Abstract
In this article, we address the problem of energy management control design in hybrid electric vehicles (HEVs) to achieve minimum fuel consumption while optimally limiting battery degradation. We use Pontryagin’s minimum principle (PMP) to solve the optimal control problem. To the end of controlling battery aging to guarantee battery performances over 150,000 miles, a battery capacity loss reference trajectory is defined and a battery aging model is used by the optimizer. The resulting optimal supervisory control strategy is able to regulate both state of charge and capacity loss to their reference values. Simulation results conducted on a pre-transmission HEV show that the battery capacity loss can be regulated to achieve the long-term objective without sacrificing much fuel economy.
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Notes
- 1.
The dependence on time will be left implicit in this paper, for simplicity.
- 2.
Under this assumption, it is possible to write (9.20) as E dep = E dep(0) + V oc,batt ∫ 0 t I batt(SOC, P batt, θ) d τ and the state of charge as \(SOC = SOC(0) - \frac{1} {3600\ Q_{\mathrm{batt}}} \,\int _{0}^{t}I_{\mathrm{batt}}(SOC,P_{\mathrm{batt}},\theta )\,d\tau\). These two equations are then combined into (9.21).
- 3.
An important aspect of the tuning algorithm concerns the tolerances on the final state values. The approach followed in this work is as follows. Regarding SOC, a tolerance interval SOC tol = ±1 % is accepted for the charge-sustainability target. This means that all the values \(\Delta SOC \in [-1, 1]\%\) are considered within the tolerance, and as such they are defined sub-optimal values. The optimal value is only one, i.e. \(\Delta SOC^{{\ast}} = 0\), and it falls inside the tolerance interval. For Q loss a similar relative tolerance is considered and computed as follows. Given an SOC tol = ±1 % and a state of charge target of SOC ref = 50 %, the relative tolerance for SOC is given by \(SOC_{\mathrm{tol}}^{\mathrm{rel}} = \frac{\pm 1[\%]} {50\,\%} \,100 = \pm 2\,\%\); the relative tolerance for Q loss is then Q loss,tol rel = SOC tol rel = ±2 %. The target for capacity loss, as explained in Sect. 9.2.1, for 4 US06 driving cycles (d f = 32. 14mi) is Q loss,ref(d f ) = 0. 16205 %, which leads to \(Q_{\mathrm{loss,tol}} = \frac{0.16205\,\%} {100} \,\left (\pm 2\,\%\right ) = \pm 0.00324\,\%\). The sub-optimal values of capacity loss deviation are \(\Delta Q_{\mathrm{loss}} \in [-0.00324, 0.00324]\%\) and the optimal value is \(\Delta Q_{\mathrm{loss}}^{{\ast}} = 0\).
References
S. Onori, L. Serrao, G. Rizzoni, Hybrid Electric Vehicles Energy Management Strategies (Springer, Berlin/Heidelberg, 2016)
L. Guzzella, A. Sciarretta, Vehicle Propulsion Systems: Introduction to Modeling and Optimization (Springer, Berlin, 2007)
C. Chan, The state of the art of electric, hybrid, and fuel cell vehicles, Proc. IEEE 95, 704–718 (2007)
F. Lewis, V. Syrmos, Dynamic programming, in Optimal Control (Wiley, New York, 1995), pp. 315–347
S. Onori, Model-based optimal energy management strategies for hybrid electric vehicles, in Optimization and Optimal Control in Automotive Systems - Lect. Notes in Control Science, ed. by H. Waschl, I. Kolmanovsky, M. Steinbuch, L. del Re (Springer, New York, 2014), pp. 199–218
R. Cipollone, A. Sciarretta, Analysis of the potential performance of a combined hybrid vehicle with optimal supervisory control, in Computer Aided Control System Design, International Conference on Control Applications, International Symposium on Intelligent Control (ASME, New York, 2006), pp. 2802–2807
R. Bellman, Dynamic programming and Lagrange multipliers, in Proceedings of the National Academy of Sciences of the United States of America, vol. 42, p. 767, 1956
L. Pontryagin, V. Boltyanskii, R. Gamkrelidze, E. Mischchenko, The Mathematical Theory of Optimal Processes (Interscience, New York, 1962)
A. Sciarretta, L. Guzzella, Control of hybrid electric vehicles - A survey of optimal energy-management strategies. IEEE Control Syst. Mag. 27, 60–70 (2007)
J. Kessels, M. Koot, P. Van den Bosch, D. Kok, Online energy management for hybrid electric vehicles. IEEE Trans. Veh. Technol. 57, 3428–3440 (2008)
C. Musardo, B. Staccia, S. Midlam-Mohler, Y. Guezennec, G. Rizzoni, Supervisory control for NOx reduction of an HEV with a mixed-mode HCCI/CIDI engine, in Proceedings of the American Control Conference, vol. 6, 2005, pp. 3877–3881
N. Shidore, J. Kwon, A. Vyas, Trade-off between PHEV fuel efficiency and estimated battery cycle life with cost analysis, in Vehicle Power and Propulsion Conference. IEEE, 2009, pp. 669–677
S. Moura, J. Stein, H. Fathy, Battery health-conscious power management for plug-in hybrid electric vehicles via stochastic control, in Dynamic Systems and Control Conference (ASME, New York, 2010)
L. Serrao, S. Onori, A. Sciarretta, Y. Guezennec, G. Rizzoni, Optimal energy management of hybrid electric vehicles including battery aging, in American Control Conference (ACC), 2011, pp. 2125–2130
L. Tang, S. Onori, G. Rizzoni, Optimal energy management of HEVs with consideration of battery aging, in IEEE Transportation Electrification Conference and Expo (ITEC), 2014
S. Ebbesen, P. Elbert, L. Guzzella, Battery state-of-health perceptive energy management for hybrid electric vehicles. Trans. Veh. Technol. 61, 2893–2900, 2012
J. Wang, P. Liu, J. Hicks-Garner, E. Sherman, S. Soukiazian, M. Verbrugge, H. Tataria, J. Musser, P. Finamore, Cycle-life model for graphite-LiFePO4 cells. J. Power Sources, 196, pp. 3942–3948, 2011
T. Pham, P. van den Bosch, J. Kessels, R. Huisman, Cost-effective energy management for hybrid electric heavy-duty truck including battery aging, in Dynamic Systems and Control Conference (DSCC), 2013
G. Suri, S. Onori, A control-oriented cycle-life model for hybrid electric vehicle lithium-ion batteries. Energy 96, 644–653 (2016)
M. Broussely, S. Herreyre, P. Biensan, P. Kasztejna, K. Nechev, R. Staniewicz, Aging mechanism in li ion cells and calendar life predictions. J. Power Sources 97–98, 13–21 (2001)
S. Grolleau, A. Delaille, H. Gualous, P. Gyan, R. Revel, J. Bernard, E. Redondo-Iglesias, J. Peter, Calendar aging of commercial graphite/LiFePO4 cell - predicting capacity fade under time dependent storage conditions. J. Power Sources 255, 450–458 (2014)
F. Todeschini, S. Onori, G. Rizzoni, An experimentally validated capacity degradation model for Li-ion batteries in PHEVs applications, in 8th IFAC International Symposium on Fault Detection, Supervision and Safety of Technical Processes (2012)
S. Onori, P. Spagnol, V. Marano, Y. Guezennec, G. Rizzoni, A new life estimation method for lithium-ion batteries in plug-in hybrid electric vehicles applications, Int. J. Power Electron. 4 (3), 302–319 (2012)
2009 National Household Travel Survey. Available: http://nhts.ornl.gov/2009/pub/stt.pdf [Online]
K. Bayar, R. Biasini, S. Onori, G. Rizzoni, Modelling and control of a brake system for an extended range electric vehicle equipped with axle motors. Int. J. Veh. Des. 58, 399–426 (2012)
L. Serrao, S. Onori, G. Rizzoni, “ECMS as a realization of Pontryagin’s Minimum Principle for HEV control, in Proceedings of the American Control Conference (IEEE Press, New York, 2009), pp. 3964–3969
A. Allam, S. Onori, S. Marelli, C. Taborelli, Battery health management system for automotive applications: a retroactivity-based aging propagation study, in 2015 American Control Conference (ACC), July 2015, pp. 703–716
A. Cordoba Arenas, S. Onori, Y. Guezzennec, G. Rizzoni, Capacity and power fade cycle-life model for plug-in hybrid electric vehicle lithium-ion battery cells containing blended spinel and layered-oxide positive electrodes J. Power Sources 278, 473–483 (2015)
Acknowledgements
The authors would like to acknowledge the support received from Honda R&D co., Ltd., Japan and they would also like to thank Girish Suri for the help in improving the vehicle simulator.
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Marelli, S., Onori, S. (2016). Multi-Objective Supervisory Controller for Hybrid Electric Vehicles. In: Automotive Air Conditioning. Springer, Cham. https://doi.org/10.1007/978-3-319-33590-2_9
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DOI: https://doi.org/10.1007/978-3-319-33590-2_9
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