RU2537852C2 - Method for matching asymmetrical four-wire power transmission line to electrical load - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: invention relates to electrical engineering and can be used during power transmission to the user by means of the asymmetrical uniform four-wire power transmission line being part of the asymmetrical power system. Matching of four-wire power transmission line with electrical load is reached in result of fulfilment of certain conditions involving comparison of actual and reference load resistance, voltages at the line end and currents supplied to the load. In result of the input data processing control signals are generated for adjustment bodies, which may be represented by constant-voltage regulators of power transformers, chokes, three-phase devices and single-phase devices that generate current and voltage such as capacitor banks, four-wire (without the fourth wire from the neutral of the power source or load) generalised loads consisting of step-down transformer, which primary and secondary windings are wye/wye-connected with neutral lead or delta/wye-connected with neutral lead.

EFFECT: reduced losses of electric energy, reduced distortions of voltage and current curves.

6 dwg

Description

The invention relates to electrical engineering and can be used in the design, installation, commissioning and operation of four-wire power lines (power lines), when transmitting electric energy through power lines from a power source to a consumer.

The transmission of electric energy through extended power lines, as well as electric energy of increased frequency through relatively non-extended power lines is ensured by: single- and two-wire power lines with one pair of electromagnetic field waves (incident and reflected); in three-wire - in three pairs; four-wire - four, etc. [12].

As a result of matching the power transmission line with the electric load, the throughput of the power lines increases due to the exclusion of the reflected wave of the electromagnetic field. In addition, the degree of distortion of the voltage and current curves decreases, the reliability of the operation of electrical equipment increases, the operation of relay protection, automation and communication is normalized, the environmental situation in the area of operation of the power transmission line and in the place where the power supply is located is improved.

The condition of the coordinated mode of operation of a single-wire power transmission line [2] is known, due to the second-order differential equation [2-6], on the basis of which the device [patent RU 2390924] operates, where the matching of a single-wire extended high-voltage power line is implemented. However, a four-wire power transmission line described by a mathematical model obtained by solving the eighth-order characteristic equation cannot be matched only by the condition of the matched mode [2] due to the specific distribution of voltages and currents along the four-wire power line [1].

Known methods for matching communication lines with the load [7, patent RU 2381627]. However, the technical elements used here, such as a differential amplifier, differential resistors, are not designed to operate at high voltage, for example, 1 kV, which means that the specifics of the implementation of the methods [7, patent RU 2381627] are quite peculiar and not applicable in long power lines high voltage.

The objective of the invention is the formation of a method for matching a homogeneous asymmetric four-wire power transmission line with an electrical load.

The technical result consists in providing the conditions for matching a homogeneous asymmetric four-wire high-voltage power line with an electric load, the implementation of which will entail a reduction in electric energy losses, an increase in the transmission capacity of the line, and a decrease in the degree of distortion of voltage and current curves.

The technical result is achieved by the fact that the method of matching an asymmetric homogeneous four-wire power line, which is part of an asymmetric electric power system with an electric load, consists in the fact that the initial information about the voltages, currents and their frequency in the line through the interface devices is supplied to the processor, characterized in that the processor checks the conditions for matching the four-wire power line with the electrical load for each wire of the line as a result of comparing actual (present in real time at the facility) and reference (determined using a specialized program) values of load resistances, voltages at the end of the line or currents supplied to the load, and control signals are generated for corrective organs, which can be used on-load tap-changers power transformers with balancing devices, reactors and three-phase or single-phase devices that generate current and voltage, such as capacitor banks, three-wire (b of the fourth neutral conductor of the power supply and load) generalized load having in its composition down transformer, the primary winding connection and the secondary windings of which star / star with the derived neutral conductor.

Corrective bodies, which can be used on-load tap-changers of power transformers with balancing devices, are used without balancing devices.

The generalized load, which may include a step-down transformer, the connection circuit of the primary and secondary windings of which the star / star with the output neutral wire has a step-down transformer, the connection scheme of the primary and secondary windings of which is a triangle / star with the output neutral wire.

The figures show:

1 - corrective body (K01), such as on-load tap-changer transformer;

2 - a transformer (T1), with a balancing device, supplying an asymmetric homogeneous power line with a voltage of 35 kV or less than a four-wire version (power source);

), каковыми являются датчики напряжения и тока, спектроанализаторы, частотомеры, установленные в начале ЛЭП напряжением 35 кВ или меньше;3 - interface devices ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D\mathrm{one}}$$

), which are voltage and current sensors, spectrum analyzers, frequency meters installed at the beginning of power lines with a voltage of 35 kV or less;

4 - analog-to-digital Converter (ADC);

5 - processor (P);

6 - digital-to-analog converter (DAC);

7 - showing or recording device (RO);

8 - asymmetric homogeneous power lines with a voltage of 35 kV or less than a four-wire version (power lines of 35 kV OR LESS 4-wire);

9 - step-down transformer (T2 (4)), with a balancing device, the connection diagram of the primary / secondary winding: star with the output of the neutral wire / star with the output of the neutral wire, voltage 10 kV / 0.4 kV;

), каковыми являются датчики напряжения и тока, спектроанализаторы, частотомеры, установленные на вторичной стороне понижающего трансформатора 9 (Т2(4));10 - interface devices ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D2}$$

), which are voltage and current sensors, spectrum analyzers, frequency meters installed on the secondary side of a step-down transformer 9 (T2 (4));

11 (T3), 26 (T4), 25 (T5), 31 (T7) - blocks of step-down transformers, voltage 220 V / 12 V;

12 - corrective body (K02), such as on-load tap-changer of a step-down transformer with a voltage of 10 kV / 0.4 kV;

13 (VD1), 28 (VD2), 27 (VD3), 33 (VD4) - converter blocks, phase A;

14 - corrective body (KON.), Three-wire (without a fourth conductor from the neutral power source) generalized load;

15 - generalized electrical load (Z _LOAD );

16 - corrective body (KO3), such as reactors and three-phase or single-phase devices that generate current and voltage, such as capacitor banks;

), понижающего трансформатора 9 (Т2(4));17 - the actual generalized load resistance ( $${\underset{\_}{Z}}_{N.\mathrm{BUT}}=\frac{{\dot{U}}_{N.\mathrm{BUT}}}{\dot{I}{2}_{.\mathrm{BUT}}}$$

), step-down transformer 9 (T2 (4));

), понижающего трансформатора 9 (Т2(4));18 - reference generalized load resistance ( $${\underset{\_}{Z}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}}$$

), step-down transformer 9 (T2 (4));

), понижающего трансформатора 9 (Т2(4));19 - actual amplitude values of the load voltage ( $${\dot{U}}_{N.\mathrm{BUT}}$$

), step-down transformer 9 (T2 (4));

), понижающего трансформатора 9 (Т2(4));20 - actual amplitude values of the load current ( $$\dot{I}{2}_{.\mathrm{BUT}}$$

), step-down transformer 9 (T2 (4));

21 is a specialized program for predicting the magnitude of the main characteristics of electric energy in a homogeneous asymmetric four-wire power line (FOUR-WIRE v LOO (1)), to generate a load of a step-down transformer 9 (T2 (4)), in which the connection circuit of the primary / secondary winding : star with the output of the neutral wire / star with the output of the neutral wire, voltage 10 kV / 0.4 kV;

), понижающего трансформатора 9 (Т2(4));22 - reference current values ( $$\dot{I}{2}_{N.\mathrm{BUT}}$$

), step-down transformer 9 (T2 (4));

), понижающего трансформатора 9 (Т2(4));23 - reference voltages ( $${\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}$$

), step-down transformer 9 (T2 (4));

24 - logical block (A ₁ );

29 - step-down transformer (T6 (3)), the connection diagram of the primary and secondary windings: star / star with the output of the neutral wire, voltage 10 kV / 0.4 kV;

), каковыми являются датчики напряжения и тока, спектроанализаторы, частотомеры, установленные на вторичной стороне понижающего трансформатора 29 (Т6(3)), схема соединения которого звезда/звезда с выведенным нулевым проводом;30 - interface devices ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D3}$$

), which are voltage and current sensors, spectrum analyzers, frequency meters installed on the secondary side of the step-down transformer 29 (T6 (3)), the connection diagram of which is star / star with the output neutral wire;

32 - corrective body (K04), such as on-load tap-changer of a step-down transformer, voltage 10 kV / 0.4 kV;

), корректирующего органа 14 (КОн.);34 - generalized electrical load ( $${\underset{\_}{Z}}_N$$

), corrective body 14 (CON);

35 - corrective body (KO5), such as reactors and three-phase or single-phase devices that generate current and voltage, such as capacitor banks;

), каковыми являются датчики напряжения и тока, спектроанализаторы, частотомеры, установленные в конце четырехпроводной однородной несимметричной ЛЭП напряжением 35 кВ или меньше 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная) до точки подключения корректирующего органа 14 (КОн.);36 - interface devices ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D\mathrm{four}}$$

), which are voltage and current sensors, spectrum analyzers, frequency meters installed at the end of a four-wire homogeneous asymmetric power line with a voltage of 35 kV or less than 8 (power line of 35 kV OR LESS 4-wire) to the point of connection of the correcting body 14 (CON);

37 - logical block (A ₂ ), the corrective body 14 (KON.);

), понижающего трансформатора 29 (Т6(3));38 - the actual amplitude values of the load current multiplied by the coefficient of the state of the mode ( $$\dot{I}{A}_{.2}=\dot{I}{2}_{.A\mathrm{.one}}\cdot Kuz$$

), step-down transformer 29 (T6 (3));

), понижающего трансформатора 29 (Т6(3));39 - actual amplitude values of the load current ( $$\dot{I}{2}_{.A\mathrm{.one}}$$

), step-down transformer 29 (T6 (3));

)>понижающего трансформатора 29 (Т6(3));40 - actual amplitude values of the load voltage ( $${\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}$$

)> step-down transformer 29 (T6 (3));

41 - coefficient of the state of the mode ((Kuz = 1) or (Kuz = 0)), equal to unity in the case of the implementation of the specified current and voltage of the four-wire load of the step-down transformer 9 (T2 (4)), powered by an asymmetric homogeneous four-wire line 8 (power transmission line 35 kV OR LESS 4-wire) (Fig. 1), otherwise 41 ((Kuz = 1) or (Kuz = 0)) has a value of zero;

), понижающего трансформатора 29 (Т6(3)), помноженные на коэффициент состояния режима 41 ((Kuz=1) или (Kuz=0));42 - reference values of currents ( $$\dot{I}{2}_{\mathrm{BUT}.N}=\dot{I}{2}_{A.N\mathrm{.one}}\cdot Kuz$$

), step-down transformer 29 (T6 (3)), multiplied by the state coefficient of mode 41 ((Kuz = 1) or (Kuz = 0));

), понижающего трансформатора 29 (Т6(3)), помноженные на коэффициент состояния режима 41 ((Kuz=1) или (Kuz=0));43 - reference values of stresses ( $${\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}={\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN\mathrm{.one}}\cdot Kuz$$

), step-down transformer 29 (T6 (3)), multiplied by the state coefficient of mode 41 ((Kuz = 1) or (Kuz = 0));

), которые в дальнейшем поступают на показывающий или самопишущий прибор 7 (РО);44 - amplitude real voltage values ( $${\dot{U}}_{\mathrm{BUT}N}$$

), which subsequently go to a indicating or recording device 7 (PO);

), которые в дальнейшем поступают на показывающий или самопишущий прибор 7 (РО);45 - amplitude real values of the four-wire load current ( $$\dot{I}{A}_2$$

), which subsequently go to a indicating or recording device 7 (PO);

), понижающего трансформатора 29 (Т6(3));46 - reference generalized load resistance ( $${\underset{\_}{Z}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}=\frac{{\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}}{\dot{I}{2}_{\mathrm{BUT}.N}}$$

), step-down transformer 29 (T6 (3));

), понижающего трансформатора 29 (Т6(3)), помноженные на коэффициент состояния режима;47 - actual amplitude values of the load voltage ( $${\dot{U}}_{\mathrm{BUT}.N}={\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}\cdot Kuz$$

), step-down transformer 29 (T6 (3)), multiplied by the state coefficient of the mode;

), понижающего трансформатора 29 (Т6(3));48 - the actual generalized load resistance ( $${\underset{\_}{Z}}_{\mathrm{BUT}.N}=\frac{{\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}\cdot Ku}{\dot{I}{2}_{.\mathrm{BUT}\mathrm{.one}}\cdot Kz}$$

), step-down transformer 29 (T6 (3));

);49 - determination of the difference in voltage ( $$\Delta \dot{U}={\dot{U}}_{N.\mathrm{BUT}}-{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}$$

);

);50 - determination of the difference in resistance ( $$\Delta \underset{\_}{Z}={\underset{\_}{Z}}_{N.\mathrm{BUT}}-{\underset{\_}{Z}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}$$

);

), понижающего трансформатора 29 (Т6(3));51 - reference current values ( $$\dot{I}{2}_{\mathrm{BUT}.N\mathrm{.one}}$$

), step-down transformer 29 (T6 (3));

), понижающего трансформатора 29 (Т6(3));52 - reference voltage values ( $${\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN\mathrm{.one}}$$

), step-down transformer 29 (T6 (3));

53 - a specialized program (FOUR-WIRE v. 1.00 (2)) for predicting the magnitude of the main characteristics of electric energy of a coordinated homogeneous asymmetric power transmission line of four-wire design 8 (power lines 3 5kV OR LESS 4-wire);

54 - transformer (T1 (8)) without a balancing device, supplying a power line 8 (power line 35 kV OR LESS 4-wire);

55 - step-down transformer (T2 (9)) without a balancing device, the connection diagram of the primary / secondary winding: a star with an output neutral wire / star with an output neutral wire, voltage 10 kV / 0.4 kV;

);56 - additional voltage error (ΔU _O ), determined using the operation of block 10 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D2}$$

);

);57 - additional voltage error (ΔU _P ), determined using the operation of block 30 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D3}$$

);

); 3 ( $${\displaystyle \sum _{i=1}^nД1}$$

); 36 ( $${\displaystyle \sum _{i=1}^nД4}$$

) и 30 ( $${\displaystyle \sum _{i=1}^nД3}$$

);58 - the actual value of the frequency (f), currents and voltages determined using 10 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D2}$$

); 3 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D\mathrm{one}}$$

); 36 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D\mathrm{four}}$$

) and 30 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D3}$$

);

59 - step-down transformer (T8 (3)) connection diagram of the primary and secondary winding: a triangle / star with a neutral wire removed, voltage 10 kV / 0.4 kV.

The essence of the proposed development is to implement, using technical means, the conditions for matching a four-wire asymmetric homogeneous high-voltage power line with an electric load [8], in the formation of an algorithm for ensuring and stabilizing the coordinated operation mode of an extended four-wire power line.

Let it be necessary to match the phase (line wire) A with the electrical load. For phases (linear wires) B and C, the matching algorithm with the electric load will be similar, except for the values of the processed phase voltages, currents, resistances, as well as triggering corrective organs.

). Блоки 9 (Т2(4)), 11 (Т3), 26 (Т4), 25 (Т5), 13 (VD1), 28 (VD2), 27 (VD3) и 15 ( $${\underset{\_}{Z}}_{НАГР.}$$

) образуют часть общего блока, полное сопротивление которого в случае реализации заданной величины тока и напряжения четырехпроводной нагрузки понижающего трансформатора 9 (Т2(4)) питаемой от несимметричной однородной четырехпроводной ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная) определяется величиной 18 ( $${\underset{\_}{Z}}_{ВОЛН.А}=\frac{{\dot{U}}_{ВОЛН.А}}{\dot{I}{2}_{Н.А}}$$

) (рис.2), а в иных случаях - 17 ( $${\underset{\_}{Z}}_{Н.А}=\frac{{\dot{U}}_{Н.А}}{\dot{I}{2}_{.А}}$$

), (рис.2). В данном случае полное сопротивление 18 ( $${\underset{\_}{Z}}_{ВОЛН.А}=\frac{{\dot{U}}_{ВОЛН.А}}{\dot{I}{2}_{Н.А}}$$

) является эталонной величиной, к которой должно стремиться действительное значение 17 ( $${\underset{\_}{Z}}_{Н.А}=\frac{{\dot{U}}_{Н.А}}{\dot{I}{2}_{.А}}$$

). По достижении эталонной величины 18 ( $${\underset{\_}{Z}}_{ВОЛН.А}=\frac{{\dot{U}}_{ВОЛН.А}}{\dot{I}{2}_{Н.А}}$$

) начинает работать следующая часть алгоритма.Figure (1) shows an algorithm for ensuring and stabilizing the matching of a four-wire homogeneous asymmetric power transmission line with an electrical load. Here, an asymmetric homogeneous power line with a voltage of 35 kV or less than a four-wire version of 8 (a power line of 35 kV OR LESS 4-wire) is used as the object of approval. In addition, the use of the following electrical equipment was implemented: transformer 2 (T1) - a transformer with a balancing device [9], supplying power lines with a voltage of 35 kV or less than 8 (power lines of 35 kV OR LESS 4-wire); a transformer with a balancing device 9 (T2 (4)) and a transformer 11 (T3), 26 (T4), 25 (T5) - these are two different groups of step-down transformers having different nominal characteristics; converter blocks 13 (VD1), 28 (VD2), 27 (VD3) - current and voltage converters for computers, phase A, representing in this case a generalized four-wire electrical load 15 ( $${\underset{\_}{Z}}_{N\mathrm{BUT}GR.}$$

) Blocks 9 (T2 (4)), 11 (T3), 26 (T4), 25 (T5), 13 (VD1), 28 (VD2), 27 (VD3) and 15 ( $${\underset{\_}{Z}}_{N\mathrm{BUT}GR.}$$

) form part of a common unit, the total resistance of which in the case of the implementation of the specified current and voltage of the four-wire load of the step-down transformer 9 (T2 (4)) powered by an asymmetric homogeneous four-wire power line 8 (35 kV power line or LESS 4-wire) is determined by the value 18 ( $${\underset{\_}{Z}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}}$$

) (Fig. 2), and in other cases - 17 ( $${\underset{\_}{Z}}_{N.\mathrm{BUT}}=\frac{{\dot{U}}_{N.\mathrm{BUT}}}{\dot{I}{2}_{.\mathrm{BUT}}}$$

), (Fig. 2). In this case, the impedance is 18 ( $${\underset{\_}{Z}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}}$$

) is the reference value to which the actual value 17 ( $${\underset{\_}{Z}}_{N.\mathrm{BUT}}=\frac{{\dot{U}}_{N.\mathrm{BUT}}}{\dot{I}{2}_{.\mathrm{BUT}}}$$

) Upon reaching the reference value of 18 ( $${\underset{\_}{Z}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}}$$

) the next part of the algorithm starts to work.

) образуют лишь часть общего блока, здесь трансформатор 9 (Т2(4)) имеет схему соединения звезда с выведенным нейтральным проводом для первичной и вторичной обмоток, другую часть общего блока образуют: трансформатор 29 (Т6(3)) по схеме соединения звезда/звезда с выведенным нулевым проводом, блок понижающих трансформаторов 31 (Т7), напряжением 220 В/12 В, блок преобразователей 33 (VD4) - преобразователи тока и напряжения компьютеров, фаза А, представляющих в данном случае обобщенную электрическую нагрузку 34 (Z _Н). Блоки 29 (Т6(3)), 31 (Т7), 33 (VD4) и 34 (Z _Н) образуют часть общего блока, полное сопротивление которого позволит реализовать согласование несимметричной однородной четырехпроводной ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная).As already mentioned, blocks 9 (T2 (4)), 11 (T3), 26 (T4), 25 (T5), 13 (VD1), 28 (VD2), 27 (VD3) and 15 ( $${\underset{\_}{Z}}_{N\mathrm{BUT}GR.}$$

) form only a part of the common block, here the transformer 9 (T2 (4)) has a star connection circuit with a neutral wire for the primary and secondary windings, the other part of the common block is formed by a transformer 29 (T6 (3)) according to the star / star connection diagram with a neutral wire removed, a step-down transformer block 31 (T7), voltage 220 V / 12 V, a converter block 33 (VD4) - current and voltage converters for computers, phase A, representing in this case a generalized electric load 34 ( Z _Н ). Blocks 29 (Т6 (3)), 31 (Т7), 33 (VD4) and 34 ( Z _Н ) form part of a common block, the total resistance of which will allow matching of an asymmetric homogeneous four-wire power line 8 (35 kV power line OR LESS 4-wire )

) и 18 ( $${\underset{\_}{Z}}_{ВОЛН.А}=\frac{{\dot{U}}_{ВОЛН.А}}{\dot{I}{2}_{Н.А}}$$

), а в иных случаях соответственно - 48 ( $${\underset{\_}{Z}}_{А.Н}=\frac{{\dot{U}}_{Н.А.1}\cdot Ku}{\dot{I}{2}_{.А.1}\cdot Kz}$$

) и 17 ( $${\underset{\_}{Z}}_{Н.А}=\frac{{\dot{U}}_{Н.А}}{\dot{I}{2}_{.А}}$$

). В данном случае полные сопротивления 46( $${\underset{\_}{Z}}_{А.ВОЛН}=\frac{{\dot{U}}_{А.ВОЛН}}{\dot{I}{2}_{А.Н}}$$

) и 18 ( $${\underset{\_}{Z}}_{ВОЛН.А}=\frac{{\dot{U}}_{ВОЛН.А}}{\dot{I}{2}_{Н.А}}$$

) являются эталонными величинами, к которым должны стремиться соответственно действительные значения 48 ( $${\underset{\_}{Z}}_{А.Н}=\frac{{\dot{U}}_{Н.А.1}\cdot Ku}{\dot{I}{2}_{.А.1}\cdot Kz}$$

) и 17 ( $${\underset{\_}{Z}}_{Н.А}=\frac{{\dot{U}}_{Н.А}}{\dot{I}{2}_{.А}}$$

), в процессе исполнения предлагаемого алгоритма.The resistance of a coordinated homogeneous asymmetric four-wire power line of 35 kV or less than 8 (power line of 35 kV or LESS 4-wire) is determined by the values of 46 ( $${\underset{\_}{Z}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}=\frac{{\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}}{\dot{I}{2}_{\mathrm{BUT}.N}}$$

) and 18 ( $${\underset{\_}{Z}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}}$$

), and in other cases, respectively - 48 ( $${\underset{\_}{Z}}_{\mathrm{BUT}.N}=\frac{{\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}\cdot Ku}{\dot{I}{2}_{.\mathrm{BUT}\mathrm{.one}}\cdot Kz}$$

) and 17 ( $${\underset{\_}{Z}}_{N.\mathrm{BUT}}=\frac{{\dot{U}}_{N.\mathrm{BUT}}}{\dot{I}{2}_{.\mathrm{BUT}}}$$

) In this case, the total resistance is 46 ( $${\underset{\_}{Z}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}=\frac{{\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}}{\dot{I}{2}_{\mathrm{BUT}.N}}$$

) and 18 ( $${\underset{\_}{Z}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}}$$

) are the reference values to which the actual values 48 ( $${\underset{\_}{Z}}_{\mathrm{BUT}.N}=\frac{{\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}\cdot Ku}{\dot{I}{2}_{.\mathrm{BUT}\mathrm{.one}}\cdot Kz}$$

) and 17 ( $${\underset{\_}{Z}}_{N.\mathrm{BUT}}=\frac{{\dot{U}}_{N.\mathrm{BUT}}}{\dot{I}{2}_{.\mathrm{BUT}}}$$

), during the execution of the proposed algorithm.

) или 18 ( $${\underset{\_}{Z}}_{ВОЛН.А}=\frac{{\dot{U}}_{ВОЛН.А}}{\dot{I}{2}_{Н.А}}$$

) (рис.2) понижающего трансформатора 9 (Т2(4)) (рис.1); о состоянии обобщенного сопротивления нагрузки 48 ( $${\underset{\_}{Z}}_{А.Н}=\frac{{\dot{U}}_{Н.А.1}\cdot Ku}{\dot{I}{2}_{.А.1}\cdot Kz}$$

) или 46 ( $${\underset{\_}{Z}}_{А.ВОЛН}=\frac{{\dot{U}}_{А.ВОЛН}}{\dot{I}{2}_{А.Н}}$$

) понижающего трансформатора 29 (Т6(3)). Эти сведения в процессор 5 (П) поступают от устройств сопряжения, каковыми являются датчики тока, напряжения и частоты 3 ( $${\displaystyle \sum _{i=1}^nД1}$$

); 10 ( $${\displaystyle \sum _{i=1}^nД2}$$

); 30 ( $${\displaystyle \sum _{i=1}^nД3}$$

) и 36 ( $${\displaystyle \sum _{i=1}^nД4}$$

), где анализируемые характеристики электрической энергии доводятся до величин, воспринимаемых компьютерной техникой. Датчики 3 ( $${\displaystyle \sum _{i=1}^nД1}$$

) устанавливаются и используются для сбора сведений о напряжениях и токах в начале исследуемой протяженной четырехпроводной однородной несимметричной ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная) с последующей передачей информации на показывающий или самопишущий прибор 7 (РО). Датчики 10 ( $${\displaystyle \sum _{i=1}^nД2}$$

) устанавливаются и используются для сбора сведений о напряжениях и токах, поступающих на вторичную сторону понижающего трансформатора 9 (Т2(4)), схема соединения которого звезда с выведенным нулевым проводом/звезда с выведенным нулевым проводом, напряжением 10 кВ/0,4 кВ. Датчики блока 30 ( $${\displaystyle \sum _{i=1}^nД3}$$

) устанавливаются и используются для сбора сведений о напряжениях и токах, поступающих на вторичную сторону понижающего трансформатора 29 (Т6(3)), схема соединения которого звезда/звезда с выведенным нулевым проводом, напряжением 10кВ/0,4кВ, или поступающих на корректирующий орган 14 (КОн.). Датчики 36 ( $${\displaystyle \sum _{i=1}^nД4}$$

) устанавливаются в конце линии электропередачи 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная) и перед точкой подключения корректирующего органа 14 (КОн.) (подключение блока 8 (ЛЭП 35кВ ИЛИ МЕНЬШЕ 4-х проводная) к блоку трансформатора 29 (Т6(3)), схема соединения которого - звезда/звезда с выведенным нулевым проводом) с последующей передачей информации на показывающий или самопишущий прибор 7 (РО).The main unit of the algorithm for matching a four-wire homogeneous asymmetric power line 8 (power line 35 kV OR LESS 4-wire) with an electrical load is processor 5 (P) (Fig. 1), where information is analyzed: on the state of the generalized load resistance 17 ( $${\underset{\_}{Z}}_{N.\mathrm{BUT}}=\frac{{\dot{U}}_{N.\mathrm{BUT}}}{\dot{I}{2}_{.\mathrm{BUT}}}$$

) or 18 ( $${\underset{\_}{Z}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}}$$

) (Fig. 2) step-down transformer 9 (T2 (4)) (Fig. 1); on the state of the generalized load resistance 48 ( $${\underset{\_}{Z}}_{\mathrm{BUT}.N}=\frac{{\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}\cdot Ku}{\dot{I}{2}_{.\mathrm{BUT}\mathrm{.one}}\cdot Kz}$$

) or 46 ( $${\underset{\_}{Z}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}=\frac{{\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}}{\dot{I}{2}_{\mathrm{BUT}.N}}$$

) step-down transformer 29 (T6 (3)). This information in the processor 5 (P) comes from the pairing devices, which are current, voltage and frequency sensors 3 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D\mathrm{one}}$$

); 10 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D2}$$

); thirty ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D3}$$

) and 36 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D\mathrm{four}}$$

), where the analyzed characteristics of electrical energy are brought to the values perceived by computer technology. Sensors 3 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D\mathrm{one}}$$

) are installed and used to collect information about voltages and currents at the beginning of the studied extended four-wire homogeneous asymmetric power line 8 (power line 35 kV OR LESS 4-wire) with subsequent transmission of information to a indicating or recording device 7 (PO). Sensors 10 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D2}$$

) are installed and used to collect information about the voltages and currents supplied to the secondary side of the step-down transformer 9 (T2 (4)), the connection diagram of which is a star with an output neutral wire / star with an output neutral wire, voltage 10 kV / 0.4 kV. Block 30 sensors ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D3}$$

) are installed and used to collect information about the voltages and currents supplied to the secondary side of the step-down transformer 29 (T6 (3)), the connection circuit of which is star / star with the output neutral wire, voltage 10kV / 0.4kV, or received on the corrective body 14 (CON). Sensors 36 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D\mathrm{four}}$$

) are installed at the end of the power line 8 (35 kV power line OR LESS 4-wire) and before the connection point of the corrective body 14 (CON) (block 8 connection (35 kV power line OR LESS 4-wire) to the transformer unit 29 (T6 ( 3)), the connection diagram of which is a star / star with a neutral wire output) with subsequent transmission of information to a indicating or recording device 7 (PO).

); 10 ( $${\displaystyle \sum _{i=1}^nД2}$$

); 30 ( $${\displaystyle \sum _{i=1}^nД3}$$

) и 36 ( $${\displaystyle \sum _{i=1}^nД4}$$

) могут быть использованы трансформаторы напряжения и тока, спектроанализаторы, частотомеры, а также делители напряжения и шунты переменного тока.As sensors 3 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D\mathrm{one}}$$

); 10 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D2}$$

); thirty ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D3}$$

) and 36 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D\mathrm{four}}$$

) voltage and current transformers, spectrum analyzers, frequency meters, as well as voltage dividers and AC shunts can be used.

); 10 ( $${\displaystyle \sum _{i=1}^nД2}$$

); 30 ( $${\displaystyle \sum _{i=1}^nД3}$$

) и 36 ( $${\displaystyle \sum _{i=1}^nД4}$$

) аналоговые сигналы преобразовать в дискретные. Цифроаналоговый преобразователь 6 (ЦАП) позволяет сформированные в виде дискретных сигналов в процессоре 5 (П) команды корректирующим органам 1 (KО1), 12 (КО2), 14 (КОн.), 16 (КО3), 32 (КО4), 35 (КО5) преобразовать в аналоговые. В данном случае в качестве корректирующих органов 1 (KО1), 12 (КО2) и 32 (КО4) использованы устройства РПН силовых трансформаторов, в качестве блока корректирующего органа 14 (КОн.) выступает трехпроводная (без четвертого проводника от нейтрали источника питания), обобщенная нагрузка питаемая от понижающего трансформатора 29 (Т6(3)), схема соединения первичной и вторичной обмотки которого звезда/звезда с выведенным нулевым проводом, а в качестве корректирующего органа 16 (КО3) и 35 (КО5) - выступают реакторы и трехфазные или однофазные устройства, генерирующие ток и напряжение, такие как конденсаторные батареи, позволяющие изменять величину действительного полного сопротивления обобщенной нагрузки 17 ( $${\underset{\_}{Z}}_{Н.А}=\frac{{\dot{U}}_{Н.А}}{\dot{I}{2}_{.А}}$$

); 48 ( $${\underset{\_}{Z}}_{А.Н}=\frac{{\dot{U}}_{Н.А.1}\cdot Ku}{\dot{I}{2}_{.А.1}\cdot Kz}$$

) путем воздействия на технологический процесс и доводить его до эталонного значения сопротивления 18 ( $${\underset{\_}{Z}}_{ВОЛН.А}=\frac{{\dot{U}}_{ВОЛН.А}}{\dot{I}{2}_{Н.А}}$$

); 46 ( $${\underset{\_}{Z}}_{А.ВОЛН}=\frac{{\dot{U}}_{А.ВОЛН}}{\dot{I}{2}_{А.Н}}$$

), на (рис.1) эти воздействия изменяют обобщенную электрическую нагрузку 15 (Z_НАГР.); 34 (Z _Н). Результаты действия описываемого алгоритма выводятся на показывающий или самопишущий прибор 7 (РО).An analog-to-digital converter 4 (ADC) (Fig. 1) allows the sensors 3 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D\mathrm{one}}$$

); 10 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D2}$$

); thirty ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D3}$$

) and 36 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D\mathrm{four}}$$

) convert analog signals to discrete. The digital-to-analog converter 6 (DAC) allows the corrective bodies 1 (KO1), 12 (KO2), 14 (KON.), 16 (KO3), 32 (KO4), 35 (KO5) generated in the form of discrete signals in the processor 5 (P) ) convert to analog. In this case, on-load tap-changers of power transformers were used as corrective organs 1 (KO1), 12 (KO2) and 32 (KO4), three-wire (without a fourth conductor from the neutral of the power supply) acts as a block of the correcting organ 14 (KOn), generalized the load supplied by the step-down transformer 29 (T6 (3)), the connection diagram of the primary and secondary winding of which is star / star with the neutral wire removed, and reactors and three-phase or single-phase devices act as corrective body 16 (KO3) and 35 (KO5) generation uyuschie current and voltage, such as capacitor banks, allowing to change the actual value of the generalized impedance load 17 ( $${\underset{\_}{Z}}_{N.\mathrm{BUT}}=\frac{{\dot{U}}_{N.\mathrm{BUT}}}{\dot{I}{2}_{.\mathrm{BUT}}}$$

); 48 ( $${\underset{\_}{Z}}_{\mathrm{BUT}.N}=\frac{{\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}\cdot Ku}{\dot{I}{2}_{.\mathrm{BUT}\mathrm{.one}}\cdot Kz}$$

) by influencing the technological process and bring it to the reference value of resistance 18 ( $${\underset{\_}{Z}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}}$$

); 46 ( $${\underset{\_}{Z}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}=\frac{{\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}}{\dot{I}{2}_{\mathrm{BUT}.N}}$$

), (Fig. 1), these effects change the generalized electrical load 15 (Z _HEAT. ); 34 ( Z _H ). The results of the described algorithm are displayed on a indicating or recording device 7 (PO).

), напряжения 19 ( $${\dot{U}}_{Н.А}$$

)и значение их частоты 58 (f) нагрузки от устройств сопряжения блока 10 ( $${\displaystyle \sum _{i=1}^nД2}$$

) (рис.1) и (рис.2), затем определяется величина 17 ( $${\underset{\_}{Z}}_{Н.А}=\frac{{\dot{U}}_{Н.А}}{\dot{I}{2}_{.А}}$$

). Определенные таким образом величины 20 ( $$\dot{I}{2}_{.А}$$

), 19 ( $${\dot{U}}_{Н.А}$$

), 17 ( $${\underset{\_}{Z}}_{Н.А}=\frac{{\dot{U}}_{Н.А}}{\dot{I}{2}_{.А}}$$

) подаются в следующий блок 24 (А₁).The algorithm diagram of the processor 5 (P) is presented in (Fig. 2). It is quite simple: from 4 (ADC), the amplitude values of current 20 ( $$\dot{I}{2}_{.\mathrm{BUT}}$$

), voltage 19 ( $${\dot{U}}_{N.\mathrm{BUT}}$$

) and the value of their frequency 58 (f) of the load from the interface devices of block 10 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D2}$$

) (Fig. 1) and (Fig. 2), then the value 17 ( $${\underset{\_}{Z}}_{N.\mathrm{BUT}}=\frac{{\dot{U}}_{N.\mathrm{BUT}}}{\dot{I}{2}_{.\mathrm{BUT}}}$$

) The quantities thus determined are 20 ( $$\dot{I}{2}_{.\mathrm{BUT}}$$

), 19 ( $${\dot{U}}_{N.\mathrm{BUT}}$$

), 17 ( $${\underset{\_}{Z}}_{N.\mathrm{BUT}}=\frac{{\dot{U}}_{N.\mathrm{BUT}}}{\dot{I}{2}_{.\mathrm{BUT}}}$$

) are served in the next block 24 (A ₁ ).

) и 23 ( $${\dot{U}}_{ВОЛН.А}$$

) формируются величины токов и напряжений, необходимые для питания понижающего трансформатора 9 (Т2(4)) (рис.1) схема соединения первичной/вторичной обмотки: звезда с выведенным нулевым проводом/звезда с выведенным нулевым проводом, напряжением 10 кВ/0,4 кВ, находящимся в конце четырехпроводного однородной несимметричной ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная), после точки подключения корректирующего органа 14 (КОн.) и после точки подключения блока 29 (Т6(3)). Эти токи и напряжения определяются следующим образом [8]:Block 21 (FOUR-WIRE v. 1.00 (1)) in (Fig. 2) illustrates the use in the proposed method of matching the asymmetric homogeneous four-wire power transmission line with the electrical load of a specialized program for predicting the magnitude of the main characteristics of electric energy in an asymmetric homogeneous power transmission line of four-wire design [10 ], which is part of an asymmetric power system. Based on a specific frequency 58 (f), the program determines the effective values of the complex values of currents and voltages, the propagation constants of electromagnetic field waves along the power lines, the magnitudes of the eigen- and mutual wave resistances. In blocks 22 ( $$\dot{I}{2}_{N.\mathrm{BUT}}$$

) and 23 ( $${\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}$$

) the values of currents and voltages necessary for powering the step-down transformer 9 (T2 (4)) are formed (Fig. 1) the connection diagram of the primary / secondary winding: a star with an output neutral wire / star with an output neutral wire, voltage 10 kV / 0.4 kV, located at the end of a four-wire homogeneous asymmetric power line 8 (power line 35 kV OR LESS 4-wire), after the connection point of the correcting body 14 (CON) and after the connection point of block 29 (T6 (3)). These currents and voltages are determined as follows [8]:

1 case (for the first propagation constant, the first pair of waves of the electromagnetic field):

; $$\frac{({\dot{U}}_{В{\gamma }_1(3)}/K_{ТР})}{({\dot{I}}_{В{\gamma }_1(3)}\cdot K_{ТР})}=\frac{{\dot{U}}_{ВОЛН.В}}{\dot{I}{2}_{Н.В}+\dot{I}{2}_{В.Н}}$$

; $$\frac{({\dot{U}}_{\mathrm{BUT}{\gamma }_{\mathrm{one}}(3)}/K_{TR})}{({\dot{I}}_{\mathrm{BUT}{\gamma }_{\mathrm{one}}(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}+\dot{I}{2}_{\mathrm{BUT}.N}}$$

; $$\frac{({\dot{U}}_{\mathrm{AT}{\gamma }_{\mathrm{one}}(3)}/K_{TR})}{({\dot{I}}_{\mathrm{AT}{\gamma }_{\mathrm{one}}(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}}{\dot{I}{2}_{N.\mathrm{AT}}+\dot{I}{2}_{\mathrm{AT}.N}}$$

;

, $$\frac{({\dot{U}}_{\mathrm{FROM}{\gamma }_{\mathrm{one}}(3)}/K_{TR})}{({\dot{I}}_{\mathrm{FROM}{\gamma }_{\mathrm{one}}(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}}{\dot{I}{2}_{N.\mathrm{FROM}}+\dot{I}{2}_{\mathrm{BUT}.\mathrm{FROM}}}$$

,

, $${\dot{U}}_{В\gamma 1(3)}$$

, $${\dot{U}}_{С\gamma 1(3)}$$

- фазные напряжения на клеммах источника питания (начало ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная)) от первой пары (условно) волн электромагнитного поля, определяемые по формулам:where K _TP is the transformation ratio of step-down transformers 9 (T2 (4)) and 29 (T6 (3)); $${\dot{U}}_{\mathrm{BUT}\gamma \mathrm{one}(3)}$$

, $${\dot{U}}_{\mathrm{AT}\gamma \mathrm{one}(3)}$$

, $${\dot{U}}_{\mathrm{FROM}\gamma \mathrm{one}(3)}$$

- phase voltages at the terminals of the power source (the beginning of the power line 8 (power line 35 kV OR LESS 4-wire)) from the first pair (conditionally) of the waves of the electromagnetic field, determined by the formulas:

$$\begin{array}{l}({\dot{U}}_{{\mathrm{BUT}}_{\gamma \mathrm{one}}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{one}}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{one}}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}N\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}N\mathrm{one}}}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}N\mathrm{one}}}}sh{\gamma }_{\mathrm{one}}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}={\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

$$\begin{array}{l}({\dot{U}}_{{\mathrm{AT}}_{\gamma \mathrm{one}}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{one}}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}\mathrm{one}}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}N\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}N\mathrm{one}}}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}N\mathrm{one}}}}sh{\gamma }_{\mathrm{one}}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}={\dot{U}}_{\mathrm{AT}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

$$\begin{array}{l}({\dot{U}}_{{\mathrm{FROM}}_{{\gamma }_{\mathrm{one}}}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{FROM}\mathrm{one}}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}\mathrm{one}}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}N\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}N\mathrm{one}}}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}N\mathrm{one}}}}sh{\gamma }_{\mathrm{one}}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}={\dot{U}}_{\mathrm{FROM}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

, $${\dot{U}}_{{В}_{.1}(3)}$$

, $${\dot{U}}_{{С}_{.1}(3)}$$

- комплексные значения действующих величин фазных напряжений источника питания четырехпроводной однородной несимметричной ЛЭП, В; $${\dot{U}}_{А.ВОЛН}$$

, $${\dot{U}}_{В.ВОЛН}$$

, $${\dot{U}}_{С.ВОЛН}$$

- эталонные комплексные значения действующих величин фазных напряжений на вторичной стороне понижающего трансформатора 29 (Т6(3)) (рис.1), В; $${\dot{U}}_{ВОЛН.А}$$

, $${\dot{U}}_{ВОЛН.В}$$

, $${\dot{U}}_{ВОЛН.С}$$

- эталонные фазные напряжения на вторичной стороне понижающего трансформатора 9 (Т2(4)) (рис.1); γ₁ - постоянная распространения первой пары волн электромагнитного поля; l - длина ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная), км; $${\dot{I}}_{A{\gamma }_1(3)}$$

, $${\dot{I}}_{В{\gamma }_1(3)}$$

, $${\dot{I}}_{С{\gamma }_1(3)}$$

- токи, передаваемые от источника питания (начало ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная)) от первой пары (условно) волн электромагнитного поля, определяемые по формулам $${\dot{U}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}$$

, $${\dot{U}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}$$

, $${\dot{U}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}$$

- complex values of the current values of the phase voltages of the power source of a four-wire homogeneous asymmetric power line, V; $${\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}$$

, $${\dot{U}}_{\mathrm{AT}.\mathrm{AT}\mathrm{ABOUT}LN}$$

, $${\dot{U}}_{\mathrm{FROM}.\mathrm{AT}\mathrm{ABOUT}LN}$$

- reference complex values of the effective values of phase voltages on the secondary side of the step-down transformer 29 (T6 (3)) (Fig. 1), V; $${\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}$$

, $${\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}$$

, $${\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}$$

- reference phase voltages on the secondary side of the step-down transformer 9 (T2 (4)) (Fig. 1); γ ₁ is the propagation constant of the first pair of waves of the electromagnetic field; l - length of power lines 8 (power lines 35 kV OR LESS 4-wire), km; $${\dot{I}}_{A{\gamma }_{\mathrm{one}}(3)}$$

, $${\dot{I}}_{\mathrm{AT}{\gamma }_{\mathrm{one}}(3)}$$

, $${\dot{I}}_{\mathrm{FROM}{\gamma }_{\mathrm{one}}(3)}$$

- currents transmitted from the power source (the beginning of the power line 8 (power line 35 kV OR LESS 4-wire)) from the first pair (conditionally) of the waves of the electromagnetic field, determined by the formulas

$$\begin{array}{l}{\dot{I}}_{\mathrm{BUT}\gamma \mathrm{one}(3)}\cdot K_{TR}=\left(\left({\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{one}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{one}}}{e}^{-\gamma {\mathrm{one}}^l}\right)\cdot K_{TR}\right)+\\ +\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}N\mathrm{one}}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}AN\mathrm{one}}}sh{\gamma }_{\mathrm{one}}l\right)\cdot K_{TR}\right)=(\dot{I}{2}_{N.\mathrm{BUT}})+(\dot{I}{2}_{\mathrm{BUT}.N})\end{array}$$

or

; $$\left(\left({\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{one}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{one}}}{e}^{-\gamma {\mathrm{one}}^l}\right)\cdot K_{TR}\right)=\dot{I}{2}_{N.\mathrm{BUT}}$$

;

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}N\mathrm{one}}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}AN\mathrm{one}}}sh{\gamma }_{\mathrm{one}}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{BUT}.N}$$

;

$$\begin{array}{l}{\dot{I}}_{\mathrm{AT}\gamma \mathrm{one}(3)}\cdot K_{TR}=\left(\left({\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{one}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}\mathrm{one}}}{e}^{-\gamma {\mathrm{one}}^l}\right)\cdot K_{TR}\right)+\\ +\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N\mathrm{one}}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N\mathrm{one}}}sh{\gamma }_{\mathrm{one}}l\right)\cdot K_{TR}\right)=(\dot{I}{2}_{N.\mathrm{AT}})+(\dot{I}{2}_{\mathrm{AT}.N})\end{array}$$

or

; $$\left(\left({\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{one}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}\mathrm{one}}}{e}^{-\gamma {\mathrm{one}}^l}\right)\cdot K_{TR}\right)\dot{I}{2}_{N.\mathrm{AT}}$$

;

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N\mathrm{one}}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N\mathrm{one}}}sh{\gamma }_{\mathrm{one}}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{AT}.N}$$

;

$$\begin{array}{l}{\dot{I}}_{\mathrm{FROM}\gamma \mathrm{one}(3)}\cdot K_{TR}=\left(\left({\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{one}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}\mathrm{one}}}{e}^{-\gamma {\mathrm{one}}^l}\right)\cdot K_{TR}\right)+\\ +\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N\mathrm{one}}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N\mathrm{one}}}sh{\gamma }_{\mathrm{one}}l\right)\cdot K_{TR}\right)=(\dot{I}{2}_{N.\mathrm{FROM}})+(\dot{I}{2}_{\mathrm{FROM}.N})\end{array}$$

or

; $$\left(\left({\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{one}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}\mathrm{one}}}{e}^{-\gamma {\mathrm{one}}^l}\right)\cdot K_{TR}\right)=\dot{I}{2}_{N.\mathrm{FROM}}$$

;

; $${\dot{U}}_{N_{.1}(3)}$$

- комплексное значение действующей величины фазного напряжения нейтрали источника питания четырехпроводной однородной несимметричной ЛЭП, В; $${\dot{I}}_{{А}_{.1}(3)}$$

, $${\dot{I}}_{{В}_{.1}(3)}$$

, $${\dot{I}}_{{С}_{.1}(3)}$$

, $${\dot{I}}_{N_{.1}(3)}$$

- токи от источника питания четырехпроводной однородной несимметричной ЛЭП, А; $$\dot{I}{2}_{Н.А}$$

, $$\dot{I}{2}_{Н.В}$$

, $$\dot{I}{2}_{Н.С}$$

- эталонные токи электрической нагрузки трансформатора 9 (Т2(4)) (рис.1), схема соединения которого звезда с выведенным нейтральным проводом/звезда с выведенным нейтральным проводом (конец линии); $${\underset{\_}{Z}}_{сА1}$$

, $${\underset{\_}{Z}}_{сВ1}$$

, $${\underset{\_}{Z}}_{сС1}$$

, $${\underset{\_}{Z}}_{сN1}$$

- собственные волновые сопротивления от первой пары (условно) волн электромагнитного поля ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная), Ом; $${\underset{\_}{Z}}_{сАВ1}$$

, $${\underset{\_}{Z}}_{сСА1}$$

, $${\underset{\_}{Z}}_{сAN1}$$

, $${\underset{\_}{Z}}_{сBN1}$$

, $${\underset{\_}{Z}}_{сCN1}$$

, $${\underset{\_}{Z}}_{сBC1}$$

- взаимные волновые сопротивления от первой пары (условно) волн электромагнитного поля ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная), Ом; $$\dot{I}{2}_{А.Н}$$

, $$\dot{I}{2}_{В.Н}$$

, $$\dot{I}{2}_{С.Н}$$

- эталонные токи электрической нагрузки корректирующего органа 14 (КОн.) или токи электрической нагрузки трансформатора 29 (Т6(3)) (рис.1), А. $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N\mathrm{one}}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N\mathrm{one}}}sh{\gamma }_{\mathrm{one}}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{FROM}.N}$$

; $${\dot{U}}_{N_{\mathrm{.one}}(3)}$$

- the complex value of the effective value of the phase voltage of the neutral power source of a four-wire homogeneous asymmetric power transmission line, V; $${\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}$$

, $${\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}$$

, $${\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}$$

, $${\dot{I}}_{N_{\mathrm{.one}}(3)}$$

- currents from the power source of a four-wire homogeneous asymmetric power transmission line, A; $$\dot{I}{2}_{N.\mathrm{BUT}}$$

, $$\dot{I}{2}_{N.\mathrm{AT}}$$

, $$\dot{I}{2}_{N.\mathrm{FROM}}$$

- reference currents of the electrical load of transformer 9 (T2 (4)) (Fig. 1), the connection diagram of which is a star with an output neutral wire / star with an output neutral wire (end of line); $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}$$

, $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}$$

, $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}$$

, $${\underset{\_}{Z}}_{\mathrm{from}N\mathrm{one}}$$

- intrinsic wave impedances from the first pair (conditionally) of the waves of the electromagnetic field of the power transmission line 8 (power transmission line 35 kV OR LESS 4-wire), Ohm; $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{one}}$$

, $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{one}}$$

, $${\underset{\_}{Z}}_{\mathrm{from}AN\mathrm{one}}$$

, $${\underset{\_}{Z}}_{\mathrm{from}BN\mathrm{one}}$$

, $${\underset{\_}{Z}}_{\mathrm{from}CN\mathrm{one}}$$

, $${\underset{\_}{Z}}_{\mathrm{from}BC\mathrm{one}}$$

- mutual wave impedances from the first pair (conditionally) of the waves of the electromagnetic field of power lines 8 (power lines 35 kV OR LESS 4-wire), Ohm; $$\dot{I}{2}_{\mathrm{BUT}.N}$$

, $$\dot{I}{2}_{\mathrm{AT}.N}$$

, $$\dot{I}{2}_{\mathrm{FROM}.N}$$

- reference currents of the electrical load of the correcting body 14 (KON.) or currents of the electrical load of the transformer 29 (T6 (3)) (Fig. 1), A.

2 case (for the second propagation constant, the second pair of waves of the electromagnetic field):

; $$\frac{({\dot{U}}_{В{\gamma }_2(3)}/K_{ТР})}{({\dot{I}}_{В{\gamma }_2(3)}\cdot K_{ТР})}=\frac{{\dot{U}}_{ВОЛН.В}}{\dot{I}{2}_{Н.В}+\dot{I}{2}_{В.Н}}$$

; $$\frac{({\dot{U}}_{\mathrm{BUT}{\gamma }_2(3)}/K_{TR})}{({\dot{I}}_{\mathrm{BUT}{\gamma }_2(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}+\dot{I}{2}_{\mathrm{BUT}.N}}$$

; $$\frac{({\dot{U}}_{\mathrm{AT}{\gamma }_2(3)}/K_{TR})}{({\dot{I}}_{\mathrm{AT}{\gamma }_2(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}}{\dot{I}{2}_{N.\mathrm{AT}}+\dot{I}{2}_{\mathrm{AT}.N}}$$

;

, $$\frac{({\dot{U}}_{\mathrm{FROM}{\gamma }_2(3)}/K_{TR})}{({\dot{I}}_{\mathrm{FROM}{\gamma }_2(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}}{\dot{I}{2}_{N.\mathrm{FROM}}+\dot{I}{2}_{\mathrm{BUT}.\mathrm{FROM}}}$$

,

, $${\dot{U}}_{В{\gamma }_2(3)}$$

, $${\dot{U}}_{С{\gamma }_2(3)}$$

- фазные напряжения на клеммах источника питания (начало ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная)) от второй пары (условно) волн электромагнитного поля, определяемые по формуламWhere $${\dot{U}}_{\mathrm{BUT}{\gamma }_2(3)}$$

, $${\dot{U}}_{\mathrm{AT}{\gamma }_2(3)}$$

, $${\dot{U}}_{\mathrm{FROM}{\gamma }_2(3)}$$

- phase voltages at the terminals of the power source (the beginning of the power line 8 (power line 35 kV OR LESS 4-wire)) from the second pair (conditionally) of the waves of the electromagnetic field, determined by the formulas

$$\begin{array}{l}({\dot{U}}_{{\mathrm{BUT}}_{\gamma 2}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="2"\; label="AT"\; filenames="00000210.png,00000211.png"\; state="\{\{state\}\}">AT</figure-callout>}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}2}}}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}2}}}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="00000210.png,00000211.png"\; state="\{\{state\}\}">N</figure-callout>}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}N2}}}ch\gamma 2l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}N2}}}sh{\gamma }_{2}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}={\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

$$\begin{array}{l}({\dot{U}}_{{\mathrm{AT}}_{\gamma }{}_2(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}2}}}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}2}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="00000210.png,00000211.png"\; state="\{\{state\}\}">N</figure-callout>}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}N2}}}ch{\gamma }_{2}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}N2}}}sh{\gamma }_{2}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}={\dot{U}}_{\mathrm{AT}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

$$\begin{array}{l}({\dot{U}}_{{\mathrm{FROM}}_{\gamma 2}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{FROM}2}}}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="2"\; label="AT"\; filenames="00000210.png,00000211.png"\; state="\{\{state\}\}">AT</figure-callout>}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}2}}}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="00000210.png,00000211.png"\; state="\{\{state\}\}">N</figure-callout>}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}N2}}}ch{\gamma }_{2}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}N2}}}sh{\gamma }_{2}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}={\dot{U}}_{\mathrm{FROM}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

, $${\dot{I}}_{В{\gamma }_2(3)}$$

, $${\dot{I}}_{С{\gamma }_2(3)}$$

- токи от источника питания (начало ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная)) от второй пары (условно) волн электромагнитного поля, определяемые по формулам γ ₂ is the propagation constant of the second pair of waves of the electromagnetic field; $${\dot{I}}_{A{\gamma }_2(3)}$$

, $${\dot{I}}_{\mathrm{AT}{\gamma }_2(3)}$$

, $${\dot{I}}_{\mathrm{FROM}{\gamma }_2(3)}$$

- currents from the power source (the beginning of the power line 8 (power line 35 kV OR LESS 4-wire)) from the second pair (conditionally) of the waves of the electromagnetic field, determined by the formulas

$$\begin{array}{l}{\dot{I}}_{{\mathrm{BUT}}_{\gamma 2}(3)}\cdot K_{TR}=\left(\left({\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}2}}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}2}}{e}^{-\gamma 2^l}\right)\cdot K_{TR}\right)+\\ +\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}N2}}ch{\gamma }_{2}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}AN2}}sh{\gamma }_{2}l\right)\cdot K_{TR}\right)=(\dot{I}{2}_{N.\mathrm{BUT}})+(\dot{I}{2}_{\mathrm{BUT}.N})\end{array}$$

or

; $$\left(\left({\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}2}}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}2}}{e}^{-\gamma 2^l}\right)\cdot K_{TR}\right)=\dot{I}{2}_{N.\mathrm{BUT}}$$

;

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}N2}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}AN2}}sh{\gamma }_{2}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{BUT}.N}$$

;

$$\begin{array}{l}{\dot{I}}_{{\mathrm{AT}}_{\gamma 2}(3)}\cdot K_{TR}=\left(\left({\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}2}}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}2}}{e}^{-\gamma 2^l}\right)\cdot K_{TR}\right)+\\ +\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N2}}ch{\gamma }_{2}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N2}}sh{\gamma }_{2}l\right)\cdot K_{TR}\right)=(\dot{I}{2}_{N.\mathrm{AT}})+(\dot{I}{2}_{\mathrm{AT}.N})\end{array}$$

or

; $$\left(\left({\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}2}}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}2}}{e}^{-\gamma 2^l}\right)\cdot K_{TR}\right)\dot{I}{2}_{N.\mathrm{AT}}$$

;

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N2}}ch{\gamma }_{2}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N2}}sh{\gamma }_{2}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{AT}.N}$$

;

$$\begin{array}{l}{\dot{I}}_{{\mathrm{FROM}}_{\gamma 2}(3)}\cdot K_{TR}=\left(\left({\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}2}}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}2}}{e}^{-\gamma 2^l}\right)\cdot K_{TR}\right)+\\ +\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N2}}ch{\gamma }_{2}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N2}}sh{\gamma }_{2}l\right)\cdot K_{TR}\right)=(\dot{I}{2}_{N.\mathrm{FROM}})+(\dot{I}{2}_{\mathrm{FROM}.N})\end{array}$$

or

; $$\left(\left({\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}2}}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}2}}{e}^{-\gamma 2^l}\right)\cdot K_{TR}\right)=\dot{I}{2}_{N.\mathrm{FROM}}$$

;

Б $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N2}}ch{\gamma }_{2}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N2}}sh{\gamma }_{2}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{FROM}.N}$$

B

, $${\underset{\_}{Z}}_{сВ2}$$

, $${\underset{\_}{Z}}_{сС2}$$

, $${\underset{\_}{Z}}_{сN2}$$

- собственные волновые сопротивления от второй пары (условно) волн электромагнитного поля ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная), Ом; $${\underset{\_}{Z}}_{сАВ2}$$

, $${\underset{\_}{Z}}_{сСА2}$$

, $${\underset{\_}{Z}}_{сAN2}$$

, $${\underset{\_}{Z}}_{сBN2}$$

, $${\underset{\_}{Z}}_{сCN2}$$

, $${\underset{\_}{Z}}_{сBC2}$$

- взаимные волновые сопротивления от второй пары (условно) волн электромагнитного поля ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная), Ом. $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}$$

, $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="2"\; label="AT"\; filenames="00000210.png,00000211.png"\; state="\{\{state\}\}">AT</figure-callout>}2}$$

, $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}$$

, $${\underset{\_}{Z}}_{\mathrm{from}N2}$$

- intrinsic wave impedances from the second pair (conditionally) of the waves of the electromagnetic field of the power transmission line 8 (power line 35 kV OR LESS 4-wire), Ohm; $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}2}$$

, $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}2}$$

, $${\underset{\_}{Z}}_{\mathrm{from}A\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="00000210.png,00000211.png"\; state="\{\{state\}\}">N</figure-callout>}2}$$

, $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="2"\; label="B\; N"\; filenames="00000210.png,00000211.png"\; state="\{\{state\}\}">B\; </figure-callout>}N2}$$

, $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="2"\; label="C\; N"\; filenames="00000210.png,00000211.png"\; state="\{\{state\}\}">C\; </figure-callout>}N2}$$

, $${\underset{\_}{Z}}_{\mathrm{from}BC2}$$

- mutual wave impedances from the second pair (conditionally) of the waves of the electromagnetic field of the power transmission line 8 (power line 35 kV OR LESS 4-wire), Ohm.

3 case (for the third propagation constant, the third pair of waves of the electromagnetic field):

; $$\frac{({\dot{U}}_{В{\gamma }_3(3)}/K_{ТР})}{({\dot{I}}_{В{\gamma }_3(3)}\cdot K_{ТР})}=\frac{{\dot{U}}_{ВОЛН.В}}{\dot{I}{2}_{Н.В}+\dot{I}{2}_{В.Н}}$$

; $$\frac{({\dot{U}}_{\mathrm{BUT}{\gamma }_3(3)}/K_{TR})}{({\dot{I}}_{\mathrm{BUT}{\gamma }_3(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}+\dot{I}{2}_{\mathrm{BUT}.N}}$$

; $$\frac{({\dot{U}}_{\mathrm{AT}{\gamma }_3(3)}/K_{TR})}{({\dot{I}}_{\mathrm{AT}{\gamma }_3(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}}{\dot{I}{2}_{N.\mathrm{AT}}+\dot{I}{2}_{\mathrm{AT}.N}}$$

;

, $$\frac{({\dot{U}}_{\mathrm{FROM}{\gamma }_3(3)}/K_{TR})}{({\dot{I}}_{\mathrm{FROM}{\gamma }_3(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}}{\dot{I}{2}_{N.\mathrm{FROM}}+\dot{I}{2}_{\mathrm{BUT}.\mathrm{FROM}}}$$

,

, $${\dot{U}}_{{В}_{\gamma 3}(3)}$$

, $${\dot{U}}_{{С}_{\gamma 3}(3)}$$

- фазные напряжения на клеммах источника питания (начало ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная)) от третьей пары (условно) волн электромагнитного поля, определяемые по формуламWhere $${\dot{U}}_{{\mathrm{BUT}}_{\gamma 3}(3)}$$

, $${\dot{U}}_{{\mathrm{AT}}_{\gamma 3}(3)}$$

, $${\dot{U}}_{{\mathrm{FROM}}_{\gamma 3}(3)}$$

- phase voltages at the terminals of the power source (the beginning of the power line 8 (power line 35 kV OR LESS 4-wire)) from the third pair (conditionally) of the waves of the electromagnetic field, determined by the formulas

$$\begin{array}{l}({\dot{U}}_{{\mathrm{BUT}}_{\gamma 3}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="3"\; label="AT"\; filenames="00000213.png,00000214.png"\; state="\{\{state\}\}">AT</figure-callout>}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}3}}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}3}}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="00000213.png,00000214.png"\; state="\{\{state\}\}">N</figure-callout>}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}N3}}}ch{\gamma }_{3}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}N3}}}sh{\gamma }_{3}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}={\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

$$\begin{array}{l}({\dot{U}}_{{\mathrm{AT}}_{\gamma 3}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}3}}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}3}}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="00000213.png,00000214.png"\; state="\{\{state\}\}">N</figure-callout>}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}N3}}}ch{\gamma }_{3}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}N3}}}sh{\gamma }_{3}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}={\dot{U}}_{\mathrm{AT}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

$$\begin{array}{l}({\dot{U}}_{{\mathrm{FROM}}_{{\gamma }_3}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{FROM}3}}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="3"\; label="AT"\; filenames="00000213.png,00000214.png"\; state="\{\{state\}\}">AT</figure-callout>}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}3}}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="00000213.png,00000214.png"\; state="\{\{state\}\}">N</figure-callout>}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}N3}}}ch{\gamma }_{3}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}N3}}}sh{\gamma }_{3}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}={\dot{U}}_{\mathrm{FROM}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

, $${\dot{I}}_{В{\gamma }_3(3)}$$

, $${\dot{I}}_{С{\gamma }_3(3)}$$

- токи от источника питания (начало ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная)) от третьей пары (условно) волн электромагнитного поля, определяемые по формуламγ ₃ is the propagation constant of the third pair of waves of the electromagnetic field; $${\dot{I}}_{A{\gamma }_3(3)}$$

, $${\dot{I}}_{\mathrm{AT}{\gamma }_3(3)}$$

, $${\dot{I}}_{\mathrm{FROM}{\gamma }_3(3)}$$

- currents from the power source (the beginning of the power line 8 (power line 35 kV OR LESS 4-wire)) from the third pair (conditionally) of the waves of the electromagnetic field, determined by the formulas

$$\begin{array}{l}{\dot{I}}_{{\mathrm{BUT}}_{\gamma 3}(3)}\cdot K_{TR}=\left(\left({\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}3}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}3}}{e}^{-\gamma 3^l}\right)\cdot K_{TR}\right)+\\ +\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}N3}}ch{\gamma }_{3}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}AN3}}sh{\gamma }_{3}l\right)\cdot K_{TR}\right)=(\dot{I}{2}_{N.\mathrm{BUT}})+(\dot{I}{2}_{\mathrm{BUT}.N})\end{array}$$

or

; $$\left(\left({\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}3}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}3}}{e}^{-\gamma 3^l}\right)\cdot K_{TR}\right)=\dot{I}{2}_{N.\mathrm{BUT}}$$

;

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}N3}}ch{\gamma }_{3}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}AN3}}sh{\gamma }_{3}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{BUT}.N}$$

;

$$\begin{array}{l}{\dot{I}}_{{\mathrm{AT}}_{\gamma 3}(3)}\cdot K_{TR}=\left(\left({\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}3}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}3}}{e}^{-\gamma 3^l}\right)\cdot K_{TR}\right)+\\ +\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N3}}ch{\gamma }_{3}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N3}}sh{\gamma }_{3}l\right)\cdot K_{TR}\right)=(\dot{I}{2}_{N.\mathrm{AT}})+(\dot{I}{2}_{\mathrm{AT}.N})\end{array}$$

or

; $$\left(\left({\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}3}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}3}}{e}^{-\gamma 3^l}\right)\cdot K_{TR}\right)\dot{I}{2}_{N.\mathrm{AT}}$$

;

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N3}}ch{\gamma }_{3}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N3}}sh{\gamma }_{3}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{AT}.N}$$

;

$$\begin{array}{l}{\dot{I}}_{{\mathrm{FROM}}_{\gamma 3}(3)}\cdot K_{TR}=\left(\left({\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}3}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}3}}{e}^{-\gamma 3^l}\right)\cdot K_{TR}\right)+\\ +\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N3}}ch{\gamma }_{3}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N3}}sh{\gamma }_{3}l\right)\cdot K_{TR}\right)=(\dot{I}{2}_{N.\mathrm{FROM}})+(\dot{I}{2}_{\mathrm{FROM}.N})\end{array}$$

or

; $$\left(\left({\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}3}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}3}}{e}^{-\gamma 3^l}\right)\cdot K_{TR}\right)=\dot{I}{2}_{N.\mathrm{FROM}}$$

;

; $${\underset{\_}{Z}}_{сА3}$$

, $${\underset{\_}{Z}}_{сВ3}$$

, $${\underset{\_}{Z}}_{сС3}$$

, $${\underset{\_}{Z}}_{сN3}$$

- собственные волновые сопротивления от третьей пары (условно) волн электромагнитного поля ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная), Ом; $${\underset{\_}{Z}}_{сАВ3}$$

, $${\underset{\_}{Z}}_{сСА3}$$

, $${\underset{\_}{Z}}_{сAN3}$$

, $${\underset{\_}{Z}}_{сBN3}$$

, $${\underset{\_}{Z}}_{сCN3}$$

, $${\underset{\_}{Z}}_{сBC3}$$

- взаимные волновые сопротивления от третьей пары (условно) волн электромагнитного поля ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная), Ом. $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N3}}ch{\gamma }_{3}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N3}}sh{\gamma }_{3}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{FROM}.N}$$

; $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}$$

, $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="3"\; label="AT"\; filenames="00000213.png,00000214.png"\; state="\{\{state\}\}">AT</figure-callout>}3}$$

, $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}$$

, $${\underset{\_}{Z}}_{\mathrm{from}N3}$$

- intrinsic wave impedances from the third pair (conditionally) of the waves of the electromagnetic field of the power transmission line 8 (power transmission line 35 kV OR LESS 4-wire), Ohm; $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}3}$$

, $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}3}$$

, $${\underset{\_}{Z}}_{\mathrm{from}A\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="00000213.png,00000214.png"\; state="\{\{state\}\}">N</figure-callout>}3}$$

, $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="3"\; label="B\; N"\; filenames="00000213.png,00000214.png"\; state="\{\{state\}\}">B\; </figure-callout>}N3}$$

, $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="3"\; label="C\; N"\; filenames="00000213.png,00000214.png"\; state="\{\{state\}\}">C\; </figure-callout>}N3}$$

, $${\underset{\_}{Z}}_{\mathrm{from}BC3}$$

- mutual wave impedances from the third pair (conditionally) of the waves of the electromagnetic field of the power transmission line 8 (transmission line 35 kV OR LESS 4-wire), Ohm.

4 case (for the fourth propagation constant, the fourth pair of waves of the electromagnetic field):

; $$\frac{({\dot{U}}_{В{\gamma }_4(3)}/K_{ТР})}{({\dot{I}}_{В{\gamma }_4(3)}\cdot K_{ТР})}=\frac{{\dot{U}}_{ВОЛН.В}}{\dot{I}{2}_{Н.В}+\dot{I}{2}_{В.Н}}$$

; $$\frac{({\dot{U}}_{\mathrm{BUT}{\gamma }_{\mathrm{four}}(3)}/K_{TR})}{({\dot{I}}_{\mathrm{BUT}{\gamma }_{\mathrm{four}}(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}+\dot{I}{2}_{\mathrm{BUT}.N}}$$

; $$\frac{({\dot{U}}_{\mathrm{AT}{\gamma }_{\mathrm{four}}(3)}/K_{TR})}{({\dot{I}}_{\mathrm{AT}{\gamma }_{\mathrm{four}}(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}}{\dot{I}{2}_{N.\mathrm{AT}}+\dot{I}{2}_{\mathrm{AT}.N}}$$

;

, $$\frac{({\dot{U}}_{\mathrm{FROM}{\gamma }_{\mathrm{four}}(3)}/K_{TR})}{({\dot{I}}_{\mathrm{FROM}{\gamma }_{\mathrm{four}}(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}}{\dot{I}{2}_{N.\mathrm{FROM}}+\dot{I}{2}_{\mathrm{BUT}.\mathrm{FROM}}}$$

,

, $${\dot{U}}_{{В}_{\gamma 4}(3)}$$

, $${\dot{U}}_{{С}_{\gamma 4}(3)}$$

- фазные напряжения на клеммах источника питания (начало ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная)) от четвертой пары (условно) волн электромагнитного поля, определяемые по формуламWhere $${\dot{U}}_{{\mathrm{BUT}}_{\gamma \mathrm{four}}(3)}$$

, $${\dot{U}}_{{\mathrm{AT}}_{\gamma \mathrm{four}}(3)}$$

, $${\dot{U}}_{{\mathrm{FROM}}_{\gamma \mathrm{four}}(3)}$$

- phase voltages at the terminals of the power source (the beginning of the power line 8 (power line 35 kV OR LESS 4-wire)) from the fourth pair (conditionally) of the waves of the electromagnetic field, determined by the formulas

$$\begin{array}{l}({\dot{U}}_{{\mathrm{BUT}}_{\gamma \mathrm{four}}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{four}}}}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{four}}}}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}N\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}N\mathrm{four}}}}ch{\gamma }_{\mathrm{four}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}N\mathrm{four}}}}sh{\gamma }_{\mathrm{four}}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}={\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

$$\begin{array}{l}({\dot{U}}_{{\mathrm{AT}}_{\gamma \mathrm{four}}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{four}}}}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}\mathrm{four}}}}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}N\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}N\mathrm{four}}}}ch{\gamma }_{\mathrm{four}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}N\mathrm{four}}}}sh{\gamma }_{\mathrm{four}}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}={\dot{U}}_{\mathrm{AT}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

$$\begin{array}{l}({\dot{U}}_{{\mathrm{FROM}}_{{\gamma }_{\mathrm{four}}}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{FROM}\mathrm{four}}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}\mathrm{four}}}}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}N\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}N\mathrm{four}}}}ch{\gamma }_{\mathrm{four}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}N\mathrm{four}}}}sh{\gamma }_{\mathrm{four}}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}={\dot{U}}_{\mathrm{FROM}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

, $${\dot{I}}_{В{\gamma }_4(3)}$$

, $${\dot{I}}_{С{\gamma }_4(3)}$$

- токи от источника питания (начало ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная)) от четвертой пары (условно) волн электромагнитного поля, определяемые по формуламγ ₄ is the propagation constant of the fourth pair of waves of the electromagnetic field; $${\dot{I}}_{A{\gamma }_{\mathrm{four}}(3)}$$

, $${\dot{I}}_{\mathrm{AT}{\gamma }_{\mathrm{four}}(3)}$$

, $${\dot{I}}_{\mathrm{FROM}{\gamma }_{\mathrm{four}}(3)}$$

- currents from the power source (the beginning of the power line 8 (power line 35 kV OR LESS 4-wire)) from the fourth pair (conditionally) of the waves of the electromagnetic field, determined by the formulas

$$\begin{array}{l}{\dot{I}}_{{\mathrm{BUT}}_{\gamma \mathrm{four}}(3)}\cdot K_{TR}=\left(\left({\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{four}}}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{four}}}{e}^{-\gamma {\mathrm{four}}^l}\right)\cdot K_{TR}\right)+\\ +\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}N\mathrm{four}}}ch{\gamma }_{\mathrm{four}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}AN\mathrm{four}}}sh{\gamma }_{\mathrm{four}}l\right)\cdot K_{TR}\right)=(\dot{I}{2}_{N.\mathrm{BUT}})+(\dot{I}{2}_{\mathrm{BUT}.N})\end{array}$$

or

; $$\left(\left({\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{four}}}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{four}}}{e}^{-\gamma {\mathrm{four}}^l}\right)\cdot K_{TR}\right)=\dot{I}{2}_{N.\mathrm{BUT}}$$

;

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}N\mathrm{four}}}ch{\gamma }_{\mathrm{four}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}AN\mathrm{four}}}sh{\gamma }_{\mathrm{four}}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{BUT}.N}$$

;

$$\begin{array}{l}{\dot{I}}_{{\mathrm{AT}}_{\gamma \mathrm{four}}(3)}\cdot K_{TR}=\left(\left({\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{four}}}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}\mathrm{four}}}{e}^{-\gamma {\mathrm{four}}^l}\right)\cdot K_{TR}\right)+\\ +\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N\mathrm{four}}}ch{\gamma }_{\mathrm{four}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N\mathrm{four}}}sh{\gamma }_{\mathrm{four}}l\right)\cdot K_{TR}\right)=(\dot{I}{2}_{N.\mathrm{AT}})+(\dot{I}{2}_{\mathrm{AT}.N})\end{array}$$

or

; $$\left(\left({\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{four}}}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}\mathrm{four}}}{e}^{-\gamma {\mathrm{four}}^l}\right)\cdot K_{TR}\right)\dot{I}{2}_{N.\mathrm{AT}}$$

;

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N\mathrm{four}}}ch{\gamma }_{\mathrm{four}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N\mathrm{four}}}sh{\gamma }_{\mathrm{four}}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{AT}.N}$$

;

$$\begin{array}{l}{\dot{I}}_{{\mathrm{FROM}}_{\gamma \mathrm{four}}(3)}\cdot K_{TR}=\left(\left({\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{four}}}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}\mathrm{four}}}{e}^{-\gamma {\mathrm{four}}^l}\right)\cdot K_{TR}\right)+\\ +\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N\mathrm{four}}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N\mathrm{four}}}sh{\gamma }_{\mathrm{four}}l\right)\cdot K_{TR}\right)=(\dot{I}{2}_{N.\mathrm{FROM}})+(\dot{I}{2}_{\mathrm{FROM}.N})\end{array}$$

or

; $$\left(\left({\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{four}}}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}\mathrm{four}}}{e}^{-\gamma {\mathrm{four}}^l}\right)\cdot K_{TR}\right)=\dot{I}{2}_{N.\mathrm{FROM}}$$

;

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N\mathrm{four}}}ch{\gamma }_{\mathrm{four}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N\mathrm{four}}}sh{\gamma }_{\mathrm{four}}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{FROM}.N}$$

;

, $${\underset{\_}{Z}}_{сВ4}$$

, $${\underset{\_}{Z}}_{сС4}$$

, $${\underset{\_}{Z}}_{сN4}$$

- собственные волновые сопротивления от четвертой пары (условно) волн электромагнитного поля ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная), Ом; $${\underset{\_}{Z}}_{сАВ4}$$

, $${\underset{\_}{Z}}_{сСА4}$$

, $${\underset{\_}{Z}}_{сAN4}$$

, $${\underset{\_}{Z}}_{сBN4}$$

, $${\underset{\_}{Z}}_{сCN4}$$

, $${\underset{\_}{Z}}_{сBC4}$$

- взаимные волновые сопротивления от четвертой пары (условно) волн электромагнитного поля ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная), Ом. $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}$$

, $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}$$

, $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}$$

, $${\underset{\_}{Z}}_{\mathrm{from}N\mathrm{four}}$$

- intrinsic wave impedances from the fourth pair (conditionally) of the waves of the electromagnetic field of the power transmission line 8 (power line 35 kV OR LESS 4-wire), Ohm; $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{four}}$$

, $${\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{four}}$$

, $${\underset{\_}{Z}}_{\mathrm{from}AN\mathrm{four}}$$

, $${\underset{\_}{Z}}_{\mathrm{from}BN\mathrm{four}}$$

, $${\underset{\_}{Z}}_{\mathrm{from}CN\mathrm{four}}$$

, $${\underset{\_}{Z}}_{\mathrm{from}BC\mathrm{four}}$$

- mutual wave impedances from the fourth pair (conditionally) of the waves of the electromagnetic field of the power line 8 (power line 35 kV OR LESS 4-wire), Ohm.

Since the load for each linear wire of a power transmission line 8 (35 kV power transmission line or LESS 4-wire) is one, and there are four pairs of electromagnetic field waves propagating through each linear wire, then matching of each wire can be realized only for one pair of electromagnetic field waves, and namely, according to the above formulas: 1 case (mathematical formulations are used) or 2 case, or 3 case, or 4 case.

) (рис.2), какое оно должно быть для питания понижающего трансформатора 9 (Т2(4)) (рис.1). Полученные результаты отправляются в блок 24 (А₁).Next, the reference load impedance 18 ( $${\underset{\_}{Z}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}}$$

) (Fig. 2), what it should be for powering the step-down transformer 9 (T2 (4)) (Fig. 1). The results are sent to block 24 (A ₁ ).

), 23 ( $${\dot{U}}_{ВОЛН.А}$$

) с действительными значениями, а именно: 17 ( $${\underset{\_}{Z}}_{Н.А}=\frac{{\dot{U}}_{Н.А}}{\dot{I}{2}_{.А}}$$

) и напряжением 19 ( $${\dot{U}}_{Н.А}$$

), полученных на вторичной стороне понижающего трансформатора 9 (Т2(4)). Здесь же из сопоставления этих величин определяются ошибки по сопротивлению ΔZ1, ΔZ2, ΔZ3 и по напряжению ΔU1, ΔU2, ΔU3. Затем определяются ошибки по току Δ101-05, Δ107, А108. При нулевых значениях ошибок по напряжению ошибки по току Δ106 и Δ109 отсутствуют, поэтому в их определении нет необходимости. Информация о величинах ΔZ1, ΔZ2, ΔZ3 и ΔU1, ΔU2, ΔU3 поступает в один из девяти блоков с приоритетом 2. Последующее действие описываемого алгоритма заключается в определении ошибок либо по сопротивлению ΔZ04p, ΔZ06p, ΔZ07p, ΔZ08p, ΔZ09p, либо по напряжению ΔU01p, ΔU02p, ΔU03Kр, ΔU05p. Полученные таким образом значения ошибок по напряжению поступают в блок суммы ошибок по напряжению $${\displaystyle \sum _{i=1}^5{U}_A}$$

, а величины ошибок по сопротивлению попадают в блок суммы ошибок по сопротивлению $${\displaystyle \sum _{i=1}^5{Z}_A}$$

. Сведения о результатах расчета ошибок поступают в один или несколько блоков корректирующих органов 1, 12, 16 (KO1, КO2, КО3) (рис.1).In block 24 (A ₁ ) (Fig. 3), logical operations are performed. Here, a comparison of the reference values of 18 ( $${\underset{\_}{Z}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}}$$

), 23 ( $${\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}$$

) with actual values, namely: 17 ( $${\underset{\_}{Z}}_{N.\mathrm{BUT}}=\frac{{\dot{U}}_{N.\mathrm{BUT}}}{\dot{I}{2}_{.\mathrm{BUT}}}$$

) and voltage 19 ( $${\dot{U}}_{N.\mathrm{BUT}}$$

) obtained on the secondary side of the step-down transformer 9 (T2 (4)). Here, from a comparison of these values, errors are determined by the resistance ΔZ1, ΔZ2, ΔZ3 and by the voltage ΔU1, ΔU2, ΔU3. Then, current errors Δ101-05, Δ107, A108 are determined. At zero voltage error values, there are no current errors Δ106 and Δ109, therefore, their determination is not necessary. Information on the values ΔZ1, ΔZ2, ΔZ3 and ΔU1, ΔU2, ΔU3 is received in one of nine blocks with priority 2. The subsequent action of the described algorithm consists in determining errors either by resistance ΔZ04p, ΔZ06p, ΔZ07p, ΔZ08p, ΔZ09p, or voltage ΔZ09p ΔU02p, ΔU03Kr, ΔU05p. The voltage error values obtained in this way go to the voltage error sum block $${\displaystyle \sum _{i=\mathrm{one}}^5{U}_A}$$

, and the values of errors in resistance fall into the block of the sum of errors in resistance $${\displaystyle \sum _{i=\mathrm{one}}^5{Z}_A}$$

. Information about the results of the calculation of errors is sent to one or several blocks of corrective bodies 1, 12, 16 (KO1, KO2, KO3) (Fig. 1).

следует собирать ошибки по току, а затем в результате сопоставления эталонного и действительного значений токов в конце ЛЭП сформировать сигнал для корректирующих органов 1,12, 16 (KO1, КO2, КО3) (рис.1).Here (Fig. 3), as a criterion for the functioning of the corrective organs, a voltage mismatch on the secondary side of the step-down transformer 9 (T2 (4)) (Fig. 1) or load resistance is selected. In principle, the mismatch of the current of the step-down transformer 9 (T2 (4)) can also be chosen as such a criterion. For this, in the block $${\displaystyle \sum _{i=\mathrm{one}}^5{Z}_A}$$

current errors should be collected, and then, as a result of comparing the reference and actual current values at the end of the power transmission line, generate a signal for the correcting organs 1.12, 16 (KO1, KO2, KO3) (Fig. 1).

)>23( $${\dot{U}}_{ВОЛН.А}$$

) и 17 ( $${\underset{\_}{Z}}_{Н.А}=\frac{{\dot{U}}_{Н.А}}{\dot{I}{2}_{.А}}$$

)>18 ( $${\underset{\_}{Z}}_{ВОЛН.А}=\frac{{\dot{U}}_{ВОЛН.А}}{\dot{I}{2}_{Н.А}}$$

) - ошибка по току не определяется. В этом случае предусмотрено определение дополнительной ошибки по напряжению 56 (ΔU_O) в виде произведения разницы между 23 ( $${\dot{U}}_{ВОЛН.А}$$

) и 19 ( $${\dot{U}}_{Н.А}$$

) и коэффициента состояния ΔIos1. Затем сведения об этой дополнительной ошибке отправляются в блок $${\displaystyle \sum _{i=1}^5{U}_A}$$

.In the process of stabilization of the specified values of currents and voltages of a step-down transformer 9 (T2 (4)) (Fig. 1) powered by a homogeneous asymmetric power line with a voltage of 35 kV or less than a four-wire version 8 (power line 35 kV OR LESS 4-wire), it was found out (Fig. .3), that at: 19 ( $${\dot{U}}_{N.\mathrm{BUT}}$$

)> 23 ( $${\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}$$

) and 17 ( $${\underset{\_}{Z}}_{N.\mathrm{BUT}}=\frac{{\dot{U}}_{N.\mathrm{BUT}}}{\dot{I}{2}_{.\mathrm{BUT}}}$$

)> 18 ( $${\underset{\_}{Z}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}}$$

) - current error is not detected. In this case, the definition of an additional voltage error 56 (ΔU _O ) in the form of the product of the difference between 23 $${\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}$$

) and 19 ( $${\dot{U}}_{N.\mathrm{BUT}}$$

) and the state coefficient ΔIos1. Then information about this additional error is sent to the block. $${\displaystyle \sum _{i=\mathrm{one}}^5{U}_A}$$

.

Block 24 (A ₁ ) (Fig. 3) is implemented in the National Instruments Lab VIEW 2009 environment.

) и 19 ( $${\dot{U}}_{Н.А}$$

) сравниваются с величинами эталонными (рассчитанными при помощи специализированной программы), а именно с 23 ( $${\dot{U}}_{ВОЛН.А}$$

) и 18 ( $${\underset{\_}{Z}}_{ВОЛН.А}=\frac{{\dot{U}}_{ВОЛН.А}}{\dot{I}{2}_{Н.А}}$$

), на основании этого сравнения определяется, на сколько они отличны друг от друга, в результате получают величины 50 ( $$\Delta \underset{\_}{Z}={\underset{\_}{Z}}_{Н.А}-{\underset{\_}{Z}}_{ВОЛН.А}$$

), 49 ( $$\Delta \dot{U}={\dot{U}}_{Н.А}-{\dot{U}}_{ВОЛН.А}$$

) и в случае, если это отличие минимально, тогда начинает работать следующая часть алгоритма (рис.2).At the same time (Fig. 2), the real quantities characterizing the electrical energy and present in real time at the object 17 ( $${\underset{\_}{Z}}_{N.\mathrm{BUT}}=\frac{{\dot{U}}_{N.\mathrm{BUT}}}{\dot{I}{2}_{.\mathrm{BUT}}}$$

) and 19 ( $${\dot{U}}_{N.\mathrm{BUT}}$$

) are compared with reference values (calculated using a specialized program), namely with 23 ( $${\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}$$

) and 18 ( $${\underset{\_}{Z}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}}$$

), based on this comparison, it is determined how much they are different from each other, as a result, 50 ( $$\Delta \underset{\_}{Z}={\underset{\_}{Z}}_{N.\mathrm{BUT}}-{\underset{\_}{Z}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}$$

), 49 ( $$\Delta \dot{U}={\dot{U}}_{N.\mathrm{BUT}}-{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}$$

) and if this difference is minimal, then the next part of the algorithm starts to work (Fig. 2).

), которая представлена на (рис.2). Здесь: из аналого-цифрового преобразователя 4 (АЦП) в процессор 5 (П) поступают амплитудные действительные значения тока 39 ( $$\dot{I}{2}_{.A.1}$$

), напряжения 40 ( $${\dot{U}}_{Н.А.1}$$

) и значение их частоты 58 (f) нагрузки, затем определяется действительная величина 48 ( $${\underset{\_}{Z}}_{А.Н}=\frac{{\dot{U}}_{Н.А.1}\cdot Ku}{\dot{I}{2}_{.А.1}\cdot Kz}$$

), которая будет отлична от нуля и бесконечности, в случае реализации эталонной величины нагрузки понижающего трансформатора 9 (Т2(4)) (рис.1), питаемой от четырехпроводной однородной несимметричной ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная) (рис.1). Определенные таким образом действительные величины 39 ( $$\dot{I}{2}_{.A.1}$$

), 40 ( $${\dot{U}}_{Н.А.1}$$

) (рис.2) умножаются на коэффициент 41 ((Kuz=1) или (Kuz=0)) и получают амплитудные действительные значения напряжения нагрузки 47 ( $${\dot{U}}_{А.Н}={\dot{U}}_{Н.А.1}\cdot Kuz$$

) и амплитудные действительные значения тока нагрузки 38 ( $$\dot{I}{A}_{.2}=\dot{I}{2}_{.A.1}\cdot Kuz$$

). Коэффициент 41 ((Kuz=1) или (Kuz=0)) равен единице в случае реализации эталонной величины нагрузки понижающего трансформатора 9 (Т2(4)) (рис.1) питаемой от четырехпроводной однородной несимметричной ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная) (рис.1), здесь данное условие выполнено, когда ΔZ<0.2 и $$\Delta \dot{U}$$

<0.2, а Ku=1 и Kz=1, в ином случае 41 ((Kuz=1) или (Kuz=0)) равен нулю, полученные действительные величины совместно с действительной величиной 48( $${\underset{\_}{Z}}_{А.Н}=\frac{{\dot{U}}_{Н.А.1}\cdot Ku}{\dot{I}{2}_{.А.1}\cdot Kz}$$

) подаются в следующий блок 37 (А₂).Here is a diagram of the algorithm of the processor 5 (P) for sensors 30 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D3}$$

), which is presented in (Fig. 2). Here: from the analog-to-digital converter 4 (ADC) to the processor 5 (P), the amplitude real values of the current 39 ( $$\dot{I}{2}_{.A\mathrm{.one}}$$

), voltage 40 ( $${\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}$$

) and the value of their load frequency 58 (f), then the actual value 48 ( $${\underset{\_}{Z}}_{\mathrm{BUT}.N}=\frac{{\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}\cdot Ku}{\dot{I}{2}_{.\mathrm{BUT}\mathrm{.one}}\cdot Kz}$$

), which will be different from zero and infinity, in the case of the implementation of the reference load value of the step-down transformer 9 (T2 (4)) (Fig. 1), powered by a four-wire homogeneous asymmetric power line 8 (35 kV power line OR LESS 4-wire) ( fig. 1). The actual values thus determined 39 ( $$\dot{I}{2}_{.A\mathrm{.one}}$$

), 40 ( $${\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}$$

) (Fig. 2) are multiplied by a coefficient of 41 ((Kuz = 1) or (Kuz = 0)) and get the amplitude real values of the load voltage 47 ( $${\dot{U}}_{\mathrm{BUT}.N}={\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}\cdot Kuz$$

) and the amplitude real values of the load current 38 ( $$\dot{I}{A}_{.2}=\dot{I}{2}_{.A\mathrm{.one}}\cdot Kuz$$

) Coefficient 41 ((Kuz = 1) or (Kuz = 0)) is equal to unity in the case of the implementation of the reference load value of the step-down transformer 9 (T2 (4)) (Fig. 1) fed from a four-wire homogeneous asymmetric power line 8 (power line 35 kV OR LESS 4-wire) (Fig. 1), here this condition is satisfied when Δ Z <0.2 and $$\Delta \dot{U}$$

<0.2, and Ku = 1 and Kz = 1, otherwise 41 ((Kuz = 1) or (Kuz = 0)) is zero, the real values obtained together with the real value 48 ( $${\underset{\_}{Z}}_{\mathrm{BUT}.N}=\frac{{\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}\cdot Ku}{\dot{I}{2}_{.\mathrm{BUT}\mathrm{.one}}\cdot Kz}$$

) are served in the next block 37 (A ₂ ).

) и 52 ( $${\dot{U}}_{А.ВОЛН.1}$$

) (рис.2) формируются величины эталонных токов и напряжений для питания вторичной стороны понижающего трансформатора 29 (Т6(3)) (рис.1). Эти токи и напряжения определяются следующим образом [8]:Block 53 (FOUR-WIRE v. 1.00 (2)) here in (Fig. 2) illustrates the use in the proposed method of matching the asymmetric homogeneous four-wire line with the electrical load of a specialized program for predicting the magnitude of the main characteristics of electric energy in a homogeneous power transmission line of a four-wire asymmetric design [ 10]. Based on a certain frequency 58 (f), the program determines the effective values of the complex values of currents and voltages, the propagation constants of the waves of the electromagnetic field along the wires of an asymmetric homogeneous four-wire power transmission line, and the magnitudes of the intrinsic and mutual wave resistances. In blocks 51 ( $$\dot{I}{2}_{\mathrm{BUT}.N\mathrm{.one}}$$

) and 52 ( $${\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN\mathrm{.one}}$$

) (Fig. 2), the values of the reference currents and voltages are formed to power the secondary side of the step-down transformer 29 (T6 (3)) (Fig. 1). These currents and voltages are determined as follows [8]:

1 case (for the first propagation constant, the first pair of waves of the electromagnetic field):

; $$\frac{({\dot{U}}_{В{\gamma }_1(3)}/K_{ТР})}{({\dot{I}}_{В{\gamma }_1(3)}\cdot K_{ТР})}=\frac{{\dot{U}}_{ВОЛН.В}}{\dot{I}{2}_{Н.В}+\dot{I}{2}_{В.Н}}$$

; $$\frac{({\dot{U}}_{\mathrm{BUT}{\gamma }_{\mathrm{one}}(3)}/K_{TR})}{({\dot{I}}_{\mathrm{BUT}{\gamma }_{\mathrm{one}}(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}+\dot{I}{2}_{\mathrm{BUT}.N}}$$

; $$\frac{({\dot{U}}_{\mathrm{AT}{\gamma }_{\mathrm{one}}(3)}/K_{TR})}{({\dot{I}}_{\mathrm{AT}{\gamma }_{\mathrm{one}}(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}}{\dot{I}{2}_{N.\mathrm{AT}}+\dot{I}{2}_{\mathrm{AT}.N}}$$

;

, $$\frac{({\dot{U}}_{\mathrm{FROM}{\gamma }_{\mathrm{one}}(3)}/K_{TR})}{({\dot{I}}_{\mathrm{FROM}{\gamma }_{\mathrm{one}}(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}}{\dot{I}{2}_{N.\mathrm{FROM}}+\dot{I}{2}_{\mathrm{BUT}.\mathrm{FROM}}}$$

,

Where

$$\begin{array}{l}({\dot{U}}_{{\mathrm{BUT}}_{\gamma \mathrm{one}}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{one}}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{one}}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}N\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}N\mathrm{one}}}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}N\mathrm{one}}}}sh{\gamma }_{\mathrm{one}}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}={\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

$$\begin{array}{l}({\dot{U}}_{{\mathrm{AT}}_{\gamma \mathrm{one}}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{one}}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}\mathrm{one}}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}N\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}N\mathrm{one}}}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}N\mathrm{one}}}}sh{\gamma }_{\mathrm{one}}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}={\dot{U}}_{\mathrm{AT}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

$$\begin{array}{l}({\dot{U}}_{{\mathrm{FROM}}_{{\gamma }_{\mathrm{one}}}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{FROM}\mathrm{one}}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}\mathrm{one}}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}N\mathrm{one}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}N\mathrm{one}}}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{one}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}N\mathrm{one}}}}sh{\gamma }_{\mathrm{one}}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}={\dot{U}}_{\mathrm{FROM}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

, $${\dot{U}}_{В.ВОЛН.1}$$

, $${\dot{U}}_{С.ВОЛН.1}$$

- фазные напряжения на клеммах электрической нагрузки: $${\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN\mathrm{.one}}$$

, $${\dot{U}}_{\mathrm{AT}.\mathrm{AT}\mathrm{ABOUT}LN\mathrm{.one}}$$

, $${\dot{U}}_{\mathrm{FROM}.\mathrm{AT}\mathrm{ABOUT}LN\mathrm{.one}}$$

- phase voltage at the terminals of the electrical load:

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}N\mathrm{one}}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}AN\mathrm{one}}}sh{\gamma }_{\mathrm{one}}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{BUT}.N\mathrm{.one}}$$

;

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N\mathrm{one}}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N\mathrm{one}}}sh{\gamma }_{\mathrm{one}}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{AT}.N\mathrm{.one}}$$

;

, $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{one}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N\mathrm{one}}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N\mathrm{one}}}sh{\gamma }_{\mathrm{one}}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{FROM}.N\mathrm{.one}}$$

,

, $$\dot{I}{2}_{В.Н.1}$$

, $$\dot{I}{2}_{С.Н.1}$$

- токи на клеммах электрической нагрузки. $$\dot{I}{2}_{\mathrm{BUT}.N\mathrm{.one}}$$

, $$\dot{I}{2}_{\mathrm{AT}.N\mathrm{.one}}$$

, $$\dot{I}{2}_{\mathrm{FROM}.N\mathrm{.one}}$$

- currents at the terminals of the electrical load.

2 case (for the second propagation constant, the second pair of waves of the electromagnetic field):

; $$\frac{({\dot{U}}_{В{\gamma }_2(3)}/K_{ТР})}{({\dot{I}}_{В{\gamma }_2(3)}\cdot K_{ТР})}=\frac{{\dot{U}}_{ВОЛН.В}}{\dot{I}{2}_{Н.В}+\dot{I}{2}_{В.Н}}$$

; $$\frac{({\dot{U}}_{\mathrm{BUT}{\gamma }_2(3)}/K_{TR})}{({\dot{I}}_{\mathrm{BUT}{\gamma }_2(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}+\dot{I}{2}_{\mathrm{BUT}.N}}$$

; $$\frac{({\dot{U}}_{\mathrm{AT}{\gamma }_2(3)}/K_{TR})}{({\dot{I}}_{\mathrm{AT}{\gamma }_2(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}}{\dot{I}{2}_{N.\mathrm{AT}}+\dot{I}{2}_{\mathrm{AT}.N}}$$

;

, $$\frac{({\dot{U}}_{\mathrm{FROM}{\gamma }_2(3)}/K_{TR})}{({\dot{I}}_{\mathrm{FROM}{\gamma }_2(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}}{\dot{I}{2}_{N.\mathrm{FROM}}+\dot{I}{2}_{\mathrm{BUT}.\mathrm{FROM}}}$$

,

Where

$$\begin{array}{l}({\dot{U}}_{{\mathrm{BUT}}_{\gamma 2}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="2"\; label="AT"\; filenames="00000210.png,00000211.png"\; state="\{\{state\}\}">AT</figure-callout>}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}2}}}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}2}}}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="00000210.png,00000211.png"\; state="\{\{state\}\}">N</figure-callout>}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}N2}}}ch\gamma 2l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}N2}}}sh{\gamma }_{2}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}={\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

$$\begin{array}{l}({\dot{U}}_{{\mathrm{AT}}_{\gamma }{}_2(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}2}}}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}2}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="00000210.png,00000211.png"\; state="\{\{state\}\}">N</figure-callout>}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}N2}}}ch{\gamma }_{2}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}N2}}}sh{\gamma }_{2}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}={\dot{U}}_{\mathrm{AT}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

$$\begin{array}{l}({\dot{U}}_{{\mathrm{FROM}}_{\gamma 2}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{FROM}2}}}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="2"\; label="AT"\; filenames="00000210.png,00000211.png"\; state="\{\{state\}\}">AT</figure-callout>}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}2}}}{e}^{-\gamma 2^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="00000210.png,00000211.png"\; state="\{\{state\}\}">N</figure-callout>}2}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}N2}}}ch{\gamma }_{2}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}2}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}N2}}}sh{\gamma }_{2}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}={\dot{U}}_{\mathrm{FROM}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}N2}}ch{\gamma }_{\mathrm{one}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}AN2}}sh{\gamma }_{2}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{BUT}.N\mathrm{.one}}$$

;

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N2}}ch{\gamma }_{2}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N2}}sh{\gamma }_{2}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{AT}.N\mathrm{.one}}$$

;

. $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N2}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N2}}ch{\gamma }_{2}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N2}}sh{\gamma }_{2}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{FROM}.N\mathrm{.one}}$$

.

3 case (for the third propagation constant, the third pair of waves of the electromagnetic field):

; $$\frac{({\dot{U}}_{В{\gamma }_3(3)}/K_{ТР})}{({\dot{I}}_{В{\gamma }_3(3)}\cdot K_{ТР})}=\frac{{\dot{U}}_{ВОЛН.В}}{\dot{I}{2}_{Н.В}+\dot{I}{2}_{В.Н}}$$

; $$\frac{({\dot{U}}_{\mathrm{BUT}{\gamma }_3(3)}/K_{TR})}{({\dot{I}}_{\mathrm{BUT}{\gamma }_3(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}+\dot{I}{2}_{\mathrm{BUT}.N}}$$

; $$\frac{({\dot{U}}_{\mathrm{AT}{\gamma }_3(3)}/K_{TR})}{({\dot{I}}_{\mathrm{AT}{\gamma }_3(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}}{\dot{I}{2}_{N.\mathrm{AT}}+\dot{I}{2}_{\mathrm{AT}.N}}$$

;

, $$\frac{({\dot{U}}_{\mathrm{FROM}{\gamma }_3(3)}/K_{TR})}{({\dot{I}}_{\mathrm{FROM}{\gamma }_3(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}}{\dot{I}{2}_{N.\mathrm{FROM}}+\dot{I}{2}_{\mathrm{BUT}.\mathrm{FROM}}}$$

,

Where

$$\begin{array}{l}({\dot{U}}_{{\mathrm{BUT}}_{\gamma 3}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="3"\; label="AT"\; filenames="00000213.png,00000214.png"\; state="\{\{state\}\}">AT</figure-callout>}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}3}}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}3}}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="00000213.png,00000214.png"\; state="\{\{state\}\}">N</figure-callout>}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}N3}}}ch{\gamma }_{3}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}N3}}}sh{\gamma }_{3}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}={\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

$$\begin{array}{l}({\dot{U}}_{{\mathrm{AT}}_{\gamma 3}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}3}}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}3}}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="00000213.png,00000214.png"\; state="\{\{state\}\}">N</figure-callout>}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}N3}}}ch{\gamma }_{3}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}N3}}}sh{\gamma }_{3}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}={\dot{U}}_{\mathrm{AT}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

$$\begin{array}{l}({\dot{U}}_{{\mathrm{FROM}}_{{\gamma }_3}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{FROM}3}}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="3"\; label="AT"\; filenames="00000213.png,00000214.png"\; state="\{\{state\}\}">AT</figure-callout>}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}3}}}{e}^{-\gamma 3^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="00000213.png,00000214.png"\; state="\{\{state\}\}">N</figure-callout>}3}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}N3}}}ch{\gamma }_{3}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}3}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}N3}}}sh{\gamma }_{3}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}={\dot{U}}_{\mathrm{FROM}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}N3}}ch{\gamma }_{3}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}AN3}}sh{\gamma }_{3}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{BUT}.N\mathrm{.one}}$$

;

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N3}}ch{\gamma }_{3}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N3}}sh{\gamma }_{3}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{AT}.N\mathrm{.one}}$$

;

. $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N3}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N3}}ch{\gamma }_{3}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N3}}sh{\gamma }_{3}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{FROM}.N\mathrm{.one}}$$

.

4 case (for the fourth propagation constant, the fourth pair of waves of the electromagnetic field):

; $$\frac{({\dot{U}}_{В{\gamma }_4(3)}/K_{ТР})}{({\dot{I}}_{В{\gamma }_4(3)}\cdot K_{ТР})}=\frac{{\dot{U}}_{ВОЛН.В}}{\dot{I}{2}_{Н.В}+\dot{I}{2}_{В.Н}}$$

; $$\frac{({\dot{U}}_{\mathrm{BUT}{\gamma }_{\mathrm{four}}(3)}/K_{TR})}{({\dot{I}}_{\mathrm{BUT}{\gamma }_{\mathrm{four}}(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}}{\dot{I}{2}_{N.\mathrm{BUT}}+\dot{I}{2}_{\mathrm{BUT}.N}}$$

; $$\frac{({\dot{U}}_{\mathrm{AT}{\gamma }_{\mathrm{four}}(3)}/K_{TR})}{({\dot{I}}_{\mathrm{AT}{\gamma }_{\mathrm{four}}(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}}{\dot{I}{2}_{N.\mathrm{AT}}+\dot{I}{2}_{\mathrm{AT}.N}}$$

;

, $$\frac{({\dot{U}}_{\mathrm{FROM}{\gamma }_{\mathrm{four}}(3)}/K_{TR})}{({\dot{I}}_{\mathrm{FROM}{\gamma }_{\mathrm{four}}(3)}\cdot K_{TR})}=\frac{{\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}}{\dot{I}{2}_{N.\mathrm{FROM}}+\dot{I}{2}_{\mathrm{BUT}.\mathrm{FROM}}}$$

,

Where

$$\begin{array}{l}({\dot{U}}_{{\mathrm{BUT}}_{\gamma \mathrm{four}}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{four}}}}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{four}}}}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}N\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}N\mathrm{four}}}}ch{\gamma }_{\mathrm{four}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}N\mathrm{four}}}}sh{\gamma }_{\mathrm{four}}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{BUT}}={\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

$$\begin{array}{l}({\dot{U}}_{{\mathrm{AT}}_{\gamma \mathrm{four}}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{BUT}\mathrm{AT}\mathrm{four}}}}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}\mathrm{four}}}}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}N\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}N\mathrm{four}}}}ch{\gamma }_{\mathrm{four}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}N\mathrm{four}}}}sh{\gamma }_{\mathrm{four}}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{AT}}={\dot{U}}_{\mathrm{AT}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

$$\begin{array}{l}({\dot{U}}_{{\mathrm{FROM}}_{{\gamma }_{\mathrm{four}}}(3)}/K_{TR})=\\ =\left(\left({\dot{U}}_{{\mathrm{FROM}}_{\mathrm{.one}}(3)}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{{\mathrm{BUT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}\mathrm{BUT}\mathrm{FROM}\mathrm{four}}}}{e}^{-\gamma {\mathrm{one}}^l}+\frac{{\dot{I}}_{{\mathrm{AT}}_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{AT}\mathrm{FROM}\mathrm{four}}}}{e}^{-\gamma {\mathrm{four}}^l}+\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}N\mathrm{four}}\cdot {\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}N\mathrm{four}}}}ch{\gamma }_{\mathrm{four}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}\mathrm{four}}}{{\underset{\_}{Z}}_{{}_{\mathrm{from}\mathrm{FROM}N\mathrm{four}}}}sh{\gamma }_{\mathrm{four}}l\right)/K_{TR}\right)=\\ ={\dot{U}}_{\mathrm{AT}\mathrm{ABOUT}LN.\mathrm{FROM}}={\dot{U}}_{\mathrm{FROM}.\mathrm{AT}\mathrm{ABOUT}LN}\end{array}$$

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{BUT}N\mathrm{four}}}ch{\gamma }_{\mathrm{four}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}AN\mathrm{four}}}sh{\gamma }_{\mathrm{four}}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{BUT}.N\mathrm{.one}}$$

;

; $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N\mathrm{four}}}ch{\gamma }_{\mathrm{four}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{AT}N\mathrm{four}}}sh{\gamma }_{\mathrm{four}}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{AT}.N\mathrm{.one}}$$

;

. $$\left(\left(\frac{{\dot{I}}_{N_{\mathrm{.one}}(3)}\cdot {\underset{\_}{Z}}_{\mathrm{from}N\mathrm{four}}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N\mathrm{four}}}ch{\gamma }_{\mathrm{four}}l+\frac{{\dot{U}}_{N_{\mathrm{.one}}(3)}}{{\underset{\_}{Z}}_{\mathrm{from}\mathrm{FROM}N\mathrm{four}}}sh{\gamma }_{\mathrm{four}}l\right)\cdot K_{TR}\right)=\dot{I}{2}_{\mathrm{FROM}.N\mathrm{.one}}$$

.

Since the load of each linear wire of a power transmission line 8 (35 kV power transmission line or LESS 4-wire) is one, and there are four pairs of electromagnetic field waves propagating through each linear wire, then matching of each wire can be realized only for one pair of electromagnetic field waves, and namely, according to the above formulas: 1 case (mathematical formulations are used) or 2 case, or 3 case, or 4 case.

) и 52 ( $${\dot{U}}_{А.ВОЛН.1}$$

) (рис.2) умножаются на коэффициент 41 ((Kuz=1) или (Kuz=0)), который равен единице в случае достижения эталонной величины тока и напряжения четырехпроводной нагрузки понижающего трансформатора 9 (Т2(4)) (рис.1) питаемого от четырехпроводной однородной несимметричной ЛЭП 8 (ЛЭП 35 кВ ИЛИ МЕНЬШЕ 4-х проводная) (рис.1), в противном случае 41 ((Kuz=1) или (Kuz=0)) (рис.2) имеет значение нуля, и получают эталонные амплитудные значения напряжения 43 ( $${\dot{U}}_{А.ВОЛН}={\dot{U}}_{А.ВОЛН.1}\cdot Kuz$$

) и тока 42 ( $$\dot{I}{2}_{А.Н}=\dot{I}{2}_{A.Н.1}\cdot Kuz$$

). Далее определяется полное эталонное сопротивление нагрузки 46) (рис.2).Values 51 ( $$\dot{I}{2}_{\mathrm{BUT}.N\mathrm{.one}}$$

) and 52 ( $${\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN\mathrm{.one}}$$

) (Fig. 2) are multiplied by the coefficient 41 ((Kuz = 1) or (Kuz = 0)), which is equal to unity if the reference current and voltage of the four-wire load of the step-down transformer 9 (T2 (4)) are reached (Fig. 1 ) fed from a four-wire homogeneous asymmetric power line 8 (power line 35 kV OR LESS 4-wire) (Fig. 1), otherwise 41 ((Kuz = 1) or (Kuz = 0)) (Fig. 2) has a value of zero , and reference voltage amplitudes 43 ( $${\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}={\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN\mathrm{.one}}\cdot Kuz$$

) and current 42 ( $$\dot{I}{2}_{\mathrm{BUT}.N}=\dot{I}{2}_{A.N\mathrm{.one}}\cdot Kuz$$

) Next, the total reference load resistance 46) is determined (Fig. 2).

The resulting values are sent to block 37 (A ₂ ).

), 43 ( $${\dot{U}}_{А.ВОЛН}={\dot{U}}_{А.ВОЛН.1}\cdot Kuz$$

) с действительным сопротивлением нагрузки 48 ( $${\underset{\_}{Z}}_{А.Н}=\frac{{\dot{U}}_{Н.А.1}\cdot Ku}{\dot{I}{2}_{.А.1}\cdot Kz}$$

) и действительным напряжением 47( $${\dot{U}}_{А.Н}={\dot{U}}_{Н.А.1}\cdot Kuz$$

), величин личин определенных при помощи устройств сопряжения 30 ( $${\displaystyle \sum _{i=1}^nД3}$$

) (рис.1).In block 37 (A ₂ ) (Fig. 4), logical operations are performed. Here, a comparison is made of reference values (calculated values using a specialized program) 46 ( $${\underset{\_}{Z}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}=\frac{{\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}}{\dot{I}{2}_{\mathrm{BUT}.N}}$$

), 43 ( $${\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}={\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN\mathrm{.one}}\cdot Kuz$$

) with actual load resistance 48 ( $${\underset{\_}{Z}}_{\mathrm{BUT}.N}=\frac{{\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}\cdot Ku}{\dot{I}{2}_{.\mathrm{BUT}\mathrm{.one}}\cdot Kz}$$

) and the actual voltage 47 ( $${\dot{U}}_{\mathrm{BUT}.N}={\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}\cdot Kuz$$

), the values of the identifiers determined using the interface devices 30 ( $${\displaystyle \sum _{i=\mathrm{one}}^{n}D3}$$

) (Fig. 1).

а величины ошибок по сопротивлению попадают в блок суммы ошибок по сопротивлению $${\displaystyle \sum _{i=1}^5{Z}_{A1}}$$

. Сведения о результатах расчета ошибок поступают в один или несколько блоков корректирующих органов 14, 32, 35 (КОн, КO4, КO5) (рис.1).Here, from a comparison of these values, errors are determined by the resistance ΔZ1, ΔZ2, ΔZ3 and by the voltage ΔU1, ΔU2, ΔU3. Then, the current errors ΔI01-05, ΔI07, ΔI08 are determined. At zero values of voltage errors, there are no current errors ΔI06 and ΔI09, therefore, their determination is not necessary. Information on the quantities ΔZ1, ΔZ2, ΔZ3 and ΔU1, ΔU2, ΔU3 is received in one of nine blocks with priority 2. The subsequent action of the described algorithm consists in determining errors either from the resistance ΔZ04 _O , ΔZ06 _O , ΔZ07 _O , ΔZ08 _O , ΔZ09 _O , or by voltage ΔU01 _O , ΔU02 _O , ΔU03K _O , ΔU05 _O. The voltage error values obtained in this way go to the voltage error sum block $${\displaystyle \sum _{i=\mathrm{one}}^5{U}_{A\mathrm{one}}}$$

and the values of errors in resistance fall into the block of the sum of errors in resistance $${\displaystyle \sum _{i=\mathrm{one}}^5{Z}_{A\mathrm{one}}}$$

. Information about the results of error calculation is sent to one or several blocks of corrective bodies 14, 32, 35 (KON, KO4, KO5) (Fig. 1).

(рис.4) следует собирать ошибки по току, а затем в результате сопоставления эталонного и действительного значений токов на вторичной стороне понижающего трансформатора 29 (Т6(3)), сформировать сигнал для корректирующих органов 14, 32, 35 (КОн, КO4, КO5) (рис.1).Here (Fig. 4), as a criterion for the functioning of corrective organs, a mismatch of the secondary load voltage 29 (T6 (3)) with a four-wire homogeneous asymmetric power line of 35 kV or less than 8 (power line of 35 kV OR LESS 4-wire) (Fig. 1) was chosen or load resistance. In principle, the mismatch of the secondary load current 29 (T6 (3)) can also be chosen as such a criterion (Fig. 1). For this, in the block $${\displaystyle \sum _{i=\mathrm{one}}^5{Z}_{A\mathrm{one}}}$$

(Fig. 4), current errors should be collected, and then, as a result of comparing the reference and actual currents on the secondary side of the step-down transformer 29 (T6 (3)), generate a signal for the corrective organs 14, 32, 35 (KON, KO4, KO5 ) (Fig. 1).

In the process of implementing stabilization of the specified values of currents and voltages on the secondary side of the step-down transformer 29 (T6 (3)) (Fig. 1), it was found out (Fig. 4) that with:

)>43( $${\dot{U}}_{А.ВОЛН}={\dot{U}}_{А.ВОЛН.1}\cdot Kuz$$

) и 48( $${\underset{\_}{Z}}_{А.Н}=\frac{{\dot{U}}_{Н.А.1}\cdot Ku}{\dot{I}{2}_{.А.1}\cdot Kz}$$

)>46( $${\underset{\_}{Z}}_{А.ВОЛН}=\frac{{\dot{U}}_{А.ВОЛН}}{\dot{I}{2}_{А.Н}}$$

) ошибка по току не определяется. В этом случае предусмотрено определение дополнительной ошибки по напряжению 57 (ΔU_P) в виде произведения разницы между 43 ( $${\dot{U}}_{А.ВОЛН}={\dot{U}}_{А.ВОЛН.1}\cdot Kuz$$

) и 47 ( $${\dot{U}}_{А.Н}={\dot{U}}_{Н.А.1}\cdot Kuz$$

) и коэффициента состояния ΔIos1. Затем сведения об этой дополнительной ошибке отправляются в блок $${\displaystyle \sum _{i=1}^5{U}_{A1}}$$

.47 ( $${\dot{U}}_{\mathrm{BUT}.N}={\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}\cdot Kuz$$

)> 43 ( $${\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}={\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN\mathrm{.one}}\cdot Kuz$$

) and 48 ( $${\underset{\_}{Z}}_{\mathrm{BUT}.N}=\frac{{\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}\cdot Ku}{\dot{I}{2}_{.\mathrm{BUT}\mathrm{.one}}\cdot Kz}$$

)> 46 ( $${\underset{\_}{Z}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}=\frac{{\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}}{\dot{I}{2}_{\mathrm{BUT}.N}}$$

) current error is not detected. In this case, the definition of an additional voltage error 57 (ΔU _P ) in the form of the product of the difference between 43 ( $${\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN}={\dot{U}}_{\mathrm{BUT}.\mathrm{AT}\mathrm{ABOUT}LN\mathrm{.one}}\cdot Kuz$$

) and 47 ( $${\dot{U}}_{\mathrm{BUT}.N}={\dot{U}}_{N.\mathrm{BUT}\mathrm{.one}}\cdot Kuz$$

) and the state coefficient ΔIos1. Then information about this additional error is sent to the block. $${\displaystyle \sum _{i=\mathrm{one}}^5{U}_{A\mathrm{one}}}$$

.

Block 37 (A ₂ ) (Fig. 4) is implemented in the National Instruments Lab VIEW 2009 environment.

The blocks of step-down transformers 2 (T1) and 9 (T2 (4)) (Fig. 1) with balancing devices can be replaced by blocks of step-down transformers without balancing devices 54 (T1 (8)) and 55 (T2 (9)) (Fig. .5).

The step-down transformer block 29 (T6 (3)), the connection diagram of the primary and secondary windings of which: a star / star with a neutral wire output, voltage 10 kV / 0.4 kV (Fig. 1) can be replaced by a step-down transformer block 59 (T8 ( 3)), the connection diagram of the primary and secondary winding of which is: a triangle / star with the output neutral wire, voltage 10 kV / 0.4 kV (Fig. 6).

Information sources

1. Bolypanin G.A. Distribution of low-quality electric energy over sections of electric power systems. In 2 book Prince 21 G.A. Bolypanin. - Bratsk: BrSU, 2006, - 807 s.

2. Bolypanin G.A. Distribution of low-quality electric energy over sections of electric power systems. In 2 book Prince 1 / G.A. Bolypanin - Bratsk: BrSU, 2006, - 807 p.

3. Venikov V.A. Distant power transmission of alternating and direct current / V.A. Venikov, Yu.P. Ryzhkov. - M.: Energoatomizdat, 1985 .- 272 p.

4. Electrical systems. Power Transmission by AC and DC High Voltage / Ed. V.A. Venikova. - M.: Higher School, 1972.- 367 p.

5. Bolypanin G.A. Correction of the quality of electric energy / G.A. Bolypanin. - Bratsk: State Educational Institution of Higher Professional Education “BrSU”, 2007.- 120 p.

6. Bolypanin G.A. Distribution of low-quality electric energy over a homogeneous section of a four-wire power line / G.A. Bolypanin, L.Yu. Bolypanina // Systems. Methods Technologies. - 2009. No. 3. - S. 65-69.

7. Kerky D. Coordination of the output impedance using a fully differential operational amplifiers / D. Kerky // Components and technologies. - 2010. - No. 5. - S.150-154.

8. Kozlov V.A. Coordination conditions for a homogeneous asymmetric four-wire high-voltage power line with voltage up to 35 kV with load / V.A. Kozlov, G.A.Bolynanin // Materials of the VIII international scientific and practical conference. - Sofia: Byal GRAD-BG OOD, 2012.- P.67-71.

9. Serdeshnov A. Balancing device for transformers. Means of voltage stabilization and reduction of losses in 0.4 kV networks. / A. Serdeshnov, I. Protosovitsky, Yu. Leus, P. Shumra // Electrical Engineering News.- 2005.-No1.-P.14-15.

10. Certificate on state registration of a computer program No. 20100614157 "Calculation of the parameters of a three-phase four-wire power line (FOUR-WIRE v. 1.00)"

Claims (1)

A method for matching an asymmetric homogeneous four-wire power line, which is part of an asymmetric electric power system with an electrical load, which consists in the fact that the initial information about the voltages, currents and their frequency in the line through the interface devices enters the processor, characterized in that the matching conditions are checked in the processor a four-wire power line with an electrical load for each wire of the line as a result of comparing the actual (present in time at the facility) and reference (determined using a specialized program) values of load resistances, voltages at the end of the line or currents supplied to the load, and control signals are generated for corrective organs, which are used as on-load tap-changers of power transformers as with balancing devices, and without them, reactors and three-phase or single-phase devices that generate current and voltage, such as capacitor banks, three-wire (without a fourth conductor from the neutral power supply and load) is a generalized load, incorporating a step-down transformer with a connection circuit of the primary and secondary windings of a star / star with an output neutral wire or a triangle / star with an output neutral wire.

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