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In this paper, we address the issue of quantifying effects of model uncertainty on transmission security in a power market. The paper addresses two types of uncertainties: 1) structural (e.g., branch outages), which are modeled by contingency scenarios, and 2) perturbations of model parameters (e.g., branch impedance), which are described by sensitivity analysis. The paper embeds these considerations in an optimization procedure that checks if transmission security is maintained and, when necessary, generates minimal corrections in existing contractual transactions that ensure security. Given our interest in real-time applications, we consider problem formulations guaranteeing solution existence and global optimality. A detailed sensitivity analysis based on approximate matrix inversion and linear programming perturbation theory is performed. The paper proposes a linearized ac power flow model to describe the transmission network. The model is studied on a benchmark example of the New England/New York interconnection with 68 nodes.