Maximal Load Shedding Verification for Neural Network Models of AC Line Switching

TL;DR

The paper addresses the risk of deploying NN-based line-switching decisions in AC grids by formulating a bilevel attacker–defender verification problem that maximizes load shedding under NN-guided topology changes. It solves the inner AC-redispatch problem via a SOC relaxation and dualization to obtain a single-level, tractable bound, implemented in MathOptAI.jl, and couples this with an outer NN-input optimization. The key contributions are (i) a bilevel verification framework for maximal load shedding, (ii) a dualized SOC-OPF approach yielding guaranteed lower bounds, and (iii) a scalable pipeline combining NN proxies with conic and AC-redispatch restorations that scales to networks with millions of NN parameters. The findings indicate the method provides meaningful lower bounds and can be solved efficiently, supporting safer deployment of ML-driven OPS decisions in practice, with future work to tighten bounds and explore upper-bound guarantees.

Abstract

Solving for globally optimal line switching decisions in AC transmission grids can be intractability slow. Machine learning (ML) models, meanwhile, can be trained to predict near-optimal decisions at a fraction of the speed. Verifying the performance and impact of these ML models on network operation, however, is a critically important step prior to their actual deployment. In this paper, we train a Neural Network (NN) to solve the optimal power shutoff line switching problem. To assess the worst-case load shedding induced by this model, we propose a bilevel attacker-defender verification approach that finds the NN line switching decisions that cause the highest quantity of network load shedding. Solving this problem to global optimality is challenging (due to AC power flow and NN nonconvexities), so our approach exploits a convex relaxation of the AC physics, combined with a local NN search, to find a guaranteed lower bound on worst--case load shedding. These under-approximation bounds are solved via MathOptAI.jl. We benchmark against a random sampling approach, and we find that our optimization-based approach always finds larger load shedding. Test results are collected on multiple PGLib test cases and on trained NN models which contain more than 10 million model parameters.

Figures (5)

• Figure 1: Given a set of inputs (grid loads, line risks, and tradeoff parameter $\alpha$), OPS (top path) will make an optimal set of switching decisions, and then those decisions are used in the AC feasibility restoration step. Alternatively, we train a NN to predict optimal switching decisions (bottom path), which are also subjected to feasibility restoration.
• Figure 2: Initially, we lower-bound the load shed by solving \ref{['eq: max_daul']}. Model I, solved via Gurobi, uses the relaxed line statuses found by \ref{['eq: max_daul']} to solve the convex AC redispatch problem. After snapping the binaries, Model II, solved via Gurobi, solves a convex relaxation of the AC feasibility restoration problem, and Model III, solved via IPOPT, solves the true AC feasibility restoration problem.
• Figure 3: Results for Model I in Fig. \ref{['fig:snapping']}. For all 12 cases, we plot the load shedding induced by random sampling (blue dots) vs the bound found by MathOptAI.jl (red dashed line). In each case, the MathOptAI.jl bound is higher than the load shedding induced by random sampling.
• Figure 4: Shown is the change in active power load, relative to the base load, when MathOptAI.jl solves \ref{['eq: max_daul']}. As depicted, most of the active power loads increase to their upper limits, given by \ref{['eq: gamma_bounds']}.
• Figure 5: Shown is the change in reactive power load, relative to the base load, when MathOptAI.jl solves \ref{['eq: max_daul']}. As depicted, most of the reactive power loads decrease to their lower limits, given by \ref{['eq: gamma_bounds']}.

Theorems & Definitions (5)

• Remark 1
• Remark 2
• proof
• Remark 3
• proof