Buildings are highly energy-consuming and therefore are largely accountable for environmental degradation. Detecting anomalous energy consumption is one of the effective ways to reduce energy consumption. Besides, it can contribute to the safety and robustness of building systems since anomalies in the energy data are usually the reflection of malfunctions in building systems. As the most flexible and applicable type of anomaly detection approach, unsupervised anomaly detection has been implemented in several studies for building energy data. However, no studies have investigated the joint influence of data structures and algorithms' mechanisms on the performance of unsupervised anomaly detection for building energy data. Thus, we put forward a novel workflow based on two levels, data structure level and algorithm mechanism level, to effectively detect the imperceptible anomalies in the energy consumption profiles of buildings. The proposed workflow was implemented in a case study for identifying the anomalies in three real-world energy consumption datasets from two types of commercial buildings. Two aims were achieved through the case study. First, it precisely detected the contextual anomalies concealed beneath the time variation of the energy consumption profiles of the three buildings. The performance in terms of areas under the precision-recall curves (AUC_PR) for the three given datasets were 0.989, 0.941, and 0.957, respectively. Second, more broadly, the joint effect of the two levels was examined. On the data level, all four detectors on the contextualized data were superior to their counterparts on the original data. On the algorithm level, there was a consistent ranking of detectors regarding their detecting performances on the contextualized data. The consistent ranking suggests that local approaches outperform global approaches in the scenarios where the goal is to detect the instances deviating from their contextual neighbors rather than the rest of the entire data.