# De Soto “Five-Parameter” Module Model

The De Soto model (De Soto et al., 2006), also known as the five-parameter model, uses the following equations to express each of the five primary parameters as a function of cell temperature $$T_c$$ and total absorbed irradiance $$S$$:

• $${I_L}= {S\over {{S_{ref}}}}{M \over {{M_{ref}}}} \left[ {{I_{L,ref}} + {\alpha_{lsc}} \left( {{T_c} – {T_{c,ref}}} \right)} \right] \qquad$$
• $$I_0 = I_{0,ref} \left[ \frac{T_c}{T_0} \right] ^3 \exp \left[ \frac{1}{k} \left( \frac{E_{g,0}}{T_0} – \frac{E_g}{T_c} \right) \right] \qquad$$
• $${E_g} \left( {{T_c}} \right) = {E_g} \left( {{T_{ref}}} \right) \left[ {1 – 0.0002677 \left( {{T_c} – {T_{ref}}} \right)} \right] \qquad$$
• $${R_s} = {\rm{constant}} \qquad$$
• $${R_{sh}} = {R_{sh,ref}}{{{S_{ref}}} \over S} \over S$$
• $${n} = {\rm{constant}} \qquad$$

Absorbed irradiance, $$S$$, is equal to POA irradiance reaching the PV cells (including incident angle reflection losses but not spectral mismatch).  In each equation, the subscript “ref” refers to a value at reference conditions. In De Soto et al., 2006, the modified ideality factor $$a$$ is used, and expressed as a linear function of cell temperature $$T_c$$, which is equivalent to a constant diode ideality factor $$n$$.

$$M$$, termed the “air mass modifier”, represents the spectral effect, from changing atmospheric air mass and corresponding absorption, on the light current. $$M$$ is the polynomial in air mass from the Sandia PV Array Performance Model (SAPM). The term $$\alpha_{lsc}$$ is the temperature coefficient (A/K) of short-circuit current, set equal to the temperature coefficient of the light current.

The term $${E_g} \left( {{T_c}} \right)$$ is the temperature-dependent bandgap (eV); given as the simplified first order Taylor series of the experimental bandgap temperature. The empirical constant 0.0002677 is representative of silicon cells at typical operating temperatures, and it is used for all cell technologies.

Content for this page was contributed by Matthew Boyd (NIST) and Clifford Hansen (Sandia)