# Optimal Fuel Consumption Modelling, Simulation, and Analysis for Hybrid Electric Vehicles
); [EMAIL_ADDRESS] (J.C.)  
2 Faculty of Mechatronics, Informatics and Interdisciplinary Studies, Technical University of Liberec, 461 17 Liberec, Czech Republic; jradschlav@tul. was presented in [8]. A review of the HEV energy management strategy depending on road condition information was introduced in [9]. Lastly, recent progress on the HEV perspective on fuel management was presented in [10]. In reviewing the development trends of HEV powertrains and transmissions, the authors in [11] introduced updated trends of HEVs using optimal energy management. The authors in [12] investigated the effect of clutch slip losses and combustion engine start on the fuel management problem. In [13], the authors studied the modelling and fuel management of powertrain split on HEVs. Six operation modes of the vehicles were discussed for the impact of different fuel management strategies on energy and energy efficiency analysis were presented in [14]. The authors in [15] studied the efficiency optimization of regenerative braking systems for HEVs. Lastly, the authors in [16] conducted simulations of full HEVs running on standard driving cycles and the Urban Dynamometer Driving Schedule (UDDS). Reviewing the control strategy for HEVs, the authors in [17] presented control strategies for HEVs depending on different online driving patterns. This study investigates the feasibility of optimising control for different driving patterns, so that the vehicle can maintain a high level of optimality regardless of the driving pattern. Another control strategy for clutch engagement during mode changing for HEVs was presented in [18]. The authors in [19] present mode transition control for single shaft parallel HEVs using a model predictive control. This optimal control strategy can be achieved by using quadratic programming in the infinite prediction horizon. The authors in [20] conducted research on the multiphase mixed integer nonlinear optimal control of HEVs for a minimal fuel energy management strategy. Lastly, the authors in [21] presented the economic aspect of different HEVs in urban conditions to reduce fuel consumption and shorten travelling time. Recent studies on modelling fuel consumption for HEVs were reviewed. The authors in [22] conducted research on HEV benefits to improve the fuel economy and reduce emissions. Trends in the design, energy management, component sizing, fuel cost, and performance of HEVs are presented and analysed. A case study for HEV energy consumption modelling and estimation is presented in [23], where a driver model was set up to control the vehicle and represent human behaviour. Lastly, a proposal to accurately estimate the fuel consumption of HEVs, depending on real-world data consisting of instantaneous energy consumption, time variation in speed, and high-frequency traffic, was presented in [24]. Recent reviews on optimal fuel management still lack an optimal estimation of HEV fuel consumption depending on the size and tires. Therefore, this paper attempts to discover the elements that affect the fuel consumption and determines the best HEV model with sizes and tires for achieving the best fuel consumption. This paper is organised as follows: Section 2 presents HEV drivetrain modelling; Section 3 presents HEV scheme simulations; Section 4 presents fuel economy modelling and regressions; and, lastly, Section 5 draws the conclusions. In this paper, most HEV dynamics, modelling, calculations, energy equations, and simulation schemes refer to our textbook [25] and to [26, 27]. The updated Internet sources for different HEVs used in the online references are [28, 29, 30, 31, 32, 33, 34, 35]. The latest mathematical formulations are referred to in [36, 37, 38, 39].