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Microgrids optimal radial reconfiguration via FORWARD algorithm

Joan Vendrell Gallart, Russell Bent, Solmaz Kia

TL;DR

This work tackles the NP-hard problem of optimally reconfiguring radial microgrid topologies while selecting a subset of generators under AC power-flow physics. It introduces a two-stage hierarchical framework in which a polynomial-time FORWARD-based inner loop solves the fixed-generator radial reconfiguration (Problem 1), and a Markov Chain–driven outer loop searches over generator subsets to solve Problem 2, with a master–subproblem decomposition. The authors prove a polynomial-time mixing bound for the outer search and demonstrate scalability to networks with thousands of buses, outperforming traditional MINLP solvers and enabling effective warm-start integration for commercial tools. Practically, the approach yields fast, feasible radial configurations and large-scale performance gains, offering a viable path toward real-time microgrid design and operation with formal feasibility guarantees.

Abstract

Microgrids offer a promising paradigm for integrating distributed energy resources, bolstering energy resilience, and reducing the impact of blackouts. However, their inherent decentralization and dynamic operation present substantial energy management complexities. These complexities, including balancing supply and demand, ensuring system stability, and minimizing operational costs, often necessitate solving computationally intractable NP-hard Mixed-Integer Non-Linear Programming (MINLP) problems. Traditional MINLP solvers struggle with the scalability and feasibility guarantees required for these challenges. To address this, this paper tackles the problem of resource allocation and radial configuration design for microgrid power distribution and proposes and abstracted problem which is solved by introducing a permutation-based iterative search method over the recently introduced FORWARD method to efficiently identify feasible, near-optimal radial network structures while inherently respecting physical constraints. Furthermore, this paper investigates the integration of the proposed method as a warm-start strategy for benchmark MINLP solvers offering a scalable solution for comprehensive microgrid design.

Microgrids optimal radial reconfiguration via FORWARD algorithm

TL;DR

This work tackles the NP-hard problem of optimally reconfiguring radial microgrid topologies while selecting a subset of generators under AC power-flow physics. It introduces a two-stage hierarchical framework in which a polynomial-time FORWARD-based inner loop solves the fixed-generator radial reconfiguration (Problem 1), and a Markov Chain–driven outer loop searches over generator subsets to solve Problem 2, with a master–subproblem decomposition. The authors prove a polynomial-time mixing bound for the outer search and demonstrate scalability to networks with thousands of buses, outperforming traditional MINLP solvers and enabling effective warm-start integration for commercial tools. Practically, the approach yields fast, feasible radial configurations and large-scale performance gains, offering a viable path toward real-time microgrid design and operation with formal feasibility guarantees.

Abstract

Microgrids offer a promising paradigm for integrating distributed energy resources, bolstering energy resilience, and reducing the impact of blackouts. However, their inherent decentralization and dynamic operation present substantial energy management complexities. These complexities, including balancing supply and demand, ensuring system stability, and minimizing operational costs, often necessitate solving computationally intractable NP-hard Mixed-Integer Non-Linear Programming (MINLP) problems. Traditional MINLP solvers struggle with the scalability and feasibility guarantees required for these challenges. To address this, this paper tackles the problem of resource allocation and radial configuration design for microgrid power distribution and proposes and abstracted problem which is solved by introducing a permutation-based iterative search method over the recently introduced FORWARD method to efficiently identify feasible, near-optimal radial network structures while inherently respecting physical constraints. Furthermore, this paper investigates the integration of the proposed method as a warm-start strategy for benchmark MINLP solvers offering a scalable solution for comprehensive microgrid design.

Paper Structure

This paper contains 21 sections, 1 theorem, 16 equations, 2 figures, 7 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Problem Definition
  3. Mathematical Formulation of the Power Flow Problem
  4. Notation and Physical Properties
  5. MINLP Formulation for Optimal Reconfiguration (Problem 1)
  6. MINLP Formulation for Joint Generator Selection (Problem 2)
  7. Methodology: A Hierarchical Framework
  8. Solving Problem 1: Optimal Reconfiguration via FORWARD Adaptation
  9. Challenges in Adapting FORWARD
  10. Problem Abstraction and Key Assumptions
  11. Key Algorithmic Adaptations for AC Power Flow
  12. Solving Problem 2: Resource Allocation via Hierarchical Decomposition
  13. A Primal Decomposition Framework
  14. Stochastic Local Search via Markov Chain
  15. Markov Chain Mixing Time Analysis
  16. ...and 6 more sections

Key Result

Theorem IV.1

Given a ground set $\mathcal{V}_D$, a source set $\mathcal{V}_g\subseteq\mathcal{V}_D$ with $n_g$ sources, an initial solution $\bar{\mathcal{V}}$, and $t$ iterations where, at each one, one element of $\bar{\mathcal{V}}$ is changed by an element in $\mathcal{V}_g\setminus\bar{\mathcal{V}}$, the lea

Figures (2)

  • Figure 1: A sample radial configuration for the IEEE 37 network SA-SI-AA:22. In this example, the network is partitioned into three trees rooted at active generators $\{1, 3, 5\}$ (colored red, green, and blue, respectively). Inactive lines and inactive generators $\{21, 22,28\}$ are colored gray.
  • Figure 2: Loss of energy for each graph.

Theorems & Definitions (3)

  • Definition 1: Set of Radial Configurations
  • Theorem IV.1
  • proof