# Comparison of Nuclear Power Plants with Solar Tower Power

A recent LA Times article and the Brightsource Energy website give data on the Solar Tower reflecting mirror power sources currently being built.  Today the first two new nuclear reactors have been approved, and the cost for an 1.1 gigaWatt on an existing site given as $7 billion per reactor. Thus the nuclear plant costs$6.36 per Watt, although for a new design and not having built US reactors in 15 years, we expect significant cost overruns.  We give data for the Brightsource plants, and then scale them up to 1.1 gigaWatt in both peak power and then average power, for comparison.

The Bright source plants are brilliantly designed in computer guidance of mirrors to reflect the sun onto the hot water boiler in the tower.  They also have molten salt tanks to store energy for the peak usage hours around 5 pm and presumably to smooth out power gaps from clouds, along with a natural gas plant.  The mirrors are garage door size, 7.2 foot by 10.5 foot, or 75.6 square feet or 7.04 square meters.  There are 174,000 heliostats consisting of two mirror each for 347,000 mirrors arrayed over 5.5 square miles in total for the three towers, each of which is surrounded by roughly a large square of deployed mirrors.  Multiplying the number of mirrors by their size gives 2.44 million square meters or 26.2 million square feet.  The site takes up 3500 acres, or 152 million square feet, or 5.5 square miles.  The peak power of the site is 370 megaWatts, or 152 Watts per square meter of mirror.  The cost of the facility is $2.2 billion. This gives about$6 per Watt of peak power.  This can be compared to a recent estimate for utility size installed photovoltaic power of $4 per Watt. However, the solar thermal site can store power into the evening peak power usage times. The peak daytime power concept is useful for a source to replace natural gas or coal during the day, leaving some clean source such as hydro, geothermal, or nuclear for nighttime base power. The usual 24 hour yearly average of solar power is roughly one fifth of peak power, or a capacity factor of 20%. The NREL site quotes the “annual solar to electric efficiency” of this site as 28.72%, but I am not sure if that is the same as I mean above, or just the peak power efficiency averaged over a year, to be compared to silicon solar cells at 15%. For comparing the cost of solar to the total power that it generates for the cost of the facility, I will use the higher number of about 29%, and multiplying by its inverse of 3.45 times the$6 per Watt of peak power, it is roughly $21 per Watt of average 24 hour, year round power, and the total 1.1 gigaWatt site would cost$23 billion.

We also want to judge the size of a facility needed to equal a 1.1 gigaWatt nuclear reactor both at peak power and at yearly 24 hour average power.  The output of 370 megaWatts has to be scaled up almost exactly by a factor of three for peak power to equal that of a nuclear reactor.  This plant has two 100 megaWatt towers with steam turbines and generator, and one 200 megaWatt site with 5 towers feeding one steam turbine and generator, for a total of 7 towers.   The scaled up plant might have 21 separate towers, and a total of 522,000 or more than a half a million heliostats, or a million mirrors.  I don’t know if the total area needs to be scaled up by the same factor of three, but if it did, the facility would be 16.5 square miles in area.

We now scale the above numbers up by a factor of 3.45 to give the same average year round power of a nuclear reactor.  Such a facility might have 72 towers, 3.5 million mirrors, and might require 57 square miles.

The superheated steam will be at 538 degrees C, or 811 degrees Kelvin, and go into steam turbines, where it expands and cools, leaving a lower pressure past the turbine, and the pressure difference drives the turbine around.  Often there is a set of such expansions and turbines to get all of the energy out.  The rotating turbines are connected axially to a generator of electricity, commonly rotating at 3600 rpm.  Once the steam is cool enough to condense to water, it can be put back into the boiler to become steam again.  I am not sure if the final water temperature is run down to room temperature at 300 degrees Kelvin, or just below boiling at 373 degrees Kelvin.  Assuming room temperature, the thermodynamic maximum efficiency is eta = (1 – 300/811) = 0.63.  The NREL site quotes a “receiver outlet temperature” of 1050 F or 838 K, and a “receiver inlet temperature” of 480 F or 523 K.  This would give eta = (1-523/838) = 0.38.  This contradicts the statement of condensing to water.  It would be nice if both the NREL site and the Brightsource site were more specific in their numbers and what the numbers mean.  The tower is 459 feet or 140 meters high.