**1. Introduction**

Engines fueled with natural gas are considered possible alternatives to diesel engines when used in heavy-duty (HD) vehicles. Diesel engines, although efficient, have complicated issues regarding exhaust emissions, which compel developers to resort to rather sophisticated solutions to conform with regularly tightened emission requirements. Two components of exhaust gases may be highlighted as problematic, namely the nitrogen oxides and the particulate matter. To reduce the emissions of the former component to the level required by the present-day legislation, a selective catalytic reduction system should be employed, which involves a complex chemical reactor with a closed-loop control system and an onboard storage for the additional chemical agent (ammonia) [1]. Reducing the particulate matter requires using filters, which also constitute complex systems that involve an electronic control that regulates the process of regeneration [1]. It should also be noted that diesel engine operating regimes having minima of the two mentioned exhaust components generally do not coincide, which complicates the engine calibration [1]. In contrast, gas-fueled engines have drastically lower raw emissions of particulate matter [2–4] and can operate with the stoichiometric air-to-fuel ratio [5,6], which makes it possible to reduce emissions using less complex three-way catalytic converters [5] that provide more efficient abatement at lower costs. Fuel costs are generally considerably lower for gas (although this is not included in the scope of this work, which is only dedicated to the technical issues). The complicating aspect of replacing diesel engines with gas engines is the necessity of having an

onboard storage for the compressed or liquefied gas, which constitutes a complex system that has its own cost, service, safety, and other issues. Therefore, whether to choose a gas-based vehicle or stay conservative with a diesel-based option becomes a trade-off decision.

During the past few years, the National Research Center "NAMI" has been conducting an R&D project in cooperation with one of the country's major producers of heavy-duty vehicles. The project was aimed toward developing a gas-fueled engine family derived from the diesel engine that was newly developed by the aforementioned HD vehicle manufacturer. One can find the details on the project and its results in References [7–9]. The main outcomes of the project were the gas-fueled engines (see example in Figure 1) operating with the Otto and Miller thermodynamic cycles. The engines were installed in vehicles intended for long-haul operations (also shown in Figure 1) and tested in road conditions.

**Figure 1.** The developed gas engine at a test bench (**a**) and a heavy-duty (HD) vehicle equipped with the developed liquefied gas system (**b**).

The present work aimed to provide further elaboration of powertrains equipped with the developed gas engines, specifically on the prospects of their hybridization. The primary motivation behind this was to compare the fuel economy improvements that can be achieved by the hybridization of a diesel-based powertrain and a gas-based powertrain. It is assumed that such a powertrain modification could be relevant for those HD vehicles, whose operating schedules include a considerable share of city and suburban haulage since the major effect of HD powertrain hybridization is expected in conditions allowing for intensive use of regenerative braking, which is the most efficient tool for increasing the fuel economy of vehicles with large masses [10].The published studies (see, for example, [11–14]) have demonstrated that hybrid HD vehicles having a gross mass ranging 16 to 36 tons possess a significant fuel-saving potential in city driving conditions, especially in the case of full hybridization, which offers up to 35% fuel consumption reduction. The mild degree of hybridization is able to provide moderate fuel savings of about 10%.

The fuel economy of powertrains, which use different kinds of fuels, cannot be compared directly. One can evaluate the energy content of the consumed fuel [15], or the CO2 emissions of compared vehicles [12,15], or the economic aspect, i.e., fuel price [12,15,16]. This work employed another approach stemming from the goal of hybridization, namely to reduce the fuel consumption relative to the baseline powertrain. This allows for comparing the percentages of vehicle fuel economy obtained for each considered powertrain rather than the absolute values of fuel consumption. The study was conducted by means of simulations based on mathematical models validated using experimental data.

The layout of the article has the following structure. The next section (Section 2) substantiates the choice of the hybrid powertrain design to be considered in the study. Section 3 describes the mathematical models of the vehicle and the powertrain components. It is followed by a section (Section 4) overviewing the control strategy implemented within the hybrid powertrain model. The driving cycles employed in the simulations are presented in Section 5. The models of conventional

vehicles equipped with all the considered engines are validated in Section 6. The model analysis of the powertrain hybridization is presented in Section 7. Finally, Section 8 contains conclusions drawn from the conducted study and outlines further research.
