Sensitivity & weather risk
The key idea
If fuel price rises, a plant with more diesel use may become less attractive. That is a sensitivity question. If a cloudy year increases diesel operation, the result may change even at the same fuel price. That is a resource-variation question.
Keep the two experiments separate before combining them. Record which variable changed, which inputs stayed fixed, and how each case was produced.
The ranking can change
For synthetic case W3, design A has USD 8,000/year fixed cost and uses 6,000 L/year. Design B has USD 13,000/year fixed cost and uses 3,000 L/year.
At USD 1/L, A costs USD 14,000/year and B costs USD 16,000/year. At USD 2/L, A costs USD 20,000/year and B costs USD 19,000/year. The resource case and fuel quantities are unchanged; only the assumed fuel price changes.
Compare a sweep with a case spread
First change fuel price and inspect the sensitivity lines for W3. Then hold the price fixed and compare all five synthetic weather cases. Switch from mean cost to cost P90. Finally select only W3 and inspect the single-case warning.
Sensitivity: change fuel price, hold W3 fixed
- Design A
- Design B
Read the exact values
| Time / step | Design A | Design B |
|---|---|---|
| $0.50/L | 11,000 | 14,500 |
| $0.75/L | 12,500 | 15,250 |
| $1.00/L | 14,000 | 16,000 |
| $1.25/L | 15,500 | 16,750 |
| $1.50/L | 17,000 | 17,500 |
| $1.75/L | 18,500 | 18,250 |
| $2.00/L | 20,000 | 19,000 |
Case spread at the selected fuel price
Dots: one synthetic case each. The tick marks the selected comparison metric for that design.
- A: MEAN
- $15800/year
- B: MEAN
- $16300/year
- Case count
- 5
Design A has the lower mean cost in this case set. These five cases are not a probability guarantee for future years.
Data table: Synthetic weather-case costs
| Case | A USD/year | B USD/year |
|---|---|---|
| W1 | 12000 | 14000 |
| W2 | 13000 | 15000 |
| W3 | 14000 | 16000 |
| W4 | 17000 | 17500 |
| W5 | 23000 | 19000 |
Data table: Fuel-price sensitivity, W3 only
| USD/L | A USD/year | B USD/year |
|---|---|---|
| 0.50 | 11000 | 14500 |
| 0.75 | 12500 | 15250 |
| 1.00 | 14000 | 16000 |
| 1.25 | 15500 | 16750 |
| 1.50 | 17000 | 17500 |
| 1.75 | 18500 | 18250 |
| 2.00 | 20000 | 19000 |
Model note · Five fixed synthetic cases W1–W5; no calendar years, weather observations or random seed. Annual costs in constant 2026 USD. A has lower fixed cost and higher fuel use; B has higher fixed cost and lower fuel use. These tables explain rankings, not an ensemble confidence level.
The five cases are invented examples, not measured calendar years. They have fixed values, no random sampling and no seed. Repeating an input therefore gives exactly the same result, but reproducibility alone does not make a dataset representative.
Always say what P90 means
In this exercise, cost P90 is the 90th percentile of the listed costs sorted from low to high. Higher cost is unfavorable, so this focuses attention toward the high-cost side of the case set.
The 90th percentile of energy sorted from low to high is a high-energy result. That is different from an energy P90 exceedance value, which is often used to describe a lower energy level expected to be exceeded. State the direction and convention; the label “P90” alone is insufficient.
A percentile from one case equals that case. It does not establish weather uncertainty. A percentile from five chosen cases is also not a guarantee about future years, climate changes or variables absent from the model.
The percentile method used hereOptional — the page reads completely without it
Each teaching case has a fixed cost and a fuel quantity; only the price changes in the sweep:
annual cost of a design in one case
C = Cfixed + Qfuel · pfuel
For the percentile, sort the n case costs ascending. At probability p the zero-based position is interpolated between neighbours:
empirical percentile, inclusive interpolation
h = ( n − 1 ) · p
Pp = x⌊h⌋ + ( h − ⌊h⌋ ) · ( x⌈h⌉ − x⌊h⌋ )
For 10, 20, 30, 40 and 50, P90 has h = 3.6 and equals 46. Other percentile conventions exist; see the NIST percentile reference. Mean cost is the arithmetic average. No likelihood weights, weather synthesis, confidence interval or Monte Carlo distribution is assigned to these five cases.
See it in Phasor
Declare the varied assumptions or weather-year set before running sensitivity and risk comparisons. Read the case count, successful cases, source years and objective definition with the result. Preserve a seed when a supported synthetic sampling method uses one.