Introducing Uncertainty Components in Locational Marginal Prices for Pricing Wind Power and Load Uncertainties

Xin Fang, Brian Hodge, Ershun Du, Chongqing Kang, Fangxing Li

Research output: Contribution to journalArticlepeer-review

83 Scopus Citations


With substantially increasing penetration levels of wind power, electric power system flexibility is needed to address the variability and uncertainty of wind power output. Thus, it has become an urgent issue to obtain an optimal tradeoff between economics and reliability, and to price system uncertainties. This paper proposes a new electricity market-clearing mechanism based on locational marginal prices (LMPs) for pricing uncertain generation and load. The uncertainty contained locational marginal price (U-LMP) is derived from a distributionally robust chance-constrained optimal power flow model in which only the first-order and second-order moments of the uncertain sources' probability distribution are needed. Compared with traditional LMPs, the proposed U-LMP formulation includes two new uncertainty components: transmission line overload uncertainty price and generation violation uncertainty price. These LMP uncertainty components are the price signals reflecting the system costs as a result of wind generation and demand uncertainty at different locations. Finally, using parametric case studies, the relationship among uncertainty levels, system generation cost, and LMP uncertainty components are established. Case studies performed on the PJM 5-bus and IEEE 118-bus systems verify the proposed U-LMP method.

Original languageAmerican English
Article number8601342
Pages (from-to)2013-2024
Number of pages12
JournalIEEE Transactions on Power Systems
Issue number3
StatePublished - May 2019

Bibliographical note

Publisher Copyright:
© 1969-2012 IEEE.

NREL Publication Number

  • NREL/JA-5D00-70712


  • Chance constrained optimization
  • Economic dispatch
  • Locational marginal price (lmp)
  • Optimal power flow
  • Uncertainty


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