3.6.2. Danger in three-phase power line with insulated neutral.

As to the ground all power line conductors have capacitance and resistance what makes insulation that separates conductors from the ground (fig. 3.6). Actually values of capacitance and resistance differ for different conductors. However to simplify analysis we’ll consider them the same: C_a=C_b=C_c=С and r_a=r_b=r_c=r.

Case of person touching one of three phase conductors (one-phase connection) of power line in normal mode results in current which can be calculated by formula:

, (3.8)

where U_ph – phase voltage, V; Z - complex resistance of phase conductor to the ground:

, (3.9)

where =2f – angular frequency of the power line, f – current frequency.

Fig. 3.6 Scheme of person connection to one-phase of power line in normal mode

If power lines are short and that’s why phase conductors have low capacitance to the ground (C=0) formula to calculate current passing through the person will look as:

, (3.10)

In case of two-phase connection (fig. 3.7) person turns out to be under linear voltage, so current will be:

,

where U_l – linear voltage, V; it is defined as: .

Fig. 3.7 Scheme of two-phase connection to power line in normal mode

Case of one-phase connection to power line in emergency mode (fig. 3.8), when another phase has short circuit with the ground, causes current:

. (3.12)

If R_sc << R_h then

. (3.13)

Fig. 3.8 Scheme of one-phase connection to power line in emergency mode

Thus, current passing through the person in case of one-phase connection to power line with insulated neutral in normal mode depends on insulation resistance and capacitance to the ground. Case of short circuit of one phase to the ground significantly rises the danger of one-phase connection since person turns out to be under voltage close to linear. The most dangerous is case of two-phase connection.

3.6.3. Danger in three-phase power line with grounded neutral.

Three-phase power line with grounded neutral has low resistance between neutral wire and the ground. In normal mode voltage of any phase wire to the ground equals to phase one. Case of one-phase connection (fig. 3.9) is characterized by current:

, (3.14)

where R_o – grounding resistance of neutral.

Since R_o << 10 ohm, it can not be considered for calculation:

. (3.15)

Fig. 3.9 Scheme of one-phase connection to power line with grounded neutral in normal mode

Two-phase connection gets person under linear voltage just like in power lines with insulated neutral and current is calculated by the formula:

. (3.16)

Fig. 3.10 Scheme of two-phase connection to power line with grounded neutral in normal mode

In emergency mode voltage of undamaged wires to the ground is different from phase voltage because damaged wire changes voltage distribution on the ground. Touching undamaged phase wire person gets under voltage , which is higher than phase one but lower than linear one (fig. 3.11) and current will be calculated as:

. (3.17)

Fig. 3.11 Scheme of one-phase connection to power line with grounded neutral in emergency mode

Thus, case of one-phase connection to power line with the grounded neutral in emergency mode is more dangerous than one in normal mode. Two-phase connection remains the most dangerous.

Analysis of various cases person can be connected to power line indicates the following:

• the least dangerous is one-phase connection to power line with insulated neutral in normal mode;

• emergency mode of power line operation is always more dangerous than normal one irrespective to neutral mode;

• the most dangerous is two-phase connection whatever neutral mode is.

Breakaway voltage – is voltage between two points of electric circuit a person simultaneously touches. It equals to the difference of potentials in place of contact with facility’s case _c and spot on the ground under the feet _f (fig. 3.12):

, (3.18)

or

U_bv = U_g. (3.19)

Symbol  is called breakaway voltage factor. In current spreading zone <1, and over its margins =1.

Breakaway voltage is growing with increasing distance to the grounding, and it equals to voltage on the power facility’s case out of the current spreading zone.

Current passing through the person is:

. (3.20)

Fig. 3.12 Breakaway voltage in presence of one grounding electrode: I – potential curve; II – curve that characterizes breakaway voltage U_bv depending on distance from grounding electrode x

Pace voltage - is voltage between two points of electric circuit, which are at one step distance between one another and which a person is simultaneously standing on. It equals to the difference of potentials in points under feet (fig. 3.13).

When one foot of person is at the distance x from grounding and another is at distance of one step  from the first one (practicable =0.8 m) pace voltage equals:

, (3.21)

or

U_pv = U_g, (3.23)

where  - pace voltage factor that depends on type of grounding electrodes, distance from grounding and step (the closer to the grounding and the wider is the step the more is );

. (3.24)

Fig. 3.13 Pace voltage

Pace voltage is maximal close to the grounding and reduces with increasing distance from it. Out of the zone of current spreading it equals to zero. Also the broader is a step the more is pace voltage.

Current caused by pace voltage is:

. (3.25)

Breakaway and pace voltages are different to harm a person because they produce current passing different ways. Breakaway voltage causes current passing through the chest, and pace voltage – through the lower loop. High pace voltage induces feet cramps making person fall down, later on current circuit gets in loop the whole body.