Spot pricing when Lagrange multipliers are not unique

Donghan Feng, Zhao Xu, Jin Zhong, Jacob Østergaard

Research output: Journal article publicationJournal articleAcademic researchpeer-review

15 Citations (Scopus)


Classical spot pricing theory is based on multipliers of the primal problem of an optimal market dispatch, i.e., the solution of the dual problem. However, the dual problem of market dispatch may yield multiple solutions. In these circumstances, spot pricing or any standard pricing practice based on multipliers cannot generate a unique clearing price. Although such situations are rare, they can cause significant uncertainties and complexities in market dispatch. In practice, this situation is solved through simple empirical methods, which may cause additional operations or biased allocation. Based on a strict extension of the principles of spot pricing and surplus allocation, we propose a new pricing methodology that can yield unique, impartial, and robust solution. The new method has been analyzed and compared with other pricing approaches in accordance with spot pricing theory. Case studies support the results of the theoretical analysis, and further demonstrate that the method performs effectively in both uniform-pricing and nodal-pricing markets.
Original languageEnglish
Article number5951825
Pages (from-to)314-322
Number of pages9
JournalIEEE Transactions on Power Systems
Issue number1
Publication statusPublished - 1 Feb 2012


  • Double-sided auction
  • duality
  • nodal price
  • spot pricing

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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