Obtaining per-device energy consumption estimates in Non-Intrusive Load Monitoring (NILM) has proven to be a challenging task. We present Power Consumption Clustered Non-Intrusive Load Monitoring (PCC-NILM), a relaxation of the NILM problem that estimates the energy consumed by devices operating in different power ranges. The Approximate Power Trace Decomposition Algorithm (APTDA) is presented as an unsupervised, data-driven solution to the PCC-NILM problem. We show that reliable energy estimates can be obtained by crowdsourcing the results from using 1,456 event detectors applied to the publicly available BLUED dataset.