Convex Relaxation of Grid-Connected Energy Storage System Models with Complementarity Constraints in DC OPF

Kaitlyn Garifi, Kyri Baker, Dane Christensen, Behrouz Touri

Research output: Contribution to journalArticlepeer-review

25 Scopus Citations

Abstract

Including complementarity constraints in energy storage system (ESS) models in optimization problems ensure an optimal solution will not produce a physically unrealizable control strategy where there is simultaneous charging and discharging. However, the current approaches to impose complementarity constraints require the use of non-convex optimization methods. In this paper, we propose a convex relaxation for a common ESS model that has terms for both charging and discharging based on a penalty reformulation for use in a model predictive control (MPC) based optimal power flow (DC OPF) problem. In this approach, the complementarity constraints are omitted and a penalty term is added to the optimization objective function. For the DC OPF problem, we provide analysis for the conditions under which the convex relaxation of the complementarity constraint ensures that a solution with simultaneous ESS charging and discharging operation is suboptimal. Simulation results demonstrating ESS behavior with and without the penalty reformulation are provided for an MPC-based DC OPF problem on multiple IEEE test systems.

Original languageAmerican English
Article number9082838
Pages (from-to)4070-4079
Number of pages10
JournalIEEE Transactions on Smart Grid
Volume11
Issue number5
DOIs
StatePublished - Sep 2020

Bibliographical note

Publisher Copyright:
© 2010-2012 IEEE.

NREL Publication Number

  • NREL/JA-5500-77407

Keywords

  • energy storage systems
  • model predictive control
  • Optimal power flow

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