# Exploring the Benefits of Photovoltaic Non-Optimal Orientations in Buildings
## 2 Materials and Methods
### Case Study #1: Residential PVSCS
#### 2.2.2 Energy Balances  
The PVSCS was installed in February 2020, so there were data for a full year, starting in March 2020. As electricity prices are rising in 2021 after the low prices during the COVID-19 pandemic, the period under study was selected from August 2020 to July 2021. The monitoring system provides data of the PV-produced electricity \(E_{PV}\), consumed electricity \(E\), self-consumed PV electricity \(E_{sc}\), and the exchanges with the grid (energy imported: \(E_{in}\), exported: \(E_{sptl}\)) every fifteen minutes. The relationships between these energies are expressed in Equations (2) and (3).  
\[E=E_{in}+E_{PV}-E_{sptl} \tag{2}\]  
Figure 3: Residential PVSCS PVSYT models (**a**) Original layout (**b**) Design using canopies (**c**) Design using modules attached to the facade.  
\[E_{sc}=E_{PV}\;if\;E>E_{PV} \tag{3}\] \[E_{sc}=\mathrm{E}\;if\;E<E_{PV}\]  
It is important to take note of the period used for the energy calculation in Equations (2) and (3) which can affect the results of the energy imported and exported to the grid when calculated from the energy consumed and PV produced. It is shown that time averaging of the instantaneous powers has a small effect on export proportions for mid-range generation levels (of the order of the average house demand), but a larger effect on import proportion [40]. An optimal 5-min period was proposed as a solution of compromise. This topic is further investigated in [41] and it is found that even a 5-min period can give noticeable errors over a 1-min period due to the variability of home appliance loads and due to some rapid variations of irradiance. As long as the PV systems under study measures the PV production and both the imported and exported energy, there is no error in the energy consumed even with fluctuations in the consumption and/or PV production.  
These data, aggregated in hourly periods, serve as a reference for comparison with simulations of alternative installations with the modules in different orientations suitable with the building.  
The simulated energy production \(E_{PV}\) was processed with the measured consumption profile \(E\). Using Equations (2) and (3), the PV self-consumed energy \(E_{sc}\), the surplus energy fed into the grid \(E_{spl}\), and the energy imported from the grid \(E_{in}\) were computed. In addition, the self-consumption and self-sufficiency degrees are calculated as defined in [42] and expressed in Equations (4) and (5).  
\[SCD=Self-consumption=\frac{E_{PV}-E_{spl}}{E_{PV}} \tag{4}\]  
\[SSD=Self-sufficiency=\frac{E_{PV}-E_{spl}}{E_{in}+E_{PV}-E_{spl}} \tag{5}\]  
Once the energy balances were calculated, the next step is the calculation of the economic balances. The energy costs saved represent the valuation of the self-consumed PV energy at the hourly retail price of electricity. The surplus energy is valuated at a price slightly lower than the wholesale electricity market hourly price.  
Regarding the electricity prices, the Spanish electrical grid operator Red Electrica de Espana (REE) provides real-time information about electricity pricing and a valuation of surplus electricity for PVSCS in its webpage ESIOS [43]. With the processed data, it is possible to compute the economic savings under Spanish self-consumption regulation [21] and the residential pricing of electricity, which will be addressed in the next subsection.