storage systems, often electrochemical batteries, those savings are not in the order of magnitude to be considered as meaningful. Nevertheless, inversely it could be stated that, with the same storage capacity, the battery utilization could be reduced. This metric is expressed in discharge cycles per year and can be used to determine the expected end of lifetime. For this analysis, the comparison is done for an east/west- and south-oriented PV and the percentage of reduction of battery utilization is calculated as follows:
with
the relative difference of the battery utilization and
and
, respectively, the discharge cycles for south-oriented and east/west-oriented PV.
represents the discharged power at time
t.
Figure 17b shows the difference in battery utilization between east/west and south-oriented PV as a function of SSI and
c. As can be seen, this difference is always positive, which means that, in any case, the battery utilization could be reduced. However, this is mainly due to the fact that, when a larger storage system is needed, it will be de facto underutilized during the summer. This underutilization is, as aforementioned, the consequence of the higher SSI of PV during the non-winter months, while during the winter the SSI is lower compared to a south-oriented PV installation (see also
Figure 9). Therefore, only the results above the black line are relevant. This line represents the sizing factor
c and the SSI for which the needed storage capacity is the same for east/west- and south-oriented PV, thus with
. For the same operating point as given in the example above (
,
), a reduction in battery utilization of 5% could be reached. For the isoline
, a reduction of 6% is possible. It is obvious to state that this will lead to a slight extension of the battery lifetime. However, it should be noted that the cyclic lifetime depends on many other factors and parameters than just the battery utilization, such as cell temperature, depth of discharge, and charge/discharge rate. However, the number of discharge cycles determines to a large extent the cyclic lifetime of batteries [
47].