# Adaptive Model Predictive Control Including Battery Thermal Limitations for Fuel Consumption Reduction in P2 Hybrid Electric Vehicles

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. The Hybrid Electric Vehicle (HEV)

#### 2.2. Vehicle Longitudinal Dynamic Model

#### 2.3. Vehicle Transmission Model (Gearbox)

#### 2.4. The Internal Combustion Engine

#### 2.5. Electric Machine (EM)

#### 2.6. Battery and Electro-Thermal Model

#### 2.6.1. Cell Electric Model

#### 2.6.2. Cell Thermal Model

#### 2.7. Energy Management System (EMS) Strategy with Adaptive MPC

#### 2.7.1. Design of an MPC Internal Prediction Model

#### 2.7.2. Design of Standard MPC

#### 2.7.3. Adaptive MPC

## 3. Results and Discussion

#### 3.1. Fuel Consumption Computation Based on On/Off Model

#### 3.2. Adaptive MPC Strategy Results

#### 3.2.1. No Thermal Limitation Constraint

#### 3.2.2. Increased Prediction Horizon with No Thermal Limitation Constraint

#### 3.2.3. Introducing Thermal Limitation Constraint

#### 3.2.4. Battery Thermal Enhancement with Battery Sizing

## 4. Summary and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**P2 Off-axis Configuration HEV powertrain integrated with an energy management system (EMS).

**Figure 3.**(

**a**) Fuel consumption map of Mazda CX9 2016 ICE as a function of ${T}_{ice}$ and ${\omega}_{ice}$. The dots are the estimated values. (

**b**) The maximum operating torque ${T}_{ice,max}$ as a function of ${\omega}_{ice}$ and the fuel consumption rate contour lines.

**Figure 4.**Efficiency map of the electric machine in both motor and generator operating modes. The maximum motor torque ${T}_{mo,max}$ and maximum generator torque ${T}_{gen,max}$ as functions of ${\omega}_{em}$.

**Figure 5.**Equivalent circuit that describes the dynamic model designed for terminal voltage and voltage loss prediction.

**Figure 6.**On/off model evaluated with 14s6p battery configuration; (

**a**) the state of charge; (

**b**) the battery surface temperature; (

**c**) the EM torque; (

**d**) the ICE torque; and (

**e**) the velocity of the UDDS drive cycle.

**Figure 7.**MPC evaluated at with $p=2$ using 14s6p battery configuration, no thermal limitations; (

**a**) is the state of charge; (

**b**) is the battery surface temperature; (

**c**) is the EM torque; (

**d**) is the ICE torque; and (

**e**) is the velocity of the UDDS drive cycle.

**Figure 8.**MPC evaluated with $p=20$ using 14s6p battery configuration, no thermal limitations; (

**a**) is the state of charge; (

**b**) is the battery surface temperature; (

**c**) is the EM torque; (

**d**) is the ICE torque; and (

**e**) is the velocity of the UDDS drive cycle.

**Figure 9.**MPC evaluated with $p=20$ using 14s6p battery configuration, applied thermal limitation; (

**a**) is the state of charge; (

**b**) is the battery surface temperature; (

**c**) is the EM torque; (

**d**) is the ICE torque; (

**e**) is the velocity of the UDDS drive cycle.

**Figure 10.**Operating torque comparison between the case with thermal limitation and without thermal limitations in the efficiency map. (

**a**) The electric machine torque comparison; and (

**b**) the ICE torque comparison.

**Figure 11.**MPC evaluated with $p=20$ using 14s10p battery configuration, (

**a**) is the state of charge; (

**b**) is the battery surface temperature; (

**c**) is the EM torque; (

**d**) is the ICE torque; and (

**e**) is the velocity of the UDDS drive cycle.

**Table 1.**The vehicle specifications for Mazda CX9 2016 [44].

Parameter | Unit | Variable | Value | |
---|---|---|---|---|

Vehicle Description | Nominal mass | kg | $M$ | 2041 |

Frontal Area | m^{2} | ${A}_{f}$ | 2.4207 | |

Aerodynamic drag coefficient | - | ${c}_{x}$ | 0.316 | |

Gear ratios | - | ${i}_{g}$ | 6-speed gear shift | |

Final Drive Ratio | - | ${i}_{final}$ | 4.41 | |

Tire size | - | P255/50VR20 | ||

Passenger Capacity | 7 | |||

Internal Combustion Engine | SAE Net Torque @ rpm | Nm | 310 @ 2000 | |

Fuel System | - | Gasoline Direct Injection | ||

SAE net power @ rpm | kW | 169 @ 5000 | ||

Displacement | L | 2.5 | ||

Electric Motor | Maximum power | kW | 27 | |

Maximum torque @ rpm | Nm | ${T}_{em.max}$ | 65 @ 4000 | |

Battery (Sanyo NCR 18650 GA Lithium-ion cell) | Single-cell nominal voltage | V | ${v}_{nom}$ | 3.6 |

Single-cell nominal capacity | Ah | ${C}_{nom}$ | 3.2 | |

Minimum battery SOC | % | $SO{C}_{min}$ | 0 | |

Maximum battery SOC | % | $SO{C}_{max}$ | 100 | |

Operating temperature | °C | ${\theta}_{surf}$ | −20~60 | |

Ambient temperature | °C | ${\theta}_{amb}$ | 20 | |

Battery Pack Configurations | - | 14s6p and 14s10p |

Variable | Units | Value | |
---|---|---|---|

Electric Model | $\mathrm{Max}\text{}\mathrm{absolute}\text{}\mathrm{analogue}\text{}\mathrm{hysteresis}\text{}\mathrm{voltage}\text{}\mathrm{at}\text{}\mathrm{ambient}\text{}\mathrm{temperature},\text{}{M}_{a}$ | - | 0.017 |

$\mathrm{Instantaneous}\text{}\mathrm{hysteresis}\text{}\mathrm{height},\text{}{M}_{0}$ | - | negligible | |

$\mathrm{Instantaneous}\text{}\mathrm{series}\text{}\mathrm{resistor},\text{}{R}_{0}$ | Ohms | 0.024 | |

$\mathrm{Parallel}\text{}\mathrm{branch}\text{}\mathrm{resistance},\text{}{R}_{j}$ | Ohm | 0.018 | |

Thermal Model | $\mathrm{Specific}\text{}\mathrm{heat}\text{}\mathrm{capacity},\text{}{c}_{p}$ | $\mathrm{J}/\mathrm{kg}\text{}\mathrm{K}$ | 1200 |

$\mathrm{Thermal}\text{}\mathrm{resistance},\text{}{R}_{conv}$ | $\mathrm{K}/\mathrm{W}$ | 14.6 | |

$\mathrm{Cell}\text{}\mathrm{mass},\text{}{m}_{cell}$ | kg | $48.5\times {10}^{-3}$ |

**Table 3.**Inputs, states, eigenvalues and output variables of the linearized nominal internal plant model.

Input | States Variable | Nominal Eigenvalue | Output |
---|---|---|---|

$\mathrm{Torque}\text{}\mathrm{of}\text{}\mathrm{EM}\text{}\left({T}_{em}\right)$ | State of charge (SOC) | 0 | SOC |

$\mathrm{Torque}\text{}\mathrm{of}\text{}\mathrm{ICE}\text{}\left({T}_{ice}\right)$ | Diffusion-resistant current $\left({i}_{Rj}\right)$ | −0.002 | ${\theta}_{surf}$ |

$\mathrm{Speed}\text{}\mathrm{of}\text{}\mathrm{ICE}\text{}\left({\omega}_{ice}\right)$ | $\mathrm{Battery}\text{}\mathrm{temperature}\text{}\left({\theta}_{surf}\right)$ | −0.0282 | ${m}_{ice}$ |

$\mathrm{Fuel}\text{}\mathrm{consumed}\text{}({m}_{ice}$) | 0 |

${\mathit{T}}_{\mathit{m}\mathit{o}}\left(\mathbf{Nm}\right)$ | ${\mathit{T}}_{\mathit{g}\mathit{e}\mathit{n}}\left(\mathbf{Nm}\right)$ | ${\mathit{T}}_{\mathit{I}\mathit{C}\mathit{E}}\left(\mathbf{Nm}\right)$ | SOC | ${\mathit{\theta}}_{\mathit{s}\mathit{u}\mathit{r}\mathit{f}}$ (°C) | |
---|---|---|---|---|---|

min | 0 | $-{T}_{EM,max}$ | 0 | 0.1 | 0 |

max | ${T}_{EM,max}$ | 0 | ${T}_{ICE,max}$ | 0.9 | 50 |

**Table 5.**Result summary for different prediction horizons, battery pack configurations and operating conditions.

Operating Condition | Prediction Horizon | Pack Configuration | Maximum Temperature [°C] | Fuel Consumption [L/100 km] | Fuel Consumed [g] | Fuel Saving [%] | CO_{2} Consumption [g/km] |
---|---|---|---|---|---|---|---|

Conventional vehicle | - | - | - | 8.03 | 699.9 | 0 | 187.1 |

On/Off | - | 14s6p | 55 | 7.54 | 672 | 4 | 175.7 |

No. Temp Limit | 2 | 160 | 6.94 | 618.5 | 11.6 | 161.8 | |

No. Temp Limit | 20 | 111 | 6.85 | 610 | 12.8 | 159.5 | |

Temp. Limited | 20 | 55 | 6.98 | 621.5 | 11.3 | 162.6 | |

Increased battery capacity | 20 | 14s10p | 55 | 6.63 | 590.4 | 15.7 | 154.4 |

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## Share and Cite

**MDPI and ACS Style**

Ezemobi, E.; Yakhshilikova, G.; Ruzimov, S.; Castellanos, L.M.; Tonoli, A.
Adaptive Model Predictive Control Including Battery Thermal Limitations for Fuel Consumption Reduction in P2 Hybrid Electric Vehicles. *World Electr. Veh. J.* **2022**, *13*, 33.
https://doi.org/10.3390/wevj13020033

**AMA Style**

Ezemobi E, Yakhshilikova G, Ruzimov S, Castellanos LM, Tonoli A.
Adaptive Model Predictive Control Including Battery Thermal Limitations for Fuel Consumption Reduction in P2 Hybrid Electric Vehicles. *World Electric Vehicle Journal*. 2022; 13(2):33.
https://doi.org/10.3390/wevj13020033

**Chicago/Turabian Style**

Ezemobi, Ethelbert, Gulnora Yakhshilikova, Sanjarbek Ruzimov, Luis Miguel Castellanos, and Andrea Tonoli.
2022. "Adaptive Model Predictive Control Including Battery Thermal Limitations for Fuel Consumption Reduction in P2 Hybrid Electric Vehicles" *World Electric Vehicle Journal* 13, no. 2: 33.
https://doi.org/10.3390/wevj13020033