【正文】 350tion, the Clark transformation is applied to the voltagetransients at the observation point (bus 4) of the distribution network of Fig. 1, for di?erent types of unbalancedfaults at various locations, also with nonzero faultvelocity equal to the speed of light with those identi?edfrom the peaks in Fig. 3.If the CWTanalysis is applied to the voltage transientsrecorded in a di?erent observation point, in other wordswe are considering a measurement system with distributedarchitecture (see Section 5), it is possible to increase theinformation relevant to the fault location. Fig. 4 andTable 2 show the results of the CWTanalysis at bus 2for the previous case of a zeroimpedance threephasefault at bus 1. For this observation point three pathsare of interest: L3 + L4, with opposite sign re?ections atthe fault location and at the bus 2, L1 + L2 + L4, withre?ection at the line terminations having the same sign,and L2 + L4 + L5 with re?ection at the line terminationshaving the same sign. As it can be seen, by joining theinformation provided by this observation point with thoseof bus 4, two fault locations can be obtained and anincrease of the reliability of the procedure thereforeachieved.Fig. 5 and Table 3 show the results for the case of a balanced fault at bus 5. In this case only two paths are ofinterest: L1 + L2, with opposite sign re?ections at the faultlocation and at the main feeder sending end and L1 + L5,with re?ection coe?cient of the same sign at the lineterminations.Fig. 6 and Table 4 show the results for the case of a balanced fault at bus 2, which is the termination of a lateral.In this case three paths are of interest: (a) L1 + L2 + L4,with opposite sign re?ections at the fault location (bus 2)and at the main feeder sending end (bus 4), (b)L1 + L2 + L3 and (c) L1 + L5, with re?ections at the lineterminations.The CWTanalysis, performed by using the Morletmotherwavelet, is able to detect only the frequencies associated with two paths, namely the ?rst and the third ones,while the frequency peak associated with the second pathappears to be hidden by the ?rst peak due to the large ?lteramplitude related to the adopted motherwavelet.The in?uence of the presence of distributed generationhas been also investigated. The analysis is repeated for balanced faults at bus 1 and bus 5 in presence of a generatorconnected at bus 2 through a transformer. The CWTidenti?ed frequency values are very similar to those of Tables1–3, showing that the presence of the generator does notimpedances.Fig. 7 illustrates the results of the CWTanalysis of thevoltage transients due to a phasetoground fault at bus1, both for the case of a grounded and ungrounded neutral.Also in this case, the considered paths are those illustrated in Fig. 1. The phase velocity of mode 0 is howeversigni?cantly lower than speed of light (as shown in Table9 of Appendix). This velocity is used to evaluate the theoretical frequency values, which, in Table 5, are paredwith those identi?ed by the CWTanalysis.For the same system in Fig. 1 and Table 6 shows theresults for a phasetoground fault at bus 5.The simulations and the analysis are repeated also bytaking into account a fault resistance equal to 10 X, andquite the same results as those shown in Tables 5 and 6have been obtained. Also the presence of unbalanced loadsdoes not appear to have evident impacts on the results.Table 7 shows the results for the case of a phasetophase fault, and Table 8 shows the results obtained for atwo phasetoground fault. For both cases, two fault locations are examined: bus 1 and bus 5. The neutral is considered ungrounded.Although some of the results show some limits of theadoption of the Morletwavelet, namely those relevant tofault at the laterals of the network in Fig. 1 (., balancedfault at bus 2), overall a reasonably good match betweenthe theoretical values and the CWTidenti?ed frequencieshas been achieved. Such a match encourages the development of a fault location system exploiting this information.Section 4 is devoted to this subject.4. Measurement system with distributed architectureThe described CWTbased algorithm is conceived to bebined with a distributed measurement system. Eachunit, located at some suitable busses of the distribution network, is equipped with a GPS synchronization device andis able to acquire both the starting instant of the transientand the relevant waveform.A measurement unit of the faultlocation distributedsystem is schematically represented in Fig. 8, which represents an improvement of the one presented in [16].Each line voltage is conditioned by means of a voltagetovoltage transducer (V–VT) whose output is sent both toA. Borghetti et al. / Electrical Power and Energy Systems 28 (2006) 608–6176130102030Frequency (kHz)405060Fig. 4. Results of the CWTanalysis of the voltage transient at bus 2, due to a zeroimpedance threephase fault at bus 5. The values are in per unit withrespect to the maximum ( 8222。Y0189。240。 0。1222。 Electromagnetic transients。 鳴謝這項(xiàng)工作得到了CESI研究計(jì)劃的支持。因此，數(shù)控技術(shù)的基礎(chǔ)上評(píng)價(jià)方式進(jìn)行模擬統(tǒng)計(jì)一些有意義的測(cè)量數(shù)目，以便估計(jì)有關(guān)概率密度函數(shù)（PDF格式）。其輸出是的TTL雙邏輯信號(hào)，在符合要求的基于GPS 設(shè)備。中立被認(rèn)為是毫無(wú)根據(jù)。在這種情況下只有兩條路對(duì)L1+L2有影響。 ，總線1 。如下： 平方和的值為所有相應(yīng)的以同樣的頻率的系數(shù)，這是為以后所有連續(xù)小波變換信號(hào)Ecwt（a） ，確定了每個(gè)頻率元件規(guī)定的重量的“尺度”：通過(guò)檢查相對(duì)應(yīng)最高的峰值就可以得到的Ecwt（a）的大小，該信號(hào)的檢測(cè)由最明顯的高頻成分確定。一個(gè)S（t）的該CWT信號(hào)是S（t）和所產(chǎn)生的諧波之間積分產(chǎn)品， 是轉(zhuǎn)換的時(shí)間和擴(kuò)大規(guī)模/壓縮版本一個(gè)函數(shù)具有有限能量的函數(shù)的基波。連續(xù)小波變換。電磁暫態(tài)。這個(gè)過(guò)程中，相當(dāng)于一個(gè)標(biāo)產(chǎn)品， 生產(chǎn)小波系數(shù)C（a,b） ，其中可以看出作為“相似性指標(biāo)”的信號(hào)和所謂的諧波位于立場(chǎng)之間，b（時(shí)間平移因數(shù)）是積分模型并且正數(shù)a:其中*表示復(fù)共軛。從現(xiàn)在起，這些高頻成分被稱為暫態(tài)的“CWT的確定頻率”。該行波反映在線路終端并在故障定位。與之相對(duì)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(shí)顯示在線端子。 雖然有些結(jié)果表明，一些限制的通過(guò)的Morlet小波，(例如，在總線2均衡故障)，其整體理論計(jì)算值確定已經(jīng)達(dá)到CWT頻率。這個(gè)裝置的捕捉時(shí)間瞬間下降邊緣的投入，與標(biāo)稱精度177。具體而言，第一步程序是表征對(duì)測(cè)量系統(tǒng)每個(gè)設(shè)備的計(jì)量性能以便獲得PDF格式的不確定性來(lái)源。 附錄在本文中，連續(xù)小波變換的分析已進(jìn)行了模擬仿真。 Distributed measurement systems