# Exploring the Benefits of Photovoltaic Non-Optimal Orientations in Buildings
## 3 Results
### Residential PVSCS
#### 3.1.2 Economic Analysis  
The hourly energy balances are evaluated with the pricing data for the two tariffs, as detailed in Equations (6)-(10), and the annual PV profits are calculated for all configurations and annual productions. The results are shown in Figure 8 and can be seen that, for the same energy production, the most profitable configuration is the one with modules coplanar with the facades. This is due to the superior self-consumption of PV-produced electricity which is valuated at a higher price than the surplus energy exported to the distribution grid. It is also visible in Figure 8 that the annual profit rises linearly with the PV production up to 9 MWh and beyond this annual production. The profit then increases at a slower pace. This is due to the Spanish simplified compensation expressed in Equation (7) which establishes that, during the one-month billing period, the energy term cannot be negative. In fact, for higher PV productions, in some months, it is possible for the value of the energy exported to the grid to be higher than the consumption, despite the lower price of the exported energy, thus reducing the profits. In addition, by comparing the profits for the two tariffs, the new tariff displays a profit of approximately EUR 100 higher than the older one for all configurations and sizes.  
Figure 7: Self-consumption (**a**) and Self-sufficiency (**b**) degree vs. PV production relative to the consumption for the simulated configurations.  
The annual profits calculated are used as the cashflow for the economic analysis. The other input are the costs of the installations. The costs were estimated as follows: 1.55 EUR/W for PV powers lower than 4 kW, 1 EUR/W for PV powers higher than 8 kW, and a linear variation of costs between these powers. This pricing scheme is supported on the information of PV installers, and it is representative of the Spanish PV residential market in the year 2021. We applied a cost increase of 11% for the configuration based on facades, 12.5% for the mixed one, and 14% for the canopies. Figure 9 presents the results for the net present value (a,d), the internal rate of return (b,e), and the time of return of investment (c,f). These results are plotted versus the annual PV production (a-c) and versus the installed PV power (d-f). The economic indicators are favorable in all cases, i.e., the optimal case is the best economic performer and the facades are the worst. The best maximum NPV is for the optimal case with EUR 12,271 and 8.1 kW installed at a cost of EUR 8116. The lowest NPV is the highest at EUR 7616, and is almost flat for a range of powers between 8 kW and 11 kW. The IRR is also very favorable, always over 7%. The best performer is the optimal, between 14% and 17% and the worst the facades, between 6.9% and 10.8%. The optimal PV power is around 8 kW in all cases. The time of return of investment is the smallest for PV power of 8 kW in all cases and ranges from 6.3 years for the optimal case to 8.6 years for the facades.  
Figure 8: Economic profit for older and new electricity tariffs in Spain: (**a**) Annual profit for older tariff 2.0A; (**b**) Annual profit for the new tariff 2.0 TD. Taxes of 5.11% of electricity and 21% VAT are included in the calculations.  
Figure 9: Economic balance. (**a**) Net present value vs. annual PV production; (**b**) internal rate of return vs. annual PV production; (**c**) time of return of investment vs. PV annual PV production; (**d**) net present value vs. PV installed power; (**e**) internal rate of return vs. PV installed power; (**f**) time of return of investment vs. PV installed power.  
Finally, the levelized cost of electricity is calculated according with Equation (13) and is shown in Figure 10a,b. For PV powers under 8 kW, the LCOE reach maximum values between 6.3 EUR/kWh and 10.3 EUR/kWh. and the minimum values are between 4.0 EUR/kWh and 7.0 EUR/kWh. All these minimum values are well below current retail electricity prices in Spain.