Beyond Relaxation and Newton-Raphson: Solving AC OPF for Multi-Phase Systems with Renewables

Emiliano Dall-Anese, Ahmed Zamzam, Nicholas Sidiropoulos

Research output: Contribution to journalArticlepeer-review

13 Scopus Citations


This paper focuses on the AC Optimal Power Flow(OPF) problem for multi-phase systems. Particular emphasis isgiven to systems with high integration of renewables, whereadjustments of the real and reactive output powers from renewablesources of energy are necessary in order to enforce voltageregulation. The AC OPF problem is known to be nonconvex(and, in fact, NP-hard). Convex relaxation techniques have beenrecently explored to solve the OPF task with reduced computationalburden; however, sufficient conditions for tightnessof these relaxations are only available for restricted classesof system topologies and problem setups. Identifying feasiblepower-flow solutions remains hard in more general problemformulations, especially in unbalanced multi-phase systems withrenewables. To identify feasible and optimal AC OPF solutionsin challenging scenarios where existing methods may fail, thispaper leverages the Feasible Point Pursuit - Successive ConvexApproximation algorithm - a powerful approach for generalnonconvex quadratically constrained quadratic programs. Themerits of the approach are illustrated using single- and multiphasedistribution networks with renewables, as well as severaltransmission systems.

Original languageAmerican English
Article number2645220
Pages (from-to)3966-3975
Number of pages10
JournalIEEE Transactions on Smart Grid
Issue number5
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© 2018 American Scientific Publishers All rights reserved.

NREL Publication Number

  • NREL/JA-5D00-67606


  • Convex relaxation
  • Feasible point pursuit
  • Optimal power flow
  • Renewable sources of energy
  • Successive convex approximation


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