Double Diode Model

Source: MDPI

The Double Diode Model in Photovoltaics

The behavior of photovoltaic devices can be accurately described by the double diode model, which is an extension of the single diode model. While the single diode model assumes a constant ideality factor, the double diode model considers the ideality factor as a function of the voltage across the device.

Equations of the Double Diode Model

Under illumination, the double diode model equation is given by:

J = J_L – J_01 * {exp[q * (V + J * R_s) / (k * T)] – 1} – J_02 * {exp[q * (V + J * R_s)² / (k * T)] – 1} – V + J * R_s * R_shunt

Practical measurements of the illuminated equation are challenging due to small fluctuations in light intensity overwhelming the effects of the second diode. Therefore, it is more common to analyze the double diode equation in the dark, where it simplifies to:

J = J_01 * {exp[q * (V – J * R_s) / (k * T)] – 1} + J_02 * {exp[q * (V – J * R_s)² / (k * T)] – 1} + V – J * R_s * R_shunt

In both cases, the -1 terms in the exponential are typically ignored for easier analysis.

Limitations of the Double Diode Model

While the double diode model provides a good approximation for many photovoltaic devices, it has limitations in accurately representing the recombination components in actual silicon devices. For highly efficient solar cells like PERL cells, where recombination behavior changes dramatically with voltage due to carrier concentration variations, a single diode model with variable ideality factor and saturation current may be more suitable. In such cases, a double diode fit may result in erroneous values.

Source: ResearchGate