# OPEM Report (Chamberline-Kim Model)

## What is Chamberline-Kim ?

Chamberlin-Kim static model is an empirical equation which was developed to fit the experimental cell potential (E) vs. current density (J) data for proton exchange membrane fuel cells (PEMFCs), at several temperatures, pressures, and oxygen compositions in the cathode gas mixture. The exponential term compensates for the mass-transport regions of the V vs. i plot; i.e., the increase in slope of the pseudolinear region and the subsequent rapid fall-off of the cell potential with increasing current density. The terms E0 and b yield the electrode kinetic parameters for oxygen reduction in the PEMFC and R represents the resistance, predominantly ohmic and, to a small extent, the charge transfer resistance of the electro-oxidation of hydrogen. The exponential term characterizes the mass-transport region of the V vs. i plot. The parameter n has more pronounced effects than the parameter m in this region. In Chamberline Kim's model, the values of the parameters(five parameters: E0, b, R, m, n) vary depending on many variables, including the composition of the Membrane Electrode Assemblies(MEA), the fuel and oxidant used, besides the local temperature, pressure, and humidity of the MEA. They also depend on the stack itself, so that it can not be transposed to another fuel cell without new parameter identification.

## Inputs

Input | Description | Value
A | Active area [cm^2] | 50.0
E0 | Open circuit voltage [V] | 0.982
N | Number of single cells | 1
R | Resistance [ohm.cm^2] | 0.328
b | Tafel's parameter for the oxygen reduction [V] | 0.0689
i-start | Cell operating current start point [A] | 1
i-step | Cell operating current step | 0.1
i-stop | Cell operating current end point [A] | 42.5
m | Diffusion's parameters [V] (*Optional) | 0.000125
n | Diffusion's parameters [(A^-1)(cm^2)] (*Optional) | 9.45

## Overall Parameters

Parameter | Description | Value
Efficiency|Pmax | Cell efficiency at maximum power | 0.4626668383075613
Pmax | Maximum power [W] | 24.106792943177172
Ptotal(Elec) | Total electrical power [W] | 35.82827697893981
Ptotal(Thermal) | Total thermal power [W] | 15.093723021060224
VFC|Pmax | Cell voltage at maximum power [V] | 0.7217602677597956

## Graphs

Parameter | Description | Value
K | Slope of the curve obtained by linear approximation [A^(-1)] | -0.01612214066335869
Pmax(L-Approx) | Maximum power obtained by linear approximation [W] | 22.8946129504538
V0 | Intercept of the curve obtained by linear approximation [V] | 1.2150887546518891
VFC|Pmax(L-Approx) | Cell voltage at maximum power obtained by linear approximation [V] | 0.6075443773259446

Generated By OPEM Version 1.4