2017 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC 2017). Ixtapa, México 978-1-5386-0819-7/17/$31.00 ©2017 IEEE Multi Scale Recurrence Quantification Analysis for Clustering Harmonics on Microgrid Systems O. C. Robles, Emilio Barocio J. Segundo U de G UASLP Guadalajara, México San Luis Potosí, México e-mail: oswisa@hotmail.com, e-mail: emilio.barocio@cucei.udg.mx juan.segundo@uaslp.mx J. C. Olivares-Galvan D. Guillen UAM UNAM Ciudad de México, México Ciudad de México, México e-mail: e-mail: jolivare_1999@yahoo.com guillenad@gmail.com Abstract—In this paper, a Multi Scale Recurrence Quantification Analysis (MSRQA) method is proposed to clustering harmonics on microgrid systems. MSRQA is composed by the Variational Mode Decomposition algorithm and the Recurrence Quantification Analysis (RQA). MSRQA decomposes a signal into a finite number of Mono-Component Signals (MCSs), then a feature extraction is carry out by the RQA on each MCS. Finally, the identification of the optimal number of clusters based on the features extracted by RQA and the Davies- Bouldin index is carry out on the monitored microgrid system test signals. At the end an index based on the cluster information and the RQA measure is proposed to identify the harmonics present on the dynamic system behavior. Keywords— Clustering Harmonic Analysis, Feature Extraction, Microgrid, Multi Scale Recurrence Quantification Analysis (MRQA), Variational Mode Decomposition (VMD). I. INTRODUCTION The increasing of non-linear loads and switching devices in distribution systems have produced several power quality issues such as [1]: increasing losses in the electric distribution networks, overheating of electric equipment (motors, transformers, etc), malfunction of relays and circuit breakers at commercial and industrial networks [2], [3], and more recently severe distortions of waveforms in microgrids that produce adverse effects on their electronic controls [4], [5]. New synchronized smart grid sensors such micro Phasor Measurement Units (μPMUs) [6] are opening new potential applications for monitoring, protection, and control of industrial and microgrid systems. These sensors are generating a large volume of data; demanding more sophisticated techniques to extract, visualize and classify the patterns hidden in data coming from these sensors [7]. In the last decade, data mining techniques [8] have been used to separate the information extracted from the data in smaller groups which allow a better visualization of the patterns hidden in the data. The new organization of the information allows to make a detailed analysis of the system and has potential application in the feature extraction process of disturbance classification [9]. Unlike the techniques found in the literature for feature extraction such as: Wavelets, Empirical Mode Decomposition (EMD), S-Transform, and Sparse Signal Decomposition [10- 13], combined with indices, data mining techniques [8] allow to extract hidden features in large amounts of data and make a pre-classification of the data information. The main disadvantage associated with data mining techniques is the determination of the optimal number of clusters formed with the data information. Therefore, it is necessary eliminate the cluster uncertainty to facilitate the determination of the optimal number of clusters. In this paper the Multi Scale Recurrence Quantification Analysis (MSRQA) method is proposed for the feature extraction of a set of signals in a microgrid system. MSRQA decomposes a multicomponent signal into a finite number of Mono-Component Signals (MCSs), then the Recurrence Quantification Analysis (RQA) is used to extract its main statistical characteristics measures. Three statistical measures based on vertical lines are proposed to extract the features of the MCSs for each analyzed signal. Finally, Davies-Bouldin index is used to determine the optimal number of cluster, facilitating the clusters harmonic identification. The paper is organized as follows: Section II describes MSRQA theory to understand the feature extraction process, Section III presents the methodology for cluster analysis that includes the clustering process and the cluster identification, Section IV shows a simple example using MSRQA to extract the features of a synthetic signal, the results are shown in Section V. Finally, the work conclusion are provided in Section VI. II. MULTISCALE RECURRENCE QUANTIFICATION ANALYSIS MSRQA is a hybrid technique which combines Variational Mode Decomposition (VMD) with Recurrence Quantification Analysis (RQA). MSRQA decomposes a multicomponent signal into a finite number of Mono-Component Signals (MCSs) for extracting its recurrence patterns using different types of statistical measures. In the literature other signal processing techniques have been reported for signal decomposition process [10], [12], [13]. A. Signal Decomposition Using VMD In contrast with other signal processing techniques like wavelets, VMD is an adaptive, quasi-orthogonal, and non- recursive method that have proved be effective in noisy