PL206226B1 - Method for the location of short-circuits in single branch power transmission lines - Google Patents

Abstract

A method for locating faults in three-terminal and multi-terminal power lines, applicable in electric power systems for overhead and underground cable transmission and distribution lines. The inventive method is characterised in that it measures current for fault and pre-fault conditions and in one terminal station of the system line phase voltage for fault and pre-fault conditions is measured, a hypothetical fault location is assumed, the distances to the hypothetical fault locations are calculated and fault resistance is calculated, the actual fault point is selected by first comparing the numerical values concerning the distances to the hypothetical fault locations and rejecting those results whose numerical values are negative or bigger than one in relative units,; and then by analysing the values of the calculated fault resistances for the fault locations and rejecting those results of the calculations for which the value of fault resistance is negative, and if there is still more than one calculation result remains not rejected then performing selection of the valid result by analysing the values of the calculated respective equivalent source impedances.

Description

Description of the invention

TECHNICAL FIELD

The subject of the invention is a method of fault location in power lines with one branch, used in the power industry for overhead and overhead-cable transmission or distribution lines.

STATE OF THE ART

Accurate determination of the fault location in power lines is of great importance both for power companies dealing with energy distribution and electricity consumers. Quick and accurate locating of fault locations affects the quality of transmitted electricity as well as the reliability and continuity of its supply. In most cases, short circuits cause mechanical damage that must be rectified before the off line is re-energized. 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 is most often part of a digital protection relay, which is 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. 6466030, there is known a system and method for locating faults in a single-branch transmission line. The method according to this invention consists in dividing the transmission line into two sections in the branch node, the sending side section and the receiving side section, and on both sides of both sections, at their ends, measuring devices are placed, by means of which the values of the current signals are measured. and tension. Then, based on the synchronously or asynchronously measured quantities and the generally known fault loop model, the branch load impedance is calculated and a first hypothetical fault location is calculated assuming that the fault occurred on the sending section side. Depending on whether the measurements are synchronized or not, either the phase angle is calculated, which is a measure of the time shift of the measured samples from the signals at both ends of the line based on the measured pre-short circuit signals, or the phase angle is set to zero for synchronous measurements. The calculation of the second hypothetical fault location in the transmission line section between the branch node and the receiving point is then performed. From the two calculated hypothetical locations, one value is selected that is within the specified range of predicted values, i.e. numerical values ranging from 0 to 1 in relative units. The described solution applies to the case of a single-circuit line with a passive branch, which means that in the adopted equivalent scheme of such a system, the presence of electric motor force in the branch line is not considered, and the load impedance of this line can be calculated on the basis of pre-short circuit measurements.

A method for locating a short circuit using the measurement of current and voltage at one end of the line is known from US patent 4559491 and from patent application WO 2004/001431. However, the solutions presented in these publications do not apply to a transmission line with one branch.

SUMMARY OF THE INVENTION

The essence of the method of locating faults in power lines with one branch, which uses the division of the transmission or distribution system lines into sections located upstream and downstream of the branch node, and assumes a hypothetical location of faults in at least one of these sections, is that

- the short-circuit and pre-short-circuit current is measured at all end stations of the system,

PL 206 226 B1

- in one end station of the system, the line phase voltage is measured for the short-circuit and pre-short-circuit condition,

- the symmetrical components of the measured current and voltage signals and the total short-circuit current at the fault location are calculated,

- the first hypothetical fault location located in the line before the branch junction point, the second hypothetical fault location located in the line behind the branch node node and the next hypothetical fault location located in the branch,

- distances dA, dB, dC are calculated, where dA is the distance from the beginning of the line to the fault location, dB is the distance from the end of the line to the fault location, dC is the distance from the end of the branch line to the fault location, and for all hypothetical fault locations in each from the section, the transition resistance is calculated,

- the selection of the appropriate fault location is made by first comparing the numerical values for dA, dB, dC 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 the fault locations and rejection of those calculation results for which the transition resistance value is negative,

- if, after selecting the appropriate fault location, it turns out that at least two numerical values for the distance dA, dB, dC 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 zero, then the negative sequence modules of the impedance of power supply systems for single-phase, two-phase and two-phase faults with earth or for positive sequence faults for three-phase faults are determined and assuming that the fault occurred in a specific section,

- the values of the equivalent impedance modules of power supply systems are compared with the realistic values that actually determine the system load, and the final result is the distance dA, dB, dC of which the value of the impedance module of the equivalent power supply systems is closest to the realistic values that actually determine the system load .

Preferably, the calculation of the total short-circuit current is performed taking into account the coefficients of the contribution of the individual current components a _F1 , and _F2 , αρ ₀ when determining the voltage drop across the transition resistance.

Preferably, for two-phase faults with earth, the positive sequence is eliminated in the estimation of the total short-circuit current, and for the negative and zero sequence, the following values of the coefficients of the contribution of individual current components are assumed when determining the voltage drop on the transition resistance:

where:

α, α-12, α 110 - means the initial coefficient of the share of symmetrical components of the current when determining the voltage drop across the resistance, b _F1 , b _F2 - means the relational coefficient

PL 206 226 B1

Preferably, the distances dA, dB, dC are determined from the following equations:

_d _ reaKKAp) imag (/ _F ) - imag (K _Ap ) real (/ _F ) ^A real (Z _1LA / _Ap ) imag (/ _F ) -imag (Z _1LA / _Ap ) real (/ _F ) '

- real (K _Tp - Z _1LB J _TBP) imag (/ _F) + imag (K _Tp - ^ lib ITB _p) ^real _(F)

Cl β - real (Z _1LB / _TBP) imag (/ _F) - imag (Z _1LB / _TBP) real (/ _F)

I _J - real (K _Tp - Zilc Ztc _p ) imag (/ _F ) + imag (K _Tp - ^ ilc Łtc _p ) real (Z _F )

Cl Q - real (Z _1LC J _TCp ) imag (/ _F ) - imag (Z _1LC J _TCp ) real (/ _F ) where:

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

VAp - short circuit loop voltage determined assuming that the short circuit occurred in the LA section, y _Tp - short circuit loop voltage determined assuming that the short circuit occurred in the LB or LC section,

IA _p - short circuit current determined assuming that the short circuit occurred in section LA, / _TBp - short circuit current determined assuming that the short circuit occurred in section LB, / _TCp - short circuit current determined assuming that the short circuit occurred in the LC line section, / _F - means total short-circuit current,

Z _iLA = Ri _LA + j ^{| B} _{iŁi LA} - is the impedance of the line section LA for the positive sequence,

Z _iLB = Ri _LB + jraiŁi _LB - means impedance of the LB line section for the positive sequence,

Z _iLC = R _iL C + j ^ro i ^ ii_c - means impedance of the LC line section for the positive sequence,

R _iLA , R _iLB , R _iLC - positive-sequence resistance for the LA, LB, LC line sections, respectively,

LiLA, LiLB, LiLC - positive-sequence inductance for the line sections LA, LB, LC, ωι - pulsation for the fundamental frequency, respectively.

Preferably, the transition resistance RFA, RFB, RFC is determined from the following equations:

real (K _Ap ) - J _A real (Z _1LA / _Ap ) imag (K _Ap ) - r / _A imag (Z _1LA / _Ap ) real (/ _F ) imag (/ _F ) J 'imag (K _Tp ) - ( 1 - _B rf) · imag (Z _1LB / _TBP) imag (/ _F) 'imag (K _Tp) - (1 -) · imag (Z _1LC 7 _TCP) imag (/ _F) _ where:

"Real" means the real part of a given quantity, "imag" means the imaginary part of a given quantity, yA _p - short circuit voltage determined assuming that the short circuit occurred in the LA section, y _Tp - short circuit loop voltage determined assuming that the short circuit occurred in the LB or LC section,

IA _p - short circuit current determined assuming that the short circuit occurred in section LA, / _TBp - short circuit current determined assuming that the short circuit occurred in section LB, / _TCp - short circuit current determined assuming that the short circuit occurred in the LC line section, / _F - means total short-circuit current,

Z _iLA = R _iLA + jro _i t iLA - is the impedance of the line section LA for the _{positive sequence,}

real (K _Tp ) (1 J _B ) real (Z j _LB / _TBp ) real (/ _F ) real (F _Tp ) - (1 - d _c ) real (Z _1LC J _TCp ) real (/ _F )

7 'fb 7' fc PL 206 226 B1

Z _1LB = R _1L B + j ^{| B} _{iLi LB} - means impedance of the LB line section for the positive sequence,

Z _1LC = R _1L C + j ^{| B} _{iLi LC} - means impedance of the LC line section for the positive sequence,

R _{1LA, 1LB} R, R _1LC - resistance for the positive sequence, respectively for the line section LA, LB, LC,

LiLA, LiLB, LiLC - positive-sequence inductance for the line sections LA, LB, LC, ω1 - pulsation for the fundamental frequency, dA - the distance from the beginning of the line to the fault location, dB - the distance from the end of the line to the fault location, dC - means the distance from the end of the branch line to the fault location.

Preferably, the equivalent source impedance for the _{negative-sequence sequence (Z 2SB} ) _Sub _ _a and for the incremental positive-sequence component (Z aisb) sub_ _a is calculated assuming that the short circuit has occurred in the line section LA, according to the formula:

(7 \ _ - ('a / a2 ~ ΙίίλίΐΑί

V ~ iSB / SUB_A ~ _T \ 'where:

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

G _iA - means the first analytical negative-sequence coefficient determined from the analysis of the equivalent system as in Fig. 11 or the consensus incremental system analytically determined from the equivalent system as in Fig. 12,

I _Ai - means the negative or positive sequence of the current measured at the beginning of the line,

Hj _A - is the second negative-sequence analytical coefficient determined from the equivalent system analysis as in Fig. 11 or the consensus incremental analysis analytically determined from the equivalent system as in Fig. 12,

I _{FAi - means the negative sequence} component of the total short-circuit current, determined from the analysis of the equivalent circuit as in Fig. 11, or the positive-sequence sequence of the total short-circuit current, determined from the analysis of the equivalent circuit as in Fig. 12,

Q _bc , - is the ratio of the negative-sequence current measured at the end of the line and the sum of the negative-sequence current signals measured at the end of the line and the end of a branch line, or the ratio of the positive sequence current measured at the end of the line by the sum of positive sequence current signals measured at the end of the line and the end of the branch line.

Preferably, the equivalent source impedance (Z 2SC) _sub _ _{a for the negative sequence sequence} and (Z ai _SC ) _sub _ _a for the incremental positive sequence are determined assuming that the short circuit has occurred in the line section LA, from the following equation:

where:

the subscript i takes the values i = 2 for the negative-sequence sequence, i = Δ1 for the positive-sequence positive-sequence, (Z _SB ) _SUB _ _A - means the equivalent source impedance for the negative-sequence or positive-sequence incremental, calculated assuming that the short circuit occurred in the line section LA,

Zi _LB - is the impedance of line section LB, or the negative sequence impedance of line section LB for the incremental positive sequence, wherein Z _{Δ ιι_ Β} = Z _1LB,

Z _1LB - means impedance of the LB line section for the positive sequence,

Z _{iLC - denotes negative sequence} LC line section impedance or positive sequence LC section impedance, with Z δ-ilc = Zi _LCC and Z _2LC = Zilc.

Z 1LC - means impedance of the LC line section for the _{positive sequence,}

I _Bi - means the negative sequence or positive sequence of the current measured at the end of the line, I _Ci - means the negative sequence or positive sequence of the current measured at the end of a branch.

Preferably, the equivalent source impedance for the _{negative-sequence sequence} (Z 2SB) _Sub _ _b and for the incremental _{positive-sequence component (Z ^ Sb} ) _Sub _ _b is determined assuming that the short circuit has occurred in the line section LB, from the following equation:

PL 206 226 B1 / 1 z / A 7 fransf. i -τ -rr transf.

/ 7 λ _ V “” “B / ~ iLB ± -TBi“ β —iLB £ βϊ “Ł.Ti ν — iSB / SUB_B” ’—Bi where:

the subscript i takes the values i = 2 for the negative sequence sequence, i = Δ1 for the positive sequence positive sequence, dB - the distance from the end of the line to the fault location,

Z _{iLB - denotes negative-sequence or positive} -sequence impedance of the LB line section, where Z2LB = Zilb and Z a-ilb = Zilb.

Z _1LB - means impedance of the LB line section for the positive sequence,

I tanst - means the current flowing to the node point T from the line section LB for the negative-sequence sequence “TBi or for the incremental positive-sequence,

I _Bi - means negative sequence or positive sequence incremental current measured at the end of the line,

V- is the voltage at node T for the negative sequence or positive sequence incremental sequence.

Preferably, the equivalent source impedance for the _{negative-sequence sequence (Z 2S} c) sub_b and for the incremental positive-sequence component (Z ^ _Sc ) _Sub _ _b is calculated assuming that the short circuit has occurred in the line section LB, from the following equation:

V — iSC / SUBB ’

i. Those where:

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

V _Ci - means negative sequence or positive sequence voltage at the end of a branch line,

I _Ci - means negative sequence or positive sequence incremental current measured at the end of a branch.

Preferably, the equivalent source impedance for the _{negative-sequence sequence (Z 2SC} ) _sub _c and for the incremental positive sequence (Z ^ _Sc ) _Sub _ _c is calculated assuming that the short circuit has occurred in the LC line section, from the following equation:

.-Z \ 7 τ · transf. 1 ry j- -rr transf.

/ 7 X _ U “a _c JZ_iLc £ TCi ^- —iLC —Ci ^- _Ti v — iSC / SUB C” _T '—Ci where:

the subscript i has the values i = 2 for the negative sequence sequence, i = Δ1 for the positive sequence positive sequence, dC - the distance from the end of the branch line to the fault location,

Z _{iLC - denotes negative sequence} LC section impedance or positive sequence LC section impedance, with Z _2LC = Z _1LC and Z ^ _LC = Z-ILc.

Z 1LC - means impedance of the LC line section for the _{positive sequence,}

I ΐΞΠί. - is the negative-sequence or positive-sequence current flowing to node T from the LC line section,

I _Ci - means negative sequence or positive sequence incremental current measured at the end of a branch,

V ^tra j ^f - is the voltage at the node T for the negative sequence or the incremental positive sequence.

Preferably, the equivalent source impedance for the _{negative-sequence sequence (Z 2SB} ) _Su b_c and for the incremental positive-sequence component (Z ^ _Sb ) _Sub _ _c assuming that the short circuit has occurred in the LC line section, is calculated from the following equation:

PL 206 226 B1

where:

subscript i takes the values i = 2 for the _{negative sequence, i = Δ1 for the positive sequence, y Bi -} means the positive sequence or positive sequence of the voltage at the end of the line,

IB - means positive or negative sequence sequence of the current measured at the end of the line.

The advantage of the method of fault location in power lines with one branch, which is the subject of the invention, is that it enables the determination of the fault location for the transmission or distribution system with both passive and active taps. It is characterized by the fact that, in comparison with the method known from the patent description US 6466030, it enables the determination of the fault location additionally in the branch line and allows the determination of the transition resistance. Due to the required input signals, the location method according to the invention can be used for residual current protection, and the functionality of the protection relay will be increased. 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 resistance to short circuit conditions, i.e. the direction and magnitude of the short circuit power flow.

EXPLANATION OF THE DRAWING

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, with the sections LA, LB and LC marked, Fig. 2 - substitute diagram of the transmission system for the correct component for the assumption, that the short circuit occurred in the line section LA, Fig. 3 - negative sequence substitute diagram of the transmission system for the assumption that a short circuit occurred in the line section LA, Fig. 4 - substitute diagram of the zero sequence transmission system for the assumption that the short circuit occurred in the line section LA, fig. 5 - substitute diagram of the positive-sequence transmission system for the assumption that a short circuit occurred in the line section LB, fig. 6 - substitute diagram of the negative-sequence transmission system for the assumption that a short circuit occurred in the line section LB, fig. 7 - equivalent diagram of the transmission system for the zero sequence for the assumption that a short circuit occurred in the LB line section, Fig. 8 - equivalent diagram of the p system sequence for the positive sequence for the assumption that the short circuit occurred in the LC line section, Fig. 9 - negative sequence substitute diagram of the transmission system for the assumption that the short circuit occurred in the LC line section, Fig. 10 - zero sequence substitute diagram of the transmission system for the assumption that the short circuit occurred in the LC line section, and Fig. 11 - negative-sequence substitute diagram for assuming that the short-circuit occurred in the LA line section to calculate the equivalent impedance of the systems, Fig. 12 - surrogate diagram for the positive sequence increment to assume that the short-circuit is occurred in the line section LA for calculating the equivalent impedance of the systems, Fig. 13 - shows a flow chart of actions performed during fault location based on the method according to the invention.

EXAMPLE FOR CARRYING OUT THE INVENTION

The transmission system shown in Fig. 1 consists of three power stations A, B and C. Station A is located at the beginning of the line, station B at the end of this line, and station C after the line, which branches from the line between AB stations. The nodal point T divides the transmission system into three sections LA, LB, and LC. There is a FL fault locator in station A. Short-circuit localization is carried out using short-circuit models and short-circuit loops for symmetrical components and 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 , αρ ₂ , a _F0 and weighting factors α ₁ , α ₂ , α ₀ , determining the share of individual components in the complete model of the fault 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:

PL 206 226 B1

- negative sequence component of the 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.

Examples of the coefficients of participation of individual current components in determining the voltage drop on the transition resistance are presented in Table 1. The type of short-circuit is defined by the symbols: ag, bg, cg, ab, bc, ca, where the letters a, b, c denote individual phases and the letter g stands for grounding, index 1 is the positive sequence, index 2 is the negative sequence and index 0 is the zero sequence.

T a b e l a 1

Short circuit (F) G [F1 gF2 2f0 a-g 0 3 0 b-g 0 3a 0 c-g 0 3a ² 0 a-b 0 1-a 0 b-c 0 aa ² 0 c-a 0 a ² -1 0 a = exp (j2n / 3); j = T-1

The FL fault locator is provided with synchronized measurements of phase currents from stations A, B, C and phase voltages from station A. Additionally, it is assumed that the fault locator is supplied with information about the type of fault and the time of the fault. The fault location process, assuming that it is a fault of the type (a-b-g) - two-phase fault with earth, is as follows:

I. Stage one

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

2. Calculate the total short-circuit current (Z _F ) from the equation:

If = 3F1 / F1 + 3F2 / F2 + 3f0 / f0 (1) where:

the first subscript "F" means the short-circuit condition, the second lower index "1" means the positive sequence, "2" - the negative sequence, "0" - the zero sequence, and the coefficients of the contribution of individual current components in determining the voltage drop on the transition resistance are as follows:

- FI ⁼ θ '

—F2 init. —FI —F2 ^- - F2 ^_ —FI init. ^ FO _ —FI ^ F1 > while init. 1 2 = 1st 5: F1 1 init. = 1 -a 5F2

_F j = "β

a = exp] 2π / 3

Zn ^- Ła h ₂ = L.

Łm = Ł

-0.5 + j ^.

(2), (3), (4).

where: the first subscript means stations, the second subscript means: 1 - positive sequence, 2 - negative sequence, 0 - zero sequence.

For short-circuits of a different type, the coefficients of individual current components in determining the voltage drop across the short-circuit resistance and the "relational coefficients" are presented in tables 1, 2 and 3.

T a b e l a 2

Short circuit (F) The initial coefficient of the participation of the symmetrical components of the current in determining the voltage drop across the transition resistance Relational coefficient α - F1 α - - F2 α - - F0 bF1 bF2 a-b-g i - a ² i - a 0 -and -a ² b-c-g a ² - a a - a ² 0 -1 -1 c-a-g a- i a ² - 1 0 -a ² -and

T a b e l a 3

Short circuit (F) Coefficient of the share of symmetrical current components in the resistance voltage drop aF1 aF2) * aF0 a-b-c, a-b-c-g 1 - a ² 1 - a 0 ) * - due to the lack of the negative component, this coefficient can be taken as = 0

II. Stage two

In the second stage, a hypothetical fault location is assumed and the distance 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 occurred in the line section LA - activities 3.1.a - 3.2.a,

- calculation of the distance from the end of the line to the fault location, assuming that the fault has occurred in the LB line section - activities 3.1.b - 3.4.b,

- calculation of the distance from the end of the branch line to the fault location, assuming that the fault occurred in the LC line section - activities 3.1.c - 3.3.c.

3.1.a. The fault loop voltage and current are determined from the following relations between the symmetrical components (Fig. 2-4):

PL 206 226 B1

Kap = «ιΚαΙ + β2ΚΑ2 + aoKAO ζ

Ζλρ ⁼ ^ iZai ⁺ £ bZA2 + βο ~ Ζ Ζαο (5), (6) where:

VA ₁ , VA ₂ , VAo - voltage measured in substation A for individual symmetrical components, positive sequence - index 1, negative sequence - index 2 and zero sequence - index 0.

Im, IA ₂ , Iao - currents measured in station A for positive sequence - index 1, negative sequence - index 2 and zero - index 0,

Z 1LA - impedance of LA line section for _{positive sequence,}

Z _0LA - impedance of the line section LA for zero sequence,

The weighting factors are as follows:

a ₁ = 1 - a ² , = 1 - a

Oo = 0

For short-circuits of a different type, the weighting factors are presented in Table 4.

T a b e l a 4

Short circuit Gf1 02 αο a-g 1 1 1 b-g a ² and 1 c-g and a ² 1 a-b, a-b-g a-b-c, a-b-c-g 1 - a ² 1 - a 0 b-c, b-c-g a ² - a a - a ² 0 c-a, c-a-g a - 1 a ² - 1 0

The short-circuit loop equation looks like this:

Ka _p ^ aKilaZap ^ faZf ~ θ (7).

As a result of writing the equation (7) separately for the real and imaginary part and further mathematical transformations, the solutions presented in item 3.2a are obtained.

3.2a. The distance to the fault location dA and the transition resistance RFA are determined from the following equations:

^rea KK AP) imag (ZF) - ™ ag (K Ap) real (ZF) ^real (KiLA Z Ap) ^im ag (Z _F ) - imag (Z _1LA I _Ap ) real (/ _F ) ^rea l (KAp) ~ ^ A ^rea XKiLAZAp) imag (K _Ap ) - J _A imag (Z _1LA / _Ap ) real (/ _F ) imag (/ _F ) where:

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

V. _p - short-circuit loop voltage according to formula (5)

I _F - means total short-circuit current according to formula (1),

Z 1LA - means the impedance of the line section LA for _{positive sequence , IA p} - means the fault loop current determined according to formula (6).

PL 206 226 B1

3.1.b. The voltages for the symmetrical components V ^łra ^ ', V, V at the nodal point T are calculated:

r transf (-ig. 5-7)

Kn = cosh (/ _iLA ^ _LA ) -K _A i- ^ ciLAsinh (/ _n / _LA ) - / _A1>

1LA

1 _T2 - cosh (y _{] r} / _LA ) -K _A2 —cila sinh (y _a ^ la) 'Im - 1LA

1LA

K? R ^f = cosh (r _T Aa) Kao - ^ cola sW _nT / la) 'l

-OLA f-OLA

-A0 where:

Yii_ _A - propagation constant of the line segment LA for positive and negative components,

Y _0LA - propagation constant of the line segment LA for the zero sequence, / La - length of the line segment LA,

Z _c1LA - wave impedance of the LA segment for the _{positive and negative sequence} Z c0LA - wave impedance of the LA segment for the zero sequence.

3.2.b. The values of the currents flowing to the nodal point T from the line section LA: / tansf are calculated. And tans ^- . I jransf and LC section I / IrOn ^ L / iTOnsL (fig 5-7)

- Ai '-Λο' Λη ' ^J - / ^ 1'-' - γίί \ O /

A2

A0

C1

C2

C0 / ™ ^!, = (- l / Z _c i _LA ) -sinh (r / la>'Ka, + «« * (/ "< _LA ) - / _Al

-1LA - 1LA and “' ^r · = (-1 / Ł, la) ·« ώΟΊ. J la) · Ί A2 + ^cosh (Z "/ LA) · / _A2 —1LA

1LA _r transf. -A0 (-1 ^Z —cOLA) · ^sinh (/ 0LA ^ LA) · KaO + ^COsh (/ nTA ¹ LA) 'Ł

OLA

-A0 / ““ ^f · = (- l / ZclLC) -tanh (z] Lc ^ LC) -Kj “ ^sf * + (l / cosh (/ |] rr _LC )) - / _cl

ΖΞ ¹ = (-1/2, ^) - ^ (/ ,, 7 ^) - 25 ^ + (1 / ^ (/ ,, / ^)) - / ^, r transf. -CO (- ¹¹ —colc) tanh (/ 0T J lc) 'Who ^' + ( ^{1 of cosh} (/ ffl J _LC )) Z - OLC

OLC

-CO where:

Y _1LC - propagation constant of the LC line segment for positive and negative components,

Y _0LC - propagation constant of the LC line segment for the zero sequence,

Z c1LC - wave impedance of the LC segment for _{positive and negative sequence,}

Z _c0LC - wave impedance of the LC segment for the zero _{sequence, l LC} - length of the LC line segment.

3.3. b. The values of the current / - ^tran f, / ^ γ ^, / flowing from the nodal point T to the station B in the line section LB are calculated:

τ transf / _ j-transf. τ transf - TB1 ^- £ ai + —Cl »» transf j transf. j transf ά-ΤΒ2 “± -A2 '—C2' τ transf. _ j transf transf £ tbo “± -A0 + ± CO

PL 206 226 B1 (10).

The short-circuit loop equation looks like this:

(11).

As a result of writing the equation (10) separately for the real and imaginary part and further mathematical transformations, the solutions presented in point 3.4 are obtained. b.

3.4.b. The distance to the dB fault location and the RFB transition resistance are calculated from the following equations:

-real (K _Tp -Z _1LB / _TBP) imag (/ _F) + imag (K _Tp -Z _1LB / _TBP) real (/ _F) real (Z _1LB / _TBP) imag (/ _F) - imag (Z _1LB / _TBp ) real (/ _F )

imag (Z _Tp) - (1 -) · imag (Z _1LB / _TBP) imag (/ _F) (13), wherein:

Z _1LB - impedance of the LB line section for the positive sequence,

Z _0LB - impedance of the LB line section for the zero sequence.

3.1.c. The value of the currents flowing to the nodal point T (Figs. 8-10) from the line section is calculated

I tansf., From tansf., I tansf., And sections I, i, and iransf., According to the formulas: A1 A2 A0 B1 B2 B0 rtransf. - BI j transf. ± -B2 τ transf. - BO j transf. - Al = (-1 / 2,118) -1 ^ (/ ^ / ^) - ^ + (1 / ^ 1, (/, ^^)) - / 32 = (-1 /2.oib) - ib) ΕΪΓ '· + (1 / “Sh (/ _OLB / _LB )) · / _M = (-1 / —ciLA) · ^smh (z | L / la)' Łai + ^cosh (/ 1L / la) Z ai /“ ^{! f} - = (-1 / Z _clLA ) - sinh (/, / _LA ) -K _A2 + cosh (/, _LA / _LA ) - / _A2

I / ™ ^f - = (-1 / Z _c0LA ) · sinh (/ _0LA l _LA ) - V _A0 + cosh (/ _0LA l _LA ) · / _A0

J where:

Y _1LB - propagation constant line segment LB for the positive sequence and the opposite Y _0LB - propagation constant line segment LB for the zero sequence (LB - length of the line section LB.

Z _c1LB - wave impedance of the LB section for the _{positive and negative sequence} , Z c0L B - wave impedance of the LB section for the zero sequence.

PL 206 226 B1

3.2.c. The value of the current, I ^^, I ^^, I, flowing from the nodal point T to the station C in the LC line section (Fig. 8-10) is calculated:

rtransf. _ .transf. .transf.

Itci ^_ Aai + £ bi rtransf. _ rtransf. rtransf. £ TC2 ~ i-A2 ⁺ i-B2 rtransf. _ rtransf. rtransf.

Itco -Iao + £ bo

The short-circuit loop equation looks like this:

As a result of writing the equation (13) separately for the real and imaginary part and further mathematical transformations, the solutions presented in item 3.3, c are obtained.

3.3.c. The distances to the fault location dC and the RFC transition resistance are calculated from the following equations:

III. Stage three

In this stage, the final results are selected.

4. It is checked whether the results of calculating the distance dA, d _B , dC to the fault location are within the range (0 + 1) in relative units:

<d _A <1, <d _B <1, <dC <1.

The results that do not fall within a given range indicate that they were calculated with a false initial assumption regarding the fault location in a given line section. These results are discarded.

5. The second calculated value, ie the transition resistance RFA, RFB, RFC, is analyzed and those calculation results for which the transition resistance is negative are discarded.

6. If, after analyzing the criteria as in steps 4 and 5, it is not clear which values determine the location of the fault, then the following steps calculate the impedance of the equivalent power supply systems for the negative sequence sequence in the event of faults:

Single-phase, two-phase, two-phase with earth or alternatively for incremental positive component. On the other hand, for three-phase short-circuits, the impedance of the equivalent supply systems is calculated for the positive-sequence sequence.

7. The current IFA2 is calculated (Fig. 11) assuming that the short circuit occurred in the LA line section:

where:

-Β2

Q = - ^BC2 Λ, + Λ ί-Β2 ¹ i-C2

8. The impedance of the equivalent source (Z _2SB ) _SUBA is calculated assuming that the short circuit has occurred in the LA line section:

where:

9. The equivalent source impedance (^ _SC ) _SUB _A is calculated assuming that the short circuit has occurred in the line section LA:

(—2SC) sUB_A ~ (- 2LB + (^ 2Sb) sUB_A) _t ^ 2LC £ C2 (19).

10. The equivalent source impedance (^ _SB ) _SUB _ _B is calculated assuming that the short circuit has occurred in the LB line section:

11. The equivalent source impedance (Z _2SC ) _SUB _ _B is calculated assuming that the short circuit has occurred in the LB line section:

PL 206 226 B1

12. The equivalent source impedance (Z2 _S B) _SUB _C is calculated assuming that the short circuit has occurred in the LC line section:

13. The equivalent source impedance (Z2 _SB ) _SUB _C is calculated assuming that the short circuit has occurred in the LC line section:

14. The calculated impedance of the equivalent power supplies is converted into a modular form, and then the correct result is selected on the basis of the impedance module of the equivalent power systems.

If the calculated value of the impedance module of equivalent power 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 power supply systems, it means that the initial data on the location of the short circuit in a given section and the result of calculating the distance to the fault location have been incorrectly assumed. the assumption is rejected.

If the calculated value of the impedance module of 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 from 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 three hypothetical distances to the fault locations and three transition resistances, assuming that the short circuit occurred in section LA, section LB and section LC, according to p .: 3.1.a - 3.2.a, 3.1.b - 3.4.b, 3.1 .c -3.3.c of an exemplary embodiment of the invention

- checking whether the individual hypothetical distances are in the range of 0 to 1 in relative units and discarding 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 has occurred in a given section, in accordance with p. 8-13 of the exemplary embodiment of the invention,

- selecting the correct result according to p.14 of an exemplary embodiment of the invention.

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 corresponding coefficients are changed: o _F1 , o _F2 , o _F0 , α ₁ , α ₂ , α ₀ . The values of these coefficients are presented in tables 1-4. The method of fault location in single-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 illustrated in the example, but may apply to another model, not shown in the drawing, in which model the presence of a transverse capacitance in the short-circuit line section is assumed. Then the equations (6), (11), (15) concerning the short-circuit loop current will be modified due to the existence of this capacitance.

PL 206 226 B1

The method according to the invention uses synchronous measurements of currents in three stations of the transmission system, additionally measuring the voltage in the station where the fault locator is located. Such availability of input signals is not considered in the current solutions.

The selection of the applicable result is made on the basis of the aggregation of three criteria: distance to the fault location, transition resistance at the fault location and the impedance module of equivalent power supply systems for those stations where voltage is not measured. This third criterion is novel and as yet unknown.

Claims (11)

Patent claims Method of locating faults in power lines with one branch, which uses the division of transmission lines of the transmission or distribution system into sections located upstream and downstream of the branch node and assuming a hypothetical fault location in at least one of these sections according to the invention, characterized by in that - the short-circuit and pre-short-circuit current is measured at all end stations of the system line, - in one end station of the system, the line phase voltage is measured for the short-circuit and pre-short-circuit condition, - the symmetrical components of the measured current and voltage signals and the total short-circuit current at the fault location are calculated, - the first hypothetical fault location in the line before the branch nodal point, the second hypothetical fault location in the line after the branch point and the next hypothetical fault location located in the branch, - the distances (dA), (dB), (dC) are calculated, where (dA) is the distance from the beginning of the line to the fault location, (dB) is the distance from the end of the line to the fault location, (dC) is the distance from the end of the branch line to the fault location, and for all hypothetical fault locations in each section, the transition resistance is calculated, - the selection of the correct fault location is made by first comparing the numerical values for distances (dA), (dB), (dC) 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 (RFA), (RFB), (RFC) and rejection of those calculation results for which the transition resistance value is negative, - if, after selecting the appropriate fault location, it turns out that at least two numerical values for the distance (dA), (dB), (dC) 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 negative sequence impedance modules for single-phase, two-phase and two-phase faults with earth or for positive sequence faults for three-phase faults are determined, assuming that the fault occurred in a specific section, - the values of the impedance modules of the equivalent power supply systems are compared with the realistic values that actually define the load on the system and the final result is the distance (dA), (dB), (dC) for which the value of the impedance module of the equivalent power supply systems is closest to realistic values, actually determining the load on 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 performed taking into account the coefficients of the contribution of the individual current components when determining the voltage drop across the transition resistance. 3. The method according to p. 2, characterized in that for two-phase faults with earth, the positive sequence is eliminated, and for the negative and zero sequence, the following values of the coefficients of the contribution of individual current components are assumed when determining the voltage drop on the transition resistance: PL 206 226 B1 where α, α, α- denotes the initial coefficient of the participation of symmetrical components of the current in determining the voltage drop of the resistance, b _F1 , b _F2 - denote the relational coefficients, determined from the relation between the zero sequence and the remaining components of the total short-circuit current flowing through the transition resistance . 4. The method according to p. 1 and 2, characterized in that the distances (dA), (dB), (dC) are determined from the following equations: real (K _Ap ) imag (/ _F ) - imag (Z _Ap ) real (/ _F ) A .................... J real (Z, _LA / _Ap ) imag (/ _F ) - imag (Z _1LA I _Ap ) real (/ _F ) ₇ - real _(Tp Z - Z _1LB / _TBP) imag (/ _F) + imag (Z _Tp - ^ lib ZTb _p) real (/ _F) CI θ - real (Z _1LB / _TBP) imag (/ _F) - imag (Z _1LB / _TBP) real (/ _F) " _J - real (K _Tp - Z _1LC Z _T c _P ) ^ima g (Z _F ) + imag (F _Tp - Z _1LC / _TCp ) real (/ _F ) c - real (Z _1LC / _TCp ) imag (/ _F ) - imag (Z _1LC i _TCp ) real (/ _F ) where: "Real" means the real part of a given quantity, "imag" means the imaginary part of a given quantity, YA _p - short circuit loop voltage determined assuming that the short circuit occurred in the LA section, y _Tp - short circuit loop voltage determined assuming that the short circuit occurred in the LB or LC section, IA _p - short circuit current determined assuming that the short circuit occurred in the section LA, I _TBp - means the short circuit current determined assuming that the short circuit occurred in section LB, I _TCp - means the short circuit loop current determined assuming that the short circuit occurred in the LC line section, I _F - means total short-circuit current, Z _1L A = R _1L a + jω ₁ L 1LA - means impedance of the line section LA for the _{positive sequence,} Z _1L B = R _1L b + jω ₁ L _1LB - means impedance of the LB line section for the positive sequence, Z _1LC = R _1LC + jω ₁ L 1LC - means impedance of the LC line section for the _{positive sequence,} R1LA, R1LB, R1LC- positive sequence resistance for the LA, LB, LC line sections, respectively, L1LA, L1LB, L1LC - positive sequence inductance for the line sections LA, LB, LC, ω1 - pulsation for the fundamental frequency, respectively. 5. The method according to p. The method of claim 1, characterized in that the transition resistance (RFA), (RFB), (RFC) is determined from the following equations: * ^FA ~ 2 real (Z _Ap ) -J _A real (Z _1LA / _Ap ) imag (K _Ap ) -ó / _A imag (Z _1LA / _Ap ) real (/ _F ) imag (/ _F ) Ab- _two real (K _Tp) (1 c? _B) · real (Z j _LB / _TBP) real (/ _F) imag _(TP) - (1 - _B rf) · imag (Z _1LB / _TBP) imag ( / _F ) PL 206 226 B1 1 real (F _Tp ) - (1 - d _c ) · real (Z _1LC J _TCp ) 1 'imag (K _T p) - (1 - ^ c) · imag (Z _1LC / _TCp ) “2 real (/ _F ) 2 _ imag (J _F ) _ where: "Real" means the real part of a given quantity, "imag" means the imaginary part of a given quantity, VA _p - short circuit loop voltage determined assuming that the short circuit occurred in the LA section, V _Tp - short circuit loop voltage determined assuming that the short circuit occurred in the LB or LC section, / _Ap - short circuit loop current determined assuming that the short circuit occurred in the LA section, / _TBp - short circuit loop current determined assuming that the short circuit occurred in the LB section, / _TCp - means the short circuit current determined assuming that the short circuit occurred in the LC line section, / _F - means the total short circuit current, Z _1LA = R _1LA +) ω ₁ ί _1Ι _ _Α - is the impedance of the LA line section for the positive sequence, Z _1LB = R _1LB +] ω-ιί-ιι_ _Β - is the impedance of the LB line section for the positive sequence, Z _1LC = R _1L C +] ω-ιί-ιι ^ - means impedance of the LC line section for the positive sequence, R _{1LA, 1LB} R, R _1lc - resistance for the positive sequence, respectively for the line section LA, LB, LC, L1LA, L1LB, L1LC - positive-sequence inductance for the line sections LA, LB, LC, ω1 - pulsation for the fundamental frequency, dA - the distance from the beginning of the line to the fault location, dB - the distance from the end of the line to the fault location, dC - means the distance from the end of the branch line to the fault location. 6. The method according to p. The method of claim 1, characterized in that the impedance of the equivalent source for the _{negative-sequence sequence ((Z 2SB} ) _Sub _ _a ) and for the incremental positive-sequence component ((Z a1SB) _S uba) is calculated assuming that the short-circuit has occurred in the line section LA, according to the formula: (~ / sb) SUBA where: the subscript i takes the values i = 2 for the negative sequence, i = Δ1 for the incremental positive sequence, G _iA - means the first analytical coefficient for the negative sequence determined from the analysis of the equivalent circuit as in Fig. 11 or compatible incremental system analytically determined from the equivalent circuit as in Fig. 12, / _Ai - means the negative or positive sequence of the current measured at the beginning of the line, Hj _A - means the second analytical negative sequence coefficient determined from the analysis of the equivalent circuit as in Fig. 11 or the consensus incremental analytically determined from the equivalent circuit as in Fig. 12, / _{FAi - means the negative sequence} component of the total short-circuit current determined from the analysis of the equivalent circuit as in Fig. 11 or the positive component of the total short-circuit current, determined from the analysis of the equivalent circuit as in Fig. 12. QB _Ci - means the quotient of the negative-sequence current measured at the end of the line and the sum of the negative-sequence current signals measured at the end of the line and the branch line end or the quotient of the positive sequence current measured at the end of the line by the sum of positive sequence current signals measured at the end of the line and the end of the branch line. 7. The method according to p. 1, characterized in that the equivalent source impedance ((Z _2SC ) _Sub _ _{a ) for the negative sequence sequence} and ((Z a1SC) _Sub _ _a ) for the incremental positive sequence is determined assuming that the short circuit has occurred in the line section LA, from the following equations: where: the subscript i takes the values i = 2 for the negative sequence, i = Δ1 for the incremental positive sequence, PL 206 226 B1 (Zi _SB ) _SUB _ _A - is the impedance of the equivalent source for the negative-sequence or positive-sequence incremental, calculated assuming that the short circuit occurred in the LA line section, Z _iLB - is the impedance of the LB line section for negative sequence or positive sequence, where ZΔ1LB = Zilb, Z _1LB - means impedance of the LB line section for the positive sequence, Z _{iLC - denotes the impedance of the negative sequence} LC line section or the impedance of the LC line section for the incremental _{positive sequence} , where Z 2LC = Z _1LC and Z ^ _LC = Z _1LC , Z 1LC - means impedance of the LC line section for the _{positive sequence,} I _Bi - means negative sequence or positive sequence incremental current measured at the end of the line, | _Ci - means negative sequence or positive sequence incremental current measured at the end of a branch. 8. The method according to p. _{A method according to claim} 1, characterized in that the impedance of the equivalent source for the _{negative-sequence sequence (Z 2SB} ) _Sub _ _b and for the incremental positive-sequence component ((Z 1Sb) _Sub _ _b ) is determined assuming that the short circuit has occurred in the line section LB, from the following equation: z / A 7 T fransf. i -r -rr transf. / 7 X _ U —iLB — TBi "" —iLB —Bi i — Ti v — iSB / SUB_B "’ —Bi where: the subscript i takes the values i = 2 for the negative sequence sequence, i = Δ1 for the positive sequence positive sequence, dB - the distance from the end of the line to the fault location, Z _iLB - denotes the impedance of the LB line section for negative sequence or positive sequence, where Z2LB = Zilb and Z δ ^ β = Zilb, Z _1LB - means impedance of the LB line section for the positive sequence, And tansf. - is the current flowing to the nodal point T from the line section LB for the negative component or for the incremental positive component, I _Bi - means negative sequence or positive sequence incremental current measured at the end of the line, V tanst - is the voltage at the node T for the negative sequence or positive sequence increment. 9. The method according to p. The method of claim 1, characterized in that the impedance of the equivalent source for the _{negative-sequence sequence} ((Z 2SC) _Sub _ _b ) and for the incremental positive-sequence ((Z ^ _Sc ) _Sub _ _b ) is calculated assuming that the short circuit has occurred in the line section LB, with the following equation: V — iSC / SlJB _B > - Those where: the subscript i takes the values i = 2 for the negative sequence, i = Δ1 for the incremental positive sequence, V _Ci - means negative sequence or positive sequence voltage at the end of a branch line, I _Ci - means negative sequence or positive sequence incremental current measured at the end of a branch. 10. The method according to p. 1, characterized in that the equivalent source impedance for the _{negative-sequence sequence ((Z2 SC} ) _Sub _c) and for the incremental positive-sequence ((Z ^ _Sc ) _Sub _ _c ) is calculated assuming that the short circuit has occurred in the LC line section, from the following equations: a_t \ * 7 j-transf. and r? τ τ rtransf. _ ““ “C7 ~ -iLC ± .TCi ~ —iLC —Ci ~ —Ti” La where: the subscript i takes the values i = 2 for the negative sequence, i = Δ1 for the incremental positive sequence, PL 206 226 B1 dC - means the distance from the end of the branch line to the fault location, Z _{iLC - is the impedance of the negative sequence} LC line section or the impedance of the LC line section for the incremental _{positive sequence} , where Z 2LC = Z _1LC and Z δ-ilc = Z _1LC Z 1LC - means impedance of the LC line section for the _{positive sequence,} 1211 / - is the current flowing to the node point T from the LC line section for negative sequence or positive sequence incremental sequence, I _Ci - means negative sequence or positive sequence incremental current measured at the end of a branch, V 2 ° ΐ2 - denotes the voltage at the node T for the negative sequence or the incremental positive sequence. 11. The method according to p. 1, characterized in that the equivalent source impedance for the negative sequence ((Z2sb) sub_ _c) and the incremental positive sequence ((Z ^ sb) sub_c) assuming that a short circuit occurred in the line LC is calculated from the following equation: where: the subscript i takes the values i = 2 for the negative sequence, i = Δ1 for the incremental positive sequence, V _Bi - means negative or positive sequence voltage at the end of the line, I _Bi - means the negative or positive sequence of the current measured at the end of the line.