1 Introduction
2 Literature review
3 Model novelty
-
It develops and introduces the first model for simulating train-following behavior that accounts for the external forces acting on the train while modeling the train as a sequence of point masses (a point mass for each locomotive and car that constitute the train) and capturing the significant latencies associated with the braking of long freight trains.
-
NeTrainSim is the first open-source simulator that focuses on energy consumption considering six different powertrain technologies: diesel, biodiesel, their hybrid variants, electric, and hydrogen fuel cells.
-
NeTrainSim offers advanced network modeling capabilities, allowing for the simulation of entire rail networks, including country-scale simulations.
-
It provides a micro-simulation model for train motion at the network scale. The simulator supports a conflict resolution mechanism in the simulation network of many intersecting lines/tracks utilizing a FIFO (first-in, first-out) strategy.
-
Given that we model the train motion second by second, the proposed simulator achieves scalability with minimum fidelity sacrifice in either modeling the train motion or in calculating the trains’ energy consumption and CO2 emissions.
-
NeTrainSim is developed in the C ++ programming language, which makes it more stable, faster, and able to handle large networks.
4 Mathematical model
Variable | Definition |
---|---|
\(\tilde{a}_{n} \left( t \right)\) | Smoothed acceleration of train \(n\) at instant \(t\) (m/s2) |
\(A_{c,l}\) | Frontal area of car \(c\) or locomotive \(l\) (m2) |
\(a_{n} \left( t \right)\) | Acceleration of train \(n\) at instant \(t\) (m/s2) |
\({\text{CF}}_{{\text{Fuel Type}}}\) | Conversion factor from energy consumption kWh to fuel quantity by fuel type |
\(C_{{{c,l}}}\) | Track curvature of car \(c\) or locomotive \(l\) (°) |
\(c + l\) | Number of cars and locomotives in the subject train |
\({\text{FCS}}_{n} \left( t \right)\) | Fuel cell status of train n in time t (%) |
\({\text{FD}}_{{{\text{Fuel type }}|{ }n}} \left( t \right)\) | Fuel depletion of fuel type for train n in time t |
\(F_{n} \left( t \right)\) | Tractive force of train \(n\) at instant \(t\) (N) |
\({\text{TGCD}}_{n} \left( t \right)\) | Total Grid Consumption/Delivery of train n at time t (kWh) |
\(G_{{{c,l}}}\) | Track gradient of car \(c\) or locomotive \(l\) (%) |
\(K_{{{c,l}}}\) | Canadian National streamlining coefficient of car \(c\) or locomotive \(l\) |
\(N_{{{\text{max}}}}\) | Number of notches in the given locomotive |
\(P_{{{l}}}^{{{\text{max}}}}\) | Maximum engine power of locomotive \(l\) (kW) |
\(R_{n} \left( t \right)\) | Resistive force of train \(n\) at instant \(t\) (N) |
\(T_{n}\) | The time it takes to activate the brakes of the train plus the operator perception reaction time (s) |
\(m_{{{c,l}}}\) | Total mass of car \(c\) or locomotive \(l\) (kg) |
\(m_{c}\) | Total mass of car \(c\) (kg) |
\(m_{{\text{c}}}^{{\text{a}}}\) | Mass on single axle of car \(c\) (kg) |
\(m_{{{l}}}\) | Total mass of locomotive \(l\) (kg) |
\(m_{{{l}}}^{a}\) | Mass on a single axle of locomotive \(l\) (kg) |
\({\text{SOC}}_{n} \left( t \right)\) | The battery state of charge of train n at time t (%) |
\(s_{n} \left( t \right)\) | Spacing from the rear bumper of train \(n\) to the rear bumper of train \(n - 1\) and is computed as \(x_{n - 1} \left( t \right) - x_{n} \left( t \right)\) (m) |
\(s_{n}^{{\text{j}}}\) | Train spacing at jam density (m). Equal to the length of train \(n\) plus a buffer (taken to be 2m) |
\(t_{1} ,t_{2} ,t_{3}\) | Calibration parameters for the throttle input level |
\(u_{{\text{d}}} \left( t \right)\) | Desired speed or max speed a train can go by at instant t (m/s) |
\(u_{{\text{f}}}\) | Track free-flow velocity (km/h) |
\(u_{{\text{m}}} \left( t \right)\) | Train speed at maximum throttle at instant t (m/s) |
\(u_{n} \left( t \right)\) | Speed of train \(n\) at instant \(t\) (m/s) |
\(x_{n} \left( t \right)\) | Position of the back of train \(n\) relative to the start of the trip (m) |
\(\lambda^{*}\) | Throttle level that equates resistance forces at instant t (\(0 \le \lambda \le 1\)) |
\(\lambda_{n} \left( t \right)\) | Throttle level of train \(n\) at instant \(t\) (\(0 \le \lambda \le 1\)) |
\({\Delta }t\) | The solution time step (s) |
\(G\left( t \right)\) | Grade of track at instant \(t\) (%) |
\(N\) | Notch number |
\(g\) | Gravitational acceleration (9.8066 m/s2) |
\(m\) | Train total mass \(m = \mathop \sum \limits_{{{c,l}}} m_{{{c,l}}}\) (sum of locomotive and car masses) (kg) |
\(\eta\) | Mechanical efficiency of the transmission and gear |
\(\mu\) | Coefficient of friction between the wheel and the track |
4.1 Traction force model
Train characteristics | Scenario I | Scenario II |
---|---|---|
Track length (km) | 162 | 322 |
Stopping stations at (km) | 40, 42, 88, 150 | 40, 42, 88, 150 |
Transmission efficiency | 0.98 | 0.82 |
Max locomotive power (kW) | 3262.0 | 2445.9 |
Number of locomotives | 3 | 11 |
Number of of axles per locomotive | 6 | 6 |
Coefficient of friction | 0.4 | 0.4 |
First locomotive \(K_{{\text{l}}}\) value | 24 | 24 |
Other locomotive \(K_{{\text{l}}}\) value | 5.5 | 5.5 |
Car \(K_{{\text{c}}}\) value | 5 | 5 |
Locomotive frontal area (m2) | 14.8645 | 14.8645 |
Car frontal area (m2) | 12.0774 | 11.1484 |
Number of cars | 71 | 139 |
Number of car axials | 4 | 4 |
Locomotive length (m) | 22.3 | 23.0 |
Car length (m) | 29.0 | 20.7 |
Locomotive weight (ton) | 198 | 190 |
Car weight (ton) | 44 | 100 |
Grade (%) | 0–2.4 | 0–2.0 |
Curvature (%) | 0 | 0–5 |
4.2 Resistance forces model
4.3 Longitudinal motion model
4.4 Energy and carbon emission models
4.5 Train delay and number of stops estimation
5 Simulator description
5.1 Simulator logic
-
The first category occurs when two trains are approaching each other and have to share a single two-way track. In this case, the first train to reach either of the entry nodes of the conflict zone has priority to use the shared track while the other train is forced to stop until the track is cleared. If several trains are queued in both directions, then the trains in the same direction as the first crossing train will be cleared first. From a network perspective, this strategy is more effective in terms of minimizing the total average delay of the trains than a FIFO strategy. While the used conflict management strategy is basic in that it only accounts for the instantaneous positions of the trains in the decision-making process, the research team will complement it later on with an Eco-cruise algorithm and enhancements to the priority of train movements. The purpose of such an algorithm is to ensure that the trains clear the conflict zones in the most energy-efficient manner.
-
The second category is quite similar to the first one with the main difference that there exist several links that the trains can utilize to cross the conflict zone. For instance, Fig. 6-case 2 illustrates a scenario in which the conflict zone could be cleared by traveling on one of three links depending on the direction of travel. The three links consist of two one-way tracks (one in each direction) as well as a bidirectional track that can serve trains traveling in either direction. The conflict management strategy presented earlier for the first category remains valid here with the main addition that the use of the two one-way tracks is prioritized over the use of the bidirectional link.
-
It is noteworthy to mention, at this level, that the first and second categories concern scenarios in which any links present in the conflict zone connect its entry node to its exit node which can only occur when the train length is smaller than the link length. In other words, trains need to cross a single link to clear it. Hence, there is a need for a third category that addresses the scenarios in which the conflict zones span over several successive links. This last category, which could be cast as a generalization of the first two categories, can happen when a train spans over several links as shown in Fig. 6(case 3). Because of that, the adopted conflict management strategy includes a module for the correct identification of the extremities of any conflict zones in the simulated network.
5.2 Simulator scalability
6 Case studies
6.1 Scenario I
6.2 Scenario II
6.3 Scenario III
-
Scenario III.1.1: Two trains T1 and T2 traveling from zones A and C to zones D and B respectively are introduced in the network one after the other. The results, presented in Fig. 17, demonstrate the simulator conflict management strategy is working as expected. Given that train T1 started its trip before train T2. It was given priority to cross the conflict area EF. As confirmed by the presented distance and speed profiles, Train T2 was forced to stop at node F before the shared track until it was cleared. At that point, it was allowed to continue proceeding toward its destination.
-
Scenario III.1.2: This scenario is similar to the previous scenario with the only difference that train T2 was introduced in the network first. Figure 18 confirms that the results of this simulation are consistent with the expected outcome that train T1 is the one to stop at the entrance of the shared track.
-
Scenario III.1.3: This scenario is also similar to scenario III.1.1. However, the trains were introduced in the network at precalculated times in such a way that train T1 clears the shared link while train T2 is reducing its speed but before completely stopping. The speed profile of Fig. 19 confirms that was the case as train T2 reduced its speed from the free-flow-speed of 10 m/s to around 3.5 m/s before accelerating again when train T1 cleared link EF.
-
Scenario III.1.4: Same as scenario III.1.3 except that train T1 is traveling from zone D to zone A and train T2 is traveling from zone B to zone C. Again, the results were as expected as shown in Fig. 20.
6.4 Scenario IV
Type | Total consumption per year | Eq. energy per year (kWh) | Relative to diesel (%) | CO2 emissions ×106 ton/year |
---|---|---|---|---|
Diesel | 3,089,551,518 Gal | 116,370,395,749 | 100.0 | 7.88 |
Diesel hybrid | 2,619,659,798 Gal | 98,671,553,356 | 84.8 | 6.68 |
Biodiesel | 3,323,887,151 Gal | 116,433,053,998 | 100.1 | 7.37 |
Biodiesel hybrid | 2,790,214,948 Gal | 97,738,952,319 | 84.0 | 6.19 |
Battery electric | 53,733,886,668 kWh | 53,733,886,668 | 46.2 | – |
Hyrogen FC | 2,947,102,078 kg | 98,226,912,261 | 84.4 | – |
Catenary electric | 49,020,429,884 kWh | 49,020,429,884 | 42.1 | – |