Every start burns fuel, emits carbon and wears the turbine before a single MWh is sold. Short runs that look profitable hour by hour often are not.
A start pays for itself only if the run that follows earns more than it costs: the break-even run length is the start-up cost divided by capacity times the spread over marginal cost. For an illustrative 400 MW combined-cycle plant, a warm start costs 86,996 in fuel, carbon and wear, so at a spread of 10.00 the plant must run 21.7 hours before the start is paid. Applied across a year, the same rule cuts a dispatch margin of 21,708,000, earned from every in-the-money hour, to 8,812,760.
Worked in full in Energy Trading by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The plant is fictional and every figure illustrative. Its marginal cost is the fuel, carbon and variable operating cost of one MWh at full load. A start costs the gas burned before the unit reaches load, the carbon on that gas, and an allowance for wear, which long-term service agreements typically charge per start. Hot, warm and cold starts follow how long the unit has been off: under 8 hours, 8 to 48 hours, more than 48 hours.
| Input | Value |
|---|---|
| Capacity | 400 MW |
| Gas, per MWh thermal | 28.00 |
| Efficiency | 56% |
| Carbon, per tonne; gas emission factor | 70.00; 0.202 |
| Variable O&M, per MWh | 2.00 |
| Marginal cost: 50.00 fuel + 25.25 carbon + 2.00 | 77.25 |
Start cost = thermal MWh burned × (gas + emission factor × carbon) + wear per MW × MW
Warm start = 1,400 × 28.00 + 1,400 × 0.202 × 70.00 + 70 × 400 = 39,200 + 19,796 + 28,000 = 86,996
| Start | Gas burned, MWh | Fuel | Carbon | Wear | Total | Per MW |
|---|---|---|---|---|---|---|
| Hot | 800 | 22,400 | 11,312 | 16,000 | 49,712 | 124.28 |
| Warm | 1,400 | 39,200 | 19,796 | 28,000 | 86,996 | 217.49 |
| Cold | 2,200 | 61,600 | 31,108 | 44,000 | 136,708 | 341.77 |
Break-even hours = start cost / (MW × spread over marginal cost)
Warm start at a 10.00 spread = 86,996 / (400 × 10.00) = 21.7 hours
Excel: =StartCost/(MW*(Price-MC))
| Spread | Hot | Warm | Cold |
|---|---|---|---|
| 5.00 | 24.9 | 43.5 | 68.4 |
| 10.00 | 12.4 | 21.7 | 34.2 |
| 20.00 | 6.2 | 10.9 | 17.1 |
| 40.00 | 3.1 | 5.4 | 8.5 |
A warm start at a 5.00 spread needs almost two days of running. A morning peak of four hours pays for a hot start only at a spread of 31.07 or more, and a three-hour peak needs 41.43.
An hour-by-hour dispatch values every hour whose price clears marginal cost. Group those hours into the runs they actually form and each run needs a start.
| Run | Number | Hours | Spread | Margin per run | Start | Net per run |
|---|---|---|---|---|---|---|
| Winter multi-day runs (cold start) | 8 | 120 | 22.00 | 1,056,000 | 136,708 | 919,292 |
| Weekday daytime runs (warm start) | 110 | 13 | 15.00 | 78,000 | 86,996 | -8,996 |
| Evening peaks (warm start) | 90 | 3 | 30.00 | 36,000 | 86,996 | -50,996 |
| Price spikes (warm start) | 20 | 2 | 90.00 | 72,000 | 86,996 | -14,996 |
Valued hour by hour, the 2,700 hours earn 21,708,000. Run every one of them with a start in front and the 228 starts cost 20,232,784, leaving 1,475,216. Only the winter runs pay for their own starts. Even the price spikes, at 90.00 over marginal cost, do not cover a warm start, though with the unit still hot they would net 22,288.
The weekday runs fail because each is preceded by a warm start after 11 hours off. The alternative is to stay on through the night at a minimum load of 200 MW, selling at an overnight price of 62.00 with a part-load efficiency penalty of 6.00 per MWh.
Night at minimum load = 200 × 11 × (77.25 + 6.00 − 62.00) = 200 × 11 × 21.25 = 46,750, against a warm start of 86,996
Week of five runs = 390,000 − one cold start after the weekend 136,708 − four nights 187,000 = 66,292
Two-shifting the same week = 390,000 − the same cold start 136,708 − four warm starts 347,984 = −94,692
Two-shifting the same week loses 94,692; staying on earns 66,292, a difference of 160,984, four nights at 40,246. (The table above charged every weekday run a warm start; the Monday start after a weekend is in fact cold, which only makes two-shifting worse.) Over 22 weeks that is 1,458,424. Add the eight winter runs, 7,354,336, and the plant earns 8,812,760 from 30 starts and 2,390 full-load hours: 40.6 per cent of the hour-by-hour figure.
The curve, the dispatch row by row and the starts that close the gap to the flat block are in the free workbooks for this book.
Fuel burned before the unit reaches load, the carbon on that fuel, and the wear each start puts on the turbine, which maintenance contracts often express per start. For the illustrative 400 MW plant here, a hot start costs 49,712, a warm start 86,996 and a cold start 136,708, about a third of it wear. Actual figures depend on the unit and its contract.
When the loss of running at minimum load through the night is smaller than the start it avoids. Here 200 MW for 11 hours at a loss of 21.25 per MWh costs 46,750, against a warm start of 86,996, so staying on saves 40,246 a night. Two-shifting the same weekday runs loses 94,692 a week, with its Monday cold start; staying on earns 66,292.
Because it values every in-the-money hour, including runs of two or three hours that cannot pay for the start that precedes them. On the illustrative plant, valuing every hour gives 21,708,000 from 228 starts; paying for starts and keeping only the runs that cover them leaves 8,812,760 from 30, or 40.6 per cent.
This article is one calculation from Energy Trading. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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