Models of photovoltaic devices are an important tool for the estimation of their I-V characteristics. These characteristics, in turn, can be used to optimize production, compare devices, or predict the output power under different illumination conditions. Equivalent circuit models are the most common model types utilized. Although these models and the estimation of their parameters are thoroughly investigated, little is known about their performance under indoor illumination conditions. This, however, is essential for applications where photovoltaic devices are used indoors, such as for PV-powered sensors, wearables or Internet of Things devices. In this paper, a comprehensive and quantitative study of parameter estimation methods for the two-diode model is conducted, focusing particularly on the performance at indoor illumination levels. We reviewed and implemented a set of six common parameter estimation methods, and evaluate the performance of the estimated parameters on a typical photovoltaic module utilized in indoor scenarios. The results of this investigation demonstrate that there is a large performance variation between different parameter estimation methods, and that many methods have difficulties to estimate accurate parameters at low illumination conditions. Moreover, the majority of methods result in physically infeasible parameters, at least under some of the evaluated conditions. When applying physically motivated parameter scaling methods to these parameters, large estimation errors are observed, which limits the model's applicability for power estimation purposes.