An outage removes particular hours, and the hours decide the bill. The average price of the window says almost nothing about it.
A planned outage costs the margin the plant would have earned in the hours it is removed from: capacity times the sum, hour by hour, of the price less the marginal cost wherever that difference is positive. For an illustrative 400 MW gas plant with a marginal cost of 75.00, the same 30-day outage costs 5,980,000 in January, 3,310,000 in July and 1,390,000 in April. Priced on the window's average price instead, April would cost nothing, and January would be understated by 1,308,000.
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 a fictional combined-cycle unit of 400 MW whose marginal cost, gas plus carbon plus variable operating cost, is 75.00 per MWh. The work takes 30 days, 720 hours, and can be scheduled in one of three windows. Each window's hours are grouped into six price levels, a price duration curve for the month. Every figure is illustrative.
| Price | January | April | July |
|---|---|---|---|
| 160 | 70 | 5 | 25 |
| 115 | 150 | 35 | 90 |
| 90 | 200 | 110 | 170 |
| 72 | 180 | 200 | 210 |
| 58 | 90 | 220 | 150 |
| 35 | 30 | 150 | 75 |
| Average price | 91.22 | 65.47 | 77.91 |
The plant runs only when the price is above its marginal cost. An outage therefore costs nothing in the hours it would have been off anyway, and the full spread in the hours it would have run.
Outage cost = MW × Σ hoursi × max(0, pricei − marginal cost)
January = 400 × (70 × 85.00 + 150 × 40.00 + 200 × 15.00) = 400 × 14,950 = 5,980,000
Excel, with the prices in A2:A7 and the window's hours in B2:B7: =MW*SUMPRODUCT(B2:B7,(A2:A7>MC)*(A2:A7-MC))
| Hours | Price | Price less marginal cost | Lost margin |
|---|---|---|---|
| 70 | 160 | 85.00 | 2,380,000 |
| 150 | 115 | 40.00 | 2,400,000 |
| 200 | 90 | 15.00 | 1,200,000 |
| 180 | 72 | -3.00 | 0 |
| 90 | 58 | -17.00 | 0 |
| 30 | 35 | -40.00 | 0 |
| 720 | 91.22 | 5,980,000 |
The 70 dearest hours, under a tenth of the window, carry 2,380,000, 39.8 per cent of the cost. That concentration is the whole story of power plant economics: the margin lives in a few hours, and an outage that lands on them is expensive however short it is.
| Window | Hours the plant would run | MWh lost | Lost margin | Per MWh lost | Window-average method |
|---|---|---|---|---|---|
| January | 420 | 168,000 | 5,980,000 | 35.60 | 4,672,000 |
| April | 150 | 60,000 | 1,390,000 | 23.17 | 0 |
| July | 285 | 114,000 | 3,310,000 | 29.04 | 838,000 |
April is the cheapest window by 1,920,000 against July and 4,590,000 against January. January costs 4.3 times as much for the same work. Put on the plan as the same 720 hours in every column, the three windows look interchangeable, and the choice gets made by contractor availability.
Divided by its 30 days, the January outage costs 199,333 a day, July 110,333 and April 46,333. That daily figure is the one to put beside the contractor's quote for extra crews or a shorter programme: paying 100,000 to finish a January outage two days early saves 398,667, while the same offer in April saves only 92,667 and does not pay. It also prices the risk of overrun. Five extra days in January cost about 996,667 if the overrun lands on average hours, and more if it lands on the cold snap that made the January prices in the first place. The overrun risk belongs in the choice of window, beside the planned cost.
| Marginal cost | January | April | July | January less April |
|---|---|---|---|---|
| 65.00 | 8,164,000 | 2,550,000 | 5,038,000 | 5,614,000 |
| 75.00 | 5,980,000 | 1,390,000 | 3,310,000 | 4,590,000 |
| 85.00 | 4,300,000 | 790,000 | 2,170,000 | 3,510,000 |
A cheaper fuel curve makes every outage dearer, and widens the gap between windows. An outage plan priced at budget time is stale as soon as gas or carbon moves, which is when it should be repriced. The marginal cost itself is built in how to calculate a clean spark spread.
The price duration curve, the dispatch row by row and the outage hours moved along the curve are live in the free workbooks for this book.
Price each candidate window on its own hours: for every hour in the window, take the price less the plant's marginal cost where positive, sum, and multiply by capacity. The window with the smallest sum is the cheapest. In the illustrative case here April costs 1,390,000 against 5,980,000 for January, a factor of 4.3, for the same 720 hours of work.
Not the economic cost. A forward sale still has to be delivered, so during the outage the desk buys the hedged volume at spot in every hour, 288,000 MWh in a 30-day January window for 26,272,000. Had the plant run, it would have generated in the 420 hours above marginal cost at 75.00 and bought back only in the 300 below, for 20,292,000 in all. The difference between the two is exactly the 5,980,000 of lost margin.
Because a higher marginal cost leaves fewer hours in the money and a thinner spread in those that remain. At a marginal cost of 85.00 the January outage costs 4,300,000 instead of 5,980,000, and the April one 790,000. The outage is cheapest exactly when the plant is earning least, which is why outage plans should be repriced when the fuel curve moves.
The outage plan read as a valuation is one of the working documents for Energy Trading, and the workbook for chapters 4 to 7 moves the outage hours along the price duration curve. 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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