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The long-term stability of solar cells is a crucial factor for the competitiveness of a technology. In this study, the accelerated aging of CIGS solar cells was studied, and the influence of an applied bias during the endurance test on the open-circuit voltage Voc and fill factor (FF) was investigated. Time constants for parameter drifts of the open-circuit voltage and the associated activation energy were determined. The observed parameter drifts will be discussed, and a model will be proposed based on SCAPS simulations, explaining the observed behavior of the electrical characteristics of the solar cells. Therefore, cells were dark annealed under dry conditions at two different temperatures and different voltage biases were applied to the cells. Our study revealed that the application of a positive bias, which is similar to light soaking, first leads to an improvement and stabilization of the open-circuit voltage and FF followed by a slow decrease of these parameters. This long-term decrease can be explained in terms of a back barrier or phototransistor, as simulated with SCAPS. However, applying a positive bias enhances the long-term stability of these devices. The appearance of a back barrier is associated with a time constant exceeding 30 years. Therefore, this degradation mechanism is not critical.