Power system capacity-expansion models are typically intractable if every operating period is represented. This issue is normally overcome by using a subset of representative operating periods. For instance, representative operating hours can be selected by discretizing the load-duration curve, which captures the effect of load levels on system-operation costs. This approach is inappropriate if system-operating costs depend on parameters other than load (e.g., renewable-resource availability) or if there are important intertemporal operating constraints (e.g., generator-ramping limits). This paper proposes the use of representative operating days, which are selected using clustering, to surmount these issues. We propose two hierarchical clustering techniques, which are designed to capture the important statistical features of the parameters (e.g., load and renewable-resource availability), in selecting representative days. This includes temporal autocorrelations and correlations between different locations. A case study, which is based on the Texan power system, is used to demonstrate the techniques. We show that our proposed clustering techniques result in investment decisions that closely match those made using the full unclustered dataset.