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Research Papers

# An Empirical Stationary Fuel Cell Model Using Limited Experimental Data for Identification

[+] Author and Article Information
M. Meiler

Deutsche ACCUmotive GmbH & Co. KG,
Neue Str. 95,
D-73230 Kirchheim/Teck, Germany
e-mail: markus.meiler@daimler.com

E. P. Hofer

University of Ulm,
Albert-Einstein-Allee 41,
D-89081 Ulm, Germany
e-mail: eberhard.hofer@uni-ulm.de

A. Nuhic

Deutsche ACCUmotive GmbH & Co. KG,
Neue Str. 95,
D-73230 Kirchheim/Teck, Germany

O. Schmid

Daimler AG,
Neue Str. 95,
D-73230 Kirchheim/Teck, Germany
e-mail: ottmar.schmid@daimler.com

1Corresponding author.

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF FUEL CELL SCIENCE AND TECHNOLOGY. Manuscript received April 1, 2011; final manuscript received April 27, 2012; published online October 17, 2012. Editor: Nigel M. Sammes.

J. Fuel Cell Sci. Technol 9(6), 061001 (Oct 17, 2012) (10 pages) doi:10.1115/1.4007195 History: Received April 01, 2011; Revised April 27, 2012

## Abstract

New technologies for efficient operation of fuel cells require modern techniques in system modeling. Such fuel cell models do not require giving any information about physical mechanisms or internal states of the system. They must be rather precise and should consume less computing time. From the point of view of system theory, polymer electrolyte membrane fuel cells (PEMFC) are multiple input and single output (MISO) systems. The inputs of a fuel cell are the drawn current, the gas pressures at anode and cathode side, and the humidity of these gases which influence the system output, namely the cell voltage, in a nonlinear way. The state of the art in the industry is to describe such nonlinear systems by the usage of lookup tables with a large amount of data. An alternative way to model the input-output behavior of nonlinear systems is the usage of so called black-box and gray-box model approaches. In the last decade, artificial neuronal networks (ANN) became more popular in black-box modeling of nonlinear systems with multiple inputs. Further, if some of the internal processes of a nonlinear system can be mathematically described, a gray-box model is more preferred. In the first part of this paper, the suitability of ANN's in the form of a multilayer perceptron (MLP) network with different numbers of hidden neurons is investigated. A way to confirm the validity for the identified network was worked out. In the second part of this contribution, a gray-box model, valid for a large operating area, based on published semi-empirical models is introduced. Six experimental campaigns for parameter identification and model validation were carried out. The five inputs previously described were varied in a wide range to cover a large operating range. In the last part of this paper, both modeling approaches are investigated with respect to their ability to identify model parameters using a limited number of experimental data.

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## Figures

Fig. 1

Basic structure of a MLP network

Fig. 2

Procedure of system identification [17]

Fig. 3

Results of MLP network size optimization

Fig. 4

Identification results campaign 1 (see Table 3: ○ 1, □ 3, ● 5, ▪ 7)

Fig. 5

Identification results campaign 2 (see Table 3: ○ 1, □ 3, ● 5, ▪ 7)

Fig. 6

Identification results campaign 3 (see Table 3: ○ 1, □ 3, ● 5, ▪ 7)

Fig. 7

Identification results campaign 4 (see Table 4: ○ 8, □ 10, ● 12)

Fig. 8

Identification results campaign 5 (see Table 4: ○ 8, □ 10, ● 12)

Fig. 9

Identification results campaign 6 (see Table 4: ○ 8, ● 12)

Fig. 10

Validation results of all different sized ANNs

Fig. 11

Validation results campaign 1 (see Table 3: ○ 2, □ 4, ● 6)

Fig. 12

Validation results campaign 2 (see Table 3: ○ 2, □ 4, ● 6)

Fig. 13

Validation results campaign 3 (see Table 3: ○ 2, □ 4, ● 6)

Fig. 14

Validation results campaign 4 (see Table 4: ○ 9, □ 11)

Fig. 15

Validation results campaign 5 (see Table 4: ○ 9, □ 11)

Fig. 16

Validation results campaign 1 using half dataset

Fig. 17

Validation results campaign 4 using half dataset

Fig. 18

Validation results campaign 1 using quarter dataset

Fig. 19

Validation results campaign 4 using quarter dataset

Fig. 20

Validation results campaign 1 using one-eighth dataset

Fig. 21

Validation results campaign 4 using one-eighth dataset

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