Mathematical Problems in Engineering

Volume 2018, Article ID 2765945, 12 pages

https://doi.org/10.1155/2018/2765945

## A Data-Driven Modeling Strategy for Smart Grid Power Quality Coupling Assessment Based on Time Series Pattern Matching

Correspondence should be addressed to Qingquan Jia; moc.anis@nauqgniqaij

Received 22 October 2017; Accepted 29 January 2018; Published 1 March 2018

Academic Editor: David González

Copyright © 2018 Hao Yu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This study introduces a data-driven modeling strategy for smart grid power quality (PQ) coupling assessment based on time series pattern matching to quantify the influence of single and integrated disturbance among nodes in different pollution patterns. Periodic and random PQ patterns are constructed by using multidimensional frequency-domain decomposition for all disturbances. A multidimensional piecewise linear representation based on local extreme points is proposed to extract the patterns features of single and integrated disturbance in consideration of disturbance variation trend and severity. A feature distance of pattern (FDP) is developed to implement pattern matching on univariate PQ time series (UPQTS) and multivariate PQ time series (MPQTS) to quantify the influence of single and integrated disturbance among nodes in the pollution patterns. Case studies on a 14-bus distribution system are performed and analyzed; the accuracy and applicability of the FDP in the smart grid PQ coupling assessment are verified by comparing with other time series pattern matching methods.

#### 1. Introduction

In recent years, the increased penetration of distributed generations and power electronic loads has aggravated power quality (PQ) pollution in power systems [1, 2]. Moreover, the extensive use of adjustable speed drive systems, computer systems, and precision production lines has brought forward higher requirements for PQ [3–5]. Furthermore, with the improvement of electricity market system, diverse PQ selection and corresponding electrovalence mechanisms are required to be provided as an important service to consumers [6]. Traditional power grids have an inability to wrestle with these challenges due to the lack of intelligent PQ monitoring and analysis management platforms. Advanced PQ monitoring and analysis techniques of smart grids have become indispensable in order to ensure the electromagnetic compatibility of various power loads, to satisfy the demand of superior power supply quality and to provide the reasonable electricity markets service [7].

Smart grids have network PQ monitoring and analysis systems. Knowledge-excavating technologies and intelligent algorithms are utilized to analyze PQ problems that generally include disturbance detection and classification [8], disturbance control [9], disturbance estimation [10], disturbance source locating [11], and PQ evaluation [12]. Most existing studies focus on the PQ problems of nodes in power networks, whereas the PQ influence analysis among the nodes is lacking. PQ disturbances have propagating and diffusing effects in power networks. The effects of disturbance sources on nodes may be superposed or counteracted. A coupling relation existed in the disturbance influence among nodes under the comprehensive action of the disturbance sources [13]. Hence, smart grid PQ coupling assessment is required to quantify the disturbance influence among nodes. This topic research not only has a theoretical value for PQ relation analysis among nodes in power networks, but also has a potential application value in associated region division, local disturbance control, and disturbance estimation on the basis of PQ coupling property.

PQ coupling among nodes is reflected by the similarity of the disturbance variation rules. Time series pattern matching can measure similarity of univariate or multivariate data [14], which provides a possibility for the coupling assessment of single or integrated disturbance. Common pattern matching methods for univariate time series are Euclidean distance (ED) and dynamic time warping (DTW) distance. ED is applicable for sample sequences of equal length [15], and DTW distance supports time stretching and warping [16]. However, the two methods consider only the data value difference and ignore the data variation characteristic, which may cause misjudgment in the pattern matching of univariate time series. Popular pattern matching methods for multivariate time series include point distribution (PD), principal component analysis (PCA), and tendency distance (TD). PD uses the distribution of local important points to represent multivariate time series, whereas the dimension and feature differences of variables are unconsidered [17]. PCA extracts principal components to reduce variables dimensions but destroys the isomorphism among low-dimensional time series [18]. TD employs bottom-up algorithm to achieve the piecewise sequence representation, and pattern matching on multivariate time series is implemented by measuring the trend feature difference [19]. However, a definite physical meaning was not reflected by the segmentation manner and the impact of variable size difference was ignored in the pattern matching of multivariate time series.

Existing time series pattern matching methods have inherent advantages and disadvantages, which render these methods inapplicable for PQ coupling assessment. An appropriate time series pattern matching method for PQ coupling assessment should comprehensively consider matching object demand, pollution pattern characteristic, and coupling property. Specifically, various disturbances may occur independently or simultaneously. According to actual demands, pattern matching object could be univariate PQ time series (UPQTS) or multivariate PQ time series (MPQTS). Moreover, PQ pollution is affected by different types of disturbance sources, thereby containing periodic variation pattern (e.g., caused by industrial loads that have a fixed production time and task) and random variation pattern (e.g., caused by renewable energy generations) [20, 21]. These PQ pollution patterns are necessary to be considered in the time series pattern matching to give an overall analysis for the disturbance influence among nodes. Additionally, PQ coupling among nodes is reflected by the similarity of the disturbance variation rules. Disturbance importance is determined by its severity. Thus, both disturbance variation trend and severity should be considered in the time series pattern matching.

In this study, a data-driven modeling strategy for smart grid PQ coupling assessment based on time series pattern matching is introduced to quantify the influence of single and integrated disturbance among nodes in different pollution patterns. Periodic and random PQ patterns are constructed by using multidimensional frequency-domain decomposition for all disturbances. A multidimensional piecewise linear representation based on local extreme points is proposed to extract the patterns features of single and integrated disturbance taking into account disturbance variation trend and severity. A feature distance of pattern (FDP) is developed to implement the pattern matching on UPQTS and MPQTS to quantify the influence of single and integrated disturbance among nodes in the pollution patterns. Case studies on a 14-bus distribution system are performed and analyzed, and the accuracy and applicability of the FDP method in the smart grid PQ coupling assessment are compared with those of other time series pattern matching methods.

#### 2. PQ Pattern Construction

##### 2.1. PQ Time Series Expression

Continuous PQ disturbances include voltage fluctuation, voltage deviation, interharmonic ratio of voltage, total harmonic distortion of voltage, and three-phase voltage unbalance. Each disturbance represents a type of PQ pollution, and the properties of the disturbances differ from each other. Various disturbances may independently or simultaneously occur in power networks. The coupling assessment object could be single or integrated disturbance according to the actual situation. The authors in research [22] constructed a PQ state space to represent the state set of continuous disturbances. PQ state change can be expressed as a multivariate function of time. Hence, MPQTS can be expressed as . In the expression, is the UPQTS of disturbance , ; is the monitoring value of disturbance at time ; and represents the five disturbances orderly.

##### 2.2. Multidimensional Frequency-Domain Decomposition

The PQ condition of nodes is determined by the common effect of different disturbance sources in a power network. The operations of some disturbance sources present certain regularity; for instance, arc furnaces and rolling mills may have a fixed working time and production task. The PQ disturbances generated by such sources usually show periodicity variations. The operations of other disturbance sources are irregular, such as the output power of wind and photovoltaic generation, which are affected by weather conditions. The PQ disturbances generated by this type of sources present random variations. Therefore, daily cycle, weekly cycle, low frequency, and high frequency patterns are defined in this study to represent the PQ pollution affected by different types of disturbance sources. Multidimensional frequency-domain decomposition is used for all disturbances to construct the four pollution patterns.

Fourier series expansion can decompose mutually orthogonal frequency components from a continuous periodic signal [23]; hence, it is used synchronously in all the dimensions of .where is the direct current component and and are the coefficients of cosine and sine components of , respectively. According to angular frequency , is reconstructed aswhere , , and represent the daily cycle, weekly cycle, low frequency, and high frequency components of , respectively.

Every 10 min is taken as a sampling interval of disturbance data, with a total of 144 sampling points per day. The frequency sets of , , , and are established as follows.

*Periodic Frequency Sets*. The cycles of and are 144 and , respectively, and their angular frequency sets and are expressed aswhere is the modulo operation.

*Random Frequency Sets*. Daily 144 sampling points are regarded as a critical condition to distinguish and , and their angular frequency sets and are expressed as

is transformed from the time domain to the frequency domain by multidimensional discrete Fourier transform.The relationship between frequency spectrum and coefficients and is derived by (1) and (5). The , , , , and are calculated by Euler formula and multidimensional inverse discrete Fourier transform.

To extract the four objective patterns, direct current component is assigned to , , , and according to the four components sizes.where is the root-mean-square value of , , , or , , and are the daily and weekly cycle patterns that, respectively, reflect the disturbance variations per day and per week, and and are the low and high frequencies patterns that, respectively, reflect the randomness of the slow and fast disturbance variations.

#### 3. PQ Pattern Representation

##### 3.1. Pattern Feature Extraction

In the PQ pollution patterns, the coupling relation of single or integrated disturbance among nodes is reflected by the similarity of the UPQTS or MPQTS variation. Trends can embody the variation rules of a PQ time series, which are important features in the coupling assessment of single or integrated disturbance. Local extreme as a critical point between two opposite trends can distinguish the features. Linear fitting can represent the features intuitively. Therefore, a multidimensional piecewise linear representation based on local extremes points is proposed in this study to extract the trend feature of UPQTS and MPQTS.

Local maximum or minimum points satisfy (9) or (10). In this definition, the extreme points on a horizontal line represent placidity tendency.

For two disturbance dimensions, the segmentations of UPQTS based on local extreme points are shown in Figure 1(a). The segmentations of MPQTS are obtained based on the local extreme points of each disturbance dimension, as shown in Figure 1(b). Multidimensional segmentations can dispose of both UPQTS and MPQTS. The purpose is to make the trend in each subsection generally consistent. The purpose of the piecewise strategy is to make the trends in each subsection consistent in general (rising, placid, or falling). Meanwhile, the similar trends of different dimensions are segmented into the same subsection.