A driver advisory system with dynamic losses for passenger electric multiple units

Speed profile optimization of catenary-free electric trains with lithium-ion batteries

“…The proposed solutions cover a wide range of applications from diesel heavy haul trains (e.g., [13]) to multiple-train operation (e.g., [14][15][16]). Apart from the methodological research in this field, there has also been research on designing driver advisory systems based on mathematical formulations and optimizations (see e.g., [17]). Hybrid electric trains have also been studied for the speed profile optimization.…”

“…In this paper, we use dynamic programming as the optimization technique for the speed profile optimization. The methodology to apply dynamic programming for the speed profile optimization and its application for designing a driver advisory system is presented by Ghaviha et al [17]. The basics of the same method have been used to solve the problem of speed profile optimization for catenary-free operated EMUs using the objective function of minimizing energy consumption on the DC link [42].…”

“…The same approach is used in this paper as the basis for the speed profile optimization considering the characteristics of the battery. Here, we briefly present the approach introduced by Ghaviha et al [17,42] and we further present the modifications needed for the consideration of the battery characteristics. The final approach uses the state of charge of the battery as an input variable.…”

“…Having the optimum decision at each state in the horizon and by forward simulation in time using Eq. (1), the optimum speed profile is found for any state during the trip [17].…”

“…Considering the fact that the tractive effort is the control variable, a is calculated using equations of motion [43]. Note that apart from the constraints on other state variables (e.g., constraints resulting from the local speed limits [17]), there is a boundary condition on the state of charge, which is presented in Eq. (5):…”