New insights from the shapley-folkman lemma on dispatchable demand in energy markets

Kari Hreinsson, Anna Scaglione, Mahnoosh Alizadeh, Yonghong Chen

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this paper we consider the aggregation of common convex and non-convex individual Demand Response (DR) models for responsive loads, and apply the Shapley-Folkman (SF) lemma to show that such an aggregate is approximately convex in its action space and cost, and strictly convex under mild conditions. We then discuss how reduced order convex aggregate models can be passed on to System Operators for inclusion in economic and operational models, including a novel polytope approximation as well as an ellipsoidal model derived in a distributed fashion. Numerical simulations confirm our application of the Shapley-Folkman lemma and show that the new reduced order models outperform conventional virtual generator approximations.

Original languageEnglish (US)
Article number9376954
Pages (from-to)4028-4041
Number of pages14
JournalIEEE Transactions on Power Systems
Issue number5
StatePublished - Sep 2021


  • Aggregate flexibility
  • convexity
  • demand response
  • dispatchable demand
  • load modeling
  • minkowski sum
  • shapley-folkman lemma

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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