Welcome to the course and module on The Solar Resource and Geometry. The main learning objective is for you to be able to calculate the irradiance received on a tilted surface on earth. If you know how much solar power is incident on your solar panel, it's possible to estimate the electric power production of your system. To maximize this power production, we must study the position of the Sun in the sky to find the perfect angle to till our module. Modeling the position of the Sun in the sky requires several solar angles and each component of solar radiation must be considered separately. But before you can do all of this the first step is to look at how power is radiated from the Sun, and how much of the solar power we receive on earth. The Sun is the star in the center of our solar system. It consists majorly of hydrogen and helium, and this hydrogen fuses into helium releasing enormous amounts of energy. This energy is radiated from the surface of the Sun in all directions. After about eight minutes, a small fraction of this energy reaches Earth. Let us look at whether we get enough power from the Sun to cover our energy demand on earth. We're currently using 18-19 Terawatts, and we expect that to stay below 30 Terawatts by the year 2050. The solar energy potential on earth has been calculated to be more than a 1000 times that of our current energy demand and this is only considering area over land. If we look at all the renewable energy sources, it's only wind and solar that are single-handedly great enough to cover our entire demand, but we also have to consider how efficiently are we converting these resources. For example, the average efficiency of photosynthesis is around one percent, whereas the current efficiencies of photovoltaics is around 20 percent. To understand how we have reached such high efficiencies and how we can make even better solar panels, we must look into how solar energy is spectrally distributed. For us to relate the spectrum of the Sun to the electromagnetic spectrum, we consider the single quantum of light called a photon. The energy of a photon can also be described in terms of wavelength using the Planck Einstein relation. This equation tells us that the shorter the wavelength, the higher the energy. If we look at the electromagnetic spectrum, we see that ultraviolet light and X-rays are actually highly energetic as they have low wavelengths, whereas infrared light has lower energy than visible light. The Sun is considered a perfect black-body meaning that it absorbs all incident light. Planck's law of radiation describes the spectrum of a perfect black-body, and it's a function of both wavelength and temperature. Here I have plotted several black-body spectrum at various temperatures to show you how it varies. If I differentiated Planck's Law to find the wavelength at maximum spectral irradiance, I would get this Displacement Law. If I then were to integrate this entire function to find the total radiated power density, I would obtain Stefan-Boltzmann's Law. If we look at these expressions, we see that the peak wavelength becomes smaller with increasing temperature and that the totally rated power density is proportional to the temperature to the power of four. Now let us apply all of these equations to our Sun. The best fit of Planck's law of radiation to the measured solar spectrum outside the atmosphere of Earth is with a temperature of 5,777 Kelvin, and this is actually how we've determined the effects of surface temperature of our Sun. Inserting this temperature into Wien's displacement law gives a peak wavelength of 502 nanometers which corresponds to green light where our eyes are the most sensitive. Finally, the radiated power on a single square meter on the surface of the Sun is 63 Megawatts. This number is however not that easy to grasp as the irradiance is distributed in all directions, and we only receive a small fraction of it. Instead, let us try calculating the total radiated power from the Sun. This is done by multiplying the power density from different Stefan-Boltzmann's law with the surface area of the Sun. This energy is radiated isotropically from the surface of the Sun in a sphere. As this sphere continues to grow, so does the radius of the sphere. Finally light reaches earth and now the radius of the sphere has grown to the distance between the Sun in the center of the sphere, and Earth on the edge. If we divide the total radiated power from the Sun with the area of this sphere, we obtain the power density on the top of the atmosphere of Earth. This power density is also called the Solar Constant, and it's both calculated here and measured to be very close to 1367 Watts per square meter. The next step would be to look at the effect of the atmosphere on the solar spectrum but first, a brief summary. We've learned that the solar resource is more than 1000 times that of our current energy demand, and that is only considering areas over land. We also saw that the power is radiated from the surface of the Sun as photons with an energy described by the Planck Einstein relation. Now I told you that the Sun is considered to be a perfect black-body, and using Planck's law of black body radiation, we predicted the effects of surface temperature of the Sun to be 5,777 Kelvin. Using these displacement law, we arrived at a peak wavelength of 502 nanometers which corresponds to green where our eyes are the most sensitive. Finally, we arrived at the Solar constant that describes the radiated power from the Sun received at the top of the atmosphere. We calculated it to be 1367 Watts per square meter, and this is very close to what we actually measure.
