Truth in labeling: Solar multiple vs. capacity factor

It is natural to discuss a solar plant in terms of its rated output (i.e., peak electrical power,) but this often gives a false impression of the plant's economic value. For example, a utility might expect a new coal-fired plant to annually generate electric energy equivalent to its producing at full power 20 hours per day (capacity factor = 20/24 = 83%.) A solar plant in a desert climate will, over the course of a year, only produce energy equivalent to its producing at full power about 6 hours per day (capacity factor = 6/24 = 25%)

With energy storage a solar plant can operate with a higher capacity factor (saving money on some aspects of the plant) and making its rated output more directly comparable with a conventional plant. In a simplistic calculation, a 6 hr/day solar plant can become an 18 hr/day solar plant if we divert 2/3 of its output to storage. That is, by later withdrawing the stored energy we can have two more 6 hr periods of full power operation, giving a total of 18 hr/day. Our hypothetical solar plant would be said to have a capacity factor of 75%, 12 hours of storage, and a solar multiple of 3 (i.e., the ratio of its rated power without storage to its rated power with storage.)

In the real world, the above calculation would require a computer simulation, but we can borrow some real world numbers from Gemasolar, a thermal solar plant in Spain, which has 15 hours of storage and a 75% capacity factor. For obvious reasons, solar plants with a significant amount of storage prefer to advertise their annual electricity production rather than their rated power. From Gemasolar's stated annual production of 110,000 MWh/yr, and stated capacity factor of 75%, we can calculate that its rated power is:

110,000 MWhr/yr * (1/0.75) * (1/8760) yr/hr = 16.7 MW

Gemasolar has 304,750 m² of mirrors, so its rated power comes to 55 w_e/m² of mirror area.

Gemasolar and the Ivanpah thermal solar plant differ in detail (and Ivapah has the better solar climate,) but it is relevant to note that Ivanpah has three units rated 123 MW + 133 MW + 133 MW = 389 MW total, no storage, and 1,079,232 MWh/yr annual output—a capacity factor of 32%. In total, Ivanpah has 2,600,000 m² of mirror area, so its rated output of 389 MW comes to 150 W_e/m² of mirror area. That suggests that Gemasolar's solar multiple is about 150/55 = 2.7

The conclusion here is that solar plants without storage should be de-rated by approximately a factor of three before being directly compared with conventional fossil-fueled plants on the basis of rated power.

Capacity factor and hours of solar storage

The Gemasolar plant in Andalucia, Spain operates at an annual capacity factor of 75% using just 15 hours of thermal storage.

The 17 MWe Gemasolar power tower in Fuentes de Andalucía, Spain is designed to operate at an annual capacity factor of 75%, and has run continuously for as long as 36 consecutive days. This remarkable accomplishment is achieved with just 15 hours of thermal storage. Clearly 15 hours of thermal storage is about the right amount for a solar plant!

Here are some statistics for Gemasolar gleaned from the National Renewable Energy Laboratory's site.

Projected annual output: 110,000 MWhr/yr = 12.6 MWe  annual average.
Rated output  (calculated from the 75% capacity factor): 16.7 MWe rated. 

Output per mirror area (304,750 m2) :
       41 We/m2 annual average,
       55 We/m2 rated.  

Land yield (1,950,000 m2; mirror/land ratio = 0.156):
        6.4 We/m2-land annual average,
        8.6 We/m2-land rated

The 15 hours of storage based on 40% thermal efficiency is:

15 hrs * 3600 s/hr * 8.6 We/m2-land * 1/0.40 = 1.2 E6 Jthermal/m2-land

A plant with telescopic heliostats and glass-melt storage would have some advantages over Gemasolar. Telescopic heliostats can be packed much more closely, increasing the mirror/land ratio to around 0.70, increasing land yield about 4.5 times that of Gemasolar. Also, because the glass melt transfers its heat to hotter steam (608°C vs. 565°C) the steam cycle efficiency can be greater, about 46% thermal efficiency as compared with 40%, a factor of 1.15 .

Now, the same Gemasolar statistics if rebuilt on the same land with telescopic heliostats and glass-melt storage:

Projected annual output: 110,000 MWhr/yr  * 4.5 * 1.15 = 65 MWe  annual average.
Rated output  (calculated from the 75% capacity factor): 87 MWe rated. 

Output per mirror area (304,750 m2 * 4.5 = 1,370,000 m2) :
       41 We/m2 * 1.15 = 47 We/m2 annual average,
       55 We/m2 * 1.15 = 63 We/m2 rated. 

Land yield (1,950,000 m2; mirror/land ratio = 0.156):
        6.4 We/m2 * 4.5 * 1.15 = 33 We/m2-land annual average,
        8.6 We/m2 * 4.5 * 1.15 = 45 We/m2-land rated.

The 15 hours of storage for the rebuilt plant becomes:

15 hrs * 3600 s/hr * 45 We/m2-land * 1/0.46 = 5.3 E6 Jthermal/m2-land

Plant Bowen in Euharlee, Georgia, is the largest coal-fired plant in the USA. It has four 800 MWe units, giving an aggregate rating of about 3.2 GWe. A telescopic heliostat / glass-melt power plant in Andalucia with 15 hours of thermal storage, having the same rated output of Plant Bowen, would occupy:

3.2 GWe-rated / 45 We/m2-land rated = 71 E6 m2,

or a circle 4.8 km in radius. The height of the central optics will be about 1/14 the field radius, or 340 m. This is about 11% higher than Plant Bowen's two 305 m smokestacks.

Plant Bowen, 3.2 GWe,