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Distributed AC Optimal Power Flow: A Scalable Solution for Large-Scale Problems

Xinliang Dai, Yuning Jiang, Yi Guo, Colin N. Jones, Moritz Diehl, Veit Hagenmeyer

TL;DR

This work tackles the scalability of large-scale AC OPF by developing a two-level distributed optimization framework that uses a barrier method to handle inequality constraints at the upper level and ALADIN to solve smoothed equality-constrained problems at the lower level. By condensing derivatives with the Schur complement and introducing distributed inertia correction, the approach reduces communication overhead while preserving convergence guarantees. The method demonstrates rapid convergence and competitive solution quality compared to centralized IPOPT on large benchmarks, highlighting its potential for privacy-preserving, scalable power-system optimization under the SPDM paradigm. Practical results show favorable initialization speed and robust performance across diverse network decompositions and operating scenarios, underscoring the method’s applicability to real-world large-scale grids.

Abstract

This paper introduces a novel distributed optimization framework for large-scale AC Optimal Power Flow (OPF) problems, offering both theoretical convergence guarantees and rapid convergence in practice. By integrating smoothing techniques and the Schur complement, the proposed approach addresses the scalability challenges and reduces communication overhead in distributed AC OPF. Additionally, optimal network decomposition enables efficient parallel processing under the single program multiple data (SPMD) paradigm. Extensive simulations on large-scale benchmarks across various operating scenarios indicate that the proposed framework outperforms the state-of-the-art centralized solver IPOPT on modest hardware. This paves the way for more scalable and efficient distributed optimization in future power system applications.

Distributed AC Optimal Power Flow: A Scalable Solution for Large-Scale Problems

TL;DR

This work tackles the scalability of large-scale AC OPF by developing a two-level distributed optimization framework that uses a barrier method to handle inequality constraints at the upper level and ALADIN to solve smoothed equality-constrained problems at the lower level. By condensing derivatives with the Schur complement and introducing distributed inertia correction, the approach reduces communication overhead while preserving convergence guarantees. The method demonstrates rapid convergence and competitive solution quality compared to centralized IPOPT on large benchmarks, highlighting its potential for privacy-preserving, scalable power-system optimization under the SPDM paradigm. Practical results show favorable initialization speed and robust performance across diverse network decompositions and operating scenarios, underscoring the method’s applicability to real-world large-scale grids.

Abstract

This paper introduces a novel distributed optimization framework for large-scale AC Optimal Power Flow (OPF) problems, offering both theoretical convergence guarantees and rapid convergence in practice. By integrating smoothing techniques and the Schur complement, the proposed approach addresses the scalability challenges and reduces communication overhead in distributed AC OPF. Additionally, optimal network decomposition enables efficient parallel processing under the single program multiple data (SPMD) paradigm. Extensive simulations on large-scale benchmarks across various operating scenarios indicate that the proposed framework outperforms the state-of-the-art centralized solver IPOPT on modest hardware. This paves the way for more scalable and efficient distributed optimization in future power system applications.

Paper Structure

This paper contains 26 sections, 3 theorems, 38 equations, 6 figures, 5 tables, 3 algorithms.

Key Result

Lemma 1

Given that is a Hermitian matrix and let $K_{11}$ be the nonsingular submatrix of $K$ and let be the Schur complement of $K_{11}$ in $K$. Then

Figures (6)

  • Figure 1: Graph-based distributed optimization in power system applications
  • Figure 2: Sequence diagram of the proposed Algorithm \ref{['alg::distIP']}
  • Figure 3: Comparison of Network Decomposition on different power systems, i.e., case13659 from pegase fliscounakis2013PEGASEjosz2016PEGASE, case24464 from ARPA-E grid optimization competition aravena2023GO, case78484 from the US Eastern Interconnection states snodgrass2021epigrids and case193k from kardovs2022beltistos.
  • Figure 4: Comparison of network decomposition on performance of the proposed Algorithm \ref{['alg::distIP']} on large-scale benchmarks.
  • Figure 5: Comparison of average wall times per iteration with different partition numbers for case78484 and case193k. Note that the parallel step encompasses the decoupled NLPs, condensing, and recovery steps.
  • ...and 1 more figures

Theorems & Definitions (14)

  • Remark 1: Decomposition of OPF shin2021graph
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Definition 1: Inertia gould1985practical
  • Lemma 1: Haynsworth inertia additivity formula haynsworth1968determinationzhang2006schur
  • Theorem 1
  • proof
  • Remark 6
  • ...and 4 more