Simulation of Battery Operated Trains on Partially Electrified Lines: A Case Study regarding the Florence-Faenza Line

1. Introduction:

About a half of European railway lines are still not electrified [1], this problem also regards highly developed countries and railway network such as Germany [2] in which there is still an high percentage of Diesel passenger trains operating under lines whose electrification is not complete, since in some cases the complete electrification of a railway line with low traffic intensities in not sustainable in terms of construction and maintenance costs.  The percentage of not electrified lines in many extra-European countries is even higher. Rolling stock that is used to manage both passenger and freight traffic on these lines is powered with internal combustion engines, mostly DIESEL engines with Hydraulic or Electric transmission systems. The substitution of ICE(Internal Combustion Engine ) with another electric power source or storage should be proposed to increase sustainability an environmental impact in terms of direct emissions of CO₂. Also a simple hybridization of a Diesel-Electric locomotive as proposed by Magelli[3] can significantly reduce emissions.

Proposed alternatives[4] are electric storages such as batteries [6] or hybrid hydrogen fuel cell systems[7,8]. Both technologies are still affected by some technological limitations that are often studied in comparative studies such as the ones recently proposed by Zenith[8] and Cole[9]. Results of this comparative studies are deeply influenced by the technological limits of considered components which are continuously shifting due to the continuous technological improvements. Usage of hybrid hydrogen fuel cell systems is constrained by poor performances of fuel cell systems during fast transients and in presence of partial loads as stated by simplified aging models that are proposed as example by Zhang[11]. This constraint involves the adoption of power buffer electric storage systems that should be realized with high power batteries, with capacitors or alternatively with an optimized mix of both technologies as investigated by Fragiacomo [12]. This feature also involves a limitation of regenerative braking due to the limited size of buffer storages and to the way in which power flows are managed. Hydrogen fuel cell systems of commercially available trains such as Alstom Coradia[13] currently exhibit an autonomy which is far higher respect to corresponding battery-operated solutions. However a further increase of the specific energy stored and consequently of autonomy is constrained by advances of Hydrogens storage systems, since current technology of pressurized hydrogen tanks it substantially constrained to maximum operating pressures of 350-700bar for which the storage of 1kg of hydrogen involve an equivalent weight of the tank from eleven to fifteen times higher, as stated by technical documentation available on line[14,15]. Also, high pressure compression of hydrogen involves an appreciable energy consumption negatively affecting “from well to wheel” efficiency and sustainability[16]. On the other hand, despite specific energy limitations of batteries[17] that are currently adopted for railway applications (less than 100-120Wh/kg) there is a clear indication of rapid trend of cells and batteries proposed for automotive market[18,19]. So, there is the well-founded opinion that in about 20-30 years from now performance of batteries should be feasible for a near to limitless application on future rolling stock. Also, it should be considered that batteries are reversible electrochemical storages that allow an extensive use of regenerative braking on railway vehicles.

There is a further opportunity for the usage of battery-operated rolling stock that is represented by partially electrified lines in which a multi-modal usage of the system should be convenient and feasible: in this case the mission is performed along lines which are electrified only in some sections. This is quite common conditions, since as example a part of the mission should be performed along a high traffic route for which cost of line electrification is tolerable. Otherwise, the remaining part of the line should remain not electrified for different reasons such as a relatively low intensity of railway traffic respect to the construction and maintenance costs of the infrastructure. This scenario has been studied since 2013 by  Hoffrichter et al.[20] which proposed a multi-modal solution in which propulsion of electric unit is alternatively granted by diesel units or collected from the line according to different availability in different sections of the simulated line.

Recent studies of Abdurahman[21] also demonstrate that the environmental impact of service on partially electrified line can be much more sustainable respect to a service managed with conventional Diesel Units

In the last two-three years multimodal solutions in which the same tram or train can be alternatively supplied by overhead line or by on board storage systems has been proposed and studied starting from tram and suburban railways[22] to railway applications [23,24]. in this article the use of multimodal passenger BEMU (Battery Electric Multiple Unit) on steep railway lines built in hilly or mountainous territories is proposed. Respect to previous studies a particular attention is focused on the following aspects which also represent the innovative or at least more significant contribution of this work:

• Proposed benchmark test train is inspired to existing industrial products (Diesel and Hybrid Multiple Units) which are quite interesting for some application scenario such as local passenger lines on western Europe, but it introduces some significant innovations especially for what concern adopted powertrain layout and power-management system.
• Adopted batteries are inspired to recent industrial products currently assessed for railway applications, also considering a proper management of their depth of discharge to assure a feasible level of reliability for proposed application.
• Proposed mission profiles correspond to existing railway lines crossing mountain or hill regions, that impose increased traction loads and regenerative braking. Simulation take count also of consumptions of auxiliaries (such as example heating, ventilation, and air conditioning) not only when the train is moving but also during train stops or during parking at terminus stations.
• Recharge of on-board batteries is supposed to be performed using exclusively the power collected under a standard 3kV catenary using a conventional railway pantograph, so the whole system is designed and simulated also considering power and current limits imposed by regulations in force[25].
• Obtained results are quite interesting for a potential immediate application of battery operated trains to partially electrified lines
• Both proposed simulation tools/models can be useful and interesting for a further optimization not only of proposed solution but also for simulation and investigation of a wide variety of hybrid powertrains for innovative rolling stock.

The discussion is organized first introducing modelling and design of proposed benchmark test train. Then proposed mission profiles in terms of simulated lines and performed optimization of driving profiles are introduced. Finally obtained results are discussed to evaluate feasibility and potential advantages of proposed tools and solutions.

2. Proposed Benchmark Test Train

As previously introduced, there is a wide interest to improve the environmental impact of local passenger service that is currently performed with DMU (Diesel-Multiple-Unit). This attention of Stake Holders has motivated industrial investments regarding the development of HDMU (Hybrid Diesel Multiple Units), FCHMU(Fuel Cell Hybrid Multiple Unit) and BEMU (Battery Electric Multiple Unit). Some of these recently proposed solutions are briefly described in Tables 1 and 2,3. Some of the data of these tables are referred to preliminary studies aiming to introduce expected features of product which are still in a development phase[27,28].

Size and expected performances of different manufacturers are quite converging in terms of speed and loading capacity. In this work authors focused their attention on the Hitachi Masaccio (HDMU version) platform with four articulated car bodies. This choice was substantially induced by previous research activities of Florence University in which the upgrade of the HDMU unit to FCHMU was investigated[29,30]. These activities involve an accurate investigation of encumbrances and loading capabilities that can be recovered on each vehicle to install the new storage system.

As visible in Figure 1 both layouts substantially share the electric traction powertrains that are installed at the extremities of this fixed/articulated composition. So, both solutions share traction equipment, power converters and a part of the battery storage that for the hydrogen powered solution is used as power buffer for fuel cells[30].For design purposes the investigated train is substantially similar to the BEMU version proposed by manufacturer in 2021[27] but at the same time some innovative modification has been introduced for what concern storage system, power management layout and more generally some innovative considerations regarding recharge and energy interaction with surrounding infrastructure.

For the purpose of this work, which is the verification of opportunities arising from the synergy between partial electrified lines and BEMU, authors focused their attention on two different benchmark test lines.

The first one is an existing partially electrified lines from Florence to Siena (about 90km of length) which is currently electrified only from Florence to Empoli (about 30km) while the remaining sections are not electrified. Main features of this line are shown in figure 2: it’s interesting to notice that the altimetric profile of the not electrified section involve a mean slope of about 4 [m/km] with a maximum slope for some kilometres of about 15[m/km], that is interesting to evaluate the stressing effect in term of required performances and opportunities arising from regenerative braking.

The second line is from Firenze to Faenza (length of about 100km) and it is completely not-electrified. This line is far more demanding in terms of performances respect to Firenze-Siena since the mean slope is higher (about 6[m/km]) with extended sections of tenths of kilometres in which the slope is 15-20[m/km]. This second example, which is shown in figure 3, is introduced as mission profile which is quite stressing for the current technology of BEMU. In this way it’s possible to evaluate how limited interventions on both vehicle and infrastructure technology can really improve performances and reliability of performed service. Timetables, such as the one described in Figure 3, are taken from corresponding mission profiles adopted by trains that have been previously used on these lines.

3. Adopted Modelling Approach

Adopted Model is a further innovative extension of the model that has been recently introduced to model hybrid fuel cell rolling stock[29,30]. The model substantially solves the longitudinal equilibrium (1) of the convoy considering applied longitudinal forces $T$and different motion resistances such as $F_p$(grav. forces due to slope),$F_a$(distributed friction and aer. resistances), $F_c$(lumped motion res.), $F_i$(inertial force):

$$T+F_p+F_c+F_a+F_i=0$$

(1)

Respect to this known formulation (1), the application of traction and braking forces is evaluated considering tabulated saturations of traction and blending forces, also considering their dynamical behaviour and the effect of applied blending strategies during mixed electric and pneumatic braking. Involved power flows are calculated considering a fixed conversion efficiency of each power electronic stages of about 92% and a fixed efficiency of mechanical transmission of about 94%.

Respect to this previous model authors have introduced a generalized structure of the powertrain layout which is visible in : the system supposed to be built around a common DC Bus to which are connected directly or with an intermediate coupling stage (a power converter) all the sources and the storages that can be potentially inserted in a Hybrid or Electric Powertrain. In this way several different solutions ranging from Diesel Electric Transmissions to Hybrid Fuel Cell or Battery Electric Solutions can be modelled. For this study, the equivalent layout is shown in figure 4/a: the DC bus is connected to the pantograph and consequently to overhead line with a converter that is supposed to be equivalent to a H bridge that can be used reversible chopper under DC lines or controlled/reversible rectifier under AC lines. For the purpose of this study this power converter was designed only for DC applications to reduce encumbrance due to transformers, while the voltages levels of battery storage, DC Bus, traction equipment were considered the same. In this way proposed solutions privilege autonomy in battery mode respect to efficiency when operating under the electrified catenary.

Otherwise the scheme proposed in a preliminary presentation by the same supplier of the train[27] is visible in figure 4/b: in this case the pantograph is supposed to be directly connected to the DC bus. So, also this layout which is a bit different can be treated as a further simplification of the same general model.

3.1. Generalized Power Management

As previously introduced the model of simulated power system is modular allowing the simulation of any combination of sources and storages that should be used to manage a multi-modal rolling stock. So, also the adopted power management system is designed to obtain a modular approach that can be easily customized and tuned respect to the chosen configuration. For this reason, authors extended the use of an approach[31] that was originally developed and introduced for the power management of multimodal buses and trucks tested by University of Florence at ENEA laboratories of Roma Casaccia (italy).

The proposed generalized layout of the control system used for power management is shown in Figure 5: all the loads of the vehicle are supposed to be fed by a primary storage system, such as a battery. Dynamic response of the chosen primary storage is supposed to be fast enough to follow the dynamics of connected loads. Without the contribution of the other power sources and storages the power $W_1$exerted by the primary storage should be equal to the load .$W_{load}$.(2)

$$W_1=W_{load}$$

(2)

Any other source of power, for example a fuel cell, or an ICE Power-Pack, or a converter connected to an external line, can be added to the system. It is assumed that an arbitrary number of different sources or storages can be added so $W_i$( with i>1) is intended as the power exchanged by the i-th component.

Each additional storage/power can regulate $W_1$to a desired value $W_{1ref}$ by suppling an additional power $W_i$ closing a loop. This loop is also called “Load Follower Loop” since the controller $G_i$acting on the open loop transfer function of the i-th source$P_i$substantially reject the action of the load as a disturbance so with a perfect tracking of the controller $W_i$should be equal to $W_{load}$. Further Saturations on exerted power and its derivatives should be introduced to model typical limitations of real power sources such as example an irreversible behaviour ($W_i$can be only positive as example for an ICE) or a limited dynamic of response.

For an arbitrary number of additional power sources, if the simulated conditions are not able to excite any modelled non-linearity of simulated components, the response of the system can be represented in terms of transfer functions(3),(4) that are relatively easy to be tuned using conventional adopted for loop shaping.

$$W_1=\frac{W_{load}+{\displaystyle \sum _{i=2}^n{W}_{1ref}{G}_i{P}_i}}{1+{\displaystyle \sum _{i=2}^n{G}_i{P}_i}};$$

(3)

$$W_i=G_i{P}_i\frac{\left(W_{load}-W_{1ref}\right)}{1+{\displaystyle \sum _{i=2}^n{G}_i{P}_i}};$$

(4)

Shaping of load follower loops, performed by tuning transfer functions $G_i$ can be used to adjust the way in which power fluxes are generally managed between different sources. However also the value of accumulated energy in the first storage $SO{C}_1$must be stabilized. For this reason a second external loop called “Range Extender” is implemented: by regulating desired power flow $W_{1ref}$it is possible to stabilize within an acceptable interval the SOC (state of charge) of the first storage system.

This loop is called “Range Extender” since the implemented functionality is quite like to the range extender approach used for hybrid road vehicle in which vehicle battery is periodically recharged according to SOC level of the battery to increase autonomy[32].

For what concern the controller $G_1$of the range extender loop non linear controller should be better suited respect to linear one, since the desired behaviour of $SO{C}_1$is nonlinear and influenced by different considerations related to expected life and reliability of the recharged battery. However for the purposes of this study it was adopted a nonlinear polynomial load described by (5): the battery can be recharged in order to keep $SO{C}_1$within a minimum($SO{C}_{1\min }$) and a maximum level($SO{C}_{1\max }$) also power flows are limited in an interval between two extreme values ($SO{C}_{1\min }$,$SO{C}_{1\max }$). In this work the value of the exponent n is equal to 2.

$$\begin{array}{l}{W}_{1ref}=\left(W_{1\min }+\left(W_{1\max }-W_{1\min }\right)\gamma \left(SO{C}_1(t)\right)\right)\left(SO{C}_1(t)\le SO{C}_{1\max }\right)\\ where\hspace{0.17em}\hspace{0.17em}\gamma \left(SO{C}_1(t)\right)=\left(1-{\left(\frac{SO{C}_1(t)-SO{C}_{1\min }}{SO{C}_{1\max }-SO{C}_{1\min }}\right)}^n\right)\end{array}$$

(5)

The resulting nested control system is quite flexible and easy to be tuned since higher gains of $G_i$ will involve a bigger contribution of the i-th source to the balancing of the vehicle loads. Otherwise by reducing the nonlinear gain$G_1$is possible to increase the amount of power and energy fluctuations that should be compensated by the primary storage/battery. In this way acting on controller gains is also possible to perform bump less transitions between different operational modes, a feature that should be very interesting for multimodal rolling stock. For Battery-Operated Rolling stock, the generalized layout described in figure 5 has been simplified, obtaining the scheme described in figure 6 which is considered in current study.

3.2. Planning of Mission Profiles and high-level control of longitudinal dynamics

Planned mission profiles and the way in which simulated/virtual drivers effectively control train dynamics play a key role for the evaluation of energy consumption of a train. in literature there are several examples such as the studies of Ghaviha [33] and Nallaperuma [34], dealing with optimization of performed mission profiles to increase efficiency and autonomy leading to a mission profile which is strongly optimized respect to the feature of a specific battery adopted along a known line.

Also proposed simulation model should be designed to allow a real time implementation for an HIL (Hardware In the Loop) testing in which the model of tested system is connected to a scaled prototype of the train storage to verify mutual interactions between state and management of the storage system with traction and auxiliary loads of the simulated train as visible in the scheme of figure 7.

For a RT implementation a deterministic allocation of computational resources with a limited jitter in term of execution time is quite mandatory as verified from previous experiences related, as example, to the HIL testing of railway WSP devices[35].

So for the purpose of this work authors adopted the approach described in Figure 8: first an inverse dynamic problem is solved iteratively offline. Starting from a known timetable describing arrival and starting time, traveling speed profile is iteratively adjusted considering imposed speed limits for every section of the line.

Further limitations in terms of maximum accelerations, decelerations and jerks are imposed also evaluating their feasibility in terms of involved traction and braking efforts. At the end it is chosen the minimum velocity profile that assure the respect of the prescribed timetable and kinematic constraints. This approach leads to an acceptable mission profile that can be further optimized adjusting speed and acceleration profiles respect to consumed energy. Calculated trajectory$x_{ref}(t)$, speed ${\dot{x}}_{ref}(t)$ and acceleration ${\ddot{x}}_{ref}(t)$ profiles are then used as reference input for a closed loop control composed by nested position and speed loops aiming to regulate reference traction torques and braking of the train during the on line simulation in which a direct dynamic trouble is solved. To avoid excessive gains on both position and speed loops a model-based feedforward term is also integrated in this control loop. Resulting control can perform a precise and smooth control of vehicle trajectory avoiding unstable oscillations of performed manoeuvres that should negatively affect efficiency and robustness of the simulated system.

4. Performed Simulations and Results

4.1. Sizing of both On-board Storage and Power Management System

Sizing of on-board storage system is a part of the activities related to simulation: proposed models allow the usage of batteries with different specific energy indexes since their sizing is scaled respect to loading capability of the train in terms of available weights and encumbrances. For this study data were available from a previous investigation concerning the installation of fuel cells on the same train[30]. For the previous study concerning hydrogen fuel cells the most important constraint was represented by available volumes for tanks, while in this one the most significant constraint is the weight that should be limited to about 11 tons. For what concern the batteries authors considered the data[36], visible in Figure 9 , of a recent high power battery assessed for railway applications: in which specific energy ($E_{spec}$) and power ($W_{spec}$) indexes are approximately equal to 117[Wh/kg] and 352[W/kg] . Homologation of the product for the railway sector is a quite important requisite since for automotive applications employed battery systems currently declare performances which are substantially doubled. The resulting size of the storage is about 1[MWh] as visible in Table 4. High power batteries have been chosen, since a maximum charge rate of 3C (three times the nominal power of the storage) which implies in theory, a complete recharge in 20minutes. All these data are coherent with the increased performances achieved as example by BEMU[37] that achieved the record of autonomy in Berlin (224km). These specifications are quite useful for proposed application since a battery with high charge rates support an extensive use or regenerative braking performed by the traction system whose main data are also described in table 4.

Also on partially electrified lines, a high charge rate allows a fast recharge under relatively short, electrified sections. However fast recharge of batteries cannot exceed limitations regarding the maximum power that can be collected from a 3kV DC line using a standard pantograph. In this way the system is designed to be fully interoperable with the energy infrastructure as standard EMU without the need of any special power-station, pantograph or other interface dedicated to recharge. These limitations, also described in table 4, are prescribed by interoperability specifications[38] and by corresponding applicable standards[39].

Power management system previously described in Figure 6 was then calibrated adopting the set of parameters described in Table 5: gains of the controller G₁ as described by (5) has been calibrated to fully exploit the features of the proposed battery. Allowable state of charge SOC₁ was reduced to a range between a minimum value SOC_1min equal to 0.2 and maximum one, SOC_1max, of 0.85. Value of SOC_1min was chosen to assure ae reasonable margin of robustness against battery aging also assuring a reasonable amount of backup power in case of unpredicted or excessive energy consumptions. The value of SOC_1max was decreased to 0.85 to assure a reasonable safety margin respect to the risk of potentially dangerous over voltages to which the battery can be subjected during regenerative braking. More generally the reduction of the maximum depth of discharge to about 65% and the exploitation of a mid-region of the OCV curve of chosen cells is in in favour of an extended life and reliability of the storage system, mitigating accelerated aging effect due to high recharge rates. This choice is confirmed by current technical literature. LTO, NMC or LiFePO₄ Lithium cells are conventionally indicated as well-suited for railway applications and there are several studies related to the way of increasing battery life and reliability due to high charging rates. Some studies focus their attention to the maintenance of restricted range of temperature of the lithium cell that a good kinematic of electrochemical reactions without compromising its thermal stability: even for LiFePO₄ cells [40] that are claimed to be very stable for a thermal point of view, for a fast recharge is suggested to operate within a limited range of SOC to improve efficiency of fast charge and discharge cycles avoiding high levels of SOC where a minimal overvoltage of about 0.1V can dramatically reduce the predicted life of the cell. Also, for LTO cells which are the more extensively especially for high power storages, recent publications[41] confirm that a reduction of the maximum DOD (Degree Of Discharge) to 60-70% substantially maximize the life of the cell especially for high power/current cycles. Also, for NMC cells[42] a substantial increase of expected life with fast charging can be obtained decreasing the maximum SOC to values between 0.8 and 0.9.

Finally, an interesting aspect is related to balancing of cells that are assembled in the battery, cell unbalance is one of the major causes of aging of storage systems, since unbalancing systematically accelerated the degradation of some cells that unevenly loaded respect to the ones. Unbalance and consequently accelerated differential aging of cells is associated to differences in terms of voltages measured on each cell which also corresponds to a dispersion of SOC values of cells that in theory should be charged in the same way. This phenomenon is often self-accelerating since degraded cells exhibit a lower capacity that further increase their voltage fluctuations respect to the other cell that are subjected to the same current. It can be easily demonstrated that the behaviour of the system is much more stable respect to unbalancing when the derivatives of OCV(Open Circuit Voltage of the cell) respect to SOC are lower. If the value of SOC is restricted to a range between 0.2 and 0.85 the behaviour of OCV vs SOC is quite flat reducing corresponding derivatives and then the sensitivity against unbalance of cells. For this reason, also research papers[43] that investigate the negative effect of fast charging in terms of battery unbalance, suggest the adoption of a reduced range of allowable SOC values as suggested in this work.

So, it can be concluded that chosen parameters of G₁ controller are quite optimal to extend the leife of proposed batteries against fast charging. For what concern the second regulator (G₂ in the scheme of figure 6), it was supposed a simple PI (proportional controller) with a high proportional gain and a very small integral one (1/100 respect to the proportional one) that assure a good tracking of required battery power $W_{1ref}$ calculated by the external range extender loop (G₁).

4.2. Simulation of the Firenze-Siena Line (Partial Electrified line)

Authors performed an extended campaign of simulation for what concern Firenze-Siena line which confirmed the feasibility of proposed solution. Some interesting results are shown in Figure 10: in this simulation it’s supposed that the train starts in the terminus station of Florence with a nearly to depleted battery (a minimum state of charge of 0.2). Then the train lift his pantograph starting to feed on board system in parking mode. Since it is supposed the usage of a standard DC pantograph under a 3kV DC catenary, collected power in standstill conditions is limited to no more than 200[A] (about 600kW). Considering a feasible consumption of auxiliaries of 120kW (30kW for each articulated carbody of the train), the remaining power to recharge on board batteries in parking mode is relatively small, so the resulting recharge of the battery is quite slow. This phase which is supposed to be about 15’ should be quite important in real operating conditions, allowing a pre-heating of cells that typically increase their reliability respect to fast charging and discharging rate.

As the train start, as visible in figure 1 the recharge rate drastically increases because the maximum value of current that can be reasonably collected from a 3kV DC line is about 6MW. In these conditions considering the size of the installed battery (1MWh) and maximum traction loads (no more than 1MW in realistic conditions), pantograph is largely capable to collect the power need for a fast recharge without penalizing traction performances. This is a direct consequence of the reduced size of BEMU trains that are usually adopted for local passenger trains. Looking at generated kinematic of the mission profile, it is clearly noticeable that the simulated train can reproduce almost perfectly both imposed timetables and trajectories which are relatively smooth respecting not only speed but also imposed limits on accelerations and jerks. The capability of reproducing also the duration of stops in intermediate stations is fundamental to calculate energy consumptions of auxiliaries during train stops. Recharge along the electrified line is concluded in about one third of the available time (about 700-800 seconds) so it can be concluded that the same recharge can be performed also admitting a maximum recharge rate of 1C, paving the way to the implementation of a predictive logic able to reduce the recharge rate according to foreseen mission profile.

As the simulated mission continues in the not electrified section it can be observed small fluctuations of the SOC associated to regenerative braking on batteries. To further verify the robustness of proposed solution is also considered the absence of an intermediate recharging infrastructure in the station of Siena, so consumptions of auxiliaries produce a constant discharge rate corresponding to about 0.12C, clearly explaining how consumption of auxiliaries should be important for the evaluation of autonomy in real operational conditions. When the train left Siena to return to Florence, consumption under the not electrified section of the line is clearly lower, since the extended usage of regenerative braking allows an efficient recover of potential energy in the downhill section of the line. Finally, when the train reachs the electrified section in Empoli the battery is completely recharged reaching the station of Florence with a full charged battery.

This simulation clearly demonstrates that in this scenario in which the length of the electrified section is about one third respect to the total length of the line, the system is substantially stable from an energetic point of view also considering the aging of the cells since the minimum level of SOC at end of the not electrified section is still about 0.4(40%). This robustness is also granted by the extended application of regenerative braking that assure an energy saving of about 100kWh compensating at least a part of the consumption of auxiliaries under the not electrified section which are evaluated to be equal to about 250kWh. This impressive value clearly gives an idea of the importance of auxiliary loads in assessing the real autonomy of a BEMU.

Looking to simulated mission profile is also possible to perform a cautious evaluation of expected life.

During a day of service (about 10-12 hours of service a day, about 500-600km/day ) about a1.6-1.7 FCE (Full Cycle Equivalent) of battery life are expended. Even considering a granted life of 2500 cycles which is considered the baseline performance for automotive batteries subjected to fast charging the expected life of the storage is supposed to be more than 4-5 years of uninterrupted service (corresponding to a mileage of about 900000km). This value is very cautious because some of the sources cited in this work[41] claim an expected life for LTO cells properly protected (good thermal management, reduced DOD) an expected life 1-2.5*10⁴ FCE which is substantially 4-10 times higher respect to the considered one. In this work reduced DOD is supposed but the second condition (perfect thermal management) is difficult to be verified in a simulation environment. However the same testing campaign [41] also consider a baseline reliability of more than 4000-5000 FCE(“cold cells” at 25C° with 5-10C charging currents) which is still able to assure an expected life of the battery of more than 8-10years of continuous service.

So, it can be concluded that in terms of expected life of the battery pack proposed solution is satisfactory but that a more precise evaluation involve a specific electro-thermal study that will be the object of ongoing activities.

4.3. Simulation of the Firenze-Faenza Line

As previously introduced this second line is longer, has a more demanding altimetric/mission profile so it can be considered a benchmark test case for the proposed rolling stock.

As in the simulation of Firenze-Siena, for this line is performed a round trip (from Florence to Faenza and the return to Florence) without any intermediate recharge. Also, the train is stopped at each terminus station for 15 minutes considering consumptions of auxiliaries of the train. This mission cannot be completed using the high-power battery that was adopted for the benchmark test run on Firenze-Siena line since estimated energy consumptions are about the 150% of the maximum quantity of energy that can be stored on the train.

So, a minimum level of specific energy$E_{spec}$ equal tool 180Wh/kg (1.5 times higher than the adopted one) is needed to complete the mission. This is not an unfeasible value for a railway application since, as example, looking to the catalogue of figure 9 [36] an Intilion™ high energy module (assessed for railway applications) can reach this desired performance which is also aligned to specifications of batteries that are currently used for many automotive applications. An example of simulation results obtained considering the installation of this high energy module (corresponding to a size of about 1.65 MWh) is shown in Figure 11: It's clearly noticeable that the final value of battery SOC is quite low (almost exactly the minimum one 0.2/20%) so flexibility and robustness of this solution respect any uncertainty should be a bit critical: maximum allowable charge and discharge rates of a high energy modules are lower, so a static recharge of about one hour should be considered. Finally, the high energy module should be a bit more sensitive to cycle aging respect to the high power one especially for what concern fast charging and loading peaks associated to regenerative braking or to train acceleration.

4.3.1. Simulation Scenario with a partial electrification of the line

A partial electrification of the line can be introduced to allow a discontinuous recharge of the train along the line. The choice of electrified sections and the way in which power is managed can be the object of different optimizations that are briefly listed in some review works as the one performed by Fedele[44]:

• Feasibility and Robustness of the proposed solution clearly depends on the capacity of the on board batteries of providing the desired autonomy along not-electrified sections. So, the distribution of partially electrified sections should tendentially minimize the maximum value of required energy to travel along the most demanding section in which the train should use batteries.
• Electrification should take count of local availability of power sources and of the orography of the line to minimize construction and maintenance costs.
• Partial Electrification should be placed in sections of the line in which higher power flows are statistically recorded such as railway stations where higher accelerations and decelerations of the train are statistically more common. Also, the slope of the line is another factor that should contribute to increase energy consumptions.
• Duration of a dynamic recharge under the catenary is limited by the length of the electrified section. So, the duration of the recharge can be inversely proportional to mean train speed. It’s more convenient to electrify sections of the line in which the mean speed is not very high. This consideration should consider that in pure standstill conditions the amount of power that can be collected is about one tenth.

Accepting these four criteria authors decided to adopt the configuration described in figure 12 and in table 6: both the two terminus stations of Firenze and Faenza are connected to electrified lines with high traffic intensities. For this reason, a recharge in standstill conditions inside both stations is possible at almost no cost if a conventional pantograph is employed. Also, the extension of the electrification of few kilometres outside the station is relatively unexpensive. Finally, it is just outside the terminus station that the train stock is accelerated so a relevant amount of power and energy should be transferred respect to the length of the electrified section. For all these reasons the electrification of the two-terminus station is considered as an imposed constraint evaluating only the possibility of optimizing the extension of the electrified section along the line. Clearly if the extension of the electrified section is too long (over ten-fifteen kilometres) additional costs infrastructural costs especially for power-stations should be evaluated.

Considering the previously calculated ratio between energy stored with high power storage and the energy consumption to complete the mission an intermediate charging section should be enough to prolong the autonomy of the train. An optimal positioning should correspond a distance which is about halfway between the two stations where the consumed energy for both traveling directions is almost a half of the total one of consumed energy can be performed directly locking the SOC and SOC derivatives calculated in the preliminary simulation of figure 11 where all the energy needed to manage the mission is taken from the onboard battery.

As visible in Figure 12, the optimal position of this intermediate electrified station is different according to the traveling direction of the train: if the train is starting from Florence the optimal position for a recharge station will be around Borgo San Lorenzo. Otherwise, if the train is returning from Faenza a good location should be approximately between the stations of Biforco and Marradi.

The first location, (around Borgo San Lorenzo) is also the most favourable in terms of construction and maintenance costs: the electrified section should be located in a flat, easily accessible, area in the Mugello valley between Campomigliaio and Panicaglia, where also connection to power grid is relatively easy since in the same valley the local line is very near to power stations of the high speed railway line Firenze-Bologna and to the high voltage electro-duct from Florence to Bologna. Also, near Borgo San Lorenzo, as visible in figure 12 there is the intersection with another not electrified line also coming from Florence through Pontassieve, so an electrification in this area should be synergic also for this second railway line.

So according to logistic evaluations it was preferred the first location which is not optimal for the return trip. To partially compensate a choice which penalizes on board batteries during return trips from Faenza, the electrified section from Faenza was extended a bit (a further increase of length or the insertion of a second intermediate recharge was considered potentially much more expensive). The length of the electrified from Florence station was minimized since a further extension was not substantially useful.

A complete simulation involving a roundtrip using high power batteries is then repeated. Some results are visible in Figure 13: the train can complete the roundtrip mission with a maximum DOD (Degree of Discharge of the Battery) of about 35% (0.35); at each terminus station (Firenze or Faenza) and even at the end of the intermediate recharge section the battery is completely refilled; also required So the performed system is stable from the energetic point of view. For the traveling direction from Florence to Faenza the maximum DOD is about 18% and it’s almost equal for the two not electrified sections of the line. So, in the direction from Florence to Faenza, the proposed layout is almost ideal. For the return trip (from Faenza to Florence) the maximum DOD is almost doubled (about 35%).

For this reason, a further optimized by simply imposing a shifting of the positioning of the intermediate electrified section between the two optimal locations, the first one, at Borgo San Lorenzo, and the second one at Biforco. For each configuration it is calculated the maximum DOD of the battery measured along a roundtrip mission: as shown in Figure 14, there is no configuration that minimize the maximum DOD under the 35% the minimum value recorded in the chosen nominal configuration. As the shift of the intermediate electrified section is increased the maximum DOD recorded when the train is traveling from Florence to Faenza increases to a maximum DOD of about 45-46%. So, it can be concluded that chosen position of the intermediate section is also optimal to minimize the maximum DOD of the battery.

4.3.2. Evaluation of Collected Currents on Added Electrified Sections

Using the power profiles, simulate with the previously described model was also possible to evaluate the entity of collected currents by the adopted pantograph under the electrified sections of the line. Aim of this calculation is not a complete simulation of the electrical layout but only a rough evaluation of the effect of estimated losses considering a simplified bilateral layout with known distributed resistances along the line and some feasible value of lumped resistances of power stations. For the purpose estimation it was performed considering a minimum and a maximum power capability of the infrastructure whose data have been taken from previous research activities[45]. As shown in Figure 15, even considering losses along the catenary collected currents are compatible in both scenarios with limits imposed by regulations in force. Also, the overall efficiency of the fixed infrastructure in terms of dissipated energy due to internal electric resistances is quite high (over 90%). Peaks of collected currents have a relatively short durations so there is a clear indication that the same mission profile can be performed lowering the max recharge rate of batteries to at least 1-2C further increasing feasibility and reliability of proposed solution. Finally, since there is no inversion of collected currents there is no need of reversible substations, also reducing cost and complexity of the fixed infrastructure. The study can be further improved considering the interaction of multiple battery-operated trains with the infrastructure.

Table 7. Parameters of the Simulated.

	Heavy Catenary[45]	Light Catenary
Distributed impedance along the line	0.05[Ώ/km]	0.1[Ώ/km]
Output Impedance of Power Station	0.09[Ώ]	0.36
No Load Voltage (Max Voltage of Power-Stations)	3700[V]	3500[V]

Table 7. Parameters of the Simulated.

	Heavy Catenary[45]	Light Catenary
Distributed impedance along the line	0.05[Ώ/km]	0.1[Ώ/km]
Output Impedance of Power Station	0.09[Ώ]	0.36
No Load Voltage (Max Voltage of Power-Stations)	3700[V]	3500[V]