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Exact and Heuristic Approaches for the Stochastic N-k Interdiction in Power Grids

Kaarthik Sundar, Andrew Mastin, Manuel Garcia, Russell Bent, Jean-Paul Watson

Abstract

The article introduces the stochastic N-k interdiction problem for power grid operations and planning that aims to identify a subset of k components (out of N components) that maximizes the expected damage, measured in terms of load shed. Uncertainty is modeled through a fixed set of outage scenarios, where each scenario represents a subset of components removed from the grid. We formulate the stochastic N-k interdiction problem as a bi-level optimization problem and propose two algorithmic solutions. The first approach reformulates the bi-level stochastic optimization problem to a single level, mixed-integer linear program (MILP) by dualizing the inner problem and solving the resulting problem directly using a MILP solver to global optimality. The second is a heuristic cutting-plane approach, which is exact under certain assumptions. We compare these approaches in terms of computation time and solution quality using the IEEE-Reliability Test System and present avenues for future research.

Exact and Heuristic Approaches for the Stochastic N-k Interdiction in Power Grids

Abstract

The article introduces the stochastic N-k interdiction problem for power grid operations and planning that aims to identify a subset of k components (out of N components) that maximizes the expected damage, measured in terms of load shed. Uncertainty is modeled through a fixed set of outage scenarios, where each scenario represents a subset of components removed from the grid. We formulate the stochastic N-k interdiction problem as a bi-level optimization problem and propose two algorithmic solutions. The first approach reformulates the bi-level stochastic optimization problem to a single level, mixed-integer linear program (MILP) by dualizing the inner problem and solving the resulting problem directly using a MILP solver to global optimality. The second is a heuristic cutting-plane approach, which is exact under certain assumptions. We compare these approaches in terms of computation time and solution quality using the IEEE-Reliability Test System and present avenues for future research.
Paper Structure (7 sections, 10 equations, 2 figures, 3 tables, 1 algorithm)

This paper contains 7 sections, 10 equations, 2 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Algorithmic Approaches
  4. Exact Approach
  5. Heuristic Cutting Plane Algorithm
  6. Computational Results
  7. Conclusion and Avenues For Future Work

Figures (2)

  • Figure 1: Buses and lines of the RTS-GMLC test system. For each scenario, between $4$ to $6$ components (i.e., generators and lines) shown in red are randomly turned off. $200$ such scenarios are considered.
  • Figure 2: Top: Average load shed (over all the $200$ scenarios) at each bus in the optimal solution for the stochastic $N$-$k$ interdiction problem for different values of $\bm k$ is shown. Larger sizes of red discs indicate larger average load shed at a bus. Bottom: the components (shown in blue) are the interdicted components in the optimal $N$-$k$ interdiction plan.