IS IT NECESSARY TO GROUND THE NEUTRAL OF TRANSFORMERS IN MINES?

(For discussion)

R. F. TROFIMOV

The question of systems with grounded and isolated transformer neutrals cannot be considered finally resolved. Up to the present time there are no definite regulations on the question of grounding the neutral. This applies not only to mine networks, but also to the networks of all surface industrial enterprises. In the mines of the USSR, systems with an isolated neutral are predominantly widespread. In systems with a solidly grounded neutral, the current that can pass through a person standing on the ground and touching a phase conductor may be determined by formula (1):

\[ I=\frac{U_{\phi}}{R+r_0+r_1}, \tag{1} \]

where
\(U_{\phi}\) — phase voltage in volts;
\(R\) — total resistance of a person who has touched the phase conductor, in ohms, which for people working in mines may take a value of the order of \(600\text{—}800\) ohms;
\(r_0\) — resistance of the neutral grounding; and
\(r_1\) — resistance of the phase conductor.

Usually \(r_0\) and \(r_1\) are very small in comparison with \(R\), and they may be neglected. In this case

\[ I=\frac{U_{\phi}}{R}, \]

i.e., the current flowing through a person is determined by the magnitude of the phase voltage and the resistance of the human body, and does not depend on the active and capacitive conductivities between the phase conductors and the earth.

For systems with an isolated neutral, the currents that can pass through a person standing on the ground and touching a phase conductor may be determined by formula (2):

\[ I=\frac{\sqrt{3}\,U_l}{\sqrt{\dfrac{(3R+r')^2+(3Rr'\omega C)^2}{1+(r'\omega C)^2}}}, \tag{2} \]

where
\(U_l\) — line voltage in volts;
\(r'\) — insulation resistance of the network in ohms;
\(C\) — capacitance of this network in farads;
\(\omega\) — angular velocity.

Kopytov N. V. gives his own formula (3):

\[ I=\frac{U_{\phi}}{R\sqrt{1+\dfrac{r'(r'+6R)}{9(1+r^2\omega^2 C^2)R^2}}}. \tag{3} \]

Recently a tendency has arisen to resolve the question of the advantages or degree of danger of one system or another by experimental means—

Table 1

Currents in mA that can pass through a person standing on the ground and touching a phase conductor, at human resistances in ohms

systems. In order to determine the degree of danger of electrical systems with an insulated neutral at voltages of 220 and 380 volts, experimental studies of local electrical networks were carried out in several Siberian coal mines. The currents that could pass through a person standing on the ground and touching a phase conductor were measured. About 150 sections were examined. The experimental studies were carried out according to the circuit shown in Fig. 1. In these studies, the person was replaced by resistances of 600, 1000, 2000, 4000, and 6000 ohms. The results of measurements carried out in mine No. 1 are given in Table 1.

If accidents are classified, according to the currents that can pass through a person, as follows: up to 30 mA as mild, from 30 to 50 mA as moderate, from 50 to 100 mA as severe, and above 100 mA as fatal, then the degree of danger of the networks for 7 mines with steep dip can be seen from the data given in Table 2. The results of measurements carried out in mine No. 2 with gentle dip are given in Table 3.

Table 2

Table 3

Generalized data on the degree of danger of electrical systems with an insulated and a grounded neutral, from the point of view of electric shock, are given in Table 4.

Table 4

On the basis of these data it may be concluded that systems with an insulated neutral are safer than systems with a grounded neutral with respect to electric shock. At the same time, another circumstance must also be taken into account, namely: the very frequent occurrence of solid single-phase ground faults. The latter can be confirmed by the data of Table 5, which pertain to the section networks of mine No. 3.

Table 5

Single-phase ground faults by month that occurred in this mine are illustrated by the data given in Table 6.

During single-phase ground faults, the sound conductors are at line voltage with respect to earth. Almost the same situation exists in other mines as well. It should be noted here that, during the experimental investigations, single-phase ground faults were found to be more—

Table 6

…even in networks operating at a voltage of 220 V, and not 380 V, as might have been expected.

From the data given in Tables 5 and 6 it is clear that single-phase earth faults are not eliminated for a very long time (up to 7–8 days). Networks operating in such a state create a danger not only with respect to electric shock, but also with respect to explosions and fires, since earth-fault currents range from 0.1 to 0.6 A (on the basis of measurements).

Fig. 1

Fig. 2

If one also takes into account the existing methods for monitoring the state of insulation, detecting the locations of damage, the danger of double and two-phase earth faults, and the impossibility of implementing simple protection against earth faults, apart from protections possessing great sensitivity, then a system with an isolated neutral may be considered equivalent to another system. The most rational system for mines should be recognized as neutral grounding through a resistance of the order of 50–100 ohms with multiple earthing (Fig. 2). Such a resistance will limit the earth-fault current to

current forming an arc (up to 3–5 A), at which sensitive and selective protection against ground faults can be implemented.

For systems with grounding without resistance \(r\) (solid) and with single grounding, in which the consumers’ power is insignificant compared with the source power, it may be assumed that during short circuits the voltage remains unchanged, and then the fault current will be equal to:

\[ I_0=\frac{U_l}{\sqrt{3}\,(r_0+r_1)}, \tag{4} \]

where \(r_0\) is the resistance of the neutral conductor and \(r_1\) is the resistance of the phase conductor.

The reactance of the conductors, as having an insignificant effect on the magnitude of the touch voltage, may be neglected.

From equation (4) it follows that:

\[ \frac{U_l}{\sqrt{3}}=I_0\cdot r_0+I_0\cdot r_1. \]

Substituting \(I_0\cdot r_0=U_{\mathrm{pr}}\), we obtain

\[ \frac{r_1}{r_0}=\frac{U_l-\sqrt{3}\,U_{\mathrm{pr}}}{\sqrt{3}\,U_{\mathrm{pr}}} =\frac{U_l}{\sqrt{3}\,U_{\mathrm{pr}}}-1, \tag{5} \]

where \(U_{\mathrm{pr}}\) is the touch voltage \(=40\) V.

For mines, at voltages of \(500/290\) V it would be necessary to have \(\frac{r_1}{r_0}=6.26\); at voltages of \(380/220\) V, \(\frac{r_1}{r_0}=4.5\), and at voltages of \(220/127\) V, \(\frac{r_1}{r_0}=2.17\), i.e., the neutral conductor must have a cross-section several times greater than that of the phase conductors.

In systems having two grounding electrodes (at the beginning and at the end of the network), the voltage drops in the neutral and phase conductors will be directly proportional to their resistances

\[ \frac{U_0}{U_1}=\frac{r_0}{r_1} \]

and in the grounding electrodes the touch voltage is

\[ U'_{\mathrm{pr}}=U''_{\mathrm{pr}}=\frac{U_0}{2}\quad(\text{when } r'_0=r''_0). \]

According to Kirchhoff’s second law,

\[ U_0+U_1=U_\phi, \tag{6} \]

but

\[ U_1=U_0\cdot\frac{r_1}{r_0} \]

or, after substitution into equation (6),

\[ U_0+U_0\cdot\frac{r_1}{r_0}=U_\phi \]

and

\[ U_0\left(1+\frac{r_1}{r_0}\right)=U_\phi. \]

or

\[ 2U'_{\text{pr}}\left(1+\frac{r_1}{r_0}\right)=U_{\phi}. \]

Whence

\[ U'_{\text{pr}}=U''_{\text{pr}}= \frac{\dfrac{U_{\phi}}{2}}{1+\dfrac{r_1}{r_0}} = \frac{\dfrac{U_{\phi}}{2}}{1+\dfrac{q_0}{q_1}}. \tag{7} \]

It follows from this that the larger the cross-section of the working conductors, the more dangerous is the servicing of current receivers.

To obtain the permissible touch voltage \(U_{\text{pr}}=40\) V, the cross-section of the neutral conductor must be greater than the cross-sections of the phase conductors. This can be proved by using the last equation

\[ U_{\text{pr}}= \frac{\dfrac{U_{\phi}}{2}}{1+\dfrac{q_0}{q_1}} = \frac{U_{\phi}\cdot q_1}{2(q_1+q_0)}, \]

or

\[ U_{\text{pr}}\cdot 2\cdot q_1+U_{\text{pr}}\cdot 2\cdot q_0 = U_{\phi}\cdot q_1. \]

Whence

\[ q_0= \frac{U_{\phi}\cdot q_1-U_{\text{pr}}2\cdot q_1}{2\cdot U_{\text{pr}}} = \frac{U_{\phi}\cdot q_1-80\cdot q_1}{80}, \]

or finally

\[ q_0=q_1\left(\frac{U_{\phi}-80}{80}\right). \tag{8} \]

For voltages
\[ \begin{aligned} U_1&=500\ \text{V} &&\text{there must be } q_0=2.63\cdot q_1,\\ &=380\ \text{V} &&\text{there must be } q_0=1.75\cdot q_1,\\ &=220\ \text{V} &&\text{there must be } q_0=0.588\cdot q_1, \end{aligned} \]

i.e., the cross-section of the neutral conductor for voltages of 500 V and 380 V must be greater than the cross-section of the phase conductors.

In systems with neutral grounding, the touch voltage is in direct dependence also on the power of the power transformers, and it may exceed the permissible touch voltage \(U_{\text{pr}}=40\) V several times over. To obtain the permissible touch voltage, it is likewise necessary to take cross-sections of neutral conductors exceeding the cross-section of the phase conductors.

Applying the limitation of fault currents, let us assume, to \(5\) A; through a resistance \(r\), the resistance of the neutral conductor and of grounding will be equal to

a) for single grounding

\[ r_0=\frac{U_{\text{pr}}}{I_0}=\frac{40}{5}=8\ \text{ohms}, \]

b) for double grounding

\[ r_0=\frac{2\cdot U_{\text{pr}}}{I_0}=\frac{2\cdot 40}{5}=16\ \text{ohms}, \]

which is considerably greater than the resistances of the working conductors and, consequently, the cross-section of the neutral conductor will have to be chosen not from the conditions of the permissible touch voltage, but from the conditions of mechanical strength, and in general this only eliminates the noted shortcomings inherent in sys-

systems with neutral grounding. In addition, the use of systems with neutral grounding and limitation of fault currents will make it possible in mines to use protective grounding with a resistance of more than 2 ohms, which is also necessary.

Multiple grounding is intended not so much to relieve the neutral conductor (with respect to current) in single-phase faults, as to prevent the formation of significant touch voltages when the neutral conductor breaks, which occurs in systems with neutral grounding and single grounding.

When analyzing electrical systems it is necessary to make use of the data of L. P. Podolsky, who reports that at voltages of 250 volts and higher the magnitude of the resistance of human skin depends little on its moisture content, and that at voltages of 250 volts and higher sharply expressed phenomena of electrical breakdown of the skin occurred, after which there followed direct contact of the electrodes with well-conducting tissues of the human body and, consequently, a sharp increase in the current passing through the person, causing injury to him. As for fires, L. P. Podolsky reports that “a fire is caused not by Joule heat, but by an alternating or sustained arc, the conditions for the occurrence and maintenance of which depend on the magnitude of the potential difference between its electrodes.” Explosions of the mine atmosphere in mines may be caused by a spark, against which there is no protection, and they are unavoidable. However, it is known that interruption of the leakage-current circuit between metallic conductors and the soil of workings can serve as the cause of a gas explosion only in the presence of an arc, for the formation of which a current of 5 A is necessary. It is unlikely that armored cables will produce open arcs; flexible cables, however, are most often located on the floor of workings or close to it, and therefore an explosion of the mine atmosphere can occur only with a ground-fault current, as indicated above, of 5 A and higher.

In addition to these factors, the danger of stray alternating currents must be taken into account. The main danger of stray alternating currents is the premature blasting of electric detonators in the event of accidental contact of the ends or exposed points of the blasting circuit with the soil.

According to the data of V. M. Fedorenko, “the electric detonators currently used in mines have a resistance on the order of 1–2 ohms, and, as experiments have shown, are detonated at voltages on the order of 1 volt and a current equal to 0.35–0.40 ampere.”

Conclusion

Theoretical investigations lead to the conclusion that a system with an isolated neutral point of the transformer should be the more rational system. Such a system has been adopted in the mines of the USSR.

Experimental investigations and operating data, as indicated above, refute this and prove the contrary. In connection with this, such systems may be abandoned by revising the rules of technical operation, and a transition made to neutral grounding through resistances and with multiple grounding electrodes. This will increase the safety of work in mines, make it possible to introduce selective protection against ground faults, and to move to a higher voltage (up to 660 V) in the presence of screened networks, for which the need has become urgent.

As for explosions and fires, systems with neutral grounding through resistance and with multiple grounding electrodes will be safer than systems with an isolated neutral point of transformers that have no protection against ground faults.

References Used

1. Gramatchikov A. S. — Safety Engineering in Electrical Installations, ONTI—NKTP—USSR, 1938.

2. Kopytov N. V. — “Safety Conditions for Low-Voltage Cable Factory and Plant Networks,” Elektrichestvo, No. 15, pp. 848–854, 1931.

3. Vainer A. L. — Grounding, ONTI—NKTP—USSR, 1938.

4. Podolsky L. P. — The Influence of Neutral Grounding in Low-Voltage Networks on Safety Conditions, Gosenergoizdat, 1946.

5. Fedorenko V. M. — Methods of Combating Premature Blasting of Electric Detonators by Stray Currents in Mines, MakNII, 1939.