Math That Matters (Part IV—Solar Power for the U.S.)

(Part A)

How big a solar array is necessary to provide all the electricity currently used in the United States?
Renewable energy (particularly, solar and wind) use is way up over the last 20 years, both globally and in the United States. Annually, rates of growth for PV (photovoltaic) solar and wind are both above 20% over this time, with solar being closer to +40%. This amazing growth appears ready to continue as more and more areas of the world are looking to install solar due to its many benefits (ref 1). However, some believe that solar would have to cover huge expanses of land in order to make a significant contributor to our energy portfolio. Let’s take a look at this belief by asking a simple question, “How big a solar array is necessary to provide all the electricity currently used in the United States?”

Well, there is some background information and a few assumptions that one needs to make in order to calculate this.
First, how much electricity do we use in the U.S.?

Looking this up, we find:
(1) 12.6 Q = 3,704 PWh (ref 2)
(1 Q = 1 Quad BTU = 294 PWh, where 1 PWh is 10 to the 12th power (or 1,000,000,000,000) Watt-hours)

Next, we need to know how much electricity is produced by a typical solar panel. This requires other information as well:
(a) Power rating for solar panel = 345 W
(b) Size of solar panel (61” x 41”) = 17.37 square feet
Thus, Maximum power output = (a)/(b) = 19.9 W/sq. ft

Note: From these values one can compute an efficiency for the panel (which is typically between 15-20%), but one need not calculate the efficiency for our purposes.

Since no panel produces maximally (due to inverting DC current to AC current, losses in wires, snow/dust on panels, etc.), a “de-rating” of 75% is typically used.
(c) Power output expected = Max. power * de-rating = 19.9 W/sq. ft * 0.75 = 14.9 W/sq. ft

Now we need to consider how many hours of sunlight there will be for this panel. Typically, this is done by computing the “average” number of “full-sun” hours per day a panel would be expected to receive at a location. In the U.S., most locations range from 3.5-6.5 hours. We’ll take 4.5 “full-sun” hours to be conservative (central IL has these types of values).

Thus,

(d) True electricity provided = Power output expected * “full-sun” hours (daily) * days in year
(2) = 14.9 W/sq. ft * 4.5 hrs/day * 365 days/year = 24.5 kWh/sq. ft

Now, we can determine how many square feet we need to provide the electricity for the entire nation of the United States:

Size of solar array = Electricity usage (nation)/Electricity production density
= (1)/(2)
= 3,704 PWh/24.5 kWh per sq. ft
= 151,184,000,000 sq. ft

Wow, 151 billion square feet. That’s huge, isn’t it? Let’s convert this to square miles:

# square feet in a square mile => 1 sq. mile = (5280 ft) * (5280 ft) = 27,900,000 sq. ft

So, 151.2 billion square feet is __X__ square miles; where,

X = 151,200,000,000 sq. ft/(27,900,000 sq. ft/sq. mile) = 5418 sq. miles

But, how much is 5,418 square miles?
Just about a squared area with 74 miles on a side!

The area of the state of Illinois is ~58,000 square miles. So, 5,418 square miles is ~9.3% of the state! It is also only 25-times the combined size of the 10 largest airports in the United States. This area, again, if covered with solar panels, would be produce enough electricity to power the entire nation!

In conclusion, the belief that solar panels sufficient to power the U.S. would have to cover a huge amount of area is just plain wrong! Wondering why this information isn’t widely distributed? Well, are you going to distribute it or not? If not, why not? This might provide you part of the answer as to why it isn’t widely known.

(Part B)

Now, what if we wanted to produce all the energy resources we use, not just electricity, with solar PV power? Understandably, most things that use fossil fuels now are not currently able to use electricity (as in, most of the cars/trucks on the road are not yet electric), but most could be made to use electricity if it was available. So, then, if we need to produce 97.3 Quad (not 12.6 Q which is the current electricity demand alone), we’d need ~7.7 times (or 97.3/12.6) more land than stated above. However, since our fossil-fuel dominant energy economy currently requires 37.5 Q of energy to produce 12.6 Q of electricity (due to the inefficiencies in the use of such sources), we actually wouldn’t need to use this wasted energy (or 24.9 Q (37.5 Q – 12.6 Q)) at all; this is a HUGE understated benefit of moving towards solar energy sources. Thus, we would need only to produce 72.4 Quad which would require 5.7 times more land than calculated in Part A, or ~31,000 square miles. This amounts to about 11% of the land area of the state of Texas, not much land considering the size of the United States. In fact, since the area of the U.S. is 3.8 million square miles, we would need to cover less than 1% of the U.S. land surface with solar PV in order to produce all the energy we would need in a fully “electrified” nation! (A recent study by the National Renewable Energy Lab (NREL) found that we could provide 1,432 TWh of electricity by putting solar panels on suitable buildings in the United States. This would be enough to provide 39% of our national electricity needs and 7% of our national energy needs!; see report.)

Caveats: The above calculations only relate to solar PV. The future renewable energy system, that will become dominate in the 21st Century, displacing almost all fossil fuels, will rely on wind, geothermal and hydropower as well. In addition, the need for the world’s poor to use more energy than they do now (in order to live fully actualized lives) will require greater amounts of energy to be produced. Additionally, as the U.S. is one of the more wasteful energy users, its consumption could easily decline (perhaps by 50%) without any detrimental impacts. These factors are important when looking at the future land needs of the entire energy system.

the “efficiency” trap and RE’s benefits

Efficiency is an overused/misused concept. It is just a measure of the closeness to maximum energy exchange of a process. So when you burn coal, the best modern engineering can extract from this “burn” is ~33% (given conventional systems) because to get “electricity” (the energy we want) from the coal we have to create steam which then spins a turbine (and in each step there are losses in conversion). Geothermal systems are actually less efficient in converting heat to electricity (see article, ref 1; though much more efficient in extracting heat, as in, geothermal heat pumps which are much better than conventional gas-powered furnaces). And solar arrays are in the same ball park as geothermal systems with efficiencies of ~15-20%.

However, the big difference between the coal and the others is the fact that while the sun provides us light for free and the Earth provides us heat for free (24/7 as well), the coal comes by way of extraction from distant areas. (Solar photovoltaic panels and geothermal components require the extraction of materials from distant lands as well, but once this initial extraction is done and manufacturing is completed, they operate for 25+ years.) Also, sun and Earth heat will continue into the distant future while coal is limited in quantity (as it takes too long to replenish). Additionally, when one burns coal, waste products are produced, many which are quite toxic to humans and life, most notably, mercury, PAHs and sulfur dioxide (ref 2).

Thus, while efficiencies of renewable energy forms may be less efficient than fossil fuel forms, the key benefits derived from RE’s are:
(1) the pollution created in using them (over a 25-year cycle) is so much less;
(2) the RE energy sources are on-site (or close by) at the point of use;
(3) the RE sources are plentiful and renewable.

Additionally, and importantly, given the nature of geopolitics right now, RE resources also create more jobs (ref 3) and can be more decentralized (which allows people to have more control over their operation and production; I say “can” because this requires forethought and intentionality regarding democratic input and collective ownership, something still missing from most RE installations).

Given all of these benefits (here is the Union of Concerned Scientists’ take on these, ref 4), investors are finally taking notice in a big way and, as expressed best by a recent (April 2016) Bloomberg article, “Wind and Solar are Crushing Fossil Fuels” (ref 5). So, don’t be squeamish at all advocating vehemently for RE creation/expansion in your neighborhood/community. Everything is now on the side of RE (economics, environmental concerns, and social/health factors). The time is right, to “flip the switch.”

only two problems?

If we could solve only one problem, which problem should it be?
This is a question that I often get asked and it is one that I have pondered on my own as well. It presupposes that there is one problem that, if solved, could lead directly to the solution of other problems. Well, I haven’t figured what that one problem is, but I can tell you that if we solve two problems, we’d be well on our way to tackling most human challenges.

What must you do, each and every day? Eat food and drink water. So, assuming that these things were provided to you, you could get on with your “life.” What else would you need? Well, obviously, shelter of some kind. Would that be enough? Water, food and shelter may be enough to live, but there are other things that have become part of our “civilized” human condition. Most importantly among them is energy. We need energy to survive and to live a modern lifestyle requires quite a bit of it—to run our refrigerators, our computers, our water heaters, our cars and lawn mowers. Clearly, any future that looks anything like the present would require sufficient amounts of energy.
Here is the rub. Despite the fact that at least a billion people on Earth have sufficient access to food, water, and energy, many more do not. And while that is horrible situation (and how can we celebrate everyday things when so many go without, especially when there isn’t really any good reason why they don’t), the question I would like to examine here is, “How key are food and energy to our collective present and future?”

Clearly, if nearly a billion people on Earth suffer from chronic malnutrition (ref 1), “we have a problem Houston.” Obviously, every effort imaginable should be made to make sure that this problem is eradicated. A comparable but less recognized evil is the energy poverty that exists in the world today. Without basic allotments of energy, many people around the world cannot satisfy basic needs, such as, cooking food, heating/cooling their homes, or perform important tasks at night; consider that 1.4 Billion people do not have access to electricity (ref 2). Even in places where some energy is available for such things, it is often dangerous (e.g., kerosene) or detrimental to local environments (e.g., firewood). Without sufficient food or energy, more than 1,000,000,000 people suffer unduly.

Obtaining food and energy isn’t just an issue for those that don’t have much of them but also to those that live in areas where food and energy is plentifully produced but improperly distributed. How much current conflict in the world is due to “resource wars”? As these two sources indicate (ref 3, ref 4), many (if not most) of the conflicts occurring right now have strong drivers in resource shortages. And these shortages are not getting alleviated much because the current unbalanced distribution is due to the increased commodification (and profit obtained) of these resources. And sadly, the $1.4+ trillion dollars spent each year on militaries (largely to protect/secure these resources) creates a huge financial well that leaves very little left for other critical needs (such as education, health care, etc.).

In closing then, if we were able to tackle the food and energy problems, we would likely be on our way to solving most of the world’s current problems. We have enough (to be clarified in an upcoming BLOG), we just must begin to share what we have and look at each other as “brothers and sisters” rather than enemies.