A Two-Stage Mixed-Integer Nonlinear Framework for Assessing Load-Redistribution False Data Injection Effects in AC-OPF-Based Power System Operation

Load-redistribution false-data-injection (LR-FDI) attacks can degrade power-system operation by reshaping the perceived nodal demand pattern, thereby inducing congestion-aware redispatch and economic inefficiency while preserving the net system load. Prior LR-FDI studies commonly adopt bilevel/Stackelberg formulations with a continuous attack vector and an embedded operator response; however, these formulations often (i) do not represent explicit compromised-load selection, (ii) become computationally restrictive when combinatorial target sets are considered, and (iii) offer limited transparency for structured, stage-wise attack planning. This paper proposes a sequential two-stage attacker–operator framework for LR-FDI vulnerability assessment that integrates sparse load compromise decisions with screening-regularized attack synthesis and post-attack operational evaluation. In Stage-1, a mixed-integer nonlinear program identifies economically influential load buses via binary selection and determines admissible perturbation magnitudes under total-load conservation and proportional shift bounds. To confine the attacker-side search region and avoid economically exaggerated solutions, a screening-derived conservative operating-cost ceiling is first estimated through a parametric load-sensitivity analysis and then used to regularize the attack-synthesis step. In Stage-2, the system operator’s corrective redispatch is evaluated by solving an active-power-oriented economic dispatch model with nonlinear network-consistent assessment of operational outcomes. Using the IEEE 24-bus RTS, results show that the hourly operating-cost deviation reaches ≈0.2% in the most adverse feasible cases, and the cumulative daily impact approaches ≈5% only under selectively realizable compromised-load patterns, accompanied by a nearly 80% increase in total active-power transmission losses relative to the base case. Overall, the framework yields a practically grounded quantification of conditionally severe economic and network stress under coordinated LR-FDI scenarios and provides actionable insight for prioritizing vulnerable load locations for protection and monitoring.