About Solar Panels


Solar Panels seem like a great idea for getting free energy from the Sun. A lot of people talk about it enthusiastically as if it is the obvious answer for solving the world's energy problems. Unfortunately, it is not so simple, as explained here.

Static Solar Panels

Solar panels are great when space is not a problem. However, several surprising factors should be considered for terrestrial installations.

First, we should determine the wattage rating of the solar panels that are being considered. The wattage depends on the panel size, technology, efficiency, etc. A typical solar panel's rated output is about 16Watts/square foot. This is the manufacturer specified ideal rating and we need to 'derate' it due to several factors:

1.     The panel's output depends on the temperature of the photo voltaic cells. The cells work well at low temperatures, like 25⁰C and the output drops when the cells get too hot. Given that the cells are in the Sun, the temperatures often zoom past 50⁰C.

2.     Solar panels should ideally track the Sun, and the tilt and azimuth angles will vary depending on the time of day and the season (summer vs winter). The tilt angle is the pitch in the vertical plane and allows the panel to follow the Sun as it moves higher and lower in the sky. The azimuth angle is the yaw in the horizontal plane and allows the panel to follow the Sun as it rises in the East and sets in the West. The output will drop if the panels are not facing the Sun. For ease of installation on homes, the panels are mounted directly on roofs and the tilt angle may not be as recommended.

3.     The output also suffers when the panel is dirty with dust or pollen.

Given the above factors, the typical output will be about 80% of the manufacturer rated output, about 13W/sqft, or 0.013KW/sqFt. This value is called the 'peak' rating.

Next, we need to determine the available sunlight in a geographic area. Different parts of the world get different amounts of sunshine. It depends on the latitude, average cloud cover, sunlight hours per day, haze & smog, air mass, etc. To get the peak Specific Photovoltaic Power Output (PVOUT) per year, see: https://globalsolaratlas.info/map. The map also shows the recommended tilt angle for panel installation so that it is optimally facing the sun.

If the solar panel is mounted statically on a house or a solar farm, at the recommended tilt angle, then the annual power generation at that location will be the product of the PVOUT and the panel's wattage rating. This will be a value in KWh and estimates the average energy collected in one year. Given the desired annual electricity requirements, the size of the solar panel needed can then be estimated. An adequate storage battery will be needed to provide electricity at night and on overcast days.

For example, in Philadelphia, USA, the PVOUTp is shown as 1432.8 kWh/kWp. The average annual power output will be 0.013 x 1432.8, or 18.6KWh/sqft. Assuming that the annual requirement for a house is 12,000 KWh, the panel area required will be 12,000 18.6, or about 650 square feet. A typical house has more than this area available on its roof. The cost of the solar panel (without installation) is currently about $1/Watt, or $70/sqft.

Mobile Solar Panels

People often fantasize about installing solar panels on cars and even on hikers' backpacks. However, this is not really practical.

Assuming that panels are installed on the roofs of cars, the area available on a large car is about 4x8 = 32 sqft. A small car would have half this area. At 13W/sqft, this yields about 420W. If the car charges under the Sun for 8 hours, it gets 3.3KWh. Note that the panels mounted on a car would be horizontal and would not be optimally tilted to follow the Sun, so the actual yield would be less. An efficient electric car today operates at about 4 miles/KWh. It can drive about 12 miles/day. The average car is driven about 35 miles/day. Solar panels can provide about one third of the energy.

On the flip side, note that solar panels are fragile, and could be easily damaged when the car goes over road bumps. They are also expensive and could be easy targets for thieves.

Solar panels make a lot more sense on Semi trailers and trains. A semi-trailer has a lot more roof area, about 400 sqft. Panels mounted there would be well protected, but susceptible to snow and road grime. The side walls are also large and could be used for solar panels. Energy gathered from these panels could cover more than 6% of the annual operational energy costs, which could be quite significant. Note that a storage battery would be needed for semi-trailers that are usually disconnected from the tractor unit. Similarly, solar panels mounted on the roofs of train carriages would be useful.

We see that solar panels are suitable for static installations but not sufficient for mobile vehicles. This is because the energy available in sunlight does not have a sufficient energy density. The obvious solution is to increase the density by using lasers. Lasers can easily transmit 100KW of power and can be focused on moving vehicles. Imagine a highway with regularly spaced laser transmitters that recharge vehicles as they zip by. In a more flexible embodiment, the lasers could be mounted on nuclear powered drones flying above the vehicle pathways. (Just kidding about lasers & drones :-)

All in fun

Oct 2023