RU2816200C1 - Method of determining point of damage on overhead power transmission line when measuring from its two ends - Google Patents

Abstract

FIELD: electric power industry.

SUBSTANCE: result is achieved by the fact that at the moment of short circuit voltage on buses, currents of the line are measured, values of their derivatives are calculated, the line is divided into a plurality of sections, for each of which calculated values of quantities and derived parameters are calculated, intervals of change of design parameters within each of the selected sections of the overhead power transmission line are determined. Probability matrices are set, which characterize probabilities of correct and erroneous recognition of damaged sections of overhead power transmission line, performing preliminary simulation or collection of statistical information, based on the results of which the calculated derived parameters of voltages and currents for different sections of the overhead transmission line are formed, computational algorithm is implemented by which the overhead power transmission line damaged point and bypass area are determined, the overhead power transmission line is divided into a plurality of numbered sections within the bypass area, performing a sequential analysis procedure with exclusion of hypotheses, according to the results of sequential analysis, a decision is made on the damaged section of the overhead power transmission line by its number corresponding to the last hypothesis remaining during the sequential analysis.

EFFECT: high accuracy of determining a damaged section of an overhead power transmission line in conditions of deviations of currents and voltages from a sinusoidal shape.

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Description

The present invention relates to the electric power industry and can be used to determine the location of a fault (LPO) on high-voltage overhead power lines (OHPL) when measuring currents and voltages from its two ends. It is advisable to use the proposed invention in industrial power supply systems in conditions of deviation of the quality parameters of electrical energy from standard values.

There are known two-way methods of OMP of overhead power lines, based on the use of instantaneous values of currents and voltages. For example, a method for determining the location of a short circuit on an overhead power line with unsynchronized measurements from its two ends [RF Patent No. 2508556, IPC G01R 31/08, publ. 02/27/2014, Bulletin. No. 6], having a length l, active R and inductive reactance X _L , connecting two supply systems, in which phase currents and voltages that are not synchronized in time during a short circuit are measured from both ends of the line, the damaged phases are determined, the relative value of the distance to short circuit location n and the physical distance to the short circuit location from the end of the line with the index ' according to the expression l'=n⋅l. According to the proposal, instantaneous values of phase currents (i' _A , i' _B , i' _C ) and voltages (u' _A , u' _B , u ' _C ), (uʺ _B , uʺ _C ) during a short circuit, obtain oscillograms of currents and voltages, combine the oscillograms from the two ends of the line along the cross-section of the beginning of the short circuit, select a cross-section on the current oscillograms at an interval of two to ten periods from the beginning of the short circuit and voltage of the damaged phase, take the instantaneous values of currents and voltages u', uʺ in the section and at neighboring points, calculate the time derivatives of the currents di'/dt, diʺ/dt, determine the relative value of the distance to the short circuit using expression (1):

where n is the relative value of the distance to the short circuit; u', uʺ - instantaneous voltage values obtained in the cross-section of voltage oscillograms of the damaged phase from one and the other ends of the line (B); i', iʺ - instantaneous current values obtained in the cross-section of oscillograms of the damaged phase currents from one and the other ends of the line (A); di'/dt, diʺ/dt - time derivatives of currents (A/s); R, X _L - active and inductive phase resistance of the power line (Ohm).

The disadvantage of this group of OMT methods for overhead power lines and the analogue method, in particular, is the ambiguity of making a decision regarding the location of the damage based on time slices of current and voltage oscillograms performed at different time intervals. This ambiguity is especially evident when using oscillograms under conditions of deviations in the quality parameters of electrical energy, as well as time-varying resistance at the site of damage.

There are known two-way methods of OMF of overhead power lines, based on the use of complex amplitudes of currents and voltages. For example, a method for determining the location of damage on overhead power lines [RF Patent No. 2526095, IPC G01R 31/08, publ. 08/20/2014, Bulletin. No. 23], in which phase voltages and currents are measured from both ends of the line, converted into calculated complex values using the proposed expressions and, using the imaginary parts of the calculated values, the relative and physical distances of the fault location from the ends of the overhead power line are calculated. In this method, equivalent parameters of power supply systems are not used, and the influence of transient resistance is eliminated.

The disadvantage of this group of methods for the use of overhead power lines and the analogue method, in particular, is the ambiguity of decision-making regarding the location of damage when the spatial (from two different ends of the overhead power line) coherence of current and voltage signals is violated [Kulikov A.L., Ilyushin P.V., Sevostyanov A.A. On the need to take into account spatial coherence in joint digital processing of spatially separated current and voltage signals in electrical networks // News of the Russian Academy of Sciences. Energy. 2022. No. 3. P.49-62]. Violations of spatial coherence can manifest themselves, for example, due to deviations of electrical energy quality parameters from standard values. It is important to note that the OMF of the overhead power line can be implemented in this case using complex amplitudes of currents and voltages obtained using filtering algorithms, for example, the discrete Fourier transform (DFT). However, filtering in the vast majority of cases (for example, in the presence of interharmonics) does not completely eliminate time-varying errors in the estimation of current and voltage parameters, as well as the OMF of overhead power lines.

An additional disadvantage of this analogue method is the need to use only imaginary components of the calculated values. This drawback can lead to an error in determining the location of the fault due to the incomplete volume of parameters taken into account, in particular, due to the lack of consideration of the distributed capacitance of the overhead power line.

The closest technical solution to the proposed invention is a method for determining the location of a short circuit in the contact network of electrified transport [RF Patent No. 2566458, IPC V60M 01/00, G01R 31/08, publ. 10/27/2015 Bulletin. No. 30], in which, at the moment of a short circuit, the voltage on the buses, the currents of the lines feeding the contact networks of the paths of the intersubstation zone with a short circuit, and the phase angles of the currents are measured at one or adjacent traction substations, the values of the derived parameters depending on the measured values and the circuit are calculated power supply, and judge the location of the damage by implementing a computational algorithm that determines the relationship between the distance to the location of the damage on the measured and calculated derivative parameters. According to the proposal, the power supply circuit of the contact network in a given inter-substation zone between two adjacent traction substations is conditionally divided along the length of the path into many sections, for each of which, with calculated short circuits at its beginning and end, the calculated values of quantities and derived parameters similar to those defined Based on the results of measurements during a short circuit, at different specified values of the transition resistance at the point of the short circuit, the intervals of change of all calculated parameters within each of the selected sections of the path are determined, these intervals are entered into the database, the measured values and derived parameters are compared with the intervals of the calculated parameters similar values from the database for each of the selected sections of the track and the section for which the number of measured values and derived parameters falling within the intervals of similar calculated values is the largest is taken as the location of the short circuit.

The disadvantage of the prototype method is the ambiguity of decision-making regarding the damaged section, when the number of measured values and derived parameters falling inside the intervals corresponding to the selected different sections of the path is the same. Moreover, the number of such plots may be more than two, and the plots themselves may not be adjacent.

This ambiguity can be especially obvious when implementing the prototype method under conditions of deviations in the quality parameters of electrical energy, as well as time-varying resistance at the site of damage.

Let's consider the implementation of the WMD procedure using the example of an overhead power transmission line with a voltage of 110 kV, length l=50 km, with two-way power supply (Fig. 1).

In fig. Figure 1 shows the equivalent circuit of a kV overhead power line in relation to a design example, having a length (l) 1, phase active resistance (R) 2 and inductance (L) 3, connecting buses 4 and 5 of two systems 6 and 7. A short circuit is shown on the overhead power line 8 behind the transition resistance (Z _P ) 9 at a distance (x=p⋅l) 10 from one end of the overhead power line. When a short circuit occurs on the overhead power line, current (i') flows through it from bus 4 and current (iʺ) from bus 5. In this case, on buses 4 and 5, non-time-synchronized instantaneous values of phase currents (i ' _A , i' _B , i' _C ), (iʺ _A , iʺ _B , iʺ _C ) and voltages (u' _A , u' _B , u' _C ), (uʺ _A , uʺ _B , uʺ _C ) at the moment short circuit.

The relative distance to the place of damage n will be determined in accordance with relation (1) of the analogue method:

This method of OMP OHL has fairly small errors in calculating the distance to damage under short circuit (SC) conditions and undistorted (sinusoidal) currents and voltages of oscillograms of an emergency event [RF Patent No. 2508556, IPC G01R 31/08, publ. 02/27/2014, Bulletin. No. 6].

Let us assume that, for example, from the side of system-1 (Fig. 1) discrete instantaneous current values f(m) are distorted by flicker [GOST 32144-2013. Electric Energy. Electromagnetic compatibility of technical equipment. Standards for the quality of electrical energy in general-purpose power supply systems. - Enter. 2014.07.01. - M.: Standartinform, 2013. - 10 p.]. The distorted current signal i'm) is illustrated in FIG. 2(a).

Let us assume that on the side of system-2 (Fig. 1) there is a nonlinear load that emits, for example, interharmonics into the electrical network. To simplify the example, we assume that the instantaneous current values iʺ(m) are distorted by the interharmonic frequency ƒ _and =135 Hz with amplitude I _and =0.15⋅lʺ and zero initial phase Fig. 2(6).

Thus, the calculated expression for the fault location in the presence of flicker and interharmonic frequency ƒ _and =135 Hz corresponds to the equality:

where k is a number (constant coefficient) characterizing the “depth of distortion” of the flicker; rnd{m) is a random number (for example, distributed according to a uniform law in the interval [0; 1], generated at each discrete time value m; U is the voltage at the damage site.

Setting numerical values in accordance with Table 1 and expression (3) leads to the following results:

- at m=20; n _and (20)=0.486; Δх=l(nn _and )=50⋅(0.5-0.486)=0.7 (km);

- at m=60; n _and (60)=0.526; Δх=l⋅(nn _and )=50⋅(0.5-0.526)=-1.30 (km).

An analysis of the obtained calculation results shows that the errors of the overhead power transmission line can have both a positive and a negative sign, and are also distributed unevenly relative to the use of different points in time.

Since the length of the overhead power line is l=50 km, therefore the bypass zone for the accepted fault location l _{short circuit} is ±10% of the length of the overhead power line [PJSC FGC UES Organization standard: STO 56947007-29.240.55.159-2013 “Standard instructions for organizing work to determine locations damage to overhead power lines with a voltage of 110 kV and higher”, date of introduction: November 28, 2013] or Δl=±50⋅0.1=±5 (km) relative to the location of the damage.

Taking into account the normal distribution law of errors in the overhead power transmission line and the three-sigma rule [Ventzel E.S. Probability theory: textbook. for universities. - 5th ed. erased M.: Higher. school, 1998. - 576 p.], we can assume that the standard deviation (standard deviation) of the normal law of distribution of errors in the overhead power transmission line is σ≈(2⋅Δl)/6=10/6=1.67 (km).

Let us explain the features of the implementation of the procedure for recognizing a damaged area in case of a power line accident.

Let us formulate the OMP problem as a classification problem, consisting in establishing the fact that the damage belongs to one of the sections within the bypass zone of the overhead power line. Due to the influence of random factors, the decision-making process during recognition is stochastic in nature and involves processing emergency oscillograms of currents and voltages recorded over a limited time interval. In this case, the vector x = {x ₁ , x ₂ , ...} of current and voltage parameters in the general case is random [Papkov B.V. Reliability and efficiency of modern power supply: monograph / B.V. Papkov, P.V. Ilyushin, A.L. Kulikov. - Nizhny Novgorod: Scientific Publishing Center “XXI Century”, 2021. 160 p.], since it may include distorting components, for example, associated with deviations of electrical energy quality indicators from standard values [GOST 32144-2013. Electric Energy. Electromagnetic compatibility of technical equipment. Standards for the quality of electrical energy in general-purpose power supply systems. Enter 2014.07.01. M.: Standartinform, 2013. 10 p.]. The components of the vector x are sequentially observed, and the task of sequential recognition of the damaged i-th section of the overhead power line (i=1, ..., M) is reduced to making a decision about whether the damage belongs to one of the k sections (k=1, ... M) based on the observation vector x, or making a decision to continue observations [Fu K. Sequential methods in pattern recognition and machine learning/Translation from English. E.F. Zaitsev, ed. L.A. Meerovich and Ya.3. Tsypkina. M.: Nauka, 1971. 255 p.].

In order to formulate a rational decision rule in case of damage to overhead power lines, it is necessary to analyze the performance indicators of the sequential procedure for recognizing the damaged area. The most general probabilistic indicators of the effectiveness of applying the sequential analysis procedure include the matrix of conditional probabilities for M - hypotheses, each of which corresponds to its own damaged area within the bypass zone of the overhead power line:

where i, k=1, …, M; P(k⎜i)=P _i (k)=Pik - conditional probability of making a decision on the number k of the damaged section on the overhead power line, provided that the damage belongs to section i.

One of the options for organizing multi-hypothesis sequential analysis was proposed by Reed [Fu K. Sequential methods in pattern recognition and machine learning/Translation from English. E.F. Zaitsev, ed. L.A. Meerovich and Ya.3. Tsypkina. - M.: Nauka, 1971. -255 p.]. Let x ₁ , x _{2 ...} be a sequence of variables, and p _m (x ₁ , x _{2 ...} ⎜H _i )=p _m (x⎜H _i ) - the joint probability density of x ₁ , x ₂ ... provided that the hypothesis is true _Hi .

Reed's decision-making algorithm is based on the formation of a generalized likelihood ratio at each step m:

When organizing OMP of overhead power lines, those sections of overhead power lines that are least suitable for the recorded set of parameters of oscillograms of emergency events are consistently excluded from the analysis. During the sequential analysis procedure, the decisive statistics λ _m (x⎜H _i ) are calculated, which is compared with the threshold (set) value λ ^pores _m (x⎜H _i ) of the stopping boundary and the corresponding i-th section of the overhead power line. Thus, if λ _m (xH⎜H _j )<λ ^por _m (x⎜H _j ), (j=1, ..., M), then a decision is made to continue observation, and the j-th section of the overhead power line is excluded from subsequent analysis with OMF of overhead power lines. The procedure for identifying a damaged section continues until the last most probable section of the overhead power line remains, which is considered damaged.

In the process of performing a sequential procedure, stopping boundaries are calculated for each of the analyzed sections of overhead power lines, based on the specified probabilistic indicators of the quality of classification of the damaged section. According to [Fu K. Sequential methods in pattern recognition and machine learning / Translation from English. E.F. Zaitsev, ed. L.A. Meerovich and Ya.3. Tsypkina. - M.: Nauka, 1971. - 255 s] the stopping limit is determined by the equality:

where P _ik is the probability of accepting the hypothesis H _i when H _k is valid.

When the condition of excluding one of the overhead power line sections from subsequent consideration is met, the total number of analyzed sections is reduced and becomes equal to (M - 1). Subsequently, the stopping boundaries are recalculated, and the multi-hypothesis sequential analysis procedure is repeated until the only, most likely damaged section of the overhead power line remains.

The objective of the invention is to ensure unambiguous decision-making regarding a damaged section of an overhead power line using a two-way OMP method in conditions of deviations of currents and voltages from a sinusoidal shape.

The task is achieved by determining the location of a fault on an overhead power line by taking measurements from its two ends, in which, at the moment of a short circuit, the bus voltage and line currents are measured at substations, the values of their derived parameters are calculated, depending on the measured values and the power supply circuit, and the location is judged damage by implementing a computational algorithm that determines the relationship between the distance to the place of damage from the measured and calculated derivative parameters, the line is divided into many sections, for each of which the calculated values of quantities and derivative parameters are calculated, the intervals of change in the calculated parameters are determined within each of the selected sections of the air power lines.

According to the proposal, they implement a method for determining the location of a fault with sequential recognition and exclusion of hypotheses regarding the damaged section of an overhead power line, set probability matrices characterizing the probabilities of correct and erroneous recognition of damaged sections of an overhead power line, carry out preliminary simulation modeling or collect statistical information, based on the results of which laws are formed probability distributions of the calculated derivative parameters of voltages and currents for various sections of the overhead power line, implement a computational algorithm by which they determine the location of the damage and the bypass zone of the overhead power line, divide the overhead power line into many numbered sections within the bypass zone, based on the obtained laws of probability distribution of derivatives parameters, voltages and currents, as well as probability matrices characterizing the probabilities of correct and erroneous recognition of damaged sections of an overhead power line, perform a sequential analysis procedure with the exclusion of hypotheses, based on the results of the sequential analysis, a decision is made about the damaged section of an overhead power line by its number corresponding to the last hypothesis , remaining during the sequential analysis.

In fig. Figure 1 shows a single-line equivalent circuit of an overhead power line in relation to a design example, having a length (l=50 km) 1, phase active resistance (R) 2 and inductance (L) 3, connecting buses 4 and 5 of two systems 6 and 7. The overhead power line shows short circuit 8 behind the transition resistance (Z _P ) 9 at a distance (x) 10 from one end of the overhead power line. When a short circuit occurs on the overhead power line, current (i') flows through it from bus 4 and current (iʺ) from bus 5. In this case, on buses 4 and 5, non-time-synchronized instantaneous values of phase currents (i ' _A , i' _B , i' _C ), (iʺ _A , iʺ _B , iʺ _C ) and voltages (u' _A , u' _B , u' _C ), (uʺ _A , uʺ _B , uʺ _C ) at the moment short circuit.

In fig. Figure 2 shows current oscillograms distorted by: a) flicker; b) interharmonic frequency ƒ=135 Hz.

In fig. Figure 3 shows a block diagram of a device that implements a method for determining the location of a fault on an overhead power line when taking measurements from its two ends.

Fig. 4 characterizes the probability distribution of hypotheses p _m (l _kz ⎜H _i ) when making a decision regarding the damaged section of the overhead power line.

Fig. 5 illustrates the decision process of sequential analysis in the apparatus of FIG. 3.

The device (Fig. 3), which implements a method for determining the location of a fault on an overhead power line when taking measurements from its two ends, includes: block 1 for processing oscillograms and estimating current and voltage parameters; memory block 2; blocks 3 ₁ ... 3 _M likelihood ratio calculation; comparison schemes 4 ₁ ... 4 _m ; block 5 analysis; block 6 for calculating threshold (set) values. The input of block 1 for processing oscillograms and estimating current and voltage parameters is the input of the device (Fig. 3), and the output of the device is connected to the output of analysis block 5.

The method for determining the location of a fault on an overhead power line when taking measurements from its two ends is implemented as follows.

Before the device starts operating, simulation modeling is carried out to obtain the statistical characteristics necessary for the implementation of sequential analysis and associated with various random factors influencing the errors in calculating the distance in the case of overhead power lines. The purpose of simulation modeling is to obtain dependencies p _m (x⎜H _i ), and the latter are formed for different numbers and combinations of hypotheses M. Probability distributions p _m (x⎜H _i ) can also be determined on the basis of statistical operational data, taking into account errors identified by linear by teams when bypassing overhead power lines, or determined from the standard values by which the bypass zone of overhead power lines is set (averaged values for overhead power lines of various lengths and voltage classes). Computations using p _m (x⎜H _i ) for different values of M are implemented in blocks 3 ₁ ... 3 _M and are necessary due to the fact that Reed’s algorithm involves the sequential elimination of hypotheses to make a final decision about the damaged section of the overhead power line.

The simulation results in the form of probabilistic distribution laws, for example, similar to Fig. 4 and corresponding to the hypotheses of damaged areas, are recorded in memory block 2. Additionally, in block 6 for calculating threshold (set) values, probabilistic indicators of the effectiveness of the sequential procedure for recognizing a damaged area are introduced in the form of values of probability matrices НР^Н, expression (4), characterizing the probabilities of correct and erroneous decisions when sequentially eliminating hypotheses. Based on the probability matrices in block 6, the calculation of threshold values using expression (6) is implemented participating at each step of the sequential decision-making procedure regarding the damaged section of the overhead power line.

The input of block 1 for processing oscillograms and estimating the parameters of currents and voltages (device input (Fig. 3)) receives either instantaneous values or complexes of currents and voltages of oscillograms of emergency events. Based on this information, block 1 calculates the components of the vector x. The vector x may include values characterizing the damaged section of the overhead power line (active, reactance; values of reactive power and current distribution coefficient, recalculated for the expected location of the fault; other parameters), as well as, for example, directly calculated values of the location of the fault of the overhead power line, calculated using various WMD algorithms and having corresponding systematic and random errors.

Based on the components of the vector x coming from the output of block 1 to the input of memory block 2, values are selected from memory that characterize the laws of distribution for different hypotheses involved in the corresponding calculations of likelihood ratios. These values are supplied to each of the M calculation blocks 3 ₁ ... 3 _M.

In blocks 3 ₁ ... 3 _M for calculating the likelihood ratio in accordance with the values of the vector x, the calculation of the likelihood ratio λ _m (x⎜H _i ) characteristic of each of the i=1, ..., M damaged sections of overhead power lines is implemented (expression (5)). When calculating each of λ _m (x⎜H _i ) from memory block 2 using the x values obtained in parameter calculation block 1, the values p _m (x⎜H _i ) and p _m (x⎜H _k ) are received.

The calculated values of the likelihood ratio for each of the hypotheses _m (x⎜H _i )) are supplied to the first inputs of comparison circuits 4 from first to M. The second input of each i-th comparison circuit 4 _i from block 6 for calculating threshold (set) values is supplied with the corresponding threshold value λ ^pores _m (x⎜H _i ) for the implementation of the operation λ _m (x⎜H _i )<λ ^pores _m (x⎜H _i ). When the value λ _m (x⎜H _i ) is reached at step m of the sequential procedure below λ ^pores _m (x⎜H _i ), a logical signal is issued from the output of the comparison circuit to analysis block 5. In accordance with this signal, analysis unit 5 makes a decision about the absence of damage in the overhead power line section numbered i, and the i-th section is excluded from subsequent analysis. Thus, the number of sections is reduced to (M - 1), which leads to the need, depending on which of the sections of the overhead power line was excluded from the analysis, to recalculate λ ^pores _m (х⎪Н _i ), and also to change the dependence involved in calculating the likelihood ratio (expression (5)).

To carry out the above changes, signals are sent from the output of analysis block 5 to the inputs of memory block 2 and block 6 for calculating threshold values. To calculate threshold values according to expression (6), in block 6 for calculating threshold (set) values, new values of the matrix ⎪⎪P _ik a⎪⎪ are used, which determine the identification of a damaged section of an overhead power line with the required indicators of recognition ability.

During the processing of oscillograms of emergency events by the device (Fig. 3), the iterative process outlined above is carried out, a decision is sequentially made to exclude hypotheses regarding the damaged section of the overhead power line according to the condition λ _m (x⎪H _i )<λ ^pores _m (x⎪H _i ). Then, when the last hypothesis remains, the process of sequential analysis stops and a decision is made that the damage to the overhead power line is located in the appropriate area. In this case, from the output of the analysis unit 5 of the OMP device (Fig. 3), information about the damaged area (for example, in the form of a number) within the bypass zone of the overhead power line is provided.

Let's consider a simplified version of the implementation of the procedure for sequential analysis in case of accidents with the division of the bypass zone of overhead power lines into three sections relative to the location of the damage (Fig. 4), corresponding to three hypotheses: H ₁ : μ = -σ, H ₂ : μ.=0 and H ₃ : μ =σ, which correspond to decisions about the correspondence of the damage location to the values of mathematical expectations μ. Here σ is the standard deviation of the normal distribution law (Fig. 4).

Let, based on the results of calculating the distance to the place of damage according to expression (2) based on the instantaneous values of oscillograms of currents (Fig. 2 a, b) and voltages, ten consecutive sample values of l _short are obtained, which are summarized in Table 2. Due to the spread of sample values of l _short , it is not possible to unambiguously make a decision regarding the validity of hypotheses H ₁ , H ₂ , H ₃ .

Note that the mathematical expectation of sample values l _kz (Table 2) is equal to M[l _kz ]=25.185 (km).

To implement sequential analysis, we introduce a matrix of conditional probabilities (expression (4)) for making a decision regarding the damaged area:

The selection of matrix elements must be made taking into account the operational features of the overhead power transmission line, as well as the economic consequences of incorrect decisions.

Let us calculate the threshold values for the sequential multi-hypothesis Reed procedure based on the elements of matrix (7):

It is advisable to calculate the likelihood ratios λ _m (l _кз ⎪Н _i ) for each of the hypotheses H _i (i=1, 2, 3) using the standard Gaussian function:

the tables of which are given, for example, in [Ventzel E.S. Probability theory: textbook. for universities. -5th ed. erased M.: Higher. school, 1998. 576 p.].

Let us explain the calculations of likelihood ratios. At the first step of sequential analysis we obtain:

At the first step of the sequential analysis, there is no decrease below the threshold values of the likelihood ratios calculated for each of the hypotheses _H1 , _H2 , _H3 :

therefore, one of the hypotheses is not excluded, and the sequential analysis procedure continues.

At the second step of sequential analysis we obtain:

At the third step of sequential analysis we obtain:

Calculations for all hypotheses H ₁ , H ₂ , H ₃ are carried out in a similar way at all steps of sequential analysis m. The calculation results are summarized in Table 3.

At the third step of the sequential analysis, the hypothesis H ₃ is excluded, since the likelihood ratio λ ₃ (-0.8891⎪H ₃ ) is below the threshold value

In the future, sequential analysis is implemented only for two hypotheses H ₁ and H ₂ . Let us set the probability matrix for hypotheses H ₁ , H ₂ in the form:

The calculation of threshold values corresponds to the following ratios:

At the fourth step of sequential analysis we obtain:

At the fifth step of sequential analysis we obtain:

At the sixth step of sequential analysis we obtain:

At the seventh step of sequential analysis we obtain:

At the eighth step of sequential analysis we obtain:

At this step, hypothesis _H2 is rejected because:

and the process of sequential analysis ends with the acceptance of hypothesis H ₂ .

The process of implementing sequential analysis using Reed's algorithm is illustrated in Fig. 5, the analysis of which allows us to draw the following conclusions:

- sequential exclusion of hypotheses using Reed's algorithm in relation to the overhead power transmission line damage leads to the selection of a damaged section in the interval M[l _kz ]±σ/2=25.185±0.835 (km);

- a sequential computational procedure implements decision-making regarding a damaged section of an overhead power line in 8 steps, does not require significant time expenditure and has virtually no impact on the performance of the overhead power line equipment;

- since the initial rejected hypothesis was H ₃ , therefore it is advisable to start bypassing the overhead power lines from the section 25.185 ± 0.835 (km) towards system-1 (Fig. 1), i.e. the most likely direction of damage;

- it is obvious that the speed of decision-making during sequential analysis depends on the degree of distortion of emergency oscillograms of currents and voltages, including deviations of power quality parameters from standard values.

Thus, we have proposed a variant of organizing the WMD, which includes dividing the bypass (inspection) zone of the overhead power line into sections with the subsequent implementation of an unambiguous procedure for recognizing the damaged area. The use of sequential multi-hypothesis analysis made it possible to adapt the decision-making process regarding the damaged section of the overhead power line to the distortion features of the oscillograms of emergency events and the conditions for assessing their parameters. The calculation results showed that the use of sequential analysis has practically no effect on the performance of the overhead power transmission line, but provides unambiguous decision-making regarding the damaged area in conditions of deviations of currents and voltages from the sinusoidal shape.

Claims (1)

A method for determining the location of a fault on an overhead power line by taking measurements from its two ends, in which, at the moment of a short circuit, the bus voltage and line currents are measured at substations, the values of their derived parameters are calculated, depending on the measured values and the power supply circuit, and the location of the fault is judged by implementing a computational algorithm that determines the relationship between the distance to the place of damage from the measured and calculated derivative parameters, the line is divided into many sections, for each of which the calculated values of quantities and derived parameters are calculated, the intervals of change in the calculated parameters are determined within each of the selected sections of the overhead power line, characterized in that they implement a method for determining the location of a fault with sequential recognition and exclusion of hypotheses regarding the damaged section of an overhead power line, specify probability matrices characterizing the probabilities of correct and erroneous recognition of damaged sections of an overhead power line, and enter their values into the block for calculating the threshold values of the device implementing method, using the values of probability matrices, the threshold values are calculated in the threshold value calculation block, preliminary simulation modeling is performed or statistical information is collected, based on the results of which the probability distribution laws of the calculated derivative parameters of voltages and currents are formed for various sections of the overhead power line, information about the distribution laws write to the device's memory unit, implement a computational algorithm in the unit for processing oscillograms and estimating current and voltage parameters, which determines the derived parameters of voltages and currents, the location of the fault and the bypass zone of the overhead power line, and divides the overhead power line into many numbered sections within the bypass zone , based on information about the laws of probability distribution of the derived parameters of voltages and currents, as well as the location of the damage from the output of the memory block in the blocks for calculating likelihood ratios, they form likelihood ratios inherent to each of the numbered sections of the overhead power line within the bypass zone, perform a sequential analysis procedure with exclusion hypotheses, by comparing the calculated values of likelihood ratios for numbered sections of the overhead power line with the corresponding threshold values from the output of the block for calculating the threshold values of the device in the device comparison schemes, based on the results of sequential analysis in the analysis block, a decision is made about the damaged section of the overhead power line according to its number corresponding To the last hypothesis remaining during the sequential analysis, from the output of the analysis unit, information about the damaged area in the form of a corresponding signal is given to the output of a device that implements a method for determining the location of a fault on an overhead power line when taking measurements from its two ends.