電氣工程畢業(yè)設(shè)計(jì)翻譯_小波包神經(jīng)網(wǎng)絡(luò)在電力系統(tǒng)繼電保護(hù)中的應(yīng)用(1)

1、譯文：小波包神經(jīng)網(wǎng)絡(luò)在電力系統(tǒng)繼電保護(hù)中的應(yīng)用摘要，本文提出解決繼電保護(hù)測試儀波形畸變問題的小波包神經(jīng)網(wǎng)絡(luò)（WPNN）方法。憑借其良好的時(shí)頻局部化的逼近能力，WPNN是用來建立一個(gè)對繼電保護(hù)測試儀非線性放大器的識別模型。有待放進(jìn)工具的錯(cuò)誤數(shù)據(jù)是用來被識別模型的調(diào)節(jié)功能補(bǔ)償?shù)?，使整個(gè)使用儀器系統(tǒng)顯示表現(xiàn)得線性，以便使產(chǎn)生的波形失真大大地被限制。模擬結(jié)果表明，提出方法具有可行性和有效性，原型已進(jìn)入實(shí)際運(yùn)行。1 介紹現(xiàn)代電力網(wǎng)絡(luò)的規(guī)模和復(fù)雜性不斷擴(kuò)大，它要求配置較高可靠性的電力系統(tǒng)繼電保護(hù)，錯(cuò)誤數(shù)據(jù)在進(jìn)入繼電保護(hù)測試儀運(yùn)算之前被放大器放大是改善他們性能的有效方式12。傳統(tǒng)的繼電保護(hù)測試儀器能夠?qū)崿F(xiàn)這

2、樣的測試功能，但他們曾經(jīng)采用模擬放大器，這是一個(gè)典型的非線性系統(tǒng)，實(shí)現(xiàn)功率放大。因此，輸出波形的非線性失真不可避免地成為繼電器保護(hù)測試的嚴(yán)重問題。在本文中，WPNN方法提出了解決這一問題的方法。WPNN是小波包理論和神經(jīng)網(wǎng)絡(luò)，它不僅具有小波包的良好的局部化性質(zhì)和特征提取能力，但也繼承神經(jīng)網(wǎng)絡(luò)的許多優(yōu)點(diǎn)，如自適應(yīng)性和最高兼容性等34。它選擇小波基為神經(jīng)元的激活函數(shù)，并規(guī)范設(shè)計(jì)程序和穩(wěn)固學(xué)術(shù)基礎(chǔ)，所以WPNN已廣泛應(yīng)用在許多技術(shù)領(lǐng)域567。在這項(xiàng)研究中，WPNN是采用了建立繼電保護(hù)測試儀的非線性放大器的識別模型，并通過比較識別模型與理論輸出，自適應(yīng)調(diào)整功能是在錯(cuò)誤數(shù)據(jù)被送進(jìn)儀器之前，這使得整個(gè)儀器

3、系統(tǒng)將顯示變得線性，使輸出波形的失真限制很大。用故障仿真數(shù)據(jù)進(jìn)行記錄，其結(jié)果證明了可行性和WPNN應(yīng)用對電力系統(tǒng)繼電保護(hù)測試的有效性，以及所提出的方法樣機(jī)已投入實(shí)際運(yùn)行。2 建設(shè)WPNNWPNN是小波神經(jīng)網(wǎng)絡(luò)的升級（WNN）。WNN小波神經(jīng)網(wǎng)絡(luò)可以被看作是使用的的正交小波變換多分辨率分析（MRA）的基礎(chǔ)上重建的組合空間的小波8910。大家都知道，小波空間可進(jìn)一步利用小波包分解，使信號可以分解為更多的頻段，來比MRA提高頻率分辨率。因此，選擇最佳小波包基由于網(wǎng)絡(luò)神經(jīng)元的激活功能將獲得更好的網(wǎng)絡(luò)時(shí)頻局部化性質(zhì)和逼近能力。所以WPNN利用小波包基的輸入信號特征提取和神經(jīng)網(wǎng)絡(luò)在WPNN識別信息。WPN

4、N可分為兩部分：小波包特征提取和神經(jīng)網(wǎng)絡(luò)信息識別，這是圖1所示。通過本文，Z表示所有整數(shù)的集合。讓 和表示波基和小波從各個(gè)的產(chǎn)生。對WPNN結(jié)構(gòu)設(shè)計(jì)包括以下三個(gè)主要步驟：第1步。規(guī)模計(jì)算范圍：用和來表示和目標(biāo)系統(tǒng) 時(shí)間范圍，他們的精力集中地區(qū)的頻率范圍內(nèi)可被看做實(shí)驗(yàn)數(shù)據(jù)，這是表示為分開的和分開。根據(jù)傅里葉變換的性質(zhì)，隨著擴(kuò)大的小波，頻率范圍將會擴(kuò)大到,即的頻率擴(kuò)大為。因此，小波尺度包含一個(gè)用于覆蓋有限的范圍，它可以通過以下計(jì)算：和分別表示較小或更大的整數(shù)第2步。選擇最佳小波包基：Shannon準(zhǔn)則引入到計(jì)算的尺度范圍內(nèi)的節(jié)點(diǎn)組系數(shù)由第一步得到。然后，如果子的總和比父節(jié)點(diǎn)少，兩個(gè)子節(jié)點(diǎn)取代它下面

5、的節(jié)點(diǎn)的直接父節(jié)點(diǎn)。在這個(gè)方法中，我們可以在最小的基礎(chǔ)上設(shè)定，可以如下表示：其中E是最佳小波包基數(shù)第3步。的節(jié)點(diǎn)數(shù)目的測定：這一步也是可以被看作是轉(zhuǎn)換因子為每小波尺度的。這是被稱為，小波包的時(shí)間范圍 是不隨著N的變化而變化的。所以小波包的時(shí)間范圍基 可表示為 ，在時(shí)間軸上滑動的程度，隨著的增加或減少。由于覆蓋的時(shí)間范圍 ，的范圍確定 由以上，結(jié)構(gòu)和WPNN第一部分參數(shù)的三個(gè)步驟可以肯定確定。因此，第二部分可以作為一個(gè)簡單的三層已知的輸入值，其連接的神經(jīng)網(wǎng)絡(luò)。整體結(jié)構(gòu)的WPNN因此以如下形式，并在圖1所示 3.總體方案的繼電保護(hù)測試儀所提到的介紹，輸出波形的非線性失真是繼電保護(hù)測試最嚴(yán)重的問題。

6、針對這個(gè)問題，一個(gè)閉環(huán)繼電保護(hù)測試儀的新計(jì)劃，提出在圖2所示。 雙CPU的配置，包括上層控制器和較低的放大器適用于本系統(tǒng)。上層控制器采用高性能便攜式計(jì)算機(jī)或嵌入式計(jì)算機(jī)為核心，實(shí)現(xiàn)了數(shù)據(jù)采集，故障分析和綜合控制。此外，還可以調(diào)整采樣頻率，釋放速度或根據(jù)測試數(shù)據(jù)諧波含量的要求輸入。數(shù)字和模擬測試軟件防護(hù)服成功嵌入到儀器。它可以模擬前的數(shù)字平臺，提高了靈活性和可重復(fù)性，避免潛在的傷害，測試設(shè)備11。較低的放大器，主要包括數(shù)字信號處理（DSP）芯片，智能功率模塊（IPM）的，反饋電路陣列。 DSP的形式接收數(shù)據(jù)通過CAN總線上控制器的計(jì)算機(jī)，并產(chǎn)生PWM（脈寬調(diào)制）通過定期抽樣方法脈搏，IPM是由P

7、WM脈沖驅(qū)動去實(shí)現(xiàn)功率放大。反饋電路設(shè)計(jì)輸出信號進(jìn)行采樣，組成閉環(huán)配置，這主要是考慮到了幅值和極性轉(zhuǎn)換。為了消除非線性失真，一個(gè)使用基于硬件的數(shù)字閉環(huán)修正算法12，可描述如下：查明實(shí)驗(yàn)數(shù)據(jù)較低的放大器的部分，建立儀器儀表系統(tǒng)的投入產(chǎn)出模型。通過比較模型的識別與理念輸出，產(chǎn)生調(diào)節(jié)作用，引導(dǎo)之前，都要輸入到儀器，使輸出波形可以最遠(yuǎn)的理想值的方法使數(shù)字區(qū)的故障數(shù)據(jù)自適應(yīng)調(diào)整。很顯然，系統(tǒng)準(zhǔn)確識別算法具有重要義，WPNN可用于完成此任務(wù)，因?yàn)槠淞己玫臅r(shí)頻局部化性質(zhì)和逼近能力。4 程序的算法與WPNN該數(shù)字閉環(huán)與WPNN修改程序顯示在圖3，可以這樣解釋：一些在有效范圍內(nèi)隨機(jī)取樣點(diǎn)輸入到建議的配置和輸出波

8、形記錄儀的實(shí)際使用反饋電路。該小組的組成由采樣數(shù)據(jù)及其相應(yīng)的反饋被視為實(shí)驗(yàn)數(shù)據(jù)集。該小組的組成由采樣數(shù)據(jù)及其相應(yīng)的反饋被視為實(shí)驗(yàn)數(shù)據(jù)集。一個(gè)識別模型，建立了作為未知非線性性能的放大器的算法代替實(shí)驗(yàn)集的數(shù)據(jù)。準(zhǔn)確的系統(tǒng)識別和調(diào)節(jié)功能的獲得是兩個(gè)算法的關(guān)鍵點(diǎn)。憑借其良好的時(shí)頻局部化的逼近能力，WPNN用于建立該系統(tǒng)的辨識模型。選擇一個(gè)合適的母小波函數(shù)和估計(jì)的非線性性能，頻率域與實(shí)驗(yàn)數(shù)據(jù)集。WPNN的網(wǎng)絡(luò)結(jié)構(gòu)和神經(jīng)元數(shù)量可確定在第二部分提出的方法，和WPNN連接權(quán)可以訓(xùn)練一些優(yōu)化算法，如反向傳播（BP），遺傳算法（GA）等。調(diào)節(jié)功能得到了迭代修正方法，如圖3所示。表示數(shù)據(jù)的故障點(diǎn)，某些數(shù)據(jù)被輸入到儀

9、器和所確定的輸出模式擴(kuò)增。和的不同點(diǎn)和放大價(jià)值觀點(diǎn), 是這個(gè)觀念的放大因素，被用來適應(yīng)從到的原始數(shù)據(jù)，然后設(shè)置是初始點(diǎn)，重復(fù)以上過程直至為記錄到調(diào)整值的形式，最后將被輸入到測試儀，實(shí)現(xiàn)故障波形放大。該算法本質(zhì)上是一種用于放大器，使儀器系統(tǒng)顯示在整個(gè)線性特性的非線性性能補(bǔ)償方法，使輸出波形的非線性誤差可大大減少。5 模擬結(jié)果為了驗(yàn)證應(yīng)用在電力系統(tǒng)繼電保護(hù)測試WPNN成效，仿真模擬實(shí)驗(yàn)中使用了江西省某地區(qū)實(shí)際過失錄得的數(shù)據(jù)。按照上面，建立一個(gè)識別模型的基礎(chǔ)上使用WPNN訓(xùn)練數(shù)據(jù)和相關(guān)的補(bǔ)償值都可以通過閉環(huán)修改，這是繪制在圖4中提到采樣數(shù)據(jù)計(jì)算出來的程序。結(jié)果表明，該模型能準(zhǔn)確地識別近似模擬非線性性

10、能，其跟蹤誤差在0.1以內(nèi)。圖5顯示了初步的模擬輸入數(shù)據(jù)段和它的補(bǔ)償值調(diào)整的過程。最初的數(shù)據(jù)是相當(dāng)前操作系統(tǒng)故障，其最大達(dá)到10A電流。而在峰值或谷點(diǎn)，輸入數(shù)據(jù)有較大的更嚴(yán)重，因?yàn)榉蔷€性衰減補(bǔ)償值。輸出波形的比較和沒有在本文提出的方法如圖6所示。從波形分析結(jié)果表明。1）由于非線性放大器的性能，將不可避免地進(jìn)入失真的輸出波形，繼電保護(hù)測試可能導(dǎo)致錯(cuò)誤的結(jié)論通2）過使用系統(tǒng)識別和閉環(huán)修改，輸出波形均方根誤差從。這樣的失真限制的輸出波形可以準(zhǔn)確地模擬電源故障3）補(bǔ)償功能是最顯著，尤其是在接近峰值或谷值點(diǎn)6 結(jié)論（1）一種新型的神經(jīng)網(wǎng)絡(luò)，WPNN，最佳小波作為神經(jīng)元的激活函數(shù)包的基礎(chǔ)是在本文中介紹了，

11、它具有精確的系統(tǒng)結(jié)構(gòu)設(shè)計(jì)和規(guī)范的程序?qū)嵤┑男阅?。?）在這項(xiàng)研究中，WPNN求解繼電保護(hù)問題測試儀器輸出波形的變形，仿真結(jié)果證明其可行性和有效性，并與該算法的原型現(xiàn)在已經(jīng)投入實(shí)際操作。（3）WPNN已逼近復(fù)雜的非線性系統(tǒng)的優(yōu)異性能，所以它也可以應(yīng)用到其他模型或在電力系統(tǒng)優(yōu)化問題模式識別，故障診斷，負(fù)荷預(yù)測和數(shù)據(jù)壓縮等。參考文獻(xiàn)1 Jodice, J.A.:：繼電器性能測試：電力系統(tǒng)繼電保護(hù)委員會出版。有關(guān)功率傳輸12（1997）169-171匯刊2 Sachdev, M.S., Sidhu, T.S., McLaren, P.G.:：問題和數(shù)值繼電器測試機(jī)會。 IEEE電力工程學(xué)會夏季會議（2

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13、.K., Lin, Z.:：預(yù)測時(shí)間序列與小波包神經(jīng)網(wǎng)絡(luò)。國際神經(jīng)網(wǎng)絡(luò)聯(lián)席會議3（2001） 1593年至1597年 7 Schuck Jr., A., Guimaraes, L.V., Wisbeck, J.O.:：Dysphonic語音分類中的應(yīng)用小波包變換與人工神經(jīng)網(wǎng)絡(luò)。一年一度的國際會議的IEEE工程醫(yī)學(xué)和生物學(xué)3（2003）2958年至2961年8 Zhang, Q.: Benveniste, A.:：小波網(wǎng)絡(luò)。電機(jī)及電子學(xué)工程師聯(lián)合會神經(jīng)網(wǎng)絡(luò)3（6）（1992）889-8989 Gao, X.P.:：一個(gè)基于小波神經(jīng)網(wǎng)絡(luò)的比較研究。的第九屆國際神經(jīng)信息處理會議（2002年）1699

14、至1703年 10 Zhao, X.Z., Ye, B.Y.:：對電機(jī)振動噪聲的自適應(yīng)小波神經(jīng)網(wǎng)絡(luò)的信號識別。第三次國際研討會神經(jīng)網(wǎng)絡(luò)2（2006）727-734 11 一種繼電保護(hù)評估測試虛擬環(huán)境系統(tǒng)會刊（2004）104-11112 Sun, X.M., Du, X.W., Liu D.C., Cai, X.:：障礙復(fù)發(fā)的擴(kuò)音設(shè)備，基于數(shù)字閉環(huán)改性技術(shù)。電氣自動化電力系統(tǒng)28（4）（2004）49-53原文：Application of Wavelet Packet Neural Network on Relay Protection Testing of Power SystemAbst

15、ract. The paper presents a wavelet packet neural network (WPNN) approach for solving the waveform distortion problem of protective relaying testing instrument. With its excellent time-frequency localization property and approximation ability, WPNN is used to establish an identification model of the

16、non-linear amplifier of the protective relaying testing instrument. The fault data to be put into the instrument is compensated by an adjusting function getting from the identification model, which makes the whole instrumentation system show linear performance so that the distortion of the output wa

17、veform is constrained greatly. Simulation results indicate the feasibility and validity of the proposed approach, and a prototype has been put into practical operation.1 IntroductionThe continuous expansion of the modern electric networks scale and complication of its configuration requires higher r

18、eliability of protection relays in power system, and testing protection relays with fault recoding data amplified by instrument before putting into operation is an effective way for improving their performance 1, 2. Traditional protective relaying testing instruments could realize such testing funct

19、ion, but they used to adopt analog amplifier, which is a typical non-linear system, to realize power amplifying. So the non-linear distortion of output waveform inevitably be comes a serious problem for the relay protection testing. In the paper, a WPNN ap proach is presented for resolving this prob

20、lem. WPNN is a combination of wavelet packet theory and conventional neural network, which not only possesses good localization property and feature extraction ability of wavelet packet, but also inherits most merits of neural network such as selfstudy, adaptability and high fault-tolerant 3, 4. It

21、selects wavelet packet basis as its neurons activation function and has normative design procedures and solid academic foundation, so WPNN has been widely applied in many technical fields 5, 6, 7. In this study, WPNN is adopted to establish an identification model of the nonlinear amplifier of the p

22、rotective relaying testing instrument. And by comparing the identification models output with idea output, an adjusting function is generated to guide adaptive adjustment of fault data before to be put into the instrument, which makes the whole instrumentation system show linear performance so that

23、the distortion of the output waveform is constrained greatly. A simulation using fault recording data is carried out, whose results demonstrate the feasibility and validity of application of WPNN on relay protection testing of power system, and a prototype with the proposed approach has been put int

24、o practical operation.2 Construction of WPNNWPNN is the development of wavelet neural network (WNN). WNN can be viewed as the combination of reconstructions using wavelet basis of orthogonal wavelet spaces of based on multi-resolution analysis (MRA) 8, 9, 10. As everyone knows, wavelet space can be

25、decomposed further using wavelet packet, so signals can be decomposed in more frequency bands to increase frequency resolution than by MRA. Therefore, selecting best wavelet packet basis to be network neurons activation function will obtain better time-frequency localization property and approximati

26、on ability for the network. So WPNN utilizes wavelet packet basis extracting feature of input signal and neural network in WPNN takes charge of information identification, i.e., WPNN can be divided into two parts: wavelet packet feature extraction and neural network information identification, which

27、 is shown in Fig.1.Throughout the paper, Z denotes the set of all integers. Let 和denote wavelet basis and wavelet packet generated from respectively. The structure design of WPNN consists of following three primary steps:Step 1. Calculating scale range: Using and to denote the time extent of and the

28、 goal system , their energy concentrating areas of frequency extent can be estimated with training data, which are expressed as and separately. According to the properties of Fourier transform, with the increase of the wavelet scale j, frequency extent will expand by , i.e., frequency extent of is .

29、 Therefore the wavelet scale j contains a finite range for covering ,and it can be calculated by below:Where and denote choosing smaller or bigger integer value nearby respectively.Step 2. Selecting best wavelet packet basis: Shannon entropy criterion is introduced to calculating the entropies for t

30、he set of coefficients of each node in scale range getting in step1. Then, replace the parent nodes by the two children nodes directly below it if the sum of childrens entropies is less than that of parent. In this method, we can uncover the set of minimum entropy basis, which can be denoted as foll

31、ows:Where E is the number of best wavelet packet basis.Step 3. Determination of number of nodes: This step is also can be seen as determination of translation factor k for each wavelet scale j. It is known as that the time extent of wavelet packet ( ) is invariable with n changes, so the time extent

32、 of wavelet packet basis can be expressed as .With the increase or decrease of k, the extent slides on the time axis. For covering the time area of , range of k is determined as:By the three steps above, the structure and parameters of first part of WPNN (feature extraction) can be definitely determ

33、ined. So the second part (information identification) can be viewed as a simple three-layered neural network with known input value, whose connection rights w( n , j , k )are also that of WPNN. The whole structure of WPNN is thus of the following form, and is illustrated in Fig.1.3 Overall Scheme of

34、 Relay Protection Testing InstrumentAs referred in introduction, the non-linear distortion of output waveform is the most serious problem for relay protection testing. Aiming at this problem, a new scheme of closed-loop relay protection testing instrument is proposed as shown in Fig.2. Double CPUs c

35、onfiguration including upper-controller and lower-amplifier is applied in this system.Upper-controller adopts high-performance portable computer or embedded computer as its core, which realizes data acquisition, fault analysis and integrated control.Besides, it can also adjust sampling frequency, va

36、lue, releasing speed or harmonic content of the input data according to the requirements of testing. And a suit of protection testing digital simulation software is successfully embedded into uppercontroller of the instrument. It can simulate the testing process before analog testing on the digital

37、platform, which improves the flexibility and repeatability and avoids potential harm to the tested equipments 11. Lower-amplifier mainly consists of Digital Signal Processing (DSP) chip, array of Intelligent Power Modules (IPM), and feedback circuit. DSP receives data form upper-controller computer

38、through CAN bus and generates PWM (Pulse WidthModulation) pulse by regular sampling method, and IPM is drove by the PWM pulse to realize power amplification. Feedback circuit is designed to sample the output signals to compose closed-loop configuration, which mainly takes charge of the transformatio

39、n of amplitude and polarity.For eliminating non-linear distortion, an algorithm of digital closed-loop modification is used based on the proposed hardware 12, which can be described as follow:Identify the lower-amplifier part with training data and establish an input-output model for the instrumenta

40、tion system. By comparing the identification models output with idea output, an adjusting function is generated to guide adaptive adjustment of fault data in numeric area before being to be input to the instrument, so that the output waveform can furthest approach to ideal value. It is clear that ac

41、curate identification of system is of great importance in the algorithm, and WPNN can be applied to complete this task because of its excellent time-frequency localization property and approximation ability.4 Procedure of the Algorithm with WPNNThe procedure of digital closed-loop modification with

42、WPNN is shown in Fig.3,which can be explained like that: Some random sampling points within the effective range are input to the actual instrument with proposed configuration and the output waveform is recorded using the feedback circuit. The group composing by the sampling data and their correspond

43、ing feedback is regarded as training data set. An identification model is established by the training data set as substitute of unknown non-linear performance of instruments amplifier in the algorithm. And then compare the output of to the idea output, and construct an adjusting function to compensa

44、te the initial to be put into the instrumentation system for realizing the goal of constraining distortion of output waveform greatly.Accurate system identification and acquirement of adjusting function are two the key points of the algorithm. With its excellent time-frequency localization property

45、and approximation ability, WPNN is used to establish the identification model for the system. Select a suitable mother wavelet function and estimate the frequency domain of the non-linear performance with training data set. Network structure and neurons number of WPNN can be determined by the method

46、 proposed in the second section, and the connection weights of WPNN can be trained by some optimization algorithm, e.g.,back propagation (BP), genetic algorithm (GA), and etc. And the adjusting function is obtained by the method of iterative modification. As shown in Fig.3, denotes a certain data po

47、int of the fault data to be input to the instrument and is its output amplified by the identified model . The difference of and idea amplifying value , where A is the idea amplification factor, is used to adjust the original data to. And then setting as initial point, repeat the process above until

48、meets the precision requirement. The last is recorded into adjusting value form and the last will be input to the testing instrument to realize fault waveform amplification.This algorithm is essentially a compensating method for the non-linear performance of the amplifier, which makes the instrument

49、ation system show linear characteristics on the whole, so that the non-linear error of output waveform can be greatly reduced.5 Simulation ResultsTo testify the effectiveness of applying WPNN on relay protection testing of power system, a simulation experiment is carried out using actual fault data

50、recorded in a certain region of Jiangxi Province. Following the procedure mentioned above, an identification model is established using WPNN based on the training data and the compensating value related to each sampling data can be calculated by close-loop modifying, which is draw out in Fig.4. The

51、results show that the identification model can accurately approximate the simulated non-linear performance and its tracking error is within 0.1%.Fig.5 displays a segment of initial input data of the simulation and its adjustment process by the compensating value. The initial data is a phase current

52、of a current oscillation fault, whose maximum reaches up to 10A. And in peak or vale points, input data has bigger compensating value because of more serious non-linear attenuation.The comparison of output waveform with and without the method proposed in the paper is shown as Fig.6. Results from the

53、 analysis of the waveforms indicate that 1) Because of non-linear performance of amplifier, the distortion will inevitably come into being in the output waveform which possibly leads to false relay protection testing conclusions; 2) By using system identification and close-loop modification, the roo

54、t mean square error of output waveform reduces from 2.09 to 0.76. The distortion is constrained so greatly that the output waveform could simulate the power fault exactly, 3) and the compensation function is most remarkable especially at the points near peak or vale value.6 Conclusion(1) A novel neu

55、ral networks, WPNN, with best wavelet packet basis as neurons activation function is introduced in the paper, which has normative procedures of structure design and accurate system approximation performance.(2) In this study, WPNN is applied to resolve the output waveforms distortion problem of prot

56、ective relaying testing instrument. The simulation results prove its feasibility and validity and a prototype with the proposed algorithm has now put into practical operation.(3) WPNN has excellent capability of approximating the complex nonlinear system, so it can also be applied to other modeling or optimizing problems in power system such as pattern recognition, fault diagnosis, load forecasting and data compress.References1. Jodice, J.A.: Relay Performance Testing: A Power System Rela