电能质量干扰的实时检测和分类系统综述

 摘要

本文对电能质量干扰（PQD）的实时检测和分类进行了系统的文献综述。本文特别关注电压骤降和电压缺口，因为电压骤降会造成巨大的经济损失，而对电压缺口的研究仍处于起步阶段。我们提出了一种基于科学计量学、文本相似性和层次分析法的系统方法，用于构建综述和选择最相关的文献。然后对文献的书目数据进行文献计量分析，以确定相关统计数据，如出版物随时间的演变、出版量最大的国家以及相关主题的分布情况。随后会选择一组文章进行批判性分析。批判性分析按照 PQD 实时检测和分类的步骤进行，即输入数据准备、预处理、转换、特征提取、特征选择、检测、分类和特征描述。整个综述还探讨了与文献中涉及的干扰类型相关的方面，包括针对多种 PQD 或专门针对电压骤降或电压缺口的研究视角。此外，还审查了所审查工具的实时性能。最后，讨论了尚未解决的问题，并强调了前景。

1 引言

电能质量 (PQ) 被定义为电力系统中给定点的一系列电能特性[1]，这些特性根据一组商定的参考参数进行评估。因此，电能质量干扰 (PQD) 是指这些特性与参考参数之间的偏差，这些偏差可被电网用户（生产商和消费者）感知[2]。因此，PQDs 被归类为电压质量和电流质量的组合进行研究[2]。PQD 的影响取决于这些偏差干扰电力系统预期运行的严重程度。明显的 PQD 将直接影响电力消费者和生产者之间的互动，导致能源效率低下、发电/用电受限、敏感设备故障和损坏、基于控制的工业流程运行不良等。[3].

PQD 的检测和分类是智能电网模式下 PQ 监测系统的主要组成部分之一[3，4]。检测过程有助于指明电压和电流偏差的时间和位置，而分类过程则有助于识别干扰和干扰源，并选择适当的缓解技术来克服当前和/或未来的设备故障。PQ 监测系统的实时方法（同步、连续、单点或多点测量）有助于了解 PQD 在电网中的传播情况，并可就 PQ 问题的缓解做出准确、快速的决策。

某些 PQD 比其他 PQD 更容易出现并导致设备故障。电压骤降又称电压骤降，是指电压有效值在 0.1 至 0.9 pu 之间的下降，持续时间为 0.5 个周期至 1 分钟[5，6]。电压骤降主要由电力系统故障、变压器通电、电机启动和重负载切换造成[5，6]。电压暂降的发生频率介于每年几十次到一千次之间，持续时间一般小于 1 秒，电压下降超过 40%[6]。众所周知，电压骤降是在工业、商业和微电网/隔离网络中产生最高经济损失的 PQD 之一[4,7,8,9,10,11]。其他被广泛研究的 PQD 还有浪涌、中断、不平衡、闪烁和谐波[4,9,11]，文献中已针对这些干扰提出了专门的算法。相比之下，还有一些 PQD 尚未得到广泛探讨，尤其是在可再生能源及其接口电力电子电路高度普及的情况下。

电压缺口是电力电子变流器在电流从一个相位换向到另一个相位时产生的稳态子周期波形失真，从而导致短时过流[5,9,12,13]。电压缺口的特征是：深度，即缺口期间线电压到理想正弦波的平均距离；宽度，即缺口持续时间，其值小于半个周期；面积，即缺口深度乘以缺口宽度的乘积[12]。在考虑电网运行时，仍然缺乏对基于周期的电压缺口进行实时检测、分类、表征和汇总的全面评估和精确技术。因此，目前主要采用非特异性、多干扰检测和分类技术（"多 PQDs "技术）来评估缺口。

人们从不同角度探讨了离线和实时应用中的 PQD 检测和分类问题。文献[14]介绍了几种对故障引起的三相不平衡电压骤降进行分类的方法。文献[13]回顾了用于若干 PQ 事件分类的信号处理和人工智能（AI）技术，其中傅里叶变换（FT）、短时 FT（STFT）和小波变换（WT）被视为主要的信号处理技术，专家系统、模糊系统、人工神经网络（ANN）和遗传算法（GA）被视为主要的人工智能技术。在[13] 中，作者还提出了 PQDs 检测和分类的初始结构，包括特征提取和分类（决策）。文献[15]介绍了用于信号分析的一些技术：FT、STFT、WT、Gabor 变换 (GT)、Stockwell 变换 (ST)、卡尔曼滤波器 (KF) 等，以及一些自动分类技术，如 ANN、模糊逻辑、支持向量机 (SVM) 和贝叶斯分类器。文献[9]对电压事件的检测和分析进行了综述，重点介绍了结合使用 WT、ANN、SVM 和模糊专家系统 (FES) 的离线和实时技术。参考文献[16] 介绍了用于 PQ 事件分类的优化技术类别，并在考虑到输入数据（合成/实际）和输入噪声的情况下给出了比较图表。文献[17]将 WT 与其他技术进行了比较，以检测电压供应系统中的瞬态干扰。 文献[18]探讨了识别电压下陷源的方法，并将其分为基于单监测器和多监测器（多点）的测量方法。这第一批作品（2003-2013 年）主要集中在 PQD 检测和分类技术上，大多数作品不包括预处理或后处理技术。

文献[19,20]对应用于 PQD 检测和分类的信号处理、人工智能和优化技术进行了全面综述。这些综述介绍了用于 PQD 检测和分类的两种互补的结构化方法，即输入数据空间、特征提取、特征选择、分类和决策空间[19]，以及预处理和后处理阶段[20]。此外，还介绍了信号处理、人工智能和优化技术的整体分类法，强调需要更多方法来检测和分类实时、有噪声、三相、单个和多个 PQD。

文献[21] 综述了有效值法、WT、ST、ANNs、SVM 和一些用于识别电压骤降扰动的指标。文献[4] 综述了 WT 和 SVM 在骤降、骤升和谐波检测和分类中的应用，包括 PQD 与相应标准的关系表。文献[22] 综述了船载电力系统的 PQDs 测量和分析，主要涉及电压和频率波动、故障检测和分类、电压骤降和骤升、瞬态和电压缺口、谐波失真和电压不平衡。除信号处理技术外，参考文献[10] 还将模糊逻辑、ANN、SVM、粒子群优化和 GA 归类为用于 PQD 特征提取和分类的软计算技术。

文献[23]对 PQD 检测和分类进行了全面回顾和比较，介绍了不同技术的优缺点。信号处理技术分为八类：FT、WT、ST、GT、KF、希尔伯特-黄变换（HHT）、数学形态学（MM）以及包括变异模式分解（VMD）在内的其他技术。对于 PQD 的分类，提出了七个类别：ANN、SVM、FES、神经模糊系统、极限学习机（ELM）、深度学习和其他模式识别技术。文献[24]提出了数字信号处理技术分类法，其中包括非参数技术和参数技术，后者包括 KF、旋转不变性技术、多信号分类和自回归移动平均等。这些著作有助于拓宽用于 PQDs 检测和分类的最新技术，同时概述了这些技术的优缺点。不过，文献综述中使用的搜索规则并未介绍。

参考文献[25]详细评估了用于 PQDs 检测和分类的 ST 理论和应用。文献[3]提出了一个缓解阶段，输入数据来自可再生能源背景下的 PQD 检测和分类阶段。

文献[11]明确提出了用于 PQD 检测和分类的实时技术，介绍了搜索规则、PQD 出版物的演变、用于 PQD 分类的典型嵌入式系统的内部结构以及其他比较分析。此外，文献[26]还强调了在没有合成（测量）PQD 的情况下测试检测和分类算法的必要性，并得出结论：这对于智能电网中的应用至关重要。同样，参考文献[27]和[28]回顾了深度学习在智能电网中的潜在应用，将 PQDs 检测和分类的连续步骤的结构化方案模糊为一种紧凑、通用的黑箱方法。最后，[29] 总结了几种 PQDs 检测和分类技术的主要优缺点，包括对不同出版物中提出的方法进行准确性评估。

基于上述综述，关于 PQD 的检测和分类已有大量文献，但一些相关主题仍需要从不同角度进行进一步研究和分析，例如实时应用的算法、现场应用的需求等。对其他课题的探索还比较少，如电压缺口的表征和分类。在这种情况下，如何正确选择相关文献来分析当前的技术水平是一项挑战。因此，本文提出了一种系统的、可重复的方法，用于识别广泛探索和少量探索主题的相关文献。此外，大量文献值得从定量角度进行研究，通过文献计量分析来确定研究趋势。本文提出的基于文献计量学的方法被应用于对 PQDs 的实时检测和分类进行系统的文献综述。本文的主要贡献如下

• 
  提出并应用可重复和系统性文献综述的新方法。

  • 
    对从书目数据库中检索到的元数据进行文献计量分析。

  • 
    说明实时检测和分类 PQD 的技术。

  • 
    用于 PQD 检测和分类阶段的技术分类及其在电气工程方面的优缺点。

  • 
    确定并重视边际探索的 PQD（电压缺口）。

图1说明了本文的结构和逻辑框架。根据图1，本文其余部分的结构如下。第2节介绍了理解 PQD 及其分类的概念和理论背景，第 3 节介绍了文献综述的系统方法阶段。第 3节介绍了文献综述系统方法的各个阶段。第4节和第 5节分别对文献计量分析和文献综述中的文献进行定量和定性分析。第5节介绍并分析了 PQD 检测和分类的各个阶段。第6 节总结了与文献综述相关的主要发现，第 7节提出了未来研究的一些展望。最后，第8节给出了结论。

 图 1

文件的结构和逻辑框架

2 电能质量干扰（PQDs）的背景情况

电力系统中某一点的电力特性与一组参考技术参数的比较被广泛称为 PQ[1]。三相系统中的参考（理想）信号是三个相位角和幅值恒定的纯正弦波形，它们之间的相移为 120°。因此，PQD 指的是与参考电压和电流之间的任何偏差。在这种情况下，PQ 被评估为电压质量和电流质量的组合[2]。

表1总结了电网中典型 PQD 的特征。PQD 的类型分为变化（连续偏差）和事件（有限偏差）。

表 1 典型 PQD 的分类

变化通常产生于电力系统的典型运行过程中，而事件通常是不可预测的现象。鉴于电力系统的动态特性（电源频率变化、电压缓慢变化、不平衡），常见变化（波形失真、缺口、波动）的主要来源是电力电子接口，例如可再生能源、节能设备、电动汽车充电器和市电通信系统。开关操作、故障和雷击是典型的事件源。通过使用这两个类别，可以对典型 PQD（连续偏差和有限偏差）进行分类，以便进行检测、处理、分类和进一步处理。

根据表1，电压缺口被归类为变化（连续偏差），而该类别中的其他干扰则是指电力系统基频偏离额定值（50 赫兹或 60 赫兹）的频率变化。此外，在变化中，缓慢电压变化指的是额定有效值电压的 20% 左右的上升（过压）或下降（欠压），持续时间超过 1 分钟。波形失真（包括谐波、谐间谐波和超谐波）是理想电源频率正弦波的周期性偏差，以偏差的频谱内容为特征。波动是电压包络的系统性变化，可被感知为闪烁。此外，不平衡是指三相系统中各相电压和电流幅值之间的差异，和/或偏离理想的相间 120°相移[5]。

根据表1，电压骤降属于事件（有限偏差）。其他事件包括电压骤升，指电压有效值上升超过 1.1 pu，持续半周期至 1 分钟。中断的特点是电压完全消失，即小于 0.1 pu。最后，瞬态是指电压或电流在短时间内发生的突然变化[5]。

3 文献审查方法

进行文献综述的一般模式以《系统综述和元分析首选报告项目》（Preferred Reporting Items for Systematic Reviews and Meta-Analyses，PRISMA）[30]为基础。根据图2，整个过程分为四个阶段，即识别、筛选、资格审查和决策。各阶段的详情见下文各小节。

 图 2

系统文献审查的阶段

3.1 识别和筛选

在识别阶段，我们在 Scopus 数据库中制定了高级搜索规则，以获取与 PQD 检测和分类相关的出版物的书目元数据。搜索规则如图3所示，由逻辑运算符和仅在标题或题名、摘要和关键词中搜索的术语集组成。集合 1 包含检测和分类等一般术语，而含义更广的术语则列在集合 2 中。为了避免这些含义更广的术语误导搜索结果，将包含在标题、摘要或关键词中的第 1 组术语的限制条件合并到门 A 中。第 3 组包含与 PQ 有关的术语，重点是下垂和凹口，而第 4 组也涉及 PQ，但术语更模糊。因此，为避免出现误导性结果，在 C 门中合并了包含集合 5 术语的限制条件。在 E 门中合并的搜索必须包括一般主题术语（B）和 PQ 术语（D）。最后，在门 F 中合并集合 6 中的术语，以包括更多与电压缺口相关的出版物，因为该主题的结果非常有限。

 图 3

在 Scopus 数据库中应用高级搜索规则

检索规则于 2022 年 3 月 2 日应用，仅限于 2021 年之前的出版物。搜索结果为 4068 条记录。然后，在筛选阶段，删除了重复的记录。由此产生的 4059 条记录，包括 2140 篇会议论文（53%）、1841 篇期刊论文（45%）、61 篇评论（2%）和 17 篇其他类型的出版物，如书籍、书籍章节等（< 1%），将在第 4 节的文献计量分析中进行定量研究。4.

3.2 资格与决定

资格审查和决策阶段介绍了筛选程序，以确定在严格审查中进行定性分析的相关和多样化研究论文的缩减集。我们只考虑期刊论文和会议论文，因为它们能很好地概括研究现状。遴选程序分以下四个步骤进行。

• 1.
  分类定义了两个维度对论文进行分类，即根据发表日期划分的时间段（即≤2005年、2006-2010年、2011-2015年和2016-2021年）和PQD类型（即多重PQD、电压下陷和电压缺口）。根据这两个维度对所有论文进行分类，最终选出按时间和干扰类型分布的论文。按时间分类非常简单，而按干扰类型分类则是通过在标题中搜索下陷（或电压骤降）和缺口这两个词来实现的。未被归类为下陷或凹槽的论文被归入多重 PQD 类别。由此得出的两个维度的论文分布如图4 中浅蓝色矩形所示。

• 2.
  评分公式从不同角度制定了一个公式来衡量论文的相关性，并提出了五个指数。标题相似性指数计算的是论文标题中重合词与总词之比，而重合词则由与主题相关的预定义词给出，如实时、下垂、检测等。同样，文摘相似度指数是根据文摘计算的，而交叉引用指数则定义为交叉引用（即检索列表中论文的引用次数）与同年或以后被引用次数最多的论文的引用次数之比。同样，综述交叉引用指数的计算也只考虑列表中综述论文的引用情况。最后，期刊指数的定义是：期刊为 1，会议论文为 0。

 图 4

按期间和 PQD 类型分列的通过严格审查遴选程序的论文数量

使用层次分析法（AHP）[31]对五个指数的权重进行估算。AHP 是一种多标准决策方法，其中各因素按层次结构排列。因此，权重是通过估算成对比较的相对大小和进一步计算得出的，详见[31]。表2 列出了所建议的五项指标的权重。每篇论文的总分是由各项指数之和乘以相应权重计算得出的。考虑到 2011 年至 2021 年（即 2011-2015 年和 2016-2021 年）期间的论文比例大于 2011 年之前（即 ≤ 2005 年、2006-2010 年）的论文比例，根据得分选出 404 篇顶级论文（占搜索列表中论文的 10%）。这种优先排序是为了考虑更多近期的论文。此外，针对干扰类型所选论文的数量也尽可能平均分配。结果如图4 中的天蓝色矩形所示。

• 3.
  质量评估对排名前 404 位的全文论文进行评估，以减少严格审查的选择范围，同时制定表3中的五个问题。为这些问题定义了三组限定条件：0（完全没有）、0.5（一般）、1（绝对）}。然后应用 AHP 估算每个问题的权重，结果见表3。对每篇论文的问题进行评估，计算出总分，即每个问题的结果之和乘以相应的权重。最后，167 篇得分高于 0.8 的论文被选中进行严格评审，如图4 中深蓝色矩形所示。

• 4.
  扩展方法由于最初检测到的有关电压缺口的论文极少（仅有 13 篇），因此又确定并收录了 12 篇与电压缺口相关的论文。用于识别其他论文的扩展方法是基于文献耦合和共同引用的概念，详见文献[32]。由此得出的论文数量见图4 中的黄色矩形。

表 2 计分方程各指数的权重

表 3 质量评估问题及其权重

通过上述四个步骤的筛选程序，得出了表4 中报告的论文，这些论文按照建议的类别，即时期和 PQD 类型进行了分类。

表 4 为干扰类型和时期确定的参考文献

4 文献计量分析

图5 显示了与 PQD 的检测和分类有关的出版物的数量，同时还显示了在标题、摘要或关键词中包含 "实时"（或 "在线 "或 "联机"）字样的出版物的数量。

 图 5

与 PQD 的检测和分类有关的各类出版物数量的长期变化情况

从 2000 年到 2010 年，人们对 PQ 检测和分类的兴趣与日俱增（见图5）。2014 年出现了明显的下降，但随后到 2019 年又出现了积极的趋势。虽然论文总数在 2020 年和 2021 年呈下降趋势，但与实时性相关的论文却明显增加。此外，图5显示，在标题、摘要或关键词中包含 "实时 "一词的出版物数量很少，仅在最近十年才大量出现。这种情况凸显了对 PQD 的实时检测和分类进行进一步研究的必要性。

为了观察各国的研究状况，表5按第一作者所属单位列出了不同国家的出版物数量。表中列出了贡献最大的七个国家，即发表论文超过 100 篇的国家。中国的贡献最大，遥遥领先于其他国家，其次是印度、美国、巴西和西班牙。表5还显示了含有 "实时 "一词的出版物数量。相应的排名与出版物总数的排名相似，但巴西除外，排在第六位。表5还报告了排名前七位的国家在出版物总数中所占的百分比，其中前三位，即中国、美国和印度，在出版物总数中所占的百分比超过 50%，在使用 "实时 "一词的出版物中所占的百分比超过 60%。

表 5 按专题出版物总数排序的前七个国家

关于出版物的原始语言，英语占 85%。此外，还有相当大的 13% 是用中文撰写的，其余 2% 是用其他语言撰写的，如西班牙语、波兰语和葡萄牙语。

图6 显示了从标题中检索出的一组类别，以及每个类别中出版物数量的结果。图 6 还显示了每个类别中标题、摘要或关键词中包含或不包含 "实时 "一词的出版物数量。

 图 6

按主题和 PQDb类型（有无 "实时 "一词）分列的出版物数量及各自的百分比

图6a报告了一般主题的结果，显示与检测有关的出版物数量最多。检测一词通常指识别 PQD 发生的算法。根据发表论文的数量，第二类是监测，指的是跟踪功率信号，包括 PQD。在这种情况下，硬件实现成为一个重要方面。第三类是分类，指的是识别 PQD 的类型，如下陷、陷波、谐波、瞬态、闪烁。类别分析的含义更广，包括其他类别中描述的几个方面。评估类别包括 PQD 影响分析方法。特征描述是指对定义 PQD 的参数进行量化，例如电压骤降的深度和持续时间。

图6a还显示了在一般主题中使用 "实时 "一词的出版物的相应百分比。监测类出版物所占比例较大，因为这类出版物通常讨论实时实施，即算法和硬件。检测在实时应用中也很重要，如动态电压恢复器（DVR）和保护系统的运行。由于 "分析 "是一个更宽泛的概念，因此也包括实时应用的某些方面。分类、评估和特征描述是比较耗时的任务，一般用于离线应用。

图6b显示了 PQDs 类型的结果。与电压骤降相关的出版物数量众多，表明有关该主题的研究已经成熟。另一方面，只有少数研究与缺口有关，这表明有关该主题的研究刚刚起步，鉴于其与工业领域的相关性，需要进一步调查。在同时考虑下垂和凹槽的研究中，不仅在标题中，还在摘要和关键词中搜索了相关术语。然而，找到的出版物很少。在这种情况下，同时分析下垂和缺口的工具可以改善研究状况，并对工业界有用。

关于使用 "实时 "一词的出版物的相应百分比，图6b显示，更多的实时应用已用于电压骤降，例如故障保护系统的运行。不过，这类应用所占比例仍然较低。在同时分析电压骤降和电压缺口方面，开发的实时应用很少。

5 文献综述

本节以 179 篇论文（见第3.2 节）为基础，对 PQD 的实时检测和分类进行了全面的文献综述。根据第 3.2 节对 PQDs 类型进行的分类，与文献综述一起使用。根据第3.2节对 PQD 类型的分类，结合文献综述，从多重 PQD、电压骤降和电压缺口的角度对文章进行分析。

多重 PQDs 类别包括对干扰进行分类的研究。因此，该类别中的大多数文章都介绍了区分从电压波形中识别出的一组 PQD 的方法。在 PQDs 检测和分类研究的初期，文章主要集中在提取特征的工具上，以区分 PQDs 的类型。例如，参考文献[33] 提出以 WT 作为变换和提取特征的手段，而[40] 则利用 ST 来提取独特的特征。因此，在第一阶段，参考文献[33] 和[40] 以及类似的研究[34,35,36,37] 为多种 PQD 的分类奠定了基础。之后的研究主要集中在 PQD 的自动分类上，大多采用人工智能技术，如 ANN[38,39] 和 SVM[50]。在此背景下，其他研究还包括组合 PQDs 的分类，如下陷与谐波、闪烁与下陷等[61]。最近，PQDs 检测和分类的实时性能也受到了关注[11]，因为它可应用于故障保护系统、根源检测和缓解。另一个实时应用是利用系统各节点的测量数据分析 PQD 的传播。

根据 PQD 类型划分的第二类是电压骤降。这组文章一般侧重于将电压暂降分为不同类别。例如，一些研究采用了电压暂降的三相分类[140,158]，这与导致电压暂降的故障类型密切相关。该类别分析的另一个方面是根据电压骤降的根本原因进行分类[133,147,149,150,180]，例如故障、感应电动机和重负载的启动以及变压器通电。一些研究[132,173,174] 还对电压骤降进行了特征描述，即量化电压骤降的持续时间、幅度、起始和终止相位角等参数。最后，这组文章还包括针对 DVR 和保护系统运行等应用的瞬变检测研究[134、136、153]。在这些应用中，实时检测至关重要。

根据 PQD 类型划分的第三类与电压缺口有关。这些研究主要涉及电压信号缺口的检测[189、190、194、205、206、209]。在某些情况下，也会对电压缺口进行表征。然而，这种表征通常是初步的、模糊的，而且会遗漏电压缺口的重要特征。此外，文献中也没有对电压缺口类型进行分类。

按干扰类型对文章进行分类旨在解决不同的关注主题：PQD 类型的分类；电压骤降的分类、特征描述和检测；以及电压缺口的分类、特征描述和检测。然而，多重 PQD 类别的研究包括电压骤降[ 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66、67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113,114、115、116、117、118、119、121、122、123、124、125、126、127、128、129、130、131]，和/或凹槽[33、37、40、43、49、52、54、55、56、61、62、65、66、67、68、74、75、77、79、82、84、85、87、91、94、95、96、97、98、99、100、102、103、105、106、107、108、109、110、112、113、114、115、116、118、121、123、124、130]，尽管在这些情况下，没有特别关注这些干扰。

从另一个角度来看，PQD 的实时检测和分类过程可以从阶段和步骤进行分析，如图7 所示。在文献综述中，确定了四个主要阶段，即：(i) 输入空间，(ii) 预处理，(iii) 特征工程，(iv) 决策空间。此外，每个主要阶段都包括实现其目标的步骤。在综合流程中确定了八个步骤。不过，并非所有步骤都是必要的，因此建议的模式应具有灵活性。在本次审查中，这些步骤定义如下：

• 1.
  输入数据准备 (i)从不同来源获取数据，用于设计和训练算法。数据来源包括实验室实验、实地测量、模拟以及用代表不同 PQD 的方程生成的合成数据。这一步骤构成了输入空间阶段。

• 2.
  数据预处理 (ii)准备输入数据以提高后续阶段效率的步骤。预处理包括分割、归一化和去噪等任务。数据验证也是数据预处理步骤的一部分，以确保数据的可靠性和正确性，即数据质量。不过，在所查阅的文献中，还没有关于数据验证的详细描述。这一步骤属于预处理阶段。

• 3.
  转换 (iii)将原始数据从一个域（如时间、频率、时频）转换到另一个域的过程。用于 PQD 检测和分类的变换包括 FT、WT 和 ST 等。转换步骤是特征工程阶段的第一步。

• 4.
  特征提取 (iii)（从转换输出/系数中）计算出可用于决策空间工具的数字指数。这些指数通常包括统计变量。特征提取步骤是特征工程阶段的一部分。

• 5.
  特征选择 (iii)选择特征和降低维度以提高决策空间效率的过程。可以使用优化方法和降维技术进行手动或自动选择。特征选择步骤提供了特征工程阶段的输出结果。

• 6.
  检测 (iv)通过阈值和触发器识别不同于正常运行的状态。检测是决策空间中的一个步骤。

• 7.
  分类 (iv)PQD 类型的区分。分类大多使用人工智能技术自动进行。分类是决策空间中的一个步骤。

• 8.
  表征（单个 PQD） (iv)计算表征单个 PQD 的参数（如电压骤降：起始/结束点 (POW)、持续时间、幅度、相角跃变）。特征描述是决策空间中的一个步骤。

 图 7

实时检测和分类 PQD 的一般方案以及审查中要处理的横向专题

文献综述按照八个步骤进行结构和开发，以对 PQD 进行实时检测和分类。在整个综合综述中，分析了根据扰动类型划分的类别，即多重 PQD、电压骤降和电压缺口。此外，还考虑了实时运行的各个方面。

5.1 输入数据准备

PQD 的检测和分类过程始于信号的采集。根据文献，这一过程可分为两类：基于测量（实验室、现场）的技术和基于模型（方程、模拟）的技术。在大多数情况下，基于模型的技术用于算法训练，基于测量的技术用于部署最终的探测器/分类器。

表6总结了输入数据准备步骤中每种方法的优缺点。表中还列出了应用这些技术的参考文献。这些参考文献按照 "干扰类型 "分类，即多个 PQD、骤降和缺口。为说明这些技术的重要性和使用情况，还列出了每个类别在参考文献总数中所占的百分比（见表4 中每个类别的参考文献总数）。

表 6 输入数据来源汇总

5.1.1 实地测量

这种方法的主要目标是在实际运行条件下采集真实信号。现场测量同样需要实验室测量所用的专业设备，但信号由电网直接提供。因此，由于事件的不可预测性，事件的可用性受到了限制。具有噪声的干扰、偏差和变化之间的同时性以及受电力需求变化影响的 PQD 的演变和传播是现场测量的特点。这些现实因素要求开发用于 PQD 检测和分类的强大算法。通常，测量的目的是捕捉最大信息量，但有时也会关注特定的 PQD，如电压骤降和缺口。

5.1.2 等式

无需专门的设备来生成和测量 PQD，有些 PQD 可以抽象为数学模型，模拟真实的波形失真。在这种波形级方法中，信号最初是作为理想的正弦波存储在计算结构（即阵列和矩阵）中，然后叠加不同种类的变化和事件。虽然这些方程非常灵活，易于更改任何参数，但在不了解系统特征的情况下，要精确复制真实的干扰及其随时间的演变是相当具有挑战性的。这些方程可扩展用于表示不同类型的干扰或特定干扰，如电压骤降和电压缺口。

5.1.3 模拟

专业软件的模拟也依赖于数学模型。不过，这种系统级方法不仅可以再现电力系统不同运行条件下的不同 PQD，还可以评估干扰在时间和空间上的相互作用和演变。因此，仿真可用于复制产生某种干扰的运行条件，修改这些条件以对系统响应施加压力，在受控环境中组合不同的干扰，包括电力系统变化以预测 PQD 的未来行为等。仿真结果在很大程度上取决于模型与真实系统的接近程度，因此在预测其他运行场景的结果之前，有必要在真实测量和仿真结果之间进行一个验证阶段。

5.2 数据预处理

在获取 PQDs 之后，需要使用一些技术在进一步处理之前对数据进行处理。这些技术是可选的，不应修改采集信号中包含的有用信息。这一阶段所需的额外硬件和/或软件可提高后续阶段检测和分类算法的性能。表7总结了这些步骤的优缺点，指出了应用的参考文献，并根据 "干扰类型 "类别报告了使用百分比。

表 7 数据预处理技术摘要

5.2.1 分类

这项技术用于在时域中分离所采集信号中最相关的部分，尤其是在需要分析事件（见表1）时。如果正确应用了分割技术，后续处理阶段的计算负担可能会减轻，因为无关数据会被丢弃。不过，当同一测量信号中同时存在不同干扰时，对相关性的判定可能会有所不同。因此，在处理多个 PQD 的检测和分类时，一般会使用一组阈值。此外，对特定干扰较少使用分段法，如表7 中有关电压骤降和电压缺口的文献所示。

5.2.2 变性/过滤

与分割技术类似，滤波或去噪技术也是为了剔除采集信号中的非相关信息。在这种情况下，对信号的光谱成分进行隔离。因此，可能需要额外的硬件（模拟滤波器）和/或处理步骤（数字滤波器）。当相关 PQD 的带宽已知，或仅对某些频率的发射感兴趣时（例如，仅对基频的电压和电流感兴趣），这种技术最为有用。与分割和归一化技术相比，去噪技术在 PQD 检测和分类中的应用较少。

5.2.3 标准化

归一化是多 PQD 和电压骤降最常用的数据预处理技术，但在缺口的具体检测和分类中使用较少（见表7）。与分割和去噪类似，归一化步骤通过避免计算大量数字来减轻计算负担。这是通过将所有数量除以一个数值基数（即信号的额定值或峰值）来实现的。然而，由于失去了标度，相关振幅和非相关振幅之间的区别将取决于数值基数的相对选择。

5.3 转变

在获取数据并最终应用一些预处理技术之后，转换是传统上信号处理中最常用的阶段。这一阶段的目的是使用原始数据的不同表示形式，通常是通过改变分析域来揭示隐藏的特征和模式。

如图8 所示，用于 PQD 检测和分类的大多数变换都可归类为时域、频域和时频域。其他杂项变换技术广泛应用于其他领域（语音识别、心律失常分类、去噪、图像压缩等），研究人员也采用这些技术对电力系统的电压和电流数据进行分解和/或聚类，以实现 PQD 的检测和分类。应用于 PQD 检测和分类的变换技术组别如图8 所示，其中时域变换又分为参数技术和非参数技术。下文将进一步介绍每种时域、频域和时频域技术。

 图 8

转型技术分类法

表8 列出了转换技术最相关的优缺点。表中还根据 PQD 的类型列出了应用的参考文献和每个类别各自所占的百分比。

表 8 转换技术一览表

5.3.1 时域

时域变换被广泛用于跟踪监测信号特征随时间的演变。它们通常用于分析 PQ 事件，如中断、瞬态、快速电压变化、电压骤升和电压骤降，因为它们原则上是不可预测的非周期性现象（见表1）。不过，像缺口这样的 PQ 偏差也可以在时域中进行处理，因为它们的频谱特征分布在很宽的频率范围内。图8所示的时域变换可细分为非参数变换和参数变换，前者如对称分量跟踪、DQ0、时域变换 (TT)、复域空间相位模型 (SPM)、相空间重构 (PSR)、MM 等，后者如 KF、锁相环 (PLL)、自适应滤波器 (AF) 等。非参数变换将原始测量信号分解成多个部分，清楚地显示 PQD 在时间上的进展情况，而参数变换则使用对样本（信号）所在群体统计分布的假设。参数变换主要用于跟踪和统计估计幅度、相位角、频率等。虽然依靠相位理论的变换（如对称分量）原则上属于频域抽象，但计算出的振幅和相位角的变化通常在时域中进行分析。

5.3.2 频域

频域变换主要是利用 FT 对稳态信号进行变换。这种变换将失真信号分解为具有不同频率的纯正弦波之和。快速 FT（FFT）是一种广为人知的离散 FT（DFT）计算技术。DFT 的计算方法如下[66]：

$$V^{n}= \sum\limits_{i = 0}^{N - 1}{v\left[ {i +\left( {n - 1} \right) \cdot N} \right]}\cdot \exp \left[ {{ - j\left( {2\pi ki} \right)} \mathord\left/ {\vphantom {{ - j\left( {2\pi ki} \right)} N}}}\right.\kern-0pt}N}}\right]$$

(1)

其中，N是一个周期内的采样个数，n是信号周期的阶数，n= 1、2、...、10，表示参数的绝对值。^Vn[k] 是第 n 个周期中包含的采样的 DFT，v[i] 表示采样输入信号，i= 0、1、2、...、L-1，L是信号的长度。

对于多重 PQD 的检测，FFT 主要用于计算基波或特定谐波的幅值、谐波分量之间的相位角偏移、有效值和总谐波失真[66,89,90,97,102]。虽然 FFT 和 DFT 可能会对非稳态信号产生不准确的结果，但一些研究已将这种变换用于电压骤降检测，还有一些研究将 FFT 用于陷波分析[188]，因为这种干扰的频谱成分相当分散在整个频率范围内。不过，FFT 也与 WT[61、80、189]、192、196] 和模式分解 (MD)[99] 技术结合使用，以应对非稳态 PQD。

5.3.3 时频域

在时频域分类的变换保持了时间和频率技术的大部分优点。这些技术可以同时提供时间和频率信息，有助于提高 PQD 检测和分类算法的准确性。

STFT 是对假定为静止的一段信号进行 FT 计算。STFT 已被用于检测多个 PQD[35,102] 和电压骤降[137,160]。

小波分解（WT）又称多分辨率分析，它将原始信号分解为不同尺度的短期波形，称为 "母小波"。离散小波分解技术（DWT）是小波分解技术的离散实现，作为主要的变换技术[33,34,37,38,39, 42,44,45,46,48,51,53,55,59,60,62,63,64, 69,76,83,95,101,110,123]或与其他技术相结合[35,36,41,61,73,80,102,117,126]，已被广泛用于多重 PDQ 的检测和分类。 它还被用作电压骤降[133,142,146,154,168,169] 和缺口[187,190,191,193,194,197,198,199,204, 208] 检测和分类的主要变换技术，或与其他电压骤降[160,181,186] 和缺口[189,192,196,202] 技术相结合。DWT 由[33] 给出：

$$DWT_\{psi }xleft( {m,n} \right) = \int_{ - \infty }^{infty }{x left( t\right)\psi_{m,n}^{*}\left( t \right)dt}$$

(2)

其中，_ψm_,n(t) 是母小波。

ST 是一种混合技术，包括对 WT 的相位校正和对 STFT 的可变高斯窗，从而将这两种技术结合起来。ST 可以通过将连续 WT 与相位系数相乘来计算[40]：

$$S\left( {\tau ,f} \right) = \exp \left( {i2\pi f\tau } \right) \cdot W\left( {\tau a} \right)$$

(3)

ST 作为主要变换技术[40、43、49、52、54、57、68、70、71、72、75、77、78、81、85、92、94、96、104、105、118、120、125]，或与花键小波[41]、TT[65、109、114]、VMD[88]、WT[117]和其他技术[102]相结合，被用于多个 PQD 的检测和分类。同样，它也作为主要技术[143,149,178] 或与 VMD[176] 和 FT[184] 结合使用，用于骤降评估。

最后，GT、希尔伯特变换 (HT) 和 Chirplet 变换 (CT) 是用于检测和分类 PQD 的其他时频技术。GT 主要作为相位估算的精确工具而闻名，并被用作分析事件（短期偏差）的测量工具。它主要与 Wigner 分布函数结合使用，形成所谓的 Gabor-Wigner 变换 (GWT)[58]，并与时频表示法结合使用。实值时域信号的 HT 可产生一个与原始信号偏移 90°（π/2 弧度）的正交实值时域信号。这种技术与经验模式分解（EMD）一起被广泛应用，形成了所谓的 HHT。研究人员已将 HHT 应用于多个 PQD 的检测和分类[56,73,79,84,102,107,113]，并特别应用于电压骤降[147,150,173]，但尚未应用于电压缺口的具体评估。CT 可视为 FT、STFT 和 WT 的一般化。与 WT 中的母小波类似，啁啾小波通常由单个母啁啾小波生成，母啁啾小波是一个窗口函数。它已被用于评估多个 PQD[98] 和电压缺口[202]。电压骤降尚未得到专门处理，也未使用 CT 对其进行表征。

5.3.4 杂项

研究人员采用广泛应用于其他领域的变换技术对 PQD 进行检测和分类。MD 技术主要包括 EMD[86,93,129] 和 VMD[88,99,100,124,130]，用于评估多个 PQD，也可用于电压骤降的具体评估[176]。EMD 采用线性或非线性输入信号，并将其迭代分解为一系列较小的分量，称为内在模式函数 (IMF)。VMD 基于约束变异优化问题，是一种非递归自适应技术，可将线性或非线性输入信号分解为有限数量的子信号或具有特定稀疏特性的模式（紧凑带限 IMF）。此外，还有其他适用于 PQD 检测和分类的技术，如在过完整混合字典矩阵上的稀疏信号分解 (SSD)[87]、奇异频谱分析 (SSA) 和 Curvelet 技术[103]、二维图像技术（灰度图像）[112,179,181]、数字铅笔[134]、矩阵铅笔[153]和 Goertzel 方法[166]。

5.3.5 转化技术的定量分析

图9描述了变换技术如何根据分析领域、使用方式（主要技术或与其他技术相结合）、干扰类型和实时应用进行分布。具体来说，图9a和 b 根据文献综述中发现的文章绝对数和相对数，分别列出了用于 PQD 检测和分类的最流行变换技术。分为时频（52%）和时域（19.7%）的技术占转换技术总数的 71.7%，而属于时频域技术的 WT 和 ST 则占转换技术总数的 44.1%。WT 要么作为主要技术使用，要么与其他技术（如 FFT、ST 和其他时域技术）结合使用。

 图 9

Distribution of papers in the identified transformation techniques. a The number of papers, b percentages and number of papers that use a combination of techniques, c percentages and number of papers from the time perspective, d the type of disturbance perspective, and e the real-time perspective

The evolution of transformation techniques is described in Fig. 9c. WT has been intensively used as the main time–frequency technique for the detection and classification of PQDs since 1996 [33], and from 2011 onwards it has been used in combination with other techniques. ST and other time–frequency techniques have increased their participation in PQDs detection and classification, as well as time-domain techniques such as SPM, PSR, and (extended) KF/AF. Nevertheless, the combination of several techniques has seen increased interest from researchers, especially in the last six years.

In terms of the PQDs to be detected and classified, Fig. 9d shows that WT, time-domain techniques, and the combination of several techniques have been used for the assessment of multiple PQDs as well as voltage sags and notches. Although WT has been the preferred technique for the assessment of voltage notches, time-domain techniques are becoming relevant for assessing this type of disturbance. The trend regarding transformation techniques is to develop one technique, or a combination of several, that can be used for the accurate detection and classification of the highest number of PQDs (variations and events, see Table 1).

Figure 9e shows that WT, ST, and time-domain techniques (SPM, PSR, and KF/AF) are used for real-time detection. Real-time detection and classification are also performed by the combination of transformation techniques such as WT and FFT, WT and ST, etc.

5.4 Feature extraction

Feature extraction aims to reduce the amount of data from the transformation stage that will be processed for the detection and classification of PQDs. A set of statistical, time series, spectral and image features can be used for this purpose. A set of features describing one PQD, e.g., variations, may not be suitable for describing another type of PQD, e.g., events. Therefore, establishing a set of comprehensive, robust, and accurate features that allow the detection of different PQDs is one of the most challenging tasks in the process.

Figure 10 depicts the categories into which the feature extraction stage can be further divided. The main advantages and disadvantages are listed in Table 9, which also includes references with applications and the respective percentage of usage according to the type of disturbance.

Fig. 10

Taxonomy of features for detection and classification

Table 9 Summary of feature extraction techniques

5.4.1 Statistical features

Mean and median are the set of most used statistical features for central tendency. Arithmetic mean (also known as arithmetic average) is a central tendency measure for a finite number of values from an observation process (sampling). This is calculated as the sum of all values divided into the amount of data and is a relatively simple way of computation (low computational cost) but sensitive to outliers (data with atypical values). This metric is widely used for feature extraction in multiple PQDs, and specifically for voltage sags and notches (see Table 9). Less sensitive to outliers but with a compulsory “ordering” process, the median is the other central tendency widely used for feature extraction. When dealing with a large enough dataset, the underlying population distribution may be assumed as normal (Gaussian). Therefore, similar values for both mean and median are obtained. However, many processes do not follow a normal distribution, and thus median may be a more accurate measure of central tendency than the mean.

In contrast to central tendency, a measure of dispersion is achieved by many different indices. Maximum and minimum values are easy-to-compute metrics that give general information about the analyzed dataset. The interquartile range is a descriptive metric defined as the difference between the 75th and 25th percentiles and needs an ordering process that may be challenging for online applications in embedded hardware. Deviation metrics in the form of maximum deviation, standard deviation, mean absolute deviation and median absolute deviation compute the distance between the observed value of a variable and a central tendency metric. Variance and Higher-Order Statistics (HOS) such as skewness and kurtosis aim at describing the shape of the underlying probability distribution function. These metrics are widely used for detection and classification of multiple PDQs, voltage sags and voltage notches (see Table 9).

5.4.2 Time series features

Time series are sequences of data points ordered in the time domain. The sampling process is usually performed at a fixed frequency, and therefore the time between successive samples is theoretically the same. In the context of electrical engineering, time-varying electrical variables such as voltages and currents are sampled through analog–digital converters, which convert the real-life analog signals into discrete signals. The cyclic nature of AC systems is defined by a cycle, which is the time that a signal repeats its values in the time domain. Therefore, it is possible to characterize a signal by extracting sample-based or cycle-based features.

Sample-based features take advantage of the evolution of discretized signals in the time domain. The features are the extracted samples and therefore very detailed information on signal evolution can be retrieved. However, a large amount of data can result from this stage if a high sampling frequency is used. Sample-based feature extraction techniques such as instantaneous values, phase angle and momentary deviation (Euclidean distance) are used for multiple PQDs, voltage sags and notches according to the references indicated in Table 9.

Cycle-based features are focused on the evolution of periodic signals over time. In this sense, the features are extracted in multiples of one cycle of the main signal and therefore the amount of processed data is much less than that using sampled-based features. However, information on sub-cycle PQDs like notches, spikes and transients is no longer available in this approach. RMS value, crest and form factors, energy, entropy, correlation, and signal-to-noise ratio are usual metrics computed from a cycle-based approach. These metrics are used for feature extraction of multiple PQDs, voltage sags and notches (see Table 9).

5.4.3 Spectral features

Spectral features are a set of indices that naturally result after the use of frequency or time–frequency domain transformation techniques. In the context of power systems, the fundamental frequency is the nominal frequency at which most of the electric power is generated and transmitted (theoretically 50 Hz or 60 Hz). In contrast, spectral distortion is the result of the nonlinear, nonconstant behavior of electrical equipment that indicates a deviation from the ideal (reference) pure sinusoidal signals. In the context of power systems, spectral distortion can be generally classified into the harmonic range (below 2 kHz), the so-called supraharmonic range (between 2 and 150 kHz) or the high-frequency range (above 150 kHz). Fundamental frequency and harmonic distortion are used for the detection and classification of multiple PQDs, voltage sags and notches (see Table 9). There is a special case of harmonic distortion, called Distortion Bands, where the distortion is computed in other ranges different from harmonic, supraharmonic or high-frequency ranges [197, 202].

5.4.4 Image features

Image features are mostly related to 2D functions and/or representations of PQDs. Taking advantage of the steady-state cyclic variation of voltage and current in power systems, some transformation techniques (SPM, PSR, instantaneous symmetrical components, etc.) describe these signals as phase vectors in the complex plane (phasors). From this, the most popular 2D feature extraction technique relies on Ellipse features since the resultant circumferences can give useful information about the features of the variations and events listed in Table 1. Ellipse features have been used for specific detection and classification of voltage sags [151,152,153, 157, 158, 163, 172]. Other features taken from the 2D representation of PQDs are shape features and factors (center of mass, eccentricity, convexity, centroid distance, chord length, etc.) [140, 169], binary image [50, 112], and image matrix [111], among others.

5.5 Feature selection

The step of feature selection involves identifying as few characteristics as possible to obtain enough information that can yield suitable results in the decision space stages (detection, classification, and/or characterization of PQDs). Hence, the ways of selection and the selected features depend on what suitable results mean in the context of each study. The feature selection also reduces the computational burden in the decision space and usually leads to more accurate results.

Different categories have been proposed for feature selection techniques in the literature. For instance, reference [76] proposes three main categories, namely, filtering, wrapper, and embedded, which are related to the level of dependence of the feature selection on the decision (learning) algorithms. Thus, filtering approaches are very independent, and embedded approaches intertwine the selection and decision algorithms. In this literature review, three groups of methods are identified, including handcrafted, optimization methods, and dimensionality reduction algorithms.

Table 10 summarizes the advantages and drawbacks of the most relevant feature selection techniques identified in the literature review according to the proposed classification. The table also reports the references where the methods are applied according to the type of disturbance categories and presents the usage percentages.

Table 10 Summary of feature selection techniques

It is worth mentioning that deep learning techniques perform an automatic process of feature selection. It is conducted in the first layers of the classifiers where the best features for the decision space are automatically selected. Therefore, no category is included in this section for this type of tool because no external intervention is required.

5.5.1 Handcrafted/empirical

In handcrafted feature selection, a detailed manual analysis is performed on the extracted features to observe the differences according to the type of PQD. For instance, this approach is observed in [33] where coefficients resulting from the WT and multiresolution analysis are analyzed for sample signals with different PQDs. The study in [33] and many others, e.g., [34,35,36,37,38,39,40,41], show how the analysis can be mostly supported by visual inspection of signals (time-domain waveforms) and extracted features (time-domain indices). Most of the handcrafted feature selections observed in the literature apply a contextual approach where a physical meaning is given to the extracted features. Some examples of contextual feature selection are [33,34,35,36,37,38,39,40,41]. The literature also shows that other empirical approaches such as sequential forward selection, sequential backward selection, and random mutation have been mainly used for the detection and classification of multiple PQDs. In these empirical approaches, a set of features are obtained beforehand based on expert knowledge or using similar features to previous studies. Then, in forward selection methods, e.g., [60, 88, 89, 91, 96, 102, 112], features from the established set are included one at a time, and the performance of the classifier is verified. The process is repeated until the performance has no apparent improvement. Conversely, backward selection, e.g., [88], uses the complete set of features and removes one at a time until the desired trade-off between accuracy and computational performance is reached. On the other hand, random mutation tests random subsets of features and selects the one with the best performance [57, 62, 64, 71, 117].

Those studies from the literature focused on voltage sags mainly use contextual feature selection. For instance, reference [132] extracts directly the features from the voltage waveforms according to standard definitions, i.e., initial phase angle shift, recovery period, voltage change. In other cases, coefficients from transforms, e.g., WT [133] and ST [143], are analyzed contextually according to their correspondence to the standard parameters that characterize voltage sags, i.e., magnitude, duration, etc. A combination of forward and backward selections with GA to select the best features to identify voltage sag source location (upstream or downstream) is proposed in [185].

In the studies focused on voltage notches, contextual feature selection is dominant for handcrafted methods [187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210]. In this case, selected contextual features are analyzed visually from the coefficients of WT.

5.5.2 Optimization methods

Optimization methods have also been used for feature selection purposes in PQD detection and classification. According to [212], a mathematical optimization method which consists of finding the best possible solution by changing variables that can be controlled, is often subject to constraints. Optimization methods can be classified as deterministic (exact) or stochastic (approximate), and stochastic methods can be further divided into heuristic and metaheuristic. Most methods used for PQD detection and classification are metaheuristic. Metaheuristic methods include exploratory search methods such as GA, and swarm optimization algorithms such as particle swarm optimization. For instance, GA is used in [55, 102, 109] to find the optimal set of features to classify multiple PQDs with high accuracy. This is based on the mechanics of selection and survival of the fittest, and consists of three operations including reproduction, crossover, and mutation [55]. The studies in [55, 102, 109, 127] show that GA maintains or improves the classification accuracy while it decreases the computational burden (reducing the number of features). A variation of GA is presented in [109], where a fast and elitist nondominated sorting is used to generate Pareto-optimal solutions. This modification offers better speed, solution spread, and convergence. The artificial bee colony optimization algorithm is used to improve the performance of a multiple PQDs classifier in [95], while the artificial bee colony is used in [123] in combination with particle swarm optimization to improve the accuracy of a PNN in PQD classification. The artificial bee colony algorithm is a swarm intelligence optimization technique where different types of bees apply strategies for finding the best sources of food (solutions). This algorithm uses three groups of bees, namely, employed bees, onlooker bees, and scout bees. Employed bees search for food in specific sources and share the information to onlooker bees, whereas scout bees search for new sources of food. This optimization method provides an optimal subset of features with fast convergence [95]. Other swarm colony algorithms have also been used for feature selection. For instance, ant colony optimization [114] is inspired by the foraging behavior of ants, and offers high accuracy in the classification of multiple PQDs and a faster solution to an optimal feature subset than other studies.

Feature selection based on optimization techniques is also used in studies focused on voltage sags. The study in [168] uses ant lion optimization to improve performance in classifying the underlying causes of voltage sags. This optimization technique mimics how ant lions hunt and consume their prey and provides advantages such as good population diversity, storing good solutions, exploitation, exploration, and flexibility [168]. Similarly, a teaching–learning-based optimization technique is used in [177]. The teaching–learning-based method is a population algorithm that mimics the influence of a teacher on the output of learners in a class. Results in [177] demonstrate good accuracy in classifying causes of voltage sags in noisy signals with a reduced subset of optimal features. GA is used in [185] for voltage sag source location classification.

5.5.3 Dimensionality reduction

In machine learning, dimensionality reduction refers to decreasing the number of input variables in a model, i.e., selecting a subset of the original variables (features) and converting the data to a lower-dimensional space [213]. Dimensionality reduction may be useful for efficiently storing and processing data. Extensive techniques are used in machine learning for dimensionality reduction. Principal Component Analysis (PCA) is one of the most used techniques. PCA is a multivariate technique that analyzes a data table with several variables and extracts the important information to represent the table as a reduced set of new orthogonal variables called principal components [214]. PCA is used for feature selection in multiple PQD classification in [62], while multiway PCA is used for the classification of voltage sags in [141]. Likewise, Independent Component Analysis (ICA) has been also used in applications of voltage sag classification [162, 177]. Other dimensionality reduction techniques observed in the literature for applications of multiple PQD classification include information gain measurement [42], Fischer linear discriminant analysis [100], k-means based apriori [76], Gini index-based threshold for selection of features [75, 98, 110, 112], and maximum relevance minimum redundancy [102]. In the case of voltage sag classification, k-means-singular value decomposition is also used [170], whereas decision trees and the Gini index are used in [211] for binary classification of voltage notches (non-notch/notch).

5.6 Detection

In this review, detection refers to the identification of states different from the ideal conditions of voltage and current waveforms (signals with no disturbance) through thresholds, triggers, and other techniques.

According to the above definition, detection may overlap in some cases with the step of classification because the classification process usually includes a category for ideal conditions of voltage and current waveforms. This situation mainly occurs in the classification of multiple PQDs, e.g., [118, 121]. In such cases, the detection should be considered as part of the classification algorithm and is mostly used in offline applications, where techniques are applied to stored signals. For real-time applications, given that no threshold or trigger occurs, the complete algorithms are constantly executed with a certain periodicity and the process requires high computational performance and storage capacity. There are exceptions in the classification of multiple PQDs, where detection is implemented as a previous and independent step of the process using techniques such as AF [36, 115], sine wave inference [64], and Euclidean square distance [106].

In the case of voltage sag classification, detection is mostly achieved as a previous independent step using techniques such as empirical/handcrafted definition of thresholds [132, 133, 137, 139,140,141, 148, 151,152,153, 163, 172], statistical-based sequential method [135], and ICA [177].

Detection has been described as an important step in combination with classification in the decision space. However, detection as the only aim of the decision space is also of interest for some applications such as the operation of DVR [134, 184], voltage sag compensators [136, 145], and protection systems [146]. In these applications, the process includes some characterization of single PQDs. For voltage sags, techniques used for detection include adaptive notch filter [136], KF [138, 156, 161], integrator model [155], harmonic footprint [160], ICA [162], and Goertzel algorithm [166]. When the interest of the study is the characterization of voltage notches, detection has been conducted using the Teager energy operator and threshold algorithm [201], and the Euclidean norm [206, 209].

5.7 Classification

The main purpose of classification is to categorize the PQDs observed in voltage and/or current signals according to the types of deviations from the ideal waveforms. For instance, Table 1 presents some of the deviation types that identify the categories of PQDs. Among the categories of PQDs there are voltage sags and swells, harmonic distortion, transients and voltage notches, flicker, imbalance, etc. Classification is mostly conducted according to those categories. However, some approaches also categorize the phenomena according to the root causes of the PQD. For instance, reference [81] presents a categorization according to different causes, namely, fault, self-extinguishing fault, line energizing, non-fault interruption, and transformer energizing. Similarly, voltage sags are usually classified according to the main underlying causes, i.e., faults, motor starting, and transformer energizing [175,176,177,178,179,180].

Several techniques for the classification of PQDs have been identified from the analysis of the selected literature. A taxonomy of these techniques is proposed in Fig. 11, which shows three major categories, namely, handcrafted, probabilistic, and AI-based methods. The latter category is divided into various subcategories as it is the most widely used in the literature for the detection and classification of PQDs. Especially, machine learning tools have been widely used for the task of classification. Machine learning is a field of AI that focuses on the development of algorithms to make computer systems able to learn from data. Machine learning can be further divided into supervised learning, i.e., when algorithms need labeled data for training, and unsupervised learning, when no labels are required but are automatically identified by algorithms. In this literature review, only supervised learning algorithms are analyzed because they are the most used ones.

Fig. 11

Taxonomy of methods for classification of PQDs

Table 11 reports the advantages and drawbacks of classification techniques, references of applications and percentage of usage according to the type of disturbance.

Table 11 Summary of classification techniques

5.7.1 Handcrafted/empirical

In handcrafted classification, thresholds to identify the categories of PQDs are defined by the observation of the extracted features during diverse experiments or by using expert knowledge on the physical interpretation of the phenomena. For instance, in [33] the coefficients of the WT are used to detect a variety of PQDs obtained from field measurements. Other approaches use handcrafted classification of voltage sags, e.g., reference [137] presents a method to classify sags according to their root causes including faults, motor starting, and transformer energizing based on thresholds for the STFT. Reference [148] classifies voltage sags according to the type of fault, based on defined ranges for indices calculated with symmetrical components. Other methods [153, 163, 172], analyze visually the ellipses generated through the SPM in the complex plane to define manually the ranges of the ellipse parameters for the types of sags.

5.7.2 Probabilistic

The probability of a signal containing a certain PQD is determined from the probability density functions of the extracted features associated with the disturbance. Examples of probabilistic methods include Parseval's theorem [34], the maximum likelihood [36], and the definition of ranges for statistical variables [40, 41]. Probabilistic methods are also used to identify the categories for classifying sags according to root causes and location (upstream or downstream). These methods include the singularity detection theory [133], the statistical-based sequential method [135], and the energy-based method [139].

5.7.3 Shallow artificial neural networks (ANNs)

ANNs are computational models of reasoning inspired by the human brain [215], and comprise a set of processors (neurons) interconnected through weights passing signals from one neuron to another. An ANN can model complex nonlinear functions using extensive simple operations. Shallow ANNs are formed by an input layer, one or two hidden layers, and an output layer. ANNs are typically used in classification problems where each neuron of the output layer represents a category and is activated according to the respective inputs. In the problem of multiple PQDs and voltage sag classification, several types of shallow ANNs have been used taking advantage of their flexibility and adaptability to problems where labels are well identified, for instance, the learning vector quantization [37,38,39], probabilistic neural network [44, 52, 56, 65, 71, 84, 95, 102, 123, 147, 168], self-organizing learning array [46], radial basis function [47, 83], multilayer perceptron [48, 53, 57, 65, 89, 93, 102, 168, 177, 178], adaptive linear network [82], feedforward [82, 85, 102], backpropagation [90], random vector functional link [113], and modular ANN [143]. Most recently, a learning algorithm known as ELM has been gaining popularity because of its remarkable efficiency. ELM randomly chooses hidden nodes and analytically determines the output weights of a single-layer feedforward network [216]. Examples of ELM applications are [81, 94, 100, 107, 108, 169, 176, 178].

5.7.4 Deep artificial neural networks (ANNs)

Deep learning has emerged as a new machine learning paradigm where deep ANNs are composed of multiple processing layers to learn representations of data with multiple levels of abstraction [217]. This paradigm can dramatically improve the automatic classification abilities in diverse areas such as speech recognition, image processing, and detection and classification of PQDs. A remarkable improvement provided by deep learning, and the main motivation to apply these types of algorithms to PQD detection and classification, is the ability of models to automatically extract the best set of features from raw data to conduct classification. Convolutional Neural Networks (CNN) have been widely used in multiple PQDs and voltage sag classification [103, 111, 116, 119, 121, 125, 130, 131, 158, 164, 167, 171, 179, 183]. Other deep learning models have been particularly used in the classification of voltage sags according to the root causes, e.g., deep feedforward ANNs [124], Long Short-Term Memory (LSTM) [129, 159, 180], Deep Belief Networks (DBN) [165, 175], and independently recurrent neural networks [182].

5.7.5 Decision trees

Decision trees are knowledge-based systems obtained by inductive inference from examples [218]. Then, these systems are driven by the explicit representation of knowledge. Simple in application, decision trees allow for high efficiency which is essential for real-time applications. Moreover, these models provide good physical interpretation of the phenomena. These advantages have motivated widespread use of decision trees, especially in the classification of multiple PQDs, though with lower usage in the classification of voltage sags and notches. Simple decision trees are used in the classification of multiple PQDs [42, 49, 66, 70, 75, 77, 85,86,87, 89, 96,97,98,99, 101, 102, 109, 114, 117, 118, 128]. Some variants such as random forest [102, 105, 112, 126] and bagging predictor [97, 98] and rule-based classifiers [72, 80, 91, 122], have been also used in the literature for multiple PQD classification. Rule-based classifiers are also used in [140, 151, 152] for voltage sag classification and in [200] for voltage notches, whereas decision trees are used in ensemble models as weak classifiers in combination with other methods [185] for voltage sag classification.

5.7.6 Support vector machines (SVM)

SVM are robust supervised learning models applied in classification and regression problems. The basic idea behind SVM is to maximize the gap between different classes [219]. Based on this feature, SVM can be trained using a reduced number of examples. This makes this tool promising in cases where extensive training data is not available as in some applications of PQD detection and classification. SVM have been widely used for detection and classification of PQDs and voltage sags, while having lower usage for voltage notches (see Table 11). Variants of SVM such as multiclass SVM [51, 110, 115], least square SVM [76, 101, 170], rank SVM [86], and directed acyclic graph SVM [92, 127] have been also used.

SVM are used for notch identification in [211], where a classifier, i.e., SVM, is used to obtain a binary categorization of voltage signals, namely, non-notch or notch.

5.7.7 k-nearest neighbor (k-NN)

The k-Nearest Neighbor (k-NN) algorithm finds a group of k objects in the training set that are closest to the test object, and bases the assignment of a label on the predominance of a particular class in this neighborhood [220]. Given the ease of implementation of the model, it has been applied in the classification of multiple PQDs and voltage sags [55, 65, 102, 114, 171]. Simplicity of the method has been the main motivation for application of k-NN in PQD detection and classification. However, it has been mainly used in combination with other methods because of its reported drawbacks such as the reduced accuracy and high sensitivity to the constant k. For instance, in [185], k-NN is used as a weak classifier in an ensemble model in combination with decision trees.

5.7.8 Fuzzy logic

Fuzzy logic approaches are based on the sound theoretical foundations of fuzzy sets [221]. The basic idea of fuzzy logic lies in the definition of true fuzzy logic values of variables between 0 and 1. Fuzzy logic allows a closer representation of human reasoning where the information usually has a level of uncertainty. In some applications of PQD detection and classification, data for training have high uncertainties and thus, in those cases, fuzzy logic represents an alternative approach. For automatic classification of PQDs, fuzzy logic has been used from the beginning of research on the topic. Some examples include [43, 48, 61, 132]. FES have also been implemented [67, 189], as well as extended fuzzy reasoning [45], and fuzzy C-means [54, 68, 96, 120].

5.7.9 Quantitative analysis of classification techniques

Figure 12 presents a quantitative analysis of the selected literature according to the classification techniques described above. In Fig. 12a, the absolute number of individual appearances of each technique is shown, i.e., the number of papers where only one technique (or set of techniques in the same category) is used for classification. It also presents the number of appearances of the techniques in combination with others and the total number of papers where classification is achieved with a combination of techniques from different categories. As seen, shallow ANNs are the most popular models in the reviewed literature, followed by decision trees, SVM, deep ANN, fuzzy logic, probabilistic and handcrafted method, and k-NN. Also, a significant number of publications (19) implement combined methods for classification. The number of papers that do not perform classification is 46, and hence, a total of 133 papers are categorized in techniques for the classification of PQDs.

Fig. 12

Distribution of papers in the identified classification techniques. a The number of papers, b percentages and number of papers that use a combination of techniques, c percentages and number of papers from the time perspective, d the type of disturbance perspective, and e the real-time perspective

Figure 12b shows the corresponding percentages of classification techniques according to the individual appearances. The distribution of combined techniques is also reported in absolute values. In this case, shallow ANNs are the most popular in combinations. For instance, shallow ANNs are used in combination with decision trees, SVM, fuzzy logic, probabilistic methods, and k-NN. Moreover, some methods include the combination of three and four types of classification approaches.

A report on the distribution of classification techniques from different perspectives is included in Fig. 12. Figure 12c shows the distribution of techniques in time divided into the periods defined for the categorization of papers, i.e., ≤ 2005, 2006–2010, 2011–2015, and 2016–2021. This indicates the absolute value of individual appearances of techniques in each period and the corresponding percentage. For instance, shallow ANNs present an increasing trend, where most of the papers were published in the period from 2016 to 2021. Similar behavior is also observed in decision trees with a more pronounced trend. An apparent observation is that all deep ANN approaches had been published in the last period, in agreement with the proliferation of deep learning. The combination of techniques exhibits a constantly increasing trend. Conversely, the use of probabilistic and fuzzy logic methods has been decreasing.

Figure 12d shows the distribution of papers according to the type of PQD, i.e., multiple PQDs, voltage sags, and voltage notches. Most papers performing classification are in the category of multiple PQDs as expected because the types of PQDs are distinguished in these cases. Classification is also used for voltage sags as they can be categorized according to the root causes. No categories are identified for voltage notches; therefore, classification is incipient in this case. It is also observed that deep ANN models are evenly used for multiple PQDs and voltage sag classification.

In Fig. 12e, the distribution of techniques according to the real-time application is presented. For instance, decision trees are more used in real-time approaches, which is attributable to the simple operation of algorithms. Similarly, the combination of techniques is mostly used for real-time applications, where the methods take advantage of each technique in terms of efficiency. Conversely, deep ANNs, fuzzy logic, and probabilistic methods are less used for real-time applications because of the cost of computation during the operation of algorithms.

5.8 Characterization

The characterization of single PQDs refers to the quantification of features that distinguish the disturbance. The single-PQD characterization referred to in this section usually differs from the characterization conducted in the stages described previously. The feature extraction stage presented in Sect. 5.4 explains methods to obtain statistical, time-series, spectral, and image-based characteristics that are useful as inputs for the classification techniques to identify the category of PQD. However, these characteristics are not necessarily representative of the physical features that describe the phenomena according to deviations and standard limits. For instance, in [168], the extracted features include the mean, variance, kurtosis, skewness, entropy, etc. of the coefficients from the WT to classify voltage sags according to their causes. Thereby, these features are not explicitly related to magnitude, duration, POW characteristics, and phase angle jump, which are the physical features that identify voltage sags. The abovementioned difference occurs because the purpose of feature extraction is to obtain characteristics that allow the most accurate and efficient results in the classification stage. Conversely, in the single-PQD characterization referred to in this section, which is mainly useful for assessing the severity and impact of the disturbance, the physical representation and interpretation of the phenomena is the most important aspect.

This review gives a particular focus to voltage sags and notches. Hence, only the aspects observed in the selected literature related to their characterization are briefly described in the following sections.

Table 12 summarizes the parameters used to characterize voltage sags and notches. A brief definition of each parameter is provided, and its relevance is highlighted. References of the selected literature that analyze each of the parameters are also indicated, as well as the usage percentage.

Table 12 Summary of parameters to characterize voltage sags and notches

5.8.1 Voltage sag characterization

A voltage sag is a decrease in the RMS voltage to between 0.1 and 0.9 pu lasting from 0.5 cycle to 1 min [5]. Voltage sag characterization is useful in assessing equipment sensitivity. For instance, sag magnitude is the main factor that determines if a piece of equipment will malfunction or stop working. Moreover, sag duration is important to establish the impact on industrial processes. Thus, for voltage sags lasting longer, the probability that industrial processes stop is higher. Other voltage sag characteristics including POW of initiation/ending and phase angle jump may affect the performance of power electronic equipment that uses phase angle information [6]. In the literature, single-event characteristics including magnitude and duration of sags have been widely addressed. However, POW characteristics and phase angle jump still require further research to be more accurately computed and to better determine the impact on equipment.

Approaches to characterizing voltage sags usually include the analysis of time domain waveforms and profiles (RMS value), or the analysis of ellipse parameters obtained by using the SPM, e.g., [140, 151,152,153, 157, 163, 172]. Interest in multistage characterization is emerging [157, 174], as the usual single-event characteristics may not be enough to describe voltage sag events in real conditions.

5.8.2 Voltage notch characterization

Voltage notches are sub-cycle waveform distortions characterized by a periodic voltage reduction lasting less than half a cycle. Notches may be caused by the normal operation of power electronic converters when current is commutated from one phase to another leading to short-duration overcurrent [5]. A voltage notch is defined by its depth, width, and area [12]. Moreover, the number of voltage notches occurring per cycle or half-cycle is an important feature in suitably assessing the aggregated impact of the disturbance. The number of notches also allows for identification of the type of converter causing the disturbance.

According to the analyzed literature, width is usually obtained in the process of voltage notch characterization. However, depth and area have been less studied. The number of notches per cycle can be extracted from various methodologies in the literature, but it is not explicitly performed. In general, the literature related to voltage notches is still incipient and there is a lack of research on the characterization of the phenomena to analyze, for instance, severity and impact on end-user equipment.

6 Discussion

The discussion is organized into remarks on the methodology for the review and the bibliometric analysis, and the development of the literature review throughout the stages for detection and classification of PQDs described in Fig. 7 i.e., input space, preprocessing, feature engineering, and decision space. Detailed technical aspects related to these stages are also presented, analyzed, and discussed.

6.1 Methodology for the review and bibliometric analysis

6.1.1 Methodology for the literature review

The methodology proposed in Sect. 3 to find the relevant literature is reproducible and scalable. However, a significant effort is required to retrieve and structure the bibliographic metadata to conduct the process. In this context, a gap in the process is observed and a possible improvement of the methodology lies in a higher level of automatization in data retrieval and cleaning. In addition, the indices formulated in the scoring equation (see Sect. 3.2—Scoring equation) to facilitate the selection of the most relevant literature are subject to improvement. Especially, the title and abstract similarity indices may be enhanced using more advanced language processing techniques.

6.1.2 Bibliometric analysis

The bibliometric analysis has revealed the increasing trend in publications related to the detection and classification of PQDs. Likewise, publications including real-time aspects are also increasing, but with a more conservative trend. Thereby, the need for more research on real-time aspects is highlighted. Data of origin of publications indicated that most of the research on the topic (more than 50% of publications) is performed in China, India, and the USA. This situation suggests that higher efforts in researching the topic should be performed worldwide because the context of power systems varies from region to region. Distribution on general topics indicates that real-time aspects are more related to monitoring and detection, and offline applications are more common in the characterization, assessment, and classification of PQDs. Looking at the type of disturbance, general-purpose approaches (multiple PQDs) and tools focused on voltage sags have extensive literature and are very mature. By contrast, research on voltage notches is still incipient. Additional quantitative analyses have been presented for the main steps in the process of real-time detection and classification of PQDs, i.e., transformation and classification. The results of these analyses indicate the most widely used techniques.

6.2 Input space and preprocessing

6.2.1 Input data preparation

The most popular techniques for the input space are the equation-and simulation-based signals. In the case of laboratory and field measurements, the signal acquisition is mainly carried out using DSP, FPGA, microcontrollers, and computers. Real-time digital simulators are a new trend in PQDs simulation. More research should be performed on the use of laboratory and field measurements for the assessment of tools for real-time detection and classification of PQDs, to deal with the uncertainties associated with real conditions.

6.2.2 Data preprocessing

Segmentation and normalization are usually applied for preprocessing of multiple PQDs and voltage sags. In addition, denoising/filtering is mostly applied to specific disturbances such as voltage notches. No extensive details regarding data validation to ensure reliability of data from field measurements have been found in the literature on PQD detection and classification. Therefore, further analysis of data validation in the context of PQD detection and classification may be useful.

6.3 Feature engineering

6.3.1 Transformation

Time–frequency and time-domain techniques are the two most popular for the transformation of PQDs in general, and voltage sags and notches. The techniques widely used in time–frequency domain are WT, ST, and HHT, or their combination with other techniques. The most used non-parametric transformation techniques in the time domain are SPM, PSR, and TT, whilst the most used parametric transformation techniques are KF (especially for voltage sags) and AF (e.g., adaptive linear network). There are still opportunities to apply real-time oriented transformation techniques to perform detection, classification, and characterization of specific disturbances such as voltage sags and notches using non-parametric techniques such as SPM, PSR, and MM, as well as parametric techniques such as Extended KF (non-linear filtering) and AF.

6.3.2 Feature extraction

The feature extraction stage is mostly performed using statistical and time series techniques. The mean value is the clear dominant statistical metric for central tendency, whilst statistical dispersion is usually measured through standard deviation, maximum/minimum value, and statistical values such as variance and HOS (skewness, kurtosis, etc.). On time series techniques, cycle-based indices as coefficients of energy (especially for voltage notches), RMS values, and Shannon entropy are the most common, whereas the most popular sample-based indices are absolute/maximum and event duration for multiple PQDs and voltage sags, and derivative as well as Euclidean distance specifically for voltage notches. The latter might be potentially useful for the assessment of sub-cycle disturbances (e.g., notches, transients).

6.3.3 Feature selection

The step of feature selection is only involved in designing the tools for detection and classification of PQDs but not in the operation. Thereby, the computation times for selecting the optimal set of features for specific applications is a process before the real-time operation. An adequate selection of features allows an enhanced operational efficiency and accuracy. Most approaches in the literature for feature selection are handcrafted based on expert and widely accepted knowledge, with the advantage of obtaining a better physical interpretation of the phenomena. However, handcrafted feature selection can be a time-consuming process. Optimization methods have also been used to provide enhanced results but usually become complicated when selecting a suitable set of features. Finally, dimensionality reduction approaches have shown promising results in the feature selection process providing a good compromise between simplicity of implementation and accuracy and efficiency of results. More effort should be expended on the automatization of dimensionality reduction techniques and the proper physical interpretation of the selected features.

6.4 Decision space

6.4.1 Detection

As a prior step in the process of classifying PQDs, detection may be essential in real-time operation because its independent implementation allows for improving efficiency and general performance. To that end, the algorithms for the detection of states different from the ideal conditions of voltage waveforms are performed constantly in a simple process in real-time. If a PQD is subsequently detected, a more complex process of classification is activated, thus reducing the computational burden of embedded systems. The abovementioned approach has not been extensively implemented and analyzed in the literature while such approach is likely to provide promising results for the implementation of PQD monitoring systems. Furthermore, in the case of voltage sags, detection is useful for applications such as the suitable operation of DVR and protection systems. In those cases, some characterization of the disturbance is necessary.

6.4.2 Classification

Techniques for automatic classification of PQDs have been widely studied in the literature, mainly focused on the categorization of multiple PQDs (sags, swells, notches, transients, harmonics, flicker, etc.). Other advances are in the classification of complex (combined) PQDs, the classification according to root causes, and real-time applications. According to the review, the latter two topics still require further research. The most popular technique for classification is shallow ANNs because of their flexibility in learning any pattern from any set of features. However, ANNs require extensive data and computational effort for training. Decision trees have also been extensively used for classification because of their simplicity, being proper for real-time applications. Recently, deep learning techniques are gaining interest because of the high level of automatization (feature extraction is performed automatically as a process within the technique). However, in these approaches, the physical interpretation of features is lost. Moreover, great potential is observed in the use of unsupervised learning techniques because they have not been yet extensively studied in the context of PQD classification.

6.4.3 Characterization

Single PQD characterization results in the physical interpretation of the phenomena and provides relevant information for the assessment of severity and impact on end-user equipment. Therefore, characterization is useful for analyzing disturbances from the electromagnetic compatibility perspective. Characterization of voltage sags has been widely addressed concerning magnitude and duration. However, POW characteristics and phase angle jump that impact on power electronic equipment still require further research. Multistage sag characterization is of emerging interest because of its occurrence in real conditions and needs further work. Voltage notch characterization is still incipient, especially regarding severity assessment. For instance, the definition of notch depth is ambiguous in the literature. Moreover, the analysis of notching ringing as described in [5] has not yet been addressed in the literature and the characterization of voltage notches may be much more challenging in this context.

6.5 Discussion of technical aspects

Technical issues associated with the steps for PQD detection and classification are discussed. The main technical issue related to input space and data preprocessing is associated to modeling of uncertainties occurring in field measurements. This requires applying data analysis techniques including data plausibility, data cleansing, statistical inference, etc. In the feature engineering stage, the real-time application of processing techniques is still challenging because of computation times in the most widely applied time–frequency-domain transforms such as WT and ST. Although promising results are obtained in the real-time application of time-domain transforms such as SPM, the challenge is the accurate representation of the phenomena and the analysis of single-phase voltages and currents. Feature selection using optimization methods is still challenging while the improvement in accuracy is limited. Therefore, a proper trade-off between complexity and accuracy should be considered in such cases. In the decision space, a challenging technical issue is the formulation of a comprehensive method considering all steps in the decision space, i.e., detection, classification, and characterization that may be useful for real-time applications, e.g., the analysis of PQD propagation to identify and localize root causes, the operation of protection systems, and the automatic implementation of mitigation measures.

7 Perspectives for future research

On transformation techniques, the research trend shows that time-domain and combinations of techniques from different domains are becoming relevant in PQD detection and classification in general. The trend also shows that research is towards the application of one transformation technique, or a combination of several, that can accurately detect the highest number of PQ variations and events rather than specific methodologies for specific disturbances.

WT, ST, and time-domain techniques (non-parametric techniques such as SPM, SPR and MM, as well as parametric techniques such as extended KF and AF) seem to have potential for real-time detection and classification of either PQDs in general (multiple) or the specific (e.g., voltage sags and notches). These techniques, among other characteristics, are flexible in detecting different PQDs and can be used in devices with restricted computational resources. Nevertheless, it is also acknowledged that the combination of different state-of-the-art techniques can also be of benefit for the detection and classification of PQDs. Opportunities for future research also exist in real-time detection, classification, characterization, and possibly in feature aggregation of sub-cycle disturbances, such as voltage notches and transients.

The use of powerful image classification techniques after the 2D transformation of signals is also a promising field of research. This approach allows the use of tools from the ever-increasing potential of the image processing and classification field, e.g., the attention mechanism to improve classification accuracy and transfer learning to reuse pre-trained models [167]. Also, a 2D transformation of signals allows the use of deep learning tools such as CNN. Alternatively, the use of simpler and robust techniques to analyze 2D figures in the complex plane such as Fourier descriptors may provide satisfactory results in classification accuracy and efficiency. Among the 2D transformations, SPM and PSR have shown good characterization capabilities and performance for real-time applications.

In the classification of multiple PQDs and voltage sags, CNN have shown promising results in recent studies [121, 158, 179]. The potential of CNN lies in its ability to automatically extract the best set of features to obtain very accurate results in the classification of PQDs, even in noisy environments. However, CNN have some drawbacks such as the high computational requirement in training and large number of model parameters that hinder real-time application and implementation in embedded systems because of the required additional storage. Moreover, the physical interpretation of features is lost because the automatic extraction is performed within the CNN. A combination of CNN with other techniques may help to overcome the drawbacks. For instance, the few-shot learning technique [171], can be used to reduce the high computational and large dataset requirements for training. Alternatively, ELM is gaining popularity [108, 176], because of its simple operation, sufficiently accurate results, and requirement of fewer training data. The efficiency of ELM also facilitates real-time application.

In the context of the ongoing digitalization of the power system and smart grid paradigm, real-time detection and classification of PQDs play an important role. By online identification of PQDs, a rapid pinpoint of the root-causes can be achieved, and prompt automatic mitigation measures can be implemented to reduce negative technical and economic impacts, e.g., fault location and clearance, flicker source location and mitigation, harmonic resonance source location and mitigation, etc. For this purpose, large amounts of data provided by advanced metering infrastructures, i.e., smart meters, PQ monitors, phasor measurement units, etc., would require advanced algorithms to perform real-time detection and classification of PQDs.

Specific research on voltage sags also offers areas for contribution. For instance, methodologies for voltage sag classification and characterization have focused on single-or three-phase voltages but, to the extent of this review, there is no comprehensive method to automatically classify and characterize single-and three-phase voltage sags. Some approaches have addressed voltage sag root cause location (upstream or downstream), but a more precise location (pinpoint) of sag origin should be achieved. This could be useful for the operation of protection systems and mitigation measures. Also, a more accurate real-time characterization of POW features and phase angle jump can be achieved. The characterization of multistage voltage sags is also of emerging interest because of their common occurrence in real conditions and the limitations of single event voltage sag characterization. Progress in this direction has been made in [157] and [174] using SPM and the multidimensional characterization, respectively, but more studies are still required to improve real-time performance.

Regarding the lack of research in voltage notches, there are several opportunities for further work. For instance, more accurate tools for detecting and characterizing notches are required, including the calculation of single PQD features such as depth, width, area, number of notches, and other indices to assess severity and impact on end-user equipment. Furthermore, automatic classification of voltage notches has not been addressed in the literature. Some categories can be identified such as normal notching and notching ringing [5], while the categorization would allow a better understanding of the notch PQD and an improved severity and impact assessment.

Only supervised learning techniques have been analyzed in this review for the AI-based classification of PQDs. However, unsupervised techniques could be useful in PQD detection and classification because no labeled data is required. This can facilitate the process of training algorithms. Furthermore, unsupervised and supervised learning algorithms can be used together to exploit the potential of both approaches. For instance, simple unsupervised learning algorithms can be used to detect states different from the ideal voltage signal, and then more complex supervised learning algorithms can be used for classification. This approach can enhance efficiency for real-time application.

8 Conclusion

The comprehensive and systematic review conducted in this paper initially develops a methodology to identify the most relevant articles in the detection and classification of PQDs. This methodology results in a scalable and reproducible process that contributed to proposed indices to assess publications in terms of topic similarity and quality of research. The narrow set of publications selected through the systematic process allows a comprehensive overview of the real-time detection and classification of PQDs.

The bibliometric analysis of the literature metadata demonstrates the increasing interest in PQD detection and classification. It also presents top publishing countries and researchers, and first quantitative insight into the relation of general topics, e.g., monitoring, detection, classification, and characterization with real-time applications. The need for further research in real-time approaches for PQD detection and classification is highlighted.

A comprehensive descriptive, qualitative, and quantitative review is performed throughout the stages for real-time detection and classification of PQDs, where techniques dealing with PQDs in general (multiple PQDs) or with specific (e.g., voltage sags and notches) are identified and described. The most relevant findings are summarized in taxonomy figures and tables. Also, more detailed quantitative analyses are provided for the most widely explored stages in the literature, i.e., transformation and classification.

The main remarks arising from the literature review are that transformation and classification techniques have been widely addressed and are very mature for offline applications. However, real-time applications still require more research to find efficient and accurate tools for real conditions in actual power systems. The computational burden is an essential aspect in this context, where embedded systems have limited resources. The proper integration of stages, e.g., preprocessing and feature engineering, and the development of new techniques can facilitate real-time applications.

Research gaps in voltage sags are addressed, including combined single-and three-phase analysis, sag root cause location, accurate and multistage sag characterization. Similarly, research gaps in voltage notches include accurate and unambiguous characterization and classification for severity and impact assessment.