# Implementation of Optimized Regenerative Braking in Energy Efficient Driving Strategies

^{*}

## Abstract

**:**

## 1. Introduction

_{2}) emissions [1]. Adoption of electric vehicles (EVs) can reduce CO

_{2}emissions, if countries adapt low-emission electricity mixes [2]. On the vehicle-manufacturer side, there is a tightening of regulatory conditions for achieving environmental, social, and governance (ESG) performance, with the former recommended monitoring and disclosure frameworks being replaced by community legal obligations. Accounting for carbon emissions can recognize the aggregate emissions of certain units of low-carbon products, which also encourages EV production [3,4].

## 2. Shell Eco-Marathon Vehicle Design

## 3. Optimization Framework for Regenerative Braking

- Determination of optimal regenerative braking-torque function to achieve maximal energy recovery;
- Parameter sensitivity analysis of optimized braking-torque function;
- Implementation of regenerative braking in the measurement-based vehicle model;
- Complete driving strategy optimization.

_{wheel}, as described in Equation (1).

_{res}, signifies the aggregated force generated by air resistance ${\mathrm{F}}_{\mathrm{air}}$, rolling resistance ${\mathrm{F}}_{\mathrm{rolling}}$, cornering resistance ${\mathrm{F}}_{\mathrm{cornering}}$, and vehicle inertia ${\mathrm{F}}_{\mathrm{inertia}}$, as expressed by Equation (3). F

_{res}can be determined from the combination of the coast-down test and speed-controller cornering test as a three-dimensional force model, which is fully applicable in the vehicle model.

_{brake}to the wheel radius R

_{wheel}, as indicated by Equation (5).

_{kinetic}, is computed according to Equation (6):

## 4. Mathematical Formulation of the Optimization Problem

_{recovered}, as given by Equation (11), is mathematically equivalent to maximizing its positive value in physical applications. Thus, the objective function can be expressed as the minimization problem given by Equation (12), which is computationally more convenient to implement in optimization software.

_{i}, is obtained as indicated by Equation (14)

_{brake i}, can take values according to Equation (16) within the bounds imposed by Equation (17).

## 5. Sensitivity Analysis of the Optimized Braking Torque

## 6. Driving Strategy Optimization with Regenerative Braking

## 7. Results and Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

3D | 3 dimensions |

BLDC | Brushless direct current |

CO_{2} | Carbon dioxide |

COVID | Coronavirus disease |

CVT–ISG | Continuously variable transmission–integrated starter generator |

DC | Direct current |

EBS | Electric braking systems |

Eco | Ecological |

EES | Energy storage systems |

E_{kinetic} | Kinetic energy |

E_{recovered} | Recovered energy |

E_{resistance_loss} | Kinetic energy loss |

ESG | Environmental, social, and governance |

EV | Electric vehicle |

F_{air} | Air resistance |

F_{cornering} | Cornering resistance |

F_{inertia} | Vehicle inertia |

F_{R_braking} | Braking force |

F_{res} | Resistance |

F_{rolling} | Rolling resistance |

F_{trac} | Traction force |

F_{vert} | Grade resistance (vertical force) |

GA | Genetic algorithm |

GHG | Global greenhouse gas |

GWO | Grey wolf optimizer |

J | Joule |

Kg | Kilogram |

Km | Kilometer |

km/h | Kilometer per hour |

m | Meter |

M_{brake} | Braking torque |

M_{drive} | Generated torque / tractive torque |

MPC | Model predictive control |

NEDC | New European driving cycle |

Nm | Newton meter |

N_{pop} | Initial population |

n_{var} | Function variable |

NYCC | New York City cycle |

PMSM | Permanent magnet synchronous machine |

PSO | Particle swarm optimization |

Ref | Reference |

Rpm | Revolutions per minute |

R_{wheel} | Wheel radius |

s | Second |

SEM | Shell Eco-Marathon |

SoC | State of charge |

SQP | Sequential quadratic programming |

T | Time |

V | Volt |

v | Speed |

VI-CRT | VI-CarRealTime |

v_{start} | Initial speed |

W | Watt |

## References

- Albuquerque, F.D.B.; Maraqa, M.A.; Chowdhury, R.; Mauga, T.; Alzard, M. Greenhouse Gas Emissions Associated with Road Transport Projects: Current Status, Benchmarking, and Assessment Tools. Transp. Res. Procedia
**2020**, 48, 2018–2030. [Google Scholar] [CrossRef] - Rietmann, N.; Hügler, B.; Lieven, T. Forecasting the Trajectory of Electric Vehicle Sales and the Consequences for Worldwide CO
_{2}Emissions. J. Clean. Prod.**2020**, 261, 121038. [Google Scholar] [CrossRef] - Tóth, Á.; Suta, A.; Szauter, F. Interrelation between the Climate-Related Sustainability and the Financial Reporting Disclosures of the European Automotive Industry. Clean Technol. Environ. Policy
**2022**, 24, 437–445. [Google Scholar] [CrossRef] - Tóth, Á.; Szigeti, C.; Suta, A. Carbon Accounting Measurement with Digital Non-Financial Corporate Reporting and a Comparison to European Automotive Companies Statements. Energies
**2021**, 14, 5607. [Google Scholar] [CrossRef] - Shell Eco-Marathon. Shell Eco-Marathon 2023 Official Rules Chapter 1. 2023. Available online: https://www.makethefuture.shell/en-gb/shell-eco-marathon/global-rules (accessed on 15 January 2023).
- Sciarretta, A.; De Nunzio, G.; Ojeda, L.L. Optimal Ecodriving Control: Energy-Efficient Driving of Road Vehicles as an Optimal Control Problem. IEEE Control. Syst.
**2015**, 35, 71–90. [Google Scholar] [CrossRef] [Green Version] - Targosz, M.; Skarka, W.; Przystałka, P. Model-Based Optimization of Velocity Strategy for Lightweight Electric Racing Cars. J. Adv. Transp.
**2018**, 2018, 3614025. [Google Scholar] [CrossRef] [Green Version] - Sawulski, J.; Ławryńczuk, M. Optimization of control strategy for a low fuel consumption vehicle engine. Inf. Sci.
**2019**, 493, 192–216. [Google Scholar] [CrossRef] - Stabile, P.; Ballo, F.; Mastinu, G.; Gobbi, M. An Ultra-Efficient Lightweight Electric Vehicle—Power Demand Analysis to Enable Lightweight Construction. Energies
**2021**, 14, 766. [Google Scholar] [CrossRef] - Stabile, P.; Ballo, F.; Previati, G.; Mastinu, G.; Gobbi, M. Eco-Driving Strategy Implementation for Ultra-Efficient Lightweight Electric Vehicles in Realistic Driving Scenarios. Energies
**2023**, 16, 1394. [Google Scholar] [CrossRef] - Ku, D.; Choi, M.; Yoo, N.; Shin, S.; Lee, S. A New Algorithm for Eco-Friendly Path Guidance Focused on Electric Vehicles. Energy
**2021**, 233, 121198. [Google Scholar] [CrossRef] - Chen, Z.; Zhou, X.; Wang, Z.; Li, Y.; Hu, B. A Novel Emergency Braking Control Strategy for Dual-Motor Electric Drive Tracked Vehicles Based on Regenerative Braking. Appl. Sci.
**2019**, 9, 2480. [Google Scholar] [CrossRef] [Green Version] - Zhang, Z.; Wang, L.; Zhang, J.; Ma, R. Study on Requirements for Load Emulation of the Vehicle with an Electric Braking System. IEEE Trans. Veh. Technol.
**2017**, 66, 9638–9653. [Google Scholar] [CrossRef] - Yang, Y.; He, Q.; Chen, Y.; Fu, C. Efficiency Optimization and Control Strategy of Regenerative Braking System with Dual Motor. Energies
**2020**, 13, 711. [Google Scholar] [CrossRef] [Green Version] - Martyushev, N.V.; Malozyomov, B.V.; Khalikov, I.H.; Kukartsev, V.A.; Kukartsev, V.V.; Tynchenko, V.S.; Tynchenko, Y.A.; Qi, M. Review of Methods for Improving the Energy Efficiency of Electrified Ground Transport by Optimizing Battery Consumption. Energies
**2023**, 16, 729. [Google Scholar] [CrossRef] - Xu, W.; Chen, H.; Zhao, H.; Ren, B. Torque Optimization Control for Electric Vehicles with Four In-Wheel Motors Equipped with Regenerative Braking System. Mechatronics
**2019**, 57, 95–108. [Google Scholar] [CrossRef] - Partridge, J.; Abouelamaimen, D.I. The Role of Supercapacitors in Regenerative Braking Systems. Energies
**2019**, 12, 2683. [Google Scholar] [CrossRef] [Green Version] - Pusztai, Z.; Kőrös, P.; Szauter, F.; Friedler, F. Vehicle Model-Based Driving Strategy Optimization for Lightweight Vehicle. Energies
**2022**, 15, 3631. [Google Scholar] [CrossRef] - Pusztai, Z.; Korös, P.; Friedler, F. Vehicle Model for Driving Strategy Optimization of Energy Efficient Lightweight Vehicle. Chem. Eng. Trans.
**2021**, 88, 385–390. [Google Scholar] [CrossRef] - Pusztai, Z.; Korös, P.; Szauter, F.; Friedler, F. Regenerative Braking Optimization of Lightweight Vehicle Based on Vehicle Model. Chem. Eng. Trans.
**2022**, 94, 601–606. [Google Scholar] [CrossRef] - Luque, P.; Mántaras, D.A.; Maradona, Á.; Roces, J.; Sánchez, L.; Castejón, L.; Malón, H. Multi-Objective Evolutionary Design of an Electric Vehicle Chassis. Sensors
**2020**, 20, 3633. [Google Scholar] [CrossRef] - Albadr, M.A.; Tiun, S.; Ayob, M.; AL-Dhief, F. Genetic Algorithm Based on Natural Selection Theory for Optimization Problems. Symmetry
**2020**, 12, 1758. [Google Scholar] [CrossRef] - Google Maps, Aerodata Inernational Surveys, GeoContent, Maxar Technologies—TT Cricuit Assen. Available online: https://www.google.com/maps/@52.9588834,6.5221272,1709m/data=!3m1!1e3!5m1!1e4 (accessed on 4 February 2023).

**Figure 6.**The measured power-loss map of the investigated powertrain with the optimized braking torque function: (

**a**) 3D power-loss map; (

**b**) contour plot of power loss.

**Figure 8.**Energy recovery in the case for varied mass optimization attempts: (

**a**) energy–time display; (

**b**) energy–distance display.

**Figure 10.**Energy recovery in the case for varied resistance force optimization attempts: (

**a**) energy–time display; (

**b**) energy–distance display.

**Figure 11.**Summarized recovered energy from the sensitivity analysis: (

**a**) mass variation; (

**b**) resistance force variation.

**Figure 12.**Elevation of TT Circuit Assen visualized on the topographical map from Ref. [23].

Parameter | SZEmission |
---|---|

Vehicle frame | carbon monocoque with paper honeycomb |

Front Suspension | double wishbone |

Rear Suspension | 4 link bridge |

Drag Coefficient | 0.1 |

Powertrain | BLDC with belt drive |

Applied Gear Ratio | 3.6 |

Drive Max Torque | 40 Nm |

Drive Max Speed | 302 rpm |

Nominal Voltage | 48 V |

Overall mass | 164.5 kg |

Parameter | Optimization Results |
---|---|

Function variable $\left({\mathrm{n}}_{\mathrm{var}}\right)$ | 13 |

Initial population (${\mathrm{N}}_{\mathrm{pop}}$) | 260 |

Generation | 71 |

Function count | 17,810 |

Recovered energy | −4121 J |

Recovery overall efficiency | 84% |

Braking distance | 64.75 m |

Parameter | Case 1 | Case 2 | Case 3 | Case 4 | Case 5 |
---|---|---|---|---|---|

Overall vehicle mass | 164.50 kg | 156.28 kg | 148.05 kg | 172.73 kg | 329.00 kg |

Mass ratio | 100% | 95% | 90% | 105% | 200% |

Optimization variable $\left({\mathrm{n}}_{\mathrm{var}}\right)$ | 13 | 13 | 13 | 13 | 13 |

Initial population (${\mathrm{N}}_{\mathrm{pop}}$) | 260 | 260 | 260 | 260 | 260 |

Generation | 71 | 85 | 98 | 93 | 100 |

Function count | 17,810 | 21,941 | 25,256 | 23,981 | 25,766 |

Recovered energy | −4121 J | −3915 J | −3709 J | −4327 J | −8242 J |

Recovery overall efficiency | 84% | 84% | 84% | 84% | 84% |

Braking distance | 64.75 m | 61.81 m | 58.59 m | 68.09 m | 129.60 m |

Parameter | Case 1 | Case 2 | Case 3 | Case 4 | Case 5 | Case 6 |
---|---|---|---|---|---|---|

Overall vehicle mass | 164.50 kg | 164.50 kg | 164.50 kg | 164.50 kg | 164.50 kg | 164.50 kg |

Resistance ratio | 100% | 90% | 80% | 50% | 0% | 200% |

Optimization variable $\left({\mathrm{n}}_{\mathrm{var}}\right)$ | 13 | 13 | 13 | 13 | 13 | 13 |

Initial population (${\mathrm{N}}_{\mathrm{pop}}$) | 260 | 260 | 260 | 260 | 260 | 260 |

Generation | 71 | 87 | 100 | 82 | 92 | 85 |

Function count | 17,810 | 22,451 | 25,766 | 21,176 | 23,726 | 21,941 |

Recovered energy | −4121 J | −4172 J | −4227 J | −4410 J | −4803 J | −3697 J |

Recovery overall efficiency | 84% | 84.2% | 84.4% | 85% | 85.6% | 82.7% |

Braking distance | 64.75 m | 67.42 m | 69.22 m | 78.21 m | 112.78 m | 52.12 m |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Pusztai, Z.; Kőrös, P.; Szauter, F.; Friedler, F.
Implementation of Optimized Regenerative Braking in Energy Efficient Driving Strategies. *Energies* **2023**, *16*, 2682.
https://doi.org/10.3390/en16062682

**AMA Style**

Pusztai Z, Kőrös P, Szauter F, Friedler F.
Implementation of Optimized Regenerative Braking in Energy Efficient Driving Strategies. *Energies*. 2023; 16(6):2682.
https://doi.org/10.3390/en16062682

**Chicago/Turabian Style**

Pusztai, Zoltán, Péter Kőrös, Ferenc Szauter, and Ferenc Friedler.
2023. "Implementation of Optimized Regenerative Braking in Energy Efficient Driving Strategies" *Energies* 16, no. 6: 2682.
https://doi.org/10.3390/en16062682