【正文】 Fig. 2 at the observation point (bus4). Table 1 pares the results inferred theoretically byassuming, in a ?rst approximation, the traveling wave Phase voltage (kV) Phase voltage (kV) CWT signal energy (.)612Table 1A. Borghetti et al. / Electrical Power and Energy Systems 28 (2006) 608–617modify signi?cantly the re?ection coe?cients at the lineFrequency values theoretically associated to the paths covered by thetraveling waves originated by a balanced fault at bus 1 observed at bus 4,and values identi?ed by the CWTanalysisPath Length Theoretical CWTidenti?edtermination.. Nonsymmetrical faults(km)L1 + L2 + L3 4 Imthreephase fault at bus 1, ., the terminal end of the mainCoe?cients ciare the propagation constant of mode i.They are plex numbers ci= ai+ jbiwhere aiis theattenuation constant and biis the phase constant of modei. The phase velocity of mode i is given byxfeeder.Fig. 1 also illustrates six paths covered by travelingwaves originated by a fault at bus 1. The traveling wavesare re?ected at the line terminations and at the fault location. Paths with partial re?ections at the point where morevi188。9222。. Balanced faultsFig. 2 shows the simulated voltage transients at threed2Vmdx2h i188。 189。 189。Y0189。Vph240。0By inspecting the relative maximum peaks of the obtainedscalogram ECWT(a), the most signi?cant frequency ponents of the signal are detected. From now on, thesefrequency ponents are called ‘CWTidenti?ed frequencies’ of the transient. The CWTidenti?ed frequencies canbe correlated to the propagation phenomena of the faultoriginated waves, traveling along the lines, and to theirre?ections at discontinuity points. For each fault location,some theoretical frequency values are calculated as a function of the length of the path covered by the travelingwaves, of the propagation velocities along the lines andof the type of re?ections. The match between these valuesthe CWTidenti?ed frequencies can provide useful information for the fault location.610A. Borghetti et al. / Electrical Power and Energy Systems 28 (2006) 608–617It is worth noting that the propagation of travelingwaves in multiconductor transmission lines, involves thepresence of di?erent propagation speeds. In this respect,the CWTbased analysis has been carried out separatelyon the various modes present in the voltage transientrecorded at the observation point.Eqs. (7) and (8), written in the frequency domain, summarize the modal transformation, as a way to make diagonal thematrixes given by the products between the impedance andadmittance perunitlength matrixes, namely [Z0][Y0] and[Y0][Z0]. These matrixes are not equal, but have the sameeigenvalues that, squared, form diagonal matrix [c]2.h icase of nonsymmetrical faults. The fault transients areobtained making reference to the distribution system con?guration shown in Fig. 1, modeled by means of the electromagnetic transient program EMTPRV [12,13]. Somedetails and data of the model are given in Appendix.For the case of balanced lines, transformation matrixes[Te] and [Ti] de?ned in (8), are identical and the elementscan be real numbers and they correspond to the Clarke’s(0, a, b) transformation matrix [14]. For the case of unbalanced lines, real matrix can be still inferred by using theprocedure implemented in EMTPbased programs [15]. Inview of the vertical symmetry of the conductor con?guration of the considered overhead line (see Fig. 9 of thed2Vphdx2h i188。222。 240。2222。a x222。 b222。5222。 1。Tsas240。 iTs222。1s240。C240。 et2=2ej2pF0t:240。? fast decrease to zero of w(t) for t ! 177。x222。 Distributed measurement systems1. IntroductionFault location in MV distribution network is a researchtopic that is receiving increased attention in recent years,due both to the most severe power quality requirementsand to the availability of improved measurement and monitoring systems. In addition, the increasing installation ofdistributed generation resources in the network requiresthe overhaul of traditional procedures based on automaticswitching systems.The most promising approach for the problem of interest appears to be the application of appropriate signal processing techniques to the voltage/current transientsproduced by short circuit events and recorded at one ormore locations in the distribution system.Recent contributions to the subject are based on the useof the wavelet transform (., [1–4]), usually adopting thediscretewavelet transform (DWT), due to its straightfor* Corresponding author. Tel.: +39 51 2093479。 variousfault types and network characteristics are examined. The paper presents also the basic concepts of a measurement and fault locationprototype system with distributed architecture.2006 Elsevier Ltd. All rights reserved.Keywords: Fault location。圖10 說明了在總線上的負荷連接。其中地面電阻率假設(shè)等于100M圖 9 配置架空電纜截面的導(dǎo)體圖8 測量系統(tǒng)示意圖。 附錄在本文中，連續(xù)小波變換的分析已進行了模擬仿真。結(jié)果表明，在考慮網(wǎng)絡(luò)配置和故障的類型基礎(chǔ)上，能夠提供達到預(yù)期的故障定位。其值分別受最大值為（）以及不接地中性點（）影響。1％傳感器其數(shù)據(jù)采集比率為177。具體而言，第一步程序是表征對測量系統(tǒng)每個設(shè)備的計量性能以便獲得PDF格式的不確定性來源。在本節(jié)中，從樣本所獲得的描述的文獻初步分析的目的是評估的不確定性影響估計的故障定位的測量結(jié)果。 1 ％和的資料存儲能力為64KB， Msa/s。比較由于時間所instants對在不同的分布式測量單位接受的電壓瞬變. 在總線4電壓暫態(tài)連續(xù)小波變換分析的結(jié)果，由于總線5零阻抗分三個階段發(fā)生故障。這個裝置的捕捉時間瞬間下降邊緣的投入，與標稱精度177。原型已具有以下的特點：以Pearson電壓差估價已使用VD305，與絕緣電壓300千伏的高峰值的大小比例10000V/1V，帶寬30 Hz至4兆赫（ 3分貝） ，上升時間100毫微秒，準確性177。它的值受最大頻率（）影響。每個單位，設(shè)在一些合適的總線的分銷網(wǎng)絡(luò)， 配備了GPS同步裝置和是能夠獲得雙方的出發(fā)瞬間的瞬態(tài)以及相關(guān)的波形。 雖然有些結(jié)果表明，一些限制的通過的Morlet小波，(例如，在總線2均衡故障)，其整體理論計算值確定已經(jīng)達到CWT頻率。那些在表5和表6存在不平衡負載似乎沒有明顯的影響結(jié)果。 此外，在這種情況下， ，但顯著低于光速的速度（如表1所顯示。在連續(xù)小波變換分析中運用Morlet 基波，是能夠偵測到只與頻率相關(guān)兩條路徑，即第一個和第三個路徑，而第二路徑的頻率最大峰值似乎是隱藏的第一高峰期，由于基波通過大型過濾器的振幅影響。與之相對應(yīng)故障位置在主饋線發(fā)送端和L1 + 15有影響，其反射系數(shù)的同時顯示在線端子。檢測這三個路徑的主要影響：L3+L4，與之相對應(yīng)故障位置在總線2的和L1+L2+L4 反映在線路終端具有相同的結(jié)果， 而L2+L3+L5則是與反射線端子相同的結(jié)果。表1比較的理論上假設(shè)和在第一次逼近結(jié)果推斷。，在總線1觀察在3個不同的節(jié)點（總線2 ，總線3及總線4 ） ，配電網(wǎng)絡(luò)所顯示的圖(1)