It is often claimed that small-scale renewable energy, such as solar photovoltaic panel arrays, will fill an important future energy niche by providing much-needed electricity to developing nations and other remote regions (such as the outback of Australia). That’s a seemingly reasonable argument, but how do the numbers stack up? Below, Gene Preston (SCGI member) provides some easy-to-follow calculations (currency is in US dollars/cents). The results might surprise many:
A friend of mine at the University of Texas and I were talking about his desire to develop a presentation for educators in Africa to use in estimating energy costs. He has just 3 hours for his presentation. He wants the teachers to be able to do the economics calculations themselves. I suggested he narrow down the discussion to just a comparison of solar versus small scale nuclear. Here’s what I came up with:
Solar – Lets go low tech with fixed solar panels. The cost is $8/watt (W) and runs about 14% of the time (its capacity factor). You will need energy storage, which costs $1/W + $.4/Wh (that is, 40c per watt hour**).
Lets say that we develop a solar system to serve a 5 kW peak load with an average load of 1 kW. The daily energy demand will be 24 kWh and peak load is 5 kW. This could be a few houses or a small school with some PCs. To produce the average amount of energy needed will require 1/.14 = 7.14 kW, so lets say 8 kW just to put in a little extra energy production factor. The 8 kW will cost $8/W (for 8000 W) = $64000. The energy storage system will cost $1/W (5000) = $5000 for the electronics and switchgear plus $.4/Wh (24000) = $9600 for one day’s energy usage. I would double this and install two days of storage just to be safe, which would cost $19,200.
Therefore the cost of the 5 kW peak demand solar system is:
$64000 for the panels (only half this cost is the PV array)
$5000 for the storage system electronics
$19200 for the batteries (2 days storage)
$88000 for the entire system. (see what I mean about this being a rich person’s energy source?)
Let’s calculate the cents per kWh energy cost. Assume a loan at 6% annual interest rate to pay for it. Assume the system has a 20 year life.
A = PW [(i)(1+i)^n] / [(1+i)^n-1] where A is the annual payment, PW is the present cost of the system, i is the interest rate of .06, and n=20 years.
Then A = (88000)(.06)(1.06)^20 / [1.06^20 - 1] = .08718 (88000) = $7672.24 annually.
The energy produced annually is 24 kWh/day (365 days/y) = 8760 kWh. The cost per kWh = 767,224 cents per year / 8760 kWh per year = 87.6 cents per kWh. (first wow — that’s expensive!)
What about if we instead generated this energy from small nuclear reactors? First, some examples/references:
The Pebble Bed Modular Reactor would have been in South Africa but there is local opposition
This is an interesting discussion of micro reactors, especially the Russian Navy’s design
This information paper from the World Nuclear Association shows the huge number of small-scale reactor technologies being considered
Here is an IEEE paper on small nuclear (2, 5, 10 and 20 MW reactors)
The objective of many of the above references is to get the nuclear power cost down to about 10 cents per kWh. Suppose we could buy into nuclear at $5000 per kW (that’s the estimated cost of the Babock & Wilcox small nuclear plant [called 'mPower'], for a 125 MWe plant). The 1 kW of nuclear power portion of the small plant would run all the time so one kW would have an average energy based on the calculations for the solar plant. All we have to do is replace the $88000 with $5000 in the previous “A =” calculation.
Therefore the small nuclear program energy cost is .08718 (5000) (100) / 8760 = 5 cents per kWh. (second wow — that’s low cost!)
However we will need some peaking power to get 5 kW peak load. We can use the battery storage system to get the peaking power. We only need 4 kW since we will have the 1 kW nuclear running all the time. Also, the energy storage need only be about 4 hours at the most at 4 kW (conservatively). The peaking power using nuclear energy is $4000 for electronics + .4 (16000) for batteries = $10,400. Note that the peaking power system costs twice as much as the base load nuclear generation. The total cost is about $15,000 and the energy cost is about 15 cents per kWh.
This small nuclear + peaking system is only about 18% the cost of the solar + storage system.
This is an example of how anyone can, fairly easily, go through the economics calculations for solar and nuclear. Such an exercise would probably an eye opener for them, and dispel the myth that solar is ‘free energy’ or even a cheap source of power. But how are they to afford any type of power plant if they do not have industries that need power and produce income for them?