PL207942B1 - The manner of location of short-circuits in power engineering lines with numerous branches - Google Patents

Description

Description of the invention

The subject of the invention is a method of fault location in power lines with multiple branches, applicable in power engineering for overhead and overhead-cable transmission or distribution lines.

Accurate determination of the fault location in power lines is of great importance for both power distribution companies and electricity consumers.

Quick and accurate location of a fault affects the quality of the transmitted electricity as well as the reliability and continuity of its supply.

In most cases, short-circuits cause mechanical damage that must be repaired before voltage is restored in the off line.

Quick removal of the damage is possible when the fault location is precisely known.

The simplest method of finding the fault location is to search the line.

This method is slow and expensive, and even dangerous in unfavorable weather conditions.

Fault locators are used to identify fault locations, which allow for a quick determination of the fault location.

Fault locator, most often is part of a digital protection relay, which are located in stations or in power substations.

Depending on the type of transmission power lines: parallel lines, lines with one branch, lines with many branches, and depending on the location of end terminals and the differentiation of measurement signals, various methods of locating faults are distinguished.

From US Patent No. 5,485,394, a system and a method for locating faults in a double-circuit transmission line with multiple branches is known.

The method according to the invention consists in that a multi-branch transmission system is equivalent to a single branch transmission system.

For such a system, the differential current amplitudes are calculated at each station, and then the distance to the fault location is calculated from their relation.

The method of fault location using the measurement of current and voltage phasors at all stations (at the ends) of a line with many branches is known from the publication "Novel Fault Location Algorithim for Multi-Terminal Lines Using Phasor Measurement Units" published in conference materials of Thirty-Seventh Annual North American Power Symposium in Ames, Iowa USA October 23-25, 2005.

The method of this method is that a multi-section transmission line is reduced to non-branch line arrangements assuming a fault is located in one of these sections, and then calculating hypothetical fault locations for this assumption.

Then, calculations of the next hypothetical fault locations are carried out, assuming that the fault is located in the next successive sections of the line.

From the so calculated hypothetical locations, one value is selected, which falls within a certain range of predicted values and indicates the actual fault location.

The Polish patent specification No. 206 226 describes a method of fault location in power lines with one branch, which is characterized by the fact that at all end stations the current for the short-circuit and pre-short circuit conditions is measured, and at one end station of the system the line phase voltage for the state short-circuit and pre-short circuit, hypothetical fault locations are assumed, distances of hypothetical fault locations are calculated and the transition resistance is calculated. The selection of the appropriate fault location is carried out by analyzing the numerical values concerning the distance of hypothetical fault locations, transition resistance and impedance modules of the equivalent power supply systems.

The essence of the method of fault location in power lines with multiple branches according to the invention, which takes into account the division of transmission lines of a transmission or distribution system into sections and a hypothetical place of fault occurrence in at least one of these sections is current input signals from individual lines for short-circuit and pre-short-circuit conditions are made, and in one end station of the system, the line phase voltages for short-circuit and pre-short-circuit conditions are measured, the distances of hypothetical fault locations are calculated and the transition resistance is calculated, and then the appropriate fault location is selected, is that:

PL 207 942 B1

- symmetrical components of phase currents measured at all end stations of the system line are calculated, symmetrical components of phase voltages for the end station of the system, where the phase voltages were previously measured, and the total short-circuit current at the fault location is calculated,

- the first hypothetical fault location situated in the line section between the beginning of the line and the first nodal point, the second hypothetical fault location located in the line section between the line end and the last nodal point, further hypothetical fault locations located in the branches, further hypothetical fault locations situated in line sections between two consecutive nodal points,

- the distances (d1), (d (2n-3)), (d (2k-2)), (d (2k-1)) are calculated, where (d1) is the distance from the beginning of the line to the fault location, (d (2n-3)) means the distance from the end of the line to the fault location, (d (2k-2)) means the distance from the end of the branch line to the fault location located in this branch, (d (2k-1)) means the distance from the node point to the fault location occurring in the line section between two nodal points, and (n) means the number of stations, and (k) the number of the node point, and then for all hypothetical fault locations in each section, the transition resistance is calculated, respectively: (R1F), ( R (2n-3) F), (R (2k-2) F), (R (2k-1) F),

- the selection of the correct fault location is made, first by comparing the numerical values concerning the distances (d1), (d (2n-3)), (d (2k-2)), (d (2k-1)) and rejecting the results whose numerical values are negative or greater than 1 in relative units, and then by analyzing the values of the calculated transition resistances for fault locations (R1F), (R (2n-3) F), (R (2k-2) F), (R ( 2k-1) F) and rejection of those calculation results for which the transition resistance value is negative,

- if only one numerical value concerning the distance (d1), (d (2n-3)), (d (2k-2)), (d (2k-1)) is in the numerical range from zero to one in units relative and the value of the calculated transition resistance for this distance to the fault location is positive or equal to zero, these results are final results and indicate the actual distance to the fault location and the value of the transition resistance at the fault location,

- if it turns out that at least two numerical values for the distance (d1), (d (2n-3)), (d (2k-2)), (d (2k-1)) are in the numerical range from zero to one in relative units and the values of the calculated transition resistances for these fault locations are positive or equal to zero, then the impedances of the equivalent supply system sources are calculated for the negative-sequence sequence for single-phase, two-phase and two-phase faults with earth or for positive sequence faults for three-phase faults and at assuming that the fault is located in a specific section, and then,

- it is checked whether the calculated values of impedance and equivalents of power supply systems are included in the first quadrant of the Cartesian system for the complex plane and the distances to the fault locations for which the impedance values are not included in this quarter of the system are rejected,

- if it turns out that only one value of the equivalent impedance of the power supply system source regarding the distance (d1), (d (2n-3)), (d (2k-2)), (d (2k-1)) is included in the first quadrant is the result of calculating the distance to the fault location, for this impedance it is considered the final result,

- if it turns out that at least two impedance values of the power supply system equivalents regarding the distance (d1), (d (2n-3)), (d (2k-2)), (d (2k-1)) are included in the first quadrant, the modules of these impedances are determined, then:

- the equivalent impedance modules of power supply systems are determined for the negative-sequence sequence for single-phase, two-phase and two-phase faults with earth or for the positive-sequence sequence for three-phase faults, assuming that the fault is located in a specific section,

- the values of the equivalent impedance modules of the power supply systems are compared with the realistic values that actually determine the supply / load of the system and one of these distances (d1), (d (2n-3)), (d (2k- 2)), (d (2k-1)), for which the value of the impedance module of the equivalent power supply systems is the closest to realistic values, actually determining the power supply / load of the system.

Preferably, the calculation of the total short-circuit current is performed taking into account the coefficients of the contribution of the individual current components when determining the voltage drop across the transition resistance, whereby a specially determined set of these coefficients is used.

PL 207 942 B1

Preferably, the distances (d1), (d (2n-3)), (d (2k-2)), (d (2k-1)) are determined from the following equations:

, realfKip) imagfZ _F ) - imag (T _lp jrealfZ _F ) real <Z _1L1 / _lp ) imagf J _F ) - imagf Z, _L1 /, _p Jrealf J _F ) '_ - ^rea 16KT (nl) e.g. ~ —lL ( 2n-3) —T (nl) e.g. Zf) + i ^has gf Κτ (η-1) ηρ ~ ΖίΐΙ / 2η-3) Ζτ (η-1) ηρ Ąęalf / _p ) 'realf Z _1U2n . ₃₎ J _{T (n4) e.g.} > imag <Z _F ) - imagf Z _{1L (2n} . ₃₎ / _{T (n} . _{1) e.g.} ) real (/ _F ) _ ^{- rea} VKTkkp - ZjL (2k-2) ZTkkp JimagfZP + iniagf ^ Tkkp ^- ^ lL (2k-2) /.Tkkp Jfealf / p) realf Z _{1L (2k} . ₂₎ Z _Tkkp ) imagf Z _F ) - imagf Z _{1L (2k} . ₂₎ Z _Tkkp ) realf / _F ) _ ~ ^rea ^ —TkT (k + l) p ~ 4iL (2k-l) ZTkT (k + l) p4 ^ma § (iF) ⁺ ™ ^a g / ^/ ŁTkT (k + l) p ~ ^ lL (2k- l) ^ TkT (k + l) p) ^rea ^^ F) realfZ, ^ -,) / _{TkT (k + 1} ) _P ) iniagf Z _F ) - imag ^ Z ^^ / ^ ψ ^ + ηρ) realf / _F )

Preferably, the transition resistances (R1F), (R (2n-3) F), (R (2k-2) F), (R (2k-1) F) are determined from the following equations:

V? If = ^1F 2 (2n-3) F realfKip) ~ <ii ™ YZ _lu I _{} p} ) imagfKip) ~ d _x imag (Z _llA I _lp ) real </ _F >

imagf / p) ^rea FKT (nl) np) Π ^ (2n-3)) ' ^rea Υ ^ .1ΐχ2π-3) Ιτ (η-1) υρ) realf / _F ) imag <r _{T (n} . _{1) e.g.} ) - (i- d _(2n . _3} ) · imag (Z _{1 (2n} . ₃₎ - T (nl) e.g.>

imag </ _F ;

R.

(2k-2) F (2k-l) F + - realfFpkkp,) (Ί ^ (2k- ₂ }) ' ^rea Y — m2k-2} i-Tkkp)' (2k-2)

L (2k-2) - Tkkp, real (7p) imagiKmgJ-n ^ (2k-2)) -imag (Z _lW) —Tkkp ^ imagf / _F >

realfF

TkT (k + l) p /) - (ld _{2k}) ) -real (Z! L (2k-l) £ TkT (k + l) p realf / p) imagfKTkT (k + i) _P ) ~ ^_ ^ <2k-i)) 'dnag (Z _{1L (} 2k-i) Ł TkT (k + i) _P ) imagf / p)

Where in determining the distance (d1), (d (2n-3)), (d (2k-2)), (d (2k-1)) and the transition resistance (R1F), (R (2n-3) F ), (R (2k-2) F), (R (2k-1) F) the following signs appear:

"Real" - means the real part of a given complex quantity, "imag" - the imaginary part of a given complex quantity, d1 - the distance from the beginning of the line to the fault location, d (2n-3) - the distance from the end of the line to the fault location,

D (2k-2) - means the distance from the end of the branch line to the fault location located in this branch, d (2k-1) - means the distance from the nodal point to the fault location located in the line section between two consecutive nodal points of the line ,

V _1p - short circuit voltage for faults located in the line section between the beginning of the line and the first nodal point,

V _T (n- ₁ ) _p - short circuit voltage for faults located in the line section between the end of the line and the last nodal point,

V _Tk1p - short circuit loop voltage for short circuits located in branches,

V _Tk ( _k + ₁ ) _p - short-circuit loop voltage for faults located in the line sections between two consecutive nodal points,

I _1p - short-circuit loop current for faults located in the line section between the beginning of the line and the first nodal point,

1τ (η- ₁ ) ρ - short circuit current for faults located in the line section between the end of the line and the last nodal point,

I _Tkp - short circuit loop current for faults located in branches,

I _Tk ( _k + ₁ ) _p - short-circuit loop current for faults located in line sections between two consecutive nodal points,

I _F - means total short-circuit current,

Z _1L1 - means impedance of the line section between the beginning of the line and the first nodal point for the positive sequence,

Z _1L ( _2n-3 ) - means impedance of the line section between the beginning of the line between the line end and the last nodal point, for the positive sequence,

Z _1L (2k-2) - means the impedance of the considered branch of the line, for the positive sequence,

Z _1L (2k- ₁ ) - means impedance of the line section between two consecutive nodal points, for the positive sequence,

R1F - is the transition resistance for faults located in the line section between the beginning of the line and the first nodal point,

R (2n-3) F - is the transition resistance for faults located in the line section between the end of the line and the last nodal point,

R (2k-2) F - is the transition resistance for short-circuits located in the branches,

R (2k-1) F - means the transition resistance for a short circuit between two consecutive line nodes.

Preferably, the equivalent source impedances for the _{negative-sequence sequence (Z 2S1} ) or for the incremental positive-sequence component (Z 1 S1) are calculated assuming that the short-circuit is located in the line section between the beginning of the line and the first nodal point, according to the formula:

-V (ZiSl).

^I 1i where:

Z _{1Si - means the impedance of the equivalent source connected to the first station for the negative sequence} or for the incremental positive sequence determined assuming that the fault is located in the line section between the beginning of the line and the first node point;

V _1i - means negative sequence or positive sequence incremental voltage measured in the first station of the line,

I _1i - means the negative sequence or positive sequence of the current measured in the first station of the line, the subscript "i" takes the values i = 2 for the negative sequence, i = Δ1 for the positive sequence increment.

Preferably, the equivalent source impedances (Z 2SW) for the _{negative-sequence sequence and (Z A1S} ( _n )) for the incremental positive sequence are determined assuming that the short-circuit is located in the line section between the end of the line and the last nodal point from the following equation:

PL 207 942 B1

where:

the subscript "i" takes the values i = 2 for the negative sequence, i = Δ1 for the incremental positive sequence,

Z _{1Sn - means impedance of the equivalent source for the negative sequence or positive sequence} increment, calculated assuming that the fault is located in the line section between the end of the line and the last nodal point,

ZiL ( ₂ n-3) - the impedance of the line section between the end of the line and the last nodal point for the negative sequence or for the positive sequence, where

ZńiL (2n-3) = ZiL (2n-3), d ( _2n-3 ) - the distance from the end of the line to the fault location,

I _ni - means the negative sequence or positive sequence of the current measured at the end of the line, τr transf.

- is the negative-sequence or positive-sequence voltage at the last node obtained from the analytical transfer (transfer) of the measurement (upper index: "transf."), r transf.

- is the negative-sequence or positive-sequence current to the last node obtained from the analytical transfer (transfer) of the measurement (upper index: "transf."),

I _Fi - stands for total negative sequence or positive sequence fault current.

Preferably, the equivalent source impedances for the negative-sequence sequence (Z2Sk) and for the positive-sequence positive-sequence component (Z _A1Sk ) are determined assuming that the short circuit is located in the branch line

where:

the subscript "i" takes the values i = 2 for the negative sequence, i = Δ1 for the incremental positive component, k is the number of the node to which the branch line approaches,

Z _Sk - means the impedance of the equivalent source for the negative sequence or positive sequence incremental value, calculated assuming that the short circuit is located in the branch line,

Z iL ( _{2k-2 ) - stands for negative sequence or positive sequence} branch line impedances, where

ZńiL (2k-2) = ZiL (2k-2), d ( _2k-2 ) - means the distance from the end of the branch line to the fault location located in this branch,

I _ki - means negative sequence or positive sequence incremental current measured at the end of a branch line, jr transf.

- is the voltage at the nodal point to which the branch line approaches for negative sequence or positive sequence incremental components, j transf.

- is the negative-sequence or positive-sequence current flowing to the nodal point of the branch line,

I _Fi - stands for total negative sequence or positive sequence fault current.

Preferably, the equivalent source impedance for the _{negative-sequence sequence} (Z 2sk) and (Z ₂ s (k + _i )) and for the _{positive-sequence incremental (Z ^ Sk} ) and (Z A1Sk ( _k + ₁ )) is calculated assuming that the fault is located in a line section between two consecutive nodal points, from the following equation:

PL 207 942 B1 transf. »R transf. x. π? τ transf. r. , fig.

_{zv (} _ L-Tki ^- “(2k-l) '—iL (2k-l)' ± -TkT (k + l) i ^{_ 1 -} “ (2k-l) / '^ -iL (2k-l) '(i-TkT (k + l) i ~ Lpi / + ~ _jLk 1_ _{ki H} χ (4iSk) - _r (4 1)

Zki (AiS (k + l)) rr transf. j r-7 - - ⁷¹⁰ ~ l ^2k -P '—iL (2k-i)' —TkT (k + l) i / τντ / νχη: (1 Xk-1) X - iL (2k-l) '( ŁTkT (k + l) i Łfi) ⁺ ^ iL (2k) f (* (2k-l) / —iL (2k-l) (> TkT (k + l) i Łfi / ^τ £ ± iL (2k) L (k + l) i - (ktl) and where:

the subscript "i" takes the values i = 2 for the negative sequence, i = Δ1 for the incremental positive sequence,

Z _{iSk - means the impedance of the equivalent source for the negative sequence or positive sequence} increment, calculated assuming that the short circuit is located in the line section between two successive branches,

Z iSk ( _k + _{1 ) - means the impedance of the equivalent source for the negative-sequence or positive-sequence} incremental, calculated assuming that the short-circuit is located in the line section between two successive branches,

ZiL (2k-i) - means impedance of the line section between two nodal points for the negative sequence or for the positive sequence, where

ZńiL (2k-1) = ZiL (2k-1),

Z iLk - is the impedance of the branch line section that comes to the starting nodal point of the line section between two consecutive nodal points for the _{negative sequence or positive sequence, where}

ZΔiLk = ZiLk,

Z _iL ( _2k ) - means the impedance of the branch line section that reaches the end nodal point of the line section between two consecutive nodal points for the negative sequence or the incremental positive sequence, where

ZńiL (2k) = ZiL (2k), d (2k-1) - means the distance from the nodal point to the fault location in the line section between two consecutive nodal points,

I _ki - means the negative sequence or positive sequence of the current measured at the end of a branch line, which comes to the starting nodal point of a line section between two consecutive nodal points,

I ( _k + ₁ ) _i - is the negative sequence or positive sequence of the current measured at the end of a branch line that comes to the end nodal point of a line section between two consecutive nodal points, y transf.

- is the voltage at the first nodal point of a line section between two consecutive nodal points for negative sequence or incremental positive sequence, r transf.

- is the current flowing to the first nodal point of a line section between two consecutive nodal points for negative-sequence or positive-sequence incremental,

I _Fi - means total short-circuit current for negative sequence or incremental sequence.

The advantage of the method of fault location in multi-branch power lines according to the invention is that it enables the fault location to be determined for a transmission and / or distribution system, with both passive and active taps. Compared to the known methods, in particular the method known from the publication "Novel Fault Location Algorithm for Multi-Terminal Lines Using Phasor Measurement Units", the method according to the invention uses the voltage measured only at the local station where the fault locator is located and additionally allows the determination of the resistance transitions. Due to the required input signals, the invention can be used for residual current protection, which will increase the functionality of the protection relay. In this way, the protection relay, in addition to its basic feature, i.e. whether the short circuit has occurred in a given protection zone or outside it, will be able to accurately determine the location of the short circuit. Moreover, the method according to the invention is distinguished by the ability to withstand the short circuit conditions defined by the direction and magnitude of the short circuit power flow.

PL 207 942 B1

The method according to the invention is explained in an embodiment in the drawing, in which Fig. 1 shows a general diagram of the transmission system for implementing the method according to the invention, Fig. 2 - substitute diagram of the transmission system for symmetrical components, assuming that the short circuit is located in the first section Fig. 3 - substitute diagram of the transmission system for symmetrical components for the assumption that the short circuit is located in the last section of the line, Fig. 4 - a fragment of the equivalent transmission system diagram for symmetrical components, assuming that the short circuit is located in the branch line section, 5 - a fragment of the equivalent transmission system diagram for symmetrical components for the assumption that the short circuit is located in the line section between two nodal points, Fig. 6 shows a flowchart of operations performed during fault location based on the method according to the invention.

The transmission system shown in Fig. 1 consists of 1, 2, ..., n power stations. Station 1 is at the beginning of the line, station n-ta at the end of the line. Node points T1, T2, ..T (n-1) divide the transmission system into lines sections L1, L2, ..., L (2n-3). In station 1 there is a FL fault locator. Short-circuits are located using models of short-circuits and short-circuit loops for symmetrical components and taking into account various types of short-circuits simultaneously, by using appropriate coefficients of participation of individual current components when determining the voltage drop on the transition resistance, defined as a _F1 , a _F2 , a _F0 and weighting factors α ₁ , α ₂ , α0 determining the share of individual components in the complete model of the short-circuit loop. The analysis of the boundary conditions for various types of short-circuits shows the existence of a certain degree of freedom in determining the coefficients of the participation of individual current components in determining the voltage drop across the transition resistance. Their selection depends on the adopted preference for the use of individual components depending on the type of short-circuit. In the presented embodiment of the invention, in order to ensure high accuracy of the fault location location, the voltage drop across the transition resistance is estimated using:

- negative sequence total short-circuit current for single-phase faults to earth (a-g), (b-g), (c-g) and for two-phase faults (a -b), (b-c) and (c-a),

- negative sequence and zero sequence for two-phase faults with earth (a-b-g), (b-c-g), (c-a-g),

- positive sequence incremental for three-phase short-circuits (a-b-c, a-b-c-g), for which the short-circuit value is reduced by the pre-short-circuit value of the positive-sequence current.

The recommended coefficients of participation of individual current components when determining the voltage drop across the transition resistance are presented in Table 1. The type of short-circuit is defined by the symbols: ag, bg, cg, ab, bc, ca, abg, bcg, cag, abc, abcg, where the letters a, b, c denote the individual current phases, and the letter g denotes grounding (earth), index 1 means positive sequence, index 2 - negative sequence, and index 0 - zero sequence.

T a b e l a 1

Short circuit aF1 aF2 aF0 a-g 0 3 0 b-g 0 1.5 + j 1.5 \ 3 0 c-g 0 -1.5 - j 1.5 \ 3 0 a-b 0 1.5 - j 1.5 \ 3 0 b-c 0 j \ 3 0 c-a 0 -1.5 - j 0.5 \ 3 0 a-b-g 0 3 - j \ 3 j \ 3 b-c-g 0 J 2 \ 3 j \ 3 c-a-g 0 -3 - j \ 3 j \ 3 a-b-c, a-b-c-g 1.5 + j 0.5 \ 3 1.5 - j 0.5 \ 3 *) 0

* ⁾ - due to the lack of the negative component, this coefficient can be taken as = 0

Table 2 presents the coefficients of the participation of individual current components α1, α2, α0, which define the share of individual components in the complete model of the short-circuit loop.

PL 207 942 B1

T a b e l a 2

FAULT α1 α2 α0 a-g 1 1 1 b-g -0.5 - j 0.5 \ 3 0.5 + j 0.5 \ 3 1 c-g 0.5 + j 0.5 \ 3 -0.5 - j 0.5 \ 3 1 a-b, a-b-g, a-b-c, a-b-c-g 1.5 + j 0.5 \ 3 1.5 - j 0.5 \ 3 0 b-c, b-c-g - j \ 3 j \ 3 0 c-a, c-a-g -1.5 + j 0.5 \ 3 -1.5 - j 0.5 \ 3 0

The fault locator FL from all end stations of lines 1,2, ..., n is provided with synchronized measurements of phase currents and phase voltages only from station 1. Additionally, it is assumed that the fault locator is provided with information about the type of fault and time short circuit. The fault location process, assuming that it is a fault of the (a-b-g) type - two-phase fault with earth, is as follows.

I. Stage one

1. Operation 610. In stations 1,2 ..... n, the current input signals from individual lines for short-circuit and pre-short-circuit states are measured. In station 1, the line phase voltages are measured for short-circuit and pre-short-circuit conditions. Then, the symmetrical components of phase currents measured in stations 1,2, ..., n and phase voltages measured in station 1 are calculated.

2. Operation 620. Calculate the total short-circuit current (Ip) from equation:

If = aF-ilF1 + aF2iF2 + ap0Ip0 (1) where:

the first "F" subscript stands for short circuit condition, the second "1" subscript stands for positive sequence, "2" - negative sequence, "0" - zero sequence, and _Fi , and _F2 , and _F0 - coefficients presented in Table 2.

The symmetrical components of the total short-circuit current are determined as the sum of the individual symmetrical components of the currents determined in all end stations 1, 2,. n:

1f1 = I11 + I21 + I31 + l (n-1) 1 + ln1 (2) lF2 = l12 + l22 + l32 + l (n-1) 2 + ln2 (3)

1f0 = I10 + I20 + I30 + l (n-1) 0 + ln0 (4) where: the first subscript means stations, the second subscript means: 1 - positive sequence, 2 - negative sequence, 0 - zero sequence.

II. Stage two

In the second step, a hypothetical fault location is assumed and the distance (operations performed in operations 630a, 630b, 630c, 630d) between the end of a given line and the hypothetical fault location is calculated with the following assumptions:

- calculation of the distance from the beginning of the line to the fault location, assuming that the fault is located in the first section of the L1 line - steps 3.1.a,

- calculation of the distance from the end of the line to the fault location, assuming that the fault is located in the last section of the L line (2n-3) - steps 3.1.b-3.3.b,

- calculation of the distance from the end of the branch line to the fault location, assuming that the fault is located in the kth branch line - steps 3.1.c-3.2.c,

- calculation of the distance from the branch point T (k) to the fault location, assuming that the fault is situated in the line section between two nodal points - steps 3.1.d-3.3d.

3.1.a. The fault loop voltage and current are determined from the following relations between the symmetrical components (Figs. 2-4) (operations performed in steps 630a):

V1p = 3 ^ 11 + O2V12 + aV10 (5)

PL 207 942 B1 lip = ^α ΐίΐ1 + ^α 2 ^Ι 12 + ^α 0 (6) where:

V ₁₁ , V ₁₂ , V ₁₀ - voltage measured in station 1 (first subscript) for individual symmetrical components (second subscript), i.e. positive sequence - index i, negative sequence index 2 and zero sequence - index 0, l ₁₁ , I ₁₂ , ho - currents measured in station 1 (first subscript) for individual symmetrical components (second subscript), i.e. positive sequence - index 1, negative sequence - index 2 and zero sequence - index o,

Z _11A - impedance of L1 line section for positive sequence,

Z _01A - line section impedance L1 for zero sequence, α ₁ , α ₂ , α ₀ - weighting factors listed in Table 2.

The short-circuit loop equation looks like this:

^V 1p ^{- d} 1 ^Z 11hp ^{- R} 1F ^l F = ^{0 (7)}

As a result of writing the equation (7) separately for the real and imaginary part and further mathematical transformations, the equation for the sought distance to the fault location (8) and the transition resistance (9) are obtained.

^{real (V} 1p ^{) ima} g ^(I F) ^{- ima} g ^(V 1p ^{) real (I} F) ^{real (Z} i11 ^I p ^{) ima} g ^(I F) ^{- ima} g ^(Z 1ii ^I p ^{) real (I} F)

1F

1 [ ^{real (V} 1p) ^{- d} i ^{real (Z} iH ^I p ⁾ + ^1ma g ^(V ip) ^{- d} i ^1ma g ^{(Z iH I} p) real (I _F ) 1mag (I _F ) (8) (9 ) where:

"Real" means the real part of a given complex quantity, "imag" means the imaginary part of a given complex quantity,

V _1p - means short-circuit loop voltage according to formula (5), l _f - total short-circuit current according to formula (1),

Z _{i11 - means impedance of L1 line section for positive sequence} , | p - short-circuit loop current determined according to formula (6).

transf. j. transf. jy transf.

3.1.b. The voltages for symmetrical components Ltu> Ł-w 'Ltio _{at the} first nodal point T2 are calculated (operations performed in operations 630b):

transf.

- V -7 T i_li _iLl -li '(10) where: ZiL1 - impedance of the L1 segment for the positive and negative sequence, and zero, respectively.

y transf. y transf. y transf.

3.2.b. The voltages for the symmetrical components - ^T ( ⁿ⁴ ) and '—τ (η-ΐ) 2 · _τ (η-ΐ) ο _{at the} last nodal point T (n-1) are calculated (activities performed in operations 630b):

transf. __ j-r transf. —T (n-1) and "- T (n-2) i

z-2

ΣΛ, y = i / = 1,2,3 (11) where:

Zii ( ₂ n-5) - impedance of the line section L (2n-3) for the positive and negative sequence and y transf respectively. y transf. y transf.

zero, where the voltages at the k-th nodal point - ™ ^Tk2 ™ are determined from the following formula:

PL 207 942 B1

r transf.

where:

- calculated voltage at (k-1),

Z _iL (2k-3) - impedance of the line section L (2k-3) of the line for symmetrical components.

r transf. j- transf. j-transf.

3.3.b. The values of the current -T (ni) m> -τ (η-ΐ) η2> £ τ (η-ΐ) ηο flowing from the nodal point T (n-1) to the n station in the line section L (2n-3) are calculated, (activities performed in operations 630b):

The short-circuit loop equation looks like this:

VT (n -1) e.g. ^{- (1-d} (2n-3) ^{) Z} 1L (2n-3) ¹ T (n-1) e.g. ^{- R} (2n-3) F ¹ F = ⁰ (14) where:

jr _ You-transf. t, transf. tz transf.

_T (nl) e.g. ^- 01 £ _T (nl) l + 027_T (nl) 2 + 001-101-1) 0 _j transf. ₍ jtransf. ₍ -0L (2n-3) jtransf.

—T (nl) e.g. ^- 01 £ -T (2n-l) nl + 02lT (nl) n2 + 00 ~ —lL (2n-3) —T (nl) n0 (14a) (14b)

As a result of writing the equation (14) separately for the real and imaginary part and further mathematical transformations, solutions for the searched distance to the short-circuit d (2n-3) (15) and the transition resistance R (2n-3) B (16) are obtained:

where:

Z _1L ( _2n-3 ) - line section impedance L (2n-3) for positive sequence,

Z ₀ L (2n-3) - impedance of the L (2n-3) line section for the zero sequence.

y transf. y transf. p, transf.

3.1. c. The voltages for symmetrical components in the k-th nodal point Tk are calculated from formula (12) assuming as k- the number of the considered station equal to the number of the node Tk from which the line in which the fault is considered leads to the station k (operations performed in operations 630c ).

j transf. y transf. j transf.

3.2. c. The values of the current - ^Tkkl '- ¹¹ ^ ² ' - ^Tkk0 flowing from the nodal point Tk to the kth station in the branch line section L (2k-2) are calculated (operations performed in operations 630c):

z “= Σ6 < ¹⁷ )

1 = 1,2,3

7 = 1.7 **

PL 207 942 B1

The short-circuit loop equation looks like this:

VTkkp - (1-d (2k-2) ZlL (2k-2) J.Tkkp - R (2k-2) klF = 0 where:

(i8)

(18a) (18b)

As a result of writing equation (i8) separately for the real and imaginary part and further mathematical transformations, solutions are obtained for the distance to the fault location d (2k-k) (i9) and the transition resistance R (2k-2) F (20):

realfr _Tkkp Zm _2k . ₂₎ / _Tkkp ) imagf / _F ) + imagf K _Tkkp ^ lL (2k-2) ZTkkp) ^rea tZF) realf Z _{1L (2k} . ₂₎ Z _Tkkp jimagf I _f ) - imagf Z _{lL (2k} . ₂₎ Jrealf i _F )

- ^ (2k-2) F ^_ 2 +2 rea] / r _Tkkp J (1 d _(2k _2)) '? Eal (Zu ^ k ^^ Tkkp) reaIf / _F ) _ imagf K _T kk _P ) “( 1 ~ Yk-2)) imag (Z _lU 2k-z) Lrkkp) imagf / _F >

(19), (20) where:

Z _1L ( _2k-2 ) - line section impedance L (2k-2) for positive sequence,

ZiL (2k-2) - impedance of the L (2k-2) line section for the zero sequence.

y transf. y transf. γ transf.

3.1. d. Calculate the voltages for symmetrical components - ^Tkl '- ^Tk2 ' - ^Tk0 at the k-th nodal point Tk from formula (12) (operations performed in operations 630d).

. transf. .transf. .transf.

3.2. d. The current values are calculated - ^TkT < ^{k + 1} ) and '-TkT (k + i) 2 »_TkT (k + i) o pfy _n ą _Ce g _{0 oc} | nodal point Tk to nodal point T (k + i) in a line section (operations performed in operations 630d):

The short-circuit loop equation looks like this:

^V TK (k + 1) p ^{- (1-} d (k + 2) ^{) Z} 1L (2k-1) j.TK (k + 1) p ^{- R} (2k-1) E.!. F = ⁰ ( 22) where:

V —TkT (k + l) p _TZ transf. , _TZ transf. , _Government Trans.

^- ^ lKfkl * 4 ₂ Κ _ΨΚ 2 * §; θΚτω γ _ _T transf. _{f T} transf. ₍ —0L (k + l) _T transf.

£ TkT (k + l) p ^- —1 — TkT (k + l) l + ^ 2 £ -TkT (k + l) 2 §: 0 ~ ± -TkT (k + l) 0 —lL (k + l ) (22a) (22b)

As a result of writing the equation (22) separately for the real and imaginary part and further mathematical transformations, the desired distance to the fault location d (2k-i) (23) and the transition resistance R (2k-i) F (24) are also obtained:

PL 207 942 B1 realfK _Tk T ( _{k + 1} ) _p ZlIX2k-l) / TkT (kH) p 7i ^has §iZf 7 ⁺ i ^has gf ΚτΥΓ (1ί + 1) Ρ ^Z lL (2k-l) Z TkT (k + l) _P 7 ^rea lfZ f7 real (Z | L (2k_ |) / TkT <k + 1) p7imag / ^Z Łf) - imagf ^Z ip2kU) Z _TkT ( _k + l) _P ? real (/ _F ) ^ ( 2k-l) F - ₂ + 2 ^rea VKTkT (k + l) P7 P ^ (2k-l) / ^rga ^ lL (2k-l) ZTkT (k + l) P7 real </ _F >

imagfK _{TkT (k + 1) p} ) - (Ί ^ (2k-l)) ' ^iffłfl gf ^ lL (2k-l) ZTkT (k + l) _P ) imagf / J (23), (24), where:

Z _1L ( _2k-1 ) - line section impedance L (2k-1) for positive sequence,

Z _0L ( _2k-1 ) - impedance of the line section L (2k-1) for the zero sequence, k- number of the node point.

III. Stage three

At this stage, the final results are selected (activities performed in operations

640a, 640b, 640c, 640d).

4. It is checked whether the results of calculating the distance d1, d (2n-3), d (2k-2), d (2k-1) to the fault location are within the range (0 ^ 1) in relative units: ⁰ - ^d 1 - ^{1 0} - ^d (2n-3) - ^{1 0} - ^d (2k-2) - ^{1 0} d ( _2k-1 ) - 1 and it is checked whether the results of calculating the transition resistance R _1F , R ( _2n-3 ) _F , R ( _2k-2 ) _F , R ( _2k-1 ) _F for the calculated fault locations d1, d (2n-3), d (2k-2), d (2k-1) is greater than zero. Result pairs: resistance-distance, e.g. d1, R1F, which are not included in the given intervals indicate that they were calculated with a false initial assumption concerning the fault location in a given line section. These results are discarded. The remaining results are processed further, except when only one pair of results falls within a given range. These results are final results, i.e. they indicate the fault location and determine the transition resistance at the fault location (operation 650).

5.If, after analyzing the criteria as in steps 4, it is not clear which values determine the location and resistance of the short-circuit, then the following steps calculate the impedances of the equivalent power supply systems for the negative sequence in the event of single-phase, two-phase, two-phase short-circuits with earth. or alternatively for an incremental positive component. On the other hand, for three-phase short-circuits, the impedances of the equivalent supply systems for the positive sequence are calculated (activities performed in operations 660a, 660b, 660c, 660d).

7. The total short-circuit current I _F2 for the negative sequence sequence is calculated from the following formula (operations performed in steps 660a),

Ζί-2 - Σ-> ²

7 = 1 (25)

8. The impedance of the equivalent source (Z _2S1 ) is calculated assuming that the fault is located in the line section L1 (operations performed in steps 660a):

^With 2S1 =

-V (26)

9. The equivalent source impedance (Z _2S ( _n )) is calculated assuming that the short circuit is situated in the last section of the L (2n-3) line (steps performed in operations 660b):

^{- V} n2

Z2Sn = (27) ^And n2

PL 207 942 B1 where:

j · τ τ 'r transf.

- n2 ⁼ _T (nl) 2 ^ (2η-3) Λ ^ 2L (2n-3) 'IT (nl) n2 ^ (2n-3)' - 2L (2n-3) a

transf.

T (n-1) n2

Lfi) (28)

10. The impedance of the k-th equivalent source (Z2 _sk ,) is calculated assuming that the short circuit is located in the section of the branch line L (2k-2) (operations performed in operations 660c):

Z2Sn = ^- i ^Vn2 (29) ^I n2 where:

jy _ j τ transf.

"K2" and "Tk2 '

Π ^ (2k-2)) '2

i.2L (2k-2) • 7 ż T '^ (2k-2)' - 2L (2k-2) s τ transf. -r \ '(± Tkk2 ~~ —F2 / (30)

11. The impedance of the equivalent sources (Z _2sk ,) and (Z _{2s (k} + ₁₎ ) is calculated, assuming that the short circuit is situated in the line section between the two branch points Tk - T (k + 1) (activities performed in 660d):

^-V k2

Z2Sk = - - (31) ^I k2 where:

—K2 ⁼ Km ^{Sf _} ^ (2k-l) '—2L (2k-l)' iw + ΐμ ^_ Π - ^ (2k-l)) · - 2L (2k-l) '(lTkT (k + l) 2 Łf2) + ^ 2Lk Lk2 (32) ^V (k + 1) 2 i ^Z 2S (k + 1) ⁾ “(33) (k + 2) where:

y _ (k + l) 2 transform. Tk2 '' ^ (2k-l) '-2L (2k-l)' ZfkT (k + l) 2 Π ^ (2k-l)) '^ 2L (2k-l) with J transform _ τ iy (—TkT (k + l) 2 - F2 / ^T -2L (2k) - (k + 1) 2 (34)

12. It is checked (activities performed in operations 670a, 670b, 670c, 670d) whether the calculated impedances of equivalent sources (Z2S1), (Zzsn) (Z2sc) sub c, (Zzsk), (Z2S (k + 1)) are included in range in the first quadrant of the complex plane Z, that is, both the real and imaginary parts of the calculated impedance are greater than zero. The impedances of the equivalent supply systems are determined for the negative sequence fault in the event of single-phase, two-phase, two-phase faults to earth or, alternatively, for positive sequence faults. On the other hand, for three-phase short-circuits, the impedance of the equivalent supply systems for the positive-sequence sequence is calculated. The results that are not included in the first quadrant indicate that they were calculated with a false initial assumption regarding the fault location in a given line section, and the result of calculating the distance to the fault location with this assumption is rejected. The remaining results are processed further, except when only one calculated impedance, assuming a short-circuit in a given line section, is included in the first quadrant. The result of calculating the distance to the fault location for this impedance indicates the correct initial assumption. This result is considered the final result (steps performed in step 680).

13. If, after analyzing the criteria, as in step 12, it is not clear which values determine the location of the fault, then in the following activities (activities performed in operations 690a, 690b, 690c, 690d) the calculated impedances of the equivalent power supply sources are calculated is trained to a modular form, and then the correct result is selected on the basis of the impedance module of the equivalent power systems.

14. Operation 700. If the calculated value of the impedance module of equivalent supply systems, assuming a short-circuit in a given section of the line, does not correspond to the actual value of the impedance module of the supply systems, it means that the preliminary data on the location of the fault in a given section and the result of the distance calculation were incorrectly assumed to the fault location is rejected under this assumption. If the calculated value of the impedance module of the equivalent supply systems, assuming a short-circuit in a given section of the line, corresponds to the actual value of the impedance module of the equivalent supply system, the result of calculating the distance to the fault location indicates the correct initial assumption and this result is considered the final result.

The flowchart in Fig. 13 includes the following steps for implementing the invention:

- measurement of currents and voltages according to point 1 of an exemplary embodiment of the invention,

- determination of symmetrical components of measured currents and voltages and calculation of the total short-circuit current in accordance with p. 2 of the exemplary embodiment of the invention,

- calculation of successive hypothetical distances to fault locations and transition resistance, assuming that the fault is located in the first section of the L1 line, the last section of the L line (2n-3), sections of branch lines (2k-2) and sections between successive branch points (2k -1), in accordance with:

3.1.a-3.2.a, 3.1.b-3.4.b, 3.1.c-3.3.c, 3.1.d-3.3.d of an exemplary embodiment of the invention,

- checking whether the individual hypothetical distances are in the range from 0 to 1 in relative units and rejecting those hypothetical distances whose values are negative or greater than 1, according to p. 4 of the exemplary embodiment of the invention,

- checking if the transition resistance values are greater than or equal to zero and rejecting the values less than zero, according to p. 5 of the exemplary embodiment of the invention,

- calculation of the impedance of the equivalent sources of individual sections, assuming that the short circuit is located in a given section, in accordance with p. 8-11 of the exemplary embodiment of the invention,

- selecting the correct result according to p. 12 of the exemplary embodiment of the invention by rejecting those hypothetical distances for which the impedances of the calculated equivalent sources are not included in the first quadrant of the complex coordinate system,

selecting the final result according to p. 14 of the exemplary embodiment of the invention by discarding those hypothetical distances for which the calculated value of the impedance modulus of the equivalent power systems does not correspond to the actual value of the impedance modulus of the equivalent power system.

The described example is for a two-phase earth fault (abg). However, this method is analogous to other types of short circuits. When analyzing other types of short-circuits, the relevant coefficients a _Fi , a _F2 , a _F0 , α ₁ , α ₂ , α ₀ are changed. The values of these coefficients are presented in Tables 1-2. The method of fault location in multi-branch power lines according to the invention also includes other types of faults, i.e. (ag, bg, cg, ab, bc, ca, bcg, cag, abc, abcg).

The method according to the invention is not limited to one model of the line model shown in the example of analyzing, but may apply to another model not shown in the drawing, e.g. a long line model. Then equations (10-34) will be modified.

The method according to the invention uses synchronous measurements of currents in all stations of the transmission system, additionally measuring the voltage in the station where the fault locator is located.

The selection of the applicable result is made on the basis of the aggregation of three calculated criteria values: distance to the fault location, transition resistance at the fault location and impedance of the equivalent power supply systems for those stations where voltage is not measured. This third criterion is a two-step one, i.e. in the first place it is checked whether the determined impedances of the equivalent power systems are located in the first quadrant of the complex plane Z, and then their modules are determined. This first element of the third criterion is innovative and hitherto unknown. Its advantage is that it does not require knowledge of the impedance of the equivalent power supply systems. Therefore, possible inaccurate knowledge of these impedances, which is the case in practice, has no effect here.

Claims (8)

1. Method of fault location in power lines with many branches, which takes into account the division of transmission lines of a transmission or distribution system into sections and a hypothetical place of fault occurrence in at least one of these sections is assumed, in which at all end stations of the system lines are measured input current signals from individual lines for short-circuit and pre-short-circuit conditions, and in one end station of the system, the line phase voltages for short-circuit and pre-short-circuit conditions are measured, the distances of hypothetical fault locations are calculated and the transition resistance is calculated, and then the selection of the appropriate fault location is carried out, in that: - symmetrical components of phase currents measured at all end stations of the system line are calculated, symmetrical components of phase voltages for the end station of the system, where the phase voltages were previously measured, and the total short-circuit current at the fault location is calculated, - the first hypothetical fault location situated in the line section between the beginning of the line and the first nodal point, the second hypothetical fault location situated in the line section between the line end and the last nodal point, further hypothetical fault locations located in the branches, hypothetical locations short-circuits located in line sections between two consecutive nodal points, - the distances (d1), (d (2n-3)), (d (2k-2)), (d (2k-1)) are calculated, where (d1) is the distance from the beginning of the line to the fault location, (d (2n-3)) means the distance from the end of the line to the fault location, (d (2k-2)) means the distance from the end of the branch line to the fault location located in this branch (d (2k-1)) means the distance from the node point to fault location in the line section between two nodal points, and (n) means the number of stations, and (k) the number of the node point, and then for all hypothetical fault locations in each section, the transition resistance is calculated, respectively: (R1F), (R (2n-3) F), (R (2k-2) F), (R (2k-1) F), - the selection of the correct fault location is made first by comparing the numerical values regarding the distances (d1), (d (2n-3)), (d (2k-2)), (d (2k-1)) and rejecting the results whose values numerical values are negative or greater than 1 in relative units, and then by analyzing the values of the calculated transition resistances for fault locations (R1F), (R (2n-3) F), (R (2k-2) F), (R (2k -1) F) and rejection of those calculation results for which the transition resistance value is negative, - if only one numerical value concerning the distance (d1), (d (2n-3)), (d (2k-2)), (d (2k-1)) is in the numerical range from zero to one in units relative and the value of the calculated transition resistance for this distance to the fault location is positive or equal to zero, these results are final results and indicate the actual distance to the fault location and the value of the transition resistance at the fault location, - if it turns out that at least two numerical values concerning distances (d1), (d (2n-3)), (d (2k-2)), (d (2k-1)) are included in numerical range from zero to one in relative units and the values of the calculated transition resistances for these) fault locations are positive or equal to zero, then the impedances of the equivalent sources of power supply systems are calculated for the negative-sequence sequence for single-phase, two-phase and two-phase faults with earth or for positive sequence faults , for three-phase faults and assuming that the fault is located in a specific section, then, - it is checked whether the calculated values of impedance and equivalents of power supply systems are included in the first quadrant of the Cartesian system for the complex plane and the distances to the fault locations for which the impedance values are not included in this quarter of the system are rejected, - if it turns out that only one value of the equivalent impedance of the power supply system source regarding the distance (d1), (d (2n-3)), (d (2k-2)), (d (2k-1)) is included in the first quadrant is the result of calculating the distance to the fault location, for this impedance it is considered the final result, - if it turns out that at least two impedance values of the power supply system equivalents regarding the distance (d1), (d (2n-3)), (d (2k-2)), (d (2k-1)) are included in the first quadrant, the modules of these impedances are determined, then: - the equivalent impedance modules of power supply systems are determined for the negative-sequence sequence for single-phase, two-phase and two-phase faults with earth or for the positive-sequence sequence for three-phase faults, assuming that the fault is located in a specific section, - the values of the equivalent impedance modules of the power supply systems are compared with the realistic values that actually determine the supply / load of the system and one of these distances (d1), (d (2n-3)), (d (2k- 2)), (d (2k-1)), for which the value of the impedance module The PL 207 942 B1 of equivalent power systems is closest to the realistic values that actually determine the power / load of the system. 2. The method according to p. The method of claim 1, characterized in that the calculation of the total short-circuit current is carried out taking into account the coefficients of the contribution of the individual current components when determining the voltage drop across the transition resistance, whereby a specially determined set of these coefficients is used. 3. The method according to p. 1 and 2, characterized in that the distances (d1), (d (2n-3)), (d (2k-2)), (d (2k-1)) are determined from the following equations: , realfĘ _lp > imagf / _F > - imag (T _lp jrealfZ _F ) real <Z _1L , / _lp > imagf / _F ) - imagf Z, _L1 /, _p Jrealf / _F ) '_ - ^rea 16KT (nl) eg ~ —1Ι / 2η-3) Ζτ (η-1) ηρ? I ^ma gf Zf J + i ^ma gf Κτ (η-1) ηρ ~ ^ 1Ι / 2η-3) Ζτ (η-Ι) ηρ Zf) 'realf With _1U2n . ₃₎ / _{T (n} . _{1) e.g.} > imag </ _F ) - imagf Z _{1L (2n} . ₃₎ / _{T (n} . _{1) e.g.} > real (/ _F ) _ ^{- rea} lfKTkkp ^- Jimagf / pJ + imagfKyjjjp - Z _1Li2 k-2) ZTkkp Jrealf / _F ) realf Z _1L (2k-2) Zykkp? I ^has gf Lf) ~ i ^has gf Z _{1L (} 2k-2) Ζτΐίΐψ 7 ^rea lf Zf) _ ~ ^reaction —TkT (k + l) p ~ ZiL (2k-l) ZTkT (k + l) pdi ^ma gf / F ^ ⁺ ™ ^a g ( ^/ ŁTkT (k + l) p ~ Z) L (2k-l) ZTkT (k + l ) p A ^ alf / p realf Z, ^ 2 ^,) / _{TkT (k + 1) p} ) imagf / _F ) - imagf Z _{1L (2k} _ _t) Jrea1 (/ _F ) where: "Real" - means the real part of a given complex quantity, "imag" - the imaginary part of a given complex quantity, d1 - the distance from the beginning of the line to the fault location, d (2n-3) - the distance from the end of the line to the fault location, d (2k-2) - means the distance from the end of the branch line to the fault location located in this branch, d (2k-1) - the distance from the node point to the fault location located in the line section between two consecutive line nodes, V _1p - short circuit voltage for faults located in the line section between the beginning of the line and the first nodal point, V _T ( _n-1 ) _p - short circuit voltage for faults located in the line section between the end of the line and the last nodal point, V _Tk1p - short circuit loop voltage for short circuits located in branches, V _Tk ( _k + i) _p - short-circuit loop voltage for faults located in line sections between two consecutive nodal points, 1 _1p - short circuit current for faults located in the line section between the beginning of the line and the first nodal point, 1 _T ( _n-1 ) _p - short circuit current for faults located in the line section between the end of the line and the last nodal point, 1 _Tkp - short circuit loop current for faults located in branches, 1 _Tk ( _k + ₁ ) _p - short-circuit loop current for faults located in line sections between two consecutive nodal points, 1 _F - means total short-circuit current, Z _1L1 - means impedance of the line section between the beginning of the line and the first nodal point for the positive sequence, Z _1L ( _2n-3 ) - means impedance of the line section between the beginning of the line between the end of the line and the last nodal point, for the positive sequence, Z _1L ( _2k-2 ) - means the impedance of the considered branch of the line, Z _1L ( _2k-1 ) - means impedance of the line section between two consecutive nodal points. PL 207 942 B1 4. The method according to p. The method of claim 1, characterized in that the transition resistances (R1F), (R (2n-3) F), (R (2k-2) F), (R (2k-1) F) are determined from the following equations: Ą _f = ^1F 2 realfKip) ~ <Α «? <Ζιπίΐρ> imag (T _lp ) - e ^ imagfZ _1L1 J _lp ) realf / _F ) imagf / _F > realf Γτ (η-1) ηρ) Π ^ (2 ^ 3)) ^rea K, Z _{] L} (2n-3) Ζτ (η-1) ηρ) (2n-3) F real <7 _F ; imagfK _T (ni) eg> -n- ^ _2n -3)> • imag (Z (2n-3). tl (2n-3) ± -T (nl) e.g. imag </ _F > A, (2k-2) F R. (2k-l) F + - real (T _Tkkp ) - Π - d _(2k _ _2} ) · real (Z, _U2k _ _2} —Tkkp) (2k-2) lL (2k-2) ± Tkkp, real </ _F > imagfK _Tklq J- (T ^ (2k-2)) imdg (ZL \ n2 \ L- ₂ ) iTkkp) imagf / J realfT TkT (k + l) p> ) Π (2k- \)) ' ^rea ^ (? L \ U2Y-i} L realfYjJ imagfK Tk _T ( _{k + 1} ) p) ~ C ~ ^ ki)) imagf / J! L (2k-l) ± TkT (k + l) p where: "Real" - means the real part of a given complex quantity, "imag" - means the imaginary part of a given complex quantity, R _1F - is the transition resistance for faults located in the line section between the beginning of the line and the first nodal point, R (2n-3) F - is the transition resistance for faults located in the line section between the end of the line and the last nodal point, R (2k-k) F - is the transition resistance for short-circuits located in the branches, R (2k-1) F - the short-circuit resistance between two consecutive line nodes, d1 - the distance from the beginning of the line to the fault location, d (2n-3) - the distance from the end of the line to the fault location, d (2k -2) - means the distance from the end of the branch line to the fault location located in this branch, d (2k-1) - the distance from the nodal point to the fault location located in the line section between two consecutive nodal points of the line, V _1p - short circuit voltage for faults located in the line section between the beginning of the line and the first nodal point, V _T ( _n - ₁ ) p - short circuit voltage for faults situated in the line section between the line end and the last nodal point, V _Tk1p - short circuit loop voltage for short circuits located in branches, V _Tk ( _k + ₁ ) p - short-circuit loop voltage for faults located in the line sections between two consecutive nodal points, PL 207 942 B1 I _1p - short-circuit loop current for faults located in the line section between the beginning of the line and the first nodal point, 1τ (η- ₁ ) ρ - short circuit current for faults located in the line section between the end of the line and the last nodal point, I _Tkp - short circuit loop current for faults located in branches, I _Tk ( _k + ₁ ) _p - short-circuit loop current for faults located in line sections between two consecutive nodal points, I _F - means total short-circuit current, Z _1L1 - means impedance of the line section between the beginning of the line and the first nodal point for the positive sequence, Z _1L ( _2n-3 ) - means impedance of the line section between the beginning of the line between the end of the line and the last nodal point, for the positive sequence, Z _1L ( _2k-2 ) - means the impedance of the considered branch of the line, for the positive sequence, Z _1L ( _2k-1 ) - means impedance of the line section between two consecutive nodal points for the positive sequence. 5. The method according to p. The method according to claim 1, characterized in that the impedances of the equivalent source for the _{negative-sequence sequence (Z 2S1} ) or for the incremental positive-sequence component (Z A1S1) are calculated assuming that the short-circuit is located in the line section between the beginning of the line and the first nodal point, according to the formula: -V (Zisi). ^I 1i where: Z _{1Si - means the impedance of the equivalent source connected to the first station for the negative sequence} or for the incremental positive sequence determined assuming that the fault is located in the line section between the beginning of the line and the first node point; V _1i - means negative sequence or positive sequence incremental voltage measured in the first station of the line, I _1i - means the negative sequence or positive sequence of the current measured in the first station of the line, the subscript "i" takes the values i = 2 for the negative sequence, i = Δ1 for the positive sequence increment. 6. The method according to p. The method of claim 1, characterized in that the impedances of the equivalent source (Z2S (n)) for the positive sequence and (Z _A1S ( _n )) for the positive sequence are determined assuming that the short circuit is located in the line section between the end of the line and the last nodal point z the following equation: where: the subscript "i" takes the values i = 2 for the negative sequence, i = Δ1 for the incremental positive sequence, Z _{1Sn - means impedance of the equivalent source for the negative sequence or positive sequence} increment, calculated assuming that the fault is located in the line section between the end of the line and the last nodal point, Z _iL ( _2n-3 ) - is the impedance of the line section between the end of the line and the last nodal point for the negative sequence or for the positive sequence, where ZńiL (2n-3) = ZiL (2n-3), d ( _2n-3 ) - the distance from the end of the line to the fault location, I _ni - means negative sequence or positive sequence incremental current measured at the end of the line, PL 207 942 B1 rr transf. - is the negative-sequence or positive-sequence voltage at the last node obtained from the analytical transfer (transfer) of the measurement (upper index: "transf."), r transf. - is the negative-sequence or positive-sequence current to the last node obtained from the analytical transfer (transfer) of the measurement (upper index: "transf."), I _Fi - stands for total negative sequence or positive sequence fault current. 7. The method according to p. 1, characterized in that the impedances of the equivalent source for the _{negative-sequence sequence} (Z 2Sk)) and for the _{positive-sequence} incremental sequence (Z A1Sk) are determined assuming that the short-circuit is located in the branch line where: the subscript "i" takes the values i = 2 for the negative sequence, i = Δ1 for the incremental positive component, k is the number of the node to which the branch line approaches, Z _{iSk - means impedance of the equivalent source for the negative sequence or positive sequence} incremental calculated assuming that the short circuit is located in the branch line, Z iL ( _{2k-2 ) - stands for negative sequence or positive sequence} branch line impedances, where ZńiL (2k-2) = ZiL (2k-2), d ( _2k-2 ) - means the distance from the end of the branch line to the fault location located in this branch, I _ki - means negative sequence or positive sequence incremental current measured at the end of a branch line, jr transf. - is the voltage at the nodal point to which the branch line approaches for negative sequence or positive sequence incremental components, j transf. - is the negative-sequence or positive-sequence current flowing to the nodal point of the branch line, I _Fi - stands for total negative sequence or positive sequence fault current. 8. The method according to p. 1, characterized in that the impedances of the equivalent source for the _{negative sequence} (Z 2sk) and (Z _2S ( _k + _i )) and for the positive _sequence increment (Zń 1Sk) and (Z _A1Sk ( _k + ₁ )) are calculated with the assumption that that the short circuit is situated in the line section between two consecutive nodal points from the following equation: jr transf. l 7-transf. Xi T \ π y transf. τ i _t r ~ rj —Tki ~ “(2k-l) * —iL (2k-l) 'ŁTkT (k + l) i ~ ¹ “ (2k-l) /' ^ -iL (2k-l) ' (ŁTkT (k + l) i ~~ ŁFi / ⁺ 4.jLk Compounds _<ISK; = rr Trans. 1 yy r transf. yy yy r .transf ri yy -—Tki ~ “(2k-l) '—iL (2k-l)' LTkT (k + l) i ( ¹ “ (2k-l) / 'Z.iL (2k-l)' (± -TkT ( k + l) i ^- Ξ-R / + Z.iL (2k) Ł iL (2k) L (k + l) i 6Z / S (k + l) ^ _T - (k + l) and where: the subscript "i" takes the values i = 2 for the negative sequence, i = Δ1 for the incremental positive sequence, Z _{iSk - means the impedance of the equivalent source for the negative sequence or positive sequence} increment, calculated assuming that the short circuit is located in the line section between two successive branches, PL 207 942 B1 Z _i sk (k + ₁ ) - means impedance of the equivalent source for the negative sequence or positive sequence increment, calculated assuming that the short circuit is located in the line section between two successive branches, Zi _L (2k-i) - is the impedance of the line section between two nodal points for the negative sequence or for the positive sequence, where ZńiL (2k-1) = ^Z iL (2k-1)> Z _iLk - is the impedance of the branch line section that comes to the starting nodal point of the line section between two consecutive nodal points for the _{negative sequence} or positive sequence increment, where Z ^ ia = Z iLk, Z _iL ( ₂ k) - is the impedance of the branch line section that reaches the end nodal point of the line section between two consecutive nodal points for the negative sequence or the incremental positive sequence, where ΖδϊΙ (2Κι = ^Ζ ίΙ (2 ^ d (2k-1) - means the distance from the nodal point to the fault location in the line section between two consecutive nodal points, I _ki - means the negative sequence or positive sequence of the current measured at the end of a branch line, which comes to the starting nodal point of a line section between two consecutive nodal points, I ( _k + ₁ ) _i - is the negative sequence or positive sequence of the current measured at the end of a branch line that comes to the end nodal point of a line section between two consecutive nodal points, y transf. - is the voltage at the first nodal point of a line section between two consecutive nodal points for negative sequence or incremental positive sequence, r transf. - is the current flowing to the first nodal point of a line section between two consecutive nodal points for negative-sequence or positive-sequence incremental, I _Fi - means total short-circuit current for negative sequence or incremental sequence.