Chapter Eleven: Solar

RETURN

The sunny side of the street

Our 60-year price tags, and our land projections for the Roadmap’s PV (photovoltaic) systems, are based on the latest NREL numbers (National Renewable Energy Laboratory) from September 2016.

Our prices include the original panel installation, with foundations, mounting racks and labor, plus one full replacement of all panels and three replacements of all inverters, including labor, based on SunPower’s standard of a 40-year average lifetime for their panels.1

Inverters are the gizmos that transform a panel’s dc current into grid-ready ac current, and last about 10,000 on-off cycles. With perpetually clear skies, an inverter would only cycle once a day and last about 27 years.

But in the real world, clouds happen. Three interruptions (cycles) a day reduces an inverter’s lifespan to 9 years, which means 6–7 replacements in a 60-year span.

To be more than fair, we presumed that our solar farms

Despite the specious claim that Moore’s Law can be applied to solar panels, improvements in photovoltaic manufacturing, installation, and conversion efficiency are flattening out.

would be sited in the very best locales, and figured on just three replacements in 60 years.

The Roadmap implies three different capacity factors expected for residential rooftop, commercial rooftop,
and utility PV (big solar farms), but they’re all right
around 21%.

Which is pretty darn optimistic, since actual rooftop
solar capacity factors in the U.S. are currently in the mid-teens.2 But since the Roadmap is probably anticipating technical improvements and optimum siting, we’ll go with their numbers.

Utility PV solar, and commercial rooftop solar, use various sized panels, but the technology is the same– they just use more or less solar cells per panel. So we’ll be calculating how many square meters (m2) of panel are needed for each system, rather than how many panels.

To be more than fair . . .

We’ll use the latest (2016) PV panel efficiency, which is substantially better than the 2013 model used in the Roadmap.

The authors of the Roadmap have always favored the SunPower E20 series, which now produces more watts.3 From the Roadmap’s Table 2, we’ve deduced that the panel used in their 2013 calculations delivers a peak performance of 134 watts-ac (watts of alternating current) per square meter, after the inverter changes it from dc to ac.

We’ll be using SunPower’s 2016 model E20-435, which cranks out a blistering 160 watts-ac / m2 after dc-ac inversion.4

We’ll also apply a 28% price discount to all utility PV systems, and a 23% discount to all PV rooftop systems. Both discounts are based on NREL’s latest near-future cost projections.5

Interestingly enough, the greatest portion of these NREL discounts don’t come from a reduction in panel cost, but from a reduction in the BOS cost (Balance Of System, meaning everything but the panels): A 21% reduction for utility PV BOS, and a 15% reduction for rooftop BOS.

We know what you’re thinking: If efficiency keeps improving and the costs keep dropping, won’t our calculations be out of date as quickly as the Roadmap’s?

Not really. Despite the specious claim that Moore’s Law6 can be applied to solar panels, improvements in photovoltaic manufacturing, installation, and conversion efficiency (see nerd note below) are flattening out. 7

Most of the recent cost improvements in solar have come from manufacturing and installation, rather than increases in panel efficiency. But there are some hopeful manufacturers with the ambitious goal of improving a panel’s conversion efficiency from its present in-the-field average of less than 17% to a dazzling 25%.8

In spite of the fact that many physicists believe this would require a dramatic technical breakthrough, we’ve factored the hoped-for 25% conversion efficiency into our cost calculations anyway.

However, we didn’t reduce our land calculations. That’s because there’s no way of knowing if 25% efficiency will ever be achieved, and if so, when. Land has to be reserved decades in advance, or other development may gobble it up. So we based our land calculations on the industry’s present-day conversion efficiency, in case we need the room.

NERD NOTE: Conversion efficiency is the panel’s ability to convert a percentage of the sun’s energy falling on the panel into dc electricity.

Don’t confuse Conversion Efficiency with Capacity Factor, which is the total energy (in watt-hrs) that is actually produced by a panel in a 365-day period.

This is expressed as a percentage of total energy that could have been produced under impossibly perfect conditions in that same period of time: A sunny, cloudless sky, 24 hrs a day, for an entire year.

Capacity Factor depends on a panel’s location. Conversion Efficiency depends on solar cell design and fabrication.

So to be way more than fair, we’ll be using:

  • The latest 160-watt (ac) panels
  • An assumed 25% solar-to-electric conversion efficiency breakthrough
    (which would up the 160-watts ac performance to nearly 200 watts)
  • 28% discount for utility PV costs
  • 3% discount for rooftop PV costs

We think you’ll agree that if we bent over backwards by any more than that, we’d fall out of our chairs. But even with all these gimmes, we’ll still show you how PV solar would be an expensive and ineffective way to power the nation.

Before we dig into the digits, however, there’s one last thing we should address: A number in the Roadmap’s Table 29 that makes their total solar farm footprint much smaller than it could possibly be.

Even if it’s just a typo, it deserves to be mentioned.

Elbow room

The technical term is “packing factor” and the idea is simple: How much wind or solar gear can you pack into a given patch of land for maximum power production?

With wind and solar’s meager EROEIs (Energy Returned on Energy Invested), it’s vitally important that no panel is ever in shadow and that every turbine’s propeller can catch a fresh breeze.

In the world of solar energy, fixed-mount (stationary) PV panels need a little less room than single-axis track-mount panels, which are motorized to follow the sun.

Taking both mounting methods into account, the average solar packing factor for the continental U.S. is about 40%: One square kilometer (1 million square meters) of a solar field will have 400,000 square meters of panel surface.

Packing factor is ultimately determined by latitude: Since panels have to face the sun, they’re tilted to compensate for how far north or south they are from the equator. At 45° latitude, panels are tilted at 45°. At the equator (0° latitude), they’re parallel to the ground.

In either case, the panels cast a shadow, below the panels at the equator or behind the panels when they’re north or south of the equator. And the farther from the equator, the longer the shadow.

The shadow area becomes the service path, the area between the solar arrays (long racks of panels) where installers and maintenance personnel can move about.

The problem is, column 7 of row 9 in Table 2 of the Roadmap (we told you we read the whole thing!) implies a packing factor of close to 100%. That means that all utility PV panels would have to be packed side by side, with almost no maintenance paths and no room for shadows.

Which of course is impossible, unless we move everything down to the equator, do the maintenance from beneath the panels, and string an HVDC cable up to our southern border. Not a likely scenario.

So it sure seems like a typo, but regardless, it greatly reduces the Roadmap’s estimate for the amount of land needed for its multitude of utility PV farms.

We wanted to walk you through the weeds on this because our estimate of total land needed for utility PV is much more than the acreage called for in the Roadmap.

☼ ︎☼ ☼
Alrighty, then!
A
fter that 25,000-word preamble,
let’s run the numbers . . .
☼ ☼ ☼

Green acres – PV solar farms

The Roadmap calls for 2,326,000 MWp-ac (megawatts peak of alternating current) generated by 46,480 PV farms.

That requires 14.5 billion m2 (square meters) of 160-watt ac panels, on land slightly greater than Maryland and Rhode Island10, with a 40% packing factor.

Granted, Maryland and Rhode Island aren’t big states, and in any case most of our solar would be in the southwest deserts. (Remember, we’re just using eastern states for illustration purposes, because they happen to be the right size for easy visual comparison.)

NREL’s cost for utility PV is $1.75 an installed watt.11 Panels are 44% of the installation price, and inverters 7% and labor 9%, totaling 60% of initial cost.12

The rest is for racks, wiring, grid connection, etc. One panel replacement and three inverter replacements (for a 60-year comparison to nuclear) adds 80% to the original price.13

The Roadmap’s utility PV solar breaks down as follows:

  • 14.5 billion m2 of panels
  • Initial installation: $4.1 Trillion14
  • With one panel replacement and three inverter replacements: $7.4 Trillion15
  • Minus 28% (NREL’s utility PV future discount), 60-year cost = $5.3 Trillion

According to the Roadmap, our utility PV farms in 2050 would deliver 488.9 GWs average, or 30.7% of the 1,591-GW grid, for 34.9% of total cost.

Utility PV quick numbers:

  • 490 GWs
  • 31% of grid
  • 35% of cost

Not such a bad deal. But there are major feasibility issues to consider, which we’ll explore in the PV summary below.

Up on the roof

The Roadmap calls for rooftop solar on more than 75 million homes, averaging a modest 5 kWp (five kilowatts peak) per installation.

We have about 100 million single-family homes and mobile homes in the U.S., so that’s 3 out of 4 dwellings.

Since only 700,000 of them currently have panels, this would be a goldmine for local contractors. Even though their skills, effort and time would be much better spent on rebuilding the rest of our national infrastructure.

One big problem with rooftop solar is that all panels have to face south. Finding 75 million south-facing residential rooftops with unobstructed exposures might be a challenge. And cutting trees to eliminate shade can be environmentally worse than having no panels at all.

That’s largely why the BOS cost of residential solar is higher: The racking is rarely a straight run, like it is on a flat commercial roof or on open ground.

But there’s an even bigger problem:

Residential solar is a big, fat waste of money

Sorry, but it had to be said.

When the homeowner doesn’t pay full boat, their fellow taxpayers have to kick in the balance.

We know how popular rooftop solar is, and since it is so popular, we’ll walk you through the numbers so you’ll understand how we arrived at our admittedly unpopular conclusion.

One thing to keep in mind as we proceed: We’re discussing actual costs, without the good-deal discounts a homeowner can snag with rebates and tax credits.

While residential solar can seem like a bargain to the consumer, we’re focused on the cost to the nation as a whole. When the homeowner doesn’t pay full boat, their fellow taxpayers have to kick in the balance.

There is no free lunch, even in “Solartopia.”16

First off, rooftop PV is traditionally expressed in terms of direct current, not alternating current like utility (big farm) solar. Probably because DC numbers are bigger – inverting from dc to ac always entails a loss of power.

And big numbers sound better in a sales pitch to the low-information homeowner. So if you ever peruse the back pages of the Roadmap, heads up on that, or the numbers won’t make sense.

The Roadmap calls for 379,500 MWp-dc (megawatts peak of direct current) from residential rooftop solar. But since inverting from dc to ac loses 15% of the energy, residential systems would actually deliver a cumulative net of 322,600 MWp-ac. (See what we mean about the numbers?)

Generating that much power would require more than 2 billion m2 of 160 watt-ac panels (2,016,093,709 to be exact, but who’s counting?)

According to NREL, sloped-roof residential is $2.93 an installed watt (dc),17 which pencils out to $1.1 Trillion for the initial installation.18

Panels and inverters are only 38% of total price,19 because the BOS cost (racks, wiring, etc.) and the soft costs like permits, interest, and insurance are pricier for residential work.

One panel replacement and four inverter replacements add about 71% to the original cost.20 Since both commercial and residential rooftop systems must contend with shade from trees, buildings, and other obstructions, their inverters cycle more often and thus wear out faster.

The Roadmap’s residential solar breaks down as follows:

  • 2 billion m2 of panels
  • Initial installation: $1.1 Trillion
  • With one panel replacement and four inverter replacements: $1.9 Trillion21
  • Minus 23% (NREL’s rooftop future discount), 60-year cost = $1.5 Trillion

According to the Roadmap, rooftop residential would deliver 63.3 GWs, or 3.98% of the 1,591-GW grid, for 9.9% of the cost.

Residential PV quick numbers:

  • 63 GWs
  • 4% of grid
  • 10% of cost

Like we said, it’s a big, fat waste of money.

Which rankles the hell out of the pro-nuclear (read: pro-math) crowd. And here’s why:

That same $1.5 Trillion, which would fund less than 4% of a 1,591-GW all-renewables grid, could fund half of an entire Molten Salt Reactor grid.

Which is something that our nation could easily afford, and actually accomplish, in the time we have to act.

Big roof = mo’ betta (but not by much)

Commercial, industrial, and government rooftops are tantalizing territory for solar expansion, but the numbers are nearly as dismal as they are for residential systems.

NREL says that flat-roof systems cost $2.13 per installed watt (dc).22 The Roadmap calls for 276,500 MWp-dc from commercial rooftop systems, which inverts down to 235,000 MWp-ac.

Since the BOS cost and soft costs are less for commercial work, panels and inverters make up 46% of total price.23 One panel replacement and four inverter replacements adds 78%.24

The Roadmap’s commercial rooftop solar breaks down as follows:

  • 1.5 billion m2 of panels
  • Initial installation: $590 Billion25
  • One panel replacement and four inverter replacements: $1,050 Billion26
  • Minus 23% (NREL’s rooftop future discount), 60-year cost = $810 Billion

According to the Roadmap, commercial rooftop PV would deliver 51.4 GWs, or 3.24% of the 1,591-GW grid for 5.7% of the cost.

Commercial PV quick numbers:

  • 51 GWs
  • 3% of grid
  • 6% of cost

Not quite as bad as residential rooftop, but it’s still a bad idea.

PV summary

Over the conservative 60-year life of a reactor, the Roadmap would need 36 billion square meters of high-performance 160-watt panels. Here’s how we arrived at that number:

  • Utility PV: 14.5 billion
  • Residential: 2 billion
  • Commercial: 1.5 billion
  • Sub-total: 18 billion
  • With one panel replacement: 18 + 18 = 36 Billion m2 of panels

Even with factoring in NREL’s future cost discounts – which partially depend upon improved panel conversion efficiency – the 60-year cost for PV would still be $7.6 Trillion.27

That’s 38% of the grid for 50% of the cost. Which isn’t such a hot deal. And as we’ve shown, there are major feasibility issues (see below).

All PV Solar quick numbers:

  • 605 GWs
  • 38% of grid
  • 50% of cost

The Roadmap requires the installation of 18 billion m2 of panels, over three-quarters of which would have to be racked and operating in the first fifteen years of the buildout.

Which, if we had started on time, would be the years 2015–2030. (To keep things simple, we’ll use the years in the Roadmap’s snazzy graphic.)

Installing 13.5 billion square meters in fifteen years comes to 2.47 million m2 a day for 5,475 days (15 years), rain or shine.

In the remaining twenty years of the buildout (2030–2050), we could kick back and install the last 25% of the panels (4.5 billion m2) at the leisurely rate of 616,400 m2 a day.

Then we could chill for five years, until the panel party starts all over again. And when it does, it’ll never end.

Treading water

…maintaining an all-renewables grid would be like an endless Cold War, waged against global warming by a renewable-industrial complex.

Assuming that SunPower’s panels will actually last 40 years28, and further assuming that their technology becomes the industry standard, the nation’s panel industry could use the five-year downtime after the buildout to gear up for a future of replacing and recycling 1.23 million m2 per day, rain or shine, forever.

And mind you, all that busy work won’t expand our grid – it’ll just maintain what we’ve already built.

As we said, if the buildout can be likened to a 35-year mobilization of World War II proportions, then maintaining an all-renewables grid would be like an endless Cold War, waged against global warming by a renewable-industrial complex.

Also keep in mind that if Dr. Jacobson’s dream comes true, and the entire industrialized world embarks on their own Roadmaps, there’s a very good chance that we will have to do all of our panel manufacturing and recycling right here at home, including the inverters.

Quite aside from the challenge of ramping up our manufacturing base (17X for wind and 29X for solar29), there are serious doubts that most Americans would tolerate the mining and waste involved in extracting and refining the raw materials.30

And we haven’t even discussed wind machines.

Mining and refining wind’s rare earth requirements (approximately one tonne of neodymium magnets per 5-MW generator)31 has been making a hellacious mess in China. They presently control 95% of the world’s rare earth production, and have few pollution controls on the industry.

The environmental costs are downright ghastly,32 and yet it’s been comfortably out of sight of the world’s WWS advocates, who by and large have ignored the situation. (We don’t pollute – China does it for us.)

But if the Roadmap gets implemented around the world, as Dr. Jacobson and his colleagues hope, we will have to fabricate most or all of our own PV panels and wind turbines. The environmental impacts of the domestic mining, manufacturing and recycling would be substantial and ongoing.

If and when domestic production skyrockets, stringent pollution controls will significantly drive up the cost of a homegrown Roadmap. Which, to be more than fair, we haven’t factored into our calculations.

Before we get into wind, there’s one other solar system we need to visit:

CSP solar

We saved concentrated solar power for last because it’s such an oddball: At 7.3% of the bare-bones fleet, it’s the only wind or solar technology with built-in backup (just for over night and just for itself, but still . . .)

And completely aside from the fleet CSP, a separate contingent of CSP farms will constitute the entirety of the Roadmap’s 4.38% overbuild.

Fleet CSP will generate 227,300 MWp-ac, contributing 116 GWs to the 1,591 grid, or 7.3% of total power. Overbuild CSP will generate 136,400 MWp-ac producing 69.7 GWs, equal to 4.38% of the grid.

Taken together, they’ll generate a total of 363,700 MWp for an average of 185.7 GWs, with the advantage that they can operate after sundown.

(By the way, if you use these numbers to calculate CSP’s capacity factor, you’ll get a misleading figure of 51%. It’s really about half that value. The reason for the discrepancy is that CSP farms play fast and loose with their numbers.33)

One drawback of CSP is that the land requirement is 2.4X of what’s needed for utility PV solar. We used the Andasol CSP plant in southern Spain as a basis of comparison, since it’s been up and running for a while and our own CSP plants are brand new. Our CSP should get similar results for land density: 0.039 km2 / MWp-ac.34

Which means that the Roadmap’s fleet CSP, plus its overbuild CSP, will need a grand total of 14,200 km2 of land, or a smidgen more than Connecticut.

Cost estimates for CSP vary, depending on how much storage the plant would have. Table S-14 of the Roadmap gives a range of costs, including projected future discounts, which we’ve boiled down to a long-term average of $5.94 per Wp-ac.35

That’s substantially less than Andasol’s price of $8.00 (USD) per watt. But we’ll go with the Roadmap’s lower number and chalk it up to American ingenuity.

Since simple curved mirrors and clean molten salt should last for decades, no replacement costs are anticipated.

Fleet CSP will generate 7.3% of the grid, and cost $1.35 Trillion.

Overbuild CSP would equal 4.38% of the grid, and cost $810 Billion.
Total CSP (fleet + overbuild) would be 363,700 MWs, and cost $2.16 Trillion.

Fleet CSP quick numbers:

  • 116 GWs
  • 7% of grid
  • 9% of cost

Overbuild CSP quick numbers:

  • 70 GWs
  • Equal to 4% of grid
  • 5% of cost

Not as good a bargain as PV solar, but CSP can work after sundown – if it was a sunny day.

Chapter Eleven End Notes

  1. https://us.sunpower.com/sites/sunpower/files/media-library/data-sheets/ds-e20-series-327-residential-solar-panels.pdf
    See page 2.
  2. http://www.timothymaloney.net/Critique_of_100_WWS_Plan.html
    Critique.
    See internal footnotes 12 and 27
  3. https://web.stanford.edu/group/efmh/jacobson/Articles/I/USStatesWWS.pdf
    Roadmap.

    See Table 2, footnote d. www.pnas.org/content/112/49/15060
    See Table 2, footnote c.

  4. Ibid. Chapter Eleven End Note #2. Critique.

    Search for “About 160 W”. See internal footnote 22.3.

  5. Ibid. Chapter Eleven End Note #2. Critique.

    Search for “US Solar PV System Cost Benchmarks”; then search for “28%”, then “23%”

    Also see: https://ourworldindata.org/grapher/number-of-patents-filed-for-renewable-energy-technologies

  6. https://en.wikipedia.org/wiki/Moore%27s_law

    https://www.greentechmedia.com/articles/read/why-moores-law-doesnt-apply-to-clean-technologies

  7. http://www.nrel.gov/docs/fy16osti/67142.pdf

    See graph on page 8.

  8. Ibid. See graph on page 42: “Modeled Impacts of Module Efficiency on Total System Costs, 2016.”
  9. https://web.stanford.edu/group/efmh/jacobson/Articles/I/USStatesWWS.pdf
    Roadmap

    Table 2, row 9, column 7 states 0.18973% as the portion of US land required for utility solar PV farms.
    0.18973% X 9.162e6 km2 total US area = 17,380 km2 land area required for utility PV, asserted by the Roadmap.

    Referring to Table 2’s column 4, using 160 W / m2 SunPower PV panels specified by the Roadmap, the total panel area (not land area), is:
    2,326,000e6 W ÷ 160 W /square meter = 14.54e9 square meters of total panel area.

    At U.S. average packing factor of 40%, the total land area required = total panel area ÷ 0.40:
    14.54e9 m2 ÷ 0.40 = 36.35e9 m2 = 36,350 km2. This is 0.397% of total U.S. land.

    Therefore the NREL / SunPower-derived land requirement for utility-scale PV solar is 2.1X greater than the Roadmap’s assertion. [36,350 km2 ÷ 17,380 km2 = 2.1. Also 0.397% ÷ 0.18973% = 2.1.]

    The Critique’s treatment of this issue can be found by searching for “would occupy only 37,100”.

    The discrepancy between the Critique’s 37,100 km2 of land and 36,350 km2 calculated here is due to the Critique’s rounding of land density values to just two significant figures, namely 0.029 and 0.016 km2 /MW.

  10. To equate utility PV solar area to Maryland plus Rhode Island:

    2,326,000 MWs ÷ 160 watts / m2 = 14,540,000,000 m2 of panels
    14,540,000,000 m2 = 14,540 km2 (square kilometers)
    With 40% packing factor: 14,540 km2 ÷ 0.40 = 36,350 km2 of land required
    Maryland = 32,130 km2 , Rhode Island = 4,000 km2
    MD + RI = 32,130 + 4,000 = 36,130 km2 (220 km2 less than required)

  11. Ibid. Chapter Eleven End Notes #7

    See Page 8, “Overall Model Results.” Utility Scale PV cost values are at the right.

    2016 fixed-tilt cost = $1.42 per dc watt. For ac divide by dc-to-ac conversion factor 0.83, the value assumed by NREL for ground-mounted PV facilities.

    $1.42 /Wdc ÷ 0.83 = $1.71 / W-ac (for ground-mounted fixed-tilt in 2016)

    Page 45, Conclusions (1), for single-axis tracking mount;
    $1.49 / W-dc ÷ 0.83 = $1.79 / W-ac (for single-axis tracking in 2016)

    $1.71 for fixed-tilt and $1.79 for tracking-mount, per ac watt. Combined average $1.75 per ac watt.

  12. Chapter Eleven End Note #7.

    See Page 8, Overall Model Results, Utility Scale PV: all dollar values are per dc watt.
    $1.42 for fixed-tilt and $1.49 for tracking-mount. Combined average $1.45 per dc watt.

    See page 36, Utility Scale PV, Modeling Inputs. All dollar values are per dc watt:

    Module Price:$0.64 ÷ $1.42 = 45% for fixed mount
    $0.64 ÷ $1.49 = 43% for tracking mount
    44% average, for PV module cost portion.

    Inverter Price:
    $0.09 ÷ $1.42 = 6.3% for fixed mount
    $0.10 ÷ $1.49 = 6.7% for tracking mount
    6.5% average, for inverter cost portion; rounded to 7% in text.

    Installation Labor: http://www.nrel.gov/docs/fy15osti/64746.pdf
    For 2015 installations, see page 29, Figure 21:

    $0.16 /Wdc for fixed mount
    $0.22 /Wdc for tracking mount
    $0.19 /Wdc average, labor cost portion in 2015.

    Labor cost declined by about one-third from 2015 to 2016. See NREL 2016 report (Ibid.), page 8, Utility Scale PV, at far right.

    Compare orange-color segments in the bar graphs for those two years. By comparison, estimate that $0.19 declined to about $0.13 /Wdc.
    $0.13 /Wdc ÷ $1.45 /Wdc = 9.0%, labor cost portion in 2016.

    44% (module cost) + 6.5% (inverter cost) + 9% (labor cost) = 60% of initial cost of utility PV solar.

  13. Assuming that initial labor cost of 9% divides as 5% for panels and 4% for inverters:
    1 PV panel replacement = 44% module + 5% labor = 49%
    3 inverter replacements = 3 X (6.5% parts + 4% labor) = 31%
    Lifetime replacement cost = 49% + 31% = 80%.

    Lifetime cost factor = 1.80X.

  14. 2,326,000 million watts (MWs, or megawatts) X $1.75 /W = $4.1 trillion for initial installation at 2016 cost.
  15. $4.1 trillion X 1.80 = $7.4 trillion lifetime cost, before NREL future discount.
  16. http://solartopia.org
  17. Ibid. Chapter Eleven End Note #7

    See Page 8, Overall Model Results: residential cost values are at the left. All values expressed in dc watts. (vertical scale factor = $0.11 /millimeter)

    $2.93 / Wdc for residential solar in 2016.

  18. 379,500 million watts X $2.93 / W = $1.1 trillion for initial installation at 2016 cost.
  19. Ibid. Chapter Eleven End Note #7

    see p. 25, Residential PV. Modeling Inputs and Assumptions:
    module + string inverter = $0.64 + $0.16 = $0.80 /Wdc
    module: $0.64 ÷ $2.93 = 22%
    inverter: $0.16 ÷ $2.93 = 6%

    p. 8, bar graph; Scale orange segment for labor: 2.7 mm.
    Vertical scale factor = $0.11 per mm;
    installation labor = 2.7 mm X $0.11 / mm = $0.30 /Wdc
    Labor: $0.30 ÷ $2.93 = 10%

    module + string inverter + labor = $0.80 + $0.30 = $1.10 / W-dc
    $1.10 ÷ $2.93 = 38%

  20. Assuming that initial labor cost of 10% divides as 5% for panels and 5% for inverters:

    1 PV panel replacement = 22% module + 5% labor = 27%
    4 inverter replacements = 4 X (6% parts + 5% labor) = 44%
    Lifetime replacement cost = 27% + 44% = 71%.

    Lifetime cost factor = 1.71X.

  21. $1.11 trillion X 1.71 = $1.90 trillion lifetime cost, before NREL future discount.
  22. Ibid. Chapter Eleven End Note #7.
    See Page 8, section on “Overall Model Results.”
    Commercial cost values are in the center. Values are expressed in dc watts.
    Scale factor = $0.11 /millimeter. $2.13 / Wdc for commercial rooftop solar in 2016.
  23. Ibid. Chapter Eleven End Note #7
    See Page 31, Commercial PV “Modeling Inputs and Assumptions”:

    module + inverter = $0.64 + $0.13 = $0.77 /W-dc
    module: $0.64 ÷ $2.13 = 30%
    inverter: $0.13 ÷ $2.13 = 6.1%

    See also Page 8, bar graph. Commercial cost values are in the center.
    Scale the orange segment for labor, get 1.8 mm.
    At $0.11 per mm, installation labor = 1.8 mm X $0.11 / mm = $0.20 / W-dc.
    Labor: $0.20 ÷ $2.13 = 9.4%

    module + inverter + labor = $0.64 + $0.13 + $0.20 = $0.97 / W-dc
    $0.97 ÷ $2.13 = 46%

  24. Assuming the initial labor cost of 9.4% divides evenly as 4.7% for panels and 4.7% for inverters:

    1 PV panel replacement = 30% module + 4.7% labor = 34.7%
    4 inverter replacements = 4 X (6.1% parts + 4.7% labor) = 43.2%
    Lifetime replacement cost = 34.7% + 43.2% = 78%

    Cost factor = 1.78X.

  25. 276,500 million watts X $2.13 / W = $590 billion for initial installation at 2016 cost.
  26. $590 billion X 1.78 = $1050 billion lifetime cost before NREL future discount.
  27. Utility + residential + commercial = $5.3 T + $1.5 T + $0.8 T = $7.6 T, if NREL’s future
    discount projection is borne out.
  28. https://us.sunpower.com/sites/sunpower/files/media-library/data-sheets/ds-e20-series-327-residential-solar-panels.pdf
  29. Ibid. Chapter Eleven End Note #2. Critique.

    Search for “factor of 16.9”. Refer to internal footnote # 13. Then refer to “factor of 58” in internal footnote # 14.

  30. See the “Material Requirements” chapter in “The Non-Solutions Project” by Mathijs Beckers:
    https://www.amazon.com/non-solutions-project-Mathijs-Beckers/dp/1537673807
  31. http://news.mit.edu/2012/rare-earth-alternative-energy-0409
  32. http://www.bbc.com/future/story/20150402-the-worst-place-on-earth
  33. A CSP farm’s capacity factor is sometimes specified in the 40% or 50% range. That’s an unrealistic range for actual solar insolation anywhere in the world, even in the sunniest locations. Such a spurious capacity factor is conjured by the solar industry with the following accounting gimmick:

    Only a portion of a CSP farm supplies immediate electric energy to the grid. The rest of the farm’s curved mirrors put heat energy directly into a pipe of molten salt, then the hot salt is stored in insulated tanks for later use.

    But instead of adding up all the energy (electric + heat) produced by the entire farm, the solar operator only counts the “immediate electric energy” portion of the farm as the total peak power rating for the entire farm.

    The farm’s electric generating equipment and steam turbine are sized to handle just the amount of power produced by the immediate electric energy mirrors, and not the entire solar field, meaning the farm’s entire collection of mirrors. The industry has coined the innocuous term “solar multiple” for this accounting gimmick.

    Solar multiple is the ratio of all the mirrors in the solar field to the mirrors that are producing immediate electric energy. For example, a solar multiple of 1.5 means that in a 150-mirror CSP farm, 100 mirrors are counted and 50 mirrors aren’t. This reduces the farm’s declared peak-power rating. However, the material use and dollar cost to build the entire field relates to the entire solar field, not just the counted mirrors.

    As described, the 50 uncounted mirrors produce and store the thermal energy that’s intended for use after sundown. The accounting trick makes it look on paper like the additional electric output obtained from the stored (and uncounted) thermal energy seems to be coming from less infrastructure than it really is. This enables the industry to (misleadingly) quote a greater capacity factor of the CSP farm, for PR purposes.

  34. https://en.wikipedia.org/wiki/Andasol_Solar_Power_Station

    Andasol’s land area is 5.85 km2. Its nominal power rating is 150 MWp. 5.85 ÷ 150 = 0.039 km2 /MWp.

  35. Ibid. Chapter Eleven End Note #2. Critique.

    Search for “$5.94”. Refer to internal footnote 46.