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Robust Co-Optimization of Distribution Network Hardening and Mobile Resource Scheduling with Decision-Dependent Uncertainty

Donglai Ma, Xiaoyu Cao, Bo Zeng, Chen Chen, Qiaozhu Zhai, Qing-Shan Jia, Xiaohong Guan

TL;DR

This work tackles resilient co-planning of distribution network hardening and mobile hydrogen energy resource scheduling under decision-dependent uncertainty. It advances a two-stage DDU-RO model with a min-max resilience constraint and a mixed-integer recourse, solved exactly via a nested, enhanced parametric C&CG (N-PC&CG) algorithm. The approach demonstrates strong resilience gains and scalable performance on 14- and 56-bus networks, outperforming non-coordinated strategies and standard formulations. The results highlight the value of coupling infrastructural hardening with flexible, multi-period routing of MHERs for robust, cost-effective disaster preparedness and response.

Abstract

This paper studies the robust co-planning of proactive network hardening and mobile hydrogen energy resources (MHERs) scheduling, which is to enhance the resilience of power distribution network (PDN) against the disastrous events. A decision-dependent robust optimization model is formulated with min-max resilience constraint and discrete recourse structure, which helps achieve the load survivability target considering endogenous uncertainties. Different from the traditional model with a fixed uncertainty set, we adopt a dynamic representation that explicitly captures the endogenous uncertainties of network contingency as well as the available hydrogen storage levels of MHERs, which induces a decision-dependent uncertainty (DDU) set. Also, the multi-period adaptive routing and energy scheduling of MHERs are modeled as a mixed-integer recourse problem for further decreasing the resilience cost. Then, a nested parametric column-and-constraint generation (N-PC&CG) algorithm is customized and developed to solve this challenging formulation. By leveraging the structural property of the DDU set as well as the combination of discrete recourse decisions and the corresponding extreme points, we derive a strengthened solution scheme with nontrivial enhancement strategies to realize efficient and exact computation. Numerical results on 14-bus test system and 56-bus real-world distribution network demonstrate the resilience benefits and economical feasibility of the proposed method under different damage severity levels. Moreover, the enhanced N-PC&CG shows a superior solution capability to support prompt decisions for resilient planning with DDU models.

Robust Co-Optimization of Distribution Network Hardening and Mobile Resource Scheduling with Decision-Dependent Uncertainty

TL;DR

This work tackles resilient co-planning of distribution network hardening and mobile hydrogen energy resource scheduling under decision-dependent uncertainty. It advances a two-stage DDU-RO model with a min-max resilience constraint and a mixed-integer recourse, solved exactly via a nested, enhanced parametric C&CG (N-PC&CG) algorithm. The approach demonstrates strong resilience gains and scalable performance on 14- and 56-bus networks, outperforming non-coordinated strategies and standard formulations. The results highlight the value of coupling infrastructural hardening with flexible, multi-period routing of MHERs for robust, cost-effective disaster preparedness and response.

Abstract

This paper studies the robust co-planning of proactive network hardening and mobile hydrogen energy resources (MHERs) scheduling, which is to enhance the resilience of power distribution network (PDN) against the disastrous events. A decision-dependent robust optimization model is formulated with min-max resilience constraint and discrete recourse structure, which helps achieve the load survivability target considering endogenous uncertainties. Different from the traditional model with a fixed uncertainty set, we adopt a dynamic representation that explicitly captures the endogenous uncertainties of network contingency as well as the available hydrogen storage levels of MHERs, which induces a decision-dependent uncertainty (DDU) set. Also, the multi-period adaptive routing and energy scheduling of MHERs are modeled as a mixed-integer recourse problem for further decreasing the resilience cost. Then, a nested parametric column-and-constraint generation (N-PC&CG) algorithm is customized and developed to solve this challenging formulation. By leveraging the structural property of the DDU set as well as the combination of discrete recourse decisions and the corresponding extreme points, we derive a strengthened solution scheme with nontrivial enhancement strategies to realize efficient and exact computation. Numerical results on 14-bus test system and 56-bus real-world distribution network demonstrate the resilience benefits and economical feasibility of the proposed method under different damage severity levels. Moreover, the enhanced N-PC&CG shows a superior solution capability to support prompt decisions for resilient planning with DDU models.

Paper Structure

This paper contains 22 sections, 4 theorems, 18 equations, 3 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Resilience-Constrained DDU-RO Model
  3. Detailed Mathematical Formulation
  4. Objective Function: Minimization of Reinforcement Cost
  5. Constraints of Proactive Actions
  6. Constraints of MHERs' Re-routing and On-Emergency Energy Scheduling
  7. Constraints of Reconfigurable Distribution Network
  8. Resilience Constraint
  9. Solution Algorithm
  10. $\mathcal{OU}$ Formulation for N-PC&CG
  11. Equivalent Single-Level Reformulation
  12. Outer-Loop Parametric C&CG Algorithm
  13. Inner-Loop C&CG Algorithm
  14. Enhancement strategies
  15. Numerical Results
  16. ...and 7 more sections

Key Result

Lemma 1

For any fixed $(\bm x, \bm z)$, the $\bf u$-portion of any extreme point of the continuous relaxation of $\mathcal{U}(\bm{x},\bm{z})$, denoted by $\mathcal{U}^r(\bm{x},\bm{z})$, is binary.

Figures (3)

  • Figure 1: 14-Bus Test Power Distribution Network
  • Figure 2: Optimal Resilience Enhancement Plan with $k=6$ and $\hat{\Upsilon}=85\%$: 56-Bus Real-World System
  • Figure 3: Optimal Re-Routing and Scheduling Results Against Worst-Case Scenario: 56-Bus Real-World System

Theorems & Definitions (9)

  • Remark 1
  • Remark 2
  • Remark 3
  • Lemma 1
  • Proposition 1
  • Proposition 2
  • Theorem 1
  • Remark 4
  • Remark 5