Short and long volumes cancel over the year. The cost does not, because a wind farm's errors move the system the same way.
A wind farm's imbalance cost is the sum, over every settlement period, of its deviation from the day-ahead position (actual minus forecast) times the gap between the imbalance price and the day-ahead price, with the sign reversed. For an illustrative 100 MW farm producing 306,600 MWh a year with an unbiased forecast, that is 1,338,700 a year, or 4.37 per MWh produced, 7.0 per cent of its capture price. Short and long volumes almost cancel; the cost comes from when the deviations happen.
Worked in full in Energy Trading by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
That last sentence is the whole subject. A wind forecast error is not a random draw against the grid. When the weather beats the forecast for one farm, it usually beats it for every farm in the region, and the system is pushed the same way as the farm. The imbalance price then punishes the farm for being on the wrong side of a move it helped cause.
The farm sells its day-ahead forecast at the day-ahead price and is settled for any deviation at a single imbalance price. The year is grouped into five states by the direction of the farm's error and of the system's imbalance. All figures are illustrative, in euros, not data from any market.
| State | Hours | Deviation, MW | Day-ahead | Imbalance price | Spread |
|---|---|---|---|---|---|
| Wind short, system short | 1,800 | −14 | 75 | 112 | 37 |
| Wind short, system long | 700 | −9 | 70 | 52 | −18 |
| Wind long, system long | 1,900 | 13 | 65 | 38 | −27 |
| Wind long, system short | 800 | 8 | 72 | 95 | 23 |
| Within tolerance of forecast | 3,560 | 0 | 68 | 68 | 0 |
The correlation is in the hours column. When the farm is short, the system is short 1,800 hours out of 2,500; when the farm is long, the system is long 1,900 hours out of 2,700.
Imbalance P&L = hours × (actual − forecast) × (imbalance price − day-ahead price)
Short, system short: 1,800 × (−14) × 37 = −932,400
Short, system long: 700 × (−9) × (−18) = +113,400
Long, system long: 1,900 × 13 × (−27) = −666,900
Long, system short: 800 × 8 × 23 = +147,200
Net cost = 932,400 + 666,900 − 113,400 − 147,200 = 1,338,700
Production = 100 × 35% × 8,760 = 306,600 MWh
Cost per MWh = 1,338,700 / 306,600 = 4.37
Excel: =-SUMPRODUCT(Hours,Deviation,ImbPrice-DAPrice)/Production
Reading the signs: when the farm is short it buys the missing energy at the imbalance price, having already been paid the day-ahead price for it, so a high imbalance price costs it money. When it is long it sells the surplus at the imbalance price, so a low imbalance price costs it money. The two costly states are the correlated ones, and they produce 1,599,300 of gross cost. The two helpful states, where the farm happens to lean against the system, give back only 260,600, 16.3 per cent of it.
| Measure | Value |
|---|---|
| Short volume, MWh | 31,500 |
| Long volume, MWh | 31,100 |
| Net deviation, MWh | −400 |
| Gross deviation, share of production | 20.4% |
| Cost per MWh of gross deviation | 21.38 |
| Cost per MWh produced | 4.37 |
The forecast is unbiased: over the year the farm delivered only 400 MWh less than it sold. A model that prices the net deviation at an average spread finds an imbalance cost of a few thousand. The real figure is 1,338,700 because the deviations, though they cancel in volume, are settled at prices that move against them.
Strip the correlation out and the point is plain. If the same short and long volumes were spread across system-short and system-long hours in proportion to the system's own hours (50.0 per cent each here), the expected spread on a short MWh and a long MWh would be the same, and the cost would collapse to 1,623, or 0.01 per MWh. Under single pricing, 99.9 per cent of this farm's imbalance cost is the correlation between its errors and the system's.
Better forecasting scales the deviations; a tighter or more volatile system scales the spreads. The cost is proportional to both.
| Deviations kept | Spreads at 75% | Spreads at 100% | Spreads at 150% |
|---|---|---|---|
| 100% (day-ahead only) | 3.27 | 4.37 | 6.55 |
| 70% | 2.29 | 3.06 | 4.58 |
| 50% | 1.64 | 2.18 | 3.27 |
Re-trading updated forecasts intraday is the usual way to cut the deviation, but it is not free. Suppose intraday updates halve the deviation and the 31,300 MWh traded intraday cost 1.50 a MWh in bid-offer. The imbalance bill falls to 669,350, the trading cost adds 46,950, and the total is 716,300, or 2.34 per MWh: a saving of 2.03 per MWh. The intraday price will also have moved partly towards the imbalance price by the time the update is traded, so the real saving is smaller; this is a ceiling, not an estimate.
Price the covariance, not the average. Imbalance cost is a covariance between a farm's errors and the system's price. Average deviation times average spread misses it entirely.
Group the year by the sign of the farm's error and of the system's, multiply deviation by spread in each state, and divide by production. This farm's 4.37 per MWh is 7.0 per cent of a 62.00 capture price, a cost every PPA and every merchant model should carry explicitly. It sits beside the shape discount in how to calculate a capture price and capture rate; the hourly mechanics behind both are in the free workbooks for Energy Trading.
It depends on the market's imbalance rules, forecast quality and portfolio size, so only an illustration can be given. In the worked case a 100 MW farm with an unbiased day-ahead forecast pays 4.37 per MWh produced, 7.0 per cent of its capture price; halving deviations through intraday trading brings it to 2.34 per MWh after bid-offer costs.
Because its errors are correlated with the system's. When wind under-delivers, the whole region usually does and the system is short, so imbalance prices are high exactly when the farm must buy. In the case the farm is short in a short system 1,800 hours out of 2,500, which produces 932,400 of cost on its own.
For each settlement period take actual minus forecast output, multiply by imbalance price minus day-ahead price, sum, reverse the sign and divide by production. In the worked case that is 1,338,700 over 306,600 MWh, or 4.37 per MWh; per MWh of gross deviation it is 21.38.
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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