Numerical Strategies for Mixed-Integer Optimization of Power-Split and Gear Selection in Hybrid Electric Vehicles
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 m...
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| Veröffentlicht in: | IEEE transactions on intelligent transportation systems Jg. 24; H. 3; S. 1 - 17 |
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| Sprache: | Englisch |
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IEEE
01.03.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1524-9050, 1558-0016, 1558-0016 |
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| Abstract | 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 <inline-formula> <tex-math notation="LaTeX">{3.6}{\%}</tex-math> </inline-formula> cost reduction compared to the rule-based strategy, while still being within <inline-formula> <tex-math notation="LaTeX">\SI{1}{\%}</tex-math> </inline-formula> of the DP solution. Moreover, for the case studied RSA takes about <inline-formula> <tex-math notation="LaTeX">\SI{35}{\%}</tex-math> </inline-formula> less mean computation time compared to SRA, while both SRA and RSA being about <inline-formula> <tex-math notation="LaTeX">99</tex-math> </inline-formula> 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. |
|---|---|
| AbstractList | 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. 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. 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 <inline-formula> <tex-math notation="LaTeX">{3.6}{\%}</tex-math> </inline-formula> cost reduction compared to the rule-based strategy, while still being within <inline-formula> <tex-math notation="LaTeX">\SI{1}{\%}</tex-math> </inline-formula> of the DP solution. Moreover, for the case studied RSA takes about <inline-formula> <tex-math notation="LaTeX">\SI{35}{\%}</tex-math> </inline-formula> less mean computation time compared to SRA, while both SRA and RSA being about <inline-formula> <tex-math notation="LaTeX">99</tex-math> </inline-formula> 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. |
| Author | Murgovski, Nikolce Ganesan, Anand Gros, Sebastien |
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| SubjectTerms | Actuators Dynamic programming Electric vehicles Energy management Gears hybrid electric vehicle Hybrid electric vehicles Mechanical power transmission Mixed integer Mixed-Integer nonlinear optimal control Nonlinear control nonlinear MPC nonlinear programming numerical optimization Optimal control optimal gear selection optimal torque-split Optimization Predictive control Real-time systems Vehicle dynamics |
| Title | Numerical Strategies for Mixed-Integer Optimization of Power-Split and Gear Selection in Hybrid Electric Vehicles |
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