Ivanpah Unit 1 specifications on a square-field basis

Ivanpah Unit 1 sits on a 1995 m x 1995 m square of land.

The previous post makes me think it is necessary to pro-rate the specifications of CSP power tower's over the area of the square of land they take out of use. Here are the specifications of Ivanpah Unit 1 on that basis.

Peak Rating of Units 1 + 2 + 3 = 392 MW

Electricity Generation Expected from Units 1 + 2 + 3 = 1,079,232 MWh/yr

Overall Capacity Factor for Units 1 + 2 + 3 = 0.314

Peak Rating of Unit 1 = 126 MW

Area of Unit 1's Square Field = 3,980,000 m2

Peak Rating of Unit 1 per unit of square field area = 31.7 W/m2

Levelized (100% capacity factor) rating of Unit 1 per unit of square field area = 0.314 * 31.7 w/m2 = 9.96 W/m2

U.S. per capita electricity consumption is 1400 W/person (at 100% capacity factor)

Per capita land claim for electricity (per Ivanpah Unit 1) would be 1400/9.96 = 141 m2 per person

According to page 1-3 of the environmental impact statement, the power tower is 140 m tall, and Unit 1 has 55,000 heliostats, each having 14.08 m2 of reflective surface.

Mirror area of Unit 1 = 14.08 m2 * 55,000 = 774,400 m2

mirror-area / square-field-area = 0.195

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Telescopic heliostat fields are expected to produce 3 times the land yield of conventional heliostats, thereby reducing the land claim to 47 m2/person, increasing levelized (100% capacity factor) rating to 30 W/m2, and giving a 75% capacity factor (representative of a plant with half-day thermal storage) rating of 40 W/m2—all on the basis of square-field area.

75% capacity factor rating for a 1600 m x 1600 m unit would be 102 MW, or 920 MW on a quarter-township.

For these numbers to hold up, the mirror-area/square-field-area of a telescopic heliostat field must be better than 3 x 0.195 = 0.585

Starting from a covering factor of 0.91, and losing another 0.02 of covering factor around the lamp means that achieving 0.585 overall requires an intrinsic fill of 0.585/(0.91-0.02) = 0.66.

Mirror/land ratios in solar power tower generating stations

Based on Google imagery, the heliostat field of Ivanpah 1 is very nearly a square, 1995 m on a side, with three corner truncations, giving a heliostat field land area of about 3,800,000 square meters. This unit has 53,527 heliostats each with a mirror area of 15 square meters, giving a total mirror area of 803,000 square meters. The mirror/land ratio is 0.21.

Based on Google imagery, the heliostat field of the Crescent Dunes Solar Energy Project is very nearly circular, with a diameter of about 2804 m, giving a heliostat field land area of about 6,200,000 square meters. This unit will have 17,170 heliostats, each carrying 62.4 square meters of mirror, giving a total mirror area of 1,070,000 square meters. The mirror/land ratio is 0.17.

The mean radius of the heliostat field (the radius of a circle having the same area as the field) is 1100 m for Ivanpah 1; 1402 m for Crescent Dunes. The tower heights are 140 m and 160 m respectively, giving mean field radius to tower height ratios of 7.9 and 8.8.

In what sense are telescopic heliostats telescopic?

A pair of binoculars focussed at infinity and aimed at the sun emit intense beams from the eyepieces.

Definition: A telescopic heliostat is a heliostat in which the emergent rays are increased in concentration and divergence.

A telescopic heliostat is not telescopic in the sense that it can throw a beam of sunlight farther. If that were the only consideration, a plane-mirror heliostat would be the best choice. A telescopic heliostat concentrates sunlight while keeping the emergent rays as parallel as possible—which is precisely the action of a telescope focussed at infinity. An inevitable consequence of the concentration, is that the emerging light rays are more divergent than a natural sunbeam, so beam spread from a telescopic heliostat is greater than from a conventional heliostat.

An optical cross-section of a telescopic heliostat shows it to be an afocal, off-axis, Cassegrain telescope. Both mirrors are parabolic.

The object of a heliostat is to hit a target of low angular elevation. (Note how much sunlight falls to the ground in the process.) Image quoted from NRG Energy.

If hitting a distant target were the object of a heliostat we would stick with plane mirrors; but the object of a heliostat is to hit a low target. There are practical limits to the height that a boiler or beam-down optics can be elevated above the ground, so the goal of a heliostat is to redirect sunlight to a target of low angular elevation.

When 100% of the sunlight incident on a horizontal surface at angle of incidence θ_i emerges redirected at an angle of reflection of θ_r, the sunlight has been concentrated by a factor of cosθ_i / cosθ_r . The Second Law of Thermodynamics forbids this concentration without a compensating increase in divergence. Since plane mirrors cannot accomplish the required increase in divergence, they cannot accomplish the desired efficient redirection of light.

Consider, for example, the Ivanpah Solar Project in California. According to the 2010 environmental impact statement for this project, each power tower is 140 m tall measured to the top of the boiler. Ivanpah units 1 and 2 each have 55,000 heliostats, with each heliostat carrying 14 m² of mirror. Let's say 1 m² of mirror typically shades 1.5 m² of ground. Each unit occupies about 915 acres (3.7 million m²) of land, but only 55,000 x 14 x 1.5 = 1.2 million m2 are typically shaded, a land utilization of only a third. To achieve full utilization we would need to squeeze three times as many heliostats into the view above—but they would only block each others' view!

Mutual blocking is worst at the farthest edge of a heliostat field, so land utilization there is really poor. Ultimately it makes more sense to build another tower than to extend a low-utilization field to greater radius. Approximating an Ivanpah unit as a circle, it has a radius of 1085 m. From the farthest edge of the field the top of the boiler has an angular elevation of arctan(140/1085) = 7.4°.