2.1 Introduction

One of the factors of electric shock is the weakening of insulation condition of a three-phase electrical network with insulated neutral voltages up to and above 1000 V. In order to ensure the increase of efficiency of the power supply system, it is necessary to develop a method of determining the parameters of isolation under operating voltage. Under the effectiveness, we accept ensuring growth of electrical safety and reliability in the operation of electrical installations with voltage up to and above 1000 V. The known [1] method of determining the parameters of isolation, "Ammeter-voltmeter" is a classical method, as it provides a satisfactory accuracy of the unknown quantities, but it does not ensure work safety in electrical installations production works and reduces the reliability of power supply of industrial machinery and equipment. Reduction of electrical installations work reliability and level of electrical safety in the operation of three-phase power networks up to and above 1000 V determined that by using the method "Ammeter-voltmeter," it is necessary to make the metal circuit of a mains phase to earth and measure the total current single-phase fault ground. Since during a metal closure of any phase to earth phase, voltage of the two other phases of the mains with respect to the ground reaches linear values and can thus lead to a short circuit in a multi-phase mains operated, which determines the reliability of power decrease in production machinery. A reduction in electrical safety determined by that in the metal closure of any phase of electrical network and ground, contact voltage, and step voltage will have the maximum value, and thereby provides maximum increase the probability electric shock to persons.

### 2.2 Method for determining the insulation parameters in an electrical network with insulated neutral

The method presented in the work [6] of determining the insulation parameters in three-phase electrical network with insulated neutral voltages above 1000 V, based on the measurement values of the modules of the line voltage, zero sequence voltage, and phase voltage with respect to ground when connected known active extra conduction between electrical network of the measured phase and ground, has a significant error. A significant error determined by that in determining the insulation parameters using the value of zero sequence voltage module, and thus, it is necessary to use a voltage transformer windings, allowing to allocate the residual voltage.

On the basis of the foregoing methods for determining the insulation parameters in three-phase mains with insulated neutral voltages up to and above 1000 V, which provides a satisfactory accuracy of the unknown quantities by eliminating the measurement of the modulus of the residual voltage, the operational safety of electrical installations, and the reliability of the electricity system, in connection excluding the measurements of the total current of the module for single-phase earth fault between a mains phase with respect to ground.

A method for determining the insulation parameters in three-phase balanced networks with voltage up to and above 1000 V, based on the measurement values of the modules of the line voltage, the phase voltages A and C relative to the ground after connecting additional active conductivity between the phase A and the mains ground was developed.

Special Issues of Ensuring Electrical Safety in Networks with Isolated Neutral Voltage… DOI: http://dx.doi.org/10.5772/intechopen.81384

As a result of the measurement values of the modules of the line voltage and phase voltage C and A with respect to the ground, taking into account the magnitude of the additional active conductivity by mathematical formulas, the following are defined:

• the total conductance of network insulation

2. The method of determining the insulation parameters in three-phase electrical networks with isolated neutral with voltages up to and

One of the factors of electric shock is the weakening of insulation condition of a

three-phase electrical network with insulated neutral voltages up to and above 1000 V. In order to ensure the increase of efficiency of the power supply system, it is necessary to develop a method of determining the parameters of isolation under operating voltage. Under the effectiveness, we accept ensuring growth of electrical safety and reliability in the operation of electrical installations with voltage up to and above 1000 V. The known [1] method of determining the parameters of isolation, "Ammeter-voltmeter" is a classical method, as it provides a satisfactory accuracy of the unknown quantities, but it does not ensure work safety in electrical installations production works and reduces the reliability of power supply of industrial machinery and equipment. Reduction of electrical installations work reliability and level of electrical safety in the operation of three-phase power networks up to and above 1000 V determined that by using the method "Ammeter-voltmeter," it is necessary to make the metal circuit of a mains phase to earth and measure the total current single-phase fault ground. Since during a metal closure of any phase to earth phase, voltage of the two other phases of the mains with respect to the ground reaches linear values and can thus lead to a short circuit in a multi-phase mains operated, which determines the reliability of power decrease in production

machinery. A reduction in electrical safety determined by that in the metal closure of any phase of electrical network and ground, contact voltage, and step voltage will have the maximum value, and thereby provides maximum increase the probability

2.2 Method for determining the insulation parameters in an electrical network

The method presented in the work [6] of determining the insulation parameters in three-phase electrical network with insulated neutral voltages above 1000 V, based on the measurement values of the modules of the line voltage, zero sequence voltage, and phase voltage with respect to ground when connected known active extra conduction between electrical network of the measured phase and ground, has a significant error. A significant error determined by that in determining the insulation parameters using the value of zero sequence voltage module, and thus, it is necessary to use a voltage transformer windings, allowing to allocate the residual

On the basis of the foregoing methods for determining the insulation parameters in three-phase mains with insulated neutral voltages up to and above 1000 V, which provides a satisfactory accuracy of the unknown quantities by eliminating the measurement of the modulus of the residual voltage, the operational safety of electrical installations, and the reliability of the electricity system, in connection excluding the measurements of the total current of the module for single-phase

A method for determining the insulation parameters in three-phase balanced networks with voltage up to and above 1000 V, based on the measurement values of the modules of the line voltage, the phase voltages A and C relative to the ground after connecting additional active conductivity between the phase A and the mains

earth fault between a mains phase with respect to ground.

above 1000 V

Industrial Engineering

electric shock to persons.

voltage.

52

ground was developed.

with insulated neutral

2.1 Introduction

$$\mathcal{Y} = \frac{1.73 U\_{\rm l} U\_{A}}{U\_{C}^{2} U\_{A}^{2}} \mathbf{g}\_{o},\tag{1}$$

• the active conductance of network insulation

$$\mathbf{g} = \left(\frac{\mathbf{3}U\_l^2 \left(U\_l^2 - \mathbf{3}U\_A^2\right)}{\left(U\_C^2 - U\_A^2\right)^2} - \mathbf{1}\right) \mathbf{0}.5 \mathbf{g}\_o,\tag{2}$$

• capacitive conductance of network insulation

$$b = \left(\mathbf{y}^2 - \mathbf{g}^2\right)^{0.5},\tag{3}$$

where Ul is the line voltage; U<sup>А</sup> is the A phase voltage with respect to the ground; U<sup>С</sup> is C the phase voltage with respect to the ground; and go is the additional active conductance.

The method developed in the implementation does not require the creation of a special measuring device, since the measuring devices, that is, voltmeters, available in the service manual. The PE-200 resistance is used as an active additional conductivity with R = 1000 Ohms, where by means of parallel and serial connection provides the required power dissipation. To switch, the active standby is used more conductivity cell load switch.

The developed method provides satisfactory accuracy and is simple and safe in its implementation in the three-phase electrical networks with isolated neutral voltages up to and above 1000 V.

#### 2.3 Analysis of error of method determining the insulation parameters in an electrical network with isolated neutral

The obtained mathematical dependences for determining the total and active conductance of electrical network insulation provide easy and safe work of electrical installations with voltage up to and above 1000 V.

Error analysis of the developed method for determining the insulation parameters in symmetrical three-phase electrical networks with isolated neutral which is based on measurement of unit line voltage, phase voltage C and A relative to the earth, after the active connection of additional conduction between phase A and the electric network and earth is performed.

To improve the efficiency of the developed method for determining the parameters of isolation in a symmetrical three-phase network with isolated neutral, based on error analysis, for each specific network, additional active conductivity is selected, in order to ensure satisfactory accuracy of required quantities.

Random relative error in determining the total conductivity of insulation and its components in three-phase balanced networks with voltage up to and beyond 1000, based on the measurement values of the modules of the line voltage, phase voltage C and A with respect to the ground, after connecting the active additional

conduction between the phase and the electric network and earth, is determined according to (1), (2), and (3).

Random relative error in determining the total conductance of mains phase insulation relative to the ground is determined from the formula (1):

$$\mathcal{Y} = \frac{1.73 U\_1 U\_A}{U\_C^2 \cdot U\_A^2} \mathcal{g}\_o.$$

where Ul, UА, UС, and go are values that define the total conductance of network insulation and obtained by direct measurement. The relative mean square error in determining the total conductance of mains phase insulation relative to the ground is determined from the expression [28, 29]:

$$
\Delta \mathbf{y} = \frac{1}{\mathcal{Y}} \left[ \left( \frac{\partial \mathbf{y}}{\partial U\_A} \Delta U\_A \right)^2 + \left( \frac{\partial \mathbf{y}}{\partial U\_C} \Delta U\_C \right)^2 + \left( \frac{\partial \mathbf{y}}{\partial U\_l} \Delta U\_l \right)^2 + \left( \frac{\partial \mathbf{y}}{\partial \mathbf{g}\_o} \Delta \mathbf{g}\_o \right)^2 \right]^{0.5}, \tag{4}$$

where <sup>∂</sup><sup>y</sup> ∂U<sup>А</sup> , <sup>∂</sup><sup>y</sup> ∂U<sup>С</sup> , ∂y ∂Ul , and <sup>∂</sup><sup>y</sup> ∂go are partial derivatives y ¼ f (Ul, UА, UС, go).

Here ΔUl, ΔUА, ΔUС, and Δgo are absolute errors of direct measurement values Ul, UА, UС, and go which are defined by the following expressions:

$$\begin{aligned} \Delta U\_l &= U\_l \times \Delta U\_{l^\*};\\ \Delta U\_{\mathcal{C}} &= U\_{\mathcal{C}} \times \Delta U\_{\mathcal{C}^\*};\\ \Delta U\_A &= U\_A \times \Delta U\_{A^\*};\\ \Delta \mathbf{g}\_o &= \mathbf{g}\_o \times \Delta \mathbf{g}\_{o^\*}. \end{aligned} \tag{5}$$

<sup>ε</sup><sup>y</sup> <sup>¼</sup> <sup>Δ</sup><sup>y</sup>

DOI: http://dx.doi.org/10.5772/intechopen.81384

<sup>ε</sup><sup>y</sup> <sup>¼</sup> <sup>Δ</sup><sup>y</sup>

relative to the ground is determined from the formula (2):

<sup>g</sup> <sup>¼</sup> <sup>3</sup>U<sup>2</sup>

network isolation and obtained by direct measurement.

þ

, and <sup>∂</sup><sup>g</sup> ∂go

> ∂g ∂Ul

∂g ∂U<sup>А</sup>

∂g ∂UC

∂g ∂go

∂g ∂UC

ΔUC � �<sup>2</sup>

Ul, UА, UС, and go, which are defined by the following expressions:

which is connected between the phase A electrical and the ground.

<sup>¼</sup> <sup>3</sup>Ul <sup>2</sup>U<sup>2</sup>

¼ � <sup>3</sup>U<sup>2</sup>

¼ � <sup>6</sup>U<sup>2</sup>

<sup>l</sup> U<sup>2</sup>

2 U<sup>2</sup>

<sup>¼</sup> <sup>3</sup>U<sup>2</sup>

2 U<sup>2</sup>

where <sup>U</sup><sup>∗</sup> <sup>¼</sup> UA

from the expression:

∂g ∂UA

ΔUA � �<sup>2</sup>

<sup>Δ</sup><sup>g</sup> <sup>¼</sup> <sup>1</sup> g

UС, and go:

55

where <sup>∂</sup><sup>g</sup> ∂U<sup>А</sup> , <sup>∂</sup><sup>g</sup> ∂U<sup>С</sup> , ∂g ∂U<sup>l</sup>

UC . <sup>Δ</sup> <sup>¼</sup> <sup>2</sup> <sup>þ</sup>

<sup>Δ</sup> <sup>¼</sup> <sup>2</sup> <sup>þ</sup>

<sup>l</sup> U<sup>2</sup>

U2 <sup>C</sup> � <sup>U</sup><sup>2</sup> A � �<sup>2</sup> � <sup>1</sup> !

4U<sup>4</sup>

Special Issues of Ensuring Electrical Safety in Networks with Isolated Neutral Voltage…

<sup>C</sup> <sup>þ</sup> <sup>U</sup><sup>2</sup>

<sup>4</sup> <sup>þ</sup> <sup>1</sup> <sup>þ</sup> <sup>U</sup><sup>2</sup>

<sup>1</sup> � <sup>U</sup><sup>2</sup> ∗ � �<sup>2</sup> !0, <sup>5</sup>

U2 <sup>C</sup> � <sup>U</sup><sup>2</sup> A � �<sup>2</sup> !0, <sup>5</sup>

The obtained Eq. (8) is expressed in relative units, and after the conversion, we obtain:

Random error in determining the active conductance of mains phase insulation

<sup>l</sup> � <sup>3</sup>U<sup>2</sup> A � �

where Ul, UА, UС, and go are values that define the active conductance of

Relative mean square error of the method when determining the active conductivity of phase insulation of electrical network relative to the ground is determined

þ

Here ΔUl, ΔUА, ΔUС, and Δgo are absolute errors of direct measurement values

ΔU<sup>l</sup> ¼ U<sup>l</sup> � ΔU<sup>l</sup>∗; ΔU<sup>С</sup> ¼ U<sup>С</sup> � ΔU<sup>С</sup>∗; ΔU<sup>А</sup> ¼ U<sup>А</sup> � ΔU<sup>А</sup>∗; Δg<sup>o</sup> ¼ g<sup>o</sup> � Δg<sup>o</sup>∗:

To determine the accuracy of measuring devices, accept that ΔU<sup>l</sup><sup>∗</sup> ¼ ΔU<sup>А</sup><sup>∗</sup> ¼ ΔU<sup>С</sup><sup>∗</sup> ¼ ΔU∗, where ΔU<sup>∗</sup> is the relative error of voltage measurement circuits and Δg<sup>о</sup><sup>∗</sup> ¼ ΔR<sup>∗</sup> is the relative error of a measuring instrument that measures resistance

> <sup>l</sup> � <sup>3</sup>U<sup>2</sup> A

� �

<sup>C</sup> � <sup>U</sup><sup>2</sup> A � �<sup>2</sup> go;

<sup>l</sup> U<sup>А</sup> 3U<sup>2</sup>

<sup>l</sup> UC U<sup>2</sup>

<sup>l</sup> � <sup>3</sup>U<sup>2</sup> A � �

U2 <sup>C</sup> � <sup>U</sup><sup>2</sup> A � �<sup>3</sup> go;

<sup>C</sup> � <sup>U</sup><sup>2</sup> A � � � <sup>0</sup>:5:

U2 <sup>C</sup> � <sup>U</sup><sup>2</sup> A � �<sup>3</sup> go;

Determine the partial derivatives g ¼ f (Ul, UА, UС, go) by the variables Ul, UА,

<sup>C</sup> <sup>þ</sup> <sup>3</sup>U<sup>2</sup>

<sup>l</sup> � <sup>3</sup>U<sup>2</sup> А � �

� �

<sup>A</sup> � <sup>2</sup>U<sup>2</sup> l

� �<sup>2</sup> " #<sup>0</sup>:<sup>5</sup>

∂g ∂U<sup>l</sup> ΔUl � �<sup>2</sup>

<sup>C</sup> <sup>þ</sup> <sup>U</sup><sup>2</sup> A � �<sup>2</sup>

∗ � �<sup>2</sup>

0:5go,

þ

are partial derivatives, g ¼ f (Ul, UА, UС, go).

∂g ∂go Δgo (8)

, (10)

(11)

(12)

, (9)

To determine the errors of measuring devices, accept that ΔUl<sup>∗</sup> = ΔU<sup>А</sup><sup>∗</sup> = ΔU<sup>С</sup><sup>∗</sup> = ΔU∗, where: ΔU<sup>∗</sup> is the relative error of voltage measurement circuits and Δg<sup>о</sup><sup>∗</sup> ¼ ΔR<sup>∗</sup> is the relative error of the measuring instrument, which measures the resistance which is connected between the phase A electrical and ground. Determine the partial derivative functions y ¼ f (Ul, UА, UС, go) by the variables Ul, UА, UС, go:

$$\begin{aligned} \frac{\partial \mathbf{y}}{\partial U\_{l}} &= \frac{1.73 U\_{A}}{U\_{C}^{2} - U\_{A}^{2}} \mathbf{g}\_{o}; \\ \frac{\partial \mathbf{y}}{\partial U\_{A}} &= \frac{1.73 U\_{1} \left(U\_{C}^{2} + U\_{A}^{2}\right)}{\left(U\_{C}^{2} - U\_{A}^{2}\right)^{2}} \mathbf{g}\_{o}; \\ \frac{\partial \mathbf{y}}{\partial U\_{C}} &= -\frac{3.46 U\_{1} U\_{A} U\_{C}}{\left(U\_{C}^{2} - U\_{A}^{2}\right)^{2}} \mathbf{g}\_{o}; \\ \frac{\partial \mathbf{y}}{\partial \mathbf{g}\_{o}} &= \frac{1.73 U\_{1} U\_{A}}{U\_{C}^{2} - U\_{A}^{2}}. \end{aligned} \tag{6}$$

Solving the Eq. (4), substituting the values of the partial derivatives of Eq. (6) and private values of absolute errors (5), at the same time, assuming that ΔU<sup>∗</sup> ¼ ΔR<sup>∗</sup> ¼ Δ, we obtain:

$$\varepsilon\_{\mathcal{V}} = \frac{\Delta \mathbf{y}}{\Delta} = \frac{\mathbf{1}.73 U\_l U\_A \mathbf{g}\_o}{U\_C^2 - U\_A^2} \left( 2 + \frac{4U\_C^4 + \left(U\_C^2 + U\_A^2\right)^2}{\left(U\_C^2 - U\_A^2\right)^2} \right)^{0.5}.\tag{7}$$

The obtained Eq. (7) is divided into the Eq. (1):

Special Issues of Ensuring Electrical Safety in Networks with Isolated Neutral Voltage… DOI: http://dx.doi.org/10.5772/intechopen.81384

$$\varepsilon\_{\mathcal{V}} = \frac{\Delta y}{\Delta} = \left( 2 + \frac{4U\_C^4 + \left(U\_C^2 + U\_A^2\right)^2}{\left(U\_C^2 - U\_A^2\right)^2} \right)^{0,5} \tag{8}$$

The obtained Eq. (8) is expressed in relative units, and after the conversion, we obtain:

$$\varepsilon\_{\mathcal{V}} = \frac{\Delta \mathbf{y}}{\Delta} = \left( 2 + \frac{4 + \left( \mathbf{1} + \mathbf{U}\_{\ast}^{2} \right)^{2}}{\left( \mathbf{1} - \mathbf{U}\_{\ast}^{2} \right)^{2}} \right)^{0,5},\tag{9}$$

where <sup>U</sup><sup>∗</sup> <sup>¼</sup> UA UC .

conduction between the phase and the electric network and earth, is determined

Random relative error in determining the total conductance of mains phase

<sup>y</sup> <sup>¼</sup> <sup>1</sup>:73UlU<sup>А</sup> U2 <sup>C</sup>‐U<sup>2</sup> A go,

where Ul, UА, UС, and go are values that define the total conductance of network insulation and obtained by direct measurement. The relative mean square error in determining the total conductance of mains phase insulation relative to the ground

þ

Here ΔUl, ΔUА, ΔUС, and Δgo are absolute errors of direct measurement values

ΔUl ¼ Ul � ΔUl

ΔU∗, where: ΔU<sup>∗</sup> is the relative error of voltage measurement circuits and

<sup>¼</sup> <sup>1</sup>:73U<sup>А</sup> U2 <sup>C</sup> � <sup>U</sup><sup>2</sup> A go;

<sup>¼</sup> <sup>1</sup>:73U<sup>l</sup> <sup>U</sup><sup>2</sup>

<sup>¼</sup> <sup>1</sup>:73UlU<sup>А</sup> U2 <sup>C</sup> � <sup>U</sup><sup>2</sup> A :

and private values of absolute errors (5), at the same time, assuming that

U2 <sup>C</sup> � <sup>U</sup><sup>2</sup> A � �<sup>2</sup> go;

¼ � <sup>3</sup>:46UlUАU<sup>С</sup> U2 <sup>C</sup> � <sup>U</sup><sup>2</sup> A � �<sup>2</sup> go;

Solving the Eq. (4), substituting the values of the partial derivatives of Eq. (6)

2 þ

4U<sup>4</sup>

<sup>C</sup> <sup>þ</sup> <sup>U</sup><sup>2</sup>

U2 <sup>C</sup> � <sup>U</sup><sup>2</sup> A � �<sup>2</sup> !<sup>0</sup>, <sup>5</sup>

<sup>C</sup> <sup>þ</sup> <sup>U</sup><sup>2</sup> A � �<sup>2</sup>

<sup>C</sup> <sup>þ</sup> <sup>U</sup><sup>2</sup> A � �

∂y ∂U<sup>l</sup>

∂y ∂U<sup>А</sup>

∂y ∂U<sup>С</sup>

∂y ∂go

<sup>Δ</sup> <sup>¼</sup> <sup>1</sup>:73UlUАgo U2 <sup>C</sup> � <sup>U</sup><sup>2</sup> A

The obtained Eq. (7) is divided into the Eq. (1):

ΔU<sup>∗</sup> ¼ ΔR<sup>∗</sup> ¼ Δ, we obtain:

<sup>ε</sup><sup>y</sup> <sup>¼</sup> <sup>Δ</sup><sup>y</sup>

ΔU<sup>С</sup> ¼ U<sup>С</sup> � ΔUС<sup>∗</sup> ; ΔU<sup>А</sup> ¼ U<sup>А</sup> � ΔUА<sup>∗</sup> ; Δgo ¼ go � Δgo<sup>∗</sup> :

To determine the errors of measuring devices, accept that ΔUl<sup>∗</sup> = ΔU<sup>А</sup><sup>∗</sup> = ΔU<sup>С</sup><sup>∗</sup> =

Δg<sup>о</sup><sup>∗</sup> ¼ ΔR<sup>∗</sup> is the relative error of the measuring instrument, which measures the resistance which is connected between the phase A electrical and ground. Determine the partial derivative functions y ¼ f (Ul, UА, UС, go) by the variables Ul, UА,

� �<sup>2</sup> " #0:<sup>5</sup>

∂y ∂Ul ΔUl � �<sup>2</sup>

∗ ;

are partial derivatives y ¼ f (Ul, UА, UС, go).

þ

∂y ∂go Δgo

, (4)

(5)

(6)

: (7)

insulation relative to the ground is determined from the formula (1):

according to (1), (2), and (3).

Industrial Engineering

∂y ∂UA

<sup>Δ</sup><sup>y</sup> <sup>¼</sup> <sup>1</sup> y

UС, go:

54

where <sup>∂</sup><sup>y</sup> ∂U<sup>А</sup> , <sup>∂</sup><sup>y</sup> ∂U<sup>С</sup> , ∂y ∂Ul

is determined from the expression [28, 29]:

þ

, and <sup>∂</sup><sup>y</sup> ∂go

∂y ∂UC

Ul, UА, UС, and go which are defined by the following expressions:

ΔUC � �<sup>2</sup>

ΔUA � �<sup>2</sup>

Random error in determining the active conductance of mains phase insulation relative to the ground is determined from the formula (2):

$$\mathbf{g} = \left(\frac{\mathbf{3}U\_l^2\left(U\_l^2 - \mathbf{3}U\_A^2\right)}{\left(U\_C^2 - U\_A^2\right)^2} - 1\right)\mathbf{0}.5\mathbf{g}\_o, 1$$

where Ul, UА, UС, and go are values that define the active conductance of network isolation and obtained by direct measurement.

Relative mean square error of the method when determining the active conductivity of phase insulation of electrical network relative to the ground is determined from the expression:

$$\Delta \mathbf{g} = \frac{1}{\mathbf{g}} \left[ \left( \frac{\partial \mathbf{g}}{\partial U\_A} \Delta U\_A \right)^2 + \left( \frac{\partial \mathbf{g}}{\partial U\_C} \Delta U\_C \right)^2 + \left( \frac{\partial \mathbf{g}}{\partial U\_1} \Delta U\_l \right)^2 + \left( \frac{\partial \mathbf{g}}{\partial \mathbf{g}\_o} \Delta \mathbf{g}\_o \right)^2 \right]^{0.5}, \tag{10}$$

where <sup>∂</sup><sup>g</sup> ∂U<sup>А</sup> , <sup>∂</sup><sup>g</sup> ∂U<sup>С</sup> , ∂g ∂U<sup>l</sup> , and <sup>∂</sup><sup>g</sup> ∂go are partial derivatives, g ¼ f (Ul, UА, UС, go).

Here ΔUl, ΔUА, ΔUС, and Δgo are absolute errors of direct measurement values Ul, UА, UС, and go, which are defined by the following expressions:

$$\begin{aligned} \Delta U\_{\text{l}} &= U\_{\text{l}} \cdot \Delta U\_{\text{l\*} \natural}; \\ \Delta U\_{\text{C}} &= U\_{\text{C}} \cdot \Delta U\_{\text{C\*} \natural}; \\ \Delta U\_{\text{A}} &= U\_{\text{A}} \cdot \Delta U\_{\text{A\*} \natural}; \\ \Delta \mathbf{g}\_{\text{o}} &= \mathbf{g}\_{\text{o}} \cdot \Delta \mathbf{g}\_{\text{o}\*}. \end{aligned} \tag{11}$$

To determine the accuracy of measuring devices, accept that ΔU<sup>l</sup><sup>∗</sup> ¼ ΔU<sup>А</sup><sup>∗</sup> ¼ ΔU<sup>С</sup><sup>∗</sup> ¼ ΔU∗, where ΔU<sup>∗</sup> is the relative error of voltage measurement circuits and Δg<sup>о</sup><sup>∗</sup> ¼ ΔR<sup>∗</sup> is the relative error of a measuring instrument that measures resistance which is connected between the phase A electrical and the ground.

Determine the partial derivatives g ¼ f (Ul, UА, UС, go) by the variables Ul, UА, UС, and go:

$$\begin{split} \frac{\partial \mathbf{g}}{\partial U\_{l}} &= \frac{3U\_{l} \left(2U\_{l}^{2} - 3U\_{A}^{2}\right)}{2\left(U\_{C}^{2} - U\_{A}^{2}\right)^{2}} \mathbf{g}\_{o}; \\ \frac{\partial \mathbf{g}}{\partial U\_{A}} &= -\frac{3U\_{l}^{2}U\_{A}\left(3U\_{C}^{2} + 3U\_{A}^{2} - 2U\_{1}^{2}\right)}{\left(U\_{C}^{2} - U\_{A}^{2}\right)^{3}} \mathbf{g}\_{o}; \\ \frac{\partial \mathbf{g}}{\partial U\_{C}} &= -\frac{6U\_{l}^{2}U\_{C}\left(U\_{l}^{2} - 3U\_{A}^{2}\right)}{\left(U\_{C}^{2} - U\_{A}^{2}\right)^{3}} \mathbf{g}\_{o}; \\ \frac{\partial \mathbf{g}}{\partial \mathbf{g}} &= \frac{3U\_{l}^{2}\left(U\_{l}^{2} - 3U\_{A}^{2}\right)}{2\left(U\_{C}^{2} - U\_{A}^{2}\right)} - 0.5. \end{split} \tag{12}$$

Solve Eq. (10), substituting the values of the partial derivatives of Eq. (12) and the values of the partial absolute errors (11), at the same time, assuming that ΔU<sup>∗</sup> ¼ ΔR<sup>∗</sup> ¼ Δ, we obtain:

<sup>Δ</sup><sup>b</sup> <sup>¼</sup> <sup>1</sup> b

DOI: http://dx.doi.org/10.5772/intechopen.81384

<sup>ε</sup><sup>b</sup> <sup>¼</sup> <sup>Δ</sup><sup>b</sup> Δ ¼

<sup>1</sup> � tan <sup>2</sup> ð Þ<sup>δ</sup> <sup>2</sup> <sup>2</sup> <sup>þ</sup>

<sup>þ</sup> <sup>9</sup> 27U<sup>2</sup> ph <sup>U</sup><sup>2</sup> ph�U<sup>2</sup> A � �� <sup>U</sup><sup>2</sup>

> 18U<sup>2</sup> ph U<sup>2</sup>

þ 3U<sup>4</sup> phU<sup>4</sup> <sup>A</sup> U<sup>2</sup> C�U<sup>2</sup> A�2U<sup>2</sup> ph � �<sup>2</sup>

0

BBBBBBBBBB@

�

0

BBBBBBBBBBBBB@

<sup>ε</sup><sup>b</sup> <sup>¼</sup> <sup>Δ</sup><sup>b</sup> Δ ¼

ground, build the dependence:

or

equation:

obtain:

57

<sup>ε</sup><sup>b</sup> <sup>¼</sup> <sup>Δ</sup><sup>b</sup> Δ ¼

∂b ∂y Δy � �<sup>2</sup>

Special Issues of Ensuring Electrical Safety in Networks with Isolated Neutral Voltage…

þ

<sup>1</sup> � tan <sup>2</sup> ð Þ<sup>δ</sup> <sup>2</sup> <sup>Δ</sup><sup>y</sup>

4U<sup>4</sup> <sup>C</sup><sup>þ</sup> <sup>U</sup><sup>2</sup> <sup>C</sup>þU<sup>2</sup> ð Þ<sup>A</sup> 2

<sup>2</sup> � �<sup>2</sup> �

ph � <sup>U</sup><sup>2</sup> A � �<sup>2</sup>

U2 <sup>C</sup>�U<sup>2</sup> ð Þ<sup>A</sup> 2

<sup>C</sup>�U<sup>2</sup> ð Þ<sup>A</sup>

U2 <sup>C</sup>�U<sup>2</sup> ð Þ<sup>A</sup> 2

Obtained Eq. (21) is expressed in relative units and after the conversion, we

<sup>1</sup> � tan <sup>2</sup> ð Þ<sup>δ</sup> <sup>2</sup> <sup>2</sup> <sup>þ</sup>

18 1 � <sup>U</sup><sup>2</sup>

<sup>ε</sup><sup>y</sup> <sup>¼</sup> <sup>Δ</sup>y<sup>∗</sup>

<sup>ε</sup><sup>g</sup> <sup>¼</sup> <sup>Δ</sup>g<sup>∗</sup>

<sup>ε</sup><sup>b</sup> <sup>¼</sup> <sup>Δ</sup>b<sup>∗</sup>

<sup>þ</sup> <sup>9</sup> 27 1�U<sup>2</sup> ð Þ <sup>A</sup><sup>∗</sup> � <sup>U</sup><sup>2</sup>

�

2 6 4

þ 3U<sup>4</sup> <sup>A</sup><sup>∗</sup> <sup>U</sup><sup>2</sup> tan <sup>2</sup>δ

� <sup>U</sup><sup>2</sup>

<sup>þ</sup>U<sup>4</sup> <sup>C</sup> U<sup>2</sup> ph�U<sup>2</sup> A � �<sup>2</sup>

4U<sup>4</sup> <sup>C</sup>∗<sup>þ</sup> <sup>U</sup><sup>2</sup> <sup>C</sup>∗þU<sup>2</sup> ð Þ <sup>A</sup><sup>∗</sup>

<sup>C</sup>∗�U<sup>2</sup> ð Þ <sup>A</sup><sup>∗</sup> <sup>2</sup> � �<sup>2</sup> �

> A∗ � �<sup>2</sup> � <sup>U</sup><sup>2</sup>

> > <sup>C</sup>∗�U<sup>2</sup> ð Þ <sup>A</sup>∗�<sup>2</sup> <sup>2</sup>

Based on the results of random relative mean square errors in determining the active, capacitive, and total conductivities of mains phase isolation relative to the

<sup>Δ</sup> <sup>¼</sup> f Uð Þ<sup>∗</sup> ;

<sup>Δ</sup> <sup>¼</sup> f Uð Þ <sup>А</sup>∗; <sup>U</sup><sup>С</sup><sup>∗</sup> ;

<sup>Δ</sup> <sup>¼</sup> f Uð Þ <sup>A</sup>∗; UC∗; tan <sup>δ</sup> ,

shown in Figures 1–3. Mathematical dependence of the relative mean square errors of the total—εy, active—εg, and capacitive—ε<sup>b</sup> conductivities of phase insulation of electrical network with insulated neutral on graphic illustrations

U2 <sup>C</sup>∗�U<sup>2</sup> ð Þ <sup>A</sup><sup>∗</sup>

tan <sup>2</sup>δ

U2 <sup>C</sup>∗�U<sup>2</sup> ð Þ <sup>A</sup><sup>∗</sup>

<sup>þ</sup>U<sup>4</sup>

2

� �

� �

Solving Eq. (19) and substituting the values of mathematical descriptions of the relative rms dependences of total (8) and active (16) conductivities of electrical installations phase insulation relative to the ground phase, we get the following

� �<sup>2</sup> " #0:<sup>5</sup>

∂b ∂g Δg

Δ � �<sup>2</sup>

� �<sup>2</sup> � �0:<sup>5</sup>

<sup>þ</sup> <sup>Δ</sup><sup>g</sup> Δ

þ

<sup>C</sup> � <sup>U</sup><sup>2</sup> A � �<sup>4</sup>

þ

2

þ

þ

3 7 5 1

0:5

CCCCCCCCCCA

2

<sup>C</sup><sup>∗</sup> � <sup>U</sup><sup>2</sup> A∗ � �<sup>4</sup>

> <sup>C</sup><sup>∗</sup> <sup>1</sup>�U<sup>2</sup> ð Þ <sup>A</sup><sup>∗</sup> 2

CCCCCCCCCCCCCA

: (20)

: (21)

1

0:5

tan <sup>2</sup><sup>δ</sup> : (19)

, (18)

$$\frac{\Delta \mathbf{g}}{\Delta} = \frac{\mathbf{3g}\_o}{\left(U\_C^2 - U\_A^2\right)^3} \left( \begin{aligned} \left(U\_C^2 - U\_A^2\right)^2 \left[2U\_I^4 \left(U\_1^2 - 3U\_A^2\right)^2 - \left(U\_C^2 - U\_A^2\right)^4\right] +\\ + U\_I^4 \left\{U\_A^4 \left[3\left(U\_C^2 - U\_A^2\right) - 2U\_I^2\right]^2 + U\_C^4 \left(U\_1^2 - 3U\_A^2\right)^2\right\} \end{aligned} \tag{13}$$

Obtained Eq. (13) divided by Eq. (2):

$$\mathbf{e}\_{\mathbf{g}} = \frac{\Delta \mathbf{g}}{\Delta} = \begin{pmatrix} \frac{2U\_l^4 \left(\boldsymbol{U}\_1^2 - 3\boldsymbol{U}\_A^2\right)^2 - \left(\boldsymbol{U}\_C^2 - \boldsymbol{U}\_A^2\right)^4}{\left[3\boldsymbol{U}\_l^2 \left(\boldsymbol{U}\_1^2 - 3\boldsymbol{U}\_A^2\right) - \left(\boldsymbol{U}\_C^2 - \boldsymbol{U}\_A^2\right)^2\right]^2} + \\\\ + \frac{U\_l^4 \left\{\boldsymbol{U}\_A^4 \left[3\left(\boldsymbol{U}\_C^2 - \boldsymbol{U}\_A^2\right) - 2\boldsymbol{U}\_l^2\right]^2 + \boldsymbol{U}\_C^4 \left(\boldsymbol{U}\_1^2 - 3\boldsymbol{U}\_A^2\right)^2\right\}}{\left(\boldsymbol{U}\_C^2 - \boldsymbol{U}\_A^2\right)^2 \left[3\boldsymbol{U}\_l^2 \left(\boldsymbol{U}\_1^2 - 3\boldsymbol{U}\_A^2\right) - \left(\boldsymbol{U}\_C^2 - \boldsymbol{U}\_A^2\right)^2\right]^2} \end{pmatrix}^{0.5}.\tag{14}$$

In the resulting Eq. (14), the value of the line voltage is expressed in terms of the phase voltages in accordance with the fact that U<sup>l</sup> ¼ 1:73Uф:

$$\begin{aligned} \varepsilon\_{\mathsf{g}} = \frac{\Delta \mathsf{g}}{\Delta} = \mathsf{3} \begin{pmatrix} \frac{18U\_{\mathsf{ph}}^4 \left(U\_{\mathsf{ph}}^2 - U\_A^2\right)^2 - \left(U\_C^2 - U\_A^2\right)^4}{\left[2\mathsf{T}U\_{\mathsf{ph}}^2 \left(U\_{\mathsf{ph}}^2 - U\_A^2\right) - \left(U\_C^2 - U\_A^2\right)^2\right]^2} +\\ + \frac{3U\_{\mathsf{ph}}^4 U\_A^4 \left(U\_C^2 - U\_A^2 - 2U\_{\mathsf{ph}}^2\right)^2 + U\_C^4 \left(U\_{\mathsf{ph}}^2 - U\_A^2\right)^2}{\left(U\_C^2 - U\_A^2\right)^2 \left[2\mathsf{T}U\_{\mathsf{ph}}^2 \left(U\_{\mathsf{ph}}^2 - U\_A^2\right) - \left(U\_C^2 - U\_A^2\right)^2\right]^2} \end{pmatrix}^{0.5} \end{aligned} \tag{15}$$

Simplifying the formula (15), we obtain the Eq. (16):

$$\varepsilon\_{\mathcal{S}} = \frac{3}{27U\_{ph}^{2}\left(U\_{ph}^{2} - U\_{A}^{2}\right) - \left(U\_{C}^{2} - U\_{A}^{2}\right)^{2}} + \begin{pmatrix} 18U\_{ph}^{4}\left(U\_{ph}^{2} - U\_{A}^{2}\right)^{2} - \left(U\_{C}^{2} - U\_{A}^{2}\right)^{4} + \\\\ + \frac{3U\_{ph}^{4}U\_{A}^{4}\left(U\_{C}^{2} - U\_{A}^{2} - 2U\_{ph}^{2}\right)^{2}}{\left(U\_{C}^{2} - U\_{A}^{2}\right)^{2}} +\\ + \frac{U\_{C}^{4}\left(U\_{ph}^{2} - U\_{A}^{2}\right)^{2}}{\left(U\_{C}^{2} - U\_{A}^{2}\right)^{2}} \end{pmatrix}^{0.5} \tag{16}$$

Obtained Eq. (16) is expressed in relative units and after the conversion, we obtain:

$$\mathbf{e}\_{\mathbf{g}} = \frac{\Delta \mathbf{g}}{\Delta} = \frac{\mathbf{3}}{27 \left( \mathbf{1} - \mathbf{U}\_{A\*}^{2} \right) - \left( \mathbf{U}\_{C\*}^{2} - \mathbf{U}\_{A\*}^{2} \right)^{2}} \begin{pmatrix} \mathbf{18} \left( \mathbf{1} - \mathbf{U}\_{A\*}^{2} \right)^{2} - \left( \mathbf{U}\_{C\*}^{2} - \mathbf{U}\_{A\*}^{2} \right)^{4} + \\\\ + \frac{3 \mathbf{U}\_{A\*}^{4} \left( \mathbf{U}\_{C\*}^{2} - \mathbf{U}\_{A\*}^{2} \right)^{2}}{\left( \mathbf{U}\_{C\*}^{2} - \mathbf{U}\_{A\*}^{2} \right)^{2}} +\\ + \frac{\mathbf{U}\_{C\*}^{4} \left( \mathbf{1} - \mathbf{U}\_{A\*}^{2} \right)^{2}}{\left( \mathbf{U}\_{C}^{2} - \mathbf{U}\_{A}^{2} \right)^{2}} \end{pmatrix},\tag{17}$$

where <sup>U</sup><sup>А</sup><sup>∗</sup> <sup>¼</sup> UA Uph and <sup>U</sup><sup>С</sup><sup>∗</sup> <sup>¼</sup> <sup>U</sup><sup>С</sup> Uph.

Relative mean square error method for determining the conductivity of the capacitive isolation mains phases relative to the ground is determined by the expression (3):

Special Issues of Ensuring Electrical Safety in Networks with Isolated Neutral Voltage… DOI: http://dx.doi.org/10.5772/intechopen.81384

$$
\Delta b = \frac{1}{b} \left[ \left( \frac{\partial b}{\partial \mathbf{y}} \Delta \mathbf{y} \right)^2 + \left( \frac{\partial b}{\partial \mathbf{g}} \Delta \mathbf{g} \right)^2 \right]^{0.5}, \tag{18}
$$

or

Solve Eq. (10), substituting the values of the partial derivatives of Eq. (12) and

<sup>l</sup> U<sup>2</sup>

� �<sup>2</sup>

<sup>C</sup>�U<sup>2</sup> ð Þ<sup>A</sup> <sup>2</sup> � �<sup>2</sup> þ

<sup>2</sup> � �

<sup>l</sup> �3U<sup>2</sup> ð Þ<sup>A</sup> � <sup>U</sup><sup>2</sup>

<sup>C</sup>�U<sup>2</sup> ð Þ<sup>A</sup> �2U<sup>2</sup> <sup>l</sup> ½ �<sup>2</sup>

In the resulting Eq. (14), the value of the line voltage is expressed in terms of the

� <sup>U</sup><sup>2</sup> <sup>C</sup>�U<sup>2</sup> ð Þ<sup>A</sup> 4

18U<sup>4</sup> ph U<sup>2</sup>

þ 3U<sup>4</sup> phU<sup>4</sup> <sup>A</sup> <sup>U</sup><sup>2</sup> C�U<sup>2</sup> A�2U<sup>2</sup> ph � �<sup>2</sup>

þ U<sup>4</sup> <sup>C</sup> U<sup>2</sup> ph�U<sup>2</sup> A � �<sup>2</sup>

Obtained Eq. (16) is expressed in relative units and after the conversion, we

0

BBBBBB@

Relative mean square error method for determining the conductivity of the capacitive isolation mains phases relative to the ground is determined by the

U2 <sup>C</sup>�U<sup>2</sup> ð Þ<sup>A</sup> 2

18 1 � <sup>U</sup><sup>2</sup>

U2 <sup>C</sup>�U<sup>2</sup> ð Þ<sup>A</sup> 2

U2 <sup>C</sup>∗�U<sup>2</sup> ð Þ <sup>A</sup><sup>∗</sup>

þ 3U<sup>4</sup> <sup>A</sup><sup>∗</sup> <sup>U</sup><sup>2</sup>

þ U<sup>4</sup> <sup>C</sup><sup>∗</sup> <sup>1</sup>�U<sup>2</sup> ð Þ <sup>A</sup><sup>∗</sup> 2

A∗ � �<sup>2</sup> � <sup>U</sup><sup>2</sup>

<sup>C</sup>∗�U<sup>2</sup> ð Þ <sup>A</sup>∗�<sup>2</sup> <sup>2</sup>

<sup>2</sup> þ

<sup>2</sup> � �<sup>2</sup> þ

<sup>2</sup> <sup>27</sup>U<sup>2</sup> ph <sup>U</sup><sup>2</sup> ph�U<sup>2</sup> A � �� <sup>U</sup><sup>2</sup>

0

BBBBBBB@

<sup>C</sup>�U<sup>2</sup> ð Þ<sup>A</sup>

<sup>þ</sup>U<sup>4</sup> <sup>C</sup> <sup>U</sup><sup>2</sup> ph�U<sup>2</sup> A � �<sup>2</sup>

ph � <sup>U</sup><sup>2</sup> A � �<sup>2</sup>

<sup>2</sup> � �<sup>2</sup>

U2 <sup>C</sup>�U<sup>2</sup> ð Þ<sup>A</sup>

<sup>C</sup>�U<sup>2</sup> ð Þ<sup>A</sup>

<sup>2</sup> <sup>3</sup>U<sup>2</sup> <sup>l</sup> <sup>U</sup><sup>2</sup>

<sup>C</sup> � <sup>U</sup><sup>2</sup> A � � � <sup>2</sup>U<sup>2</sup>

<sup>l</sup> � <sup>3</sup>U<sup>2</sup> A � �<sup>2</sup> � <sup>U</sup><sup>2</sup>

� �<sup>4</sup> h i

l

� �<sup>2</sup> n o

<sup>þ</sup>U<sup>4</sup> <sup>C</sup> U<sup>2</sup> <sup>l</sup> �3U<sup>2</sup> ð Þ<sup>A</sup>

<sup>2</sup> � �<sup>2</sup>

<sup>C</sup>�U<sup>2</sup> ð Þ<sup>A</sup>

<sup>þ</sup> <sup>U</sup><sup>4</sup> <sup>C</sup> U<sup>2</sup>

<sup>C</sup> � <sup>U</sup><sup>2</sup> A

þ

1

0:5

(13)

(15)

þ

1

0:5

CCCCCCCA

(16)

þ

1

0:5

,

(17)

CCCCCCA

CA

: (14)

<sup>l</sup> � <sup>3</sup>U<sup>2</sup> A

1

0:5

CCCCA

1

0:5

CCCCA

� <sup>U</sup><sup>2</sup>

<sup>C</sup><sup>∗</sup> � <sup>U</sup><sup>2</sup> A∗ � �<sup>4</sup>

<sup>2</sup> þ

<sup>C</sup> � <sup>U</sup><sup>2</sup> A � �<sup>4</sup>

the values of the partial absolute errors (11), at the same time, assuming that

<sup>A</sup> 3 U<sup>2</sup>

<sup>l</sup> �3U<sup>2</sup> ð Þ<sup>A</sup> � <sup>U</sup><sup>2</sup>

ΔU<sup>∗</sup> ¼ ΔR<sup>∗</sup> ¼ Δ, we obtain:

U2 <sup>C</sup> � <sup>U</sup><sup>2</sup> A � �<sup>2</sup> 2U<sup>4</sup>

0

B@

Obtained Eq. (13) divided by Eq. (2):

<sup>ε</sup><sup>g</sup> <sup>¼</sup> <sup>Δ</sup><sup>g</sup> Δ ¼

<sup>ε</sup><sup>g</sup> <sup>¼</sup> <sup>Δ</sup><sup>g</sup>

ph � <sup>U</sup><sup>2</sup> A

� �

<sup>Δ</sup> <sup>¼</sup> <sup>3</sup> 27 1 � <sup>U</sup><sup>2</sup>

Uph

A∗ � � � <sup>U</sup><sup>2</sup>

and <sup>U</sup><sup>С</sup><sup>∗</sup> <sup>¼</sup> <sup>U</sup><sup>С</sup>

<sup>ε</sup><sup>g</sup> <sup>¼</sup> <sup>3</sup> 27U<sup>2</sup> ph U<sup>2</sup>

obtain:

<sup>ε</sup><sup>g</sup> <sup>¼</sup> <sup>Δ</sup><sup>g</sup>

where <sup>U</sup><sup>А</sup><sup>∗</sup> <sup>¼</sup> UA

expression (3):

56

<sup>Δ</sup> <sup>¼</sup> <sup>3</sup>

<sup>þ</sup>U<sup>4</sup> <sup>l</sup> U<sup>4</sup>

0

BBBB@

2U<sup>4</sup> <sup>l</sup> <sup>U</sup><sup>2</sup> <sup>l</sup> �3U<sup>2</sup> ð Þ<sup>A</sup> 2 � <sup>U</sup><sup>2</sup> <sup>C</sup>�U<sup>2</sup> ð Þ<sup>A</sup> 4

3U<sup>2</sup> <sup>l</sup> <sup>U</sup><sup>2</sup>

phase voltages in accordance with the fact that U<sup>l</sup> ¼ 1:73Uф:

0

BBBB@

� <sup>U</sup><sup>2</sup>

18U<sup>4</sup> ph <sup>U</sup><sup>2</sup> ph�U<sup>2</sup> A � �<sup>2</sup>

27U<sup>2</sup> ph <sup>U</sup><sup>2</sup> ph�U<sup>2</sup> A � �� <sup>U</sup><sup>2</sup>

U2 <sup>C</sup>�U<sup>2</sup> ð Þ<sup>A</sup>

<sup>C</sup> � <sup>U</sup><sup>2</sup> A � �<sup>2</sup>

<sup>C</sup><sup>∗</sup> � <sup>U</sup><sup>2</sup> A∗ � �<sup>2</sup>

Uph.

þ 3U<sup>4</sup> phU<sup>4</sup> <sup>A</sup> <sup>U</sup><sup>2</sup> C�U<sup>2</sup> A�2U<sup>2</sup> ph � �<sup>2</sup>

Simplifying the formula (15), we obtain the Eq. (16):

U2 <sup>C</sup>�U<sup>2</sup> ð Þ<sup>A</sup>

þ U<sup>4</sup> <sup>l</sup> <sup>U</sup><sup>4</sup> <sup>A</sup> 3 U<sup>2</sup>

<sup>Δ</sup> <sup>¼</sup> <sup>3</sup>go U2 <sup>C</sup> � <sup>U</sup><sup>2</sup> A � �<sup>3</sup>

Industrial Engineering

Δg

$$\varepsilon\_{b} = \frac{\Delta b}{\Delta} = \frac{\left[\left(\mathbf{1} - \tan^{2}\delta\right)^{2} \left(\frac{\Delta y}{\Delta}\right)^{2} + \left(\frac{\Delta y}{\Delta}\right)^{2}\right]^{0.5}}{\tan^{2}\delta}.\tag{19}$$

Solving Eq. (19) and substituting the values of mathematical descriptions of the relative rms dependences of total (8) and active (16) conductivities of electrical installations phase insulation relative to the ground phase, we get the following equation:

$$\varepsilon\_{b} = \frac{\Delta b}{\Delta} = \frac{\begin{pmatrix} \left(\mathbf{1} - \left[\tan^{2}\delta\right]^{2} \left[2 + \frac{4U\_{c}^{4} + \left(U\_{C}^{2} + U\_{A}^{2}\right)^{2}}{\left(\upsilon\_{C}^{2} - \upsilon\_{A}^{2}\right)^{2}}\right] + \\\\ \frac{9}{\left[2\Im U\_{ph}^{2}\left(U\_{ph}^{2} - U\_{A}^{2}\right) - \left(U\_{C}^{2} - U\_{A}^{2}\right)^{2}\right]^{2}} \times \\\\ \times \begin{pmatrix} \mathbf{18U}\_{ph}^{2} \left(U\_{ph}^{2} - U\_{A}^{2}\right)^{2} - \left(U\_{C}^{2} - U\_{A}^{2}\right)^{4} + \\\\ + \frac{3U\_{ph}^{4}U\_{A}^{4}\left(\upsilon\_{C}^{2} - U\_{A}^{2} - 2U\_{ph}^{2}\right) + U\_{C}^{4}\left(U\_{ph}^{2} - U\_{A}^{2}\right)^{2}}{\left(\upsilon\_{C}^{2} - \upsilon\_{A}^{2}\right)^{2}} \end{pmatrix}}{\tan^{2}\delta} \end{pmatrix}^{0.5}$$

Obtained Eq. (21) is expressed in relative units and after the conversion, we obtain:

$$\varepsilon\_{b} = \frac{\Delta b}{\Delta} = \frac{\left(\left(\mathbf{1} - \tan^{2}\delta\right)^{2} \left[\mathbf{2} + \frac{4U\_{\mathrm{Ca}}^{4} + \left(U\_{\mathrm{Ca}}^{2} + U\_{\mathrm{As}}^{2}\right)^{2}}{\left(U\_{\mathrm{Ca}}^{2} - U\_{\mathrm{As}}^{2}\right)^{2}}\right] + \right.}{\left[\left.\left.\left(\mathbf{1} - U\_{\mathrm{As}}^{2}\right) - \left(U\_{\mathrm{Ca}}^{2} - U\_{\mathrm{As}}^{2}\right)^{2}\right]^{2} \times \right.}} \times \left. \begin{aligned} \left.\left(\mathbf{1} - \mathbf{1} - \mathbf{1} \right)^{2} & \leq \\ \left.\mathbf{1} - \left(U\_{\mathrm{As}}^{2} \right)^{2} - \left(U\_{\mathrm{Ca}}^{2} - U\_{\mathrm{As}}^{2}\right)^{4} + \right. \\ \left. \left. + \frac{3U\_{\mathrm{As}}^{4} \left(U\_{\mathrm{Ca}}^{2} - U\_{\mathrm{As}}^{2} - \right)^{2} + U\_{\mathrm{Co}}^{4} \left(\mathbf{1} - U\_{\mathrm{As}}^{2}\right)^{2}}{\left(U\_{\mathrm{Co}}^{2} - U\_{\mathrm{As}}^{2}\right)^{2}} \right. \right] \end{aligned} \right] \right) \tag{21}$$

Based on the results of random relative mean square errors in determining the active, capacitive, and total conductivities of mains phase isolation relative to the ground, build the dependence:

$$\varepsilon\_{\mathcal{Y}} = \frac{\Delta \mathcal{Y}\_{\*}}{\Delta} = f(U\_{\*});$$

$$\varepsilon\_{\mathcal{Y}} = \frac{\Delta \mathbf{g}\_{\*}}{\Delta} = f(U\_{A\*}, U\_{C\*});$$

$$\varepsilon\_{b} = \frac{\Delta b\_{\*}}{\Delta} = f(U\_{A\*}, U\_{C\*}, \text{ } \mathbf{tan}\ \delta),$$

shown in Figures 1–3. Mathematical dependence of the relative mean square errors of the total—εy, active—εg, and capacitive—ε<sup>b</sup> conductivities of phase insulation of electrical network with insulated neutral on graphic illustrations

(Figures 1–3) characterize the change in error depending on the amount of additional active conduction gо, which is inserted between the A-phase of electrical network and earth.

In determining the parameters of isolation in a symmetrical three-phase electrical network with isolated neutral on the basis of the method of analysis of error for each specific network, select additional active conduction, so as to ensure the satisfactory accuracy required.

In determining the total conductance of mains phases isolation relative to the ground is chosen such additional active conductivity, the values were within U<sup>∗</sup> = 0.2–0.8, at the same time as shown in Figure 1, the error does not exceed 5% when using measuring devices with accuracy class 1.0, and 2.5% when using measuring devices with accuracy class 0.5.

In determining the value of the active conductance in the three-phase electrical network with insulated neutral voltage up to 1000 V and above, select this additional gо, so that U<sup>А</sup><sup>∗</sup> = 0.2–0.8, when U<sup>С</sup><sup>∗</sup> = 1.1–1.6, then on the basis of graphic illustrations of Figure 2, error does not exceed 3.5% when using measuring devices with accuracy class 1.0.

In determining the capacitive conductance mains phase isolation relative to the ground selection of additional active conductance g<sup>о</sup> based on a graphic illustrations of Figure 3 so that U<sup>А</sup><sup>∗</sup> = 0.2–0.8, when U<sup>С</sup><sup>∗</sup> = 1.1–1.6, when tan δ = 1.0, to provide error to 4% when using measuring devices with accuracy class 1.0.

It should be noted that when using measuring instruments with an accuracy class of 0.5, errors of εy—total, εg—active, εb—capacitive admittances of isolation is reduced by half, to provide more reliable data when determining the insulation parameters developed method.

According to the research undertaken by Professor L. Gladilin, a method was developed for determining the parameters of the insulation in networks with an isolated neutral voltage up to 1000 V (method ammeter-voltmeter) [1]. The disadvantage of the method ammeter-voltmeter is the production of single-phase ground

fault current measurement in the study of a three-phase power network with an isolated neutral. When measuring single-phase ground fault current in three-phase power network, the magnitude-phase voltage is equal to zero. The voltages of the other two phases achieve linear value, it can lead to a two- or three-phase short circuit, and it is emergency operating mode. This leads to a break in supply, as well

Analysis of the error in determining the capacitive conductance of the network insulation when tan δ = 1.0.

Analysis of the error in determining the active conductance of the network insulation. UC<sup>∗</sup> = 1.1; 1.2; 1.3; 1.4.

Special Issues of Ensuring Electrical Safety in Networks with Isolated Neutral Voltage…

DOI: http://dx.doi.org/10.5772/intechopen.81384

as increased contact voltage, which is dangerous in the operation of mining

machines and systems [1].

Figure 2.

Figure 3.

59

UC<sup>∗</sup> = 1.1; 1.2; 1.3; 1.4.

Figure 1. Analysis of the error in determining the total conductance of the network insulation.

Special Issues of Ensuring Electrical Safety in Networks with Isolated Neutral Voltage… DOI: http://dx.doi.org/10.5772/intechopen.81384

Figure 2. Analysis of the error in determining the active conductance of the network insulation. UC<sup>∗</sup> = 1.1; 1.2; 1.3; 1.4.

#### Figure 3.

(Figures 1–3) characterize the change in error depending on the amount of additional active conduction gо, which is inserted between the A-phase of electrical

In determining the parameters of isolation in a symmetrical three-phase electrical network with isolated neutral on the basis of the method of analysis of error for each specific network, select additional active conduction, so as to ensure the

In determining the total conductance of mains phases isolation relative to the ground is chosen such additional active conductivity, the values were within U<sup>∗</sup> = 0.2–0.8, at the same time as shown in Figure 1, the error does not exceed 5% when using measuring devices with accuracy class 1.0, and 2.5% when using measuring

In determining the value of the active conductance in the three-phase electrical network with insulated neutral voltage up to 1000 V and above, select this additional gо, so that U<sup>А</sup><sup>∗</sup> = 0.2–0.8, when U<sup>С</sup><sup>∗</sup> = 1.1–1.6, then on the basis of graphic illustrations of Figure 2, error does not exceed 3.5% when using measuring devices

In determining the capacitive conductance mains phase isolation relative to the ground selection of additional active conductance g<sup>о</sup> based on a graphic illustrations of Figure 3 so that U<sup>А</sup><sup>∗</sup> = 0.2–0.8, when U<sup>С</sup><sup>∗</sup> = 1.1–1.6, when tan δ = 1.0, to provide

It should be noted that when using measuring instruments with an accuracy class of 0.5, errors of εy—total, εg—active, εb—capacitive admittances of isolation is reduced by half, to provide more reliable data when determining the insulation

According to the research undertaken by Professor L. Gladilin, a method was developed for determining the parameters of the insulation in networks with an isolated neutral voltage up to 1000 V (method ammeter-voltmeter) [1]. The disadvantage of the method ammeter-voltmeter is the production of single-phase ground

error to 4% when using measuring devices with accuracy class 1.0.

Analysis of the error in determining the total conductance of the network insulation.

network and earth.

Industrial Engineering

satisfactory accuracy required.

devices with accuracy class 0.5.

parameters developed method.

Figure 1.

58

with accuracy class 1.0.

Analysis of the error in determining the capacitive conductance of the network insulation when tan δ = 1.0. UC<sup>∗</sup> = 1.1; 1.2; 1.3; 1.4.

fault current measurement in the study of a three-phase power network with an isolated neutral. When measuring single-phase ground fault current in three-phase power network, the magnitude-phase voltage is equal to zero. The voltages of the other two phases achieve linear value, it can lead to a two- or three-phase short circuit, and it is emergency operating mode. This leads to a break in supply, as well as increased contact voltage, which is dangerous in the operation of mining machines and systems [1].

The developed method provides satisfactory accuracy when determining the parameters of isolation, as well as the ease and safety of production work in existing electrical installations voltages up to and above 1000 V.

To determine the conductance network isolation by using the equal quantities of module phase voltage to earth and zero phase-sequence voltage Uph<sup>о</sup> ¼ Uо,

ph � <sup>2</sup>U<sup>2</sup>

Capacitive susceptance of isolation is found as a geometric difference between

The method for determining the parameters of insulation in a network with an isolated neutral voltage above 1000 V describes circular chart changes in the modulus phase voltage to earth and zero phase-sequence voltage as shown in Figure 4. Changes in the modulus phase voltage to earth and zero phase-sequence voltage are produced in accordance with the circular chart of changes in the magnitude of the

Figure 4 shows the phase voltages Uph of three phases A, B, and C, before connecting additional conductance to phase A; neutral-point displacement voltage Uо; and phase voltage to earth after connecting additional conductance go to phase

Experimental studies of the circular chart have shown that changes of the modulus phase voltage to earth and zero phase-sequence voltage depends on the selection of the magnitude of the additional conductance. Hereby it is consistent with the fundamental provisions of the theoretical fundamentals of electrical

3.3 The method of measuring the admittance in a network with an isolated

voltage with the connected additional conductance, an additional conductance

To ensure the equal quantities of phase voltage to earth and zero phase-sequence

A circular chart changes the modulus phase voltage to earth and zero phase-sequence voltage, depending on the

A—Uph<sup>о</sup>. Point 02 corresponds to equal quantities of Uph<sup>о</sup> and Uо2.

2U<sup>2</sup> pho pho

go: (23)

<sup>y</sup> <sup>¼</sup> <sup>U</sup><sup>2</sup>

Special Issues of Ensuring Electrical Safety in Networks with Isolated Neutral Voltage…

the admittance of insulation and conductance [7].

DOI: http://dx.doi.org/10.5772/intechopen.81384

equation is

additional conductance.

neutral voltage up to 1000 V

engineering.

Figure 4.

61

size of the additional conductance.

## 3. Modeling method for measuring the admittance of insulation in a network with an isolated neutral voltage up to 1000 V in mines using Matlab/Simulink

#### 3.1 Introduction

Note that the conductance characterizes the insulating properties of the dielectric, and the susceptance, respectively, characterizes the network capacity, that is, the number of connected electrical receivers and the length of overhead lines and cables. Admittance characterizes the single-phase ground fault current. Therefore, in practice, it is necessary to know the operation of the electrical conductance, susceptance, and admittance of phase of electrical network with respect to earth. This will allow choosing the right strategy to develop organizational and technical measures to increase the level of electrical networks up to 1000 V in the development of coal deposits [30].

Developed in [31], a phase-sensitive method for determining the parameters of insulation in a symmetric network with an isolated neutral voltage up to 1000 is based on the measurement of the modulus of the line voltage and phase voltage to earth after the connection between it and the earth an additional conductance and measuring the phase angle between the vector of the line voltage and vector of the phase voltage to earth. The above phase-sensitive method for determining the insulation contains significant disadvantages in using a special measuring device for measuring the phase angle between the voltage vectors.

#### 3.2 Theoretical studies of the insulation on the basis of a circular chart

For simplicity of measurements, consider a method for measuring the admittance of insulation in a network with an isolated neutral voltage up to 1000 V [7]:

$$\mathbf{y} = \frac{U\_{\text{pho}}}{U\_o} \mathbf{g}\_o. \tag{22}$$

where Uph<sup>о</sup> is phase voltage to earth after connecting additional conductance go; go is additional conductance; and U<sup>о</sup> is zero phase-sequence voltage.

To measure the admittance of insulation in a network in accordance with the formula (22), it is necessary to enter into the electrical network adjustable resistance between the phase of network and earth. Changing the value of resistance between the phase of network and earth will change the quantities of module phase voltage to earth and zero phase-sequence voltage. From Eq. (22) is obtained the conclusion that with equal admittance of insulation in a network and additional conductance, which is inserted between the phase of network and earth, measured values of the quantities of module phase voltage to earth and zero phase-sequence voltage will be equal:

$$\mathcal{Y} = \mathcal{g}\_o \text{ at } U\_{\text{pho}} = U\_o.$$

On the basis of the foregoing information, for measuring the admittance of insulation in a network with an isolated neutral, it is necessary to enter adjustable resistance to fulfill equality conditions between the values of the modules phase voltage to earth and zero phase-sequence voltage Uph<sup>о</sup> ¼ Uо.

Special Issues of Ensuring Electrical Safety in Networks with Isolated Neutral Voltage… DOI: http://dx.doi.org/10.5772/intechopen.81384

To determine the conductance network isolation by using the equal quantities of module phase voltage to earth and zero phase-sequence voltage Uph<sup>о</sup> ¼ Uо, equation is

$$\mathbf{y} = \frac{\mathbf{U}\_{\mathrm{ph}}^2 - 2\mathbf{U}\_{\mathrm{pho}}^2}{2\mathbf{U}\_{\mathrm{pho}}^2} \mathbf{g}\_o. \tag{23}$$

Capacitive susceptance of isolation is found as a geometric difference between the admittance of insulation and conductance [7].

The method for determining the parameters of insulation in a network with an isolated neutral voltage above 1000 V describes circular chart changes in the modulus phase voltage to earth and zero phase-sequence voltage as shown in Figure 4. Changes in the modulus phase voltage to earth and zero phase-sequence voltage are produced in accordance with the circular chart of changes in the magnitude of the additional conductance.

Figure 4 shows the phase voltages Uph of three phases A, B, and C, before connecting additional conductance to phase A; neutral-point displacement voltage Uо; and phase voltage to earth after connecting additional conductance go to phase A—Uph<sup>о</sup>. Point 02 corresponds to equal quantities of Uph<sup>о</sup> and Uо2.

Experimental studies of the circular chart have shown that changes of the modulus phase voltage to earth and zero phase-sequence voltage depends on the selection of the magnitude of the additional conductance. Hereby it is consistent with the fundamental provisions of the theoretical fundamentals of electrical engineering.

#### 3.3 The method of measuring the admittance in a network with an isolated neutral voltage up to 1000 V

To ensure the equal quantities of phase voltage to earth and zero phase-sequence voltage with the connected additional conductance, an additional conductance

#### Figure 4.

A circular chart changes the modulus phase voltage to earth and zero phase-sequence voltage, depending on the size of the additional conductance.

The developed method provides satisfactory accuracy when determining the parameters of isolation, as well as the ease and safety of production work in existing

3. Modeling method for measuring the admittance of insulation in a network with an isolated neutral voltage up to 1000 V in mines using

Note that the conductance characterizes the insulating properties of the dielectric, and the susceptance, respectively, characterizes the network capacity, that is, the number of connected electrical receivers and the length of overhead lines and cables. Admittance characterizes the single-phase ground fault current. Therefore, in practice, it is necessary to know the operation of the electrical conductance, susceptance, and admittance of phase of electrical network with respect to earth. This will allow choosing the right strategy to develop organizational and technical measures to increase the level of electrical networks up to 1000 V in the develop-

Developed in [31], a phase-sensitive method for determining the parameters of insulation in a symmetric network with an isolated neutral voltage up to 1000 is based on the measurement of the modulus of the line voltage and phase voltage to earth after the connection between it and the earth an additional conductance and measuring the phase angle between the vector of the line voltage and vector of the phase voltage to earth. The above phase-sensitive method for determining the insulation contains significant disadvantages in using a special measuring device for

3.2 Theoretical studies of the insulation on the basis of a circular chart

For simplicity of measurements, consider a method for measuring the admittance of insulation in a network with an isolated neutral voltage up to 1000 V [7]:

where Uph<sup>о</sup> is phase voltage to earth after connecting additional conductance go;

To measure the admittance of insulation in a network in accordance with the formula (22), it is necessary to enter into the electrical network adjustable resistance between the phase of network and earth. Changing the value of resistance between the phase of network and earth will change the quantities of module phase voltage to earth and zero phase-sequence voltage. From Eq. (22) is obtained the conclusion that with equal admittance of insulation in a network and additional conductance, which is inserted between the phase of network and earth, measured values of the quantities of module phase voltage to earth and zero phase-sequence voltage will be equal:

y ¼ go at Uph<sup>о</sup> ¼ Uо:

On the basis of the foregoing information, for measuring the admittance of insulation in a network with an isolated neutral, it is necessary to enter adjustable resistance to fulfill equality conditions between the values of the modules phase

go, (22)

<sup>y</sup> <sup>¼</sup> <sup>U</sup>ph<sup>о</sup> U<sup>о</sup>

go is additional conductance; and U<sup>о</sup> is zero phase-sequence voltage.

voltage to earth and zero phase-sequence voltage Uph<sup>о</sup> ¼ Uо.

60

electrical installations voltages up to and above 1000 V.

measuring the phase angle between the voltage vectors.

Matlab/Simulink

ment of coal deposits [30].

3.1 Introduction

Industrial Engineering

#### Figure 5.

Electrical schematic diagram of a method of measuring the admittance of network.

variable resistance is used. The variable resistor is connected between the measured electrical network phase and earth. Then the resistance regulation is provided to ensure equality between the voltage phase to earth and zero sequence voltage. In case of equal voltage, magnitude of admittance will correspond to the value of variable resistance, which is connected between the phase of network and earth. The method for measuring the admittance of insulation in a network with an isolated neutral voltage up to 1000 V will provide improved accuracy and speed measurement admittance network insulation [32].

comprises three-phase source voltage 380/220 V; active-reactive resistance RC-RC2; zero phase-sequence voltage filter made by three single-phase voltage transformers; voltage and current measurements; oscillograph (scope) to display network settings; and displays to show the amplitude and true values of the electrical

Special Issues of Ensuring Electrical Safety in Networks with Isolated Neutral Voltage…

In the metal single-phase A ground short circuit operating conditions, the amplitude value of phase C voltage to earth was equal to 537 V, which corresponds to the true value of 380 V. The RMS value of phase A voltage to earth after the metal single-phase ground short circuit corresponds to 0.001009 V, with the current value of the faulty phase A being equal to 0.1057 A. From the findings of the zero phase-sequence voltage filter, the true value of the voltage increased from zero to

The simulation model of the method of measuring the admittance of insulation

An application of the variable resistor enables the production of multiple controls for the electrical network parameters. According to the method described previously, a switching device is introduced to adjust the additional conductance. A block breaker is then added to the switching device. The additional conductance is represented by a variable resistor, namely, nonlinear R. A subsystem of the variable resistor R is shown in Figure 9. It is possible to use block slider gain to adjust the

In the diagram, the controlled current source is connected in parallel with a voltage measurement. Between the output of the voltage measurement and the input of the controlled current source, the Simulink model is turned on, which implements the voltage-current characteristic of the device. In parallel to the controlled current source, decoupling resistor series RLC branch is also connected. Its

with variable resistor R is shown in Figure 8. From the diagram, as a variable resistor R is connected between the measured phase of network and earth, a

To test the electrical schematic diagram, operating conditions were simulated by using a metal single-phase ground short circuit, which was carried out by way of a block breaker. A time-modulating circuit of 0.2 s was implemented by way of a block step. Block RMS allows for the calculation of the true RMS value of the input

parameters.

Figure 6.

signal [33].

218.4 V (Figure 7).

parameters of the resistor.

63

nonlinear resistor R diagram is used [34].

Simulation model of the metal single phase ground short circuit.

DOI: http://dx.doi.org/10.5772/intechopen.81384

The measurements of phase voltage to earth and zero phase-sequence voltage produced an AC voltmeter. The zero phase-sequence voltage is released from the network by using three single-phase transformers; the primary windings are connected in a star and the secondary windings are connected into an open triangle.

Developing the method of measuring the admittance in a network with an isolated neutral voltage 1000 V is explained in the schematic circuit diagram shown in Figure 5. The electrical schematic circuit comprises the electrical network, with phases А, В, and С; three single-phase voltage transformers TV1,TV2, and TV3; voltmeter PV1, measured quantities of module of the zero phase-sequence voltage; voltmeter PV2, measured module of phase voltage to earth; switching device QF1, introduction of adjustable additional conductance; additional conductance go; and admittance of network y.

The method is as follows: for measuring the admittance of the network, the voltmeter PV2 measures the phase voltage to earth; the voltmeter PV1 measures the zero phase-sequence voltage on the secondary winding of single-phase voltage transformers TV1,TV2, and TV3. Switching device QF1 connects the adjustable additional conductance go, making the regulation of the magnitude of additional conductance to achieve the equality of the modulus of the phase voltage to earth and the zero phase-sequence voltage. In this case, the value of additional conductance will fit the admittance of network [32].

#### 3.4 Modeling method of measuring the admittance of insulation in a network with an isolated neutral voltage up to 1000 V using Matlab/Simulink

As a tool for analyzing the operating conditions of power network, the package Matlab/Simulink has been used. The package has a sufficiently developed set of special blocks for modeling elements of the power system.

Matlab/Simulink enables an electrical schematic diagram of a method of measuring the admittance of insulation to be implemented (Figure 6). The diagram

Special Issues of Ensuring Electrical Safety in Networks with Isolated Neutral Voltage… DOI: http://dx.doi.org/10.5772/intechopen.81384

#### Figure 6.

variable resistance is used. The variable resistor is connected between the measured electrical network phase and earth. Then the resistance regulation is provided to ensure equality between the voltage phase to earth and zero sequence voltage. In case of equal voltage, magnitude of admittance will correspond to the value of variable resistance, which is connected between the phase of network and earth. The method for measuring the admittance of insulation in a network with an isolated neutral voltage up to 1000 V will provide improved accuracy and speed

The measurements of phase voltage to earth and zero phase-sequence voltage produced an AC voltmeter. The zero phase-sequence voltage is released from the network by using three single-phase transformers; the primary windings are connected in a star and the secondary windings are connected into an open triangle. Developing the method of measuring the admittance in a network with an isolated neutral voltage 1000 V is explained in the schematic circuit diagram shown in Figure 5. The electrical schematic circuit comprises the electrical network, with phases А, В, and С; three single-phase voltage transformers TV1,TV2, and TV3; voltmeter PV1, measured quantities of module of the zero phase-sequence voltage; voltmeter PV2, measured module of phase voltage to earth; switching device QF1, introduction of adjustable additional conductance; additional conductance go; and

The method is as follows: for measuring the admittance of the network, the voltmeter PV2 measures the phase voltage to earth; the voltmeter PV1 measures the zero phase-sequence voltage on the secondary winding of single-phase voltage transformers TV1,TV2, and TV3. Switching device QF1 connects the adjustable additional conductance go, making the regulation of the magnitude of additional conductance to achieve the equality of the modulus of the phase voltage to earth and the zero phase-sequence voltage. In this case, the value of additional conduc-

3.4 Modeling method of measuring the admittance of insulation in a network with an isolated neutral voltage up to 1000 V using Matlab/Simulink

As a tool for analyzing the operating conditions of power network, the package Matlab/Simulink has been used. The package has a sufficiently developed set of

Matlab/Simulink enables an electrical schematic diagram of a method of measuring the admittance of insulation to be implemented (Figure 6). The diagram

measurement admittance network insulation [32].

Electrical schematic diagram of a method of measuring the admittance of network.

tance will fit the admittance of network [32].

special blocks for modeling elements of the power system.

admittance of network y.

62

Figure 5.

Industrial Engineering

Simulation model of the metal single phase ground short circuit.

comprises three-phase source voltage 380/220 V; active-reactive resistance RC-RC2; zero phase-sequence voltage filter made by three single-phase voltage transformers; voltage and current measurements; oscillograph (scope) to display network settings; and displays to show the amplitude and true values of the electrical parameters.

To test the electrical schematic diagram, operating conditions were simulated by using a metal single-phase ground short circuit, which was carried out by way of a block breaker. A time-modulating circuit of 0.2 s was implemented by way of a block step. Block RMS allows for the calculation of the true RMS value of the input signal [33].

In the metal single-phase A ground short circuit operating conditions, the amplitude value of phase C voltage to earth was equal to 537 V, which corresponds to the true value of 380 V. The RMS value of phase A voltage to earth after the metal single-phase ground short circuit corresponds to 0.001009 V, with the current value of the faulty phase A being equal to 0.1057 A. From the findings of the zero phase-sequence voltage filter, the true value of the voltage increased from zero to 218.4 V (Figure 7).

The simulation model of the method of measuring the admittance of insulation with variable resistor R is shown in Figure 8. From the diagram, as a variable resistor R is connected between the measured phase of network and earth, a nonlinear resistor R diagram is used [34].

An application of the variable resistor enables the production of multiple controls for the electrical network parameters. According to the method described previously, a switching device is introduced to adjust the additional conductance. A block breaker is then added to the switching device. The additional conductance is represented by a variable resistor, namely, nonlinear R. A subsystem of the variable resistor R is shown in Figure 9. It is possible to use block slider gain to adjust the parameters of the resistor.

In the diagram, the controlled current source is connected in parallel with a voltage measurement. Between the output of the voltage measurement and the input of the controlled current source, the Simulink model is turned on, which implements the voltage-current characteristic of the device. In parallel to the controlled current source, decoupling resistor series RLC branch is also connected. Its

#### Figure 7.

Voltage and current for metal single phase ground short circuit: 1—phase C voltage to earth, V; 2—phase A voltage to earth, V; 3—current under A phase-to-ground fault, A; 4—zero phase-sequence-voltage, V. Phaseto-ground fault time 0.2 s.

#### Figure 8.

Simulation model of a method of measuring the admittance of insulation in Simulink: display RMS—display of the actual data of power grid; nonlinear R—variable resistor to adjust extra conductance, the rest of legend find in Figure 3.

Due to the data received in the regulation of the variable resistor to 2068 Ohms, the true value of the zero phase-sequence voltage and phase A voltage to earth are equal to 140.8 V. Figure 10 shows the amplitude values of the phase voltage and current and zero phase-sequence voltage for the value of the variable resistor

Phase voltage, current and zero phase-sequence voltage: 1—phase A voltage to earth, V; 2—phase A current to

Subsystem of the variable resistor R: VM—voltage meter; transfer Fcn—gain transfer characteristic block; SG—

resistor adjustment slide; RLC branch—decoupling resistor; CCS—adjustable current source.

Special Issues of Ensuring Electrical Safety in Networks with Isolated Neutral Voltage…

DOI: http://dx.doi.org/10.5772/intechopen.81384

Thus, according to the circular chart above, when phase voltage to earth U<sup>А</sup> equals the zero phase-sequence voltage Uо, the variable of the admittance of insulation y corresponds to the variable resistance which is connected between A phase

According to the developed method of measuring the admittance of isolation in a network with isolated neutral voltage up to 1000 V, the variable of the admittance

The simulation model of the method of measuring the admittance of insulation in the Matlab/Simulink environment allows for the regulation of variable resistor to be used and to simplify the calculations of the magnitude of the admittance of insulation in a network with isolated neutral voltages up to 1000 V. The method for measuring the admittance of insulation in a network with an isolated neutral voltage up to 1000 V will allow for an increase in the accuracy and speed of measure-

y corresponds to 2068 Ohms which composes 0.48 mS.

ment of the admittance of network.

earth, A; 3—zero phase-sequence-voltage, V.

R = 2068 Ohms.

and earth.

65

Figure 10.

Figure 9.

presence is due to the fact that a large number of SimPowerSystems blocks are made on the basis of the current sources. When these blocks are connected in series, the current sources are also connected in series which is unacceptable. The presence of the decoupling resistor enables the connection of these blocks in series. The value of the resistor chosen should be sufficiently large to minimize its effect on the characteristics of the created block [34].

The Simulink model of the variable resistor is implemented using a block slider gain, which allows for a change in scalar gain during the simulation using the slider. Thus, the value of the slider gain is regulated until the zero phase-sequence voltage equals the A phase voltage to earth.

Special Issues of Ensuring Electrical Safety in Networks with Isolated Neutral Voltage… DOI: http://dx.doi.org/10.5772/intechopen.81384

#### Figure 9.

Subsystem of the variable resistor R: VM—voltage meter; transfer Fcn—gain transfer characteristic block; SG resistor adjustment slide; RLC branch—decoupling resistor; CCS—adjustable current source.

#### Figure 10.

Phase voltage, current and zero phase-sequence voltage: 1—phase A voltage to earth, V; 2—phase A current to earth, A; 3—zero phase-sequence-voltage, V.

Due to the data received in the regulation of the variable resistor to 2068 Ohms, the true value of the zero phase-sequence voltage and phase A voltage to earth are equal to 140.8 V. Figure 10 shows the amplitude values of the phase voltage and current and zero phase-sequence voltage for the value of the variable resistor R = 2068 Ohms.

Thus, according to the circular chart above, when phase voltage to earth U<sup>А</sup> equals the zero phase-sequence voltage Uо, the variable of the admittance of insulation y corresponds to the variable resistance which is connected between A phase and earth.

According to the developed method of measuring the admittance of isolation in a network with isolated neutral voltage up to 1000 V, the variable of the admittance y corresponds to 2068 Ohms which composes 0.48 mS.

The simulation model of the method of measuring the admittance of insulation in the Matlab/Simulink environment allows for the regulation of variable resistor to be used and to simplify the calculations of the magnitude of the admittance of insulation in a network with isolated neutral voltages up to 1000 V. The method for measuring the admittance of insulation in a network with an isolated neutral voltage up to 1000 V will allow for an increase in the accuracy and speed of measurement of the admittance of network.

presence is due to the fact that a large number of SimPowerSystems blocks are made on the basis of the current sources. When these blocks are connected in series, the current sources are also connected in series which is unacceptable. The presence of the decoupling resistor enables the connection of these blocks in series. The value of the resistor chosen should be sufficiently large to minimize its effect on the charac-

Simulation model of a method of measuring the admittance of insulation in Simulink: display RMS—display of the actual data of power grid; nonlinear R—variable resistor to adjust extra conductance, the rest of legend find

Voltage and current for metal single phase ground short circuit: 1—phase C voltage to earth, V; 2—phase A voltage to earth, V; 3—current under A phase-to-ground fault, A; 4—zero phase-sequence-voltage, V. Phase-

The Simulink model of the variable resistor is implemented using a block slider gain, which allows for a change in scalar gain during the simulation using the slider. Thus, the value of the slider gain is regulated until the zero phase-sequence voltage

teristics of the created block [34].

Figure 8.

Figure 7.

to-ground fault time 0.2 s.

Industrial Engineering

in Figure 3.

64

equals the A phase voltage to earth.
