Analysis of optimal energy management strategies for the hybrid electric Formula 1 car under consideration of the finite battery size
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Contemporary Formula 1 racing cars feature a high-performance hybrid-electric powertrain. Beside the fuel tank, the battery is a second on board energy storage. The energy management strategy in terms of battery deployment must be carefully optimized in order to minimize the lap time on a given race circuit. In particular, the finite size of the battery must be taken into account, since the electric boosting and recuperation capabilities of the powertrain are restricted when the battery is depleted and fully charged, respectively. So far, this problem has scarcely been investigated in a time-optimal racing context. Using a previously developed convex optimization framework, we study the optimal solution to the energy management problem when either the lower or the upper bound on the battery state-of-charge is attained. First, we show that the operating strategy differs substantially for these two cases: Whilst it is optimal to hit the upper bound only in one particular time instant and then discharge the battery again, it can be kept at the lower bound for prolonged sections of the lap. We highlight that these differences are related to the interaction between the two electric motor-generator units of the powertrain. Second, based on Pontryagin’s minimum principle, we analyze the trajectory of the costate variable associated with the battery energy, which in such scenarios is crucial for the parameterization of an optimal control policy. The results underline the importance of correctly considering the cross-couplings between the battery deployment and the limit on electric recuperation imposed by the technical regulations. Show more
Organisational unit08840 - Onder, Christopher (Tit.-Prof.)
NotesConference lecture held on September 15, 2021.
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