Mathematical modeling of a dye-sensitized solar cell

Dye sensitized solar cells (DSSCs) have drawn extensive attention since the seminal report of O'Regan and Grätzel . DSSCs have been able to achieve photoconversion efficiencies of up to 11.1% under 1-sun AM1.5 illumination . This method of harvesting sunlight is a promising alternative to the silicon-based solar cells due to the lower manufacturing cost and sufficiently high energy conversion efficiency. To be commercially feasible, the cells need to show stable performance and long durability of at least 10 years . It has been reported that photovoltaic characteristics, i.e., open circuit voltage, short circuit current, fill factor and efficiency, decrease at elevated temperatures . The cell temperature can be increased to as high as 72°C under severe environmental conditions . A dynamic model of the cell that accurately predicts the response of the cell to different changes will allow one to optimize the cell design and operation. In a DSSC, a photoactive sensitizer (dye) adsorbed within a thin mesoporous TiO ₂ film harvests the sunlight. The excited dye injects an electron into the TiO ₂ conduction band which diffuses through the interconnected network of the semiconductor and eventually is collected at the transparent conductive glass and moves through the external circuit to the counter electrode, where it reduces the tri-iodide ions to iodide ions. The iodide ions diffuse through the electrolyte and reach the TiO ₂/dye interface, where they regenerate the oxidized dye molecules . This paper presents mathematical modeling of a DSSC and investigates steady-state and dynamic behaviors of the cell. To develop the model, the equations of continuity and transport for all species in the cell including electrons, iodide, tri-iodide and cation are considered. The Butler-Volmer kinetics is applied at the platinum counter electrode. Under steady state conditions, the developed model is validated against the current-voltage characteristics of the cell. Parameter estimation is conducted to determine the unknown parameters of the model. The dynamic responses of the cell to changes in solar irradiance, ambient temperature and load resistance are simulated.