Electrified guided vehicles typically face routes having a large number of acceleration and braking phases. The braking energy, since the feeding line presents nonreversible electrical feeding substations, can be recovered in the presence of other nearby vehicles. To improve braking energy recovery, one or more storage systems can be positioned along the track. Analysis of effectiveness for the considered solution requires time-domain simulation models, to be created through suitable simulation general-purpose languages or specialised languages/software. In this paper, three different tools for the considered existing tramway were developed, and the main examined characteristics have been compared to each other. Then, analysis of output results was also performed, demonstrating the real cost-effectiveness of introducing one storage device on the considered tramline in operation.
Electrified guided vehicles such as trams typically face routes with a large number of acceleration and braking phases. In this regard, only a fraction of the initial kinetic energy can be partially recovered [
Analysis of the cost-effectiveness of the proposed solution involves the development of time-domain simulation tools. Obviously, solicitations on the storage system are influenced by timetable of the trams, positioning of substations, etc. Typically, the storage is installed through the interposition of a DC/DC converter, in order to limit current within safety limits, or to avoid battery State-of-Charge drift, to maintain unaltered its capability to adsorb or deliver energy.
In order to make time-domain simulations, it is possible to create models by utilisation of general-purpose programming languages, i.e., FORTRAN or C, or specialised languages or software, i.e., Modelica or Matlab-Simscape, respectively.
As example of modelling and simulation in railway applications, modelling of short-circuit protections or DC electrical railway systems to simulate stray currents and touch voltages, has been already developed in [
In this paper, simulation tools aimed at correctly representing the railway system, including the electric power supply, the storage systems, and the vehicles moving along the rails have been widely developed. In particular, three simulation models were developed. The first tool has been realised in FORTRAN. It has been made a long time ago and used in many applications [
On the other hand, Dymola [
In the last years, many other commercial tools were also developed, as Matlab-Simscape [
Therefore, after mutually validating the three tools under consideration, a technical-economic analysis for a tramway line in operation has been performed. In this way, energy consumption in realistic traffic conditions was taken into account, and energy saving due the installation of a storage device accurately calculated. Finally, payback time of the investment was evaluated, thus demonstrating the cost-effectiveness of the considered solution.
As said, in order to evaluate the amount of the braking recoverable energy, it is mandatory to develop a simulation tool capable of correctly simulating the feeding network and the vehicles dynamic. Then, different running phases and frequency of the trains have to be considered. Following modelling criteria were implemented.
FORTRAN language is a consolidate code to develop electrical model to represented power network. For DC railway application, calculation code Train-sim, consisting of two computational tools, is presented in [
The first one allows calculating all the electromechanical characteristics and performance of trains on a specific railway line. Based on altimetry profile of the track and rolling stock features, it is possible to carry out the train performance due to motion stages. Dynamic and kinematic profiles are obtained. It is possible to set also various traffic scenarios. The tool also calculates the amount of recoverable energy at each braking phase.
The second one makes the DC electrified network load flow calculation. It builds an equivalent electrical network at each step, based on the tram positions along the route. ESSs, vehicles, and parallel points are the electrical nodes of the considered equivalent network.
The calculation code due to the model reported below permits the calculation of the electrical parameter of the network considering also the energy recovered during braking phase. The models are as follows: Electrical substation (ESS). Figure Trams in traction. The vehicles are represented as a constant power load. However, if the current exceeds the maximum allowed value during operation, the constraint Trams in braking. Braking energy recovering depends on the receptivity of the system. If the system allows it, the traction line can accept all the power generated during braking phase, according to the solution of the system equations. If the voltage increases up to
Voltage-current characteristic of an electrical substation (ESS).
Voltage-power characteristic during traction and braking stages.
Finally, simple laws implemented for traction (
For each electrical substation, the software calculated electrical parameters about power, current, etc. including the amount of recoverable energy during braking and the voltage along the line.
The procedure for determining the matrix coefficients of the admittance constituting the traction line refers to electrical networks in permanent sinusoidal regime and, therefore, to complex admittance and impedance. The software, dealing with DC networks, considers all the magnitudes to be real, the admittance as conductance, and the impedance as resistance.
Regarding numerical solving methods, Newton-Raphson or Gauss-Seidel method is typically applied. Some variants of Newton-Raphson method particularly suitable for small- and medium-size networks can be also considered, in order to improve conditions of convergence and to reduce number of iterations [
As said, the simulation tool realised in Dymola is based on Modelica language [
Graphical representation of the electrical feeding system.
In addition, the electrical feeding substations in operation are subjected to variation, when a train moves from a section to another, along the track. This difficulty can be easily addressed in Modelica, considering the possibility of changing the system equations after some events happen [
Finally, modelling of trains requires modelling of the electric drive, resistance forces, and the driver’s behaviour. Electric drive is modelled as a system able to produce the tractive force as required by the driver, within the allowed force and power limits, generating some power losses expressed as a function of the mechanical speed and the required force. Then, each train must avoid feeding power to the catenary when this would cause the line voltage to become too large, and a controller of the DC power must be implemented. A much more sophisticated control strategy has been used, having feedback on the instantaneous pantograph voltage and modulating the braking power conveyed along the catenary, in order to avoid reaching instantaneously the upper allowed limit. Resistance to movement has been modelled using the formula including aerodynamic drag and rolling resistance:
Further details regarding different submodel and control logic, in particular the blending strategy depicted in Figure
In parallel with object-oriented interface, the user can directly insert physical or control equations. These last are written exactly as in textbooks. Starting from individual subsystems description, Modelica-based tool automatically performs many operations: first, the identification of a set of differential algebraic equations (DAEs) representing the system under study and, then, after some additional operations to simplify the set of equations [
Last simulator is realised in Matlab-Simscape [
The three tools were tested by analysing their flexibility, simulation efficiency, and man-machine interface.
In conclusion, the Modelica-based and Matlab-Simscape tools require high memory requirements but also guarantee much more flexibility. The FORTRAN based tool, developed many years ago, is very useful because it is able to produce benchmark results, to be used as main reference. On the other hand, the other two tools allow fast creation of models, whose simulation results need to be carefully verified.
The tools have been tested having as reference case study an existing tramway, in Rome. The path length is about 5.7 km, as noticeable from Figure
Input model parameters of the system under study.
| |
| |
No load voltage (V) | 1680 |
| |
| 0.13 |
| |
Number of ESSs | 1 |
| |
ESS position (km) | 0 |
| |
| |
| |
Max line voltage (V) | 1800 |
| |
Nominal line voltage (V) | 1650 |
| |
Min line voltage (V) | 1100 |
| |
Number of line trunks | 6 |
| |
Line Resistance (Ω/km) | |
| |
| |
| |
Full mass (t) | 92 |
| |
Auxiliary power adsorption (kW) | 40 |
| |
ED max power (kW) | 1242 |
| |
ED max traction force (kN) | 96 |
| |
| |
| |
Number of trams | 2 |
| |
Number of stops | 14 |
| |
Average distance between stops (km) | 0.4 |
| |
Max speed (m/s) | 14 |
| |
Track length (km) | 5.4 |
Pattern profile.
The simulation results were evaluated in terms of energy and power flows of the considered tramway. In the first examined condition, the trams make use of on-board resistors to dissipate all the braking energy. In the second scenario, they send braking energy on the catenary, until the voltage does not reach the maximum admitted value fixed at 800 V. Finally, trams send braking energy as before, but with one storage system installed about halfway along the tramway.
First, simulations were performed without considering braking energy recovery. As said, model parameters were slightly updated, in order to match the results provided by the new tools with the oldest one. Figure
Plot results, trams without braking energy recovery.
Then, simulations have considered the possibility of recovering the braking energy. In this case, parameters acting on control voltage at pantograph have been tuned, to perform modulation of the inlet power, without overcoming voltage limits. Figure
Plot results, trams with braking energy recovery.
As noted, different blending strategies according to Figure
Naturally, braking energy recovery can be enhanced through energy storage systems installed along the route. In this way, one storage system has been introduced, with the main aim of validating the tools under test, also in the new considered system configuration. The lithium battery is positioned about halfway along the tramway (i.e., about 3.8 km from the terminal), whose characteristics are in Table
Lithium battery main characteristics.
Nominal energy (MWh) | 0.33 |
| |
Nominal capacity (Ah) | 200 |
| |
Nominal voltage (V) | 1650 |
| |
Number of cells in series | 446 |
| |
Max allowed current (A) | 2000 |
| |
Charging-discharging efficiency | 0.9 |
Relation among the nominal energy and nominal capacity is given by
where
Plot results, system equipped with storage.
Installation of one storage system can significantly reduce the energy delivered by the electrical feeding substations (ESSs). The considered simplified case study with two trains obviously cannot correctly evaluate the cost-effectiveness of the considered solution. Thus, the full analysis will be described in the next section, following the same approach already considered by the authors in [
Energy saving evaluation has been performed by considering an experimental measurement campaign carried on by the authors. Results are summarized in Table
ESS energy consumption.
ESS working day daily energy (MWh) | 15.8 |
| |
ESS holiday daily energy (kWh) | 11.1 |
| |
ESS Annual energy (MWh) | 5386 |
Therefore, the Modelica-based tool presented before has been used to exactly reproduce the energy consumption shown in Table
After simulating exactly the same level of the measured energy demand, i.e., obtaining the daily consumption shown in Table
The cost-effectiveness of the proposed solution has been investigated by considering the initial cash outlay due the introduction of the storage system, with respect to the annual return of the investment due to the above-mentioned electrical energy saving. The initial cash outlay due to the storage system and its balance of plant has been calculated by considering a value of 500 €/kWh including cells, BMS, and battery packaging. As discussed in detail in [
Main objective of the analysis was related to the evaluation of the net present value (NPV) and of the payback time (PBT) for a whole life of ten years and an interest rate of 4%. Results are shown in Table
Economic benefit analysis.
Storage system cost (k€) | 226.1 |
| |
Annual energy saving (k€) | 122.5 |
| |
NPV (k€) | 738.2 |
| |
PBT (y) | 2 |
The results show that installation of a stationary storage system may guarantee a payback time within just two year. These numbers are so favourable not to be affected by any possible storage substitution, during the plant life. Indeed, the cost-effectiveness of the proposed solution has been clearly demonstrated.
This paper has demonstrated how innovative languages and software allow rapid creation of numerical models, having electrical, mechanical, and control parts to be simulated.
The Modelica-based model was realised through the commercial Dymola tool. However, it could run inside any other Modelica-compliant tool. They proved to be fast, with relatively small memory occupation. Nearly the same can be said about Matlab-Simscape, although characterised by less flexibility, due to the fact that it is not inspired by an open-source language platform. The quality has been verified by comparing results with those obtained using a well validated FORTRAN based simulator.
With reference to an existing case study, the cost-effectiveness due to the utilisation of stationary storage system to enhance braking energy recovery has been clearly demonstrated, since on a high-traffic tramway with high number of stops, payback time has been reached within only two years. Naturally, it is of great importance, in order to correctly achieve energy saving for the considered application, to preliminary calibrate the considered tool on actual electrical energy consumption, experimentally measured.
As future direction of this work, it is also possible to consider the extension of the considered methodology to other tramlines in operation, in order to investigate the potential cost-effectiveness of similar, or different, energy saving solutions.
The data used to support the findings of this study are included within the article.
The authors declare that they have no conflicts of interest.