A Two-Stage Decomposition Approach for AC Optimal Power Flow

Shenyinying Tu*, Andreas Wachter, Ermin Wei

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The alternating current optimal power flow (AC-OPF) problem is critical to power system operations and planning, but it is generally hard to solve due to its nonconvex and large-scale nature. This paper proposes a scalable decomposition approach in which the power network is decomposed into a master network and a number of subnetworks, where each network has its own AC-OPF subproblem. This formulates a two-stage optimization problem and requires only a small amount of communication between the master and subnetworks. The key contribution is a smoothing technique that renders the response of a subnetwork differentiable with respect to the input from the master problem, utilizing properties of the barrier problem formulation that naturally arises when subproblems are solved by a primal-dual interior-point algorithm. Consequently, existing efficient nonlinear programming solvers can be used for both the master problem and the subproblems. The advantage of this framework is that speedup can be obtained by processing the subnetworks in parallel, and it has convergence guarantees under reasonable assumptions. The formulation is readily extended to instances with stochastic subnetwork loads. Numerical results show favorable performance and illustrate the scalability of the algorithm which is able to solve instances with more than 11 million buses.

Original languageEnglish (US)
Article number9115808
Pages (from-to)303-312
Number of pages10
JournalIEEE Transactions on Power Systems
Issue number1
StatePublished - Jan 2021


  • Optimal power flow
  • decomposition
  • distribution networks
  • primal-dual interior point method
  • smoothing technique
  • stochastic optimization
  • transmission networks
  • two-stage optimization

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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