## 4 Added Value of the Results  
In trying to depict the results of this work in a practical manner for solar energy planners, investors, and engineers, two maps were prepared based on Figure 1. Figure 13 shows the distribution of the choice of the optimum tilt angles in Greece at either 25\({}^{\circ}\) S or 30\({}^{\circ}\) S. Two zones are apparent that divide the country in half: a northern part with \(\beta\) = 30\({}^{\circ}\) S and a southern one where \(\beta\) = 25\({}^{\circ}\) S. These zones have been drawn in an approximated way, as no intermediate stations among those selected existed in this study. Moreover, this division was in complete agreement with the solar potential map of Figure 11a, where higher insolation was found in the (south)eastern region of Greece, and a lower one was found in its northern part. Therefore, sites at lower latitudes would need south-facing solar convertors at lower tilt angles (i.e., 25\({}^{\circ}\)), and those at higher latitudes would require higher tilt angles (i.e., 30\({}^{\circ}\)). Figure 14 gives the approximate distribution of the four PV\({}_{\text{ctts}}\) zones across Greece. The approximation has the same meaning as that in the map of Figure 13.  
Figure 13: Spatial distribution of the optimum tilt angle \(\beta\) for south-facing flat-plate solar convertors in Greece for the maximum annual energy yield. A recent study by [PERSON] et al. [69] showed that the PV solar power output would increase in the time period of 2010-2080 by a few percent in Europe and about 3% for Greece due to the impact of climate change. This means that the PV\({}_{0}\) and PV\({}_{\text{ctts}}\) thresholds of Table 4 will change in the future, and the new thresholds are shown in Table 7.  
Finally, an extra algorithm was developed in the frame of the present work. The algorithm calculated the maximum annual solar energy received at the 33 sites in Greece. The algorithm varied both the tilt angle (\(\beta\)) and the azimuth angle (\(\psi\)) of the inclined surface in the ranges of 0-90\({}^{\circ}\) and 130-230\({}^{\circ}\) in steps of 1\({}^{\circ}\), respectively. Table 8 shows the maximum energy received for an optimal (\(\psi\), \(\beta\)) pair. These results only have theoretical \begin{table}
\begin{tabular}{c c c} \hline \hline
**PV Scheme** & \
\begin{tabular}{c} **Historical Annual \(G_{e}\)** \\ **(kWhm\({}^{-2}\).year\({}^{-1}\))** \\ \end{tabular} &
\begin{tabular}{c} **Future Annual \(G_{e}\)** \\ **(kWhm\({}^{-2}\).year\({}^{-1}\))** \\ \end{tabular} \\ \hline PV\({}_{0}\) upper threshold & 1775 & 1828.25 \\ \hline PV\({}_{0}\) middle threshold & 1700 & 1751.00 \\ \hline PV\({}_{0}\) lower threshold & 1625 & 1673.75 \\ \hline PV\({}_{\text{ctts}}\) upper threshold & 1900 & 1957.00 \\ \hline PV\({}_{\text{ctts}}\) middle threshold & 1850 & 1905.50 \\ \hline PV\({}_{\text{ctts}}\) lower threshold & 1800 & 1854.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Change of the PV\({}_{0}\) and PV\({}_{\text{ctts}}\) thresholds from their historical (this study) values to the new values in the time period of 2010–2080 due to the impact of climate change. The future values are the historical ones increased by 3% on average, according to [69]. Figure 14: Division of Greece into four PV\({}_{\text{ctts}}\) zones for the operation of solar flat-plate convertors with optimal tilt angles to the south. value because, in practice, they would impose an extra cost to the solar flat-plate convertor installers in Greece. It is interesting to observe that (1) all surface azimuths were oriented almost toward due south (180\({}^{\circ}\)), (2) the optimum angle of inclination was within the 25-30\({}^{\circ}\) range, and (3) the site of Kozani showed a quite different (\(\psi\)', \(\beta\)) pair than that of the other 32 locations.