Recently, accurate modeling of the differences between the current and voltage (I–V) characteristics of solar cells has been the main focus of many research studies. Mostly the results were obtained only for single diode or double diode solar cells, not for both or even for photovoltaic (PV) modules. Moreover, the effect of different shading conditions and different temperatures should be considered; otherwise, the obtained results would be reliable for specific weather conditions and unreliable for all real conditions. In this study, a novel nature-inspired optimization method known as the lightning search algorithm (LSA) was developed to extract the parameters of single diode and double diode solar cells as well as for a PV module. LSA is formulated based on lightning, which originates from thunderstorms. Experimental data from multicrystalline KC200GT solar panels were used to test the single diode and double diode solar panel models, and experimental data from the monocrystalline SQ150-PC solar panels were used to test the PV module model. The experimental data are first collected at the same temperature at five different irradiance levels. In the second stage, variations in temperature are considered at the same irradiance level. The extraction results in the LSA I–V curves accurately fit the entire range of the experimental data, while many fluctuations were seen in the particle swarm optimization (PSO) and bee colony optimization (BCO) I–V curves. The convergence characteristics of LSA were also evaluated in terms of accuracy and speed. For all cases, when LSA was used, the accuracies matched well with the entire range of experimental data. In addition, the value of the objective function using LSA was lower, and that method converged much faster than PSO and BCO.