Moment-SOS Approach to Interval Power Flow

Chao Duan, Lin Jiang, Wanliang Fang*, Jun Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Intermittent renewable sources and market-driven operation have brought many uncertainties into modern power systems. Power flow analysis tools are expected to be able to incorporate uncertainties into the solution process. Interval power flow (IPF) analysis which aims at obtaining the upper and lower bounds of power flow solutions under interval uncertainties, thereby emerges as a promising framework to meet such expectation. This paper describes a novel optimization-based method to obtain high-accuracy or even exact global solutions to IPF problems. At first, the IPF problems are formulated as polynomial optimization problems probably with rational objective functions. Then Lasserre's hierarchy, or moment-SOS approach, is introduced to relax the non-convex problems to convex semidefinite programming (SDP) problems. Correlative sparsity in the polynomial optimization problems is exploited to improve numerical tractability and efficiency. Finally, case studies on IEEE 6-bus, 9-bus and 14-bus systems demonstrate the second-order moment relaxation is capable of obtaining exact global interval solutions on small-scale systems, and numerical results on IEEE 57-bus, 118-bus and 300-bus systems show the proposed method can significantly improve the interval solutions compared with recent Linear Programming (LP) relaxation method on larger systems.

Original languageEnglish (US)
Article number7439871
Pages (from-to)522-530
Number of pages9
JournalIEEE Transactions on Power Systems
Issue number1
StatePublished - Jan 2017


  • Interval power flow
  • correlative sparsity
  • moment relaxation
  • polynomial optimization

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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