Numerical Strategies for Mixed-Integer Optimization of Power-Split and Gear Selection in Hybrid Electric Vehicles
Artikel i vetenskaplig tidskrift, 2023

This paper presents numerical strategies for a computationally efficient energy management system that co-optimizes the power split and gear selection of a hybrid electric vehicle (HEV). We formulate a mixed-integer optimal control problem (MIOCP) that is transcribed using multiple-shooting into a mixed-integer nonlinear program (MINLP) and then solved by nonlinear model predictive control. We present two different numerical strategies, a Selective Relaxation Approach (SRA), which decomposes the MINLP into several subproblems, and a Round-n-Search Approach (RSA), which is an enhancement of the known ‘relax-n-round’ strategy. Subsequently, the resulting algorithmic performance and optimality of the solution of the proposed strategies are analyzed against two benchmark strategies; one using rule-based gear selection, which is typically used in production vehicles, and the other using dynamic programming (DP), which provides a global optimum of a quantized version of the MINLP. The results show that both SRA and RSA enable about 3.6% cost reduction compared to the rule-based strategy, while still being within 1% of the DP solution. Moreover, for the case studied RSA takes about 35% less mean computation time compared to SRA, while both SRA and RSA being about 99 times faster than DP. Furthermore, both SRA and RSA were able to overcome the infeasibilities encountered by a typical rounding strategy under different drive cycles. The results show the computational benefit of the proposed strategies, as well as the energy saving possibility of co-optimization strategies in which actuator dynamics are explicitly included.

nonlinear MPC

hybrid electric vehicle

Mixed-Integer nonlinear optimal control

energy management

optimal torque-split

numerical optimization

optimal gear selection

nonlinear programming


Anand Ganesan

Volvo Cars

Nikolce Murgovski

Norges teknisk-naturvitenskapelige universitet

Sebastien Gros

Chalmers, Elektroteknik, System- och reglerteknik

IEEE Transactions on Intelligent Transportation Systems

1524-9050 (ISSN) 1558-0016 (eISSN)

Vol. 24 3 3194-3210 1524-9050

En ny generation algoritmer för modern drivlinereglering

VINNOVA (2017-05506), 2018-09-01 -- 2024-12-31.


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