Solar light 2

Referencing:

1. ET3034Tux - 1.6.2 – Solar light 2, https://www.youtube.com/watch?v=wizhej5qUNM
2. Solar Energy - the Physics and Engineering of Photovoltaic Conversion, Technologies and Systems, Chapter 5.

Referring to the diagram below, the spectral power density of irradiance from the sun (also known as spectral irradiance) reaching the outer side of Earth's atmosphere is shown in yellow.  This spectrum is the extraterrestrial spectrum and the irradiance is approximately 1361 W/m².  The spectrum of a black body radiator at 5800K temperature is indicated by the grey line.  The spectrum of solar light arriving at the Earth's surface is indicated in red.  Much of the spectral power density is lost in the Earth's atmosphere due to scattering and absorption by molecules and particles, such as ozone, oxygen, water and carbon dioxide.

The depth of the Earth's atmosphere is shortest at the equator, and longer at higher latitudes.  Hence, the path of solar light is shortest at the equator, and correspondingly, the spectral losses are least.  The path of light is indicated by the optical air mass, where an air mass of 1 indicates the shortest path length at the equator.  Air mass AM is described by this equation:

AM = 1 / cosθ

where θ is the latitude in degrees.

An AM of 1.5, or AM1.5, would be the path length of sunlight through the atmosphere at a latitude of 48.2 degrees at noon, ignoring the seasons.  The AM1.5 spectrum is defined as the Standard Test Conditions (STC) for the solar spectrum, where the irradiance is 1000 W/m².  (And under STC, the solar cell temperature is 25°C.)  This spectrum is shown in the diagram below.

When we consider light in terms of photons, the photon flux ϕ is defined as the number of photons per unit time per unit area.  This doesn't come with spectral information, analogous to irradiance.  The spectral photon flux Φ is defined as the number of photons per unit time per unit area per wavelength range.  The spectral photon flux and spectral power density are related by this equation:

Φ(λ) = P(λ) λ/hc

Essentially, the spectral photon flux (also known as spectral photon flux density) is the spectral power density divided by the energy of a photon at a particular wavelength.  If we integrate the spectral photon flux over a wavelength range as follows, we get the photon flux for that wavelength range:

ϕ = ∫₀^λ Φ(λ) dλ

Due to the fact that every photon can create a collected charge carrier in solar cells, the amount of photon flux would in theory determine the maximum current per unit area that can be created in a solar cell.  Hence, the maximum possible conversion efficiencies of solar cells can be also determined.

Another useful tool is the Estimated Sun Hours (ESH), where:

1 ESH = 1 kWh/m²

This means a STC irradiance of 1000 W/m² for one hour on the Earth's surface.  In addition, the Watt-peak (Wp) refers to the maximum power a solar module can deliver under STC.  Hence, for a 100Wp solar module operating at a location on Earth with 5 ESH, the solar energy generated is 500Wh per day. 

Another term is Capacity Factor.  It refers to the time that an electricity generator works at maximum nominal power, and usually averaged over one year.  Hence:

Capacity Factor = ESH * 365 / (24*365)