The formula takes three lines. The mistake is applying it to the annual average price when the plant only runs in the hours above its marginal cost.
The clean spark spread is the power price less the gas cost of one MWh (gas price divided by efficiency) less the carbon cost of that MWh (carbon price times tonnes emitted). At 92.00 baseload power, 35.00 gas, 54 per cent efficiency and 70.00 a tonne of carbon, it is 1.00 per MWh, and minus 2.00 once variable O&M is paid. The same 400 MW plant, dispatched hour by hour, still earns 32.6M a year, because it never runs at the average price.
Worked in full in Energy Trading by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
An illustrative combined-cycle gas turbine sells into a market whose annual baseload forward is 92.00 per MWh. Prices are in euros per MWh, gas is quoted per MWh of thermal energy, and carbon per tonne of CO2. None of these levels is a market quote; they are chosen so the arithmetic is easy to follow.
| Input | Value |
|---|---|
| Baseload power forward, per MWh | 92.00 |
| Peak power forward, per MWh | 108.00 |
| Gas, per MWh thermal | 35.00 |
| Electrical efficiency | 54% |
| Gas emission factor, tCO2 per MWh thermal | 0.202 |
| Carbon allowance, per tonne | 70.00 |
| Variable O&M, per MWh | 3.00 |
| Capacity | 400 MW |
Efficiency is the hinge. A plant at 54 per cent turns 1 MWh of gas into 0.54 MWh of power, so it burns 1.852 MWh of gas for each MWh it sells. That factor, the heat rate, converts both the gas price and the emission factor into per-MWh-of-power terms.
Fuel cost = gas price / efficiency = 35.00 / 0.54 = 64.81
Carbon cost = carbon price × emission factor / efficiency = 70.00 × 0.374 = 26.19
Spark spread = power − fuel cost = 92.00 − 64.81 = 27.19
Clean spark spread = spark spread − carbon cost = 27.19 − 26.19 = 1.00
Excel: =Power-Gas/Eff-CO2*EF/Eff
Deduct variable O&M of 3.00 and the margin per MWh on baseload is minus 2.00. Add the three cost lines together and you have the plant's marginal cost: 64.81 plus 26.19 plus 3.00, or 94.00 per MWh. That is the number that decides whether the plant runs in a given hour.
| Product | Power | Spark spread | Clean spark spread | Net of variable O&M |
|---|---|---|---|---|
| Baseload | 92.00 | 27.19 | 1.00 | −2.00 |
| Peak | 108.00 | 43.19 | 17.00 | 14.00 |
Read on its own, the baseload line says the plant is worth minus 2.00 on each of 3,504,000 MWh, a loss of 7.0M a year. That is the valuation a careless desk sends upstairs.
The plant does not sell baseload. It runs when the hourly price is above 94.00 and stays off when it is not. Sort the year's 8,760 hours by price, the price duration curve, and the same forward of 92.00 breaks into rows that sit far above and far below the marginal cost. The bottom row is solved so that the time-weighted average is exactly 92.00.
| Hours | Price | Price less marginal cost | Hours run | Margin |
|---|---|---|---|---|
| 500 | 165.00 | 71.00 | 500 | 14.2M |
| 1,000 | 125.00 | 31.00 | 1,000 | 12.4M |
| 1,500 | 104.00 | 10.00 | 1,500 | 6.0M |
| 2,000 | 92.00 | −2.00 | 0 | 0.0M |
| 2,260 | 78.00 | −16.00 | 0 | 0.0M |
| 1,500 | 54.76 | −39.24 | 0 | 0.0M |
| 8,760 | 92.00 | 3,000 | 32.6M |
The plant runs 3,000 hours, a 34.2 per cent load factor, sells 1,200,000 MWh at an average captured price of 121.17 and earns 32.6M, or 27.17 per MWh generated and 81.50 per kW of capacity a year. Between the baseload reading and the dispatch reading there is 39.6M, and none of it is a view on the price level: both use the same forward. It is the value of the option to switch off, which the annual average deletes.
This margin is before start costs, minimum run times and ramp limits. A plant that runs 3,000 hours in short bursts pays for every start, so the real figure sits below 32.6M. But it sits a long way above minus 7.0M.
Each 10.00 a tonne on carbon adds 3.74 per MWh to the marginal cost; each 1.00 on gas adds 1.85. The table moves both and reprices the baseload spread and the dispatch margin on the same curve.
| Gas | Carbon | Marginal cost | Baseload, net | Hours run | Dispatch margin |
|---|---|---|---|---|---|
| 30.00 | 50.00 | 77.26 | 14.74 | 7,260 | 65.2M |
| 30.00 | 90.00 | 92.22 | −0.22 | 3,000 | 34.7M |
| 35.00 | 50.00 | 86.52 | 5.48 | 5,000 | 46.0M |
| 35.00 | 70.00 | 94.00 | −2.00 | 3,000 | 32.6M |
| 35.00 | 90.00 | 101.48 | −9.48 | 3,000 | 23.6M |
| 40.00 | 90.00 | 110.74 | −18.74 | 1,500 | 16.6M |
The baseload spread swings from 14.74 to minus 18.74 across the grid; the dispatch margin never goes below 16.6M. Two break-evens are worth carrying on the front page: at 92.00 power the baseload spread net of O&M reaches zero at a gas price of 33.92 or a carbon price of 64.65. Above them the plant is out of the money on average and still in the money in its best hours.
There are two. The first is arithmetic: applying the emission factor to the power output rather than to the gas burned. 0.202 tonnes per MWh thermal is 0.374 tonnes per MWh of power at 54 per cent efficiency, nearly twice as much, and leaving out the division understates the carbon cost by 12.05 per MWh. The second is conceptual: quoting a clean spark spread on the annual baseload forward as if it were the plant's margin. It is the margin of a plant forced to run every hour. A real plant earns the spread of the hours it chooses, and the shape of the curve matters more than its level. The same logic, turned round, explains how much of a fixed-price retail margin the load shape takes.
The curve, the dispatch row by row and the gas and heat-rate thresholds are live in the free workbooks for this case, so you can replace these rows with your own market and watch the margin move.
The spark spread is the power price less the cost of the gas burned to make one MWh. The clean spark spread also deducts the cost of the carbon allowances that MWh requires. At 92.00 power, 35.00 gas and 54 per cent efficiency the spark spread is 27.19 per MWh; at 70.00 a tonne of carbon the clean spark spread is only 1.00.
Divide one by the efficiency. A 54 per cent plant burns 1.852 MWh of gas for every MWh of power. In MMBtu terms multiply by 3.412: about 6.32 MMBtu per MWh. The heat rate of 1.852 is also what turns the gas price into a fuel cost per MWh of power and the gas emission factor into tonnes of CO2 per MWh.
Solve the clean spark spread net of variable O&M for zero. With 92.00 power, 35.00 gas and 3.00 of variable O&M, the break-even carbon price is 64.65 a tonne, because each 10.00 a tonne adds 3.74 per MWh at 0.374 tonnes per MWh. Above it the baseload spread is negative, but the plant can still earn in peak hours.
Not on its own. A negative baseload spread says the plant loses money if it runs every hour, which it never does. Value it against the hours: in this case a minus 2.00 baseload spread coexists with 32.6M of annual margin from the 3,000 hours priced above the 94.00 marginal cost.
The plant's marginal cost and its dispatch off the price duration curve are worked in the Chapters 4 to 7 workbook of 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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