Opportunity Cost Bidding by Wind Generators in Forward Markets: Analytical Results

C Dent, J Bialek, B Hobbs

Research output: Contribution to journalArticlepeer-review


Wind generation must trade in forward electricity markets based on imperfect forecasts of its output and real-time prices. When the real-time price differs for generators that are short and long, the optimal forward strategy must be based on the opportunity costs of charges and payments in real-time rather than a central estimate of wind output. We present analytical results for wind's optimal forward strategy. In the risk-neutral case, the optimal strategy is determined by the distribution of real-time available wind capacity, and the expected real-time prices conditioned on the forward price and wind out-turn; our approach is simpler and more computationally efficient than formulations requiring specification of full joint distributions or a large set of scenarios. Informative closed-form examples are derived for particular specifications of the wind-price dependence structure. In the usual case of uncertain forward prices, the optimal bidding strategy generally consists of a bid curve for wind power, rather than a fixed quantity bid. A discussion of the risk-averse problem is also provided. An analytical result is available for aversion to production volume risk; however, we doubt whether wind owners should be risk-averse with respect to the income from a single settlement period, given the large number of such periods in a year.
Original languageEnglish
Pages (from-to)1600-1608
Number of pages9
JournalIEEE Transactions on Power Systems
Issue number3
Publication statusPublished - Jan 2011


  • power generation economics
  • wind power generation
  • risk analysis


Dive into the research topics of 'Opportunity Cost Bidding by Wind Generators in Forward Markets: Analytical Results'. Together they form a unique fingerprint.

Cite this