Mathematical modelling of µPSCs has not been considered due to the complexities involved in modelling of systems such systems as explained in Tanneru et.al . Recently, an attempt was made to develop mathematical models for µPSCs considering lumped parameter  and one dimensional diffusion of species in anode and cathode chambers . Tanneru et.al  have shown that the mathematical models developed can be used to increase the performance of µPSCs through design optimization. Tanneru et.al , have used the electrochemical part of one dimensional model to find optimal electrode surface area and optimal aspect ratio of µPSCs.
In this work, the mathematical model developed by Tanneru et.al  is extended to modelling of proton exchange membrane separating anode and cathode chambers. Appropriate changes to the model developed by Tanneru et.al  are made to capture the effect of light intensity, temperature on the growth of micro-organisms and their influence on the performance of µPSCs. The unknown parameters of the new model are estimated using the experimental data through optimization and the new model is validated using experimental data. The use of developed model to predict optimal operating conditions such as pH, temperature and light intensity to enhance the performance of µPSCs is investigated. Design optimization studies to improve the performance of µPSCs using the model developed in this work are described. Results on cost optimization of µPSCs are also outlined.
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