# Optimized EMS and a Comparative Study of Hybrid Hydrogen Fuel Cell/Battery Vehicles

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## Abstract

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## 1. Introduction

## 2. Formulation of the Optimization Problem

#### 2.1. Overall Multi-Criteria Optimization Formulation

#### 2.2. The Constraints

#### 2.3. The Optimization Criteria

#### 2.4. Hydrogen Consumption and Overall Efficiency

#### 2.5. Global Optimization

## 3. Modeling of the Hydrogen Fuel Cell/Battery Hybrid Vehicle

#### 3.1. The Static Model of PEMFC

#### 3.2. The Energy Storage Element

#### 3.2.1. The Battery Model

#### 3.2.2. The Supercapacitor

#### 3.3. DC/AC and DC/DC Converter Models

## 4. Hybrid System Energy Management Algorithms

#### 4.1. EMS Based on the State Machine Strategy

#### 4.2. EMS Based on Fuzzy Logic Rules

#### 4.3. Strategy Based on Frequency Decoupling and Fuzzy Logic Control

#### 4.4. Strategy Based in the Minimization of the Equivalent Consumption

#### 4.5. Proposed FC Fuel Consumption Minimization Strategy

#### 4.6. FC Fuel Consumption Minimization Based on Offline Optimization

## 5. Simulation and Validation Results

#### Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

HFC | Hydrogen-powered Fuel Cell |

FC | Fuel Cell |

HEVs | Hybrid Electric Vehicles |

ICE | Internal Combustion Engine |

ESS | Energy Storage System |

SOC | State Of Charge |

CD/CS | Charge Depleting/Charge Sustaining |

GIS | Geographical Information System |

EMS | Energy Management Strategy |

NN | Neural Network |

MPC | Model Predictive Control |

PMP | Pontryagin Minimum Principle |

ECMS | Equivalent Fuel Consumption Minimization |

SE | Storage Element |

FCS | Fuel Cell System |

EM | Electric Motor |

PEMFC | Proton Exchange Membrane Fuel Cells |

HP | Hydraulic Pump |

HM | Hydraulic Motor |

SMC | State Machine Strategy |

FLC | Fuzzy Logic Control |

FDFLC | Frequency Decoupling (FD) and FLC |

FCFCMS | FC Fuel Consumption Minimization Strategy |

UDDS | Urban Dynamometer Driving Schedule |

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**Figure 1.**Hybrid system configuration and the powertrain power flows (ICE: Internal Combustion Engine, HP: Hydraulic Pump, HM: Hydraulic Motor, EM: Electric Motor).

**Figure 3.**Power vs. energy density [52].

**Figure 5.**Representation of the implementation of the energy management strategy (SMC: State Machine Strategy, FLC: Fuzzy Logic Control, FDFLC: Frequency Decoupling and FLC, ECMS: Equivalent Consumption Minimization Strategy, FCFCMS: FC Fuel Consumption Minimization Strategy).

**Figure 10.**Power demand (${P}_{demand}$), FC power (${P}_{FC}$), battery power (${P}_{bat}$), and supercapacitor power (${P}_{SC}$) for the EMS based on SMC.

**Figure 11.**Power demand (${P}_{demand}$), FC power (${P}_{FC}$), battery power (${P}_{bat}$), and supercapacitor power (${P}_{SC}$) for the EMS based on FLC.

**Figure 12.**Power demand (${P}_{demand}$), FC power (${P}_{FC}$), battery power (${P}_{bat}$), and supercapacitor power (${P}_{SC}$) for the EMS based on FDFLC.

**Figure 13.**Power demand (${P}_{demand}$), FC power (${P}_{FC}$), battery power (${P}_{bat}$), and supercapacitor power (${P}_{SC}$) for the EMS based on the ECMS.

**Figure 14.**Power demand (${P}_{demand}$), FC power (${P}_{FC}$), battery power (${P}_{bat}$), and supercapacitor power (${P}_{SC}$) for the EMS based on the FCFCMS.

**Figure 18.**SOC, ${\mathrm{H}}_{2}$ consumption, and overall efficiency for the EMS based on the ECMS.

**Figure 19.**SOC, ${\mathrm{H}}_{2}$ consumption, and overall efficiency for the EMS based on the FCFCMS.

SOC | ${\mathit{P}}_{\mathit{demand}}$ | ${\mathit{P}}_{\mathit{FC}\left[\mathit{req}\right]}$ |
---|---|---|

High | ${P}_{demand}<{P}_{FC,min}$ | ${P}_{FC\left[req\right]}={P}_{FC,min}$ |

High | ${P}_{demand}\in [{P}_{FC,min},{P}_{FC,max}]$ | ${P}_{FC\left[req\right]}={P}_{demand}$ |

High | ${P}_{demand}\ge {P}_{FC,max}$ | ${P}_{FC\left[req\right]}={P}_{FC,max}$ |

Normal | ${P}_{demand}<{P}_{FC\left[opt\right]}$ | ${P}_{FC\left[req\right]}={P}_{FC\left[opt\right]}$ |

Normal | ${P}_{demand}\in [{P}_{FC\left[opt\right]},{P}_{FC,max}]$ | ${P}_{FC\left[req\right]}={P}_{demand}$ |

Normal | ${P}_{demand}\ge {P}_{FC,max}$ | ${P}_{FC\left[req\right]}={P}_{FC,max}$ |

Low | ${P}_{demand}<{P}_{FC,max}$ | ${P}_{FC\left[req\right]}={P}_{demand}-{P}_{bat,min}$ |

Low | ${P}_{demand}\ge {P}_{FC,max}$ | ${P}_{FC\left[req\right]}={P}_{FC,max}$ |

SOC | ${\mathit{P}}_{\mathit{demand}}$ | ${\mathit{P}}_{\mathit{FC}\left[\mathit{req}\right]}$ |
---|---|---|

H | VL | VL |

H | L | L |

H | M | ML |

H | H | H |

M | VL | VL |

M | L | L |

M | M | M |

M | H | H |

L | VL | L |

L | L | M |

L | M | H |

L | H | H |

Design Requirements | Value |
---|---|

FC power [${P}_{FC,min}-{P}_{FC,max}$] (kW) | [1–10] |

Energy power [${P}_{bat,min}-{P}_{bat,max}$] (kW) | [−1.2–4] |

Energy SOC [$SO{C}_{min}-SO{C}_{max}$] [%] | [60–90] |

DC bus voltage [${V}_{DC,min}-{V}_{DC,max}$] (kW) | [250–280] |

**Table 4.**Overall performance obtained for the different studied energy management strategies. SMC: State Machine Strategy, FLC: Fuzzy Logic Control, FDFLC: Frequency Decoupling and FLC, ECMS: Equivalent Consumption Minimization Strategy, FCFCMS: FC Fuel Consumption Minimization Strategy; the initial value is $SOC\left({t}_{o}\right)$ = [$65\%$].

EMS Strategies | $\mathit{SOC}\left({\mathit{t}}_{\mathit{f}}\right)$ (%) | ${\mathbf{H}}_{2}$ Consumption (g) | Overall Efficiency (%) |
---|---|---|---|

SMC | 59.10 | 59.10 | 85.20 |

FLC | 62.01 | 60.92 | 84.93 |

FDFLC | 62.50 | 61.50 | 84.09 |

ECMS | 66.65 | 61.01 | 84.88 |

ECMS (offline) | 66.65 | 58.20 | … |

FCFCMS | 58.57 | 58.40 | 85.01 |

FCFCMS (offline) | 58.57 | 57.90 | … |

**Table 5.**Comparative table of the characteristics of the SMC, FLC, FDFLC, ECMS, and FCFCMS algorithms.

EMS Strategies | Imp | Setting | ET | $\mathit{SOC}\left({\mathit{t}}_{\mathit{f}}\right)$ | ${\mathbf{H}}_{2}$ Consumption |
---|---|---|---|---|---|

SMC | simple | ER | L | not satisfied | M |

FLC | DM | Comp | M | satisfied | M |

FDFLC | DM | Comp | M | satisfied | The largest |

ECMS | complex | DM | H | satisfied | M |

FCFCMS | complex | DM | H | satisfied | The least |

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**MDPI and ACS Style**

Kamal, E.; Adouane, L. Optimized EMS and a Comparative Study of Hybrid Hydrogen Fuel Cell/Battery Vehicles. *Energies* **2022**, *15*, 738.
https://doi.org/10.3390/en15030738

**AMA Style**

Kamal E, Adouane L. Optimized EMS and a Comparative Study of Hybrid Hydrogen Fuel Cell/Battery Vehicles. *Energies*. 2022; 15(3):738.
https://doi.org/10.3390/en15030738

**Chicago/Turabian Style**

Kamal, Elkhatib, and Lounis Adouane. 2022. "Optimized EMS and a Comparative Study of Hybrid Hydrogen Fuel Cell/Battery Vehicles" *Energies* 15, no. 3: 738.
https://doi.org/10.3390/en15030738