Closed-form model for the open circuit voltage of solar cells with shunt resistance, bias-dependent photocurrent and double exponential terms

The parasitic shunt resistance, bias dependence of the photocurrent and phenomena causing a second exponential term in the current density (J)-voltage (V) equation reduce the open circuit voltage, V_oc, of illuminated solar cells below the ideal value predicted by the J-V equation having only a single exponential term. This study reports an approximate closed-from solution of the transcendental V_oc equation which directly reflects these losses. The solution estimates V_oc as a weighted parallel combination of the limiting V_oc values corresponding to the domination of one of the several terms of the V_oc equation. The solution allows quick design calculation of the V_oc of a wide variety of cells in terms of all physical parameters, and provides insight into the influence of losses owing to various factors.