An Energy Scheduling Algorithm for New Energy Vehicles Based on Continuous-Time Differential Equation Modeling and Model Predictive Control

Xue Li

Abstract


The core contradiction in energy scheduling for new energy vehicles arises from a mismatch between the high-dimensional nonlinear characteristics of the energy system under complex dynamic driving conditions and the dual requirements of computational efficiency and accuracy in real-time optimization scheduling.To address this issue, this paper presents an energy scheduling algorithm based on continuous-time differential equation modeling within a model predictive control framework. A continuous-time differential equation model incorporating battery SOC (State of Charge) dynamics, vehicle dynamics, and regenerative braking is established, and an MPC (Model Predictive Control) framework is embedded to construct a physically constrained finite-time optimal control problem. Efficient numerical discretization and solution strategies are employed to achieve real-time optimization. Simulation and hardware-in-the-loop testing show that under four typical operating conditions, the algorithm's energy consumption per 100 km is 15.2 to 21.5 kWh/100 km, lower than regular strategies, classic MPC, and DQN (Deep Q-Network). The SOC change rate is reduced to between 0.35% and 1.25%, meeting the millisecond-level real-time requirements of the onboard system. This method combines physical interpretability and engineering deployability, and has application value in intelligent electric vehicle energy management, V2G (Vehicle-to-Grid) scheduling, and personalized energy-saving driving systems.

Keywords


Differential Equation Optimization; Energy Dispatch Algorithm; Model Predictive Control; Battery SOC Dynamic Modeling; New Energy Vehicles

Full Text:

PDF

References


S. Qin, Y. Xiong, and X. Wang, “Can non-subsidised policies for new energy vehicles improve the quality of enterprise innovation? evidence from China,” Asian Journal of Technology Innovation, vol. 33, no. 2, pp. 655-687, 2025.

Z. Yang, H. Huang, and F. Lin, “Sustainable electric vehicle batteries for a sustainable world: perspectives on battery cathodes, environment, supply chain, manufacturing, life cycle, and policy,” Advanced Energy Materials, vol. 12, no. 26, p. 2200383, 2022.

W. Zhao and B. Luethje, “Disintegration, core competency, and industry structure: Chinese automotive OEMs in electrification and digitalisation,” International Journal of Automotive Technology and Management, vol. 25, no. 2, pp. 148-166, 2025.

Y. Yi, Z. Y. Sun, B.-A. Fu, W.-Y. Tong, and R.-S. Huang, “Accelerating towards sustainability: policy and technology dynamic assessments in China’s road transport sector,” Sustainability, vol. 17, no. 8, p. 3668, 2025.

M. S. H. Lipu, M. A. Hannan, A. Hussain, M. H. Saad, A. Ayob, M. Uddin, and F. Blaabjerg, “Battery management, key technologies, methods, issues, and future trends of electric vehicles: a pathway toward achieving sustainable development goals,” Batteries, vol. 8, no. 9, p. 119, 2022.

H. E. Ghadbane, S. Barkat, A. Houari, S. Ferahtia, A. Djerioui, and T. Mesbahi, “A new energy management strategy for electric vehicles based on optimal adaptive state machine control,” Smart Grids and Sustainable Energy, vol. 9, no. 2, p. 28, 2024.

B. Huang, W. Yu, M. Ma, X. Wei, and G. Wang, “Artificial-intelligence-based energy management strategies for hybrid electric vehicles: a comprehensive review,” Energies, vol. 18, no. 14, p. 3600, 2025.

P. Pillai, S. Sundaresan, P. Kumar, K. R. Pattipati, and B. Balasingam, “Open-circuit voltage models for battery management systems: a review,” Energies, vol. 15, no. 18, p. 6803, 2022.

S. Liu, Z. Li, H. Ji, L. Wang, and Z. Hou, “A novel anti-saturation model-free adaptive control algorithm and its application in the electric vehicle braking energy recovery system,” Symmetry, vol. 14, no. 3, p. 580, 2022.

A. Recalde, R. Cajo, W. Velasquez, and M. S. Alvarez-Alvarado, “Machine learning and optimization in energy management systems for plug-in hybrid electric vehicles: a comprehensive review,” Energies, vol. 17, no. 13, p. 3059, 2024.

L. Zhu, F. Tao, Z. Fu, M. Li, and G. Deng, “Safety-involved co-optimization of speed trajectory and energy management for fuel cell-battery electric vehicle in car-following scenarios,” Complex & Intelligent Systems, vol. 11, no. 1, p. 89, 2025.

A. R. Singh, R. S. Kumar, M. Bajaj, C. B. Khadse, and I. Zaitsev, “Machine learning-based energy management and power forecasting in grid-connected microgrids with multiple distributed energy sources,” Scientific Reports, vol. 14, no. 1, p. 19207, 2024.

X. Guo, X. Zhang, J. Dong, and X. Yang, “Optimal allocation of urban new energy vehicles and traditional energy vehicles considering pollution and cost,” Environment, Development and Sustainability, vol. 26, no. 3, pp. 6007-6026, 2024.

J. Uralde, O. Barambones, A. del Rio, I. Calvo, and E. Artetxe, “Rule-based operation mode control strategy for the energy management of a fuel cell electric vehicle,” Batteries, vol. 10, no. 6, p. 214, 2024.

J. Zhuang, P. Li, L. Liu, H. Ma, and X. Cheng, “Energy management strategy for hybrid electric vehicles based on experience-pool-optimized deep reinforcement learning,” Applied Sciences, vol. 15, no. 17, p. 9302, 2025.

Q. Zhang and X. Fu, “A neural network fuzzy energy management strategy for hybrid electric vehicles based on driving cycle recognition,” Applied Sciences, vol. 10, no. 2, p. 696, 2020.

E. Türker, E. Bulut, A. Kahraman, M. Çak?c?, and F. Öztürk, “Estimation of energy management strategy using neural-network-based surrogate model for range extended vehicle,” Applied Sciences, vol. 12, no. 24, p. 12935, 2022.

C. Du, S. Huang, Y. Jiang, D. Wu, and Y. Li, “Optimization of energy management strategy for fuel cell hybrid electric vehicles based on dynamic programming,” Energies, vol. 15, no. 12, p. 4325, 2022.

R. Schmid, J. Buerger, and N. Bajcinca, “Energy management strategy for plug-in-hybrid electric vehicles based on predictive PMP,” IEEE Transactions on Control Systems Technology, vol. 29, no. 6, pp. 2548-2560, 2021.

B. Zhao, R. Liu, D. Shi, S. Li, Q. Cai, and W. Shen, “Optimal control strategy of path tracking and braking energy recovery for new energy vehicles,” Processes, vol. 10, no. 7, p. 1292, 2022.

H.-B. Yuan, W.-J. Zou, S. Jung, and Y.-B. Kim, “Optimized rule-based energy management for a polymer electrolyte membrane fuel cell/battery hybrid power system using a genetic algorithm,” International Journal of Hydrogen Energy, vol. 47, no. 12, pp. 7932-7948, 2022.

S. Singh, S. N. Singh, and A. N. Tiwari, “PMSM drives and its application: an overview,” Recent Advances in Electrical & Electronic Engineering, vol. 16, no. 1, pp. 4-16, 2023.

Y. Ji, J. Zhang, C. He, X. Hou, W. Liu, and J. Han, “Wheel braking pressure control based on central booster electrohydraulic brake-by-wire system,” IEEE Transactions on Transportation Electrification, vol. 9, no. 1, pp. 222-235, 2022.

X. Zhang, J. Hou, Z. Wang, and Y. Jiang, “Study of SOC estimation by the ampere-hour integral method with capacity correction based on LSTM,” Batteries, vol. 8, no. 10, p. 170, 2022.

Z. Qin, L. Chen, M. Hu, and X. Chen, “A lateral and longitudinal dynamics control framework of autonomous vehicles based on multi-parameter joint estimation,” IEEE Transactions on Vehicular Technology, vol. 71, no. 6, pp. 5837-5852, 2022.

C. Li, Y. Zhang, H. Wang, J. Sun, Z. Li, and Y. Xu, “A review of electro-mechanical brake (EMB) system: structure, control and application,” Sustainability, vol. 15, no. 5, p. 4514, 2023.

N. T. Anh, C.-K. Chen, and X. Liu, “An efficient regenerative braking system for electric vehicles based on a fuzzy control strategy,” Vehicles, vol. 6, no. 3, pp. 1496-1512, 2024.

J. Xiao, X. Li, H. Wang, D. Long, Y. Liu, and J. Liu, “Understanding and applying coulombic efficiency in lithium metal batteries,” Nature Energy, vol. 5, no. 8, pp. 561-568, 2020.

D. Salazar and M. Garcia, “Estimation and comparison of SOC in batteries used in electromobility using the Thevenin model and Coulomb ampere counting,” Energies, vol. 15, no. 19, p. 7204, 2022.

Y. Wang, C. Li, Q. Sun, and Y. Chang, “Research on SOC estimation of lithium-ion batteries based on robust full order proportional integral observer,” International Journal of Electrochemical Science, vol. 19, no. 8, p. 100645, 2024.

M. Aida, “Fourth-order Runge-Kutta method for solving applications of system of first-order ordinary differential equations,” Enhanced Knowledge in Sciences and Technology, vol. 2, no. 1, pp. 517-526, 2022.

X. Xiong, Y. Bai, R. Shi, S. Kamal, Y. Wang, and Y. Lou, “Discrete-time twisting algorithm implementation with implicit-Euler ZOH discretization method,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 69, no. 8, pp. 3435-3439, 2022.

N.-A. Nguyen, P.-H. La, and S.-J. Choi, “Novel high-speed state-of-charge alignment algorithm for EV battery maintenance,” IEEE Transactions on Industrial Electronics, vol. 71, no. 12, pp. 15724-15733, 2024.

K. Chang, Y. Zhang, H. Wang, X. Liu, J. Li, and Q. Chen, “Novel energy management strategy for fuel cell hybrid vehicles considering power following based on improved deep Q-network,” Automotive Innovation, vol. 8, no. 4, pp. 1031-1046, 2025.




DOI (PDF): https://doi.org/10.20508/ijrer.v16i2.17008.g9224

Refbacks

  • There are currently no refbacks.


Online ISSN: 1309-0127

Publisher: Gazi University

IJRER is indexed in EI Compendex, SCOPUS, EBSCO, WEB of SCIENCE (Clarivate Analytics)and CrossRef.

IJRER has been indexed in Emerging Sources Citation Index from 2016 in web of science.

WEB of SCIENCE in 2025; 

h=35,

Average citation per item=6.59

Last three Years Impact Factor=(1947+1753+1586)/(146+201+78)=5286/425=12.43

Category Quartile:Q4