# Optimal Hybridization with Minimum Fuel Consumption of the Hybrid Fuel Cell Train

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- Zero harmful emissions of exhaust gases;
- Energy savings by recuperation of regenerative braking;
- Reduced mass of all power sources;
- Optimal power distribution on each auxiliary power source.

**Table 1.**UIC624 ICE Emission Standards [4].

Stage | Date | Power, P [kW] | Engine Speed, r [min ^{−1}] | CO | HC | NOx | PM | Smoke |
---|---|---|---|---|---|---|---|---|

g/kWh | ||||||||

UIC I | up to 31 December 2002 | 3 | 0.8 | 12 | - | 1.6–2.5 ^{a} | ||

UIC II | 1 January 2003 | P ≤ 560 | 2.5 | 0.6 | 6.0 | 0.25 | ||

P > 560 | r > 1000 | 3 | 0.8 | 9.5 | 0.25 ^{b} | |||

r ≤ 1000 | 3 | 0.8 | 9.9 | 0.25 ^{b} |

^{a}—Bosch smoke number (BSN) = 1.6 for engines with an air throughput of above 1 kg/s; BSN = 2.5 for engines below 0.2 kg/s; linear BSN interpolation applies between these 2 values.

^{b}—For engines above 2200 kW, a PM emission of 0.5 g/kWh is accepted on an exceptional basis until 31 December 2004.

## 2. Materials and Methods

#### 2.1. Model and Topology of the Train

#### 2.2. Energy Management System

_{sc}= 0.01, and then the battery is used. If, during acceleration and cruising, the climb is greater than 15%, all devices are switched on. If SOC

_{b}= 0.2, traction is performed by supercapacitor, and fuel cell will charge the battery. The battery drives the traction only after the supercapacitor is discharged (SOC

_{sc}= 0.01). Regenerative braking will first charge the supercapacitor to SOC

_{sc}=1, and the battery only will be charged after supercapacitor is fully charged. Energy management does not allow SOC

_{b}= 0.2 and SOC

_{sc}= 0.01 at the same time.

#### 2.3. Traction Force

_{tot}is the total force for movement in N, v

_{tr}is the train speed in m/s, P

_{fc}is the fuel cell power in W, η

_{fc}is the fuel cell efficiency, η

_{dc}is the DC/DC converter efficiency, P

_{b}is the battery power in W, P

_{sc}is the supercapacitor power in W, η

_{ti}is the traction inverter efficiency, η

_{tm}is the traction motor efficiency, and η

_{ti}is the gear box efficiency. For regenerative braking, each efficiency is calculated reciprocally (1/η), except for the fuel cell.

_{tr}is the traction force on wheels in N (positive for traction, negative for braking); m

_{tot}is the total mass of the train in kg, increased by 6% due to the inertia of the rotating masses [20]; r

_{rr}is the rolling resistance force in N; r

_{pm}is the resistance coefficient of parasitic movements in N/kmh

^{−1}; r

_{ar}is the air resistance coefficient in N/(kmh

^{−1})

^{2}; v

_{tr}is the train speed in km/h; g is the gravitational acceleration; g

_{rt}is the gradient of the railway in ‰; and R is the radius of curvature of the railway in m.

#### 2.4. Fuel Cell

^{2}to 1 A/cm

^{2}. To obtain higher power, the cells are joined in stacks. The fuel is hydrogen, and pure oxygen or oxygen from the air can be used as an oxidant.

_{fc}is the fuel cell stack voltage in V, I

_{Load},

_{fc}is the fuel cell current load in A, E

_{oc}is the open circuit voltage in V, U

_{ohm}is the ohmic voltage drop in V, and U

_{act}is the activation voltage drop in V [22].

#### 2.5. Battery

_{4}) is the safest cathode material used for the high-power modules required in hybrid vehicles. The advantages of this type of battery are the theoretical specific capacity of 170 Ah/kg and greater thermal stability against the release of oxygen, which makes it safer and more tolerant under extreme operating conditions [23].

_{b}is the battery cell voltage in V, E

_{0}is the constant voltage in V, K is the polarization constant or the polarization resistance in Ω, Q

_{b}is the standard battery capacity in Ah, I

_{Load,b}is the battery current load in A, R

_{b}is the battery internal resistance in Ω, A is the voltage drop during the exponential zone in V, and B is the exponential time inverse constant in Ah

^{−1}.

#### 2.6. Supercapacitor

_{sc}is the voltage of the supercapacitor cell in V, R

_{1}is the resistance of the supercapacitor’s main cell in Ω, I

_{Load,sc}is the supercapacitor’s load current in A, U

_{1}is the voltage of the supercapacitor’s main cell in V, C

_{0}is the constant capacitance in F, C

_{v}is the constant parameter in F/V, and Q

_{1}is the instantaneous charge in the supercapacitor’s main cell in As.

#### 2.7. Method of Sequential Quadratic Programming

_{i}(x) are the inequality constraints, λ

_{i}are Lagrange multipliers under the non-negativity constraint, and m is the total number of restrictions.

_{k}is the Hessian Matrix, and m

_{e}is the equality constraints number. Updated, the Hessian Matrix is:

_{Load,sc}is the discharge current of the supercapacitor, I

_{Load,b}is the discharge current of the battery, SOC

_{sc}is the state of charge of the supercapacitor, SOC

_{b}is the state of charge of the battery, hr

_{sc}is the supercapacitor hybridization ratio, and hr

_{b}is the battery hybridization ratio.

#### 2.8. Model Parameters

_{par,sc}is the number of supercapacitor cells in parallel, n

_{ser,sc}is the number of supercapacitor cells in series, n

_{par,b}is the number of battery cells in parallel, n

_{ser,b}is the number of battery cells in series, and P

_{tot}is demand power.

_{fc}is the fuel cell stack hybridization ratio, and n

_{par,fc}is the number of fuel cell stacks in parallel.

_{b}/hr

_{fc}= 0.33, the vehicle can travel the most kilometers per kilogram of hydrogen. Since the supercapacitor also participates in traction, the upper boundary is 0.45 for both energy stores, as there is space for optimization. If the system does not converge, the values will expand [28].

## 3. Results and Discussion

_{fc}= 1 − hr

_{b}− hr

_{sc}, which determines the power of the fuel cell and can be said to be optimal.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Fuel Cell Stack | Battery Cell | ||||

Rated power | P_{fc} | 150 kW | Rated voltage | U_{0} | 3.3 V |

Idle power | P_{fc}_{,min} | 6 kW | Rated capacity | Q_{0} | 2.56 Ah |

Maximum load current | I_{fc,}_{max} | 320 A | Maximum charging current | I_{ch}_{,max} | 10 A |

Mass | m_{fc} | 404 kg | Maximum discharging current | I_{dis}_{,max} | 20 A |

Average hydrogen consumption | m_{H2} | 2.5 g/s | Mass | m_{B} | 76 g |

Supercapacitor Cell | Train | ||||

Nominal capacitance | C_{sc} | 3000 F | Tractive power | P_{tr,}_{max} | 1255 kW |

Rated voltage | U_{sc} | 2.7 V | Tractive force | P_{tr,}_{max} | 125 kN |

Maximum discharging current | I_{sc}_{,max} | 160 A | Braking power | P_{br,}_{max} | 2200 kW |

Mass | m_{sc} | 506.7 g | Braking force | P_{br,}_{max} | 110 kN |

Mass | m_{tot} | 191 t |

Parameter | Start | Optimized | |
---|---|---|---|

Battery hybridization ratio | hr_{b} | 0.25 | 0.39 |

Supercapacitor hybridization ratio | hr_{sc} | 0.05 | 0.06592787 |

Battery discharge current | I_{dis,b} | 0.01 kA | 0.017 kA |

Supercapacitor discharge current | I_{dis,sc} | 0.090.08 kA | 0.0801 kA |

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**MDPI and ACS Style**

Mišić, M.; Stojkov, M.; Tomić, R.; Lovrić, M.
Optimal Hybridization with Minimum Fuel Consumption of the Hybrid Fuel Cell Train. *Designs* **2023**, *7*, 45.
https://doi.org/10.3390/designs7020045

**AMA Style**

Mišić M, Stojkov M, Tomić R, Lovrić M.
Optimal Hybridization with Minimum Fuel Consumption of the Hybrid Fuel Cell Train. *Designs*. 2023; 7(2):45.
https://doi.org/10.3390/designs7020045

**Chicago/Turabian Style**

Mišić, Mario, Marinko Stojkov, Rudolf Tomić, and Mario Lovrić.
2023. "Optimal Hybridization with Minimum Fuel Consumption of the Hybrid Fuel Cell Train" *Designs* 7, no. 2: 45.
https://doi.org/10.3390/designs7020045