Three-phase three-wire AC electrical network with isolated neutral (in IT system).
Two-phase contact with current-carrying parts (Fig. 3).
Rice. 3. Two-phase (two-pole) contact with live parts in the IT system
U f - phase voltage; I h - the strength of the current flowing through a person;
R h - human resistance; L 1, L 2, L 3 - phase conductors.
The strength of the current (I h, A) flowing through a person is determined by the formula
where U l - linear voltage, V;
U f - phase voltage, V;
R h - human resistance, Ohm.
For example, in an electrical network with a linear voltage of 380 V (U f \u003d 220 V), with a human body resistance of 1000 Ohms, the current flowing through a person is:
This current strength is deadly to humans.
With a two-phase touch, the current passing through a person is practically independent of the neutral operating mode. The danger of touching will not decrease even if a person is reliably isolated from the ground.
A single-phase touch (Fig. 4.) occurs many times more often than a two-phase one, but it is less dangerous, since the voltage under which a person finds himself does not exceed the phase one, i.e. less than linear by 1.73 times and, in addition, the current flowing through a person returns to the source (mains) through the insulation of the wires, which in good condition has high resistance.
Fig.4. Single-phase (single-pole) touching of live parts in an IT system
r 1 , r 2 , r 3 - insulation resistance of electrical wires; s 1 , s 2 , s 3 - capacitance of electrical wires
The strength of the current (I h, A) flowing through a person is determined for this case by the formula
where R p - transition resistance, Ohm (resistance of the floor on which the person stands and shoes); Z is the insulation resistance of the phase wire relative to earth, Ohm (active and capacitive components).
In the most unfavorable situation, when a person has conductive shoes and stands on a conductive floor (R p ~ 0), the current flowing through the body is determined by the formula
if U f \u003d 220 V, R h \u003d 1 kOhm, Z \u003d 90 kOhm, then I h \u003d 220 / (1000 + (90000 / 3)) \u003d 0.007 A (7 mA).
Three-phase four-wire AC electrical network with grounded neutral (in TN system).
Single-phase contact with live parts.
Fig.5. Single-phase (single-pole) touching of live parts in a TN system
R 0 - earthing resistance of the neutral of the electrical network
In a four-wire AC electrical network with a solidly grounded neutral (TN system), the current passing through a person returns to the source (mains) not through the insulation of the wires, as in the previous case, but through the neutral grounding resistance (R 0) of the current source (Fig. 5 ). The strength of the current passing through the human body is determined by the formula:
where R 0 is the grounding resistance of the neutral of the current source, Ohm.
The resistance of the grounding device, to which the neutral of the current source is connected, at any time of the year should be no more than 2, 4 and 8 ohms, respectively, at line voltages of 660, 380 and 220 V. This resistance must be provided taking into account the use of natural grounding conductors, as well as grounding conductors re-grounding PEN- or PE-conductor of overhead power lines (VL) with voltage up to 1 kV. The resistance of the ground electrode located in close proximity to the neutral of the current source should be no more than 15, 30 and 60 ohms, respectively, at the same line voltages of 660, 380 and 220 V.
Example. In the most unfavorable situation discussed above, with U f = 220 V, R h = 1000 Ohm, R p ~ 0 Ohm R 0 = 30 Ohm, the current flowing through the human body will be:
I h \u003d 220/1000 + 30 \u003d 0.214 A (214 mA), which is deadly for humans.
If the shoes are not conductive (for example, rubber galoshes with a resistance of 45 kOhm) and the person is standing on a non-conductive floor (for example, a wooden floor with a resistance of 100 kOhm), i.e. R p \u003d 145 kOhm, then the current flowing through the human body will be:
I h \u003d 220/1000 + 60 + 145000 \u003d 0.0015 A (1.5 mA), which is not dangerous to humans.
Thus, ceteris paribus, a person touching one phase wire of an electrical network with an isolated neutral is less dangerous than in an electrical network with a grounded neutral.
The above schemes for including a person in an electrical circuit of a three-phase alternating current are valid for normal (fail-safe) operating conditions of electrical networks.
In emergency operation of a three-phase AC mains, one of the phase wires, for example, an electric network with a grounded neutral (in a TN system), can be shorted to ground (when the protective grounding system is triggered, a phase wire falls to the ground, etc.) through resistance R zm (Fig. 6).
Rice. 6. Single-phase (single-pole) contact with current-carrying parts in emergency operation of the power grid.
R zm - the resistance of the circuit of the phase wire (L 2) to the ground
The strength of the current passing through the human body, touching in this situation one of the serviceable phase wires (L 1, L 3), is determined from the equation
where R zm is the resistance of the phase wire to ground, Ohm.
If at the same time R zm ~ 0 or much less than both R 0 and R h, then they can be neglected, then the strength of the current passing through the human body will be determined by the formula
i.e., a person will be included in the electrical circuit in two phases, and the second phase is connected to him through his legs and the value of I h will be significantly affected by the transition resistance R p.
At voltages up to 1000 V in production conditions, both of the above three-phase AC electrical networks considered above are widely used: three-wire with an isolated neutral (IT system) and four-wire with a grounded neutral (TN system).
It is advisable to use an electrical network with an isolated neutral in cases where it is possible to maintain a high level of insulation resistance of the phase wires and a small capacitance of the latter relative to the ground. These are electrical networks with little branching, not exposed to aggressive environments and under the constant supervision of qualified personnel. So, for example, in coal mines, only electrical networks with isolated neutral are used.
An electrical network with a grounded neutral should be used where it is impossible to ensure good wire insulation (for example, due to high humidity or an aggressive environment), when it is impossible to quickly find or eliminate damage to the insulation, or when the capacitive currents of the electrical network, due to its significant branching, reach large values, dangerous to humans.
At voltages above 1000 V, for technological reasons, electrical networks with voltages up to 35 kV inclusive have an isolated neutral, over 35 kV - grounded. Since such electrical networks have a large capacity of wires relative to the ground, it is equally dangerous for a person to touch their phase wires, regardless of the mode of operation of the power source neutral. Therefore, the operating mode of the neutral of the mains voltage above 1000 V is not selected for safety reasons.
There are various schemes for including a person in an electric current circuit:
Single-phase contact - touching the conductor of one phase of an existing electrical installation;
Two-phase contact - simultaneous contact with the conductors of two phases of an existing electrical installation;
Touching non-current-carrying parts of electrical installations that are energized as a result of damage to the insulation;
Switching on step voltage - switching between two points of the earth (soil) that are under different potentials.
Consider the most characteristic schemes for including a person in an electric current circuit.
Single-phase touch in a network with a solidly grounded neutral. The current flowing through the human body ( I h) with a single-phase touch (Fig. 6) closes in the circuit: phase L 3 - human body - base (floor) - neutral grounding - neutral (zero point).
Rice. 6. Scheme of single-phase touch in the network
with solidly grounded neutral
According to Ohm's law:
Where R o - neutral grounding resistance,
R osn - base resistance.
If the base (floor) is conductive, then R base ≈ 0
Given the fact that R about " R h, then
U h = U f
Such contact is extremely dangerous.
Single-phase contact in a network with isolated neutral. The current flowing through the human body (Fig. 7) will close in circuits: phase L 3 - human body - floor and then returns to the network through phase isolation L 2 and L 1 , i.e. then the current follows the circuits: phase isolation L 2 - phase L 2 - neutral (zero point) and phase isolation L 1 - phase L 1 - neutral (zero point). Thus, in the circuit of current flowing through the human body, phase isolations are switched on in series with it. L 2 and L 1 .
Rice. 7. Scheme of single-phase touch in the network
with isolated neutral
Phase insulation resistance Z has active ( R) and capacitive components ( With).
R- characterizes the imperfection of the insulation, i.e. the ability of insulation to conduct current, although much worse than metals;
With- the capacitance of the phase relative to the ground is determined by the geometric dimensions of an imaginary capacitor, the "plates" of which are phases and grounds.
At R 1 = R 2 = R 3 = R f and With 1 = With 2 = With 3 = With F current flowing through the human body:
where Z- impedance of the insulation of the phase wire relative to the ground.
If the capacitance of the phases is neglected With f = 0 (aerial networks of small extent), then:
whence it follows that the magnitude of the current depends not only on the resistance of the person, but also on the resistance of the insulation of the phase conductor to earth.
If, for example, R 1 = R 2 = R 3 = 3000 Ohm, then
; U h= 0.0111000 = 110 V
Biphasic touch. With a two-phase touch (Fig. 8), regardless of the neutral mode, a person will be under the line voltage of the network U l and according to Ohm's law:
at U l=380V: I= 380/1000 = 0.38 A = 380 mA.
Rice. 8. Scheme of two-phase human touch
Two-phase contact is extremely dangerous, such cases are relatively rare and are usually the result of working under voltage in electrical installations up to 1000 V, which is a violation of the rules and regulations.
Touching a metal case that is energized. Touching the body of the electrical installation (Fig. 9), in which the phase ( L 3) closed on the case, tantamount to touching the phase itself. Therefore, the analysis and conclusions for the cases of single-phase contact, considered earlier, fully apply to the case of a ground fault.
Rice. 9. Scheme of a person touching a metal
hull under tension
The inclusion of a person in the electrical network can be single-phase and two-phase. Single-phase switching is a connection of a person between one of the phases of the network and the ground. The strength of the striking current in this case depends on the mode of the neutral network, the resistance of a person, shoes, floor, phase insulation relative to earth. Single-phase switching occurs much more often and often causes electrical injuries in networks of any voltage. With two-phase switching, a person touches two phases of the electrical network. With a two-phase connection, the current flowing through the body (damaging current) depends only on the mains voltage and the resistance of the human body and does not depend on the neutral mode of the mains supply transformer. Electrical networks are divided into single-phase and three-phase. The single-phase network can be isolated from earth or have a ground wire. On fig. 1 shows possible options for connecting a person to single-phase networks.
Thus, if a person touches one of the phases of a three-phase four-wire network with a dead-earthed neutral, then he will be practically under phase voltage (R3≤ RC) and the current passing through a person during normal operation of the network will practically not change with a change in insulation resistance and capacitance wires to ground.
The effect of electric current on the human body
Passing through the body, the electric current has a thermal, electrolytic and biological effect.
Thermal action is manifested in burns of the skin or internal organs.
During the electrolytic action, due to the passage of current, decomposition (electrolysis) of blood and other organic fluid occurs, accompanied by the destruction of erythrocytes and metabolic disorders.
The biological effect is expressed in irritation and excitation of living tissues of the body, which is accompanied by spontaneous convulsive contraction of muscles, including the heart and lungs.
There are two main types of electric shock:
§ electrical injury,
§ electric shocks.
Electric shocks can be roughly divided into four levels:
1. convulsive muscle contractions without loss of consciousness;
2. with loss of consciousness, but with the preservation of breathing and heart function;
3. loss of consciousness and impaired cardiac activity or breathing (or both);
4. clinical death, i.e. lack of respiration and circulation.
Clinical death is a transitional period between life and death, it begins from the moment the activity of the heart and lungs stops. A person who is in a state of clinical death does not show any signs of life: she has no breathing, heartbeat, reactions to pain; The pupils of the eyes are dilated and do not react to light. However, it should be remembered that in this case the body can still be revived if help is given to it correctly and in a timely manner. The duration of clinical death can be 5-8 minutes. If help is not provided in a timely manner, then biological (true) death occurs.
The result of electric shock to a person depends on many factors. The most important of them are the magnitude and duration of the current, the type and frequency of the current, and the individual properties of the body.
Determination of the current spreading resistance of single grounding conductors and the procedure for calculating the protective ground loop for stationary technological equipment (GOST 12.1.030-81. SSBT. Protective grounding, zeroing)
Implementation of grounding devices. There are artificial ground electrodes, intended exclusively for grounding purposes, and natural - third-party conductive parts that are in electrical contact with the ground directly or through an intermediate conductive medium used for grounding purposes.
For artificial ground electrodes, vertical and horizontal electrodes are usually used.
The following can be used as natural grounding conductors: water and other metal pipes laid in the ground (with the exception of pipelines of flammable liquids, flammable or explosive gases); casing pipes of artesian wells, wells, pits, etc.; metal and reinforced concrete structures of buildings and structures that have connections to the ground; lead sheaths of cables laid in the ground; metal sheet piles of hydraulic structures, etc.
The purpose of the calculation of protective grounding is to determine the main grounding parameters - the number, size and order of placement of single grounding conductors and grounding conductors, at which the touch and step voltages during the phase closing to the grounded case do not exceed the allowable values.
To calculate the grounding, the following information is required:
1) characteristics of the electrical installation - type of installation, types of main equipment, operating voltages, methods of grounding the neutrals of transformers and generators, etc.;
2) electrical installation plan indicating the main dimensions and placement of equipment;
3) the shapes and sizes of the electrodes, from which it is planned to build the designed group ground electrode system, as well as the estimated depth of their immersion in the ground;
4) measurement data of the soil resistivity in the area where the ground electrode system is to be built, and information about the weather (climatic) conditions under which these measurements were made, as well as the characteristics of the climatic zone. If the earth is assumed to be two-layer, then it is necessary to have measurements of the resistivity of both layers of the earth and the thickness of the upper layer;
5) data on natural grounding conductors: what structures can be used for this purpose and the resistance to their current spreading, obtained by direct measurement. If for some reason it is impossible to measure the resistance of a natural grounding conductor, then information must be provided to determine this resistance by calculation;
6) Rated earth fault current. If the current is unknown, then it is calculated by the usual methods;
7) calculated values of admissible contact (and step) voltages and the duration of the protection, if the calculation is made on the basis of contact (and step) voltages.
The calculation of grounding is usually carried out for cases where the ground electrode is placed in a homogeneous ground. In recent years, engineering methods for calculating grounding conductors in multilayer soil have been developed and began to be applied.
When calculating grounding conductors in homogeneous soil, the resistance of the upper layer of the earth (layer of seasonal changes) due to freezing or drying of the soil is taken into account. The calculation is carried out by a method based on the use of ground electrode conductivity utilization factors and is therefore called the utilization factor method. It is performed both with simple and complex designs of group ground electrodes.
When calculating grounding conductors in a multilayer earth, a two-layer earth model is usually taken with the specific resistances of the upper and lower layers r1 and r2, respectively, and the thickness (power) of the upper layer h1. The calculation is made by a method based on taking into account the potentials induced on the electrodes that are part of the group ground electrode, and therefore called the method of induced potentials. The calculation of grounding conductors in multilayer earth is more laborious. However, it gives more accurate results. It is advisable to use it for complex designs of group grounding, which usually take place in electrical installations with an effectively grounded neutral, i.e. in installations with a voltage of 110 kV and above.
When calculating a grounding device in any way, it is necessary to determine the required resistance for it.
The determination of the required resistance of the grounding device is carried out in accordance with the PUE.
For installations with voltage up to 1 kV, the resistance of the grounding device used for protective grounding of exposed conductive parts in an IT type system must comply with the condition:
where Rz is the resistance of the grounding device, ohm; Upr.adm - touch voltage, the value of which is assumed to be 50 V; Iz is the total earth fault current, A.
As a rule, it is not required to accept the resistance value of the grounding device as less than 4 ohms. Grounding device resistance up to 10 Ohm is allowed if the above condition is met, and the power of transformers and generators supplying the network does not exceed 100 kVA, including the total power of transformers and (or) generators operating in parallel.
For installations with voltages above 1 kV above 1 kV, the resistance of the grounding device must correspond to:
0.5 ohm with an effectively grounded neutral (i.e. with high earth fault currents);
250 / Iz, but not more than 10 ohms with an isolated neutral (i.e., at low earth fault currents) and provided that the earthing switch is used only for electrical installations with voltages above 1000 V.
In these expressions, Iz is the rated earth fault current.
During operation, an increase in the resistance to the spreading of the current of the grounding conductor in excess of the calculated value may occur, therefore, it is necessary to periodically monitor the value of the resistance of the grounding conductor.
Ground loop
The ground loop is classically a group of vertical electrodes of small depth connected by a horizontal conductor, mounted near the object at a relatively small mutual distance from each other.
As grounding electrodes in such a grounding device, a steel angle or reinforcement 3 meters long was traditionally used, which were driven into the ground with a sledgehammer.
A 4x40 mm steel strip was used as a connecting conductor, which was placed in a previously prepared ditch 0.5–0.7 meters deep. The conductor was connected to the mounted ground electrodes by electric or gas welding.
To save space, the ground loop is usually “folded” around the building along the walls (along the perimeter). If you look at this earth electrode from above, you can say that the electrodes are mounted along the contour of the building (hence the name).
Thus, the ground loop is a ground electrode, consisting of several electrodes (a group of electrodes) connected to each other and mounted around the building along its contour.
Schemes of inclusion in the current circuit can be different. However, the most characteristic are the connection schemes: between two phases and between one phase and the ground (Fig. 1). Of course, in the second case, it is assumed that there is an electrical connection between the network and the ground.
The first circuit corresponds to a two-phase contact, and the second - to a single-phase one.
The voltage between two conductive parts or between a conductive part and the ground when a person or animal touches them at the same time is called touch voltage (U etc).
Two-phase contact, ceteris paribus, is more dangerous, since the greatest voltage in this network is applied to the human body - linear, and the current through a person, being independent of the network scheme, neutral mode and other factors, is of the greatest importance:
where 
-
line voltage, i.e. voltage between the phase wires of the network, V;
U f - phase voltage, i.e. voltage between the beginning and end of one winding of the current source (transformer or generator) or between the phase and neutral wires of the network, V;
R h- resistance of the human body, Ohm.
Rice. 6.1. Cases of a person touching live parts under voltage: a - two-phase inclusion: b and c - single-phase inclusions
Cases of two-phase touch are very rare and cannot serve as a basis for evaluating networks for safety conditions. They usually occur in installations up to 1000 V as a result of work under voltage, the use of faulty protective equipment, as well as the operation of equipment with unprotected bare current-carrying parts (open circuit breakers, unprotected terminals of welding transformers, etc.).
Single-phase contact, ceteris paribus, is less dangerous than two-phase, since the current passing through a person is limited by the influence of many factors. However, single-phase contact occurs much more often and is the main scheme in which people are injured by current in networks of any voltage. Therefore, only cases of single-phase contact are analyzed below. In this case, both allowed for use three-phase current networks with voltages up to 1000 V are considered: four-wire with a solidly grounded neutral and three-wire with an isolated neutral.
6.2.4. Three-phase networks with solidly grounded neutral
In a three-phase four-wire network with a solidly grounded neutral, the calculation of the touch voltage U etc , and current I h passing through a person, in case of touching one of the phases (Fig. 6.2), it is easiest to perform the symbolic (complex) method.
Let us consider the most general case, when the insulation resistance of the wires, as well as the capacitance of the wires relative to the ground, are not equal to each other, i.e.
r 1 ≠ r 2 ≠ r 3 ≠ r n ; With 1 ≠ With 2 ≠ With 3 ≠ With n ≠ 0,
where r 1 , r 2 , r 3 , r n- insulation resistance of phase L and zero (combined) PEN wires, Ohm;
C 1 , C 2 , C 3 , C n - dispersed capacitances of phase L and zero (combined) PEN wires relative to the ground, F.
Then the total conductivities of the phase and neutral wires relative to the ground in complex form will be:
;
;
;
where w- angular frequency, rad/s;
j
-
imaginary unit equal to ( 
).
Rice. 6.2. A person touching a phase wire of a three-phase four-wire network with a grounded neutral during normal operation: a - network diagram; b - equivalent circuit; L1, L2, L3, - phase conductors; PEN - neutral (combined) wire.
The total conductivities of the grounding of the neutral and the human body are equal, respectively
;
,
where r 0 - neutral grounding resistance, Ohm.
The capacitive component of human conductivity can be neglected due to its small value.
When a person touches one of the phases, for example, the phase conductor L1, the voltage under which he will be determined by the expression
, (6.1)
The current is found by the formula
where 
- complex voltage of phase 1 (phase voltage), V;
-
complex voltage between the neutral of the current source and earth (between the points 00"
on the equivalent circuit).
Using the well-known two-node method, 
can be expressed as follows:
Bearing in mind that for a symmetrical three-phase system
;
;
,
where U f - phase voltage of the source (module), V;
a - phase operator that takes into account the phase shift, where
,
we will have equality
.
Substituting this value in (6.1), we obtain the desired equation of the touch voltage in complex form, acting on a person who has touched the phase conductor L1 of a three-phase four-wire network with a grounded neutral:
. (6.2)
The current passing through a person, we get if we multiply this expression by Y h :
. (6.3)
In the normal mode of operation of the network, the conductivity of the phase and neutral wires relative to the ground compared to the conductivity of the neutral grounding has very small values and, with some assumption, can be equated to zero, i.e.
Y 1 = Y 2 = Y 3 = Y n = 0
In this case, equations (6.2) and (6.3) become much simpler. So, the touch voltage will be
,
or (in real form)
,
(6.4)
and the current is
(6.5)
According to the requirements of the PUE, the resistance value r 0 should not exceed 8 ohms, the resistance of the human body R h , does not fall below a few hundred ohms. Therefore, without a large error in equations (6.4) and (6.5), we can neglect the value r 0 and assume that when touching one of the phases of a three-phase four-wire network with a grounded neutral, a person is practically under phase voltageU f , and the current passing through it is equal to the quotient of divisionU f on theR h .
From equation (6.5) one more conclusion follows: the current passing through a person who has touched the phase of a three-phase four-wire network with a grounded neutral during its normal operation practically does not change with a change in the insulation resistance and capacitance of the wires relative to the ground, if the condition is maintained that the total conductivities of the wires relative to the ground are very small compared to the conductivity network neutral grounding.
In this case, the safety of the resistance of shoes, soil (floor) and other resistances in the human electrical circuit is significantly increased.
A dead short to ground in a network with a solidly grounded neutral does little to change the voltage of the phases relative to the ground.
In emergency mode, when one of the phases of the network, for example, the phase conductor L3 (Fig. 6.3, a), is closed to the ground through a relatively small active resistance r gp, and a person touches the phase conductor L1, equation (6.2) will take the following form:
.
Here we also accept that Y 1 , Y 2 and Y n small compared to Y 0 , i.e. equated to zero.
After making the appropriate transformations and taking into account that
,
and 
,
get the touch voltage in real form
.
To simplify this expression, let us assume that
.
As a result, we finally obtain that the voltage U etc equals
. (6.6)
The current passing through a person is determined by the formula
.
(6.7)
Rice. 6.3. A person touching a phase wire of a three-phase four-wire network with a grounded neutral in emergency mode: a - network diagram; b - vector voltage diagram.
Let's consider two typical cases.
If the resistance of the wires to ground r gp be considered equal to zero, then equation (6.6) takes the form
.
Therefore, in this case, a person will be under the influence of the linear voltage of the network.
2. If we take equal to zero the neutral grounding resistance r 0 , then from equation (6.6) we obtain that U np = U f , those. the voltage that a person will be under will be equal to the phase voltage.
However, in practical conditions of resistance r gp and r 0 always greater than zero, so the voltage under which a person who touches a working phase wire of a three-phase network with a grounded neutral turns out to be, is always less than linear, but more than phase, i.e.
> U etc > U f . (6.8)
This position is illustrated by the vector diagram shown in fig. 6.3, b and corresponding to the case under consideration. It should be noted that this conclusion also follows from equation (6.6). So, for small values r gp
and r 0
compared with R h ,
the first term in the denominator can be neglected. Then the fraction for any ratio r gp
and r 0
will always be greater than one, but less 
, i.e. we obtain expression (6.8).
II . ELECTRICAL SAFETY
3. Analysis of the electrical safety of various electrical networks
Outcome of electric shock to a person, determined by the current flowing through the human body I h and touch voltage U h , significantly depends on the type of network supplying electricity consumers and its parameters, including:
- network voltage and frequency;
- network neutral mode;
- schemes for including a person in an electrical circuit;
- insulation resistance of the phase wires of the network relative to the ground;
- capacitance of the phase wires of the network relative to the ground;
- network mode.
Typical schemes for including a person in an electrical circuit
There are various “connection schemes” for a person in an electrical current circuit (typical “connection schemes” are shown in Fig. 3.5 using the IT network as an example):
Rice. 3.5. Typical schemes for including a person in an electrical circuit
(3.1.)
From expressions (3.1.) and (
3.2. ) follows that with two-phase when touched, a person falls under the line voltage of the network regardless of the type of network, neutral mode, network operation mode, conductivity of phase wiresY L1 , Y L2 , Y L3relative to the ground. Such a scheme for including a person in an electrical circuit is a great danger.Cases of two-phase contact are relatively rare and are usually the result of working under voltage in electrical installations up to 1 kV, which is a violation of the rules and instructions for performing work.
Rice. 3.6. Generalized scheme for the analysis of three-phase networks
(3.3)
(3.4)
