A novel algorithm for Kramers–Kronig validity test on photovoltaic modules impedance spectra

Impedance spectroscopy (IS) has been recently used for characterization and diagnosis of photovoltaic (PV) modules by using different laboratory equipment. However, most of the papers do not propose a procedure to determine if a measured impedance spectrum is valid or not. Although there are some approaches available in the literature, they are focused on other applications, like batteries, and have not been validated for PV modules. Therefore, this paper proposes a procedure to determine if an impedance spectrum measured at different operating points of the current vs voltage (I-V) curve of a PV module is valid or not. The procedure determines the number of RC branches in a Voigt circuit required to reproduce an experimental impedance spectrum, avoiding under- and over-fitting. Then, the residuals for the real and imaginary parts of the impedance are calculated to evaluate the average absolute percentage error for each part. Finally, those values must be under 1% for the spectrum to be considered valid. The proposed procedure is validated with simulated spectra of a linear circuit and experimental spectra on two different bifacial PV modules operating under stable irradiance conditions resulting from sunny days. Moreover, the proposed approach is compared with a procedure available in the literature to illustrate its advantages. The results show that the proposed procedure can determine valid and invalid impedance spectra at different operating points of the I-V curve between the maximum power point (MPP) and open-circuit (OC), which contrasts with the reference approach that can identify valid experiments only close to OC.