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This paper proposes an improved trajectory sensitivity method for transient stability constrained optimal power flow (TSCOPF) based on one-machine infinite bus (OMIB) equivalence after analyzing several problems existing in the trajectory sensitivity method for TSCOPF under multi-contingency condition, in which critical stable rotor angle is used as a threshold in stability constraint and the prediction-correction method is introduced to modify this threshold to highly improve this threshold's precision and optimization accuracy. According to OMIB equivalence, faults are classified into stable, extreme stable, generally unstable, and very unstable faults. Extreme stable faults are filtered out from transient stability constraints to avoid computing of relative trajectory sensitivity to these faults. Furthermore, in order to take advantage of fast convergence of the improved trajectory sensitivity method and global search capability of the differential evolution (DE) method, a hybrid algorithm for TSCOPF under multi-contingency condition is constructed by the combination of these two methods. Population size and computational burden are greatly decreased in this DE method. The DE's fitness value better evaluates the individual's stability and economic index by means of normalized stable margin for unstable faults. Efficiency and practicality of the proposed method are validated on the 10-machine 39-bus New England system.