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Analysis of optimal battery state-of-charge trajectory patterns for blended mode of a parallel plug-in hybrid electric vehicle and a wide range of driving conditions


In Plug-in hybrid electric vehicles (PHEVs) typically combine several power sources, which are coordinated by means of an optimal energy management strategy. When considering the so-called blended mode, in which the engine is regularly used over a trip, the shape of battery state-of-charge (SoC) trajectory over travelled distance is of particular importance for achieving minimum fuel consumption. The paper deals with in-depth analysis of optimal SoC trajectories obtained by off-line control variable optimization of a PHEV-type city bus given in parallel (P2) powertrain configuration. The optimization is conducted by using a dynamic programming-based optimization algorithm for a wide range of driving cycles and operating scenarios. It is found that, as opposed to usually assumed linear-like near-optimal shape, the SoC vs. travelled distance trajectory can take on significantly different optimal shapes for non-zero road grade profiles or driving cycle with relatively long distance. The emphasis is on analyzing root causes for such behavior and its implications to fuel consumption.

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It is gratefully acknowledged that this work has been supported by the Croatian Science Foundation under the project No. IP-2018-01-8323 (Project Acronym: ACHIEVE, web site:

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Correspondence to Jure Soldo.

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Appendix 1: PHEV model parameters

Appendix 1: PHEV model parameters

The PHEV model parameters are given as follows: final drive ratio io = 4.72, effective tire radius rw = 0.481 m, rolling resistance factor R0 = 0.012, vehicle mass Mv = 12,635 kg, air density rair = 1.225 g/m3, frontal vehicle surface Af = 7.52 m2, vehicle aerodynamical drag factor Cd = 0.7, battery charge capacity Qmax = 30 Ah. The transmission gear ratios are listed in Table

Table 4 Transmission gear ratios


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Soldo, J., Škugor, B. & Deur, J. Analysis of optimal battery state-of-charge trajectory patterns for blended mode of a parallel plug-in hybrid electric vehicle and a wide range of driving conditions. Optim Eng 22, 1955–1977 (2021).

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  • Plug-in hybrid electric vehicle
  • Power management
  • Battery state-of-charge trajectory
  • Energy efficiency
  • Optimization
  • Dynamic programming
  • Analysis