The switching price is where a gas plant's and a coal plant's marginal costs, fuel, carbon and variable O&M, meet. Above it gas runs first; below it, coal does.
The coal-to-gas switching price is the carbon price at which a gas plant and a coal plant have the same marginal cost: the gap in fuel and variable costs per MWh of power divided by the gap in tonnes of CO2 per MWh of power. With illustrative gas at 35.00 euros per MWh, coal at 110 dollars a tonne and plants at 54 and 38 per cent efficiency, it is 48.93 euros a tonne. Above it the gas plant runs ahead of the coal plant; each 1.00 on gas moves the threshold by 3.54.
Worked in full in Energy Trading by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The gas plant is the illustrative combined-cycle unit used in the clean spark spread; the coal plant is an older hard-coal unit. Prices are in euros per MWh unless stated, and none is a market quote.
| Input | Gas plant | Coal plant |
|---|---|---|
| Fuel price | 35.00 per MWh | 110.00 $/t |
| Fuel price, euros per MWh thermal | 35.00 | 14.33 |
| Electrical efficiency | 54% | 38% |
| Emission factor, tCO2 per MWh thermal | 0.202 | 0.341 |
| Variable O&M, per MWh | 3.00 | 4.50 |
Coal is quoted per tonne in dollars, so convert it first: 110.00 at 1.10 dollars per euro is 100.00 euros a tonne, and at 6.978 MWh of heat in a tonne of 6,000 kcal coal, 14.33 euros per MWh thermal.
Fuel per MWh of power = fuel price / efficiency: gas 35.00 / 0.54 = 64.81; coal 14.33 / 0.38 = 37.71
CO2 per MWh of power = emission factor / efficiency: gas 0.202 / 0.54 = 0.374; coal 0.341 / 0.38 = 0.897
Coal burns cheap fuel badly and emits 2.40 times as much CO2 for each MWh it sells. The whole switching question is the trade between those two facts.
Gas marginal cost = 64.81 + 3.00 + CO2 × 0.374; coal marginal cost = 37.71 + 4.50 + CO2 × 0.897
Switching price = (64.81 + 3.00 − 37.71 − 4.50) / (0.897 − 0.374) = 25.60 / 0.523 = 48.93
Excel: =(Gas/EffG+VomG-Coal/EffC-VomC)/(EFc/EffC-EFg/EffG)
Check: at 48.93 both plants cost 86.12 per MWh. At the 70.00 carbon price of the clean spark spread case, gas costs 94.00 and coal 105.03, so gas is 11.03 cheaper and runs first.
| Plant | Fuel | Carbon | Spread before carbon | Clean spread |
|---|---|---|---|---|
| Gas (spark) | 64.81 | 26.19 | 27.19 | 1.00 |
| Coal (dark) | 37.71 | 62.82 | 54.29 | -8.53 |
Before carbon the coal plant earns twice the gas plant's spread. After it, the order reverses. The switching price is the single number that says where the reversal happens, and turned round, the gas price at which it happens for a given carbon price: at 70.00 a tonne, gas plants stay ahead of coal as long as gas is below 40.96.
| Gas, per MWh | Coal 90 $/t | Coal 110 $/t | Coal 130 $/t |
|---|---|---|---|
| 25.00 | 26.64 | 13.54 | 0.43 |
| 30.00 | 44.33 | 31.23 | 18.13 |
| 35.00 | 62.03 | 48.93 | 35.82 |
| 40.00 | 79.72 | 66.62 | 53.52 |
| 45.00 | 97.42 | 84.31 | 71.21 |
Gas moves the threshold 3.54 a tonne per euro; 10 dollars on coal moves it 6.55 the other way. Efficiency matters as much as fuel. At 35.00 gas the switching price is 33.66 against a 34 per cent coal plant and 66.68 against a 42 per cent one; on the gas side it is 62.40 for a 50 per cent unit and 38.49 for a 58 per cent unit. There is no single switching price for a market, only a band, one for each pair of plants in the merit order.
Using emission factors per MWh of fuel rather than per MWh of power. The thermal factors differ by only 0.139 tonnes, while the gap per MWh of power is 0.523, because coal plants are less efficient. Divide the same 25.60 cost gap by the thermal gap and the switching price comes out at 184.19, almost four times the right answer. Leave out efficiency and O&M on the cost side as well and it is 148.70. Either error tells a desk that coal will run ahead of gas at any plausible carbon price, which is exactly the wrong conclusion here.
The second mistake is reading the switching price as a forecast. It says which plant is cheaper in an hour, not how many hours either runs. The plant that runs is decided hour by hour against the price duration curve, which is why the clean spark spread on the annual average understates what a gas plant earns.
The dispatch of the gas plant against the hours of the year, and the gas and carbon thresholds that set it, are in the free workbooks for this case. The gas side alone is worked in how to calculate a clean spark spread, and the power price expressed as a heat rate in the implied heat rate.
Both are the power price less fuel and carbon per MWh generated: the spark spread for gas plants, the dark spread for coal. At an illustrative 92.00 power price and 70.00 carbon, a 54 per cent gas plant earns a clean spark spread of 1.00 and a 38 per cent coal plant a clean dark spread of minus 8.53, so gas runs first.
Efficiency sets both the fuel bill and the tonnes emitted per MWh of power. A 38 per cent coal plant emits 0.897 tonnes per MWh against 0.374 for a 54 per cent gas plant. At 35.00 gas the switching price is 33.66 against a 34 per cent coal plant and 66.68 against a 42 per cent one.
Solve the same equation for gas. With illustrative coal at 14.33 euros per MWh thermal and carbon at 70.00 a tonne, gas plants run ahead of coal as long as gas is below 40.96 euros per MWh. Above that, the coal plant has the lower marginal cost despite paying for 2.40 times the carbon.
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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