Stochastic model of the electric power purchase system on a railway segment

Proposed was a mathematical optimization model of the power supply system of a railway segment where the electric power is bought from more than one supplier with allowance for the random demand. Consideration was given to several time periods with different tariffs for electric power. The system model represents a two-step problem of stochastic programming with a quantile criterion. At its first step, a primary purchase plan is generated. At the second step, an additional purchase is done to compensate for the lack of electric power arising because of the random demand. The model takes into consideration the losses arising at transmitting the electric power from the supplier to the segment, as well as the pent-up demand. The total operational costs of the power supply system under consideration are minimized. An algorithm was proposed to solve the problem by reducing the stated problem by discretizing the probabilistic measure and confidence method to the problem of mixed integer linear programming. A model example was discussed.