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1、 A Wavelet Based Approach for Fast Detection of Internal Fault in Power Transformers The power transformer is one of the most expensive elements of power system and its protection is an essential part of the overall system protection strategy. The differential protection provides the best protection
2、 for power transformer. Its operation principle is based on this point that the differential current during an internal fault is higher than normal condition. But, a large transient current (inrush current) can cause mal-operation of differential relays. Then, studies for the improvement of the tran
3、sformer protection have focused on discrimination between internal short circuit faults and inrush currents in transformers. The magnetizing inrush current has a large second order harmonic component in comparison to internal faults. Therefore , some transformer protection systems are designed to ha
4、lt operating during the inrush current by sensing this large second order harmonic. The second harmonic component in the magnetizing inrush currents tend to be relatively small in modern large power transformers because of improvements in the power transformer core materials. Also , it has been seen
5、 that the fault current can contain higher second order harmonics than the inrush current due to nonlinear fault resistance, CT saturation .the distributed capacitance in the transmission line, which transformer is connected to, or due to the use of extra high voltage underground cables. Various met
6、hods have been suggested for overcoming this protection system mal-operation. This paper presents a wavelet based method for discrimination among inrush current, internal short circuit ,external short circuit and energizing and it is not affected by CT saturation and it is able to detect internal fa
7、ults while transformer energization. Unlike Artificial Neural Network and Fuzzy logic based algorithms. This approach is not system dependent. The operating time of the scheme is less than 10ms. The Daubechies mother wavelet is used with a sample rate of 5 kHz. Then , the differential currents of th
8、e three phases are decomposed into two details and only the second level will be considered by using db5 mother wavelet.Discrete Wavelet TransformThe wavelet transform is a powerful tool to extract information from the non-stationary signals simultaneously in both time and frequency domains. The abi
9、lity of the wavelet transform to focus on short time intervals for high-frequency components and long intervals for low-frequency components improves the analysis of transient phenomena signals. Various wavelet functions ,such as Symlet,Morlert and Daubechies are used to analyze different power syst
10、em phenomena. The mother wavelet must be selected performed based on its application and the features of signal .which should be processed. In this paper, Daubechies wavelet is used. There are three types of wavelet transform. Which are Continuous Wavelet Transform(CWT). Discrete Wavelet Transform(D
11、WT) and Wavelet Packet Transform(WPT). DWT is derived from CWT. Assume that x(t) is a tome variable signal, then the CWT is determined by (1): (1)Where, and are translating and scaling parameters, respectively. Also , is the wavelet function and is the complex conjugate of . Wavelet function must sa
12、tisfy(2) and should have limited energy: (2)Then ,the discretized mother wavelet is as follows : (3)Where, 1 and 0 and they are fixed real values. Also , and are positive integers. DWT is expressed by (4): (4)Where, is the complex conjugate of . In (4), the mother wavelet is dilated and translated d
13、iscretely by selecting and . and (5)DWT can be easily and quickly implemented by complementary low pass and high-pass filters.Proposed AlgorithmIn the proposed algorithm, the DWT is applied to the differential currents of three phases. The Daubechies Db-5 type wavelet is used as the mother wavelet a
14、nd the signals are decomposed up to the second-level. Then , the spectral energy and standard deviation of the decomposed signals in thelevel are calculated. The proposed method consists of two steps; detection and discrimination.Disturbance Detection Under normal conditions and external faults, the
15、 differential currents have smaller values than internal faults. However in some operating conditions, the external faults can result in high differential currents due to ratio mismatch of CTs or tap changes of power transformer. Then ,these conditions may cause mal-operation of the relay. Therefore
16、 ,a threshold current is used in order to prevent malfunctions caused by non-faulty currents. If one of differential currents exceeds this threshold value, it will be identified as a fault. The threshold value id defined, as follows: (6)Where and are the secondary and primary CT currents, respective
17、ly, and is the slope of the differential relay characteristic. If , then the detection algorithm defines it as an internal fault.Disturbance DiscriminationIn order to classify disturbances, the differential currents are decomposed up to the second level, using Daubechies Db5 type wavelet with data w
18、indow less than the half of the power frequency cycle. A sampling rate of 5 kHz, is considered for the algorithm(i.e . 100 samples per power frequency cycle based on 50 Hz). Then, the energy and standard deviation in the second detail are calculated for each differential current. It is seen that the
19、 spectral energy as well as the standard deviation in level tends to have high values during inrush currents. Then , a discrimination index ()can be calculated by multiplying the spectral energy by standard deviation in the second detail for each differential current, as follows: (7)Where, STD is th
20、e standard deviation in detail and E is its spectral energy. The STD can be determined using the following equation: (8)Where, is n-th coefficient from detail 2. is its mean value and M is the total number of existed coefficients. Then , the spectral energy of the wavelet signal in the level is calc
21、ulated by (9): (9)Then , then discrimination index () will be compared with a threshold value (). The relay will be activated, if any one of the three-phase differential currents exceeds this threshold value().译文：一个基于小波变换对电力变压器内部故障快速检测的方法电力变压器是电力系统中最重要的部分之一并且其保护是整个系统的保护策略中重要组成部分。差动保护为电力变压器提供最好的保护。其工
22、作原理是差动电流在内部故障时的值高于正常状态。但是,一个大的瞬态电流(涌流)会导致差动继电器的误动。然后,对变压器保护的改进的研究集中变压器内部短路电流和冲击电流的识别。与内部故障相比励磁涌流有大量二阶谐波分量。因此,一些变压器保护系统会在检测到大量的二阶谐波分量判断涌流而中断变压器工作。现代大型电力变压器由于电力变压器的核心材料的改进使励磁涌流的二次谐波分量变得相对较小。同时,故障电流会比涌流包含更高的二阶谐波分量，原因有非线性故障电阻、CT饱和、连接变压器输电线路的分布电容、或因使用过高压地下电缆。已经提出了各种方法来克服这一保护系统的误动。本文提出了一种在判别涌流、内部短路、外部短路与励
23、磁的基于小波变换的方法,它不受CT饱和的影响并且当变压器励磁时它可以探测到内部故障。不同与人工神经网络和模糊逻辑基础算法。该方法不依赖系统。该方案的响应时间少于10毫秒。基小波采样频率为5 kHz。那么,三项电的差动电流分解成两个步骤并且只有第二阶段会考虑使用db5基小波。离散小波变换小波变换在同时在时域和频域提取非平稳信号的信息是一个功能强大的工具。小波变换能够在高频时时频窗变窄和低频时变宽来提高对瞬变电流的分析。有多种小波变换,例如Symlet Morlert和Daubechies小波变换用于分析不同的电力系统现象。基小波的选择必须依赖于他的应用及信号的特点。在本文中, 使Daubechi
24、es小波变换。有三种小波变换方式。连续小波变换(CWT)。离散小波变换(DWT)和小波包变换(WPT)。DWT来源于CWT。假设x(t)是一个时变信号,那么CWT就由 (1)式决定: (1)其中，和分别是转换和尺度参数。同时, 是小波函数和是共轭复数。小波函数必须满足(2)并且应该有限能量: (2)那么，离散基小波如下: (3)其中，1和0并且它们是固定实数。另外，和是正整数。DWT由（4）表示如下: (4)其中，是共轭复数。在（4）中，基小波通过选定和来表述和转化： and (5)待添加的隐藏文字内容1DWT可以由互补的低通和高通滤波器方便而快速地实现。处理算法在处理算法中，DWT用于三相电
25、的差分电流。Daubechies的Db-5类型的小波为作为基小波,信号分解到第二层。然后, 分解信号的光谱能量和标准偏差在水平进行了计算分析。该方法有两个步骤;检测和鉴别。干扰检测在正常的条件和外部故障时的差分电流比在内部故障时要小。但是,在某些条件下,由于CT比率不匹配或电力变压器的振动变化会导致较高的差分电流。然后,这些状况可能引起继电器的误动。因此,一个阈值电流用于防止非故障电流引起的误动。如果差分电流超过阈值,它将被认定为发生了故障。阈值定义如下: (6)其中，和分别是CT的次级和初级电流, 是差动继电器特征斜率。如果,然后检测算法将它定义成为一个内部错误。干扰识别为了对干扰进行分类,我们把差分电流分解到第二层,用窗口少于一半工频周期的Daubechies Db5型基小波，考虑到算法，采样速率为5 kHz, (例如, 每工频周期100点基于50Hz)。然后,在第二层计算每一个差分电流的能量和标准偏差。我们可以发现的光谱能量以及标准偏差水平会在涌流保持较高的值。然后,鉴别指数可以由下式计算出来: (7)其中，STD是层次的标准偏差，STD可以有下式确定： (8)其中，是层的n相式的系数，是它的平均值M是总系数和。那么，在层的小波信号的光谱能量可以由9式计算： (9)那么，鉴别指数就会和阀值联系起来。如果三相差分电流的任何一相超过阀值，继电器就会动作。
