The adjustment of rail traffic in the event of an electrical infrastructure disruption presents an important decision-making process for the smooth operation of the network. Railway systems are complex, and their analysis relies on expensive simulations, which makes incident management difficult. This paper proposes the use of sensitivity analysis in order to evaluate the influence of different traffic adjustment actions (e.g., spacing between trains and speed reduction) on the train supply voltage, which must never drop below the critical value prescribed by technical standards. Three global sensitivity analysis methods dedicated to black box, multivariate, nonlinear models are considered: generalized Sobol indices, energy distance-based indices, and regional sensitivity analysis. The three methods are applied to a simple traffic rescheduling test case and give similar results, but at different costs. Regional sensitivity analysis appears to be the most suitable method for the present application: it is easy to implement, rather fast, and accounts for constraints on the system output (a key feature for electrical incident management). The application of this method to a test case representative of a real rescheduling problem shows that it provides the information needed by the traffic manager to reschedule traffic in an efficient way. The same type of approach can be used for any power system optimization problem with the same characteristics.