Power over gas, compared with the plant's own heat rate plus variable cost, hour by hour rather than on the annual average.
The implied market heat rate is the power price divided by the gas price, in MMBtu per MWh: the heat rate a plant could have and still break even on fuel alone. A plant runs when the implied heat rate beats its own heat rate plus variable cost divided by gas. At 8.60 gas, a 7.2 heat rate and 3.40 of variable cost the hurdle is 7.595; the annual forward of 70.19 implies 8.161, but the hours that clear the hurdle earn 60.79 million, not the 24.14 million the annual figure suggests.
Worked in full in Energy Trading by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A gas plant's margin depends on two prices, and a power forward on its own says nothing about whether the plant is in the money. Dividing power by gas removes the gas level and leaves a single number that can be compared directly with the plant's physical efficiency. If power is 72.00 and gas 8.60, the market is paying for 8.372 MMBtu of gas per MWh of power; a plant that burns 7.2 has 1.172 MMBtu of headroom to cover its other variable costs. Heat rate call options and many tolling agreements are struck in these units, and spark spread desks watch the ratio alongside the spread, because it strips the gas level out of the power price.
| Input | Value |
|---|---|
| Capacity | 620 MW |
| Plant heat rate, MMBtu per MWh | 7.20 |
| Gas, per MMBtu | 8.60 |
| Variable operating cost, per MWh | 3.40 |
| Annual baseload forward, the time-weighted average of the curve | 70.19 |
| Outage, taken in the cheapest hours | 760 hours |
Implied heat rate: power price ÷ gas price. Forward: 70.19 ÷ 8.60 = 8.161.
Plant break-even heat rate: plant heat rate + variable cost ÷ gas = 7.20 + 3.40 ÷ 8.60 = 7.20 + 0.395 = 7.595.
Dispatch test: run in an hour if implied heat rate > 7.595, which is the same test as price > marginal cost: 7.20 × 8.60 + 3.40 = 65.32.
Gas threshold for an hour priced P: (P − variable cost) ÷ plant heat rate. The plant runs in that hour only while gas is below it.
In Excel: =Power/Gas for the implied heat rate and =IF(Power/Gas>HR+VOM/Gas,1,0) for the dispatch flag. With carbon, subtract the carbon cost per MWh from power first: =(Power-CO2Cost)/Gas.
| Hours | Price | Implied heat rate | Net of marginal cost | Gas threshold | Margin |
|---|---|---|---|---|---|
| 100 | 260.00 | 30.23 | 194.68 | 35.6389 | 12,070,160 |
| 250 | 155.00 | 18.02 | 89.68 | 21.0556 | 13,900,400 |
| 550 | 105.00 | 12.21 | 39.68 | 14.1111 | 13,530,880 |
| 1,100 | 85.00 | 9.88 | 19.68 | 11.3333 | 13,421,760 |
| 1,900 | 72.00 | 8.37 | 6.68 | 9.5278 | 7,869,040 |
| 2,400 | 63.00 | 7.33 | -2.32 | 8.2778 | 0 |
| 1,700 | 50.00 | 5.81 | -15.32 | 6.4722 | 0 |
| 760 | 34.00 | 3.95 | -31.32 | 4.2500 | 0 |
| 8,760 | 70.19 | 8.16 | 60,792,240 |
Five bands clear the 7.595 hurdle: 3,900 hours, a 44.5 per cent load factor, 2,418,000 MWh and a gross margin of 60,792,240. The 2,400 hours at 63.00 imply 7.33, above the plant's raw 7.20 but below the 7.595 that includes variable cost, so the plant stays off. That is the reason to compare against the break-even heat rate and not the nameplate one: on the nameplate test the plant would run 2,400 hours at a loss of 2.32 per MWh.
The annual forward tells a much smaller story. Its implied heat rate of 8.161 clears the hurdle by 0.566, and 620 MW across 8,000 available hours at a spread of 70.19 less 65.32 gives 24.14 million. The hours give 2.52 times that. The first two bands alone, 350 hours, earn 25.97 million, 42.7 per cent of the year.
| Gas | Marginal cost | Break-even heat rate | Forward implied heat rate | Hours run | Margin |
|---|---|---|---|---|---|
| 7.60 | 58.12 | 7.647 | 9.235 | 6,300 | 85.46 |
| 8.00 | 61.00 | 7.625 | 8.773 | 6,300 | 74.21 |
| 8.60 | 65.32 | 7.595 | 8.161 | 3,900 | 60.79 |
| 9.00 | 68.20 | 7.578 | 7.799 | 3,900 | 53.83 |
| 9.60 | 72.52 | 7.554 | 7.311 | 2,000 | 44.00 |
The dispatch holds only while gas sits between 8.2778 and 9.5278, the thresholds of the 63.00 and 72.00 bands. Below 8.2778 the plant picks up 2,400 more hours; above 9.5278 it loses 1,900. At 9.60 the forward's implied heat rate, 7.311, is below the break-even 7.554, and a desk reading the annual figure would value the plant at minus 11.57 million. It still earns 44.00 million in its 2,000 best hours. Note too that the break-even heat rate falls as gas rises, because a fixed variable cost is a smaller share of a dearer fuel bill.
Computing one implied heat rate from the annual forward and treating the plant as in or out of the money on that number. The average hides the hours: an implied heat rate of 8.161 is not something that happens in any of the year's eight price bands. It is a blend of hours at 30.23 and hours at 3.95, and the plant only sells into the top of that distribution. Comparing the forward heat rate with the nameplate heat rate compounds the error by ignoring variable cost. Use the break-even heat rate, and apply it hour by hour.
Implied heat rate = power ÷ gas; run when it exceeds plant heat rate + variable cost ÷ gas. On this plant the hurdle is 7.595, the forward implies 8.161, and the hours that clear the hurdle earn 60.79 million against 24.14 million on the annual reading. The curve, the dispatch and the gas thresholds are live formulas in the free workbook for this case. For the same test with carbon and efficiency instead of heat rate, see how to calculate a clean spark spread; for the base and peak split of the same forward, how to calculate the off-peak price from base and peak.
The implied heat rate at which a plant just covers its fuel and variable cost: plant heat rate plus variable operating cost divided by the gas price. For a 7.2 MMBtu per MWh plant with 3.40 of variable cost and gas at 8.60 it is 7.595. Any hour whose power price divided by gas exceeds that number is worth running.
They test the same thing in different units. The spark spread is power minus heat rate times gas, in money per MWh; the implied heat rate is power divided by gas, in MMBtu per MWh. At 72.00 power and 8.60 gas the spark spread on a 7.2 plant is 10.08 and the implied heat rate 8.372; both say the hour is worth running.
Because the variable operating cost is fixed per MWh and is converted into heat rate by dividing by gas. With 3.40 of variable cost on a 7.2 heat rate plant, the break-even is 7.647 at 7.60 gas and 7.554 at 9.60 gas. A dearer fuel makes the other costs a smaller share of the hurdle.
The plant's dispatch off the price duration curve is worked in chapters 4 to 7 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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