[Paper Review] On the Radiality Constraints for Distribution System Restoration and Reconfiguration Problems

Ying Wang, Yin Xu+3 more|arXiv (Cornell University)|Dec 11, 2019

Optimal Power Flow Distribution12 references4 citations

TL;DR

This paper identifies critical limitations of spanning tree (ST) constraints in distribution system restoration and reconfiguration, demonstrating they can produce pseudo-roots and non-radial topologies when multiple sources exist. It proposes single-commodity flow (SCF0) and a combined SCF+ST constraint set, showing SCF0 ensures radiality and SCF+ST significantly improves computational efficiency in reconfiguration problems, while SCF0 is more effective for restoration due to additional binary variables.

ABSTRACT

Radiality constraints are involved in both distribution system restoration and reconfiguration problems. However, a set of widely used radiality constraints, i.e., the spanning tree (ST) constraints, has its limitations which have not been well recognized. In this letter, the limitation of the ST constraints is analyzed and an effective set of constraints, referred to as the single-commodity flow constraints, is presented. Furthermore, a combined set of constraints is proposed and case studies indicate that the combined constraints can gain computational efficiency in the reconfiguration problem. Recommendations on the use of radiality constraints are also provided.

Motivation & Objective

• To identify the limitations of widely used spanning tree (ST) constraints in ensuring radial distribution network topology.
• To propose a robust alternative radiality constraint set, single-commodity flow (SCF0), that guarantees radiality even with multiple sources.
• To develop a combined constraint set, SCF+ST, to enhance computational efficiency in reconfiguration problems.
• To provide practical recommendations on selecting radiality constraints based on problem type (restoration vs. reconfiguration).

Proposed method

• Analyzes the ST constraints (1)-(3) and demonstrates they are insufficient for radiality when multiple sources exist, leading to pseudo-roots and loops.
• Introduces SCF0 constraints as a proven method to enforce radial topology by modeling flow from each node to a root.
• Proposes a combined constraint set SCF+ST that integrates parent-child relationships (ST) with flow-based constraints (SCF0) to tighten the feasible region.
• Employs mixed-integer second-order cone programming (MISOCP) models with CVXPY and solvers MOSEK and CPLEX to test performance.
• Conducts case studies on 32-node, IEEE 123-node, and larger systems (83, 135, 201 nodes) under restoration and reconfiguration scenarios.
• Uses average computation time and percentage of scenarios hitting time limits as performance metrics to compare SCF0 and SCF+ST.

Experimental results

Research questions

• RQ1 Why do standard spanning tree (ST) constraints fail to guarantee radial topology in distribution systems with multiple sources?
• RQ2 How does the single-commodity flow (SCF0) constraint set ensure radiality in multi-source distribution networks?
• RQ3 What is the impact of combining ST and SCF0 constraints (SCF+ST) on computational efficiency in reconfiguration problems?
• RQ4 Why does SCF0 outperform SCF+ST in restoration problems despite SCF+ST's efficiency in reconfiguration?
• RQ5 What are the optimal radiality constraint sets for restoration versus reconfiguration problems?

Key findings

• The ST constraints alone are insufficient for radiality, as they can produce pseudo-roots and loops in multi-source systems.
• SCF0 guarantees radial topology in all tested scenarios, including those with multiple sources, and ensures feasibility in both restoration and reconfiguration problems.
• For reconfiguration problems, SCF+ST reduces computation time significantly—e.g., from over 10 hours (SCF0) to 6966.86s (SCF+ST) on the 201-node system with MOSEK.
• In restoration problems, SCF0 achieves faster average computation time and fewer time-limit violations than SCF+ST, indicating better performance under complex binary variable interactions.
• The performance difference between SCF0 and SCF+ST stems from the presence of load status binaries in restoration, which complicates the solution space and reduces the benefit of additional ST constraints.
• The study recommends using SCF0 for restoration and SCF+ST for reconfiguration to maximize computational efficiency while ensuring radiality.