Haute Lumière
Commerce · IV.05 · MMXXVI · daylight
TEN CONCEPT BRIEFS · Chapter IV.05 — Energy Systems That Compound
One page each. A reader who reads only these ten pages has the chapter.
BRIEF 1 — Wright's Law
The idea. The cost of making a thing falls by a roughly constant proportion each time the total number ever made doubles. Not each year. Each doubling of cumulative production.
C(Q) = C0 · (Q / Q0)^(−b)
Q cumulative units ever produced C cost per unit
b the learning exponent LR the fraction taken off per doublingTheodore Wright published it in 1936 about airframes, having noticed that labour hours per aircraft fell about a fifth per doubling. He was pricing a contract, not proposing a law. Nagy, Farmer, Bui and Trancik tested it against sixty-two technologies in 2013 and found it the best of the competing forms.
Worked example. Solar modules: 106 dollars a watt at 0.3 MW cumulative in 1976, 0.15 dollars a watt at 1,419,000 MW in 2023. That is 22.17 doublings, and the fitted rate is 22.5 percent per doubling.
Why it matters. It makes cost a decision variable. If cost is a function of cumulative volume, then anybody who can commit volume can move the price — which is a completely different management problem from negotiating one.
You already know this because the fifth time you did anything difficult it took less time than the first, and nobody had to retrain you in between.
BRIEF 2 — The Learning Rate and the Learning Exponent
The idea. Two numbers describe the same curve and they are not interchangeable. The learning rate LR is the fraction taken off per doubling. The learning exponent b is what you put in the equation.
b = −log2(1 − LR)| LR | b | cost after three doublings |
|---|---|---|
| 10.0 % | 0.1520 | 0.7290 |
| 19.1 % | 0.3058 | 0.5295 |
| 20.0 % | 0.3219 | 0.5120 |
| 22.5 % | 0.3677 | 0.4655 |
| 25.7 % | 0.4286 | 0.4102 |
| 30.0 % | 0.5146 | 0.3430 |
Worked example. At a 20 percent learning rate, three doublings leave you at 0.8³ = 0.512 — a little under half. At 30 percent the same three doublings leave you at 0.343. A ten-point difference in the rate is a fifty percent difference in the answer after only three doublings, which is why quoting a rate without an interval is not a forecast, it is a preference.
Why it matters. Anybody can multiply by 0.8. The discipline is knowing whether it is 0.8, and how sure you are.
You already know this because you have seen two people quote the same growth story with different compounding assumptions and arrive at numbers a factor of two apart, both of them sincere.
BRIEF 3 — Moore Against Wright: Time or Experience
The idea. Two rival hypotheses about the same falling price. Moore's form says cost falls at a constant rate per year. Wright's form says it falls at a constant rate per doubling of cumulative production. On any historical series where deployment grew smoothly, both fit, because time and experience moved together.
Worked example. The module series from 1976 to 2023: 47 years, a compound price fall of 13.0 percent a year, and 22.17 doublings at 22.5 percent each. Both descriptions fit the same eleven points.
Where they come apart. Exactly when it matters. If deployment accelerates, Wright predicts faster price falls and Moore does not. If deployment stalls, Wright predicts the price stops falling and Moore says it continues. A forecast is always requested at precisely the moment somebody is contemplating changing the deployment rate — and at that moment the two models give different answers and only one of them is about anything you control.
Why it matters. Choosing Wright makes the forecast conditional on a policy or a purchase. That is not a weakness of the model. It is the entire usefulness of it.
You already know this because you have watched a skill improve with practice rather than with the calendar, and you know which one stops when you stop.
BRIEF 4 — The Curve Is Not a Law: Modularity and Negative Learning
The idea. Cumulative production does not cause cost reduction. It creates an opportunity that some manufacturing architectures can take and others cannot.
The counter-case, which is the important one. France built 58 pressurised- water reactors, largely to a small number of designs, by one utility — 5.86 doublings — and real overnight construction cost rose by a factor of about 3.5. That is a learning rate of −23.8 percent. Grubler calls it negative learning by doing; Lovering, Yip and Nordhaus find more heterogeneity across countries, and both belong on the page.
The mechanism. Malhotra and Schmidt: small, modular, mass-produced units of low design complexity learn quickly; large, bespoke, site-assembled units do not. A solar module is made a hundred million times a year indoors under controlled conditions. A reactor is made a few dozen times in a career, outdoors, by a workforce that will not build another one.
The measured spread confirms it. Rubin and colleagues report published onshore-wind capital learning rates from −11 percent to 32 percent. The band contains zero and goes negative.
Why it matters. It tells you what to design for. If you want a learning curve, build something small, repeated and made in a factory. The exponent is a consequence of the architecture, and the architecture is a choice.
You already know this because you have seen a firm get faster at the thing it does every week and no faster at the thing it does every four years.
BRIEF 5 — LCOE, and What It Leaves Out
The idea. Levelised cost of energy divides the lifetime cost of a generator by its lifetime output, both discounted. It is a true statement about a generator and an incomplete one about a grid, because it prices energy and not energy at a time and a place.
utility solar PV, LCOE $0.460/kWh (2010) -> $0.044/kWh (2023) −90.4 %
onshore wind, LCOE $0.111/kWh -> $0.033/kWh −70.3 %What is outside the boundary. Transmission to where the demand is. Balancing, reserves and frequency control. Curtailment when the energy arrives in an hour nobody wants it. Firming — the cost of moving a kilowatt-hour to a later hour. None of these appear in an LCOE and all of them appear on a bill.
Worked example. Germany's congestion-management cost in 2023 was about €3.1 bn against 465 TWh of consumption — €6.67/MWh spread across every kilowatt-hour, and not in anybody's LCOE table.
Why it matters. LCOE is the right instrument for comparing two generators and the wrong one for designing a system. Used for the second job it produces confident answers that operations teams know are wrong, which is how a procurement loses its credibility in month eight.
You already know this because you know the difference between the price of a flight and the cost of the journey.
BRIEF 6 — The Value Factor
The idea. A megawatt-hour is worth what it is worth when it arrives. As a variable source grows, it increasingly arrives at the same time as itself, and it competes with its own output. The value factor is the ratio of the price a technology actually earns to the average market price.
The measurements. Hirth finds the market value of wind falling from about 1.1× the average price at zero penetration to 0.5–0.8× at a 30 percent share. Solar falls faster — from about 1.3× to roughly 0.5× by about a 15 percent share, because solar output is more strongly correlated with itself across a whole market than wind is.
Worked example. A solar generator at a headline $0.044/kWh in a market whose average price is $0.060/kWh does not earn $0.060. At a value factor of 0.5 it earns $0.030 — and the project that looked comfortable on an LCOE comparison is now underwater on revenue, with nothing about its cost having changed.
Why it matters. It explains why cost declines have not produced proportional returns for developers, and it is the quantity a merchant project actually lives or dies on.
You already know this because you know that everybody's tomatoes ripen in the same week, and what that does to the price of tomatoes.
BRIEF 7 — Curtailment: Being Early to the Hour
The idea. Curtailment is energy that could have been produced and was not, because the system could not use it or could not move it. It is not waste in the moral sense; it is the visible price of an arrival-time mismatch.
The measurements. CAISO curtailed 0.19 TWh of wind and solar in 2015 and about 3.40 TWh in 2024 — 17.9× in nine years, and roughly 6.8 percent of utility-scale solar output. Germany in 2023 curtailed about 10.5 TWh of some 272 TWh of renewable generation: 3.9 percent.
The finding that stops the easy story. Germany curtails a smaller share at a higher penetration — about 52 percent renewables against California's solar share of about 20 percent. Network depth and interconnection, not penetration alone, set the number. Any single monotone curve of curtailment against renewable share is a sales aid.
Why it matters. Curtailment is a siting and interconnection signal, not a verdict on the technology. Two systems at the same penetration can differ by a factor of two on how much they throw away, and the difference is infrastructure somebody chose whether or not to build.
You already know this because you know that a road being full at five o'clock is not an argument against cars; it is an argument about the road.
BRIEF 8 — The Cost of a Shifted Kilowatt-Hour
The idea. Firming is the cost of moving energy from the hour it arrived to the hour it is wanted. It is computable from four inputs and it is the number most often missing from a renewable procurement.
Worked example. A four-hour utility battery at $250/kWh installed, 300 full cycles a year, 85 percent round-trip efficiency, fifteen-year life, 7 percent cost of capital:
capital recovery factor, 7% / 15 yr 0.1098
annual capital charge per kWh capacity $27.45
kWh delivered per kWh capacity per year 255.0
COST OF SHIFTING one kWh $0.1076
delivered shifted kWh, all in $0.1516
against prompt solar at $0.0440 3.4 xThe non-linearity. At low penetration almost nothing needs shifting. At high penetration most of it does. On an illustrative shape — labelled illustrative, because three real systems are an ordering and not a regression — a blended $0.0440/kWh at 10 percent penetration becomes $0.1263/kWh at 80 percent, a factor of 2.9×.
Why it matters. It converts an argument into an arithmetic. And it tells you that the cheapest firm kilowatt-hour is often the one that was never stored, because a process moved four hours instead.
You already know this because you know what it costs to keep food fresh until Thursday, and that it is not what the food cost.
BRIEF 9 — The Depletion Exponent
The idea. Extraction has the same equation with the opposite sign. Cost per unit rises with cumulative extraction, because the best deposit is mined first.
learning asset C(Q) = C0 · Q^(−b) b > 0
extractive asset C(Q) = C0 · Q^(+B) B > 0Worked example. Global average mined copper head grade fell from about 1.6 percent in 1990 to about 0.55 percent in 2021 — a ratio of 0.3438 — while cumulative copper ever mined roughly doubled. Energy per tonne scales roughly as one over grade, so energy intensity rose about 2.91× over approximately one doubling: a depletion exponent of about 1.5406.
The part that matters. The real price of copper did not rise by that factor. Extraction has a learning curve too — flotation chemistry, haulage, autonomous fleets, larger mills — and it spent that learning holding the price roughly level against a grade that fell by two thirds. The learning was real and it bought standing still.
Why it matters. This is the asset-class distinction in one sentence. Both industries learn. In one, learning compounds into a falling price. In the other, learning is consumed by depletion and the price stays where it was. Net exponent, not gross effort, is what you are buying.
You already know this because you know the difference between running to get somewhere and running on a moving walkway going the other way.
BRIEF 10 — Deployment as Purchase
The idea. If cost falls with cumulative volume and the benefit accrues to everybody who buys afterwards, then buying early is not consumption. It is the purchase of a permanent price reduction, most of which is enjoyed by people who did not pay for it. Arrow said this in 1962 and almost every subsequent argument about subsidy is a rediscovery of it.
Worked example. The world generated 1,630 TWh of solar in 2023. That quantity costs $71.7 bn at 2023 costs and $749.8 bn at 2010 costs — an annual difference of $678.1 bn. Cumulative German differential cost attributable to solar, carried as a band because the accounting boundary moves, is €150–250 bn, or $162 bn to $270 bn — repaid by that annual difference in 0.24 to 0.40 years. Even on a deliberately wide and unverified global band of $500 bn to $1,000 bn, the payback is 0.74 to 1.47 years.
Why it matters. It is an accounting claim, not a moral one. A payment that produces a durable, non-expiring, non-excludable price reduction is capital expenditure, and it was filed as consumption in every contemporary account of it. Change the classification and the entire argument about deployment policy changes with it.
You already know this because you know the difference between paying rent and paying off a mortgage, and that both of them leave your account the same way.