## 1 Introduction  
Road vehicles, both heavy and light duty, are primarily responsible for the pollutant and greenhouse gas emissions of the transportation sector. In recent decades, great research efforts have been made to reduce the environmental impact of road vehicles following two main strategies: the implementation of non-fossil fuels (bio-fuels, green hydrogen and electricity from renewable sources) and overall vehicle efficiency increases. Hybrid Electric Vehicles (HEV) are an example of the second strategy since they implement an Internal Combustion Engine (ICE), which is the main energy source, coupled with one or more electric machines and a battery pack that are meant to support the ICE during transient operations and to recover the vehicle's kinetic energy during deceleration phases. The power-split powertrain configuration is one of the most economic and efficient; it is endowed of a planetary gear set (the power split device) that couples together the ICE, two electric motor/generators and the driveshaft connected to the wheels. This particular arrangement allows to operate the engine independently from the wheels and then to exploit, for each road load condition, the best ICE efficiency operating condition [1, 2]. As far as greenhouse gasses emission reductions are concerned, the most promising alternative to fossil fuels, as an energy carrier, is represented by the so-called green hydrogen, produced by water electrolysis with renewable energy sources [3, 4]. A stoichiometric air-hydrogen mixture has a volumetric power density comparable with gaseous hydrocarbons, hydrogen can be stored and transported, and its combustion produces only water. There is a huge amount of literature on the use of hydrogen as a fuel in ICE [5, 6, 7, 8] exploring the pro and cons of its application; however, one undeniable conclusion is that the engine emissions are almost free from carbon dioxides (except the few coming from engine lubricant) and under fuel lean combustion operation, also free from nitrous monoxide [5]. Starting from the two important conclusions that hybridization improves the ICE engine efficiency and that the hydrogen-fueled ICE is the cleanest possible, the author explored the possibility to hybridize a hydrogen-fueled ICE in order to compare its efficiency with that of the same hybridized engine when fueled with gasoline; a series of numeric simulations, detailed in the subsequent section, was made with the purpose to compare the hydrogen-fueled ICE with the gasoline one in terms of the Brake Thermal Efficiency (BTE) and total energy consumption in a driving cycle (DC). The implementation of a hydrogen-fueled ICE in an HEV is not new, some examples can be found in the literature--both theoretical [9; 10; 11] and practical [12; 13; 14]--proving that the topic is attractive, and the present work fit perfectly into this trend. In [11], a fuel consumption reduction of 12.6% was reported for a hydrogen-fueled engine, in an HEV, compared to its gasoline counterpart; in [12], a 14.32% reduction in DC fuel consumption was reported for a hydrogen-enriched diesel engine, in an HEV, with respect to the standard diesel engine equipped in a conventional vehicle. In [13], a 20% fuel consumption reduction was reported when comparing a hydrogen-fueled HEV with a gasoline-fueled conventional vehicle. All the above-mentioned studies either refer to hydrogen-enriched conventional fuels or refer to existing conventional engines converted to hydrogen and implemented in HEV but are experimental studies; there are few pure theoretical studies proving the superiority of hydrogen over gasoline in an HEV based on engine fuel consumption maps as performed in this work. The results of the present theoretical study largely confirm the engine efficiency and fuel consumption improvements reported in the literature.