Optimal Degree of Hybridization for Spark-Ignited Engines with Optional Variable Valve Timings

The electric hybridization of vehicles with an internal combustion engine is an effective measure to reduce CO2 emissions. However, the identification of the dimension and the sufficient complexity of the powertrain parts such as the engine, electric machine, and battery is not trivial. This paper investigates the influence of the technological advancement of an internal combustion engine and the sizing of all propulsion components on the optimal degree of hybridization and the corresponding fuel consumption reduction. Thus, a turbocharged and a naturally aspirated engine are both modeled with the additional option of either a fixed camshaft or a fully variable valve train. All models are based on data obtained from measurements on engine test benches. We apply dynamic programming to find the globally optimal operating strategy for the driving cycle chosen. Depending on the engine type, a reduction in fuel consumption by up to 32% is achieved with a degree of hybridization of 45%. Depending on the degree of hybridization, a fully variable valve train reduces the fuel consumption additionally by up to 9% and advances the optimal degree of hybridization to 50%. Furthermore, a sufficiently high degree of hybridization renders the gearbox obsolete, which permits simpler vehicle concepts to be derived. A degree of hybridization of 65% is found to be fuel optimal for a vehicle with a fixed transmission ratio. Its fuel economy diverges less than 4% from the optimal fuel economy of a hybrid electric vehicle equipped with a gearbox.