*The calculations below are complicated. The results are found on my page *What must we do to reduce the rate of warming. Please feel free to modify the results if you believe I have made an error. I believe such changes will not change my conclusions on the above-mentioned page.

The dark red area are the best for solar panels. The legend for the above map, divided by 365, indicates that for a dark red area a panel surface with a 1 kilowatt rating will produce 6.57 kWh per day (El Paso, Texas) , a slightly red yellow area, 4.10 (southern Italy, St. Louis), a yellow area 3.56 (Cleveland, Lyon, France) and a mid-green area 2.74 (London). I checked these numbers for El Paso, Texas: in summer 7.82 kWh, in winter only 4.32 kWh, which is 55% of the summer amount; for Boston, the kilowatt-hours per day were 22% higher in July and 33% lower than they early average in December, so again the lowest month was 55% of the highest.

##### This page considers first: solar panel emissions; then rooftop solar panels without batteries; then roof top solar panels with batteries; and finally, utility scale solar power.

#### CO2 emissions from solar panels:

Online you will find varying statements of the lifetime CO2 per kWh from the manufacture of a 1kW solar panel (2.5 average residential panels of 2 square meters): 60, 50, 40, and one at 6.

I finally located the old unharmonized data and the method for harmonization^{1}: Lifetime 30 years, 75% efficiency for rooftop mounted, monocrystalline nameplate panel efficiency 14% (average overlifetime 13%), solar strength 1,700 (4.65 per day), harmonized result 45 grams CO2 per kWh (median result 60 g/kWh).

*The CO2 value per panel should be increased by 15% compared to the above reference, because China uses far more coal. *^{2}*, China accounted for nearly 78% of all panels. Coal emits double the CO2 of natural gas and 30% more CO2 than oil.*^{3}* * On the other hand, panel name-plate efficiency has increased from 14% in the study to 22.4% for new, now prevelant, monocrystalline panels , so a reduction of CO2 used muat be reduced by 37.5%. The net effect is a 28% reduction, or about 32 grams of CO2 per kWh where the annual solar strength is 1,700 kWh (4.65 kWh per day).

All panels are believed to have a 25-30 year life, so a panel that produces more kWh in its lifetime obviously has a lower CO2 emissions rate per kWh. **Thus, in El Paso, Texas, a panel has embedded CO2 of about 22 grams per kWh, while the one in England has about 58 grams per kWh.** This is a year-round average. In summer the CO2 per kWh is roughly 20% less, and in winter roughly 30% more. Cost for the panels alone: According to Forbes good panels are at least $2.40 a watt installed, so that comes to $2,400 per KW, so depending on one’s location, $600 to $1200 per kWh per day, $1.64 to $3.28 per year, over 30 years 5.5 to 11 cents a kWh.

**CO2 savings using Rooftop Panels without batteries:**

For the calculations that follow I assume that energy use while the sun shines is 30% more than when it doesn’t shine. This varies by location and season^{4}, and of course on some days there is no sun at all, but this assumption will suffice here for these ballpark calculations. The energy available from the grid is 24 kWh per kW. Subtracting the solar hours from 24 and reducing the result by 30% we for El Paso we have 12.2 hours of grid use; for St.Louis, 13.93; for Cleveland 14.3; for London 14.8.

If, as is usually the case, the grid has flexible fossil fuel use, t it can use the surplus solar energy generated in summer and supply the energy needed to fill the solar deficit in winter. ** In this scenario, the entire amount of solar electricity generated by panels results in fossil fuel saved.** So, using yearly averages, for El Paso, for the percentage relative percentage of CO2 emissions we have (6.57 hours solar x 28 CO2 emitted per kWh + 12.20 hours x 330 grid CO2 emitted) divided by all grid 6.57 +12.20 x 330) =68%. In other words, a savings of 32% of CO2 emitted. **This is better than no savings, but only a small contribution to slowing global warming.**

For London the same calculation yields a savings of only 13%. *For southern Europe and the eastern United states, interpolating, the savings of CO2 may be about 20 percent.*

(If the grid cannot accept surplus electricity from the panels — for example if the utility has reached its limits on accepting non-baseload power — the savings will be less than calculated above— unless the system so little capacity that there is never wasted energy when the sun shines.)

**CO2 savings using Rooftop Panels with battery support **.

**These calculations assume that the objective is to have complete grid independence when the sun shines. This is a much more expensive alternative that does not have a payback, but it saves more CO2 than panels without batteries.** Twice as many panels must be purchased to get through the average winter night in El Paso, five times as many in London, as well as enough batteries to store 15 to 20 kWh worth of power. As an example of costs, a 13 kWh Tesla Powerwall battery and system in 2024 installed will cost about $12,000 per battery for two batteries, $24,000. Tesla only warrants 70% capacity in the 10 year battery guarantee. So for full capacity over the 10 years we need to multiply by 1.43. Furthermore, summer peak usage of energy for air conditioning exceeds the average I used to calculate CO2 above by 30%, so we must multiply by 1.3 to store the energy, as air conditioning use peaks hours later than the mid-day sun. Thus we need 86% more batteries than it seems at first, that is 2. We divide this by 10, 365 and 12, for a cost per average kWh stored of $ 0.55 per kWh.

As noted above, panels produce only 55% as much energy in winter, but usage is about 75% of summer on average in the USA or Western Europe (a greater percentage in snow country). For the environment, the best CO2 savings will occur if at least 1.3kW of panels are used rather than 1.0 kW for average conditions, but 1.5KW is better, so that there is no need to draw on the grid on winter days with sub-par sun. Thus, for 1 kilowatt face pace we have panel emissions of 42 grams of CO2.

**Lithium Ion Phosphate Batteries are the most economical a battery with the lowest CO2 emissions.** ** It takes about 2,043,000 grams of CO2 to produce a 12 kWh battery.** (See long analysis here: https://yourenergyanswers.com/environmental-impact-solar-batteries/.) I make no additions to this for the CO2 embedded in the inverter and other electrical components.

The calculations depend upon the system and the number of batteries. I am using a Tesla Powerwall as an example. Using the above numbers , since El Paso needs on average 12 kWh of storage per day per kilowatt average use, we multiply the number of batteries by 1.86 (as calculated above), that is by 2, so the system has caused the emission of roughly 4,086,000 grams of CO in production. The battery is good for 10 years, so we divide this by 3,650 for grams of CO2 per day and by 12 for KWh stored per day, which equals 93 grams of CO2 per kWh

In El Paso we have total emissions 99 + 42 = 141 grams of CO2/per kWh and a cost of $0.55 + $ 0.14 for the panels = $ 0.69 per kWh. This is, not economic, even with a nice subsidy!

However, grid energy is still needed, as there are days without sun. El Paso has 43 days of precipitation per year and 25 very cloudy days. Arguably, therefore, there are 65 days with 330 grams of fossil fuel. However the sun availability data takes these into account. So we should increase the solar incidence by 365/300 = 21%, which reduces the panel CO2 use per kWh to 34 grams, the system to 133 grams. Therefore the annual CO2 emissions per kWh are (65 days x 330 grid CO2 emissions plus 300 days x 133 solar system emissions) / 365 = 42330 or **168 grams of CO2 per kWh**. **That is a saving of 49% compared to natural gas.**

*If we undersize the system so that it only operates 80% in average, spring and fall, conditions, the cost per kWh will be about one half of the above, $ 0.34 per kWh. This is still uneconomic, even in El Paso. With a 3o% subsidy on the equipment cost, it still will cost more than the average El Paso retail electricity rate of $ 0.14 per kWh. The energy savings will * be reduced to around 40%.

##### CO2 savings with Utility Scale solar power.

*An extensive review of utility scale solar is* here^{5}:

Utility solar power is produced with normal panels, or by focusing the sun with lenses or mirrors, and collecting the energy either with solar panels or with with molten salts that produce steam to drive turbines. Installations can store the electricity in batteries or by means of the heated salts.

Many r*ecent versions of these thermal plants with day-long storage produce about 35 grams of CO2 per kWh, which is much better than rooftop solar in full sun locations. This obviously does not count the days with no sun. And the storage technology has to be much cheaper than lithium phosphate batteries.*

**Above: Solar Farm of 250 Acres in Datong, China, Image source: Forbes.**

The 1 square kilometer (250 acres) Chinese array of panels pictured above, apparently without battery backup, is rated at 100 megawatts^{6}. Hence it is 10,000 square meters per megawatt, which produces 6.57 average mWh per day, and would provide 59,951 mWh of electricity over 25 years. Hence roughly **16,700 square meters are required per 100,000 mWh.**

**Below: Gemasolar power plant**

For a mirror molten salt system, the Gemasolar plant near Seville is interesting: https://www.renewable-technology.com/projects/gemasolar-concentrated-solar-power-seville/. Using heliostats, it has 24 hour storage, produces 19.9 megawatts for each of 24 hours on 270 days a year, and saves about 30,000 tons of CO2 per year. I calculate the stated savings as 171 grams per kWh, which suggests emissions of about 160 grams of CO2, if the comparison was combined cycle gas. This is just over a 50% savings. The Gemasolar plant cost $358 million dollars In equivalent 2020 US$, which works out to about $ 013 per kWh. It occupies 1.85 square kilometers. So we have 19.9 x 24 x270 x 25 or 3,223,800 mWh over an estimated 25 year lifetime., or **57,000 square meters per 100,000 megawatt hour**

- https://onlinelibrary.wiley.com/doi/full/10.1111/j.1530-9290.2011.00439.x. ↩︎
- https://valveandmeter.com/blog/marketing/solar/solar-panels-made-in-usa-vs-china/ ↩︎
- https://group.met.com/en/mind-the-fyouture/mindthefyouture/natural-gas-vs-coal. ↩︎
- see https://www.eia.gov/todayinenergy/detail.php?id=42915) ↩︎
- https://www.sciencedirect.com/science/article/pii/S2451904923000239 ↩︎
- https://www.targray.com/media/articles/solar-project-types ↩︎