Solar Energy, Wind Power, Intermittency, and Storage

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In ordinary conversations about renewable energy, the issue of energy storage is often overlooked. Renewable sources generate energy on their own schedules, not customers' schedules. The difference must be met either by backup energy supplies or by energy storage. This article describes some storage calculations in the absence of fossil-fired or nuclear sources. The calculations can be downloaded from here.

This is a plot of electricity generation for the US. This writer doesn't have data for any other countries and wouldn't presume to offer advice if he did.

[DOE]

For the rest of this analysis, the average generation for the years 2003-2007 will constitute the model year.

First, compare the demand curve with the availability of wind energy. Wind energy is approximately proportional to the cube of wind speed. Density is also a factor, and there is considerable mismatch at very high and very low wind speeds, but those differences won't change the conclusions. This analysis is based on wind-speed cubed.

The data show wind speeds for 265 cities. We have deleted cities with low winds or high differences between high-wind and low-wind months. We also have deleted Alaska cities, owing to their unique characteristics and their separation from the US power grid. 244 cities are left.

[NOAA]

Clearly, wind energy doesn't match electricity demand well. Next, compare electricity generation with solar potential. Cities with poor solar characteristics were deleted from the data, leaving 221 out of 238.

[NREL]

So we see that solar energy matches the electricity demand somewhat better. For our first cut we shall calculate the maximum amount of solar energy that can be generated and used within a month, and we find that 80.6% of the yearly demand can be met with solar energy on these terms. Now we can consider the remaining demand after all that solar energy is accounted for.

Now we can compare the remaining demand with available wind energy.

The calculations show that 200 billion KWH of storage is required.

We can do the same calculations for other shares of supply from solar energy, with the results shown here:

Our calculations show that the storage requirement ranges from 141 to 386 billion KWH.

There is no way to store that amount of energy. In fact, we'll have to devise a fictional example to illustrate the problem.

Imagine that a lake exists, named Upper Lake Fead, which is equal in size to Lake Mead. Lower Lake Fead is the same size and is located at the bottom of Foover Dam, which is identical to Hoover Dam. However, all the water in Upper Lake Fead can drain through the water turbines.

Lake Volume = 30,000,000 acre-feet

Average head at dam = 520 feet

If the efficiency were 100%, then

  Energy = volume x pressure = volume x head x weight-density
         = 30,000,000 acre-feet x 43560 sq-ft/acre x 520 feet x 62.4 lb/cu-ft
         = 4.24 x 10^16 ft-lb
         = 16 billion KWH

We'll set the turbine efficiency at 85% and account for pump inefficiency by upsizing where necessary. Thus, Upper Lake Fead is good for 13.6 billion KWH.

So we have calculated that the US would need between 10 and 28 Foover Dams, each with Upper and Lower Lake Feads, depending on how much electricity is generated with solar energy. There are, in fact, no Foover Dams and no locations for building any.

The Dimensions of the Challenge

Most people don't understand the scale of the energy we use. This article will try to put it in perspective. The data will apply to the United States; nationals of other countries will have to interpret it for themselves. Generally speaking, though, nationals of other advanced countries will face challenges of the same scale or higher and those living in developing countries will increasingly find themselves in the same dilemma.

We will compare the different non-fossil energy sources that have been proposed with respect to their capabilities.  Where appropriate, we will compare the land areas required for each with the land area available.

Electricity

First, consider the amount of electricity the US uses, a total of just over 4 billion MWH/year.[source]

Wind

What really limits wind power is the small amount of storage available; hydroelectric dams can treat a small part of their capacity as short-term storage for wind power.  For the purpose of this calculation, we shall pretend that the limitation doesn't apply but we'll discuss storage later in this article.

Currently, typical wind-turbines on wind farms are sized at 1.5 MW, with a rotor-tip height of 450 feet and a rotor diameter of 231 feet.[source][source]. Allowing a generous load factor of 0.35 [source], each turbine yields 4602 MWH/year, so 869,000 turbines would be required. The minimum turbine spacing recommended is five times the rotor diameter [source], so each 1.5 MW turbine requires (5 X 231 ft)^2 = 1,334,025 feet, or 0.048 sq mile.

To provide all the electricity the US uses would require more than 41,720 square miles.  That would be a strip of land 40 miles wide running from the Montana/Canada border to the Arizona/Mexico border. To get good efficiency, a strip 60 miles wide would be needed.

Solar

Solar energy has the same storage limitations as wind power, but we still shall pretend that the limitation doesn't apply.

For the US, an average insolation would be around 5.5 KWH/m^2/day[source], or 2 MWH/m^2/year.  Allowing a generous 20% efficiency[source], the output would be 0.4 MWH/m^2/year.  To provide all the electricity the US uses would require 10 billion square meters or 3861 square miles of solar panels.  That would be a panel 1-1/2 miles wide running from San Diego to Boston.

Nuclear

Nuclear plants are operating at about 90% capacity factors.[source] 

However, new ones will run somewhat lower, so an average capacity factor of 80% will be assumed. 

For 1000 MW power plants, 571 would be required to provide all the electricity the US uses, compared with 104 that currently are in operation.

Up to now, this discussion has ignored the difference between peak power demands and gross power generation.  In the case of solar and wind power, it didn't matter because neither can reliably supply energy at any time, let alone meet peak demands.  Nuclear power is available at all times, though, so peak demand can be met.  The current US electric capacity is about 890,000 MW[source], so about a thousand 1000-MW power plants would be required, or a smaller number of larger plants.

Motor Fuels

The US uses about 140 billion gallons of gasoline per year.[source]  Since ethanol has only 70% of the energy content of gasoline[source], at 439 gallons per acre[source], the US would have to plant 456 million acres, or 713,000 square miles in corn to displace gasoline with ethanol.  That is about one-fourth of the area of the 48 contiguous US states.

The US consumes 63 billion gallons of diesel fuel per year.[source]  The land area required to grow enough soybeans to displace the petrodiesel with biodiesel, at 63 gallons per acre[source], would be one billion acres or 1,563,000 square miles, about half of the area of the 48 contiguous US states.

These calculated land areas seem too high to be correct, but they are in line with calculations done by others.  For example, this analysis finds that, if all vehicles were diesel-powered, the land area required would be 58% of the US including Alaska.  Another calculation shows that if all the corn and soybean crops in the US were converted into biofuels they would replace just 12 percent of the gasoline used and just 6 percent of the diesel fuel.

Of the land in all of the US, only 18% or 650,000 square miles is arable[source], and most all of that is being cultivated for food and fiber.  Also, the calculations shown above assume that all the land would have the same yields as the prime farmland currently under cultivation and that there would be sufficient water for irrigation.  Neither of those conditions is true, of course, so plainly there isn't enough land.

Clearly, biofuels won't provide much liquid fuel.  There is a possibility that these land requirements can be reduced by two thirds if hydrogen is injected into the biomass during processing.  For example, 0.77 gallons of biodiesel can be produced by adding 1 kg of hydrogen[source], which requires 39.3 KWH of energy to produce from water.  The biodiesel equivalent of US diesel consumption is 70 billion gallons per year; to produce enough hydrogen would require 2.75 trillion KWH per year.  The fact remains, though, that biofuels can only be part of the solution.

For a long time, fuel cells have been the holy grail in the quest to free the world from fossil-based motor fuels. The barrier seems to be the catalyst; platinum so far is the only material that works. Not only is it very expensive, several thousand dollars per vehicle [source] but if fuel cells drove up the demand then the cost would be even higher. There also is the unsolved problem of storing enough hydrogen on board for a reasonable driving range. But suppose these problems could be overcome.

As a rough estimate, let's say the amount of hydrogen needed would be the energy-equivalent of 100 billion gallons of diesel fuel per year, chosen mainly because it's a round number about half of the total of gasoline and diesel fuel: 50 billion gallons probably is too little and 150 billion gallons probably is more than necessary.  The heat value of diesel fuel is about 38 KWH/gallon[source], so our energy equivalent is 3.8 billion MWH/year.  For our rough purposes, this is the same as our current electrical usage. 

Unfortunately, the process for converting water to hydrogen at normal temperatures is less than 30% efficient. So, the electricity required would be more than three times our current electrical usage.  To generate that much electricity with solar panels would require a panel 5 miles wide running from San Diego to Boston.  To generate the electricity with wind turbines would require a strip of land 130 miles wide running from the northern Montana border to the southern Arizona border with 2,870,000 turbines, all rated at 1.5 MW.

It is possible to produce hydrogen efficiently in a thermochemical process, using nuclear-generated heat.  The nominal efficiency is over 45%.[source] But the heat left over from the conversion can be used to generate electricity, so the hydrogen production is nearly 100% efficient.  The nuclear plants can produce electricity and hydrogen at the same time.  More power plants aren't required because the additional heat will be available during off-peak hours.

Currently, hydrogen storage is the weak link.  It's practical only for local transportation, but intense research is underway.

Bulk Energy Storage

Pumped Energy Storage
The purpose of this admittedly rough calculation is to estimate the amount of pumped storage that would be required if wind power provided all the electricity the US uses.

First, consider the amount of electricity the US uses, a total of just over 4 billion MWH/year.[source] On an average day, not a high-demand day, that's 11,000,000 MWH/day.

We have to make up a fictitious example because there aren't any real examples. Suppose we use Lake Erie, Niagara Falls, and Lake Ontario as our pumped-storage, pretending that we could increase the capacity of the turbines enough.

We know that Niagara Falls' power capacity is 2400 MW, using 375,000 gallons/second of water.[source] We also know that the capacity of Lake Erie is 484 cubic kilometers of water, which is 128,000 billion gallons.[source] At present, the falls could produce 57,600 MWH/day, using 32.4 billion gallons/day. So, to serve all of the US for one day, the water required would be (11,000,000/57,600) X 32.4 billion gallons = 6,187 billion gallons, which is 4.8% of Lake Erie. That means that Lake Erie could provide storage for three weeks.

How much storage would be required? Looking at data for all of the US, we see that, with surprising consistency, low-wind months have average speeds about 70% of the average speeds for the high-wind months.[source] Based on the cubic relationship between wind speed and power, we would expect seasonal variations in energy generation of around 0.35 to 1, so the average would be something like the rated capacity times (1 + 0.35)/2 or 0.675. Conversely, for the generation to equal the load, the rated capacity of the wind farms would have to be the yearly average load divided by 0.675, or multiplied by 1.48. Since we can expect the generation in a slow-wind month to be 0.35 times the rated capacity, the storage capacity would have to be about 1 - 0.35 X 1.48 (= 0.48) times the yearly average load times the length of the low-wind period.

21 days' capacity would be good for 21/0.48 = 43 days of low winds. But low-wind seasons last longer than 100 days.

The power grid allows for some redistribution of power from areas experiencing high winds to areas with low winds. But the wind-variation patterns cover large regions so there are limits to what can be achieved. Allowing for redistribution still leaves a need for more than three-weeks' capacity.

To provide adequate pumped-storage capacity for wind power as the main electical-energy source for the US would require damming canyon streams to create twin lakes around the country equal in volume to something bigger than Lakes Erie and Ontario. Even if enough locations could be found, the projects would not be permitted because of the high ecological cost.

Compressed Air
Another scheme that sometimes is mentioned is storing compressed air in caves. There is a facility in Huntorf, Germany that we can use for an example.[source] It compresses air to 1000 pounds per square inch pressure.

The data show that it stores 3 x 290 = 870 MWH of energy and the cave volume is 310,000 cubic meters.

For one day of electricity storage for the US, the volume needed would be

      11,000,000/870 X 310,000 = 3.92 billion cubic meters = 138.4 billion cubic feet.

Suppose a cave had an average cross-section of 50 ft X 50 ft = 2500 sq ft.

For one day's electricity storage, the cave's length would have to be 138.4 billion / 2500 = 55.34 million feet = 10,490 miles. Granted that most big caves have never been surveyed, it's still safe to say that there aren't ten-thousand miles of caves in the US. So there is no possible way enough energy could be stored to see the country through 100 days of low winds.

Conclusion

Barring some startling new energy development, what all this shows is that solar panels and wind turbines won't provide major parts of the world's energy; biofuels can only be important if a large amount of hydrogen is available.  If global warming is to be avoided, the only two technologies that can provide sufficient energy are nuclear and hydrogen.

In the next article we'll look at the obstacles to solving this problem. In the article after that we'll see a scheme for reducing the consumption of fossil fuels.