3 - Advances in compression algorithms for PMU and Smart Meter data based on tensor decomposition

Abstract

Smart meters (SMs) and phasor measurement units (PMUs) are two of the most important devices for the monitoring system in the smart grids, since with the sensed data it is possible to carry out a wide range of applications. Consequently, there is a global trend to install more SMs and PMUs worldwide. For example, in Europe until 2018, 33.83% of all the electricity metering points were equipped with a SM (99 million), whereas 400 PMUs were installed [1]. Meanwhile, in China until the mid of 2017, there were 340 million SMs and 4100 PMUs [2], [3], and the number of these installed devices is growing exponentially. However, with this, a new challenge emerges “Big Data.” For instance, one million of SMs generate 23.7 TB of information per month [13], whereas 100 PMUs generate 56 GB of data per day [4], and these data must be transmitted and stored for further analysis. Therefore data compression algorithms have become an essential tool in managing electrical power systems data. Inspired by that, in this chapter, we present the advances in SM and PMU data compression algorithms based on tensor decomposition. Tensor decomposition for data compression has not been fully exploited in electrical power systems; therefore this chapter represents the first overview of techniques for data compression through dimensional reduction based on tensor decompositions. To do so, the problem of compression is reformulated using three-dimensional arrays, instead of classical matrices in two dimensions. Thus the proposed approach exploits the benefits of organizing time series in multidimensional arrays (tensors) to achieve higher compression ratios of the original data, while preserving most of the properties in this form, achieving a low reconstruction error. To show the ability of this approach, two cases are presented: (1) First, the electrical load profiles from the smart meters of the Electrical Reliability Council of Texas (ERCOT) are compressed using the parallel factor model (PARAFAC) tensor decomposition. Then, (2) the compression of real voltage measurements from the European Network of Transmission System Operators (ENTSO-E) through Tucker tensor decomposition. Since to apply the proposed approaches, it is necessary to arrange the data into a tensor (multidimensional array), the first case shows how to construct a tensor directly from a multivariate data set, whereas the second case presents the process of building the tensor when the data are initially organized into a matrix. In both cases, a toy example is presented to illustrate the compression processes based on tensor decomposition, which can be reproduced using the main code provided at the end of the chapter. The results are compared with the traditional two-dimensional reduction approach, such as SVD, showing that using the approaches based on Tensor decomposition, a higher compression ratio can be achieved, while a small error reconstruction is obtained.