Optimal Sizing of Onboard Hybrid Energy Storage Devices Considering the Long-Term Train Operation

Abstract

With the fast development of energy storage technology, more applications of Energy Storage Devices (ESDs) have been found in rail transportation in recent years. This paper aims to address the optimal sizing problem of on-board Hybrid Energy Storage Devices (HESDs) which are installed to assist train traction and recover the regenerative braking energy. On-board HESDs combining Li-ion battery and supercapacitor can further enhance the capacity and instant power rating. In this paper, a mixed integer linear programming (MILP) model is proposed to minimize the economic cost in terms of energy consumption and installation, and the degradation cost of on-board HESDs considering the long-term train operation constrained by the initial investment of on-board HESDs. Train operation is found to be highly related to characteristics of on-board HESDs including the maximum power, capacity, and state of health (SOH). By changing the investment ratio between Li-ion battery and supercapacitor, the energy-saving rate and economic cost for various investment ratios have been obtained. Compared with the results of train optimal control with Li-ion battery only, supercapacitor only and no on-board HESDs, the results indicate an energysaving rate up to 25.59%, from the perspective of the long-term train operation. When the allowable capital cost is relaxed from 20 k$ to 60 k$, the cost per kilometer is reduced from 0.55 USD/km to 0.53 USD/km, showing higher capital cost is closely linked to higher cost reduction in the long-term train operation.INDEX TERMS Optimal sizing, mixed integer linear programming (MILP), on-board hybrid energy storage device (HESD), the long-term train operation.

Impact of On-Board Hybrid Energy Storage Devices on Energy-Saving Operation for Electric Trains in DC Railway Systems

“…Many researchers have found that the use of on-board HESDs allows for a more flexible system, where SCs and Li-ion BATs can improve the power density and energy density of the integrated system, respectively [19,39,40]. After considering the optimized scenarios and commonly used commercial components, the proposed integrated system in this work is mainly composed of: (1) each cell for Li-ion BATs is 10 Ah and 2.3 V. When the rated charge/discharge rate is 4 C, the rated charging power is −93.3 W and rated discharging power is 93.3 W [22]; (2) each module for BMOD0063-P125-B08 supercapacitor is 63 F, which is specifically designed for heavy transport applications such as electric trains, trolleys, cranes, etc.…”

“…Although the researchers in our group have published some works on distance-based MILP models [19,35,37], which have been proved to have excellent robustness and fast optimization characteristics, heavy computational burdens are obtained when calculating the nonlinear constraints, especially the derivation of SOC for on-board HESDs and product operation of multiple time-varying parameters. Alternatively, as shown in Figure 2, the discretization process of the proposed, time-based MILP model is revealed, where each time segment ∆t is a known parameter and the distance S i (i = 1, 2, 3 .…”

“…In recent years, some studies considering both the on-board energy storage devices and the energy-saving operation for electric trains have become increasingly popular. Zhang et al [19] introduced the Mixed Integer Linear Programming (MILP) model to optimize the speed profile and the capacity configuration for on-board HESDs, which focused on minimum economic costs considering the long-term train operation. In [20], the authors showed that the capacity of SCs and speed trajectory for Fuel-cell hybrid trains could be co-optimized to achieve minimum net hydrogen consumption.…”

“…The maximum acceleration a a,max and deceleration a d,max are both set at 1 m/s 2 . The average energy efficiency of on-board HESDs η bat and η sc is set to be 0.9 considering negligible transmission loss [19]. In [44,45], the efficiency of the advanced DC and induction motors are about 90-94% and 93-95%, respectively, and then approximately set as 90%.…”

The operation, stability analysis and active damping of multi-port converter-based DC traction power systems

“…Their case study shows the train equipped with on-board ESS can save 14.2% of total energy consumption. Others use various optimization methods to determine the capacity of on-board ESS for train [33]- [35].…”