Comprehensive numerical models are pivotal to analyze the decarbonization of electricity systems. However, increasing system complexity and limited computational resources impose restrictions to model-based analyses. One way to reduce computational burden is to use a minimum, yet representative, set of system states for model simulation. These states characterize fluctuating renewable generation and variable demand for electricity prevailing at a certain point in time. A review of possible time series aggregation techniques identifies cluster algorithms as most adequate, with k-Means and the Ward algorithm predominating. However, throughout the surveyed literature, the line of reasoning for the selection of these algorithms remains unclear. To support the electricity system modeling community in selecting an algorithm, this paper devises a systematic multi-stage evaluation approach to compare a large variety of cluster analysis configurations, differing in algorithm, cluster representation, and number of clusters. Results show that electricity demand and renewable energy generation time series can be compressed to below one percent while sustaining global characteristics of the original data. Two potent cluster configurations are identified, confirming k-Means and WARD as being prevalent. Beyond electricity market data, the methodology can be applied to various types of fundamental time-dependent input data.