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.

Nuclear Energy Costs

Every responsible study has shown that nuclear electricity is as cheap as any of the non-fossil alternatives and is competitive with fossil-fired electricity.

For example, the International Energy Agency and the Organisation for Economic Co-operation and Development's Nuclear Energy Agency determined the costs as follows:

Cost per MWH in US Dollars

Discount Rate	5%	10%
Coal	25-50	35-60
Nat Gas	37-60	40-63
Nuclear	21-31	30-50
Wind	35-95	45-140
Micro Hydro	40-80	65-100
Solar PV	~150	200+

The University of Chicago compared several detailed calculations with a range of discount rates and summarized the results thus:

Cost per MWH in US Dollars

Coal	37-49
Nat Gas	56-68
Nuclear (assuming old designs)	65-77
Nuclear (assuming new designs)	36-55
Nuclear (assuming advanced-fuel designs)	57-64
Wind	55-77
Solar PV	202-308
Solar Thermal	158-235

A question that immediately presents itself is, why do the two studies give different numbers? The answer is that every study depends on assumptions, such as interest rates and fuel costs. Both these factors, and other factors such as taxes, pollution controls, and equipment lifetimes vary in time and place. This introduces an opportunity to do mischief, since a motivated commentator can pick-and-choose results to bolster his intended conclusion. These numbers only have significance if they're calculated on equal terms and only if they're read relatively, not absolutely.

A common argument being made now is that nuclear construction costs have risen so fast they have rendered nuclear plants too expensive to build. This argument is anchored on a report about some calculations made by Cambridge Energy Research Associates (CERA) that allegedly show a cost increase of 185% between 2000 and 2007. Imagine, an almost tripling of costs in seven years! However, CERA doesn't publish the results in a public forum; nor does it show the calculations so they can be verified. Indeed, there's no way even to know what methods it used.

It is true, though, that costs have risen strongly since China and India began their notable advances in material progress. These cost rises apply to all kinds of construction and, in particular, apply to alternative energy sources.

Here is some information on the cost of windpower construction, which has doubled:


And some data (Oct. 28, 2008) on solar-electric construction. It has essentially held constant, but at US$4700 per KW rated power or over US$20,000 per average KW, it still is hopelessly expensive. What this shows is that the pressure on material prices has kept solar energy from getting cheaper.
Finally, here is some information from Power Engineering International on nuclear construction costs, which shows a cost increase of 125%, not much different from the increase for windpower.


What all these numbers show is what energy analysts have been telling us right along. Nuclear energy is as cost-effective as any non-fossil energy source, even ignoring the intermittency problem of part-time energy sources. But if intermittency is considered, then the comparison widens. There aren't any practical ways to overcome intermittency, as shown here. But if there were some way, the economic and environmental costs would drive the total cost out of sight.

As the world grapples with this issue, one other point has to be considered. A new generation of nuclear power plants is being born. These new plants use passive safety systems so the active systems can be simpler, thereby reducing costs. Furthermore, they operate at higher efficiencies, lowering fuel costs. As shown in the University of Chicago data, these improvements make nuclear energy cheaper than any alternative other than coal.