In this study, it is proposed to carry out an efficient formulation in order to figure out the stochastic transmission capacity expansion planning (S-TCEP) problem. The main idea is related to directly compute the partial transmission distribution factors which could be applied to model the operational problem using a disjunctive approach. In the stochastic mathematical formulation, the wind uncertainty has been incorporated employing a two-stage multi-period framework. The main advantage of this methodology is the feasibility to quickly use the linear factors applied to the S-TCEP problem. Traditionally, the optimization problem has been formulated decomposing the yearly load duration curve in blocks; however, the main advantage of the introduced methodology is the straightforward approach to model the hourly load curve using a typical day. Moreover, it is conducted several experiments using several electrical power systems to validate the proposed framework, and authors have also made comparisons with the classical DC-based disjunctive approach. Finally, this study provides effects and insights on how the number of hourly wind scenarios affects the simulation time solving the stochastic planning problem.