# Optimization of Energetic Train Cooperation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- using directly on non-traction vehicle needs, e.g., lighting or air conditioning,
- storing in stationary or onboard energy storage devices, and then use at the time of increased demand,
- transmitting recovered energy back to the national power grid,
- transferring recovered electricity back to the catenary, given the possibility of its immediate absorption by another, accelerating train.

## 2. Energy Recovery in Railway Systems Literature Review

#### 2.1. Energy Storage

- large number of load cycles,
- high power capacities,

- intermediate energy storage capacity,
- reduced weight and volume.

#### 2.2. Reversible Substations

#### 2.3. Energetic Cooperation of Trains (ECT)

- increasing the probability of the braking and accelerating cycles of several trains at the same time existing by elongating the length of power sections,
- reducing the distance between cooperating trains or resistance of catenary which also means reducing losses and voltage drops in the energy transmission path,
- additional use of energy storage for excess electricity,
- increasing the voltage difference between the nearest power substation and the braking vehicle pantograph.

## 3. Materials and Methods

#### 3.1. Energetic Cooperation of Trains (ECT+)

#### 3.1.1. Choosing the Method of Using Recovered Energy

#### 3.1.2. Model for Using Recovered Energy

^{A}, v

^{B}. Indirectly this allows for controlling the arrival time t

_{EB}(v) of the braking train B at the station within the permissible range (T

_{a}

_{1},T

_{a}

_{2}). This model is similar to that by Su et al. [34], which assumes the control of the departure time. In our approach, we distinguished three variants. In each of the variants the departure time of the train A from the station S is constant, but the arrival time of the train B at the same station is changed (Figure 3).

_{2}where ${P}_{a}^{A}\left({t}_{2},{t}_{SA}^{A}\right)={P}_{r}^{B}\left({t}_{2},s\right)$. As a result, train A uses the amount of the regenerative energy equal to:

#### 3.1.3. Optimization Model

- ${E}_{P}$: the actual value of the energy consumed during the passage of the train B and the passage fragment of the train A,
- $E$: the amount of energy needed to perform the passage of the train B and the passage fragment of the train A,
- ${E}_{RS}$: energy recovered during the electrodynamic braking of vehicle B and used in the energetic cooperation of both trains B and A.

_{1}and w

_{2}are weights of individual component functions which sum should be equal to 1. They reflect the importance of each criterion in existing railway network conditions. It should be also noted that the higher w

_{1}value corresponds to a lower traction energy demand for the analyzed journey section, and the higher w

_{2}value leads to larger amount of energy that can be recovered during recuperation and used (e.g., with additional energy storage). We can also write the global cost function in the following form:

_{j}= 0) is denoted as β

_{0}and the light absorption coefficient, which controls the decrease of the light intensity is described as γ. The less bright (attractive) firefly is attracted and moved to the brighter one in order to find the optimal solution [37,38]. The procedure of the firefly optimization technique can be represented as in Figure 4.

#### 3.2. Optimization of Using Recuperative Braking Energy at Sample Railway Line

#### Characteristics of the Rolling Stock and Selected Railway Line

## 4. Results

#### 4.1. Optimization Results for Selected Train Stops

_{1}= 0.6 and w

_{2}= 0.4 have been adopted. If we increase the weight of w

_{2}, the results obtained will favor faster travel speeds allowing for the recovery more volume of electric energy E

_{R}. At the same time, this will affect the greater real energy demand of E

_{P}. Conversely, if we increase the weight of w

_{1}then the results obtained will favor lower travel speeds requiring less volume of electric energy, but also giving less potential for recovery and storage energy.

_{RA}of the train No. 59708 for three basic weights of the optimization subcriteria is shown in Figure 11, where the points marked on the graph indicate the values of the solutions (fireflies) in each iteration. It is found that increasing the weight w

_{2}(and simultaneously lowering w

_{1}= 1 − w

_{2}) leads to earlier optimal arrival time T

_{RA}, corresponding to the minimum of the objective function. This is so because an earlier T

_{RA}corresponds to the shorter passage of train B between the stations and thus its larger speed v

^{B}and, consequently, to a greater volume E

_{R}of energy recovered during braking, as already mentioned above. In the specific case presented in Figure 11, the optimal arrival time T

_{RA}does not change significantly (around 0.0006 h, i.e., 2.2 s) when w

_{2}is changed from 0 to 1 because the earliest possible arrival time (T

_{RA}= 5.4905 h) is limited the timetable. Let us also note that, for sufficiently large value of w

_{2}(in particular for w

_{2}= 1), the global objective function is negative since it dominated by its second term −w

_{2}∙E

_{R}where the negative sign has been chosen to define the global objective function which has a minimum (the energy E

_{R}alone can be maximized).

#### 4.2. Summary of Findings

- the value of energy that can be reused during energetic cooperation of a train pair E
_{RS}= 5.7555 kWh, - the value of energy recoverable in the recuperation process E
_{R}= 8.7745 kWh, - the value of energy required to make a selected part of the drive E
_{P}= 15.3863 kWh, - the value of global function F(v
^{A}^{*}, v^{B}^{*}) = 7.8826 kWh.

## 5. Discussion and Conclusions

_{RA}). The proposed weighted objective function takes into account the actual value of energy consumed by a pair of cooperating trains (E

_{P}) as well as the total energy recovered during recuperative braking possible to be used in a different way than a direct transmission to the catenary (E

_{R}, e.g., by using energy storage or reversible substations).

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The scheme of using regenerative braking energy by another vehicle. Source: own study based on [27].

**Figure 2.**The diagram of the order of methods of using energy from regenerative braking. Source: own study based on [21].

**Figure 3.**Control of arrival time at the station. Source: own study based on [24].

**Figure 5.**The general scheme of the system solving the described optimization problem. Source: own study based on [36].

**Figure 6.**Profile of track No. 1 of railway line No. 250. Source: own study based on PKP PLK S.A. data.

**Figure 7.**Selected trains pairs at the Gdańsk Żabianka AWFiS stop with the possibility of energy cooperation.

**Figure 8.**Variation of the objective function FC = F(v

^{A},v

^{B}) [kWh] depending on the real arrival time T

_{RA}[h] (within the range allowed by the timetable) at a constant speed v

^{A}of train A without considering the optimization algorithm.

**Figure 9.**Results of the optimization using the FA algorithm at a variable speed of the train A (v

^{A}) or the train B (v

^{B}) or depending on the real arrival time T

_{RA}[h] train B (within the range allowed by the timetable) for weights of the optimization subcriteria w

_{1}= 0.6, w

_{2}= 0.4.

**Figure 10.**Values of the objective function in successive iterations of the FA algorithm for weights of the optimization subcriteria w

_{1}= 0.6, w

_{2}= 0.4.

**Figure 11.**Chart variation of FC = F(v

^{A},v

^{B}) [kWh] value based on FA algorithm depending on the actual train No. 59708 arrival time T

_{RA}[h] at the stop within the range allowed by the timetable.

**Figure 12.**Variation of FC = F(v

^{A},v

^{B}) [kWh] value based on FA algorithm depending on the speed of trains No. 95601 (v

^{A}) and 59708 (v

^{B}) for weights of the optimization subcriteria w

_{1}= 0.6, w

_{2}= 0.4.

Technology | Main Features | Application in Urban Rail | Year |
---|---|---|---|

EDLC | Rated power: 288 kW Capacity: 0.85 kWh Weight: 820 kg Dimensions: 2000 × 1520 × 630 mm | Commercial application in Innsbruck tramway (Germany) | 2012 |

EDLC | Rated power: N/A Capacity: 0.8 kWh Weight: 800 kg Dimensions: N/A | Commercial application in Seville, Saragossa (Spain) and Granada tramway systems, in service (France) | 2012/2010 |

Li-ion | Rated power: N/A Capacity: 40 kWh Weight: 3200 kg Dimensions: N/A | Prototype tests in Charlotte (USA) | 2010 |

NiMH | Rated power: 250 kW Capacity: 120 kWh Weight: 3200 kg Dimensions: N/A | Prototype tests in Sapporo Municipal Transport network (Japan) | 2011 |

Technology | Main Features | Application in Urban Rail | Year |
---|---|---|---|

EDLC | Generated voltage: 750 V Rated power: 300–1000 kW Capacity: 1–4 kWh | Pilot project for Lyon tramway | 2011/Adetel |

EDLC | Generated voltage: 500–1850 V Rated power: 750–4500 kW Capacity: 0.8–16.5 kWh | Warsaw metro, to be implemented, pilot project for Philadelphia transit system (battery-based) | 2012/2016/ABB |

Flywheel | Generated voltage: N/A Rated power: 500 kW Capacity: N/A | Los Angeles metro line | 2013/Vycon |

NiMH | Generated voltage: 600–1500 V Rated power: N/A Capacity: 150–400 kWh | New York City Transit network, pilot project | 2011/Ogura |

Li-ion | Generated voltage: 700 V Rated power: 900–1500 kW Capacity: 600–40 kWh | Philadelphia transit system, pilot project | 2012/Polulin |

Company | Main Features | References | Year |
---|---|---|---|

Alstom | Rated voltage: 750 V Rated power: 0.3 MW | Metro line in London and Milan | 2011 |

Siemens | Rated voltage: 750–1500 V Rated power: 1.5–2.2 MW | Tested in Oslo’s and Holmenkollen’s metro line | 2011 |

ABB | Rated voltage: 600/750 V Rated power: 0.5–1 MW | Tramway in Łódź and Olsztyn (Poland) | 2014/2016 |

Number of cars | 5 |

Formation | Bo′2′2′Bo′ + Bo′2′2′Bo′ |

Own weight | 159 t +/− 3% |

Gross weight | 202 t +/− 3% |

Rated power | 2000 kW |

Traction system | 3000 V |

Maximum speed | 160 km/h |

Acceleration for 0–40 km/h | 1.0 m/s^{2} |

Acceleration above 40 km/h | ≥1.0 m/s^{2} |

Deceleration of operational braking | ≥0.8 m/s^{2} |

Deceleration of emergency braking | ≥1.0 m/s^{2} |

Recuperation | yes |

Trains No. | E_{RS} [kWh] | E_{R} [kWh] | E_{P} [kWh] | F(v^{A}^{*}, v^{B}^{*}) [kWh] | T_{RA} [h:min:s] (Clock Time) | v^{A} [km/h] | v^{B}^{*} [km/h] | |
---|---|---|---|---|---|---|---|---|

A | B | |||||||

Gdańsk Żabianka AWFiS | ||||||||

95601 | 59708 | 5.8775 | 9.6785 | 15.3720 | 7.4583 | 5:29:27 | 50.33 | 65.37 |

95603 | 59600 | 5.9587 | 9.6937 | 15.4080 | 7.4800 | 6:04:28 | 50.58 | 65.47 |

95605 | 59710 | 6.4261 | 9.0374 | 15.9351 | 7.9553 | 6:29:29 | 55.36 | 63.17 |

95415 | 59810 | 5.9587 | 8.9380 | 16.0514 | 8.0478 | 8:34:29 | 55.82 | 62.8 |

59610 | 95419 | 6.2534 | 8.9019 | 16.9899 | 8.6430 | 8:55:29 | 51.49 | 63.47 |

95761 | 59760 | 6.2441 | 9.6005 | 15.6576 | 7.6534 | 14:59:28 | 53.29 | 65.16 |

59468 | 95467 | 6.4237 | 8.9019 | 17.8147 | 9.1379 | 17:55:29 | 57.06 | 63.47 |

95791 | 59782 | 6.3837 | 9.7561 | 15.3900 | 7.4527 | 18:04:27 | 50.2 | 65.65 |

95685 | 59478 | 6.5921 | 9.5957 | 15.3779 | 7.4853 | 19:59:28 | 50.44 | 65.09 |

95697 | 59694 | 6.3807 | 9.8391 | 15.4240 | 7.4520 | 22:49:27 | 50.1 | 65.94 |

Gdynia Orłowo | ||||||||

59716 | 95719 | 7.0043 | 9.16.59 | 18.3182 | 9.3757 | 7:13:27 | 58.02 | 64.67 |

59606 | 95721 | 7.1109 | 9.2190 | 18.3029 | 9.3671 | 7:28:28 | 58.06 | 64.9 |

Gdynia Cisowa | ||||||||

95601 | 59710 | 6.1607 | 7.9193 | 15.6092 | 8.4376 | 5:58:03 | 56.81 | 56.71 |

95757 | 59760 | 5.3625 | 7.8543 | 14.0660 | 7.4898 | 14:28:25 | 49.75 | 56.4 |

95759 | 59816 | 0.0780 | 5.6043 | 8.8120 | 6.2017 | 15:09:01 | 47.06 | 45.87 |

95633 | 59612 | 5.0299 | 7.9012 | 13.7099 | 7.2853 | 15:20:24 | 47.17 | 56.59 |

95761 | 59766 | 4.5986 | 7.9514 | 13.3286 | 7.0807 | 15:29:23 | 44.03 | 56.87 |

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**MDPI and ACS Style**

Urbaniak, M.; Kardas-Cinal, E.; Jacyna, M.
Optimization of Energetic Train Cooperation. *Symmetry* **2019**, *11*, 1175.
https://doi.org/10.3390/sym11091175

**AMA Style**

Urbaniak M, Kardas-Cinal E, Jacyna M.
Optimization of Energetic Train Cooperation. *Symmetry*. 2019; 11(9):1175.
https://doi.org/10.3390/sym11091175

**Chicago/Turabian Style**

Urbaniak, Michał, Ewa Kardas-Cinal, and Marianna Jacyna.
2019. "Optimization of Energetic Train Cooperation" *Symmetry* 11, no. 9: 1175.
https://doi.org/10.3390/sym11091175