# Optimal Fuel Consumption Modelling, Simulation, and Analysis for Hybrid Electric Vehicles

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions. HEVs help to save fuel consumption and reduce CO

_{2}emissions by less than 50% of conventional vehicles using only internal combustion engines (ICEs). In the future, electric vehicles (EVs) may replace ICEs, but EVs still have serious problems of high costs, limited range, and long-term charging. Therefore, HEVs can overcome all the disadvantages of both ICEs and EVs since HEVs are the combination of the advantages of both ICEs and EVs, with broad range, low emissions, high fuel efficiency, high reliability, and low costs. In 2021, roughly 10 million HEVs were globally produced and sold. HEV production is projected to reach 100 million by 2050. A comprehensive review on the state of the art and trends in HEVs was reported in [1]. Another systematic review of the recent technologies, control methods, and energy optimization managers for HEVs was presented in [2].

## 2. HEV Powertrain Modelling

## 3. HEV Scheme Simulations

#### 3.1. Battery Modelling

#### 3.2. DC–DC Converter

#### 3.3. Model of the Starter/Generator

**Operation at Propulsion:**

**Operation at Regenerative Power:**

**Operation at Spinning:**

#### 3.4. Model of the Planetary Gear

#### 3.5. Model of the Vehicle Dynamics

^{2}, and ${F}_{rolling}$, ${F}_{aero}$, and ${F}_{grade}$ are the resistances of the rolling, aero drag, and grade of the weighing forces, correspondingly. These forces are calculated as:

^{3}; C

_{d}is the coefficient for the force aerodynamics in $N\times \frac{{s}^{2}}{kg}\times m$; ${F}_{a}$ is the HEV front crossing area in m

^{2}; and $\alpha $ is the road angle(up or down) in rad.

#### 3.6. Model of the ICE

^{2}, correspondingly. ${x}_{\theta e}$ is assumed as a position variable ranging from 0% to 100%. The ICE of the HEV is modelled and shown in Figure 9.

#### 3.7. Model of the Control System

#### 3.8. Model of the Integrated HEV

## 4. Fuel Economy Modelling and Regressions

_{1}is the first-order regression model for the fuel consumption, W is the HEV’s Weight, T is the Tire radius, and the coefficients of ${P}_{00}$, ${P}_{10}$, and ${P}_{01}$ are generated as P

_{00}= 0.02015; P

_{10}= 0.0006672; and P

_{01}= 0.0002534, correspondingly. The first-order fuel regression model from (42) has the determination coefficient of R-square = 0.5364, or this regression prediction fits the data of 53.64%.

_{2}is the consumption of fuel in the second-order regression model; W is the HEV’s Weight, T is the Tire radius, and the coefficient of ${P}_{00}$, ${P}_{10}$, ${P}_{01}$, ${P}_{20}$, ${P}_{11}$, and ${P}_{02}$ are generated as ${P}_{00}$ = 0.01946; ${P}_{10}$ = 0.0004894; ${P}_{01}$ = 0.0002958; ${P}_{20}$= 0.0005422; ${P}_{11}$ = 0.0004614; and ${P}_{02}$ = 0.0001364, correspondingly. The second-order regression equation model in (43) has the determination coefficient of R-square = 0.8875, or this regression prediction fits the data of 88.75%.

^{−5}; ${P}_{01}$ = −8.597 × 10

^{−5}; ${P}_{20}$ = 0.0004235; ${P}_{11}$ = 0.0004004; ${P}_{02}$ = 0.0001391; ${P}_{30}$ = 0.0003122; ${P}_{21}$ = 0.0003401; ${P}_{12}$ = 0.000162; and ${P}_{03}$ = 2.06 × 10

^{−5}. The third-order regression equation model in (44) has the determination coefficient of R-square = 0.9914, or this regression prediction fits the data of 99.14%.

_{min}at W

_{min}and T

_{min}.

## 5. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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No. | HEV Models | HEV Weights in Kg |
---|---|---|

1. | Hybrid Toyota Prius 2021 | 1335 [28] |

2. | Hybrid Honda Insight 2021 | 1247 [29] |

3. | Hybrid Kia Niro 2021 | 1419 [30] |

4. | Hyundai Sonata 2021 | 1578 [31] |

5. | Hybrid Kia Optima 2021 | 1595 [32] |

6. | Hybrid Hyundai Avante LPi 2021 | 1287 [33] |

7. | Hybrid Toyota Camry 2021 | 1639 [34] |

8. | Hybrid Honda Civic 2021 | 1270 [35] |

No. | Parameters | Rolling Radius in Meters | Rim Width in Inch |
---|---|---|---|

1. | 154/65/R13 | 0.242 | 4.5 |

2. | 154/80/R13 | 0.262 | 4.5 |

3. | 164/60/R14 | 0.252 | 5.0 |

4. | 164/65/R13 | 0.246 | 5.0 |

5. | 164/65/R14 | 0.257 | 5.0 |

6. | 164/70/R14 | 0.267 | 5.0 |

7. | 164/80/R13 | 0.268 | 4.5 |

8. | 174/65/R14 | 0.265 | 5.0 |

9. | 174/65/R15 | 0.275 | 5.0 |

10. | 204/50/R15 | 0.276 | 6.5 |

1335 | 1247 | 1419 | 1578 | 1595 | 1287 | 1639 | 1270 | |
---|---|---|---|---|---|---|---|---|

0.242 | 0.01983 | 0.01983 | 0.01984 | 0.01992 | 0.01994 | 0.01983 | 0.02008 | 0.01983 |

0.262 | 0.01962 | 0.01962 | 0.01965 | 0.02033 | 0.02053 | 0.01962 | 0.02182 | 0.01962 |

0.252 | 0.01972 | 0.01972 | 0.01972 | 0.0198 | 0.01994 | 0.01972 | 0.02052 | 0.01972 |

0.246 | 0.01978 | 0.01978 | 0.01978 | 0.01992 | 0.01994 | 0.01998 | 0.02025 | 0.01978 |

0.257 | 0.01967 | 0.01965 | 0.01969 | 0.01996 | 0.02026 | 0.01965 | 0.02122 | 0.01965 |

0.267 | 0.01955 | 0.01956 | 0.01956 | 0.02056 | 0.02087 | 0.01956 | 0.02254 | 0.01956 |

0.268 | 0.01954 | 0.01955 | 0.01958 | 0.02092 | 0.02128 | 0.01952 | 0.02323 | 0.01955 |

0.265 | 0.01957 | 0.01958 | 0.01961 | 0.02044 | 0.02062 | 0.01957 | 0.02208 | 0.01957 |

0.275 | 0.01947 | 0.01947 | 0.01955 | 0.02187 | 0.02237 | 0.01946 | 0.02512 | 0.01946 |

0.276 | 0.01961 | 0.01961 | 0.01964 | 0.02024 | 0.02045 | 0.01961 | 0.0215 | 0.01961 |

Rolling Tire Radius in Meters | 0.242 | 0.248 | 0.252 | 0.259 | 0.262 | 0.265 | 0.267 | 0.269 | 0.277 | 0.278 |

Optimal HEV Weights in Kg | 1472 | 1429 | 1402 | 1354 | 1333 | 1312 | 1298 | 1277 | 1229 | 1222 |

No | HEV Type | Driving Cycle | HEV Weight in Kg | Tire Radius in Meters | Fuel Consumption in Litres |
---|---|---|---|---|---|

1. | Normal Optimal | FTP75 | 1200 1222 | 0.262 0.278 | 0.03667 0.03648 |

2. | Normal Optimal | NYCC | 1200 1222 | 0.262 0.278 | 0.03294 0.03262 |

3. | Normal Optimal | HWFET | 1200 1222 | 0.262 0.278 | 0.03968 0.03914 |

4. | Normal Optimal | EUDC | 1200 1222 | 0.262 0.278 | 0.03714 0.03654 |

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**MDPI and ACS Style**

Minh, V.T.; Moezzi, R.; Cyrus, J.; Hlava, J.
Optimal Fuel Consumption Modelling, Simulation, and Analysis for Hybrid Electric Vehicles. *Appl. Syst. Innov.* **2022**, *5*, 36.
https://doi.org/10.3390/asi5020036

**AMA Style**

Minh VT, Moezzi R, Cyrus J, Hlava J.
Optimal Fuel Consumption Modelling, Simulation, and Analysis for Hybrid Electric Vehicles. *Applied System Innovation*. 2022; 5(2):36.
https://doi.org/10.3390/asi5020036

**Chicago/Turabian Style**

Minh, Vu Trieu, Reza Moezzi, Jindrich Cyrus, and Jaroslav Hlava.
2022. "Optimal Fuel Consumption Modelling, Simulation, and Analysis for Hybrid Electric Vehicles" *Applied System Innovation* 5, no. 2: 36.
https://doi.org/10.3390/asi5020036