For the automated analysis of I/V-characteristics of solar cells and modules, descriptive parameters are essential. In particular with the rise in machine-learning techniques and the related increase data volumes, there is a need for good, general purpose, descriptive parameters. The most commonly used descriptive parameters for I/V are the standard solar cells parameters, consisting of V oc , I sc , V mpp , and I mpp . Also other representations may be considered, such as one diode model parameters corresponding to a particular I/V. However, these representations are very coarse and cannot distinguish or represent many common (non-ideal) features of an I/V (e.g. an S-shape). In this work we propose an extended set of solar cell parameters, which are well defined, and easy to determine. We evaluate the effectiveness of the extended solar cell parameters by reconstructing the I/V from the extracted parameters. This allows one to “measure” information loss. We compare the accuracy of our parameters with other commonly used curve models for I/V, namely the one diode model, and the Karmalkar-Haneefa model. The models are applied to a large set of I/V (about 2.2 million curves), covering a wide range of technologies and conditions. We demonstrate our extended solar cell parameters consistently provide an accurate description of nearly all I/V in these datasets. Furthermore, we present our I/V analysis tool which we use to process these datasets. This tool is fast and capable of extracting the extended solar cell parameters, as well as parameters for the one diode model and the Karmalka-Haneefa model. Finally, we exemplary show how the extended solar cell parameters may be used to detect partial shading in outdoor data, by training a simple random-forest classifier based on extended solar cell parameters.