【正文】 es 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 ( 1012V2s).Table 2Frequency values theoretically associated to the paths covered by thetraveling waves originated by a balanced fault at bus 5 observed at bus 2,and values identi?ed by the CWTanalysisthe transient. The DAQ output is o?line analyzed throughthe above described algorithm.A prototype of the unit has also been realized, with thefollowing characteristics. A voltagetovoltage capacitivePathL3 + L4Length (km) Theoretical frequency(traveling wave atlight speed) (kHz)4 7 CWTidenti?edfrequency (kHz)divider Pearson VD305 A has been used, with insulationvoltage 300 kV peak, nominal ratio 10 000 V/1 V, bandwidth 30 Hz to 4 MHz ( 3 dB), rising time 100 ns, accuL1 + L2 + L4 2 7L2 + L4 + L5 2 621racy 177。1%. Its output signal feeds the event detectionblock, which has been implemented by means of an analogcircuit described in [16]. Its output is a TTL duallogic signal, in conformity with the requirements of the GPSbasedan event detection block (EDB) and to an analogtodigitalconversion board (DAQ). The EDB is speci?cally designedto detect the presence of transients superimposed to thesupply voltage waveform and provides a logic signal that,at the occurrence of a transient, acts as a pretrigger forthe DAQ for the data acquisition and as a trigger for theGPSbased device in order to record the starting time ofdevice. This device captures the time instant of a fallingedge of its input, with a nominal accuracy of 177。250 ns.Moreover, it provides TTL pulses, with 1 s period and anominal accuracy of 177。250 ns, used to synchronize all thefunctions performed by the measurement system. The parison of the time instants of the received voltage transients at di?erent distributed measurement unit improves0102030Frequency (kHz)405060Fig. 5. Results of the CWTanalysis of the voltage transient at bus 4, due to a zeroimpedance threephase fault at bus 5. The values are in per unit withrespect to the maximum ( 1012V2s). CWT signal energy (.) CWT signal energy (.)614Table 3A. Borghetti et al. / Electrical Power and Energy Systems 28 (2006) 608–617Table 4Frequency values theoretically associated to the paths covered by thetraveling waves originated by a balanced fault at bus 5 observed at bus 4,and values identi?ed by the CWTanalysisFrequency values theoretically associated to the paths covered by thetraveling waves originated by a balanced fault at bus 2 observed at bus 4,and values identi?ed by the CWTanalysisPathLength (km) Theoretical frequency(traveling wave at lightspeed) (kHz)CWTidenti?edfrequency (kHz)PathLength (k