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Proactive Robust Hardening of Resilient Power Distribution Network: Decision-Dependent Uncertainty Modeling and Fast Solution Strategy

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

TL;DR

The paper addresses proactive hardening of distribution networks under extreme weather by incorporating decision-dependent uncertainty to reflect how hardening alters worst-case contingencies. It proposes a DDU-RSO framework with a trilevel defender-attacker-defender structure, where first-stage hardening decisions feed into a worst-case contingency set and an inner scenario-based stochastic program over exogenous loads and storage. To solve the model, the authors develop an enhanced Parametric C&CG algorithm that enumerates extreme points of the recourse duals and uses resilience importance indices to tighten cuts, achieving orders-of-magnitude speedups over basic C&CG and BD on 33- and 118-bus systems. Results show substantial reductions in load shedding with increasing hardening budgets and demonstrate scalability and practical applicability for resilience planning in real distribution networks, supported by robust computational performance gains.

Abstract

To address the power system hardening problem, traditional approaches often adopt robust optimization (RO) that considers a fixed set of concerned contingencies, regardless of the fact that hardening some components actually renders relevant contingencies impractical. In this paper, we directly adopt a dynamic uncertainty set that explicitly incorporates the impact of hardening decisions on the worst-case contingencies, which leads to a decision-dependent uncertainty (DDU) set. Then, a DDU-based robust-stochastic optimization (DDU-RSO) model is proposed to support the hardening decisions on distribution lines and distributed generators (DGs). Also, the randomness of load variations and available storage levels is considered through stochastic programming (SP) in the innermost level problem. Various corrective measures (e.g., the joint scheduling of DGs and energy storage) are included, coupling with a finite support of stochastic scenarios, for resilience enhancement. To relieve the computation burden of this new hardening formulation, an enhanced customization of parametric column-and-constraint generation (P-C&CG) algorithm is developed. By leveraging the network structural information, the enhancement strategies based on resilience importance indices are designed to improve the convergence performance. Numerical results on 33-bus and 118-bus test distribution networks have demonstrated the effectiveness of DDU-RSO aided hardening scheme. Furthermore, in comparison to existing solution methods, the enhanced P-C&CG has achieved a superior performance by reducing the solution time by a few orders of magnitudes.

Proactive Robust Hardening of Resilient Power Distribution Network: Decision-Dependent Uncertainty Modeling and Fast Solution Strategy

TL;DR

The paper addresses proactive hardening of distribution networks under extreme weather by incorporating decision-dependent uncertainty to reflect how hardening alters worst-case contingencies. It proposes a DDU-RSO framework with a trilevel defender-attacker-defender structure, where first-stage hardening decisions feed into a worst-case contingency set and an inner scenario-based stochastic program over exogenous loads and storage. To solve the model, the authors develop an enhanced Parametric C&CG algorithm that enumerates extreme points of the recourse duals and uses resilience importance indices to tighten cuts, achieving orders-of-magnitude speedups over basic C&CG and BD on 33- and 118-bus systems. Results show substantial reductions in load shedding with increasing hardening budgets and demonstrate scalability and practical applicability for resilience planning in real distribution networks, supported by robust computational performance gains.

Abstract

To address the power system hardening problem, traditional approaches often adopt robust optimization (RO) that considers a fixed set of concerned contingencies, regardless of the fact that hardening some components actually renders relevant contingencies impractical. In this paper, we directly adopt a dynamic uncertainty set that explicitly incorporates the impact of hardening decisions on the worst-case contingencies, which leads to a decision-dependent uncertainty (DDU) set. Then, a DDU-based robust-stochastic optimization (DDU-RSO) model is proposed to support the hardening decisions on distribution lines and distributed generators (DGs). Also, the randomness of load variations and available storage levels is considered through stochastic programming (SP) in the innermost level problem. Various corrective measures (e.g., the joint scheduling of DGs and energy storage) are included, coupling with a finite support of stochastic scenarios, for resilience enhancement. To relieve the computation burden of this new hardening formulation, an enhanced customization of parametric column-and-constraint generation (P-C&CG) algorithm is developed. By leveraging the network structural information, the enhancement strategies based on resilience importance indices are designed to improve the convergence performance. Numerical results on 33-bus and 118-bus test distribution networks have demonstrated the effectiveness of DDU-RSO aided hardening scheme. Furthermore, in comparison to existing solution methods, the enhanced P-C&CG has achieved a superior performance by reducing the solution time by a few orders of magnitudes.

Paper Structure

This paper contains 18 sections, 2 theorems, 14 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. DDU-RSO Based Resilient Hardening Model
  3. Enhanced Parametric C&CG Algorithm
  4. Single-Level Reformulation of DDU-RSO
  5. Algorithm Designs of Parametric C&CG
  6. Subproblem
  7. Master Problem
  8. Algorithm Procedures
  9. Comparative Analysis with the Basic C&CG
  10. Enhancement Strategy Based on Structural Information
  11. Numerical Results
  12. 33-Bus Test Distribution Network
  13. Resilient Hardening Results Under Different Budget Levels
  14. Impact of System Damage Levels
  15. Comparative Solution Tests of P-C&CG with Other Methods
  16. ...and 3 more sections

Key Result

Lemma 1

For the inner-most problem of $\mathbf{DDU-RSO}$, the more lines and DGs are damaged, the larger the optimal value is.

Figures (4)

  • Figure 1: Demonstration of 33-bus Power Distribution Network
  • Figure 2: Resilient Hardening Results under Different Budget Levels ($\overline{\Upsilon}$): 33-Bus Test System
  • Figure 3: Iterative procedures of P-C&CG algorithm with/without enhancement ($k=6$ and $\overline{\Upsilon}=8$)
  • Figure 4: Resilient Hardening Results ($\overline{\Upsilon}=8$, $k^L=8$, and $k^{DG}=3$): 118-Bus Test System

Theorems & Definitions (10)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Lemma 1
  • proof
  • Proposition 1
  • proof
  • Remark 5
  • Remark 6