Workload-aware power management and scheduling techniques have the potential to save energy while minimizing negative impact on performance. The effectiveness of these techniques depends on the stability of a workload's power consumption pattern across different input data, resource allocations (e.g. number of cores), and hardware platforms.In this paper, we show that the power consumption behavior of HPC workloads can be accurately captured by concise signatures built from their power traces. We validate this approach using 255 traces collected from 13 high-performance computing workloads on 4 different hardware platforms. First, we use both feature-based and time-series-based distance metrics to cluster our traces, and we quantitatively show that feature-based clusterings segregate traces by workload just as effectively as the more compute-and space-intensive time-series-based clusterings. Second, we demonstrate that unlabeled traces can be classified by workload with over 85% accuracy, based only on these concise statistical signatures.