We report the analytical solution to a problem of voltage and current distribution in a two-cell stack with the small amplitude resistive spot in one of the cells. Voltage disturbance in the defective cell increases almost linearly with the characteristic spot radius. The general expression for voltage loss due to a spot in an $N$-cell stack is obtained; it is stack current density times peak spot resistivity times square of the characteristic spot radius. Based on the solutions derived, a method for spot detection in a stack is discussed.

1.
Thirumalai
,
D.
, and
White
,
R. E.
, 1997, “
Mathematical Modeling of Proton-Exchange-Membrane Fuel-Cell Stacks
,”
J. Electrochem. Soc.
0013-4651,
144
, pp.
1717
1723
.
2.
Baschuk
,
J. J.
, and
Li
,
X.
, 2004, “
Modelling of Polymer Electrolyte Membrane Fuel Cell Stacks Based on Hydraulic Network Approach
,”
Int. J. Energy Res.
0363-907X,
28
, pp.
697
724
.
3.
Karimi
,
G.
,
Baschuk
,
J. J.
, and
Li
,
X.
, 2005, “
Performance Analysis and Optimization of PEM Fuel Cell Stacks Using Flow Network Approach
,”
J. Power Sources
0378-7753,
147
, pp.
162
177
.
4.
Lee
,
J. H.
,
Lalk
,
T. R.
, and
Appleby
,
A. J.
, 1998, “
Modeling Electrochemical Performance in Large Scale Proton Exchnage Membrane Fuel Cell Stacks
,”
J. Power Sources
0378-7753,
70
, pp.
258
268
.
5.
Lee
,
J. H.
and
Lalk
,
T. R.
, 1998, “
Modeling Fuel Cell Stack Systems
,”
J. Power Sources
0378-7753,
73
, pp.
229
241
.
6.
Kulikovsky
,
A. A.
, 2006, “
Electrostatic Broadening of Current-Free Spots in a Fuel Cell Stack: The Mechanism of Stack Aging
,”
Electrochem. Commun.
1388-2481,
8
, pp.
1225
1228
.
7.
Kulikovsky
,
A. A.
, 2007, “
Mirroring of Current-Free Spots in a Fuel Cell Stack
,”
J. Electrochem. Soc.
0013-4651,
154
, pp.
B817
B822
.
8.
Santis
,
M.
,
Freunberger
,
S. A.
,
Papra
,
M.
,
Wokaun
,
A.
, and
Büchi
,
F. N.
, 2006, “
Experimental Investigation of Coupling Phenomena in Polymer Electrolyte Fuel Cell Stacks
,”
J. Power Sources
0378-7753,
161
, pp.
1076
1083
.
9.
Kulikovsky
,
A. A.
, 2006, “
Voltage Loss in Bipolar Plates in a Fuel Cell Stack
,”
J. Power Sources
0378-7753,
160
, pp.
431
435
.