CALC-061

The CRF rescaling method, and the two real data points it was checked against

Feeds CLM-0377. Answers QST-004. Basis: methodological validation, dimensionless; not a currency-denominated record.

Script. restate-lcoe.py SECTION 2 (crf() line 195, rescale_lcoe() line 202) and SECTION 3 (section_validate_crf_method(), line 224). Check B is run in SECTION 4.

Why it was needed. Six of the restated figures in CALC-063 have no bottom-up model behind them and are rescaled by a shortcut. A shortcut that has never been checked against a known answer is an assumption wearing a formula. This section is the check, and it is the reason CALC-062 exists as a separate record: wherever a real rebuild was possible, the rebuild was used and the shortcut was not.

Inputs.

Both limbs checked, and this is the favourable case. Both limbs of Check A are STATED by the source, not assumed by the claim. Frazer-Nash published its own 15-year sensitivity, which is what makes this a validation rather than a plausibility argument. A method checked against a number the source itself published is the strongest shape a methodological claim in this register takes, and it is worth naming because a finding withdrawn earlier was the opposite shape: a model built on a parameter assumed where the source in fact specified it.

Working, transcribed.

-- Check A: against Frazer-Nash's own published 15-year sensitivity --
predicted 15-yr from 30-yr baseline, CRF ratio at 20 per cent hurdle
                                              GBP 52.9 /MWh
Frazer-Nash's own reported 15-yr figure       GBP 50.9 /MWh
error                                              +4.0 per cent

-- Check B: against the bottom-up NASA rebuild at CALC-062, 20 yr --
CRF shortcut over-predicts the full rebuild by
    RD1   +22.0 per cent (3 per cent)   +29.3 per cent (10 per cent)
    RD2   +21.6 per cent (3 per cent)    +9.4 per cent (10 per cent)

Result: about 4 per cent error on a small change of basis, 9 to 29 per cent on a large one.

Conclusion. Good enough for direction and rough magnitude, not for the last few percentage points. That is why CALC-062 uses the full rebuild wherever one exists, and why the six figures in CALC-063 carry roughly plus or minus 25-30 per cent of additional uncertainty beyond their own stated parameters. The shortcut is not used anywhere a rebuild was available.

Where this fails. Two data points, both from the low-discount-rate-to-high-discount-rate direction, and the pure-annuity assumption is not testable from the held evidence for CASSIOPeiA, because no bottom-up CASSIOPeiA model is held.

A DIRECTION-WORD DEFECT IN THE SCRIPT'S OWN PROSE, IN THE VALIDATION SECTION. NOT FIXED HERE, AND THE CLAIM IS CLEAN. The script's commentary immediately after Check A (lines 244-247) reads: "The CRF method under-predicts the true sensitivity slightly (Frazer-Nash's own model shows MORE increase than a pure-annuity approximation would suggest ...)". The numbers the same function prints run the other way. Frazer-Nash's own model moves p50 from 49.7 to 50.9, an increase of 1.2 GBP/MWh. The CRF method moves it from 49.7 to 52.9, an increase of 3.2 GBP/MWh. The approximation shows the larger increase, so it over-predicts the life-shortening sensitivity, by a factor of about 2.7 on the change and by +4.0 per cent on the level.

This is a reading of a direction word, and I did the one arithmetic step needed to establish it, which the transcription standard does not otherwise permit. Stating that plainly: I subtracted 49.7 from each of two numbers already printed by the script. I did not re-derive 52.9, which is the script's own output and which CLM-0377 transcribes correctly. No figure anywhere in this section moves, and this is not an arithmetic error - it is the same defect class the previous pass named at CALC-051, a correct number described as something it is not.

Two further consequences, because the sentence does more than mislabel a direction:

1. The explanation attached to it explains the wrong thing. The script offers "shortening satellite life also forces an earlier/second manufacturing batch, a real cost this approximation does not capture" as the reason. That would make the true increase larger than the approximation's. The true increase is smaller. A correct explanation would have to run the other way - a substantial cost component that does not scale with the annuity - which is precisely the pure-annuity assumption CLM-0377 already flags in its own assumes field. 2. The trustworthiness conclusion drawn from it may not follow. The same passage concludes the method "is more trustworthy at LOW discount rates (3%) ... and least trustworthy at HIGH discount rates (20%)". Check B's own numbers do not obviously support that ordering either: RD2's error is +21.6 per cent at 3 per cent and +9.4 per cent at 10 per cent, which is the opposite ordering to RD1's. I am not resolving this and I have not recomputed anything to test it. It is flagged because the claim's headline - that the shortcut is good for direction and magnitude only - is unaffected either way, while the discount-rate-dependent refinement in the script's prose is not established by the evidence the script prints.

CLM-0377 itself repeats neither the backwards direction word nor the trustworthiness ordering. The claim transcribes only the four numbers and the +4.0 per cent, all of which are right. The defect is in the script's narration of its own output, not in the register.

Cite this