A Preliminary Techno-Economic Comparison between DC Electrification and Trains with On-Board Energy Storage Systems

Abstract

The paper presents a preliminary technical-economic comparison between a 3 kV DC railway and the use of trains with on-board storage systems. Numerical simulations have been carried out on a real railway line, which presents an electrified section at 3 kV DC and a non-electrified section, currently covered by diesel-powered trains. Different types of ESS have been analyzed, implementing the models in Matlab/Simulink environment. A preparatory economic investigation has been carried out.

1. Introduction

The International Energy Agency and the International Union of Railways have stated that the 23.1% of worldwide CO₂ emissions from fuel combustion are attributable to the transport sector (8258 million tons of CO₂). The breakdown of the emissions in this sector is attributable as follows: 73.2% to road transport, 10.4% to maritime transport, 10.5% to air transport and 3.6% to railways [1]. Regarding the European situation, the amount relating to the transport sector is around 30.4% (71.1% road transport, 13.9% maritime transport, 12.7% air transport and 1.5% railways). In the United States, the transport sector accounts for 34.4% of emissions from fuel combustion, in Japan for 20.6%, in Russia for 17.5%, in India 12.7% and in China for 9.6% [2,3]. According to the Statistical Compendium on Transport published annually by the Commission, net of emissions indirectly attributable to rail transport (which are accounted in electricity generation phase), therefore 44% of total emissions are attributable to road passenger transport, 28% for road freight, while air and maritime transport accounted for 13.0 and 13.4%, respectively. Overall, urban mobility would account for 25% of greenhouse gas emissions from transport, interurban for 54% and intercontinental for 22%) [1,4].

From the point of view of railway line electrification, Europe has 55% of the total length of the railway line electrified. Italy has 72% of electrified lines and 28% with diesel-powered trains [5].

E-mobility will be widespread thanks to the European Union funding programs and capital investments from the automotive industry. However, several technical, financial and social challenges need to be overcome. Although electric vehicles present higher purchase and infrastructure costs, they present lower operating costs than a conventional car [6,7,8]. Due to the limited autonomy and required charging times, battery electric vehicles are indicated for consumers with a limited daily range, but the technology, especially for storage systems, is constantly improving. In the long term, options like plug-in hybrid vehicles are expected to have a relatively big market share [9].

The worldwide diffusion of electric vehicles is still very limited. One of the main reasons of different trends in the sales of electric cars is the presence in some parts if the world of incentive mechanisms such as purchase incentives and free access to controlled priority circulation zones. Another relevant factor is the presence of proper charging infrastructures, which requires the companies involved to adapt their business models [10].

One of the main target areas of the climate goals is road freight transport, since about 25% of the CO₂ emissions from road transport in the European Union are produced by heavy-duty vehicles. Although shifting from road freight transport to electrified railways is a possible solution, several studies indicate that the potential for this is limited. New technologies such as electrified highways (eHighways) are proposed, in which an overhead line supply energy to trucks provided with an integrated pantograph. A two-pole catenary system has been developed, ensuring a stable current transmission at speeds up to 100 km/h [11]. This technology is already being used in several projects in countries such as Sweden and United States [12], and several such projects are in the planning phase.

The design of electrified mass transit systems for urban railway traffic, such as trams, trolleybuses and metros, requires taking into consideration several elements: safety, efficiency, cost and visual impact. Traditional electrified transit systems are based on electrical contact wires, such as active rails or catenary. Catenary-free systems have advantages of as low electromagnetic radiation and good visual design [13] In the absence of fixed traction systems, the rolling stock has on board the energy storage system (e.g., batteries, hydrogen, diesel, ultracapacitors, flywheels). Moreover, catenary-free systems are being consolidated in public transportation, especially to restrict the electrical infrastructure, for example in city historical centers, limiting the environmental impact and reducing costs of electrical installations for traction [14].

In the current state some form of on-board storage system is often used for heavy traction (passenger and freight trains), but generally only to recover braking energy and not to operate in catenary-free mode. Battery-powered locomotives were one of the first technologies to be adopted in the early 1900s but due to the limited storage capacity available at that time, it was decided to focus on electrified solutions. Use thus became limited to mining locomotives and shunting locomotives [15].

Nowadays several studies have focused on the possibility to design new trains to operate autonomously because of the advances in energy storage technologies [16]. Trains with on-board storage systems could be adopted for expansion of already electrified railways, point-to-point connections or commuter transport systems [17,18,19]. It will be important in the near future to considerate the need for prospective analysis of the marketing of rolling stock approved for bimodal operation (i.e., with and without contact lines supplying different voltages). The diffusion of a new system will strongly depend on the cost and the development of new rolling stock with on board storage technology for traction [20,21,22].

It is well known that for heavy traction, the electrified solution via catenary represents a consolidated and highly reliable approach that is economically sustainable for high traffic lines [23,24]. Moreover, considering the contribution of renewable sources it is possible to increase the energy savings from the primary network. For this reason, several studies and projects have been carried out highlighting the trend of replacing diesel locomotives with electric locomotives to cover long distances, powered by AC or DC electrification systems [25].

For solutions involving on-board energy storage systems (ESS), several technologies can be used, as shown in Figure 1. Since each one of them presents different characteristics, it is important to choose the most suitable technology for the particular case under study. Currently, there are different types of electrochemical accumulators. Lead-acid accumulators, widely used in the automotive sector, represent an economical and reliable solution. However, they have a very low specific energy. Those with nickel cadmium (Ni-Cd), initially used as substitutes for the aforementioned lead-acid accumulators, have been nowadays abandoned due to the toxicity of the cadmium present in them, and the focus has shifted to nickel-metal hydride accumulators (NiMH), which have the disadvantage of presenting memory effects. Finally, lithium batteries (Li-ion) are characterized by high energy and specific power.

Technologies such as flywheels offer a high specific power and a large number of charge and discharge cycles but they present low specific energy. The use of fuel cells in railway transport systems is currently in the early development state and they present many advantages such as zero emissions fuel and high specific energy [26]. Though fuel cell sources can be coupled with high-power density storage elements [27], the combination of Li-ion batteries with supercapacitors (SC) is currently found to be the most economical solution for ESS [26].

Supercapacitors, also known as ultracapacitors, are an innovative electrical EES that has considerably higher capacity values than those of ordinary capacitors and high specific power. The combination of Li-ion batteries and SC in a hybrid energy storage system (H-ESS) allows one to reduce battery stress and aging effects, depending on the charge and discharge cycles. The sizing of the ESS is strictly linked to the control strategy used for the management of energy resources and is limited by the maximum weight and volume allowed by the rolling stock [28,29].

Several studies have been carried out on the applications of storage systems that use lithium-ion cells with high specific power (power-oriented) or high specific energy (energy-oriented). Usually, energy-oriented lithium-ion cells are accompanied by supercapacitors, which deliver the stored energy during power peaks in traction and absorb energy during regenerative braking [31,32]. It is possible to find different applications on electric vehicles [33,34], electric buses [35], small boats [36], water buses [37], and even machines for lifting and displacement of loads [38].

In [39], a battery pack of about 250 kWh and about 2 tons of mass is used on a freight train, in order to solve the problem of the absence of the catenary in the connections of the railway lines to the freight terminals and production plants, avoiding the use of diesel-powered vehicles. In [40], prototypes of battery packs of 200 kWh and about 2 tons are reported for a railway locomotive and of 500 kWh and 5 tons of mass for powering a mining truck. In [41], the authors present a battery pack of 2.22 MWh and 11 tons of mass to power a rolling stock with a total mass of 276 tons that must travel a route of 212 km.

Among the few solutions commercially available for trains equipped with energy storage systems there is a Spanish tramway in Seville, which uses a hybrid storage system consisting of supercapacitors and batteries [42]. In addition, the same train constructor has developed a battery-powered regional train, proposing it as a solution for non-electrified railway lines. The roof-mounted traction batteries provide the power and energy required to propel the train for distances up to 100 km [43,44]. It is important highlight that the adoption of storage system on board trams and trolleybuses is economically convenient for short route sections. There are already design solutions and rolling stock equipped with on-board storage systems available on market.

In addition to the technical and infrastructural characteristics of a given traction system, it is important to carry out a cost assessment, especially when comparing different achievable solutions. In the technical and scientific literature, several studies have been published using the annual cost of energy (ACOE) in order to evaluate the effectiveness in terms of costs of different types of energy resources [45]. In this study, the ACOE is also used to compare the different technical solutions proposed.

This paper presents the evaluation taken into consideration to perform a comparison between direct current electrification and the use of trains with on-board energy storage systems. Numerical simulations have been performed on a real railway line to carry out a preliminary techno-economic comparison showing the models and procedure used. The case study presents an electrified 3 kV DC section and a non-electrified section, currently being covered by diesel-powered trains. For the non-electrified section, the following scenarios have been analyzed: 3 kV DC electrification, since it is the feeding system currently used in the preceding section; high autonomy ESS and ESS with recharge station. For the ESS it has been considered the use of power-oriented Li-ion battery cells and, in the case of hybrid ESS, energy-oriented Li-ion battery cells accompanied by supercapacitors. For the sake of simplicity, only recharging the ESS has been considered, the possibility of swapping the ESS is outside the scope of this work, as it would have an impact on capital costs. It is highlighted that, in cost assessment is not taken into account the cost associated with the purchase of new trains. In this paper, it is assumed that the cost of the on board ESS is the difference cost between traditional electric trains and new trains equipped with on board ESS.

The paper is structured as follows: Section 2 describes the electric models of the vehicle, energy storage systems and DC feeder system, as well as the economic model. Section 3 presents the on-board ESS sizing procedure. Section 4 introduces the simulation software and procedures while Section 5 presents the case study and the numerical results of the simulations. Section 6 concludes the paper.

2. Modeling of the Railway System

The proposed model is obtained by using three different sub-models: the railway vehicle and its kinematics, the DC feeder system and the on-board ESS. An economic model is also introduced for calculating the annual energy cost of the proposed solutions.

2.1. Train

The longitudinal dynamic of vehicles is evaluated applying Newton’s second law and kinematic equations:

$$\{\begin{array}{c}m\epsilon \frac{dv}{dt}=F\left(t\right)-R_{BASE}\left(v\right)-R_{TRACK}\left(x\right)\\ x=x_0+v_{0}t+\frac{1}{2}\frac{dv}{dt}{t}^2\\ v=\frac{dx}{dt}\end{array}$$

(1)

where m is the mass of the vehicle, $\epsilon$ is a correction factor taking into account the rotating mass, v and x are the train speed and position respectively, F is the traction (if positive) or braking (if negative) force. R_BASE(v) is the basic resistance including roll resistance and air resistance, and R_TRACK(x) is the line resistance caused by track slopes and curves, described by:

$$R_{BASE}\left(v\right)={\alpha }_1+{\alpha }_2\left|v\right|+{\alpha }_3{v}^2$$

(2)

$$R_{TRACK}\left(x\right)=mgsin\left(\gamma \left(x\right)\right)+mg\frac{a}{r\left(x\right)-b}$$

(3)

where ${\alpha }_1$, ${\alpha }_2$ and ${\alpha }_3$ are the coefficients of the Davis formula, related to the train and track characteristics, and they can be estimated by empirical measures; g is the gravitational acceleration and $\gamma \left(x\right)$ is the slope grade. The second term of R_TRACK is the curve resistance given by empirical formulas, as the Von Röckl’s formula, where $r\left(x\right)$ is the curvature radius, and a, b are coefficients which depend on the track gauge; in this paper it is considered a = 0.65 m and b = 55 m [46].

From a given a speed cycle, it is possible to calculate the value of the force (F_MECH) on the wheels required to overcome the vehicle inertia, slopes and curves, aerodynamic friction and rolling friction. Going upstream the vehicle components and their related efficiencies, the power requested to the contact wire P_TRAIN is calculated as follows:

$$P_{TRAIN}=\{\begin{array}{cc}\frac{F_{MECH}v}{{\eta }_t}+P_{AUX},& F_{MECH}\ge 0\\ (F_{MECH}v){\eta }_t+P_{AUX},& F_{MECH}<0\end{array}$$

(4)

where P_AUX is the power absorbed by board auxiliary services (lighting, cooling or heating), m is the total mass of the train (including the passengers), v is the vehicle speed and η_t the total efficiency of the locomotive, which takes into account the efficiency of the gear box, the electric motor and the inverter. To bring into account that the voltage along the track is not constant, the railway vehicle is modeled as an ideal current source I_TRAIN, whose is calculated as the ratio between vehicle power and line voltage V_LINE:

$$I_{TRAIN}=\frac{P_{TRAIN}}{V_{LINE}}$$

(5)

2.2. DC Feeder System

Conventional substations are represented by ideal DC voltage sources, series resistance and series diode if the substations are not reversible [28]. The contact wire is modelled as a set of electric resistances that change their value according to the vehicle position. If x(t) is the train position at the time t, the value of the resistance upstream R_a and downstream R_b to the vehicle towards a generic node of the railway feeding system (conventional substation or another train) are calculated by:

$$\{\begin{array}{c}{R}_a\left(t\right)=\rho ·x\left(t\right)\\ R_b\left(t\right)=\rho ·\left[d-x\left(t\right)\right]\end{array}$$

(6)

where R_a and R_b are expressed in [Ω], $\rho$ [Ω/km] represents the resistive coefficient, d [km] is the distance between the two nodes (upstream and downstream the train). In order to improve the train electric model, describing the receptivity of the network under regenerative braking conditions, a small capacitance is connected in parallel to current source that represents the vehicle [46]. In Figure 2 it is shown the electric model of the overall railway system, one side supplied contact line.

2.3. On-Board ESS

The electric model of the ESS is reported in Figure 3, it includes the battery and supercapacitor pack, the DC/DC converter and the power flow controller. The on-board ESS is modelled as a pair of ideal current sources describing the battery-based and the SC-based energy storage system, respectively.

Figure 4a presents the equivalent circuit of the battery pack, which consists of an ideal voltage source that represents the open circuit voltage (OCV), which depends on battery state of charge (SOC); the series resistor R_INT represents the internal resistance, whereas r_d and C_d are the RC parallel circuit describing the charge transfer and double layer capacity, respectively. The set of equations that describes the electric model of the battery pack is reported in Equations (7) to (10): the first equation represents Kirchhoff’s voltage law, the second one is the n-polynomial relationship between OCV and SOC. The third equation models the SOC update law according to the required current from the battery pack and the last one is the differential equation describing the RC parallel circuit [29].

$$V_{BATT}\left(t\right)=OCV\left(t\right)-R_{INT}{I}_{BATT}\left(t\right)-u_d\left(t\right)$$

(7)

$$OCV\left(\mathrm{SOC}\right)={\beta }_n{\mathrm{SOC}}^n+{\beta }_{n-1}{\mathrm{SOC}}^{n-1}+{\beta }_0$$

(8)

$$\mathrm{SOC}\left(t\right)=\mathrm{SOC}\left(t=0\right)-\frac{1}{3600·C_{AH}}{\int }_0^t{I}_{BATT}\left(\tau \right)d\tau$$

(9)

$$u_d\left(t\right)+r_d{C}_d\frac{d{u}_d\left(t\right)}{dt}=r_d{I}_{BATT}\left(t\right)$$

(10)

where u_d(t) is the r_dC_d parallel circuit voltage, β₀ … β_n are the interpolation coefficients and C_AH [Ah] is the battery pack capacity. The electrical model of the SC pack, shown in Figure 4b, consists of the capacitor C, modelling SC’s capacity; an equivalent series resistance R_S that describes the power loss during the charging and discharging operations; the self-charge resistance R_L models the losses due to the leakage current, which is usually neglected [28,47]:

$$V_{SC}\left(t\right)=V_C\left(t\right)-R_s{I}_{SC}\left(t\right)$$

(11)

$$V_C\left(t\right)=V_{SC}\left(t=0\right)-\frac{1}{C}{\int }_0^t{I}_{SC}\left(\tau \right)d\tau$$

(12)

$${\mathrm{SOC}}_{SC}\left(t\right)=\frac{1}{3}\left[4·{\left(\frac{V_C\left(t\right)}{V_{nom}}\right)}^2-1\right]$$

(13)

It is highlighted that, in order to represent the equivalent circuit of a battery or supercapacitor pack, starting from the characteristics associated with the individual cells or modules, it is used an equivalent circuit: n RC blocks in series and m in parallel [48]. The DC/DC converters are modeled by its average efficiency η describing power losses. It operates as step-up or step-down converter according to the control characteristic. Given the power reference value P_ref provided by the power flow control characteristic, the ESS current value to be delivered during the traction phase is computed by using the following equation:

$$I_{ref}=\frac{1}{\eta }\frac{P_{ref}}{V_t}$$

(14)

where $V_t$ is the battery pack or supercapacitor pack voltage.

2.4. Economic Model

The annual cost of energy is used to compare the different technical solutions proposed. Therefore, it is necessary to estimate the present value of the total cost, which includes: the cost of capital, the present value of the operating costs and the present value of the replacement cost of the energy storage system [45]. The ACOE is mathematically expressed as:

$$ACOE=CRF·C_{TOT}$$

(15)

where CRF is the capital recovery factor converting a present value into a stream of equal annual payments over a specified lifetime N, at a specified interest rate r, and C_TOT is the present value of the total cost. The capital recovery factor is computed by using the following equation:

$$CRF=\frac{r{\left(1+r\right)}^N}{{\left(1+r\right)}^N-1}$$

(16)

2.4.1. Costs of an Electrified Railway Line

Measuring the performance of an electrified railway is particularly complex as it involves a service that requires rolling stock, tracks, safety and signaling systems, stops or stations, and a variety of personnel types. Another factor that affects transport, if it is public, is government intervention to subsidize costs [49]. In the present study, the cost of capital associated with fixed electrical systems has been estimated based on the main components that characterize this scenario:

$$C_I^{ELE}=C_{TPS}+C_{CAT}+C_{MSC}$$

(17)

where $C_I^{ELE}$ is the capital cost of the electrification of the railway line, $C_{TPS}$ is the cost associated with the traction power substation, $C_{CAT}$ is the cost associated with the installation of the catenary and $C_{MSC}$ represents other costs related to the electrification intervention such as track lowering in correspondence of tunnels already present in the route and raising of the overpasses. The present value of operation and maintenance (O&M) costs associated with the electrified railway line is calculated as follows:

$$C_{O\&M}^{ELE}={\displaystyle \sum _{n=1}^N}\frac{C_n^{ELE}}{{\left(1+r\right)}^n}$$

(18)

where $C_n^{ELE}$ is the annual operations cost of year $n$ including both fixed and variable costs:

$$C_n^{ELE}=C_e{N}_d{E}_d^{TPS}+C_n^{TPS}+C_n^{CAT}$$

(19)

where $E_d^{TPS}$ is the energy supplied by the traction power substation in a day, during $N_d$ days within a year, $C_e$ the average cost of electricity, $C_n^{TPS}$ and $C_n^{CAT}$ represent the average of the annual costs associated with the maintenance of the traction power substation and the catenary, respectively, estimated from 1% to 3% per year of the investment cost, referring to the date of commissioning of the equipment [50]. Finally, the annual cost of energy is calculated by using the following equation:

$$ACO{E}_{ELE}=CRF·\left(C_I^{ELE}+C_{O\&M}^{ELE}\right)$$

(20)

2.4.2. Costs of Associated with the Use of Trains Equipped with On-Board ESS

The costs taken into account are the capital cost of the on-board ESS, the annual operation costs of the on-board ESS, operation and maintenance (O&M) costs of the on-board ESS and the replacement cost of the on board ESS.

The use of trains equipped with ESS might reduce capital costs as there is no catenary, but the construction of new specialized trains could significantly increase the total costs of realization. Moreover, depending on how the sizing of the energy storage system is carried out, it may be necessary to install a charging system with an installed power comparable to that of a traction power substation, thus affecting capital costs. Furthermore, it is necessary to respect the limits of the state of charge within which the ESS must deliver and absorb energy, even with high discharge current peaks provided they occur for short periods of time, resulting in a useful life of 10÷15 years [51]. However, is needed an expertise in train operation and real work cycle of storage system to know if this useful life is respected.

Consequently, the cost assessment must include the future replacement of the energy storage system following life expectancy and battery life reported in data sheet (not considering battery disposal).

In cost assessment is not taken into account the cost due to the buy of new trains, but is assumed that the cost of the on board ESS is the difference cost between traditional electric trains and new trains equipped with on board ESS. So, the following analysis is relevant on the hypothesis of complete renewal of the rolling stock, as diesel trains.

The cost of capital of the equipment of the storage systems $C_I^{\mathrm{ESS}}$, has been estimated as follows:

$$C_I^{\mathrm{ESS}}=C_P{P}_{\mathrm{ESS}}+C_E{E}_{\mathrm{ESS}}+C_{FC}$$

(21)

where $C_P$ [€/kW] and $C_E$ [€/kWh] are the ESS specific costs, $P_{\mathrm{ESS}}$ and $E_{\mathrm{ESS}}$ are the power and energy capacities and $C_{FC}$ are the ESS fixed costs associated, for example, with the installation of a recharging system. The present value of operation and maintenance costs associated with the use of trains equipped with on-board ESS $C_{O\&M}^{\mathrm{ESS}}$, is calculated by:

$$C_{O\&M}^{\mathrm{ESS}}={\displaystyle \sum _{n=1}^N}\frac{C_n^{\mathrm{ESS}}}{{\left(1+r\right)}^n}$$

(22)

where $C_n^{\mathrm{ESS}}$ is the annual operations cost of year $n$ including both fixed and variable costs, and is computed by using the following equation:

$$C_n^{\mathrm{ESS}}=C_f{P}_{\mathrm{ESS}}+C_v{N}_d{E}_d^{\mathrm{ESS}}+N_d\frac{E_d^{\mathrm{ESS}}}{{\eta }_{ch}}{C}_{ch}$$

(23)

where $C_f$ [€/kW-yr] represents the specific operating costs, $C_v$ [€/kWh] the variable operating costs, $C_{ch}$ [€/kWh] the cost of recharging ESS, $N_d$ the number of days the ESS is active within one year, $P_{\mathrm{ESS}}$ [kW] and $E_d^{ESS}$ [kWh] the nominal power and energy supplied by the ESS, and finally ${\eta }_{ch}$ is the charge efficiency. The replacement cost of the ESS is expressed in the following equation:

$$C_R^{\mathrm{ESS}}=C_{FR}\left[{\left(1+r\right)}^{-L_R}+{\left(1+r\right)}^{-2L_R}+\dots \right]$$

(24)

where $C_{FR}$ represents the future value of replacement cost and $L_R$ is the ESS lifetime. Finally, the annual cost of energy is calculated by using the following equation:

$$ACO{E}_{\mathrm{ESS}}=CRF·\left(C_I^{\mathrm{ESS}}+C_{O\&M}^{\mathrm{ESS}}+C_R^{\mathrm{ESS}}\right)$$

(25)

3. On-Board ESS Design

In the railway sector, the applications of electrical energy storage systems are usually characterized by the power and energy they must provide. A good sizing of the ESS must allow compliance with the required energy and power constraints, without too many margins.

3.1. ESS Specification

The sizing is performed considering a nominal voltage for the battery pack and for the supercapacitor pack, and a power profile assigned for each [28,32]. The subdivision of the original power profile is achieved through a low pass filter and an amplitude limiter [47,52,53]. Several optimization studies have been carried out on this topic [32,35,54]. In this paper, it is considered that the ESS may be composed of high-power lithium-ion cells or high-energy lithium-ion cells and supercapacitors (H-ESS). Shape and weight of the energy storage system are binding constraints since they limit the energy that can be stored on-board. Therefore, the sizing depends on several factors: autonomy and maximum power required; where the charging is performed; the type of storage system.

3.2. ESS Sizing

Given a commercial battery cell characterized by a nominal cell voltage $U_{CEL{L}_B}$ the number of cells to be connected in the series $N_{S{E}_B}$ to obtain a given rated voltage of the battery pack, $U_B$ is obtained by:

$$N_{S{E}_B}=\frac{U_B}{U_{CEL{L}_B}}$$

(26)

It is highlighted that it represents a simplified model for the preliminary study developed in this paper, but in the case of a cell pack, balancing and operating safety should be added. The number of branches to be connected in parallel $N_{PA{R}_B}$ is determined as the maximum number between $N_{PA{R}_B}^P$, which represents the number of branches in parallel to satisfy the power requirement to be delivered in traction $P_B^{max}$, and $N_{PA{R}_B}^E$ which is the one necessary to satisfy the energy required by the battery, $E_B$. In order to increase battery lifetime, the variations in the state of charge are limited between a $SO{C}_{min}$ of 0.2 ÷ 0.3 and a $SO{C}_{max}$ of 0.8 ÷ 0.95. This involves an oversizing with respect to the energy required by the reference cycle but allows to exploit the supply or absorption of high currents for short intervals of time, provided that the fluctuations in the SOC are less than 5% (micro-cycles). An energy storage system of this type, subject to this type of stress, has an expected useful life of 10 ÷ 15 years [51,52,55]. Moreover, several studies have been carried out evaluating the use of degraded batteries, since they still have remaining capacity for grid support applications or emergency power supply [56,57,58]:

$$N_{PA{R}_B}=\max (N_{PA{R}_B}^P;N_{PA{R}_B}^E)$$

(27)

$$N_{PA{R}_B}^E=\frac{E_B}{N_{S{E}_B}·U_{CEL{L}_B}·C_{A{H}_{CEL{L}_B}}·\left({\mathrm{SOC}}_{max}-{\mathrm{SOC}}_{min}\right)}$$

(28)

$$E_B={\int }_{t_0}^{t_0+T}{P}_B\left(t\right)dt$$

(29)

$$N_{PA{R}_B}^P=\frac{P_B^{max}}{N_{S{E}_B}·P_{CEL{L}_B}^{max}}$$

(30)

where $P_{CEL{L}_B}^{max}$ is the maximum power that the single electrochemical cell can deliver, determined in the discharge phase by using Equation (31), where $R_{DIS}$ [h⁻¹] is the discharge C-rate, which is a measure of the rate at which the cell is discharged relative to its nominal capacity $C_{A{H}_{CEL{L}_B}}$ [Ah]. The maximum power that the single cell can absorb in the charging phase is computed as a function of the charge C-rate $R_{CH}$ [h⁻¹] [31]:

$$P_{CEL{L}_{B_{DIS}}}=R_{DIS}·C_{A{H}_{CEL{L}_B}}·U_{CEL{L}_B}$$

(31)

$$P_{CEL{L}_{B_{CH}}}=R_{CH}·C_{A{H}_{CEL{L}_B}}·U_{CEL{L}_B}$$

(32)

Given a commercial supercapacitor of rated voltage $U_{CEL{L}_{SC}}$, the number of cells to be connected in series $N_{S{E}_{SC}}$ to obtain a given rated voltage of the supercapacitor pack $U_{SC}$ is determined by:

$$N_{S{E}_{SC}}=\frac{U_{SC}}{U_{CEL{L}_{SC}}}$$

(33)

The number of supercapacitor branches to be connected in parallel, $N_{PA{R}_{SC}}$, is determined through Equation (34), where $E_{SC\_max}$ is the maximum energy that the supercapacitor pack must deliver. It is highlighted that the voltage range is limited between V_NOM/2 (SOC_SC = 0) and V_NOM (SOC_SC = 1), delivering 75% of the stored energy:

$$N_{PA{R}_{SC}}=\frac{8}{3}\frac{E_{SC\_max}}{{(N_{S{E}_{SC}}·U_{CEL{L}_{SC}})}^2}·\frac{N_{S{E}_{SC}}}{C_{CELL}}$$

(34)

$$E_{SC}\left(t_p\right)={\int }_{t_0}^{t_0+t_p}\left[P_{SC}\left(t\right)-P_{SC}\left(t_0\right)\right]dt$$

(35)

Finally, the total mass $W_{TOT}$ and volume $V_{TOT}$ linked to each energy storage system can be computed as follows:

$$W_{TOT}=\left(1+\gamma \right)·N_{SE}·N_{PAR}·W_{CELL}$$

(36)

$$V_{TOT}=\left(1+\delta \right)·N_{SE}·N_{PAR}·V_{CELL}$$

(37)

where the coefficients $\gamma$ and $\delta$ represent mass and volume rations of DC/DC converters and all the other additional elements necessary for the assembly and use of the energy storage system.

4. Simulation Procedures

The railway system model was implemented in a rail simulator based on the ‘quasi static’ backwards looking method, due to its short simulation times for estimating energy consumption of vehicles following an imposed speed cycle [46]. The rail simulator is a multi-stage program, implemented in Visual Basic and Fortran language and operating in MS-DOS and the Microsoft Excel workspace [59,60,61], including:

• an electro-mechanical simulator for the evaluation of the rolling stock power consumption for defined traffic scenarios;
• an electrical and thermal simulator to evaluate the energy state of the traction system.

The software allows one to perform high-quality studies from an energy point of view, with a high degree of flexibility in the simulation by means of a graphical interface where it is possible to set many parameters such as trains’ departure times, specific train sequences and trains’ stop time period in each station.

For the sizing and verification of the energy storage systems, models have been implemented in the Matlab/Simulink environment. Given the parameters of the electrochemical cells and supercapacitors, and given the power profile to be supplied, it is possible to evaluate electrical variables such as voltage, current, state of charge, power and energy supplied and absorbed.

The numerical simulations have been divided into three parts. The first part is related to the train performance simulations, to determine the power profile required by the rolling stock. The second part is related to the traction system simulations, in which the system is studied from an energy point of view, inserting traffic data and imposing simulation constraints. The last part is related to the on-board energy storage systems, which presents the ESS performance given a power profile reference.

4.1. Train Performance Simulation

The train performance, computed in the Microsoft Excel environment, requires the main characteristics of the route as input data, namely the plano-altimetric characteristics of the line (slopes), the curvature radius of the curves, speed limits and tunnels. Moreover, it requires electromechanical information of the rolling stock such as: weight, aerodynamic resistance, traction and braking force [46,59]. Given these inputs, and with a calculation step in meters, it is possible to obtain several outputs such as:

• kinematic parameters: travel and braking times, speed and acceleration profiles in time and space;
• dynamic parameters: aerodynamic resistance, resistance associated with curves, slopes and inertia, traction effort at the wheels and power required at the pantograph.

4.2. Electrical Model of the Traction System

The electrical computation software, implemented in Fortran language, allows to solve load flows calculation for a direct current electrified system [46,60,61]. For each simulation step, the software creates an equivalent electric network in which the nodes represent the traction power substation, vehicles present on the route and parallel points, as shown in Figure 5. In this model, V_TPS and R_TPS represent the substation DC voltage and internal resistance; R_BIN is the rail electric resistance and P^BIN is the electric power required by each train.

The software requires as input the data related to the power profiles of trains, the electrical substation features and the resistance of contact line equivalent section and rails. As output, the software provides the line voltage profile and currents flowing in the substation feeders, as well as the power provided by each electrical substation [61,62].

4.3. Electrical Model of the On-Board Energy Storage System

Simulink/Matlab models have been developed for the battery pack and supercapacitor pack, starting respectively from the characteristics of the electrochemical and supercapacitor cells. The models have been implemented as dynamic continuous-time systems, thus using mainly integrator, sum and gain blocks. In the case of electrochemical cells, a lookup table dynamic block is used to represent the open circuit voltage as a function of the state of charge (OCV-SOC curves). Figure 6 shows the battery based ESS Simulink model.

In addition to the parameters related to the energy storage system, the software requires as input data the reference power profile required, which is obtained directly from the evaluation of the train performance in the case of high-power lithium cells. In the case of H-ESS, the reference power profiles for the high-energy lithium cells and supercapacitors are obtained from a Simulink model that applies a low pass filter and an amplitude limiter to the original power profile.

5. Numerical Simulations

5.1. Case Study

A real single-track railway line has been chosen as case study. It presents an electrified section at 3 kV DC and a non-electrified section, currently covered by diesel-powered trains. Therefore, passengers are obliged to transfer to a diesel-powered train at the end of the electrified section, in order to reach one of the following stops or stations. The attention is focused to the non-electrified section in order to determine the technical-economic convenience of electrification at 3 kV DC or the use of trains equipped with on-board energy storage systems. Figure 7 reports an overview of the case study.

The non-electrified section is about 16.5 km long and links Station A, at the end of the electrified section with Station B, at the end of the non-electrified section (City II), in about 30 min for each direction. Between Station A and B there are 5 stops, as shown in Figure 8.

Figure 9 shows the plano-altimetric profile of the railway line. It is characterized by an average slope of 9‰, with a maximum slope of 24‰. There are 22 curves with a minimum bending radius of 200 m.

For the non-electrified section, the following scenarios have been analyzed: 3 kV DC electrification, since it is the feeding system currently used in the preceding section; high autonomy ESS and ESS with recharge station. For the ESS it has been considered the use of power-oriented Li-ion battery cells (lithium iron phosphate, LFP) and, in the case of hybrid ESS, energy-oriented Li-ion battery cells (lithium nickel manganese cobalt oxide, NMC - lithium nickel cobalt aluminium oxide, NCA) accompanied by supercapacitors.

The electrification at 3 kV DC involves the installation of a catenary and traction power substation, to be located at Stop 2 (progressive km 5.29). Contrariwise, the use of trains equipped with high autonomy on-board ESS allows to minimize the capital costs since it involves the recharge of the battery and supercapacitor pack in the electrified section of the line. However, in this case the ESS weight is high. The installation of a charging infrastructure at Station B (progressive km 16.5), allows reducing the on-board ESS rated capacity and therefore, the total weight of the system. In this paper, it is considered for all the scenarios, the use of the same electric train, whose traction curve is presented in Figure 10.

The main characteristics of the lithium-ion and supercapacitor cells are illustrated in

Table 1. Li-ion cell features.

Parameter	LithiumWerks ANR26650M1B	Saft MP 176,065 xlr
Mass [g]	76	150
Rated capacity [Ah]	2.5	6.8
Nominal voltage [V]	3.3	3.65
Specific energy [Wh/kg]	109	165
Max. discharge current [A]	50 (20C)	14 (2C)
Max. charge current [A]	10 (4C)	6.8 (1C)
Technology	Power-oriented	Energy-oriented

and

Table 2. Ultracapacitor cell features.

Parameter	Maxwell K2 UC–2.85V/3400F
Mass [g]	520
Rated capacity [F]	3400
Nominal voltage [V]	2.85
Max. voltage [V]	3
Specific energy [Wh/kg]	7.6
Specific power [W/kg]	8500

, respectively. This data is used to size the ESS as reported in the Section 3 of this paper.

Table 3. Railway System Parameters.

Parameter		Value
Rolling Stock
	Net weight	184 t
	Loaded weight	256 t
	Rotating mass coefficient	1.05-
	Max. train speed	160 km/h
	Nominal deceleration	0.8 m/s2
	Accessories power	200 kW
	Power train overall efficiency	0.8-
Track
	Track’s length	16.5 km
	Von Röckl formula coef. A	0.65 m
	Von Röckl formula coef. B	55 m
DC Feeder System
	Catenary section	320 mm2
	Rail electric resistance	0.083 Ω/km
	Substation location	5.29 km
	Substation nominal power	3.6 MVA
	AC/DC conversion units	2-
	Substation DC voltage	3000 V
	Substation internal resistance	0.2 Ω
	Maximum line voltage (+20%-CEI EN 50163)	3600 V
	Minimum line voltage (−33%-CEI EN 50163)	2000 V
On-board ESS
	DC link nominal voltage	3000 V
	Max. (Min.) battery SOC value	90 (30)%
	Battery pack nominal voltage	1500 V
	Supercapacitor pack nominal voltage	1000 V
	DC/DC efficiency	95%

shows the main characteristics of the different components of the traction system: rolling stock, track, DC feeder system and on-board ESS.

5.2. Results and Discussion

Several simulations are carried out in order to determine the technical and economic convenience of the proposed scenarios, using the procedures reported on Section 4.

5.2.1. Train Performance

The train performance has been performed for each direction of travel: from Station A to Station B and vice versa. Figure 11 shows the speed profile from Station A to Station B, highlighting that the train that travels the line from one stop to another, accelerating until the speed limit is reached and decelerating accordingly of stops.

Starting from the speed profile, it is possible to obtain the power profile of each direction of travel, as shown in Figure 12 and Figure 13. For each single section present between one stop and another, the train uses all the effort theoretically available only in the acceleration phases until the limit speed of the track is reached. Subsequently, in the steady state phase, the tractive effort applied at the wheels follows the trend of the resistance offered by the various accidentalities present in the track, influencing the power requested by the train. It is also noted that the maximum power at the pantograph in the traction phase is 3.7 MW and the maximum power in the regenerative braking phase is 2 MW. During stops, the only power consumed by the train is related to auxiliary services.

From Station A to Station B, the energy consumption is about double respect of the opposite direction, where the regenerative braking energy is high as the rolling stock must brake to contain its speed. It is due to the negative sign of the track resistance since the train goes downhill.

Figure 14a shows the energy consumption of the train and the regenerative braking energy, for each direction of travel. Figure 14b reports the timetable of the railway line under study (26 min and 51 s from Station A to Station B and 26 min, and 38 s in the opposite direction).

5.2.2. Electrification at 3 kV DC

The electrification of the section under study include the installation of a traction power substation and the contact line. Therefore, it is necessary to determine the nominal power of the transformer groups present in the substation and the catenary to be used, considering the limits allowed by the CEI EN 50163 standards. For the TPS, located at Stop 2, it has been analyzed the use of two different types of substations: 2 AC/DC conversion units with a nominal power of 3.6 MVA or 5.4 MVA each. For the catenary, it has been considered the use of an equivalent section of 320 mm² or 440 mm². For simplicity purposes, only the numerical results related to the 2 × 3.6 MVA TPS with a 320 mm² are here reported.

Figure 15 reports the minimum line voltage, highlighting that the voltage drop along the line is critical only at 7:30 and 8:30, at the departure of the train from Station B, towards Station A. In this case, the TPS must feed the train that is more than 11 km away. In fact, it is necessary to limit the power to the pantograph to 3 MW in order to contain the voltage drop on the line, obtaining a voltage at the pantograph is 2.19 kV. However, this minimum voltage is present only for a single sample of the simulation (10 s).

Figure 16 shows the TPS power absorption and given that the power required to the primary network does not exceed 10 MVA, it is possible to provide for the medium voltage connection to the primary network.

5.2.3. On-Board ESS

The main constraints of the on-board ESS sizing are the energy required by the cycle and the maximum power to be delivered. In the case of an electrochemical storage system, this must provide both the energy required by the cycle and the power during peaks related to accelerations. Instead, in the case of a H-ESS consisting of batteries and supercapacitors, the power profile required by the train is divided into two parts, obtaining a reference profile for the battery pack and another for the supercapacitor pack.

The high autonomy ESS implies an autonomy to go from Station A to Station B and recharge the storage system at Station A. According to this cycle, the energy to be supplied to the rolling stock is equal to 585 kWh. First, the use of high-power lithium-ion cells has been analyzed, whose characteristics are shown in Table 1. In this case, the sizing results in a 980 kWh (650 Ah) battery pack, of which only 586 kWh can be used, due to SOC limits. In Figure 17, P_BATT represents the power associated with the battery pack, positive in the traction phase, and negative in the braking phase. The voltage of the battery pack is identified as V_BATT and presents variations that re less than ±5%. The supplied current is identified as I_BATT and is positive in the discharge phase (traction) and negative in the charging phase (regenerative braking). Since the capacity of the battery pack (C) is equal to 650 Ah, it is observed that both the maximum discharge and charge current are much lower than the maximum allowed by the battery pack (20C and 4C respectively, in the discharge phase and charge). Moreover, it is observed that the sizing is appropriate because the SOC does not drop too low, and over time (despite greater discharges), the SOC will not drop below a certain minimum (30%).

Afterwards, a high autonomy H-ESS has been analyzed. It is composed of the high-energy lithium-ion and supercapacitor cells, whose characteristics are shown in Table 1 and Table 2. The subdivision of the original power profile is achieved through a low pass filter with a cut-off frequency of 1 Hz and an amplitude limiter which limits the maximum power supplied by the batteries to reference value equal to 2 MW, in order to reduce the maximum power peak that they must supply to about 50% of the original one. Instead, the regenerative braking power is limited in absolute value to about 5% of the maximum braking power (0.1 MW), in order to make the supercapacitors recover as much energy as possible during the braking phase. In this way two reference profiles are obtained to carry out the sizing: P_REF_B for the battery pack and P_REF_SC for the supercapacitors, as shown in Figure 18.

Carrying out the verification simulations of the H-ESS, it is observed in Figure 19a that the current required to the battery pack (in blue) tends to exceed the limits set by the manufacturer during discharge and is therefore limited to a lower current (in orange). Moreover, the supercapacitor SOC reaches too low values, as shown in Figure 19b. To avoid these situations, it is necessary to increase the quantity of parallel branches of high-energy lithium and supercapacitors cells, further increasing the total mass of the storage system. This hybrid solution is thus abandoned because it is too heavy.

The ESS with recharge station implies an autonomy to go from Station A to Station B, where the recharge needs to be performed. According to this cycle, the energy to be supplied to the rolling stock is equal to 383 kWh. It has been considered the use of high-power lithium-ion cells and the sizing procedure results in a 640 kWh (425 Ah) battery pack, which does not exceed the limits set by the manufacturer. The recharge at Station B can be performed from the 30% to the 50% of the SOC, since it allows arriving to Station A within the available SOC range. Therefore, the recharge must have a duration of 6 min, at 2C rate, implying a recharge station of at least 1.4 MW.

In Figure 20 it is shown the charging time for both high autonomy ESS and ESS with recharge station, to be performed at Station A (in the electrified section). This recharge takes the SOC from 30% to 90% and it is performed, at 2C, in 18 min (LFP cells).

Table 4. On-board ESS scenarios.

	High Autonomy ESS	ESS with Recharge Station
Rated capacity [Ah]	650	427.5
Rated capacity [kWh]	976	642
Available capacity [kWh]	586	385
ESS weight [t]	9	6
Train Performance energy impact [%]	3	2
Recharge power @2C (C-rate) [MW]	2.2	1.4

presents a synthesis of the viable on-board ESS scenarios, including the ESS impact in the energy required by the rolling stock because of the weight increase.

5.2.4. Economic Comparison

As reported in Section 2, the present value of total cost and the annual cost of energy are computed, considering the following hypothesis: an expected lifetime of 30 years; ESS lifetime of 10 years; an interest rate of 4% for electrification and 6% for ESS [45]; an average cost of electricity of 15 €/MWh [49]; charge efficiency equal to 90%; four daily connections between Station A–Station B. In Figure 21 it is shown the total cost (a) and the ACOE of the proposed scenarios. 3 kV DC electrification shows a present value of the total costs of approximately €13 M and an ACOE of over 700,000€ per year. Most of these costs come from the high investment cost necessary for the electrification, estimated at €10 M, as it is necessary to install a traction power substation, a contact line and carry out works such as track lowering in correspondence of tunnels already present in the route and raising of the overpasses. The ESS with recharge station has a present value of the total cost of approximately €7 M, considering the replacement of the storage system every 10 years (it will depend on the correct operation in charge/discharge phases), and the installation of the necessary system for charging. The ACOE of this solution is about 500,000€ per year, due to the lower costs associated with the charging station compared to those associated with the installation of TPS. Finally, the high autonomy ESS, with a total cost of €5.5 M and ACOE of 400,000€ per year, could be advantageous solution from the economic point of view, since it does not involve the installation of any infrastructure for the recharge.

The main advantage of on-board ESS with high autonomy is that it does not require the installation of additional charging systems as this is provided for in the already electrified section of the railway line. Consequently, investment costs are limited. Moreover, on-board storage systems work with shallower charge and discharge cycles.

It should be emphasized, once again, that apparently the total costs linked to the solutions related to the use of trains with on-board storage would seem to be lower but it is necessary to underline that the total cost will strongly depend on the costs related to the construction of new rolling stock. Subsequently the real lifecycle of the batteries could lead to a further increase in costs due to their early replacement. However, investments in e-mobility lead to an increasing mass production of batteries. Consequently, if high demand growth is sustained, battery solutions are expected to be more profitable.

The feasibility of trains with on board ESS is similar to that of fully electrifying the ships that will sail the North Sea in the near future [63]. In both cases, current reliable solutions (i.e., electrified railway lines and heavy fuel oil powered shipping vessels, respectively) may lead to a previous hybridization stage before achieving the complete on-board energy supply system.

6. Conclusions

In the very near future more technical-economic comparisons between diesel/electrified railway and the use of trains with on-board energy storage systems will be carried out in order to define the best solution achievable from an environment and economic point of view in relation to different railways lines. It will be necessary define the adoption of these systems for expansion of already electrified railways, point-to-point connections, commuter transport systems and so on.

The times are becoming ripe and consequently the paper defines methodologies, procedures, simulation models considering the main economic aspects, in order to increase the scientific literature on these innovations that will be increasingly investigated.

The methodology and the model developed in this paper could help to define a series of aspect to consider when is necessary compare different system adoptable to modernize a railway line.

The paper shown numerical simulations on a real railway line that presents a 3 kV DC electrified section and a non-electrified section, currently covered by diesel-powered trains. Different types of ESS have been analyzed, evaluating the use of high-power lithium cells or high-specific lithium cells and supercapacitors. The models of the battery pack and supercapacitor pack have been implemented in the Matlab/Simulink environment. Three main scenarios have been evaluated for the non-electrified section: 3 kV DC electrification, on-board ESS with high autonomy and on-board ESS with recharge station.

The results showed that the use of trains equipped with on-board energy storage system could be a good solution, but from a preliminary economic point of view, today many cost parameter are still not well known. Consequently, over the years, through the first realizations and the monitoring of the operation, it will be possible to definite clarification of the costs, as well as they are well established and consolidated in the electrification at 3 kV DC.

It is also shown that the most suitable storage technology for the case under study is that of high-power lithium ion batteries. The on-board ESS with high autonomy presents an ACOE of about €400 k/year, apparently 40% less than the 3 kV DC electrification scenario (costs of new train manufacture, battery disposal are not taken into account). Since the case study concerns a single-track railway line in which maximum speeds are limited, two trains allow to cover the entire section without any impact on the service offered to passengers, given the charging times and autonomy of the chosen solution.

Finally, it should be noted that the electrification of railway lines represents a consolidated and highly reliable solution. Contrariwise, the use of trains equipped with on-board energy storage systems represents a solution currently being tested, which will take many years before a consolidation.

It will be very important to know the cost of the new trains equipped with ESS on board, taking into account the long homologation procedure until they are placed on the market, and the real behavior of the storage systems in relation to life expectancy.