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RESEARCH PAPERS

Optimum Battery Size for Fuel Cell Hybrid Electric Vehicle With Transient Loading Consideration—Part II

[+] 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 to losses in the internal resistance and due to the charging efficiency, $ηbtt$(1).

Note that the gasoline equivalent fuel consumption is measured in $l∕100km$ and that the US fuel economy, measured in miles per gallon, is $CgasV∣US≈235.2∙(CgasV)−1mpg$.

Note that the PC does not ensure that $SoC(T)≈SoC(0)$. The PC is therefore allowed to recharge the battery after the end of the cycle. However, the average energy losses, which includes losses after the cycle, are calculated per second of the cycle length (in Table 2).

Note that if the OER limit, $λO2lim$, is set to zero, thus disregarding the OER dynamics, the controller would, for the mild and medium cycle, only use the FCS as power source making the battery useless.

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), 176-184 (Dec 20, 2006) (9 pages) doi:10.1115/1.2713779 History: Received May 03, 2006; Revised December 20, 2006

Abstract

This study presents a simplified model of a midsized vehicle powered by a polymer electrolyte membrane fuel cell stack together with a lead-acid battery as an energy buffer. The model is used with dynamic programming in order to find the optimal coordination of the two power sources while penalizing transient excursions in oxygen concentration in the fuel cell and the state of charge in the battery. The effects of the battery size on the overall energy losses for different drive cycles are determined, and 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 with constraints on dynamically varying variables. Finally, a causal nonpredictive controller is presented. The battery sizing results from the dynamic programming optimizations and the causal controller are compared.

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Figures

Figure 1

Signal flow overview of the two methods used to control the power split in the FCHEV. Top figure (a) shows the signal flow during the dynamic programming optimizations. Bottom figure (b) shows an overview of the proposed controller and the signal flows between the controller and the FCHEV model.

Figure 2

Oxygen excess ratio map used to calculate the OER in the fuel cell system when changing the reference current. The examples (a) and (b) shown in Fig. 3 are also marked.

Figure 3

Steps in the reference current and the resulting oxygen excess ratio. A step of 10A from 10A (a) and the resulting OER drop, and a step of 10A from 100A (b) and the resulting OER drop.

Figure 4

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

Figure 5

The OER distributions for different battery sizes for the three drive cycles. The percentages gives how much of the time is spent above the OER values.

Figure 6

Average electric energy expended in the battery and its equivalent hydrogen energy (left) together with the average electric energy loss due to the added mass and its equivalent hydrogen energy loss (right) (using DP)

Figure 7

The average energy loss per second in the three drive cycles (using DP). Equivalent hydrogen energy loss from added weight (Δm), expended energy in the battery (btt), and FCS energy loss (fcs). The solid line shows the gasoline equivalent fuel consumption CgasV.

Figure 8

Step response of the proportional controller with a time constant τ=30s, an OER limit λO2lim=1.75, and a vehicle with a battery pack with ten modules. The power demand Pdem with a step from 10kW to 30kw (top, solid) and the FCS output power (top, dashed). The resulting SoC and OER (middle two) and reference current (bottom).

Figure 9

Average energy loss for the proportional controller for the three drive cycles, with different battery sizes and time constants τ. The OER limit, λO2lim, is set to 1.75.

Figure 10

The average energy loss per second (left column) in the three drive cycles when the proportional controller with different time constants controls the SoC (fixed battery size). Equivalent hydrogen energy loss from added weight (Δm), expended energy in the battery (btt), and total FCS energy loss (fcs), which comprises of the FCS energy loss during the cycle duration (fcsT). Average FCS efficiency (right column) during the cycle duration (dashed) and total average FCS efficiency (solid) together with extra time used after the cycle duration (dashed dotted).

Figure 11

Average FCS efficiency, η¯fcs, (left) together with the reference current distribution (right) for different battery sizes and drive cycles (when the PC, with τc=50s, is controlling the SoC). The FCS efficiency curve is shown in the left part of the reference current distribution plot.

Figure 12

The average energy loss per second in the three drive cycles when the proportional controller, with τc=50s, controls the SoC. Equivalent hydrogen energy loss from added weight ElossΔm∕η¯fcs(Δm), expended energy in the battery Elossbtt∕η¯fcs (btt), and FCS energy loss Elossfcs∕η¯fcs (fcs). The solid line shows the gasoline equivalent fuel consumption CgasV.

Figure 13

Acceleration power demand (top) for a vehicle with ten battery modules for a portion of the medium FTP-72 cycle. The reference current (middle) and the battery state of charge (bottom) for both the DP (solid) and the PC with τc=50s (dotted).

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