Consolidated dynamic pricing of power system regulation

Joshua A. Taylor, Ashutosh Nayyar, Duncan S. Callaway, Kameshwar Poolla

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


The cost and quality of regulation have been brought to the forefront of power system operations by renewable variability. We propose a regulation pricing methodology based on an idea of Berger and Schweppe: in the same manner that locational marginal prices are derived from the dual of economic dispatch, let regulation prices be the dual multipliers or costate of an optimal control problem. By specializing to the linear quadratic regulator, we formulate a regulation pricing policy, which in turn allows us to derive statistically correct payments such as imbalance fees. We then construct a Vickrey-Clarke-Groves mechanism to induce selfish agents to honestly report their private valuations and costs of regulation. Semidefinite programming descriptions of the formulation can be embedded within standard convex economic dispatch constraint sets, enabling cooptimization of base load and regulation pricing. The approach mechanistically produces prices for any dynamic scenario, and can therefore be used to consolidate diverse regulation services. We demonstrate this feature by combining traditional frequency regulation, area control error, and the California Independent System Operator's Flexible Ramping Product in an example.

Original languageEnglish (US)
Pages (from-to)4692-4700
Number of pages9
JournalIEEE Transactions on Power Systems
Issue number4
StatePublished - 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


  • Dynamic pricing
  • Frequency regulation
  • Linear optimal control
  • Vickrey-Clarke-Groves mechanism


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