Optimum allocation of flexible AC transmission system (FACTS) can improve the power grids performances such as available transmission capacity (ATC) and voltage stability. Optimal allocation of FACTS with multiple optimization objectives for power systems comprise multiple random variables is still a challenging task to be solved. This paper derives a scenario generation method for systems containing multiple random variables first. Then, a thyristor-controlled series capacitor (TCSC) multi-objective optimal allocation model with ATC and voltage stability L index as an objective function is established. By adding the chaos initialization and the variable inertia weight setting, an improved multi-objective particle swarm optimization (MOPSO) algorithm is also proposed to easily solve the established model. Finally, based on the improved IEEE-30 bus system, the non-inferior solutions of multiple system scenarios are compared and analyzed. Simulation results show that the proposed scenario processing method, the TCSC multi-objective optimal allocation model and the improved MOPSO algorithm are effective in solving related problems.