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Radial Partitioning with Spectral Penalty Parameter Selection in Distributed Optimization for Power Systems

Mehdi Karimi

TL;DR

This work tackles scalable optimal power flow (OPF) in large power networks by combining intelligent radial partitioning with a group-based distributed optimization framework. It introduces DiCA, a distributed consensus algorithm, and a spectral penalty parameter selection to adapt penalties without extensive tuning; the subproblems induced by radial partitions leverage tree-like structures to enable efficient solution. Numerical results on MATPOWER instances show that DiCA achieves higher accuracy with fewer iterations than adaptive component-based DO, validating the partitioning strategy and adaptive parameter tuning. The open-source DiCARP package in Pyomo promotes reproducibility and practical deployment of distributed OPF on large networks.

Abstract

This paper proposes group-based distributed optimization (DO) algorithms on top of intelligent partitioning for the optimal power flow (OPF) problems. Radial partitioning of the graph of a network is introduced as a systematic way to split a large-scale problem into more tractable sub-problems, which can potentially be solved efficiently with methods such as convex relaxations. Spectral parameter selection is introduced for group-based DO as a crucial hyper-parameter selection step in DO. A software package DiCARP is created, which is implemented in Python using the Pyomo optimization package. Our numerical results for different power network instances show that our designed algorithm returns more accurate solutions to the tested problems with fewer iterations than component-based DO. Our results confirm the importance of smart partitioning and parameter selection for large-scale optimization problems on networks.

Radial Partitioning with Spectral Penalty Parameter Selection in Distributed Optimization for Power Systems

TL;DR

This work tackles scalable optimal power flow (OPF) in large power networks by combining intelligent radial partitioning with a group-based distributed optimization framework. It introduces DiCA, a distributed consensus algorithm, and a spectral penalty parameter selection to adapt penalties without extensive tuning; the subproblems induced by radial partitions leverage tree-like structures to enable efficient solution. Numerical results on MATPOWER instances show that DiCA achieves higher accuracy with fewer iterations than adaptive component-based DO, validating the partitioning strategy and adaptive parameter tuning. The open-source DiCARP package in Pyomo promotes reproducibility and practical deployment of distributed OPF on large networks.

Abstract

This paper proposes group-based distributed optimization (DO) algorithms on top of intelligent partitioning for the optimal power flow (OPF) problems. Radial partitioning of the graph of a network is introduced as a systematic way to split a large-scale problem into more tractable sub-problems, which can potentially be solved efficiently with methods such as convex relaxations. Spectral parameter selection is introduced for group-based DO as a crucial hyper-parameter selection step in DO. A software package DiCARP is created, which is implemented in Python using the Pyomo optimization package. Our numerical results for different power network instances show that our designed algorithm returns more accurate solutions to the tested problems with fewer iterations than component-based DO. Our results confirm the importance of smart partitioning and parameter selection for large-scale optimization problems on networks.
Paper Structure (10 sections, 1 theorem, 11 equations, 2 figures, 5 tables, 2 algorithms)

This paper contains 10 sections, 1 theorem, 11 equations, 2 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Notations
  3. Group-based Consensus Optimization
  4. Optimal Power Flow Problem
  5. Radial Partitioning
  6. Distributed Consensus Algorithm (DiCA)
  7. Spectral Penalty Parameter
  8. Numerical Results
  9. Conclusion
  10. Acknowledgements

Key Result

Theorem 4.1

Algorithm 1 partitions a connected graph into sub-graphs that each induces a tree.

Figures (2)

  • Figure 1: (a) Graph of the problem case9 from the MATPOWER library. The red nodes are the buses with generators. The dashed line shows a radial partitioning into two partitions. (b) The node set for the two sub-graphs, both induce trees. The dashed lines and nodes appear in both regions. The variables shown are the ones each region needs to send to the other one for the DiCA.
  • Figure 2:

Theorems & Definitions (2)

  • Theorem 4.1
  • proof