Three-way unsupervised data mining for power system applications based on tensor decomposition.

Until now, measurements from SM were expressed only as vectors (1D) or matrices (2D). In this work, a higher order representation, 3D in this case, is proposed. The new format allows to store multivariate data in a more natural form, and at the same time is possible to retrieve more information about a certain event. It should be stressed that, although in other disciplines such as data science the introduction of more dimensions is not required and it actually complicates the formulation of the problem, in power systems applications where data have multivariate nature, working with two dimensions leads to insufficient visibility of the problem and consequently to misinterpretation of the phenomena under investigation. Thus, although the proposed approach would certainly add complexity to find the solution when working with conventional algorithms such as PCA or LLE, the higher dimension does not represent an obstacle for the proposed approach and guarantees a more accurate interpretation of the solution. To validate the effectiveness of the proposed methodology, a three-way tensor built with data from the Electrical Reliability Council of Texas (ERCOT) is presented. The results demonstrate that is possible to extract more information than using conventional approaches based on 2-way arrangements (matrices). The innovation of using tensor decomposition for smart sensors data results on the following contributions: • Significant data compression. After the tensor decomposition has been performed, the original data sets are kept on new formats of the decomposition, which require significant less memory space. • Reduction and Visualization : The reduction is carried out for each dimension and thus, visualization and clustering of each variable is achieved. • Reconstruction of missing data. The iterative nature of the algorithm for solving the objective function during the tensor decomposition process, indirectly allows the estimation and reconstruction of missing data. Sophisticated geospatial metering devices used in today's networks such as the advanced metering infrastructure (AMI), wide area measurement system (WAMS) and supervisory control and data acquisition (SCADA) open new opportunities to monitor the security of the system in real time. Consequently, these metering infrastructures have received significant attention in recent years from data mining communities because of the new challenges involved on managing this information. One of the main challenges is the analysis of multivariable data, which represents datasets containing variables of different nature, which are linked. In this document a data mining technique that allows the analysis of multivariate data is presented. Moreover, an innovative application of an unsupervised data mining algorithm for smart meters data, particularly to Electrical Load Profile using tensor decomposition is presented. Since the proposed tensor representation allows to assign a given dimension to a particular variable involved; data reduction, data compression, data visualization and data clustering is archived separately for every variable. To validate the effectiveness of the proposed methodology, a three-way tensor built with data from the Electrical Reliability Council of Texas (ERCOT) is presented. The results demonstrate that is possible to extract more information than using conventional approaches based on 2-way arrangements (matrices). Additionally, the proposed algorithm is solved using an iterative approach, which indirectly enable to estimate missing data. [ABSTRACT FROM AUTHOR]