# Evaluating the Effect of Financing Costs on PV Grid Parity by Applying a Probabilistic Methodology
## 2 Materials and Methods
### Annual Energy Production  
Before considering the peak power of the installation, the amount of electricity that can be produced by PV panels must be calculated. The amount of electricity produced by a panel is measured in kWh. These units are the same as the units on an electricity bill and are therefore directly comparable; the other unit that is often referred to when discussing output performance is the irradiation, which is the amount of energy from sunlight that hits the surface of a solar panel during a specified time. It is generally measured in kilowatt hours per square metre (kWh/m\({}^{2}\)). Irradiance is the power of the sunlight, usually measured in kW/m\({}^{2}\). The PV panel power and, therefore, the PV system power (composed of several serial and/or parallel panels), is measured in terms of peak power using the unit Wp (watts of peak power), which is the power produced when the irradiance is 1 kW/m\({}^{2}\) in specific conditions. The nominal power of the PV system is usually considered as the nominal power of the inverter. Generally, the nominal power of the system (inverter power) is \(\sim\)20% lower than the peak power of the system (peak power of the PV panels). The PV array power is usually oversized relative to the inverter nominal power, achieving a lower cost of delivered energy (\(\epsilon\)/kWh), but if this DC-to-AC ratio is too high, then a significant amount of generated energy will be lost by clipping losses. When the DC input power of an inverter exceeds its AC output power, saturation losses occur (clipping losses). The ratio between the peak power of the panels and the nominal power of the inverter has been considered in this work is equal to 1.2, which is commonly recommended for the design of PV systems because it results in low clipping losses. Several studies verify that for values up to 1.2 the clipping losses are negligible [26; 27]. On the other hand, grid-connected inverters usually have to work with a power factor equal to the unit [28; 29], so the PV system only generates active power. The annual energy production (\(E\)), in kWh, is calculated by Equation (2):  
\[E=Annual\ Yield\cdot Peak\ Power \tag{2}\]  
In Equation (2), _Annual Yield_ is the annual energy generated by the PV system per kWp of peak power. This figure varies based on location, the tilt and azimuth angle of the panels and the sun-tracking system. For optimal tilt angle and no tracking system it varies from 1100 kWh/kWp in the north of Spain to 1500 kWh/kWp in the south of Spain. In this case, we define a whole range of annual yield from 1100 kWh/kWp to 1500 kWh/kWp. In our case, a fixed structure is considered, without trackers and with a tilt angle of the panel of 35\({}^{\circ}\) (average optimal tilt angle in Spain to maximise the total energy produced in the year). _Peak Power_ is the peak power of the PV system. It is usually set as 20% more than the nominal power (inverter). The PDF considered for the annual yield is a normal one with a range between 1100 and 1500 kWh/kWp. The mean is set at 1300 kWh/kWp, and from this set point the standard deviation is applied. This allows us to survey different locations between the ranges and to apply the annual yield throughout all the cases regardless of the power installed. Given this, we believe that we are representing a wider and realistic range of cases. This approach is applied for the three cases studied (500 kW, 50 kW and 5 kW). In Figure 1, the PDF for the yield used in this work can be observed. The use of this distribution is justified because sometimes some variables have a distribution that may not seem normal, this is usually due to the fact that the available historical data are not sufficient [17]. According to the central limit theorem [30], the distribution of a sample is approximately normal if the sample size is large enough.