  A simple first-principles mathematical model is developed to predict the
performance of a micro photosynthetic power cell ($\mu$PSC), an electrochemical
device which generates electricity by harnessing electrons from photosynthesis
in the presence of light. A lumped parameter approach is used to develop a
model in which the electrochemical kinetic rate constants and diffusion effects
are lumped into a single characteristic rate constant $K$. A non-parametric
estimation of $K$ for the $\mu$PSC is performed by minimizing the sum square
errors (SSE) between the experimental and model predicted current and voltages.
The developed model is validated by comparing the model predicted $v-i$
characteristics with experimental data not used in the parameter estimation.
Sensitivity analysis of the design parameters and the operational parameters
reveal interesting insights for performance enhancement. Analysis of the model
also suggests that there are two different operating regimes that are observed
in this $\mu$PSC. This modeling approach can be used in other designs of
$\mu$PSCs for performance enhancement studies.
