Solar Radiation and Energy
Solar Radiation on a Surface
The solar radiation incident on a surface is a fundamental quantity in photovoltaics, as it determines the available energy.
Incident Solar Radiation (
Where:
: Direct radiation component (W/m²). : Diffuse radiation component (W/m²). : Reflected radiation component (W/m²).
Extraterrestrial Solar Radiation (
Where:
: Solar constant. : Day of the year.
Angle of Incidence (
For an inclined surface with an angle
Where:
: Solar declination. : Latitude of the location. : Hour angle. : Inclination angle of the surface.
Solar Radiation on an Inclined Surface
Calculations in Photovoltaic Panels
Power Generated by a Panel (
The power generated by a solar panel depends on its area, the incident irradiance, and its efficiency.
Where:
: Power generated by the panel (Watts). : Solar irradiance on the panel surface (W/m²). : Area of the solar panel (m²). : Efficiency of the panel.
Output Current Equation (
The electrical behavior of a photovoltaic panel is modeled by the solar cell equation.
Where:
: Photogenerated current (A). : Reverse saturation current (A). : Electron charge ( C). : Voltage at the cell terminals (V). : Ideal factor of the cell. : Boltzmann constant ( J/K). : Absolute temperature (K).
Maximum Power (
The maximum output power of a panel is achieved at the maximum power point (MPP).
Where:
: Voltage at the maximum power point. : Current at the maximum power point.
Efficiency and Losses in Photovoltaic Systems
Panel Efficiency (
The efficiency of a photovoltaic panel is the ratio of the electrical power generated to the solar power incident on it.
Where:
: Electrical power generated (W). : Solar power incident on the panel (W).
Losses in the Photovoltaic System
In PV systems, losses can occur in various components such as the inverter, cables, and due to environmental conditions (such as temperature and shading).
Temperature Losses (
Where:
: Temperature correction factor. : Temperature coefficient of efficiency (%/°C). : Cell temperature (°C). : Reference temperature (25°C).
Total System Efficiency (
Where:
: Inverter efficiency. : Transmission efficiency in cables. : Temperature correction.
Sizing Photovoltaic Systems
Daily Energy Generated (
To size an FV system, it is essential to calculate the energy it will produce over a period of time.
Where:
: Total installed power of the system (kW). : Peak solar hours (hours of sun equivalent to 1000 W/m²). : Total efficiency of the system.
System Capacity (
The capacity of a PV system can be calculated based on energy demand.
Number of Panels (
The number of panels needed to generate a certain amount of energy is calculated by dividing the total power by the individual power of each panel.
Where:
: Power of a single solar panel (W).
Inverters and Batteries
Inverter Efficiency (
The inverter converts the direct current (DC) generated by the panels into alternating current (AC) usable by electrical devices.
Where:
: Output power in alternating current (W). : Input power in direct current (W).
Battery Capacity
Battery capacity required based on consumption:
: Battery capacity in Ah. : Total energy required (Wh). : Battery voltage (V). : Depth of Discharge.
Financial Calculations
Return on Investment (ROI)
The return on investment (ROI) for a photovoltaic system:
: Return on investment (%). : Savings on the annual electricity bill. : Total cost of the system installation.
Payback Period
The payback period of the photovoltaic system:
: Payback period (years). : Total cost of installation. : Annual savings on the electricity bill.