Main characteristics of the mountainous rail route between the towns of Oštarije and Knin (Lika region, Republic of Croatia) in terms of elevation profile and speed limits are illustrated in Figure 2, wherein black curve represents the route elevation profile (h), while green dashed trace represents railway train speed limits (v_limit). These traces were defined in Cipek et al. [43] using free on-line Global Positioning System (GPS) Visualizer utility software [46] and an on-line source for the particular track speed limitation [47], respectively. Additional information in Figure 2 is related to the relative adhesion coefficient (k_va), (ratio of available adhesion with respect to the nominal case), whose availability is assumed based on the remote sensors grid data (see discussion in subsequent sections). In particular, the presented relative adhesion coefficient values roughly correspond to dry track and wet track adhesion conditions. Since the variable adhesion (wheel-to-track friction) coefficient (μ_a) within the freight train model can be expressed by multiplying the theoretical result from Pichlík and Zděnek [48] with the relative adhesion coefficient k_va, this results in the following adhesion coefficient expression:

${\mu }_a=({\mu }_{min}+\frac{\beta }{v+\gamma })k_{\text{v}\text{a}}$ (1)

with μ_min = 0.161 representing the adhesion coefficient minimum value, and other velocity-related constants parameterised as β = 7.5 km/h and γ = 44 km/h according to Pichlík and Zděnek [48].

Finally, blue curve in Figure 2 represents the average wind velocity (v_wind) profile, which is also assumed to be available from the distributed remote sensors grid (see subsequent sections). According to Valter [45], this additional relative wind velocity affects the specific motion resistance (w_k0) [N/t]. Due to the same train configuration from Cipek et al. [16] used in this paper, a specific motion resistance for heavy cargo trains can be defined as:

$w_{\text{k}}=25+0.0025(v+v_{\text{wind}}{)}^2$ (2)

Note that the minimum value of wind velocity addition v_wind is 12 km/h (Figure 2), which is according to Valter [45] a commonly used value within the above wind resistance model.

Figure 2.

Altitude, traction coefficient, head wind speed, and train speed limit profiles for the rail route considered in this work

According to Valter [45], the train movement is also subject of the railway track curvature radius effects and track gauge. For the sake of simplicity, an equivalent constant-valued average curvature resistance ($w_r={\overline{w}}_r=4.99$ [N/t]) is adopted herein, as proposed in Cipek et al. [16].

Figure 3a shows the overall quasi-steady-state model of the battery-hybrid locomotive [16], comprising the train driver, longitudinal dynamics, electrical traction and mechanical brake system sub-models (framed by dashed lines), which are given in more detail in Figure 3b. The power-train sub-models are modelled by means of static characteristics (maps), which are originally developed in Cipek et al. [16].

The driver model subtracts the freight train model velocity (v) from the velocity reference (target) (v_ref), and the resulting difference is used to generate the train driver control output in terms of throttle ‘Notch’ position and braking ‘Brk’ commands. These are partitioned into eight positive ‘Notch’ levels corresponding to constant traction power operation, one zero-valued neutral ‘Idling’ position, and eight negative ‘Notch’ levels for regenerative braking at constant braking power [16]. The driver model is configured as a simple proportional term with gain (K_Dr) [16], and its output is subsequently quantized resulting in seventeen integer values related to ‘Notch/Idle/Brk’ commands, and also saturated so that the ‘Notch/Brk’ command selection does not exceed the definition range from –8 to +8 (Figure 3b) [43]. In the case of deceleration, additional braking action by means of mechanical brakes can be applied if train velocity exceeds 1 km/h over the targeted value, i.e., when regenerative braking cannot effectively dissipate the train’s kinetic energy (i.e., at low train longitudinal speeds). The combined braking command ‘Brk’ (utilising traction system regenerative braking and mechanical brakes in Figure 3a) also takes into account the wheel vs. track braking potential [16].

Figure 3.

Block diagram of battery-hybrid locomotive model (a) and electrical traction sub-model (b)

Percentage of maximum electrical traction power (P_t,max = 1,402.08 kW [43]) at each ‘Notch’ position is shown in Figure 4a, whereas Figure 4b shows the overall efficiency of the electrical traction system η_el(%P) as a function of the percentage of nominal power. The traction force (F_t) based on the ‘Notch’ position-related engine-generator set power output, traction system overall efficiency and train velocity v as follows [16]:

$F_{\text{t}}=\frac{3.6{\eta }_{\text{e}\text{l}}[\mathrm{\%}P(\text{Notch})]P_{\text{t},\text{max}}\times \mathrm{\%}P(\text{Notch})}{v}$ (3)

where v is the locomotive (and train) longitudinal velocity given in km/h, %P(Notch) is the electric power percentile of ‘Notch’ position and P_t,max [W] is maximum locomotive power. The traction power is included within the model as a static map [16], utilising the train velocity and ‘Notch’ as inputs to calculate the electrical transmission power (P_t).

Figure 4.

Locomotive power production vs. ‘Notch’ command (a) and overall electric power conversion efficiency curve (b) [43]

Maximum traction force is also limited by the maximum wheel vs. track adhesion characteristic, as discussed above. This, in turn, is limited by the normal force exerted by the locomotive weight m_l × g according to the following expression:

$F_{\text{t},\text{max}}={\mu }_{\text{a}}\times m_{\text{l}}\times g\times \cos \alpha \approx {\mu }_{\text{a}}\times m_{\text{l}}\times g$ (4)

where α is the track slope, typically within ±2.5 degrees (thus the approximation cosα ≈ 1 is valid in this case). Note that, in the case when conventional brakes are applied overall train weight is taken into account for maximum braking force.

Hence, the maximum traction force can be obtained by combining eq. (3) and eq. (4) utilising the overall hybrid locomotive weight (m_l = 107.85 t [16]). These traction force curves for each ‘Notch’ are shown in Figure 5, wherein negative wheel-to-track force values are obtained for the case of regenerative braking. Figure 5 also shows the maximum locomotive traction for 100%, 75% and 50% of adhesion, which illustrates that the variable adhesion effect to traction characteristic is dominant in low-speed high-power operating regimes.

The sub-model for longitudinal motion in Figure 3b represents the simplified dynamics of a lumped overall mass of the train (m_a) [kg] subject to locomotive traction and total braking forces F_t and F_b, respectively, along with aerodynamic drag and rolling resistance forces, and the overall gravity force component m_a × g × sinα due to the track slope. The final model is given by Valter [45]:

$F_{\text{t}}-F_{\text{b}}=\frac{dv}{dt}{m}_{\text{a}}+m_{\text{a}}\times g\times \sin \alpha +\frac{m_{\text{a}}}{1000}(w_{\text{k}}+w_{\text{r}})$ (5)

Figure 5.

Maximum traction force vs. velocity curves with ‘Notch’ command and wheel-to-track adhesion as parameters

In the above eq. (5), w_k and w_r [N/t] are the specific resistance coefficients corresponding to air drag and curvature motion, respectively. In the proposed model, traction and braking forces F_t and F_b are affected by adhesion and head wind variations (simulated through varying the relative adhesion coefficient k_va and head wind velocity v_wind, as shown in Figure 2). These adhesion and head wind variations are assumed to also be available to the driver from the remote sensors measurements.

The traction power is also included as a static map [16], and uses the same train velocity and ‘Notch’ inputs for the electrical transmission power P_t calculation. The difference between transmission power P_t and generator power (P_g) feeds the battery model directly over the common Direct Current (DC) link. The battery energy storage model is derived in Bin et al. [49] from the battery equivalent electrical circuit, and is presented in Figure 6a (note that positive values of battery input power (P_batt) correspond to battery discharging operation). For the particular battery model, characterised by State of Charge (SoC)-dependent open circuit voltage (U_oc) and internal resistance (R) (with the internal resistance also being dependent on current/battery power sign), the parameters of a single Li-Ion battery cell have been adopted from Autonomie software, and are shown in Figure 6b and Figure 6c. Battery sizing has been performed in Cipek et al. [16] and results in 900 kWh of total battery energy storage system capacity (arranged in 75 parallel modules comprising 200 series-connected cells each), which is characterised by the overall battery system weight of 9,450 kg [16].

A rule-based controller shown in Figure 3a (also developed in Cipek et al. [16]) uses the transmission power demand P_t and the battery SoC controller power demand (P_bR) to calculate the power required from the main engine-generator (P_gR), and, subsequently the required throttle Notch_RB by means of the ‘Notch’ selector map. In the case when the requested power P_gR is lower than the power generated when Notch_RB = 4 is selected, low-efficiency operation of the engine is avoided by bringing it to idling ([16]) to avoid the highly-impractical engine on/off operation. The engine-generator sub-model provides the fuel and emission rates and the electricity generator power output P_g for each Notch_RB as shown in Table 1.

Figure 6.

Battery power flow model (a); cell open-circuit voltage vs. SoC (b) and cell internal resistance vs. SoC and current sign (c)

The battery charging/discharging power demand is commanded by the proportional-type SoC controller (Figure 3a), characterised by its gain (K_SoC) and a dead-zone (Δ_SoC) to avoid controller output ‘chattering’ when the control error signal e_SoC = SoC_R – SoC is near zero. Cipek et al. [43] suggested that it would be convenient to use a variable SoC reference due to mountainous route being characterized by significant variations in elevation profile resulting in notable variations of train potential energy. This approach is also used based on the known lowermost and uppermost elevation levels h_min and h_max as input parameters [43]:

$\text{SoC}(h)=\text{So}{\text{C}}_{\text{bh}}-\frac{h-h_{\text{min}}}{h_{\text{max}}-h_{\text{min}}}(\text{So}{\text{C}}_{\text{bh}}-\text{So}{\text{C}}_{\text{bl}})$ (6)

with SoC_bl and SoC_bh representing the minimum and maximum values of the variable battery SoC target.

In this study, the SoC controller parameters (K_SoC, Δ_SoC, SoC_bl, SoC_bh) have been obtained by using a DIviding RECTangles (DIRECT) search-based optimisation [50], aimed at minimising the overall locomotive fuel consumption for two different simulation scenarios, subject to the minimum battery SoC constraint of 20% and without considering battery aging effects over a single train driving mission. The first scenario corresponds to a fully-loaded train (630 t of cargo hauled by the locomotive [43]) and constant wind velocity of 12 km/h and 100% adhesion, representing the nominal (benchmark) case herein. The second scenario corresponds to variable adhesion and wind velocity profiles from Figure 2. Each optimisation run performed for the particular train load results in a unique set of locally-optimal SoC controller parameters listed in Table 2.

Figure 8 shows the integration of the freight train and driver (control strategy) sub-models with the geographical railway route sub-model and the remote sensor network model, wherein individual model components are implemented within Matlab/Simulink software environment [54].

The freight train simulation model is fed rail track elevation and slope data from GPS coordinates (geographical data) from the general database which also contains the corresponding set of atmospheric variable data for each geographic location. In this way, all parts of the simulation model receive relevant data, which is updated based on the distance travelled by the train along the railroad track. The same geographical data is also fed to the driver model (and the battery energy storage system SoC control strategy) for the purpose of energy consumption optimisation (see previous chapter). Based on the train geographical location (position along the rail track), relevant remote sensor data corresponding to traction adhesion potential and head wind is selected and used within the driver model in order to select appropriate throttle ‘Notch’ (or ‘Brk’) command in order to maintain the train motion (to avoid wheel slipping). The same data is also used within the freight train model to emulate the realistic wind resistance (drag) and traction force potential variations with changes in adhesion characteristics.

Finally, the overall simulation model also comprises a visualisation interface which can be used for online monitoring of key freight train variables (such as speed, travelled distance, traction force and others).

Figure 8.

Block diagram representation of integrated simulation model comprising freight train and driver, smart remote sensor node and track data exchange sub-models

Train driving simulations are conducted for the round trip over the mountain route characterised by the elevation profile shown in Figure 2, wherein the locomotive hauls 630 t of cargo wagons (roughly corresponding to the maximum load of a single locomotive over that particular route, as indicated in Škrobonja et al. [44]). Simulations are carried out within Matlab/Simulink^TM software environment. Figure 9 shows the throttle ‘Notch’ and braking ‘Brk’ commands wherein the blue trace marked (Co) represents the scenario where constant (benchmark) values of wind velocity and adhesion are used (v_wind = 12 km/h, k_va = 100% [16]), while the red trace marked (Vo) corresponds to the scenario with variable values defined in Figure 2. The results in Figure 9 also indicate that over that route electrical (regenerative) braking is not always sufficient, thus mandating utilisation of additional mechanical (friction) brakes, in particular during train descending from higher elevation (Figure 9 and Figure 2).

Figure 9.

Train driver commands

Figure 10 shows corresponding train velocity over travelled distance and time. Using a-priori known train speed limitations (Figure 2), the train speed target v_ref (black trace in Figure 10a) emulates the train driver behaviour who would gradually increase and decrease the ‘virtual’ train from one to another speed limitation value. Such train speed target generation is performed herein over a 2 km window, as indicated in Cipek et al. [16]. For the given speed target v_ref and constant values of v_wind and k_va, the actual train velocity (v_Co) for the nominal (benchmark) case is obtained in simulation and represented by the blue trace in Figure 10, while the red trace represents the actual train velocity (v_Vo) when variable values from Figure 2 are used. The difference in velocities of the aforementioned driving scenarios is not emphasized, as shown by spatial speed traces (i.e., speed vs. the travelled distance) in Figure 10a. However, when these velocity traces are plotted vs. the elapsed driving mission time (Figure 10b), the considered simulation scenarios are characterised by different driving mission durations. This indicates that the proposed simulation model also may be helpful for the prediction of possible train delays for the a-priori known rail track adhesion and head wind conditions. As expected, adhesion below nominal value and head wind increase deteriorate the locomotive traction performance and result in lower train speeds, especially during ascending phases of the journey, which results in lower train velocities and slower driving mission completion (Figure 10b). It should also be noted that in the case of notable upward track slope, the freight train velocity profile following performance would also be deteriorated, especially when adverse track conditions are present. Namely, in those cases the electric motor-based traction system cannot provide enough traction action in order to keep the train velocity close to the target value, which is manifested in lower train velocities than the speed limit for the particular track segment. Thus, the track slope effect also contributes to the prolonged duration of the driving mission and its completion.

Figure 10.

Train velocity over distance (a) and over time (b)

Figure 11 shows the locomotive fuel consumption and battery SoC for three different scenarios concerning a battery-hybrid locomotive:

• Constant v_wind and adhesion k_va (benchmark case) are used in simulation and controller parameters are optimised for these constant parameters (CoC scenario), which directly relates to the main optimisation result presented in Cipek et al. [16];

• Variable v_wind and adhesion k_va are used in simulation, while the control strategy parameters are derived for benchmark values (VoC scenario);

• Variable v_wind and adhesion k_va are used in simulation, and the control strategy parameters are optimised for these variable track parameters (VoV scenario).

Figure 11a shows that the fuel consumption traces, while Figure 11b shows the SoC traces for the considered CoC, VoC and VoV scenarios. The benchmark CoC scenario originally presented in Cipek et al. [16] is, unsurprisingly, characterized by the lowest fuel consumption result, while also maintaining the battery SoC above the minimum recommended value (SoC_MIN = 20%). The aforementioned fuel consumption ‘optimality’ of this benchmark case is primarily related to the absence of adhesion variability which enables the locomotive powertrain to utilize the regenerative braking potential for battery recharging to its full extent. In the VoC case, battery SoC exhibits deeper discharges (SoC falls below 20%) compared to the cases of CoC and VoV target. Namely, in the cases of CoC and VoV scenario, the optimised SoC controller parameters are derived subject to the minimum battery SoC constraint of 20%. In this way, by using data from remote sensors grid of track conditions, and properly optimised control strategy parameters, deep battery discharging is effectively avoided. This would in turn result in less emphasised aging of the battery pack, and, consequently, in extension of battery cycle and calendar life compared to the case when no such measures could be applied. In all of the aforementioned cases, battery SoC profiles are highly reminiscent of the actual railway track elevation profiles (Figure 2). In particular, the positive (rising) SoC trends are associated with downward track slopes characterised by extensive utilisation of regenerative braking via the electric traction system, whereas the negative (falling) SoC trends are associated with upward track slopes mandating additional utilisation of battery power (battery discharging operation) for improved traction performance. The fuel consumption data in Figure 11a indicates that VoC and VoV scenarios are characterized by noticeable fuel consumption increase over the CoC case. Final values (V_fCoC = 2,320 L, V_fVoC = 2,552 L, V_fVoV = 2,556 L) confirm that track conditions variability (i.e., variable head wind and traction coefficient) may yield up to 10% higher fuel consumption, which is caused by the increased drag due to additional variable wind velocity combined with less available regenerative braking power when adhesion is decreased. VoV scenario shows that that the locomotive consumes negligibly more fuel (only 4 L more) than in the VoC case. Even though the control strategy parameters for the VoV case are optimised having in mind altered track conditions, this result is justified by the requirement to maintain the battery SoC within prescribed bounds.

Figure 11.

Comparative cumulative fuel consumption of locomotive (a) and SoC variable (b)

Since track conditions (head wind and adhesion) may vary during a single journey, the data from the remote sensors grid could be used within the developed model to estimate the journey’s duration and its feasibility for the particular track segment. The time frame map of the first 50 km of the proposed route from Figure 2 and the case of fully-loaded train is given in Figure 12. Normal passage time over this segment with this kind of load and with nominal 100% adhesion and 12 km/h head wind velocity, is 1.4 hour. Reduction of adhesion to around 70% and increase of head wind velocity to 40 km/h has negligible impact to the time increase. However, further reduction of adhesion or further increase of wind velocity significantly increases the segment passage time. White area in Figure 12 shows adhesion values and wind velocities corresponding to unfeasible driving missions for the particular train configuration, which could be used within the locomotive ‘telematic’ interface to alarm the driver of unfavourable driving conditions. Moreover, the data shown in Figure 12 may also be used to predict the possible problem of unscheduled stopping of the train due to insufficient powertrain capability to overcome the adverse weather-related track conditions. This might also prove to be highly useful in terms of managing train schedules by including an additional locomotive into the freight train in order to increase the traction capabilities and, thus, to reduce possible delays.

Figure 12.

Train driving mission duration estimated for initial 50 km track segment under variable track conditions

Please note that the presented results have been obtained for the case of ideal availability of the remote sensor data in real time. Obviously, with the decrease of the availability of remote sensor data, the freight train control strategy adaptation would also deteriorate, thus resulting in the train driver model relying solely on the on-board train velocity measurements and slope information based on a-priori known rail track elevation profile. Thus, the presented adaptive control strategy would be reduced to the basic control strategy proposed in Cipek et al. [16] over the track segment characterised by low availability of real time remote sensor data. However, this type of scenario is beyond the scope of this work.