Numerical analyses of minimum energy operation of multiple trains under DC power feeding circuit

An algorithm optimizing total energy consumption of multiple inverter train operation considering DC feeding circuit is investigated in this paper. The proposed mathematical formulation can deal with several characteristics of trains, especially the effect of regenerative braking system. The developed optimization algorithm based on the gradient method is applicable to solve the formulated problems. The algorithm is ready to apply practical large-scale problems. The formulation and algorithm enables us to discuss energy-saving operation quantitatively. Several numerical analyses are demonstrated to verify the reliability and validity of the proposed method and clarify the energy-saving operation for two trains. The results shows that train speed profiles and control inputs strongly depend on the phase of departure times. The proposed algorithm can reduce energy consumption by 4.2~17.9% from that based on the conventional operation rule. These results indicates that the numerical analyses are significant to realize energy-saving operation. Furthermore, it is also demonstrated that the method can be applied to the optimal voltage control of a substation.