A New Method for Estimating Line-to-Ground Capacitance of Low-Current Systems

The system capacitance current is one of the system parameters that the dispatching and operation units need to understand, and it is the basis for the design unit to select compensation equipment, so it is of great significance to study this work. At present, the main methods for measuring capacitance current are single-phase metal grounding method, relative additional capacitance method and neutral point additional capacitance method.

The single-phase metal grounding method is prone to cause two-phase short circuit and ferromagnetic resonance overvoltage, which is very dangerous. The relative ground additional capacitance method mainly causes safety hazards in the additional capacitor itself. For example, when measuring cable lines, the additional capacitor is generally placed near the switch cabinet. If there is a defect in the additional capacitor and it explodes during the measurement process, it may endanger other distribution cabinets and cause major accidents. In addition, when measuring the capacitance current of the 35kV system, due to the high system voltage and large additional capacitance capacity, some test units may not have suitable capacitors. When using the neutral point additional capacitance method, if the system is single-phase grounded during the measurement process, the neutral point voltage rises to the phase voltage, which will endanger the safety of the operator and the meter, and the measurement error is large.

In actual operation, for a distribution system with a large number of outgoing lines, long lines or a large number of cable lines, when a single-phase grounding fault occurs, the capacitive current to the ground will be quite large. If the grounding arc cannot be extinguished by itself, it is very easy to produce intermittent arc grounding overvoltage or excite ferromagnetic resonance, which will last for a long time and have a large impact area. The weak points of line insulation will often develop into two-phase short circuit accidents. Therefore, DL/T620-1997 "Overvoltage Protection and Insulation Coordination of AC Electrical Installations" stipulates that systems composed of overhead lines of 3-10KV reinforced concrete or metal towers and all 35KV and 66KV systems should be equipped with arc suppression coils when the single-phase grounding fault current is greater than 10A; systems composed of 3-10KV cable lines should adopt arc suppression coil grounding when the single-phase grounding fault current is greater than 30A and need to operate under grounding fault conditions.

Arc suppression coils are generally operated in overcompensation mode (i.e. the inductive current flowing through the arc suppression coil is greater than the capacitive current). This means that the inductance of the installed arc suppression coil must be determined based on the capacitance current to ground, in order to prevent arc overvoltage caused by single-phase grounding in a neutral point ungrounded system. However, the actual situation is that the on-site operators do not have a detailed understanding of the grounding capacitance current value of the system, or the data they have is based on experience, or the data is too old and cannot be relied upon.

Therefore, in view of the importance of studying this issue and the various disadvantages of previous methods, this paper proposes a new method to estimate the ground capacitance current of a small current system using single-phase grounding fault data.

1 Method Introduction

For a neutral point insulated system, the equivalent circuit when a single-phase grounding fault occurs is shown in Figure 1. Since the leakage conductance of each phase to ground in the distribution network line is much smaller than the admittance of the line-to-ground capacitance, the leakage conductance is ignored in the analysis and the three-phase-to-ground capacitance is assumed to be equal.

Next, the zero-sequence voltage and zero-sequence current data of a single-phase grounding fault are used to estimate the system-to-ground capacitance. Since the current waveform is relatively messy, using the formula to calculate the capacitance will inevitably cause a large error. Therefore, this method uses the instantaneous value of the zero-sequence voltage and zero-sequence current to calculate the capacitance. From the formula, it can be written in a discretized form as:

Since each term of F [i*(k)-i(k)]2 can be expanded into a polynomial of capacitance C:

In this way, when a single-phase grounding fault occurs in a certain outgoing line i (i=1,2,...,n) of the system, the sum of the capacitance values ​​of the other lines of the system except the faulty line can be calculated by using the system zero-sequence voltage and the zero-sequence current of the faulty line; the capacitance value of the non-faulty line to the ground can be calculated by using the zero-sequence voltage and the zero-sequence current of any non-faulty line; and for the same fault, the calculation results can be considered accurate for long lines, and for short lines, the calculation error is slightly larger, which can be improved through some specific ways, which will not be described in detail in this article.

In this way, the capacitance to ground of each line in the system can be calculated by using two sets of fault data occurring on different lines, and as the number of faults increases, the system capacitance to ground can be corrected by using multiple fault data. After the system capacitance to ground value is calculated, the formula I=jωCU can easily estimate the effective value of the system capacitance current, which can be used to determine whether the system needs to install an arc suppression coil and the size of the arc suppression coil inductance.

2 EMTP Simulation Verification

Next, an EMTP simulation is performed on a system to verify the method. The system is a substation with five outgoing lines, the fundamental frequency f=50Hz, and the sampling frequency fs=5000 Hz. The simulation uses a three-phase distributed parameter concentrated resistance line model. It is known that the lengths of each outgoing line are l1=l4=l5=10 km, l2=30 km, and l3=6 km; the line parameters are: R0=0.23 Ω/km, ωL0=1.72Ω/km, ωC0=4.175 μΩ/km; R1=0.17Ω/km, ωL1=0.28Ω/km, ωC1=5.715μΩ/km. When t=0.0075s, a single-phase metal grounding fault occurs in the middle of the A-phase line of the first outgoing line (see Figure 2). Take 200 points of data from 2 cycles of 0 to 0.04 seconds for analysis.

The above method is programmed with Matlab, and the simulation data is analyzed to solve the system-to-ground capacitance value. Considering the existence of noise pollution and various random interferences, the fault data is first digitally filtered, and the harmonics above 17 are removed before the simulation or measured data is calculated. The current calculated by the capacitor and the fitted waveform of the filtered current are shown in Figure 3 (this article uses Butterworth filter to filter the data to remove the high-order harmonics above the 9th harmonic).

The capacitance to ground obtained from the zero-sequence voltage and the zero-sequence current of the fault line is: C∑=-0.75462μF. The capacitances obtained from the zero-sequence voltage and the zero-sequence current of the non-fault lines 2, 3, 4, and 5 are:

Among them, C∑ is negative because the zero-sequence current of the fault line and the zero-sequence current of the non-fault line are in reverse phase.

Thus, we can get: C2+C3+C4+C5=0.75462μF, which is equal to C∑ in value. Moreover, from the system parameter ωC0=4.175μS/km, we can infer C0=4.175/314=0.013296μF, and from Ci=C0*li, we can get: C2=0.39888μF, C3=0.07978μF, C4=0.13296μF, C5=0.13296μF. It can be seen that these values ​​are very different from the capacitance values ​​of each line to ground estimated by this method.

The same system was simulated using this method to further verify the method. At t=0.0075s, a single-phase resistive grounding occurred in the middle of the A-phase line of the first outgoing line, with a grounding resistance of 100Ω. Similarly, 200 points of data from 0-0.04s were taken for two cycles.

3 Conclusion

Traditional methods for measuring capacitive current can be divided into direct method and indirect method. The direct method is to ground the line and directly measure the grounding capacitive current. This method is complicated to operate and wire, and may endanger the insulation of the weak insulation of the non-grounded phase, causing a short circuit between the two phases. It is unsafe for operators and the distribution system, so it is rarely used. The indirect method is currently widely used, that is, adding a capacitor to the line, measuring the voltage change, and indirectly calculating the capacitive current value. Although this method can measure the capacitive current value more accurately, it still needs to deal with the primary side during measurement, and the safety of personnel and equipment cannot be guaranteed. In addition, since it involves primary equipment, the operation is cumbersome, the preparation time is long, and the work efficiency is low. Usually most of the time is spent on waiting for dispatching orders, issuing work tickets, switching operations and preparing safety measures, and the work efficiency is very low [2][3].

The method introduced in this paper is simple and easy to use. It only uses the fault data of the system when the single-phase grounding is used for calculation. It does not need to use instruments for on-site field measurement, does not affect the normal operation of the power grid, eliminates trouble and avoids danger. This method is suitable for occasions where the error requirements are not very strict and the workload is large. After simulation, it is shown that the results are relatively accurate.