Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
  • G01R31/08—Locating faults in cables, transmission lines, or networks
  • G01R31/081—Locating faults in cables, transmission lines, or networks according to type of conductors
  • G01R31/086—Locating faults in cables, transmission lines, or networks according to type of conductors in power transmission or distribution networks, i.e. with interconnected conductors
• • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
  • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
  • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
  • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
  • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
  • Y04S10/52—Outage or fault management, e.g. fault detection or location

Definitions

• the present method concerns a method of locating a single-phase ground fault in a power distribution network.
• the invention is particularly related to a computational method of locating a single-phase ground fault in medium-voltage overhead and underground-cable networks.
• electric power transmission and distribution is implemented using a three-phase AC system with 50 Hz nominal frequency.
• the nominal, or principal voltage of an AC transmission system indicates the phase-to-phase voltage.
• the power transmission and distribution system may be hierarchically classified into the interconnecting transmission network, the medium-voltage or intermediate-voltage distribution network and the low-voltage secondary-network system.
• the interconnecting network comprises transformers and lines operated at 123 kV, 245 kV and 420 kV nominal voltages serving to deliver bulk electric energy from power plants to large load centers.
• medium-voltage distribution networks are typically operated at nominal voltages of 10 and 20 kV.
• Distribution networks in rural regions are chiefly 20 kV overhead line networks, while 10 or 20 kV underground cable networks are used in urban areas.
• the medium-voltage network serves to transmit electricity to both large commercial loads at the secondary distribution level and to 20/0,4 kV distribution transformer substations, from which power is delivered to residential consumers in a 0.4 kV low- voltage secondary-network system.
• a single-phase ground fault causes in the distribution network a transient disturbance in which the voltage of the faulty phase falls and its phase-to-ground capacitances are discharged resulting in a discharge current transient. Simultaneously, the voltages of the intact phases rise and their phase-to-ground capacitances are charged resulting in a charge current transient.
• a single-phase ground fault can be located by computational means from the charge/discharge current transients.
• the required measurement signals comprise the waveforms of the current and voltage of the faulty phase and the neutral point potential ofthe line as measured at the substation.
• the phase voltage is measured from the voltage measurement cell and the phase current from current measurement cell of the faulty feeder line, or alternatively, from primary side cell of the substation.
• the faulty phase is modelled using a first-order differential equation.
• ground faults have been located using, among other methods, numerical integration, computing the energy spectral density function of the measurement signals by a Fourier transform and using a damped-signal model.
• a drawback of the numerical integration method is that at near-zero values of the denominator, noise present even at the smallest levels causes a large error in the computed end result. Furthermore, the method is unreliable at high values of ground fault resistance after the transient has died away. Methods based on a Fourier transform are hampered by the large number of samples required for a reliable estimate of the signal spectrum. Moreover, the signal must be assumed to be stationary when using the periodogram spectrum. Due to the instantaneous and nonstationary nature ofthe transient (allowing only a small number of samples), the computed spectrum may not necessarily give reliable results. In fact, low reliability of a single spectral value is the weakness of the periodogram analysis. Additionally, the weighting of samples used in the computation of the FFT, that is, multiplication by a window function, distorts the computed spectrum, because the shape ofthe window function can be seen in the final estimate ofthe spectrum.
• noise corrupting the measurement signal causes a major problem in the use of the Prony method.
• No separate noise model is included in the Prony method.
• the noise may have a very wide spectrum, whereby the high- frequency components of the noise are folded over on the lower frequencies.
• the reliability of the parameter estimation process may be improved also when applied to a noisy signal.
• reliable separation of the actual signal from the noise requires that an order estimate of the background process is available. Computation using such a higher order can cause a singularity or near- singularity of the data matrix being processed, whereby correctness ofthe results may be lost.
• bandwidth-limiting filtration can be applied to reduce the noise power of the signal. It must be noted herein, however, that noise power over the filter passband will not be reduced.
• the instantaneous values representing the line inductance between the distribution station and the fault location are computed only from a few waveform samples of the phase voltage transient. Therefore, this method is extremely sensitive to noise and modelling errors, and particularly to fault resistances larger than 50 ohms, the estimates of distance to fault location are highly erroneous or no estimate for the distance can be computed.
• the goal of the invention is achieved by determining the inductance of the line section between the distribution station and the fault location through a signal processing procedure comprising first filtering the measured charge/discharge transient by a comb filter and then processing the filtered signal by the least squares Prony method and examining Prony spectrum computed using the singular value decomposition theorem.
• the invention offers significant benefits.
• the fault distance estimation process uses only such data that have been gathered during the charge/discharge transient.
• the frequency estimate of the transient is obtained with a higher accuracy than that achievable by means of a Fourier transform.
• the effect of noise on the results can be reduced with the help of singular value decomposition of the data matrix.
• the Prony method is particularly suited for modelling a damped sinusoidal signal.
• the energy spectral density estimate can be computed as densely as desired with an arbitrary choice ofthe frequency points.
• Figure 1 is the amplitude characteristic curve of a comb filter suited for use according to the invention, plotted for 50 Hz fundamental frequency;
• Figure 2 is a plot illustrating the principle according to the invention of determining the end instant ofthe transient
• Figure 3 is a plot of an autocorrelation function of a transient signal processed according to the invention.
• Figure 4 is a plot ofthe current and voltage waveform of a faulty phase during a ground fault
• Figure 5 is a plot ofthe signals of Fig. 4 after filtration according to the invention.
• Figure 6 is a plot of a portion of the autocorrelation function of the current signal of Fig. 5;
• Figure 7 is an autoregressive (AR)-type plot of fault current and voltage signal spectra computed at 20 Hz frequency increments;
• Figure 8 is a plot of the Prony spectra of fault current and voltage signals computed according to the invention at 20 Hz frequency increments.
• Figure 9 is another plot of the Prony spectra of fault current and voltage signals computed according to the invention.
• the method according to the invention for estimation of fault distance based on the Prony spectra ofthe fault transient signals is outlined as follows:
• the start instant of the transient is determined from the change of the neutral point voltage. 2.
• the current and voltage waveforms of the faulty phase are filtered using a comb filter.
• the frequency of the charge/discharge transient is estimated from the autocorrelation function ofthe transient. 5.
• the measured current and voltage signals are low-pass filtered in both directions using an IIR filter of at least fourth order. To obtain a reliable filtration result, the train of transient waveform samples must contain measurement values not belonging to the actual transient, whereby the response of the filter itself to a transient signal input cannot corrupt the filtered transient signal.
• the final value of fault distance is computed as follows: If the maxima ofthe current and voltage spectra and occur at the same frequency, the fault distance is computed from the impedance spectrum at said frequency. Otherwise, the final value of fault distance is computed as a weighted average of the values obtained at the frequency corresponding to the maximum ofthe spectrum ofthe current transient and two frequency points (that is, totally at max. 3 frequency points) about said frequency using the equation given below: n
• the spectrum can be computed at a desired number of frequency points.
• the start instant of the fault that is, the first measurement point representing the transient process must be known.
• the identification of the start instant of the transient can be performed by monitoring a change in the neutral point potential U 0 measured at the substation.
• the only method today applicable for this purpose is to set a suitable limit for the neutral point potential whose violation is considered indicative of a ground fault.
• the measured phase current waveform comprises a stationary fundamental frequency component and a nonstationary transient
• the measured phase voltage waveform comprises a nonstationary fundamental frequency component and a nonstationary transient.
• n is a discrete time index
• yfnj is the filter output signal
• x[n] is the filter input signal
• f s is the sampling rate
• / is the fundamental frequency of the signal.
• Figure 1 is shown a portion of the amplitude characteristic of the comb filter defined by Eq. (5) when the fundamental frequency is 50 Hz. As can be seen from the graph, the zero points of the passband coincide exactly with the fundamental frequency and its harmonics. Because of the nonstationary nature of a transient, the filter amplitude characteristic shown in Fig. 1 does not tell the effect ofthe filtration process on the transient waveform that is dependent on the damping coefficient. With a large value of the damping coefficient, the transient will die out in a shorter time than the cycle time of the fundamental frequency component, whereby the filter will not distort the transient waveform.
• the amplitude error caused by the filter is 0.0025A, where A is the amplitude of the transient. Because the amplitude characteristic shown in Fig. 1 is valid for stationary components ofthe input signal only, the filter will not distort such damped transients whose frequency is a harmonic of the fundamental frequency or which decay to zero in a shorter time than the cycle time of the fundamental frequency. In practice, the transient can be assumed to decay away during one cycle of the fundamental frequency. When desired, the delay of the filter may be designed longer, e.g., doubled, whereby the distortion caused by the filter will be further reduced.
• the fundamental frequency of the network can be estimated from the steady-state measurement of the phase current performed after the decay of the fault transient.
• Frequency estimation of a single sinusoidal signal can be made using the maximum likelihood estimation (MLE) method. In this method, the frequency is sought at which the periodogram of the signal reaches its maximum value, that is, the value ofthe equation below is maximized:
• the fundamental frequency can be estimated by computing the MLE values for frequencies about 50 Hz and then selecting the frequency corresponding to the largest value.
• Determination of the transient end instant is necessary, because the spectral estimate computed from the signal samples of the transient will be significantly corrupted, unless specifically computed over the duration ofthe charge/discharge transient.
• the end instant of the transient may be determined after the low-pass filtration using a relatively simple procedure. From the data gathered after the start ofthe transient for one full cycle ofthe network fundamental frequency, the signal value of maximum magnitude is selected. This value is then inte ⁇ reted as the maximum value of noise associated with the measurement. Next, the values of this signal sample sequence are compared proceeding from the end toward the start of the sequence until a limit value is reached that is, e.g., 10 % larger than the maximum value of the noise component in the measurement. Finally, the first signal sample exceeding the limit value thus defined is chosen as the end instant of the transient.
• the method is illustrated in Fig. 2 showing a simulated transient with superimposed noise. In the diagram is drawn by horizontal dashed lines a corridor within which the instantaneous values of the measurement signal fall after the decay ofthe transient.
• the measurement signals are assumed to contain only the charge/discharge transient occurring at the onset of a ground fault. Since the Prony method is sensitive to noise, the transient signal must be filtered free from other frequency components.
• the filtration method chosen in this invention is low-pass filtration.
• the design of a low-pass filter comprises the selection of the order and cutoff frequency ofthe filter.
• the filter cut-off frequency is chosen on the basis ofthe estimated frequency ofthe transient waveform.
• Estimation of the transient frequency can be performed using the autocorrelation function which is used for examination of the dynamic changes in the measurement signals.
• the autocorrelation function of a discrete data signal is computed using the equation below:
• the autocorrelation function is computed for the data extending from the start instant to the end instant ofthe transient.
• the time value of the autocorrelation function at which the function reaches a minimum corresponds to the duration of half- cycle in the decaying sinusoidal input signal.
• the frequency estimate of the transient is obtained by dividing half the sampling rate with the delay time corresponding to minimum value of the autocorrelation function.
• Fig. 3 is shown a portion of the autocorrelation function ofthe simulated transient.
• the cutoff frequency of the low-pass filter is automatically determined by the frequency of the charge/discharge transient.
• a practical realization of a low-pass filter cannot have a zero-width passband.
• a safety margin of a few hundred hertz must be added to the estimated cutoff frequency to avoid distortion to the waveform of the transient by the filter.
• the low-pass filter can be selected to be, e.g., a Butterworth-type IIR (Infinite Impulse Response) filter of at least fourth order.
• IIR filters e.g., a Butterworth-type IIR (Infinite Impulse Response) filter of at least fourth order.
• a benefit of IIR filters is that a relatively steep flank ofthe passband can be obtained already with a filter of a very low order.
• a further beneficial characteristic of Butterworth low-pass filter is its flat-topped passband.
• IIR filters are hampered by an infinite impulse response, which means that their phase delay is nonlinear.
• phase delay can be eliminated by filtering the measurement signal bidirectionally (two times), first forward from the beginning of the data sequence to its end and then backward from the end to the beginning.
• the amplitude distortion caused by the filtration is very small in practice.
• the initial transient response ofthe filter can be minimized by selecting proper initial values for the filter and then adding to the filter input a short inverted portion of the original input signal sequence. The best possible filtration result is obtained when the length of the signal sequence to be filtered is at least three-fold relative to the order ofthe filter and when the signal values at the start and end ofthe data sequence approach zero.
• parametric methods Spectral estimation methods based on a parametric signal model are called parametric methods.
• the goal of parametric methods is to find a linear difference equation model capable of describing the signal.
• the use of parametric models in describing a signal presumes that the model of the signal is known, or alternatively, the signal is known to obey a model having a finite number of parameters which are independent from the number of samples in the data sequence. In the adaptation of the model, the coefficients of the difference equation and the order of the model are optimized.
• the use of parametric models in estimation of a spectrum comprises three steps:
• the signal When estimating the energy spectral density function on the basis of the parametric model, the signal is assumed to be compliant with the model also outside the data range used in the computation.
• This method dispenses with the weighting of the signal data with a window function, whereby also the distortion caused by the window function on the spectrum is avoided. Additionally, a certain reliability level ofthe computed spectrum is attained with an appreciably shorter data length than is required in Fourier transform methods.
• a disadvantage of this method is that the reliability assessment ofthe computed spectrum is not as easy as in the Fourier transform methods.
• the degree of improvement in the resolution and reliability of the computed spectrum is dependent on the suitability ofthe model for use in conjunction with the signal being processed and its ability to fit the coefficients ofthe model to the measurement data or its autocorrelation function. As normally some background information is available on the process producing the signal to be examined, this information can be used in the selection of a suitable type of model.
• a further benefit of parametric estimation methods of energy spectral density functions is that the signal spectrum may be computed at desired discrete points of frequency, thus giving an arbitrarily high plotting resolution ofthe spectrum.
• the estimation ofthe fault distance is examined by way of modelling the waveforms of the current and voltage transients using both the autoregressive, or AR model, and a model based on the least squares Prony method.
• the AR-model is selected as the basis of the examination, because it is more suitable for particularly short data sequencies than the Fourier transfer methods and it is capable of extracting frequency components from which a signal sample sequence of less than a full cycle can be retrieved. Due to these reasons, the AR model may also possibly be used for modelling nonstationary signals such as charge/discharge transients.
• the model based on the Prony method is preferentially investigated herein, because it is particularly developed for modellling a damped sinusoidal signal.
• the autoregressive (AR) model ofthe signal computes the expected present value of the signal as a weighted sum of its preceding values.
• An autoregressive model AR(p) of order p is described by the equation:
• x[n] is the output of the autoregressive filter at instant n
• e[n] is a process generating at the filter input a white noise signal with zero average value and variance p 2 and a k ,k - ⁇ ,...,p are the coefficients ofthe model.
• the energy spectral density function ofthe signal as given by the AR model is:
• the AR model in a fault distance estimation method based on the spectra of the current and voltage transients of the faulty phase is favoured by its simple form and the easy interpretation of the spectrum produced by the method.
• the spectral peaks corre ⁇ sponding to the poles of the AR-spectral estimate are narrow, and owing to the zero order ofthe denominator, the zeros ofthe AR estimate are seen as smooth valleys.
• the model To adapt parametric methods to the modelling of a signal, the model must be compatible with the process being modelled. In fact, this is problem in the use of the AR model for fault distance estimation, because in the AR model the input signal is assumed to be white noise, while the charge/discharge transient caused by a ground fault is closer to an impulse function. Moreover, the input signal to the AR model is assumed to be stationary or slowly changing, which is not true in the present case.
• the Prony method is sensitive to noise. Hence, if the input signal contains additive noise by a significant amount, the parameters of the original transient waveform cannot be determined correctly any more. In particular, the values of the damping coefficients become extremely unreliable and typically greater than the actual values.
• the effect of additive noise on the signal is reduced by using a higher order of the exponential model and low-pass filtration of the transient signal.
• Significant additional reduction of the noise effect can be attained by using a further developed version of the least squares Prony method in which the data matrix formed from the signal sample sequence is divided on the basis of the singular values of the matrix into two parts so that the signal components of appreciably larger singular values are considered to represent the original transient, while the rest ofthe signal components are taken as noise. If the transient is strongly damped or the signal-to-noise ratio ofthe data is poor, the separation of the actual signal from noise may sometimes be difficult even when using the singular value decomposition theorem.
• the definition of the Prony spectrum makes an initial assumption that the measured transient is symmetrical about the origin. Then, the transient can be modelled using a two-sided function:
• the width of the Prony spectrum peak is determined by the magnitude of the damping coefficient.
• the height of the peak in the Prony spectrum computed according to
• Eq. (14) is (2A k I a k ) ⁇ and its -6 dB bandwidth is al ⁇ .
• the resolution of the spectrum varies as a function of the damping coefficient. For a large value of the damping coefficient, wide spectral peaks are obtained, while a small value ofthe damping coefficient results in narrow spectral peaks.
• the Prony method was particularly developed for modelling a damped sinusoidal signal, this type of model is extremely well suited for modelling a charge/discharge transient occurring in the beginning of a ground fault. Hence, the estimate of the energy spectral density function obtained by virtue of this method is more reliable than that computed by other Fourier transform methods. Analogously to other parametric spectral estimation methods, the Prony spectrum of a signal can be computed for as many frequency points as is desired independently from the length of the data sequence used for the determination ofthe parameters.
• a disadvantage of the method is that the computation of the model parameters is rather laborious due to large size of the data matrices processed. In turn a reduction of the computation task can be accomplished by focusing the computation of the spectrum to the frequency range of interest, that is, about the estimated frequency of the charge/discharge transient.
• the start instant of the transient is determined from the change of the neutral point ofthe network. 2.
• the measurement signals ofthe faulty phase current and voltage are filtered using a comb filter defined by Eq. (5).
• the frequency of the charge/discharge transient is estimated from the autocorrelation function (7) ofthe transient. 5.
• the current and voltage measurement signals are low-pass filtered using, e.g., an ILR filter of 4th order. 6.
• the complex- value spectra U( ⁇ ) and l( ⁇ ) of the current and voltage transients are computed using either Eq. (10) or Eq. (13).
• the fault distance is computed from the impedance spectrum at said frequency. Otherwise, the final value of fault distance is computed as a weighted average of the values obtained at the frequency corresponding to the maximum ofthe spectrum ofthe current transient and two frequency points (that is, totally at max. 3 frequency points) about said frequency using Eq. (3).
• a precondition for the use ofthe frequency points adjacent to this frequency of current spectrum maximum is that the spectral amplitude at the adjacent frequency points is at least 80 % of the maximum amplitude ofthe signal spectrum.
• the signal recordings used in the example were measured at a substation having an artificial ground fault of zero ohms made to a 20 kV medium- voltage network operated with its neutral point isolated from ground. The actual distance to the fault was 14.2 km from the substation.
• FIG. 4 the current and voltage transient waveforms of the faulty phase are shown at the occurrence ofthe ground fault. The fault has occurred just prior to the time instant 0.04 s ofthe plot.
• the start instant of the transient is determined on the basis of the time instant corresponding to the change of the neutral point voltage.
• the ground fault can be assumed to have occurred when the neutral point voltage exceeds a preset limit.
• the tripping instant ofthe neutral point voltage relay is taken the start instant ofthe ground fault.
• the measurement signals are filtered by means of a comb filter defined by Eq. (5) to eliminate the fundamental frequency and harmonic components.
• the signals of Fig. 4 are shown in Fig. 5 after filtration by the comb filter.
• the fundamental frequency component of the signal existing prior to the occurrence of the fault cannot be removed entirely from the current signal due to the nonideal performance ofthe filter.
• this has no meaning to the estimation ofthe fault distance, because the start instant of the transient is known from the change of the neutral point voltage and the estimation method of fault distance uses only signal sample sequences following the start instant ofthe ground fault.
• the duration of the transient is determined. Using the procedure described above, the duration of the transient is determined as approximately 150 data samples. In real time this corresponds to 7.5 ms when the sampling rate has been 20 kHz.
• Fig. 6 shows a portion ofthe autocorrelation function computed according to Eq. (7) for the current transient waveform of Fig. 5. With the 20 kHz sampling rate used and the first minimum ofthe autocorrelation function coinciding with a delay of 27 samples, the estimate ofthe transient frequency is 10000 Hz / 27 « 370 Hz.
• the measurement signals Prior to the final step of fault distance estimation, the measurement signals are low-pass filtered.
• a Butterworth-type IIR filter of 4th order is used herein.
• the filter cutoff frequency is selected on the basis of the frequency estimate obtained for the charge/discharge current transient as described above.
• the filter cutoff frequency is set a few hundred hertz above the estimated frequency fo the charge/discharge transient.
• the fault distance is estimated based on the spectra ofthe current and voltage transients. Two modelling alternatives were described above: the AR model and the damped sinusoid model defined by the Prony method using a parameter solution utilizing the singular value decomposition theorem for processing the data matrix.
• Fig. 7 the spectra of the current and voltage transients computed according to Eq. (10) are shown for 20 Hz spacing ofthe frequency points.
• the result is 15.3 km.
• the order of the AR model for computation of the results given below was set as 20. This order ofthe model was arrived at experimentally by comparing the results computed using different data and different order ofthe model.
• the maxima of the current and voltage transient spectra are seen to occur at different frequencies.
• the transient waveforms need not necessarily have exactly the same frequency and damping coefficient. An additional error is caused therefrom that the AR model is not initially intended for the modelling of fast-changing signals ofthe impulse type.
• the order of the exponential function model used for modelling the transients was set a 6, whereby two of the exponential functions were used to represent the actual signal Then, the model contains only one frequency intended to correspond to the charge/discharge transient. Four of the exponential functions were set to represent the additive noise corrupting the actual signal. The choise of the model order was based on tests in which noise of normal distribution was added on a simulated transient, after which the parameters ofthe transient were estimated.
• Table 2 gives the singularity values of the data matrices formed from the sampled current and voltage measurements illustrated in Fig. 8.
• the table shows that the two largest singularities of the data matrices corresponding to the current and voltage tran ⁇ sients are clearly larger than the other singularities.
• the values of the singularities prove a successful selection of the model and the measured transients contain only one damped sinusoid corresponding to the actual transient waveform. Also when tested with other measured transients, the selection of the model was successful as evaluated on the basis ofthe relative magnitudes ofthe singularity values in the data matrices representing the transients.
• Table 2 Singularity values of data matrices formed from current and voltage transient measurement. Measurement site Tuovila, fault distance 14.2 km and fault resistance 0 ohms.
• the current transient may also be measured from the primary side cell cell instead of the feeder side cell.
• the end instant of the transient can also be determined with the help of the autocorrelation function of the transient when the function is computed over a longer time (e.g., comprisng a full cycle of the fundamental frequency after the occurrence ofthe fault).
• a longer time e.g., comprisng a full cycle of the fundamental frequency after the occurrence ofthe fault.
• the duration of the transient and the frequency estimate of the could be determined in a single step.
• the transient may alternatively be defined for positive instants of time only in the following manner:

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• Physics & Mathematics (AREA)
• General Physics & Mathematics (AREA)
• Locating Faults (AREA)
• Testing Relating To Insulation (AREA)
• Measurement Of Resistance Or Impedance (AREA)

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