Determining the Maximum Power of a Fuel Cell

Determine (a) the maximum power of a PV cell and (b) the cell current at the maximum power. The polarization curve of an FC can be represented by the following nonlinear $V-I$ relationship
$v = 0.75 - 0.125 \times \tan (i - 1.2)$

Question

Determining the Maximum Power of a Fuel Cell

Determine (a) the maximum power of a PV cell and (b) the cell current at the maximum power. The polarization curve of an FC can be represented by the following nonlinear [latex]V–I[/latex] relationship

[latex]v = 0.75 - 0.125 imes an (i - 1.2)[/latex]

Accepted Answer

The cell power is

[latex]PC = vi = i imes [0.75 - 0.125 imes an (i - 1.2)][/latex]

The maximum power will occur when [latex]dP_C/di = 0[/latex]. That is,

[latex]\frac{dP_C}{di}=0.75 - 0.125 imes an (i - 1.2) - 0.125 imes i imes sec ^2(i - 1.2) = 0[/latex]

which can also be written as

[latex]0.75 - 0.125 imes an (i - 1.2) - 0.125 imes i imes \frac{1}{\cos ^2(i - 1.2)}=0[/latex]

which, after solving by an iterative method by Mathcad or Mathlab software, gives [latex]I_{mp} = 2.06[/latex] Substituting [latex]i = I_{mp} = 2.06 A[/latex] gives the corresponding voltage

[latex]V_{mp} = v = 0.75 - 0.125 × an (2.06 - 1.2) = 0.6048 V[/latex]

Therefore, the maximum cell power [latex]P_{\max} = V_{mp} I_{mp} = 0.6048 × 2.06 = 1.246 W[/latex].

Question 16.10: Determining the Maximum Power of a Fuel Cell Determine (a) t...

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