外文翻譯--普羅尼法分析在消弧線圈保護(hù)網(wǎng)絡(luò)的接地故障電流的有效工具（英文）

1、1234 IEEE Transactions on Power Delivery, Vol. 10. No. 3, July 1995 PRONY'S METHOD : AN EFFICIENT TOOL FOR THE ANALYSIS OF EARTH FAULT CURRENTS IN PETERSEN-COIL-PROTECTED NETWORKS Oinis CHAARI Patrick BASTARD

2、Michel MEUNIER Service ':Electrotechnique et Electronique Industrielle“ ECOLE SUPERIEURE D'ELECTRICITE (SUPELEC). 91 190 Gif-Sur-Yvette. FRANCE Abstract-Prony's method is a technique for estimating the

3、modal components present in a signal. Every modal component is defined by four parameters : frequency, magnitude, phase, and damping. This method is used to analyse earth fault currents in Petersen-coil-prote

4、cted 20 kV networks. The variations of Prony's parameters in terms of some of the power system characteristics (distance between the busbar and the fault, fault resistance and capacitive current of the whole netw

5、ork) are presented. It is shown that some of the Prony's parameters relating to the fault current transient may be useful to determine what kind of fault occured, and where it did. Key Words-Prony, Signal anal

6、ysis, Singular value decomposition, Petersen-coil-protected network, Transient, Earth fault. I. INTRODUCTION Among all the faults likely to occur in a power network, earth-phase faults are the most frequent ones. T

7、he effects of the earth faults depend on the neutral grounding method. In this paper we treat with the Petersen-coil earthing in which a reactor is connected between the neutral of the power system and the ground [1,

8、2]. This reactance is adjusted to match, at the fundamental system frequency, the value of the zero- sequence capacitance of the network. It is claimed that during an earth fault the current flowing through the fault

9、 is of insufficient value to support an arc. Petersen-coil earthing has been used a great deal in Europe and EDF (Electricid D eFrance) has decided to generalize its application to 95 W M031-5 PWRD by the IEEE Power

10、System Relaying Committee of the IEEE Power Engineering Society f o r presentation a t the 1995 IEEE/PES Winter Meeting, January 29, t o February 2, 1995, New York, N Y .Manuscript submitted December 16, 1993; mad

11、e available f o r printing December 12, 1994. A paper recommended and approved the whole French distribution system. It is believed that this kind of neutral grounding has a somewhat limited use in North America on a

12、ccount of the predominance and the popularity of the solidly grounded neutral. Nevertheless, there are some systems favorable to the use of the Petersen-coil neutral grounding [3]. Digital relays should allow a fast

13、detection of any fault through a real-time analysis of the power signals. Most of the time, a 50 Hz analysis is implemented to diagnose a fault. But in a compensated power network, the 50 Hz component of the zero-se

14、quence current may be very weak and its use is consequently hazardous. Morerover, during a few milliseconds after an earth fault, transient components of fault currents have magnitudes which may be much higher than t

15、hose of the steady state component. Above all, earth faults are often formed by a succession of transient short duration self extinguishing faults. Meaningful information is thus contained in the transient terms of

16、the fault signals; it should be used in zero-sequence protections to increase their speed and accuracy. Hecce there is a need for precise tools that should be able to analyse the current signal and find a small numb

17、er of parameters which define such waveforms. Several algorithms have been used in the analysis of the electrical signals. The most widely used method to observe spectral components of a signal is the Fast Fourier Tr

18、ansform (FIT) [4]. This real time decomposition yields a complete description of stationary signals. FFT meets severe limitations when the characteristics of the signal to be analysed are strongly time dependent. An

19、 event is always spread on the whole FFT analysing window. Moreover, FIT is very sensitive to the presence of aperiodic components in the signal. Techniques based on Kalman filtering theory have been applied for th

20、e optimal estimation of the fundamental frequency from the noisy signal [5,6]. However, Kalman filtering has limited capability for modelling the aperiodic components. Least square linear fitting methods have been pr

21、oposed for power system relaying [7]. But the linear fitting requires a prior knowledge of the signal model. ' The problem is that the transient components of fault signals are quite difficult to study. Moreover,

22、it is difficult to establish relations between the fault itself and the characteristics of the transient signals. Therefore a good description of the non stationary transient signals calls for 0885-8977/95/$04.00 Q 19

23、95 IEEE 1236 B. Simulation with EMTP III. SIGNAL ANALYSIS METHOD The network drawn in Fig. 1 is simulated with the EMTP (ElectroMagnetic Transient Program). The power transformer is represented by a [SL] matrix compu

24、ted with the help of the BCTRAN subroutine. A distributed parameter circuit model is used to simulate the seven feeders emanating in radial fashion from the busbar. The earth-phase fault consists in earthing phase A

25、through the earth-phase fault resistance Rd. For this kind of earth fault, Rd is equal to 2 R in the sections IV-A and IV-B and it is varying between 2 R and 16 R in the section IV-C. x(t) is then the current in Rd

26、(Fig. 2a). On the other hand, the earth-phase-phase fault consists in short-circuiting phase A and phase B and earthing each of them through one 2 Q resistor. In this case, x ( t ) is the phase A-to-earth current,

27、through the 2 R resistor (Fig. 2b). Notice that, in this case, x(t) is the half of the sum of phase A to earth plus phase B to earth currents. LT , the total length of the 7 outgoing feeders D, the distance between t

28、he fault and the busbar Rd, the earth-phase fault resistance Let us simulate, as an example, an earth-phase fault occurring at the time origin. We suppose that Rd = 2 R, D = 5 Km, Xn = 60 R, Rn = 600 R and LT = 70

29、Km. Fig.3 shows the fault current in Rd. The various parameters of EMTP simulations are : 4 (a: (b) (b) in the case of an earth-phase-phase fault. Fig. 2. The fault current, x(f), (a) in the case of an earth-phase fa

30、ult, Fault current I I -600 -0.02 0 0.02 0.04 0 . 0 60.08 Time (ms) Fig. 3 The fault current, x(f), in the phase A-to-earth resistance Rd. -“L “““ The earth-phase fault occurs at the time origin. A. Basic Hypothes

31、is We suppose that the earth fault occurs at the time origin. Thus, the time-dependent signal, x(t), standing for the fault current in the phase A-to-earth resistance, is to be analysed in positive time. We suppose th

32、at nonlinear dynamics in the power system described in Fig. 1, are negligible. We can then consider that the fault current signal is given by a linear system response to a sinusoidal excitation. It follows that the

33、signal to be analysed, x(t), is the sum of conjugate complex and real exponentials. Thus, x(t) is the sum of exponentially damped and pure sinusoids and it may be expressed as : (1) 4 k=l X ( t ) = XAk e-ffk'

34、cos(2nfkt -k 6,) where q is the number of elementary functions, Ak is a magnitude, a kis a damping factor, fk is a frequency in hertz, and 6, is a phase in radians. fk =O and 6, =O or R for damped exponentials, and

35、a k=O for pure sinusoids. we suppose that x ( t ) is formed by q1 purely damped exponentials and 42 sinusoids, damped or not (q= q1 + 42). Let 2 be the real measured data of N equally spaced samples. x 'can

36、be written : where“T“ denotes matrix complex conjugate transpose. From (1) we derive, for n=O,I ,..., N-1 : T Z=[x(l,x1 ,-, XN-11 , ' ffkndf X , ,= X(t,, = nAt) = COS(2nfkkndt + 6,) (2) k=l where At is t

37、he sampling period in seconds. Equation (2) yields the following complex expression formed by q1 real terms, corresponding to the purely damped exponentials, and 4 2complex terms plus their conjugates : P k=l X,, = cp

38、kZ$ n=O,I, ..., N-I (3) where p is the signal order @ = q1 + 242), p k is the complex magnitude, and Zk is the complex frequency. p k and Zk can be written in terms of the real parametres as follows : p k = f

39、or purely damped exponentials f - UZ for purl? and damped sinusoids (4) [ ' k- e(-ak+j21gk)At B. Numerical Method To analyse the signal x(t), we choose an appropriate method that is well suited for exponentially