# Long-Term Forecasting Potential of Photo-Voltaic Electricity Generation and Demand Using R
## 4 Discussion  
Two different types of models were used to estimate the relationships between the micro-grid parameters on the one hand, and weather and time parameters on the other. This is due to the dependencies found in the exploratory data analysis phase. This analysis showed a linear relationship between solar power generation and solar irradiance, which was not always improved by applying support vector regression. The effects of temperature on solar power generation were different than anticipated. Figure 4 shows that whereas higher temperatures of 30-35 degrees Celsius indeed lead to less produced solar power (a maximum of around 60 kWh whereas colder temperatures showed higher production); lower temperatures of -5-0 degrees Celsius lead to far less produced solar power of 40 kWh. Although the efficiency may be higher, the lack of solar irradiation has a far greater effect than temperature. The electricity costs saved by generated solar power were overestimated by 3% in 2016 and 5% in 2017, suggesting that degradation has a considerable effect on the total generated solar power and, although hidden, should be taken into account in future models. To examine the hypothesis that temperature could have a large influence on purchased energy, a quadratic equation was found to describe this relationship. At times when the building was occupied, temperature extremes did show a higher effect on purchased electricity (Figure 4). Applying the equation to hourly electricity costs led to over- and underestimations of the actual costs of 6% and 8% respectively. With annual costs running up to around 100,000,000 JPY, it is desirable to have an accuracy within 1% or less, which this simplified equation has not yet achieved. Purchased energy was found to be dependent on numerous other variables, namely, month, hour of day, day of week, holiday or not, and other weather parameters. Splitting the data into groups as per table IV did not lead to a clear distinction, as the month of the year still had a substantial influence as shown in Figure 9. A more inclusive approach incorporating all of these parameters might produce better results, especially if the hidden factor of building occupancy, or of purchased electricity base demand, is estimated for each hour. To enable predictions of up to one year into the future by means of machine learning, the first step in improving these equations are to incorporate solar power generation efficiency degradation on the one hand, and the complex interactions of time parameters leading to building occupancy on the other hand. If these improvements can lead to more accurate cost predictions within 1% error margin, the second step is to predict associated weather parameters for up to one year, mainly solar irradiance and temperature. As these two parameters influence each other, and this study showed that purchased electricity had a higher correlation to solar irradiance than to temperature (Figure 5), it may even be possible to have a single weather parameter predict both micro-grid parameters. This would simplify the number of unknowns that have to be predicted. Alternatively, if many weather factors can be predicted with great accuracy, the reverse approach may be taken. [PERSON] et al. [PERSON] et al. (2018) found that solar irradiance can be inferred from the parameters day of the year, temperature, dew point, \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Parameter** & **2015** & **2015** & **\%** & **2016** & **2016** & **\%** & **2017** & **2017** & **\%** \\ \hline total\_pv\_ac (costs saved) & 1579 & 1557 & \(-\)1.36\% & 1594 & 1643 & +3.08\% & 1651 & 1740 & +5.41\% \\ purchased\_electricity\_kwh (costs made) & 86,669 & 92,049 & +6.21\% & 99,253 & 97,304 & \(-\)1.96\% & 107,646 & 99,142 & \(-\)7.90\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Electricity prices in 1000 JPY and % correctly modeled per micro-grid parameter (costs saved vs. remaining costs) for both actual data and estimated data based on modeled equations.