[Paper Review] Distribution Systems Hardening against Natural Disasters

Yushi Tan, Arindam K. Das+2 more|arXiv (Cornell University)|Nov 6, 2017

Infrastructure Resilience and Vulnerability Analysis19 references3 citations

TL;DR

This paper proposes a robust, two-stage optimization framework for hardening distribution networks against natural disasters by integrating post-disaster repair sequencing with component hardening decisions. Using a deterministic robust reformulation and a multi-run greedy heuristic, the method achieves near-optimal resilience improvement in seconds—even for large systems—demonstrating significant computational efficiency and scalability on IEEE 37- and 8500-node test feeders.

ABSTRACT

Distribution systems are often crippled by catastrophic damage caused by a natural disaster. Well-designed hardening can significantly improve the performance of post-disaster restoration operations. Such performance is quantified by a resilience measure associated with the operability trajectory. The distribution system hardening problem can be formulated as a two-stage stochastic problem, where the inner operational problem addresses the proper sequencing of post-disaster repairs and the outer problem the judicious selection of components to harden. We propose a deterministic robust reformulation with two solution methods, an MILP formulation and a heuristic approach. We provide computational evidence on various IEEE test feeders which illustrates that the heuristic approach provides near-optimal hardening solutions efficiently.

Motivation & Objective

• Address the challenge of optimizing distribution system hardening to improve post-disaster resilience, particularly in response to natural disasters like hurricanes and earthquakes.
• Integrate the operational problem of repair crew scheduling with the planning problem of component hardening into a unified optimization framework.
• Develop a computationally tractable reformulation of the two-stage stochastic hardening problem to enable efficient solution for large-scale systems.
• Provide a scalable solution method that maintains near-optimal performance while drastically reducing computation time compared to exact MILP approaches.

Proposed method

• Formulate the hardening problem as a two-stage stochastic program, where the outer stage selects hardened components and the inner stage sequences repairs to minimize customer interruption.
• Apply Jensen’s inequality to reformulate the stochastic problem into a deterministic robust counterpart, enhancing computational tractability.
• Propose a multi-run greedy heuristic framework that iteratively updates expected repair times and re-optimizes repair sequences after each hardening decision.
• Use a modified version of the repair sequencing model to compute the optimal single-crew repair sequence at each iteration, based on updated component reliability.
• Implement three heuristic options with varying degrees of schedule re-optimization, with Option 1 selected as the preferred due to speed and near-optimality.
• Evaluate performance using the resilience measure defined as the integral of the operability trajectory, minimizing the area between the actual and ideal functionality curves.

Experimental results

Research questions

• RQ1 How can distribution system hardening be optimally coordinated with post-disaster repair sequencing to maximize system resilience?
• RQ2 To what extent can a deterministic robust reformulation of the stochastic hardening problem maintain solution quality while improving computational efficiency?
• RQ3 How does the performance of a multi-run greedy heuristic compare to exact MILP solutions in terms of resilience and computation time across different network sizes?
• RQ4 What is the impact of iterative schedule re-optimization on the quality of hardening decisions, particularly for intermediate budget levels?
• RQ5 How does the proposed framework scale to large, real-world distribution networks such as the IEEE 8500-node system?

Key findings

• The heuristic approach achieved near-optimal solutions with an average performance gap of only 4.7% compared to the MILP solution, with Option 3 outperforming others in 158 out of 200 random trials.
• On the IEEE 37-node system, the MILP formulation required up to 10 hours to solve, while all heuristic variants produced solutions in under a second.
• The heuristic framework demonstrated consistent performance across varying hardening budgets, with minimal differences in resilience improvement for intermediate budgets (21–303), indicating stable convergence.
• On the large IEEE 8500-node system, the heuristic solved the problem in just 9.36 seconds, while the MILP model was infeasible to run due to computational complexity.
• The results showed a clear trend of diminishing returns in resilience improvement as the hardening budget increased, confirming the economic trade-off between investment and benefit.
• Option 1 was recommended for practical deployment due to its fast execution and strong performance, achieving 842.04 in expected harm reduction (f(𝔼[⋅])) on the 37-node system with a budget of 200.