Optimization Dynamics: A Bus-Level Distributed Approach for Optimal Power Flows

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6 Scopus citations


We propose a continuous-time optimization dynamics approach in this paper to solve the nonconvex optimal power flow (OPF) problem. The proposed approach naturally uses the distributed power flow structure for computation. Specifically, each bus in the power network plays as an individual computing agent, which only uses local information to update its own voltage variables as well as Lagrange multipliers. Therefore, the proposed approach is completely distributed at the bus level. Under mild conditions, we first prove the local existence of a unique, continuous solution (with respect to the initial condition) to our optimization dynamics. Next, we show that every trajectory starting from a local neighborhood converges to a pair of primal and dual optima (saddle point) for the associated OPF problem. Simulations based on the IEEE benchmark systems are provided to verify the effectiveness of the proposed approach.

Original languageEnglish (US)
Article number8428461
Pages (from-to)642-652
Number of pages11
JournalIEEE Transactions on Control of Network Systems
Issue number2
StatePublished - Jun 2019

Bibliographical note

Funding Information:
This work was supported by the National Science Foundation under Grant CNS 1239319.

Publisher Copyright:
© 2014 IEEE.


  • Bus-level distributed computation
  • continuous-time optimization dynamics
  • non-convex optimization
  • optimal power flow (OPF)


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