Transient stability emergency control (TSEC) enhances power system transient stability during large disturbances but faces challenges in the high-penetration wind power grid where the wind power forecast error still cannot be ignored even with state-of-the-art forecasting methods. In this paper, the TSEC problem is modeled as robust nonlinear programming with the objective of maintaining rotor angle stability by generator tripping and load shedding while the uncertain wind power outputs are regarded as intervals. Interval programming is employed to solve the robust TSEC problem where the trajectory sensitivity analysis is applied to approximate the bounds of transient stability constraints. Numerical results on two test systems demonstrate that the proposed method improves computational efficiency and shows good performance on robustness.INDEX TERMS Interval programming, trajectory sensitivity analysis, transient stability emergency control, wind power uncertainties, worst case