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Hybrid Vehicle CO_{2} Emissions Reduction Strategy Based on Model Predictive Control

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## Abstract

**:**

## 1. Introduction

## 2. HEV Drive System

#### 2.1. Electric Machine Dynamics

#### 2.2. T-Type Inverter Fundamental Principle

#### dc-Link

#### 2.3. Buck-Boost Converter Fundamental Principle

## 3. Vehicle Dynamics

#### Vehicle Load Torque

## 4. Emissions Profile Model

## 5. Optimization Strategy and Control Scheme

#### 5.1. Model Predictive Control Scheme

#### 5.2. Convergence of the MPC Algorithm

## 6. Results

#### 6.1. Simulation Results

#### 6.2. Hardware-in-the-Loop Validation

## 7. Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Symbols: | |

${R}_{s}$ | Stator resistance |

${L}_{d}$ | Direct axis inductance |

${L}_{q}$ | Quadrature axis inductance |

${i}_{s}^{dq}$ | Stator current space vector in the $d\phantom{\rule{0.277778em}{0ex}}q$ synchronous reference frame |

${v}_{s}^{dq}$ | Stator voltage space vector in the $d\phantom{\rule{0.277778em}{0ex}}q$ synchronous reference frame |

C | dc-Link capacitors capacitance |

D | Duty cycle of the Buck-Boost converter |

${\psi}_{m}$ | Permanent magnets flux linkage |

${T}_{ce}$ | Combustion engine torque |

${T}_{e}$ | Electromechanical torque |

${T}_{req}$ | Required torque at the drivetrain |

Abbreviations: | |

AC | Alternating current |

ac | Alternating current |

CCM | Continuous current mode |

DC | Direct Current |

dc | Direct current |

EV | Electric vehicle |

EPA | Environmental Protection Agency |

HEV | Hybrid electric vehicle |

HIL | Hardware-in-the-loop |

HWFET | Highway Fuel Economy Test |

ICE | Internal combustion engine |

IGBT | Isolated gate bipolar transistor |

MCR | Maximum continuous rating |

MEOP | Minimum emissions operating point |

MOSFET | Metal oxide semiconductor field effect transistor |

MPC | Model predictive control |

NPC | Neutral point clamped |

PMSM | Permanent magnet synchronous machine |

P&O | Perturb & Observe |

sfc | specific fuel consumption |

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**Figure 14.**Dynamic operation of Torques at the drive train, $\alpha -\beta $ currents, and dc-voltages.

**Figure 15.**(

**a**) Stator $\alpha -\beta $ currents HIL validation. (

**b**) Torques from Minimum emission optimization algorithm HIL validation.

**Figure 16.**HIL dynamic response against step up high torque demand. (

**a**) Torques at the drivetrain. (

**b**) $\alpha -\beta $ Currents. (

**c**) dc-Link voltages.

**Figure 17.**HIL dynamic response against step down high torque demand. (

**a**) Torques at the drivetrain. (

**b**) $\alpha -\beta $ Currents. (

**c**) dc-Link voltages.

${\mathbf{S}}_{\mathbf{x}}$ | ${\mathbf{S}}_{1}$ | ${\mathbf{S}}_{2}$ | ${\mathbf{S}}_{3}$ | ${\mathbf{S}}_{4}$ | ${\mathbf{v}}_{\mathbf{xN}}$ |
---|---|---|---|---|---|

+ | 1 | 1 | 0 | 0 | $+{v}_{dc}/2$ |

0 | 0 | 1 | 1 | 0 | 0 |

- | 0 | 0 | 1 | 1 | $-{v}_{dc}/2$ |

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

Weight | 1531 [kg] |

A | 82.3 [N] |

B | 0.222 [N/ms${}^{-1}$] |

C | 0.403 [N/m${}^{2}$s${}^{-2}$] |

Gear ratio | 3.04 [−] |

Wheel radius | 0.313 [m] |

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

Converter Parameters | ||

${V}_{dc}$ | dc-Link voltage | 800 [V] |

$\phantom{\rule{0.166667em}{0ex}}C$ | dc-Link capacitor | 5000 [$\mathsf{\mu}$F] |

PMSM Parameters | ||

$\phantom{\rule{0.166667em}{0ex}}{R}_{s}$ | Stator resistance | 0.005 [$\Omega $] |

${L}_{d}$ | direct-axis Stator inductance | 0.3 [mH] |

${L}_{q}$ | quadrature-axis Stator inductance | 0.3 [mH] |

${\psi}_{m}$ | PM Flux Linkage | 0.192 [Wb] |

p | Pole pairs | 4 [−] |

Sampling Time | ||

${T}_{disc}$ | Base system discretization time | 5 [$\mathsf{\mu}$s] |

${T}_{s}$ | MPC Sampling time | 10 [$\mathsf{\mu}$s] |

${T}_{dc}$ | Buck-Boost optimization algorithm | 1 [ms] |

MPC | Prediction Horizon | One |

Hardware In the Loop | Processing capability | 95% |

Engine Condition | Specific Fuel Consumption | CO${}_{2}$ Emissions |
---|---|---|

[g/kWh] | [kg/h] | |

100% load | 212.0 | 51.0 |

75% load | 211.4 | 50.7 |

50% load | 215.1 | 51.7 |

25% load | 223.3 | 53.6 |

Emission reduction strategy | 211.1 | 50.7 |

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**MDPI and ACS Style**

Reusser, C.A.; Herrera Hernández, R.; Lie, T.T.
Hybrid Vehicle CO_{2} Emissions Reduction Strategy Based on Model Predictive Control. *Electronics* **2023**, *12*, 1474.
https://doi.org/10.3390/electronics12061474

**AMA Style**

Reusser CA, Herrera Hernández R, Lie TT.
Hybrid Vehicle CO_{2} Emissions Reduction Strategy Based on Model Predictive Control. *Electronics*. 2023; 12(6):1474.
https://doi.org/10.3390/electronics12061474

**Chicago/Turabian Style**

Reusser, Carlos A., Ramón Herrera Hernández, and Tek Tjing Lie.
2023. "Hybrid Vehicle CO_{2} Emissions Reduction Strategy Based on Model Predictive Control" *Electronics* 12, no. 6: 1474.
https://doi.org/10.3390/electronics12061474