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Robust Partitioning and Operation for Maximal Uncertain-Load Delivery in Distribution Grids

Hannah Moring, Harsha Nagarajan, Kshitij Girigoudar, David M. Fobes, Johanna L. Mathieu

Abstract

To mitigate the vulnerability of distribution grids to severe weather events, some electric utilities use preemptive de-energization as the primary line of defense, causing significant power outages. In such instances, networked microgrids could improve resiliency and maximize load delivery, though the modeling of three-phase unbalanced network physics and computational complexity pose challenges. These challenges are further exacerbated by an increased penetration of uncertain loads. In this paper, we present a two-stage mixed-integer robust optimization problem that configures and operates networked microgrids, and is guaranteed to be robust and feasible to all realizations of loads within a specified uncertainty set, while maximizing load delivery. To solve this problem, we propose a cutting-plane algorithm, with convergence guarantees, which approximates a convex recourse function with sub-gradient cuts. Finally, we provide a detailed case study on the IEEE 37-bus test system to demonstrate the economic benefits of networking microgrids to maximize uncertain-load delivery.

Robust Partitioning and Operation for Maximal Uncertain-Load Delivery in Distribution Grids

Abstract

To mitigate the vulnerability of distribution grids to severe weather events, some electric utilities use preemptive de-energization as the primary line of defense, causing significant power outages. In such instances, networked microgrids could improve resiliency and maximize load delivery, though the modeling of three-phase unbalanced network physics and computational complexity pose challenges. These challenges are further exacerbated by an increased penetration of uncertain loads. In this paper, we present a two-stage mixed-integer robust optimization problem that configures and operates networked microgrids, and is guaranteed to be robust and feasible to all realizations of loads within a specified uncertainty set, while maximizing load delivery. To solve this problem, we propose a cutting-plane algorithm, with convergence guarantees, which approximates a convex recourse function with sub-gradient cuts. Finally, we provide a detailed case study on the IEEE 37-bus test system to demonstrate the economic benefits of networking microgrids to maximize uncertain-load delivery.
Paper Structure (17 sections, 11 equations, 3 figures, 2 tables, 1 algorithm)

This paper contains 17 sections, 11 equations, 3 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Notation and Preliminaries
  4. Network Configuration Constraints
  5. Radiality Constraints
  6. Grid-Forming DER Constraints
  7. Single-Stage Robust Partitioning and Operation Problem
  8. A Cutting-Plane Algorithm to solve the RPOP
  9. Two-stage Robust Partitioning and Operation Problem
  10. A Cutting-plane Algorithm
  11. Numerical Results
  12. Implementation details
  13. Test case: IEEE 37-bus test system
  14. RPOP's performance for varying levels of load uncertainty
  15. RPOP's performance against deterministic counterparts
  16. ...and 2 more sections

Figures (3)

  • Figure 1: Dynamic partition of networked microgrids using switches. Load blocks are interconnected by switches to form connected components (CCs), acting as independent microgrids. Each CC contains uncertain loads and a set of DERs, with at least one designated as a Grid-Forming DER (GF-DER) when it's CC is energized.
  • Figure 2: Single-line diagram of the 37-bus network without loads shown.
  • Figure 3: Optimal partitioning of the 37-bus network with varying levels of uncertain loads. We assume the substation is out-of-service. Energized and de-energized CCs are colored green and red, respectively. GF-DER and closed switches are highlighted in blue.