# Compensation for capacitive earth fault current

An effective means of reducing the magnitude of the current of a single-phase earth fault in a network with an isolated neutral to a value not exceeding the above allowable ones is to compensate for the capacitive component of this current with the help of an arcing reactor included in the neutral of the network (Fig. 7, a). Under favorable conditions, such compensation can actually be a non-contact means of extinguishing the ground arc at the fault location. Fig.7. Ground fault in a network with a resonantly grounded neutral:

a) network diagram; b) equivalent circuit for determining the conditions of current resonance

The compensation method uses the phenomenon of current resonance known in electrical engineering and consists, in fact, in superimposing the capacitive current component at the point of ground fault (Fig. 7, b) inductive component , due to the inductive resistance of the arc-quenching reactor included in the neutral network. In this regard, the condition for choosing the optimal value of the inductive resistance of the reactor, which provides a minimum current , can be obtained under the assumption that in the circuit corresponding to the current resonance and , the reactive component of the current of the external source should be equal to zero. Let’s define this condition.

The balance of currents at the ground fault point for the circuit in Fig. 7, and taking into account (9) can be written as: (33)

or, using (24): , (34)

where ; (35) and active and inductive components of the reactor conductivity .

Neglecting in (34) the components of the earth fault current, due to the asymmetry of the conductivities of the phases to earth, taking into account (27) and (28), we obtain: . (36)

It can be seen from the last expression that in the absence of active losses in the network, the condition for choosing the inductive reactance of the reactor, which provides full compensation for the current of a single-phase earth fault , can be written as: (37)

or . (38)

It also follows from expression (36) that in real networks, even if conditions (37) or (38) are fulfilled when setting up the arcing reactor, it is impossible to achieve full compensation of the current of a single-phase earth fault (Fig. 8), since in Fig.8. Vector diagram of voltages and currents during a single-phase ground fault in a network with a resonantly grounded neutral ( )

In this case, a residual active current will flow through the fault, due to the active conductivities of the phases, as well as the reactor itself: (39)

or , (40)

where .

The value of the active component of the earth fault current in a network with a resonantly grounded neutral is usually characterized by the damping factor already mentioned above. However, in this case it is defined as the ratio of the modulus of the active component of the current at the place of the earth fault taking into account the reactor, determined by (39) or by (40), to the capacitive component of the fault current, determined by (27) or (31), (32): . (41)

Based on numerous measurements for air networks with a normal state of insulation, this coefficient can be taken equal to the following values: for air networks 6 kV – 5%, 10 kV – 4%, 35 kV – 3%; in case of contamination and dampening of insulation in air networks can be taken equal to 10%. In cable networks, the value can be taken equal to 3%, and if there are cables with aged insulation in the network – 6%.

Thus, the active component of the current of a single-phase earth fault in both networks with isolated and networks with a resonantly grounded neutral is most often not large and, as a rule, does not prevent the self-extinguishing effect of the arc, although it can worsen it in very branched networks.

Due to the limited power scale of the produced reactors, the stepwise regulation of their inductance, the impossibility of its quick and smooth change with changes in the network configuration and changes in the capacitances of power transmission lines with changing weather conditions, and also because of the possible occurrence of unacceptable neutral displacements, it is not always possible to actually achieve and resonant compensation of the capacitive component of the earth fault current. The degree of compensation detuning is characterized by the ratio of the reactive component of the earth fault current in a network with an arcing reactor in the neutral to the capacitive component of the earth fault current in the same network during its operation without an arcing reactor: . (42)

If a , then they speak of resonant (full) compensation of the capacitive current of a single-phase earth fault. If a > 0, i.e. > , then the network works

in capacitive current undercompensation mode. If a < 0, i.e. < – overcompensation.

In order to obtain the greatest effect from compensation, when choosing the inductive reactance of the arc-quenching reactor, one tends to ensure that the degree of compensation detuning would be as close as possible to zero, i.e. so that, if possible, the relation = . If the resonant tuning of the reactor is not possible, then the Rules for Technical Operation (PTE) recommend tuning the reactor with overcompensation up to 5 – 10%. In extreme cases, after checking the admissibility of this mode (see below), a setting with undercompensation up to 5% can be used.

With a known degree of compensation detuning and damping factor the approximate value of a single-phase earth fault in a network with a resonantly earthed neutral can be determined by the following expression: . (43)

Proper use of capacitive earth fault current compensation improves the reliability of isolated neutral networks. This is the main purpose of so-called networks with resonantly grounded neutral. Compensation efficiency is characterized by the ratio of the number of short circuits that did not develop into phase-to-phase short circuits to the total number of short circuits. For networks with a resonantly grounded neutral, this ratio may be equal to 0.6 – 0.9, while for networks with an isolated neutral, in some cases, it may not exceed 0.3. In accordance with the recommendations, if the number of two-phase short circuits in an isolated neutral network does not exceed 10% of the total number of emergency shutdowns, then an arcing reactor should not be installed.

With reasonable use of compensation, at least 85% of ground faults are eliminated in the network without damage to the power supply of consumers. Automatic reclosing is used only in the event of two- or three-phase short circuits, which are relatively rare in these networks. As in the case of networks with an isolated neutral, networks with a resonantly earthed neutral can be operated for a long time with one phase shorted to earth. In these networks, the requirements for grounding devices are facilitated. Switching overvoltages are limited in case of arc faults to earth to values of 2.5 – 2.6 (with a compensation detuning degree of 0 – 5%), safe for the isolation of operational equipment and power lines. A significant reduction in the voltage recovery rate on the damaged phase contributes to the restoration of the dielectric properties of the network damage site after each extinction of the “intermittent” grounding arc. If the network complies with restrictions on the use of fuses on power lines, then the presence of an arc-quenching reactor in the network neutral will prevent the development of ferroresonant processes in the network (in particular, spontaneous displacement of the neutral).