{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:55:26Z","timestamp":1760237726324,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,6,11]],"date-time":"2020-06-11T00:00:00Z","timestamp":1591833600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["WEVJ"],"abstract":"<jats:p>This paper presents a braking strategy analysis for a Formula SAE electric race car. The proposed braking strategy aims to increase the recovery energy by a relevant distribution of the braking forces between the rear and front wheels. A mathematical model of the car is presented, and a simulation is performed in Matlab-Simulink. The model is organized using the energetic macroscopic representation graphical formalism. A real racetrack driving cycle is considered. Three braking strategies are compared considering the energy recovery and the vehicle stability. The simulation results show that the proposed strategy enables higher energy recovery while avoiding locking on both rear and front wheels. As in such a race the driving range is fixed, the reduction in energy consumption can be used to reduce the battery size. The battery weight can thus be decreased to improve the vehicle performance during competition.<\/jats:p>","DOI":"10.3390\/wevj11020045","type":"journal-article","created":{"date-parts":[[2020,6,12]],"date-time":"2020-06-12T05:02:24Z","timestamp":1591938144000},"page":"45","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Regenerative Braking Strategy of a Formula SAE Electric Race Car Using Energetic Macroscopic Representation"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3439-9577","authenticated-orcid":false,"given":"Andr\u00e9s Camilo","family":"Henao-Mu\u00f1oz","sequence":"first","affiliation":[{"name":"Coimbra Polytechnic-ISEC, 3030-199 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3514-4544","authenticated-orcid":false,"given":"Paulo","family":"Pereirinha","sequence":"additional","affiliation":[{"name":"Coimbra Polytechnic-ISEC, 3030-199 Coimbra, Portugal"},{"name":"INESC-Coimbra DEEC, 3030-790 Coimbra, Portugal"}]},{"given":"Alain","family":"Bouscayrol","sequence":"additional","affiliation":[{"name":"Univ. Lille, Centrale Lille, Arts et M\u00e9tiers Paris Tech, HEI, EA 2697 \u2013 L2EP, F-59000 Lille, France"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,11]]},"reference":[{"key":"ref_1","unstructured":"European Commission (2016). A European Strategy for Low-Emission Mobility, European Commission."},{"key":"ref_2","unstructured":"Niestadt, M., and Bj\u00f8rn\u00e5vold, A. (2019). Electric Road Vehicles in the European Union\u2014Trends, Impacts and Policies, European Parliamentary Research Service (EPRS)."},{"key":"ref_3","unstructured":"IEA (2019). Tracking Transport, IEA."},{"key":"ref_4","unstructured":"IEA (2018). Global EV Outlook 2018. Towards Cross-modal Electrification, IEA Publications."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1504\/IJEHV.2015.071081","article-title":"Development of regenerative braking for electric vehicles in China: A review","volume":"7","author":"Guo","year":"2015","journal-title":"Int. J. Electr. Hybrid Veh."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Ehsani, M., Gao, Y., Longo, S., and Ebrahimi, K.M. (2018). Modern Electric, Hybrid Electric, and Fuel Cell Vehicles, Taylor & Francis Group. [3rd ed.].","DOI":"10.1201\/9781420054002"},{"key":"ref_7","unstructured":"Benson, K.W., Fraser, D.A., Hatridge, S.L., Monaco, C.A., Ring, R.J., Sullivan, C.R., and Taber, P.C. (2005, January 7). The Hybridization of a Formula Race Car. Proceedings of the IEEE Vehicle Power and Propulsion Conference, Chicago, IL, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1240","DOI":"10.1016\/j.apenergy.2016.09.057","article-title":"The dynamic performance and economic benefit of a blended braking system in a multi-speed battery electric vehicle","volume":"183","author":"Ruan","year":"2016","journal-title":"Appl. Energy"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Xiao, B., Lu, H., Wang, H., Ruan, J., and Zhang, N. (2017). Enhanced Regenerative Braking Strategies for Electric Vehicles: Dynamic Performance and Potential Analysis. Energies, 10.","DOI":"10.3390\/en10111875"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/j.enconman.2016.05.094","article-title":"Comparison between two braking control methods integrating energy recovery for a two-wheel front driven electric vehicle","volume":"122","author":"Itani","year":"2016","journal-title":"Energy Convers. Manag."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.mechatronics.2018.11.006","article-title":"Torque optimization control for electric vehicles with four in-wheel motors equipped with regenerative braking system","volume":"57","author":"Xu","year":"2019","journal-title":"Mechatronics"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/j.energy.2017.12.138","article-title":"Hierarchical control strategy with battery aging consideration for hybrid electric vehicle regenerative braking control","volume":"145","author":"Wu","year":"2018","journal-title":"Energy"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/j.enconman.2016.04.044","article-title":"New evaluation methodology of regenerative braking contribution to energy efficiency improvement of electric vehicles","volume":"119","author":"Qiu","year":"2016","journal-title":"Energy Convers. Manag."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.energy.2018.02.046","article-title":"A novel control strategy of regenerative braking system for electric vehicles under safety critical driving situations","volume":"149","author":"Qiu","year":"2018","journal-title":"Energy"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/j.mechatronics.2017.06.005","article-title":"Control of regenerative braking systems for four-wheel-independently-actuated electric vehicles","volume":"50","author":"Chen","year":"2018","journal-title":"Mechatronics"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1177\/0954407015581082","article-title":"Cooperative control of regenerative braking and friction braking for a hybrid electric vehicle","volume":"230","author":"Kumar","year":"2016","journal-title":"Proc. Inst. Mech. Eng. Part D J. Automob. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"828","DOI":"10.4271\/2008-01-1561","article-title":"Effect of Different Regenerative Braking Strategies on Braking Performance and Fuel Economy in a Hybrid Electric Bus Employing CRUISE Vehicle Simulation","volume":"1","author":"Sangtarash","year":"2009","journal-title":"SAE Int. J. Fuels Lubr."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Le Solliec, G., Chasse, A., and Geamanu, M. (2013, January 4\u20137). Regenerative braking optimization and wheel slip control for a vehicle with in-wheel motors. Proceedings of the 7th IFAC Symposium on Advances in Automotive Control, Tokyo, Japan.","DOI":"10.3182\/20130904-4-JP-2042.00043"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.repl.2016.04.070","article-title":"Formula student electric: Checking out the future of automotive engineering","volume":"60","author":"Mathijsen","year":"2016","journal-title":"Reinf. Plast."},{"key":"ref_20","unstructured":"SAE International (2019, August 30). About Formula SAE\u00ae\u00ae Series. Available online: https:\/\/www.sae.org\/attend\/student-events\/formula-sae-electric\/about."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Hall, T.J. (2017). An Analysis of Braking Behavior in Formula-E Racing, SAE International.","DOI":"10.4271\/2017-01-2533"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.robot.2018.12.010","article-title":"Testing of a torque vectoring controller for a Formula Student prototype","volume":"113","author":"Antunes","year":"2019","journal-title":"Robot. Auton. Syst."},{"key":"ref_23","unstructured":"Saurabh, Y.S., Kumar, S., Jain, K.K., Behera, S.K., Gandhi, D., Raghavendra, S., and Kalita, K. (2015, January 14\u201317). Design of Suspension System for Formula Student Race Car. Proceedings of the International Conference on Vibration Problems, ICOVP, Guwahati, India."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Chepkasov, S., Markin, G., and Akulova, A. (2016, January 19\u201320). Suspension Kinematics Study of the \u201cFormula SAE\u201d Sports Car. Proceedings of the International Conference on Industrial Engineering, ICIE, Yekaterinburg, Russia.","DOI":"10.1016\/j.proeng.2016.07.288"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Boretti, A. (2013). Kinetic Energy Recovery Systems for Racing Cars, SAE International.","DOI":"10.4271\/PT-159"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Bouscayrol, A., Hautier, J.-P., and Lemaire-Semail, B. (2012). Graphic Formalisms for the Control of Multi-Physical Energetic Systems: COG and EMR. Systemic Design Methodologies for Electrical Energy Systems, ISTE Willey Editions.","DOI":"10.1002\/9781118569863.ch3"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Transi, T., Pereirinha, P.G., Bouscayrol, A., and Degano, M. (2019, January 10). Study of Regenerative Braking Effects in a Small Electric Race Car using Energetic Macroscopic Representation. Proceedings of the International Young Engineers Forum (YEF-ECE), Costa da Caparica, Portugal.","DOI":"10.1109\/YEF-ECE.2019.8740815"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Transi, T., Pereirinha, P.G., Bouscayrol, A., Degano, M., and Henao-Mu\u00f1oz, A.C. (2019, January 14\u201317). Hardware-In-the-Loop Emulation of a Small Electric Race Car Using Energetic Macroscopic Representation. Proceedings of the IEEE Vehicle Power and Propulsion Conference (VPPC), Hanoi, Vietnam.","DOI":"10.1109\/VPPC46532.2019.8952276"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Montesinos-Miracle, D., Fontan-Tebar, C., and Vidal-Salvia, H. (2014, January 27\u201330). Simulation of an Electric Racing Car Using Energetic Macroscopic Representation. Proceedings of the IEEE Vehicle Power and Propulsion Conference (VPPC), Coimbra, Portugal.","DOI":"10.1109\/VPPC.2014.7007130"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"LeBel, F.-A., Messier, P., Pelletier, L., and Trovao, J.P. (2017, January 11\u201314). Benefits of Regenerative Braking for an Electric Superbike using Energetic Macroscopic Representation. Proceedings of the IEEE Vehicle Power and Propulsion Conference (VPPC), Belfort, France.","DOI":"10.1109\/VPPC.2017.8330986"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Guo, J., Wang, J., and Cao, B. (2009, January 28\u201331). Study on Braking Force Distribution of Electric Vehicles. Proceedings of the Asia-Pacific Power and Energy Engineering Conference, Wuhan, China.","DOI":"10.1109\/APPEEC.2009.4918806"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Sparacino, A.R., Reed, G.F., Kerestes, R.J., Grainger, B.M., and Smith, Z.T. (2012, January 22\u201326). Survey of Battery Energy Storage Systems and Modeling Techniques. Proceedings of the 2012 IEEE Power and Energy Society General Meeting, San Diego, CA, USA.","DOI":"10.1109\/PESGM.2012.6345071"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1109\/TVT.2013.2280727","article-title":"Comparison of Different Models and Simulation Approaches for the Energetic Study of a Subway","volume":"63","author":"Mayet","year":"2014","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"11420","DOI":"10.1109\/TVT.2019.2949215","article-title":"Impact of the Velocity Profile on Energy Consumption of Electric Vehicles","volume":"68","author":"Anatole","year":"2019","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.4130\/jaev.6.1097","article-title":"Energetic Macroscopic Representation and Inversion-based Control: Application to an Electric Vehicle with an Electrical Differential","volume":"6","author":"Chen","year":"2008","journal-title":"J. Asian Electr. Veh."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Xu, J., and Zhang, X. (2016, January 12\u201315). Optimization Algorithm for Vehicle Braking Force Distribution of Front and Rear Axles Based on Brake Strength. Proceedings of the World Congress on Intelligent Control and Automation (WCICA), Guilin, China.","DOI":"10.1109\/WCICA.2016.7578257"},{"key":"ref_37","unstructured":"(2019, July 26). OptimumG Vehicle Dynamics Solutions, \u201cOptimumLap\u201d. Available online: http:\/\/www.optimumg.com\/software\/optimumlap\/."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.est.2016.08.012","article-title":"Characterization and comparison between lithium iron p hosphate and lithium-polymers batteries","volume":"8","author":"Sergi","year":"2016","journal-title":"J. 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