An approximated expression for the calculated solar cell current is usually used in parameters estimation of the 7-parameter double diode model (DDM) and the 9-parameter triple diode model (TDM) of solar photovoltaic (PV) equivalent circuits. Then the root mean square error (RMSE) is calculated between the measured and estimated values of the output current. In the mathematical sense, the RMSE calculation procedure is not correct. In this work, a novel iterative approach based on the Lambert W function is proposed to calculate the solar cell current in both DDM and TDM. Then, the RMSE values computed using the parameters found by many optimization algorithms presented in the literature are presented and discussed for the RTC France PV cell and Solarex MSX & ndash;60 PV module. The results obtained show that RMSE values were not accurately calculated in most of these methods. Further, an improved LSHADE optimization algorithm called Chaotic LSHADE algorithm is proposed to solve the 7-parameter and 9-parameter estimation problem of the PV equivalent circuits. The proposed methodology is also applied to current & ndash;voltage characteristics measured in the laboratory for solar modules of Clean Energy Trainer Setup. The 7 and 9 unknown parameters are esti-mated using the CLSHADE algorithm based on the minimization of the RMSE values calculated. The results obtained show that the proposed algorithm achieves better solutions than the solutions obtained by many optimization algorithms presented in the literature.