# Spectral mismatch

Fabian Plag, Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116, Braunschweig, Germany

## Spectral mismatch calculations in accordance with the standard requirements

The measured spectral responsivity (SR) of a DUT PV module is required to consider and compensate the spectral mismatch effect in the performance measurement of the module when using solar simulators or natural sunlight. The reference device rates the apparent irradiance during a measurement differently than the DUT PV module does. For a world-wide comparability, the measurement needs to be corrected by referring to the reference spectrum Eλ,STC(λ) defined in the standard .

A spectral mismatch of the modules short-circuit current that is measured under a spectral irradiance Eλ(λ) that differs from Eλ,STC(λ), occurs if the SR s(λ) of the module differs from this of the reference device sref(λ).

The spectral mismatch factor SMM is defined as follows:

(1): $\displaystyle{ SMM=\frac{\int_{\lambda}{E_{\lambda\mathrm{,STC}}(\lambda)\ s_{\mathrm{ref}}(\lambda)\ d\lambda}}{\int_{\lambda}{E_\lambda(\lambda)\ s_{\mathrm{ref}}(\lambda)\ d\lambda}}\frac{\int_{\lambda}{E_\lambda(\lambda)\ s(\lambda)\ d\lambda}}{\int_{\lambda}{E_{\lambda,\mathrm{STC}}(\lambda)\ s(\lambda)\ d\lambda}} }$

Note that also the relative SRs can be used in equation (1) because the absolute values cancel out.

By dividing the measured short-circuit current ISC,meas trough SMM, the (corrected) ISTC can be obtained.

(2) $\displaystyle{ I_{STC}=\frac{I_{\mathrm{SC,meas}}}{SMM}. }$

Another application of spectral corrections is described in energy rating procedures in accordance with the standard IEC61853-3  to compensate the impact of varying spectral irradiances on the calculated standardized energy yield.