Distribution Locational Marginal Pricing by Convexified ACOPF and Hierarchical Dispatch

Zhao Yuan*, Mohammad Reza Hesamzadeh, Darryl R. Biggar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

40 Citations (Scopus)


This paper proposes a hierarchical economic dispatch (HED) mechanism for computing distribution locational marginal prices (DLMPs). The HED mechanism involves three levels: 1) the top level is the national (regional) transmission network; 2) the middle level is the distribution network; and while 3) the lowest level reflects local embedded networks or microgrids. Each network operator communicates its generalized bid functions (GBFs) to the next higher level of the hierarchy. The GBFs approximate the true cost function of a network by a series of affine functions. The concept of Benders cuts are employed in simulating the GBFs. The ac optimal power flow (ACOPF) is convexified and then used for dispatching generators and calculating GBFs and DLMPs. The proposed convexification is based on the second order cone reformulation. A sequential optimization algorithm is developed to tighten the proposed second order cone relaxation of ACOPF. The properties of the sequential tightness algorithm are discussed and proved. The HED is implemented in the GAMS grid computing platform. The GBFs and DLMPs are calculated for the modified IEEE 342 node low voltage test system. The numerical results show the utility of the proposed HED and GBF in implementing DLMP.

Original languageEnglish
Pages (from-to)3133-3142
Number of pages10
JournalIEEE Transactions on Smart Grid
Issue number4
Publication statusPublished - Jul 2018

Bibliographical note

Publisher Copyright:
© 2010-2012 IEEE.

Other keywords

  • Convexified ACOPF
  • DLMP
  • generalized bid function
  • hierarchical economic dispatch


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