Solar Energy

Solar energy is the most abundant primary energy source on Earth. The sun is a huge nuclear fusion reactor that is continuously streaming electromagnetic waves and subatomic particles in all directions. Only a tiny portion of this solar flux is aimed at the Earth, but even that portion is estimated to contain 170 million GW, a power millions of times greater than the maximum power demand of the Earth’s entire population.

The instantaneous power density reaching the Earth from the sun is called solar irradiance. It is measured in unit power per unit area, usually watts per square metre (W/m^2), with the area taken to be in the plane perpendicular to the direction of the solar flux. Since the earth is roughly spherical with a radius of 6367+/-20 km, the area of solar flux it intercepts is A=pi r2, or 40.5 million square km, or 40.5×10^12 square metres. The irradiance at the Earth’s orbital distance is therefore 170×10^15W / 40.5×10^12 m2 = 4.2 kW / m^2.

Of course, from our point of view standing on some particular spot on the surface of the Earth, we aren’t as interested in the gross irradiance in space as in the time-average usable irradiance reaching our piece of the surface. This value is complicated by the fact that the Earth spins on its axis (so there is a dependence on the time of day), revolves around the sun in an eliptical orbit with an inclination (so there is a dependence on the time of year) but also on latitude, altitude, and local climate. Not all of the energy in the solar irradiance is usable. Much of it never reaches the surface of the Earth thanks to the atmosphere. Most of the particles (except neutrinos) are absorbed by the atmosphere, as are some parts of the electromagnetic spectrum. It turns out that the most useful portion of the electromagnetic spectrum is visible light, both because that is where the greatest power density is concentrated, and because we are better able to capture that energy than gamma, x-rays, UV, or infrared radiation. The effect of the atmosphere is modelled using “air mass” units. One air mass or AM1 is the effect of the atmosphere when the sun is directly overhead at sea level, e.g at the seacoast at the equator at noon. At higher latitudes, the sunlight must pass through a greater amount of atmosphere to reach the surface. A commonly used estimate of the usable solar irradiance after passing through AM1 of atmospheric absorption and scattering is 1 kW / m^2. At the latitudes of the continental USA, AM1.5 is considered a reasonable estimate of conditions, and is used to rate the maximum output of solar photovoltaic panels. The year-round average solar irradiance, taking time of day and everything else into account is considerably less still. This gives the “capacity factor” of the solar panel. At the latitudes of the northern continental US states or southern Canada, the capacity factor is about 12%. In other words, a solar panel that is never shaded but does not use a directional tracker will, on average over the course of a year, deliver 12% of its maximum rated output.

Solar energy systems come in two basic flavours, photovoltaics that convert solar energy directly to electricity, and solar thermal systems that collect heat from the sun (and may be used to generate electricity from that heat). We will look at both.

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