# Optimal Sizing of Storage Elements for a Vehicle Based on Fuel Cells, Supercapacitors, and Batteries

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- The vehicle can recover a fraction of the kinetic energy while braking (regenerative breaking)
- The main power source might be shut down during idle periods and low-load phases without compromising vehicle drivability
- The main power source can operate at high efficiency points independently of the vehicle trajectory.
- The main power source can be designed with a slightly lower capacity.

## 2. Vehicle Architecture

**${p}_{sup}$**is the supercapacitor power,

**${p}_{bat}$**is the battery power,

**${p}_{fc}$**is the fuel cell power and

**${p}_{break}$**is the power dissipated in the mechanical brake. As expressed in Equation (2), the sum of the powers of the elements must be equal to the mechanical power.

#### 2.1. Battery Modelling

**${p}_{db}$**and

**${p}_{cb}$**, and is called

**${p}_{bat}^{*}$**. The battery is also associated with a converter efficiency ${\delta}_{bat}$, which represents the losses in the converters and takes a value of 0.98. Then, we can define the total battery power

**${p}_{bat}$**as shown.

#### 2.2. Supercapacitor Model

**${p}_{cs}$**and discharging power

**${p}_{ds}$**is given by

**${p}_{sup}^{*}$**is the sum of

**${p}_{cs}$**and

**${p}_{ds}$**. The supercapacitor system is associated with an efficiency of the converter shown in Figure 1, ${\delta}_{sup}$, which represents the losses in the converters. In the current work, this parameter will take a value of 0.95. Then, the total output power of the supercapacitor system

**${p}_{sup}$**is given by

#### 2.3. Fuel Cell Model

- Supply of oxidant.
- Fuel supply.
- Heat management.
- Water management.
- Power conditioning, instrumentation, and controls.

**${p}_{fc}$**is the electrical power produced and

**${p}_{{H}_{2}}$**is the theoretical power associated with the hydrogen consumed, which is defined as

**${p}_{com}$**is the power that the compressor demands, ${\eta}_{therm}$ is thermodynamic efficiency (0.98 at 298 K), ${\eta}_{util}$ is the efficiency of cell use, defined as a relationship between the mass of fuel that reacted and the mass that entered in the fuel cell; and ${\eta}_{fci}$ is the efficiency of each cell, calculated as the relationship between the cell voltage ${v}_{fc}$, and the open-circuit voltage ${E}_{oc}$. This relationship can also be expressed as a function of cell voltage and current

## 3. Driving Profiles

#### 3.1. Buenos Aires City Driving Cycle

#### 3.2. Manhattan Driving Cycle

## 4. Dynamic Programming

#### 4.1. Cost Function

- The operational life of the elements.
- The amount of hydrogen consumed.

- To preserve the operational life of the elements (state of health of the elements) abrupt variations
- The amount of hydrogen consumed by the fuel cell, expressed as a function of the power delivered, ${p}_{fc}\left(k\right)$, which determines the economic cost should be minimized.

#### 4.1.1. Coefficient Sweep for BADC

#### 4.1.2. Coefficient Sweep for Manhattan Driving Cycle

## 5. Results

#### 5.1. Fuel Cell Operation Only

#### 5.1.1. Buenos Aires Driving Cycle

#### 5.1.2. Manhattan Driving Cycle

#### 5.2. Hybrid Operation

#### BADC Driving Profile

#### 5.3. Manhattan Driving Profile

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

DP | Dynamic Programing |

ESS | Energy storage system |

SC | Supercapacitor |

FC | Fuel cell |

${P}_{bat}$ | Battery power |

${P}_{sup}$ | Supercapacitor power |

${P}_{fc}$ | Fuel cell power |

${P}_{break}$ | Break power |

SOC | Battery state of charge |

SOH | Battery state of health |

SOE | Supercapacitor state of energy |

EV | Electric vehicle |

HEV | Hybrid electric vehicle |

BADC | Buenos Aires Driving Cycle |

## References

- Jia, S.; Peng, H.; Liu, S.; Zhang, X. Review of Transportation and Energy Consumption Related Research. J. Transp. Syst. Eng. Inf. Technol.
**2009**, 9, 6–16. [Google Scholar] [CrossRef] - Mahlia, T.; Saidur, R.; Memon, L.; Zulkifli, N.; Masjuki, H. A review on fuel economy standard for motor vehicles with the implementation possibilities in Malaysia. Renew. Sustain. Energy Rev.
**2010**, 14, 3092–3099. [Google Scholar] [CrossRef] - Sciarretta, A.; Guzzella, L. Control of hybrid electric vehicles. IEEE Control Syst.
**2007**, 27, 60–70. [Google Scholar] [CrossRef] - Mesbahi, T.; Khenfri, F.; Rizoug, N.; Chaaban, K.; Bartholomeüs, P.; Moigne, P.L. Dynamical modeling of Li-ion batteries for electric vehicle applications based on hybrid Particle Swarm–Nelder–Mead (PSO–NM) optimization algorithm. Electr. Power Syst. Res.
**2016**, 131, 195–204. [Google Scholar] [CrossRef] - Hu, X.; Moura, S.J.; Murgovski, N.; Egardt, B.; Cao, D. Integrated Optimization of Battery Sizing, Charging, and Power Management in Plug-In Hybrid Electric Vehicles. IEEE Trans. Control Syst. Technol.
**2016**, 24, 1036–1043. [Google Scholar] [CrossRef] [Green Version] - Hoke, A.; Brissette, A.; Smith, K.; Pratt, A.; Maksimovic, D. Accounting for Lithium-Ion Battery Degradation in Electric Vehicle Charging Optimization. IEEE J. Emerg. Sel. Top. Power Electron.
**2014**, 2, 691–700. [Google Scholar] [CrossRef] - Redelbach, M.; Özdemir, E.D.; Friedrich, H.E. Optimizing battery sizes of plug-in hybrid and extended range electric vehicles for different user types. Energy Policy
**2014**, 73, 158–168. [Google Scholar] [CrossRef] [Green Version] - Sakti, A.; Michalek, J.J.; Fuchs, E.R.; Whitacre, J.F. A techno-economic analysis and optimization of Li-ion batteries for light-duty passenger vehicle electrification. J. Power Sources
**2015**, 273, 966–980. [Google Scholar] [CrossRef] - Hemi, H.; Ghouili, J.; Cheriti, A. Combination of Markov chain and optimal control solved by Pontryagin’s Minimum Principle for a fuel cell/supercapacitor vehicle. Energy Convers. Manag.
**2015**, 91, 387–393. [Google Scholar] [CrossRef] - Zou, Z.; Cao, J.; Cao, B.; Chen, W. Evaluation strategy of regenerative braking energy for supercapacitor vehicle. ISA Trans.
**2015**, 55, 234–240. [Google Scholar] [CrossRef] [PubMed] - Rodatz, P.; Paganelli, G.; Sciarretta, A.; Guzzella, L. Optimal power management of an experimental fuel cell/supercapacitor-powered hybrid vehicle. Control Eng. Pract.
**2005**, 13, 41–53. [Google Scholar] [CrossRef] - Ayad, M.; Becherif, M.; Henni, A. Vehicle hybridization with fuel cell, supercapacitors and batteries by sliding mode control. Renew. Energy
**2011**, 36, 2627–2634. [Google Scholar] [CrossRef] - Shen, J.; Dusmez, S.; Khaligh, A. Optimization of Sizing and Battery Cycle Life in Battery/Ultracapacitor Hybrid Energy Storage Systems for Electric Vehicle Applications. IEEE Trans. Ind. Inform.
**2014**, 10, 2112–2121. [Google Scholar] [CrossRef] - Choi, M.E.; Lee, J.S.; Seo, S.W. Real-Time Optimization for Power Management Systems of a Battery/Supercapacitor Hybrid Energy Storage System in Electric Vehicles. IEEE Trans. Veh. Technol.
**2014**, 63, 3600–3611. [Google Scholar] [CrossRef] - Thounthong, P.; Chunkag, V.; Sethakul, P.; Davat, B.; Hinaje, M. Comparative Study of Fuel-Cell Vehicle Hybridization with Battery or Supercapacitor Storage Device. IEEE Trans. Veh. Technol.
**2009**, 58, 3892–3904. [Google Scholar] [CrossRef] - Hannan, M.; Azidin, F.; Mohamed, A. Hybrid electric vehicles and their challenges: A review. Renew. Sustain. Energy Rev.
**2014**, 29, 135–150. [Google Scholar] [CrossRef] - Hemi, H.; Ghouili, J.; Cheriti, A. A real time fuzzy logic power management strategy for a fuel cell vehicle. Energy Convers. Manag.
**2014**, 80, 63–70. [Google Scholar] [CrossRef] - Fotouhi, A.; Yusof, R.; Rahmani, R.; Mekhilef, S.; Shateri, N. A review on the applications of driving data and traffic information for vehicles energy conservation. Renew. Sustain. Energy Rev.
**2014**, 37, 822–833. [Google Scholar] [CrossRef] - Hu, X.; Murgovski, N.; Johannesson, L.M.; Egardt, B. Optimal Dimensioning and Power Management of a Fuel Cell; Battery Hybrid Bus via Convex Programming. IEEE/ASME Trans. Mechatron.
**2015**, 20, 457–468. [Google Scholar] [CrossRef] - Sharaf, O.Z.; Orhan, M.F. An overview of fuel cell technology: Fundamentals and applications. Renew. Sustain. Energy Rev.
**2014**, 32, 810–853. [Google Scholar] [CrossRef] - Fatás, E.; Pérez-Flores, J.C.; Ocón, P. Pilas de combustible: una alternativa limpia de producción de energía. Revista Española de Física
**2013**, 27, 26–34. [Google Scholar] - Tie, S.F.; Tan, C.W. A review of energy sources and energy management system in electric vehicles. Renew. Sustain. Energy Rev.
**2013**, 20, 82–102. [Google Scholar] [CrossRef] - Ren, G.; Ma, G.; Cong, N. Review of electrical energy storage system for vehicular applications. Renew. Sustain. Energy Rev.
**2015**, 41, 225–236. [Google Scholar] [CrossRef] - Gao, L.; Dougal, R.A.; Liu, S. Power enhancement of an actively controlled battery/ultracapacitor hybrid. IEEE Trans. Power Electron.
**2005**, 20, 236–243. [Google Scholar] [CrossRef] - Schupbach, R.M.; Balda, J.C.; Zolot, M.; Kramer, B. Design methodology of a combined battery-ultracapacitor energy storage unit for vehicle power management. In Proceedings of the 34th Annual Power Electronics Specialist Conference, Acapulco, Mexico, 15–19 June 2003; Volume 1, pp. 88–93. [Google Scholar] [CrossRef]
- Nielson, G.; Emadi, A. Hybrid energy storage systems for high-performance hybrid electric vehicles. In Proceedings of the 2011 IEEE Vehicle Power and Propulsion Conference, Chicago, IL, USA, 6–9 September 2011; pp. 1–6. [Google Scholar] [CrossRef]
- Qu, X.; Wang, Q.; Yu, Y. Power Demand Analysis and Performance Estimation for Active-Combination Energy Storage System Used in Hybrid Electric Vehicles. IEEE Trans. Veh. Technol.
**2014**, 63, 3128–3136. [Google Scholar] [CrossRef] - Chen, Z.; Mi, C.C.; Xu, J.; Gong, X.; You, C. Energy Management for a Power-Split Plug-in Hybrid Electric Vehicle Based on Dynamic Programming and Neural Networks. IEEE Trans. Veh. Technol.
**2014**, 63, 1567–1580. [Google Scholar] [CrossRef] - Jeong, J.; Kim, N.; Lim, W.; Park, Y.I.; Cha, S.W.; Jang, M.E. Optimization of power management among an engine, battery and ultra-capacitor for a series HEV: A dynamic programming application. Int. J. Automot. Technol.
**2017**, 18, 891–900. [Google Scholar] [CrossRef] - Sabri, M.M.; Danapalasingam, K.; Rahmat, M. A review on hybrid electric vehicles architecture and energy management strategies. Renew. Sustain. Energy Rev.
**2016**, 53, 1433–1442. [Google Scholar] [CrossRef] - Wu, G.; Zhang, X.; Dong, Z. Powertrain architectures of electrified vehicles: Review, classification and comparison. J. Frankl. Inst.
**2015**, 352, 425–448. [Google Scholar] [CrossRef] - Feroldi, D.; Serra, M.; Riera, J. Energy management strategies based on efficiency map for fuel cell hybrid vehicles. J. Power Sources
**2009**, 190, 387–401. [Google Scholar] [CrossRef] - Carignano, M.G.; Adorno, R.; van Dijk, N.; Nieberding, N.; Nigro, N.; Orbaiz, P. Assessment of Energy Management Strategies for a Hybrid Electric Bus. In Proceedings of the 5th International Conference on Engineering Optimization, Iguassu Falls, Brazil, 19–23 June 2016. [Google Scholar]
- Feroldi, D.; Carignano, M. Sizing for fuel cell/supercapacitor hybrid vehicles based on stochastic driving cycles. Appl. Energy
**2016**, 183, 645–658. [Google Scholar] [CrossRef] - Aditya, J.P.; Ferdowsi, M. Comparison of NiMH and Li-ion batteries in automotive applications. In Proceedings of the Vehicle Power and Propulsion Conference, Harbin, China, 3–5 September 2008; pp. 1–6. [Google Scholar]
- Parvini, Y.; Siegel, J.B.; Stefanopoulou, A.G.; Vahidi, A. Supercapacitor electrical and thermal modeling, identification, and validation for a wide range of temperature and power applications. IEEE Trans. Ind. Electron.
**2016**, 63, 1574–1585. [Google Scholar] [CrossRef] - Hoogers, G. Fuel Cell Technology Handbook; CRC Press: Boca Raton, FL, USA, 2002. [Google Scholar]
- Barbir, F. PEM Fuel Cells: Theory and Practice; Academic Press: Cambridge, MA, USA, 2013. [Google Scholar]
- Zhou, R.; Zheng, Y.; Jaroniec, M.; Qiao, S.Z. Determination of the electron transfer number for the oxygen reduction reaction: from theory to experiment. ACS Catal.
**2016**, 6, 4720–4728. [Google Scholar] [CrossRef] - Tzirakis, E.; Pitsas, K.; Zannikos, F.; Stournas, S. Vehicle emissions and driving cycles: comparison of the Athens driving cycle (ADC) with ECE-15 and European driving cycle (EDC). Glob. NEST J.
**2006**, 8, 282–290. [Google Scholar] - Bellman, R. Dynamic programming; Dover Publications: Mineola, NY, USA, 2003. [Google Scholar]
- Bertsekas, D.P.; Bertsekas, D.P.; Bertsekas, D.P.; Bertsekas, D.P. Dynamic Programming and Optimal Control; Athena Scientific: Belmont, MA, USA, 1995; Volume 1. [Google Scholar]
- Haifeng, D.; Xuezhe, W.; Zechang, S. A new SOH prediction concept for the power lithium-ion battery used on HEVs. In Proceedings of the Vehicle Power and Propulsion Conference, Dearborn, MI, USA, 7–11 September 2009; pp. 1649–1653. [Google Scholar]
- Zou, C.; Manzie, C.; Nešić, D.; Kallapur, A.G. Multi-time-scale observer design for state-of-charge and state-of-health of a lithium-ion battery. J. Power Sources
**2016**, 335, 121–130. [Google Scholar] [CrossRef] - Ouyang, M.; Feng, X.; Han, X.; Lu, L.; Li, Z.; He, X. A dynamic capacity degradation model and its applications considering varying load for a large format Li-ion battery. Appl. Energy
**2016**, 165, 48–59. [Google Scholar] [CrossRef] [Green Version] - Wang, J.; Liu, P.; Hicks-Garner, J.; Sherman, E.; Soukiazian, S.; Verbrugge, M.; Tataria, H.; Musser, J.; Finamore, P. Cycle-life model for graphite-LiFePO4 cells. J. Power Sources
**2011**, 196, 3942–3948. [Google Scholar] [CrossRef] - Hu, X.; Johannesson, L.; Murgovski, N.; Egardt, B. Longevity-conscious dimensioning and power management of the hybrid energy storage system in a fuel cell hybrid electric bus. Appl. Energy
**2015**, 137, 913–924. [Google Scholar] [CrossRef] - Johannesson, L.; Murgovski, N.; Ebbesen, S.; Egardt, B.; Gelso, E.; Hellgren, J. Including a battery state of health model in the HEV component sizing and optimal control problem. IFAC Proc. Vol.
**2013**, 46, 398–403. [Google Scholar] [CrossRef] - Ebbesen, S.; Elbert, P.; Guzzella, L. Battery State-of-Health Perceptive Energy Management for Hybrid Electric Vehicles. IEEE Trans. Veh. Technol.
**2012**, 61, 2893–2900. [Google Scholar] [CrossRef] - Das, V.; Padmanaban, S.; Venkitusamy, K.; Selvamuthukumaran, R.; Blaabjerg, F.; Siano, P. Recent advances and challenges of fuel cell based power system architectures and control—A review. Renew. Sustain. Energy Rev.
**2017**, 73, 10–18. [Google Scholar] [CrossRef] - Dicks, A.; Rand, D.A.J. Fuel Cell Systems Explained; Wiley Online Library: Hoboken, NJ, USA, 2018. [Google Scholar]
- Kongkanand, A.; Mathias, M.F. The priority and challenge of high-power performance of low-platinum proton-exchange membrane fuel cells. J. Phys. Chem. Lett.
**2016**, 7, 1127–1137. [Google Scholar] [CrossRef] [PubMed] - Li, L.; You, S.; Yang, C.; Yan, B.; Song, J.; Chen, Z. Driving-behavior-aware stochastic model predictive control for plug-in hybrid electric buses. Appl. Energy
**2016**, 162, 868–879. [Google Scholar] [CrossRef] - Song, Z.; Hofmann, H.; Li, J.; Hou, J.; Han, X.; Ouyang, M. Energy management strategies comparison for electric vehicles with hybrid energy storage system. Appl. Energy
**2014**, 134, 321–331. [Google Scholar] [CrossRef] - Sockeel, N.; Shi, J.; Shahverdi, M.; Mazzola, M. Pareto Front Analysis of the Objective Function in Model Predictive Control Based Power Management System of a Plug-in Hybrid Electric Vehicle. In Proceedings of the 2018 IEEE Transportation Electrification Conference and Expo (ITEC), Long Beach, CA, USA, 13–15 June 2018; pp. 1–6. [Google Scholar]
- Sockeel, N.; Shi, J.; Shahverdi, M.; Mazzola, M. Sensitivity Analysis of the Battery Model for Model Predictive Control: Implementable to a Plug-In Hybrid Electric Vehicle. World Electr. Veh. J.
**2018**, 9, 45. [Google Scholar] [CrossRef]

**Figure 5.**Saving in energy supplied by fuel cell and energy supplied by batteries for the different combination of coefficients of the cost function for BADC.

**Figure 6.**Saving in energy supplied by fuel cell and energy supplied by supercapacitor for the different combination of coefficients of the cost function for BADC.

**Figure 7.**Saving in energy supplied by fuel cell and energy supplied batteries for the different combination of coefficients of the cost function for Manhattan Driving Cycle.

**Figure 8.**Saving in energy supplied by fuel cell and energy supplied batteries for the different combination of coefficients of the cost function for Manhattan Driving Cycle.

**Figure 12.**Reduction in fuel cell consumption versus energy supplied by supercapacitor for BADC profile.

**Figure 16.**Reduction in fuel cell consumption versus energy supplied by battery for Manhattan profile.

**Figure 17.**Reduction in fuel cell consumption versus energy supplied by supercapacitor for Manhattan profile.

Name | Symbol | Value | Unit |
---|---|---|---|

Air density | p | 1.2 | kg/m${}^{3}$ |

Coefficient of resistance to movement | ${c}_{rro}$ | 0.008 | s/u |

Coefficient of resistance to movement | ${c}_{rrl}$ | 0.00012 | s${}^{2}$/m${}^{2}$ |

Aerodynamic coefficient | ${c}_{x}$ | 0.65 | s/u |

Front area | s | 8.06 | m${}^{2}$ |

Total mass | m | 14,000 | kg |

Gravity | g | 9.8 | m/s${}^{2}$ |

Parameter | Data |
---|---|

Manufacturer | PEVE |

Shape | Prismatic |

Case | Plastic |

Cell capacity (Ah) | 6.5 |

Cell voltage (V) | 7.2 |

Specific energy (Wh/kg) | 46 |

Specific power (W/kg) | 1300 |

Mass (kg) | 1.04 |

Operation temperature (°C) | −20 to 50 |

Cost (€/kg) | 33.88 |

Parameter | Data |
---|---|

Manufacturer | Maxwell Technologies |

Packaging | Bulk |

Cell capacitance (F) | 3000 |

Rated Voltage (V) | 125 |

Temperature (°C) | −40 to 65 |

Mass (kg) | 1.3 |

Specific power (W/Kg) | 1700 |

Specific energy (Wh/Kg) | 2.3 |

$SO{E}_{max}$ | 1 |

$SO{E}_{min}$ | 0 |

Cost (€/Kg) | 88.34 |

Parameter | Data |
---|---|

Maximum voltage | 580 V |

Maximum current | 288 A |

Number of cells | 560 |

Operating temperature | 330 ${}^{\circ}$K |

Nominal air pressure | 2.24 bar |

Maximum power | 100 kW |

Mass | 285 kg |

Temperature of reference | 298 ${}^{\circ}$K |

Temperature constant | 44.43 |

Cost | 100 k€ |

Parameter | Value |
---|---|

Total cycle time | 1864 s |

Average Speed | 3.92 m/s |

Maximum speed | 15.6 m/s |

Maximum acceleration | 9.2155 × 10${}^{-5}$ m/s${}^{2}$ |

${e}_{v}^{+}$ | 22,678.62 kJ |

${e}_{v}^{-}$ | 11,870.63 kJ |

Parameter | Value |
---|---|

Total cycle time | 1089 s |

Average Speed | 3.033 m/s |

Maximum speed | 11.24 m/s |

Maximum acceleration | 2.044 m/${\mathrm{s}}^{2}$ |

${e}_{v}^{+}$ | 13,747.04 kJ |

${e}_{v}^{-}$ | 8090.08 kJ |

Component | Mass | Power | Energy |
---|---|---|---|

Battery | 8 kg | 10.4 kW | 368 Wh |

Supercapacitor | 12 kg | 20.4 kW | 27.6 Wh |

Weights | Energy | ||||||
---|---|---|---|---|---|---|---|

${w}_{u2}$ | ${w}_{u1}$ | ${w}_{SOH}$ | ${w}_{soc}$ | ${w}_{\alpha}$ | Battery (%) | Supercapacitor (%) | Fuel cell (%) |

0 | 0.33 | 0.33 | 0.33 | 0 | 13.24 | 23.84 | 19.41 |

0.05 | 0.3 | 0.3 | 0.3 | 0.05 | 16.79 | 27.74 | 23.31 |

0.1 | 0.267 | 0.267 | 0.267 | 0.1 | 18.00 | 29.35 | 24.78 |

0.15 | 0.23 | 0.23 | 0.23 | 0.15 | 18.76 | 29.48 | 25.25 |

0.2 | 0.2 | 0.2 | 0.2 | 0.2 | 18.99 | 29.57 | 25.32 |

0.25 | 0.167 | 0.167 | 0.167 | 0.25 | 19.68 | 29.80 | 25.73 |

0.3 | 0.13 | 0.13 | 0.13 | 0.3 | 19.96 | 30.15 | 26.22 |

0.35 | 0.1 | 0.1 | 0.1 | 0.35 | 20.96 | 30.19 | 26.72 |

0.4 | 0.067 | 0.067 | 0.067 | 0.4 | 21.71 | 30.84 | 27.22 |

Weights | Energy | ||||||
---|---|---|---|---|---|---|---|

${w}_{u2}$ | ${w}_{u1}$ | ${w}_{SOH}$ | ${w}_{soc}$ | ${w}_{\alpha}$ | Battery (%) | Supercapacitor (%) | Fuel cell (%) |

0 | 0.33 | 0.33 | 0.33 | 0 | 11.02 | 25.66 | 19.57 |

0.05 | 0.3 | 0.3 | 0.3 | 0.05 | 13.20 | 25.89 | 20.33 |

0.1 | 0.267 | 0.267 | 0.267 | 0.1 | 14.52 | 26.36 | 21.16 |

0.15 | 0.23 | 0.23 | 0.23 | 0.15 | 15.51 | 27.89 | 22.73 |

0.2 | 0.2 | 0.2 | 0.2 | 0.2 | 15.84 | 28.08 | 23.56 |

0.25 | 0.167 | 0.167 | 0.167 | 0.25 | 16.43 | 28.47 | 23.76 |

0.3 | 0.13 | 0.13 | 0.13 | 0.3 | 17.21 | 28.83 | 24.38 |

0.35 | 0.1 | 0.1 | 0.1 | 0.35 | 18.15 | 29.23 | 24.58 |

0.4 | 0.067 | 0.067 | 0.067 | 0.4 | 21.29 | 30.72 | 25.19 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sampietro, J.L.; Puig, V.; Costa-Castelló, R.
Optimal Sizing of Storage Elements for a Vehicle Based on Fuel Cells, Supercapacitors, and Batteries. *Energies* **2019**, *12*, 925.
https://doi.org/10.3390/en12050925

**AMA Style**

Sampietro JL, Puig V, Costa-Castelló R.
Optimal Sizing of Storage Elements for a Vehicle Based on Fuel Cells, Supercapacitors, and Batteries. *Energies*. 2019; 12(5):925.
https://doi.org/10.3390/en12050925

**Chicago/Turabian Style**

Sampietro, José Luis, Vicenç Puig, and Ramon Costa-Castelló.
2019. "Optimal Sizing of Storage Elements for a Vehicle Based on Fuel Cells, Supercapacitors, and Batteries" *Energies* 12, no. 5: 925.
https://doi.org/10.3390/en12050925