Fault detection method and calculation formula of different cable fault types

Cable fault search and locating work is always a big problem of the electric industry. This is mainly because most of the cable buried in the ground, laying distance from several meters to several kilometers, dozens of kilometers, coupled with the complex environment of the scene. In addition to the cable fault test equipment for high quality requirements, the technicians’ comprehensive quality is also requested very strict.

There are three commom types of cable faults. They are low resistance faults, high resistance short circuit ground fault and flashover fault. Three kinds of cable fault detection methods are also different for different types of cable faults.

1.  Low resistance faults

The general availability of Wheatstone bridge to loop measurement to the point of failure. The single phase earth fault point is measured by loop method, as shown in figure 1.

Single phase to ground fault measuring connection

When the fault point is connected to the X2 , the fault distance is Lx＝A÷（A＋B）×2L

When the fault point is connected to the X1, the fault distance is Lx＝B÷（A＋B）×2L

Among them, A is the bridge arm unit variable readings, unit is Ω,

B is the other arm bridge readings, unit is Ω;

L is the long lines, unit is m;

Lx is the cable test end away from the fault point, unit is m.

When the two phase short circuit is used, the method is connected with a single ground, and the positive end of the power supply is connected to another bad cable core, and the end of the tested fault phase is short connected with the intact phase to form a loop.

When the three-phase short circuit is applied, the other line or temporary line is used as the loop line, as shown in figure 2.

Three phase short circuit grounding fault point measuring wiring

When the fault is connected to X2, a fault location from the end is Lx＝A÷（A＋B＋R）×L;

When the fault is connected to X1, a fault location from the end is Lx＝B÷（A＋B＋R）×L;

The single line resistance R is the temporary line, such as R≤（A+B）, can be ignored.

If there is no proper bridge, the voltage drop or current method can be adopted. The wiring is shown in figure 3.

With the voltage drop method, the fault distance is L_x＝U₁÷（U₁＋U₂）×2L.

With the current meter method, the fault distance is L_x＝R_x×L÷R＝（I₂-i₁）i₂R_L÷i₁（I₁－i₂）＋i₂（I₂－i₁）, R_L＝R_x＋R_y

2. High resistance grounding short circuit fault

Basically, the loop method is used, but because of the large resistance to the fault, the fault current must not be too small. High voltage power supply is obtained by rectifier. In the test, the insulated platform, the distributor and the insulation rod of the bridge shall be used, and the handshake part shall be grounded. The pilot shall be grounded, and the wiring diagram shall be shown in figure 4.

High voltage grounding fault test guide wire

When the fault point is connected to the "0" , the fault distance is L_x=A÷100×2L;

When the fault point is connected to the "100" , the fault distance is L_x=2L×(1－A÷100).

 A is a sliding wire resistance reading.

When detecting a high resistance fault, it can be tested by DC high voltage breakdown, and then by AC burning to make it low resistance grounding, and then test with low resistance measuring method.

3. Flashover fault

The flashover fault refers to the breakdown after the insulation resistance is still the same as the normal fault. It can be dealt with in the following manner:

(1) Repetitive breakdown of the fault point with DC voltage. It is changed into low resistance grounding, and then it is changed into stable low resistance grounding by AC burning.

(2) The acoustic method is used to measure the conduction. This is the use of capacitor C charging, after discharging the ball gap S to the fault point discharge, there is a larger sound, arrange people to listen to each part of the discharge electroacoustic, you can find the fault point, as shown in figure 5.

Acoustic test wiring diagram

The function of impulse voltage generator and the waveform

Impulse voltage generator is a high voltage generator that generates pulse waves.

Originally, it was used only to study the insulation performance of power equipment which subjected to atmospheric over-voltage (lighting）, and now it is used to study the insulation performance of power equipment subjected to over-voltage operation. Therefore, for impulse voltage generator, we require it not only can produce the lightning waveform but also the operating overvoltage waveform . The destructive of impulse voltage not only depends on the amplitude,it’s also associated with the wavefront steepness. Some of the equipment is also tested by the chopping wave.

In addition, impulse generator can also be used as an important component of nanosecond pulsed power device. It can be used as power supply in high power resistance beam and ion beam generator and CO₂ laser.

 According to the actual measurement, the lightning wave is a non periodic pulse, and its parameters are statistical. The front time (the time required is about from zero up to the peak) is 0.5μs~10μs, half peak time (about from zero up to a peak and peak time reduced to 1/2) is 20μs~90μs, the cumulative frequency is 50% for the wavefront and the half peak time is about1.0μs~1.5μs and 40μs~50μs.

The duration of impulse wave is much more than the operating voltage of lightning impulse voltage wavelength, with more complex shapes, and his shape and duration, in line with the specific parameters and length vary, but the current international tend to use a few hundred microseconds long wavelength wavefront and thousands of microsecond pulse representing it. Lightning wave can be divided into two kinds of full wave and chopped wave. The chopped wave is used to cut off the impulse wave produced by the impulse voltage generator and cut off the voltage sharply. The truncation time can be adjusted or taken place at the wave front or at the wave tail.

In order to ensure the repeatability of the test results and the comparability of the test results between each test, the definition of waveform and waveform should be clear. To this end, the IEC and the national standard set the standard lightning impulse, full wave, chopping wave waveforms and standard operating impulse voltage waveforms, as shown in Figures 1 through 4.

Figure 1: Lightning impulse voltage full wave

In Figure 1, 0 is the origin. Sometimes the waveform taken by an oscilloscope tends to be blurred near or near 0, or there is an initial oscillation. When the generator of the impulse voltage is big inductance, the beginning of the waveform may also be a little more flat. At this point, the origin of the waveform (the real starting point) is not easily determined on the time axis. The peak point of the voltage wave, due to its flatness, is not easily determined in time. The IEC and the national standard employ the method shown in Figure 1 to obtain the origin O1, and then calculate the wavefront time T_f and the half peak time T_f from O1. The prescribed wave front time T_f is T/0.6. The standard lightning impulse test, the wave front time T_f of voltage wave is 1.2μs±30%, and the half peak time T_t is 50μs±20%.

Figure 2: Record voltage waveform and test voltage waveform

(a) recording and testing voltage waveforms;(b)After the basic waveform superposition filter, the residual waveform becomes the test voltage waveform

If the wavefront peak overshoot or oscillation with wave (Figure 2a), according to new rules of IEC60060 1 , processing steps at this time should be specified by the standard, the recorded waveform is converted into test voltage waveform (Fig. 2b), the amplitude of latter is

U_t＝U_mp＋k（f）（U_e－U_mp）

K（f）＝1/（1＋2.2f²）

In the formula, f-the overshoot oscillation frequency, MHz;

K (f) - test voltage factor, it is a function of frequency, and is a variety of insulation, applied the superposition of different frequency overshoot impulse voltage wave of amplitude frequency relationship and insulation breakdown strength.

The standard stipulates that each end of the record waveform will be discarded a little bit, and the good waveform should be fitted by double exponential waveform fitting.  

Although the final test waveform contains the components of the filtered residual waveform, the standard specifies the wave front time, the half peak time and the relative overshoot amplitude beta from the test voltage waveform

β’ ＝[（U_t－U_mp）/U_t]×100%

The new IEC standard provides that the maximum allowable value of the overshoot β’ of impulse test voltage is 10%, but the maximum allowable value of  β’  is 20% when the test voltage amplitude is higher than 2MV.

According to the calculation results of impulse voltage generator with higher order lumped parameter, the frequency of the overshoot wave is unlikely to be higher than 0.5MHz when the standard lightning impulse voltage wave is generated. However, considering the spurious oscillations and multiple reflections of flow waves in the test loop, the impulse wave front may be superimposed with higher frequency oscillation waves. Its maximum oscillation frequency f_max, can be estimated by the press type:

f_max＝c/[4（H_g＋H_c）]

In the formula, C - the propagation velocity of electromagnetic waves in the air,C＝300m/μs,

Hg - the height of the impulse voltage generator, m,

Hc - the height of the load capacitor, m.

The chopping wave of lightning impulse voltage is shown in figure 3. The lightning impulse chopping time Tc is the time interval between the origin and the truncation moment. The apparent characteristics of the voltage period during truncation are defined by breaking the 70% of the instantaneous voltage value and the C and D points of 10%. The voltage drop duration is 1.67 times the time interval between point c and point D. The steepness of the voltage drop I cut off the ratio of the instantaneous voltage to the voltage drop duration.

Figure 3: Lightning impulse voltage chopped wave

(a) the lightning impulse truncated at the wave tail  (b) the lightning impulse at the wave front truncation

The operation shock waveform defined by the IEC60060 1 is shown in figure 4. Its half peak time T_t is the time interval from the actual origin to the half peak of the wave tail. The wavefront time T_m is the time interval from the actual origin to the peak.

Since the amplitude is flat and the peak point is not easily determined, the new standard specifies the following formula to determine the wavefront time

T_m=KT_AB

K＝2.42－3.08×10^-3×t_ab＋1.51×10^－4T_t

T_t,T_AB, shown in Figure 4, are all in units of μs.

Figure 4: Operating impulse voltage waveform

The IEC 60060 -1 also specifies a time limit of 90% peak over the standard operating impulse voltage, T_d which refers to the duration of the impulse voltage exceeding the peak value of 90% T_d. The standard wave front time of operation impulse voltage  Tm is2 50us±20%, and half peak time Tt is 2500us±60%. IEC 60076-3: 2000 test more than 220 kV rated voltage transformer and reactor internal insulation switching impulse voltage waveform as shown in figure 5. As the front time Tf of at least 1 00μs, usually not more than 250μs, 90% above the peak time of T_d  is more than 200μs, from the first zero time T_z more than 500μs at the origin. The impulse voltage wave specified by the relevant national standards (GB, 1094., 3--2003) is the same as that of the above IEC documents.

Figure 5: Operating impulse voltage waveform of internal insulation in test transformer

According to the test standard and taking into account the sufficient margin, the relation between the nominal voltage of the impulse generator and the voltage of the device under test is shown in the following table. The lower and lower values of the table meet the need of type test, and the upper limit is used for research and test.

Rated voltage of test sample/KV	35	110	220	330	500
Nominal voltage of impulse voltage generator/MV	0.4~0.6	0.8~1.5	1.8~2.7	2.4~3.6	2.7~4.2