Grey Wolf Optimizer-Based Optimal Torque Control and Power Splitting for Parallel Hybrid Electric Vehicles

Abstract

A new energy management scheme for the optimal torque distribution and power splitting of a parallel Hybrid Electric Vehicle (HEV) using the Grey Wolf Optimizer (GWO) is presented in this paper. The method proposed in this approach minimizes fuel consumption and battery energy depletion while meeting the drivetrain constraints such as the engine torque limit, motor torque limit, battery State of Charge (SOC) limits, and speed tracking limits for the vehicle. The optimization of the control parameter which controls the power-split ratio between the Internal Combustion Engine (ICE) and the Electric Motor (EM) is carried out over the New European Driving Cycle (NEDC) using GWO. The simulations are performed in MATLAB/ADVISOR and the results are compared to Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA), Genetic Algorithm (GA) and Differential Evolution (DE). GWO gives a fuel economy of 16.82 km/L on the final SOC of 0.78, which is best compared to all competing algorithms with regard to convergence speed, solution quality and robustness. The results show the validity of GWO as an effective and computationally efficient framework for energy management in parallel HEVs.

Introduction

The text discusses the challenges of wind energy systems and the role of battery storage and advanced control techniques in improving stability and reliability. Although wind energy is a clean and widely available renewable source, its output is highly variable due to changing wind speeds, which leads to power fluctuations, voltage instability, and reliability issues, especially in standalone systems.

To address these problems, the study proposes integrating a Wind Energy Conversion System (WECS) with a Battery Energy Storage System (BESS). The battery stores excess energy during high wind conditions and supplies power during low wind periods, ensuring continuous and stable energy delivery. The system also uses key control strategies such as Maximum Power Point Tracking (MPPT) for optimal energy extraction, pitch angle control for turbine protection during high wind speeds, and PI-based DC-link voltage regulation for stable power output.

The system is modeled and simulated in MATLAB/Simulink and includes components such as a wind turbine, Self-Excited Induction Generator (SEIG), rectifier, DC–DC converter, and battery storage unit. Simulation results show that the integrated WECS-BESS system effectively reduces power fluctuations, improves voltage regulation, enhances system stability, and provides reliable power for standalone applications.

Conclusion

In this paper, a Grey Wolf Optimizer (GWO) based energy management approach to the optimal torque distribution in a parallel Hybrid Electric Vehicle (pHEV) has been presented. The optimization algorithm ensures minimisation of a composite objective function related to fuel consumption under the NEDC and deviation of the battery SOC from the initial battery state with realistic drivetrain constraints. GWO\'s hierarchical 3-wolf guidance mechanism is well suited to balance global exploration and local exploitation leading to consistent convergence to high quality solutions. The peak fuel economy of GWO is 16.82km/L in MATLAB/ADVISOR simulation that is 35% improvement over a conventional vehicle and 2.3% improvement over the best competing algorithm (GSA). Among five algorithms tested, GWO is able to achieve the best SOC preservation, lowest solution variance (CoV=0.11%), and the fastest convergence (52 iterations) on average. The future plans are to expand the GWO framework to multi-objective optimization with NO? and particulate emission minimization, dynamic adaptation of the GWO and co-optimization of the sizing of the powertrain components based on the velocity driving pattern. Plug-in HEV architectures are also to be applied and validated on the Worldwide Harmonized Light-duty vehicle Test Cycle (WLTC).

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Copyright

Copyright © 2026 Abhik Hazra, Mihir Kumar Manna, Arnab Ganguly, Amartya Roy, Rakesh Naskar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.