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RESEARCH PAPERS

# Optimum Battery Size for Fuel Cell Hybrid Electric Vehicle— Part I

[+] Author and Article Information
Olle Sundström1

Measurement and Control Laboratory, Swiss Federal Institute of Technology, CH-8092 Zurich, Switzerlandolles@ethz.ch

Anna Stefanopoulou

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109annastef@umich.edu

Note that even though the DP ensures that $SoC(T)≈SoC(0)$, there is always energy expended in the battery $(Elossbtt>0)$ due the internal resistance and the charging efficiency, $ηbtt$17.

Note here that it would have been more meaningful to perform this investigation with a fixed vehicle net power and varying the power split ratio between the FCS and the battery. A scalable FCS model with accurate parasitic losses that allows the power split ratio to be varied is, however, not available.

Since $ElossΔm$ is the energy lost due to the added mass, the energy $Elossfcs$ includes both the electric energy lost in the FCS and the electric energy lost when providing the acceleration energy $Eaccm0$. However, we will show these as one throughout this study.

The US fuel economy, measured in miles per gallon, is $CgasV∣US≈235.2$$(CgasV)−1$$mpg$.

1

This work was done at the Fuel Cell Control System Laboratory at the University of Michigan, Ann Arbor. Olle Sundström is now affiliated with the Measurement and Control Laboratory at the Swiss Federal Institute of Technology, Zurich.

J. Fuel Cell Sci. Technol 4(2), 167-175 (Dec 20, 2006) (9 pages) doi:10.1115/1.2713775 History: Received May 03, 2006; Revised December 20, 2006

## Abstract

This study explores different hybridization levels of a midsized vehicle powered by a polymer electrolyte membrane fuel cell stack. The energy buffer considered is a lead-acid-type battery. The effects of the battery size on the overall energy losses for different drive cycles are determined when dynamic programming determines the optimal current drawn from the fuel cell system. The different hybridization levels are explored for two cases: (i) when the battery is only used to decouple the fuel cell system from the voltage and current demands from the traction motor to allow the fuel cell system to operate as close to optimally as possible and (ii) when regenerative braking is included in the vehicle with different efficiencies. The optimal power-split policies are analyzed to quantify all the energy losses and their paths in an effort to clarify the hybridization needs for a fuel cell vehicle. Results show that without any regenerative braking, hybridization will not decrease fuel consumption unless the vehicle is driving in a mild drive cycle (city drive with low speeds). However, when the efficiency of the regenerative braking increases, the fuel consumption (total energy losses) can be significantly lowered by choosing an optimal battery size.

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## Figures

Figure 1

Fuel cell hybrid electric vehicle components and the signal flow during the dynamic programming optimizations

Figure 2

Fuel cell system output power Pfcs (dashed line), hydrogen consumption WH2 (dotted line), and the fuel cell system efficiency ηfcs

Figure 3

Battery model characteristics: The open-circuit voltage (left) and internal resistance (right) both when charging (dashed line) and when discharging (solid line)

Figure 4

Worst-case efficiency ηbttwc (solid line), the maximum discharging output power Pbttdis∣max (dashed line), and the optimal SoC reference (dotted line) for different initial state of charge and discharging output power

Figure 5

FCS reference current Iref distribution and the FCS efficiency ηfcs for a vehicle with ten modules for the medium (FTP-72) drive cycle. The median value of the reference current is shown with dashed line together with the regions (50%, 95%, and 100%) around this median.

Figure 6

Average FCS efficiency η¯fcs (left) together with the reference current distribution (right) for different battery sizes and drive cycles (without regenerative braking). The FCS efficiency curve is shown in the left part of the reference current distribution plot.

Figure 7

Average expended electric energy in the battery and its hydrogen equivalent energy (left) together with the average electric energy loss due to the added mass and its hydrogen equivalent energy loss (right) without regenerative braking

Figure 8

Average hydrogen equivalent energy loss per second and its origins in the three drive cycles for different battery sizes (without regenerative braking). The solid line shows the gasoline equivalent fuel consumption.

Figure 10

Average energy expended in the battery and its hydrogen equivalent energy together with expended energy in the battery due to the regenerative braking and its hydrogen equivalent energy (with 50% regenerative braking)

Figure 9

Fuel cell system efficiency η¯fcs (left) together with the reference current distribution (right) for different battery sizes and drive cycles (with 50%regenerative braking). The FCS efficiency curve is shown in the left part of the reference current distribution plot.

Figure 11

Average hydrogen equivalent energy loss per second and its origins in the three drive cycles for different battery sizes (with 50% regenerative braking). The solid line shows the gasoline equivalent fuel consumption.

Figure 12

Average hydrogen equivalent energy loss per second and its origins in the three drive cycles for different battery sizes with regenerative braking efficiencies of 0% to 50%. The solid line shows the gasoline equivalent fuel consumption.

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