Inertia Pricing in Stochastic Electricity Markets

Zhirui Liang, Robert Mieth, Yury Dvorkin

Research output: Contribution to journalArticlepeer-review


Maintaining the stability of renewable-dominant power systems requires the procurement of virtual inertia services from non-synchronous resources (e.g., batteries, wind turbines) in addition to inertia traditionally provided by synchronous resources (e.g., thermal generators). However, the pricing of inertia provision has not been studied in a stochastic electricity market, where the uncertainty characteristics of renewable energy sources (RES) are considered. To fill in this research gap, this paper formulates a chance-constrained stochastic unit commitment model with inertia requirements and computes equilibrium energy, reserve and inertia prices using convex duality. Numerical experiments on an illustrative system and a modified IEEE 118-bus system show the performance of the proposed pricing mechanism. By allowing new virtual inertia providers to contribute to system inertia requirements, the total operating cost reduces. Moreover, the proposed stochastic electricity market internalizes RES uncertainty, which yields additional cost reductions by co-optimizing energy, reserve and inertia procurement.

Original languageEnglish (US)
Pages (from-to)2071-2084
Number of pages14
JournalIEEE Transactions on Power Systems
Issue number3
StatePublished - May 1 2023


  • Inertia pricing
  • chance constraints
  • low-inertia systems
  • stochastic electricity market
  • unit commitment (UC)

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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