1. The flexible direct-current power grid fault location method based on clustering and iterative algorithm is characterized by comprising the following steps:

step 1, measuring the positive voltage U of the line after the RCB is tripped_pAnd negative electrode voltage U_nThen calculating the line mode voltage U_mode；

Step 2, obtaining a series of linear mode voltage spectrums when the signal dimension N takes different values by utilizing an MUSIC algorithm, and extracting the frequencies corresponding to all spectrum peaks;

step 3, setting a category number K by using a K-means clustering method, and clustering all the spectrum peak frequencies obtained in the step 2And (4) class. Fitting the density functions of all categories, and regarding the frequency corresponding to the peak value of the obtained density function as the natural frequency f_f1,f_f2,f_f3…；

Step 4, assuming the first natural frequency f obtained in step 3_f1Is an inherent main frequency f₁Calculating the fault distance d₁The expression is as follows:

wherein, theta_fPhase angle which is the reflection coefficient at the fault point;

step 5, estimating the natural frequency f₂' and a third frequency f₃', the formula is as follows:

step 6, searching the natural frequency obtained in step 3, and respectively selecting the nearest f₂'，f₃' as the true second natural frequency f₂And a true third natural frequency f₃(ii) a Then by f₂，f₃Calculating the fault distance d₂And d₃；

Step 7, according to the formulaCalculating d₁、d₂、d₃The standard deviation std of (a); if std<std_setThen average fault distance d is taken_mean＝(d₁+d₂+d₃) (ii)/3 as the final failure distance; but if std>std_setThen the frequency f is adjusted_f1Treated as spurious frequencies and then steppedThe next natural frequency f obtained in step 4_f2As an inherent main frequency f₁And 4, repeating the steps 4 to 7.

Background

The development of a flexible direct-current transmission technology and a flexible direct-current power grid occupies more and more important positions, however, a high-voltage direct-current overhead line exposed in the air is easy to break down, the precise positioning of the fault is realized, and the flexible direct-current power grid protection and rapid fault clearing device has important significance for protecting and rapidly clearing the flexible direct-current power grid.

The current fault location method of the high-voltage direct-current transmission line mainly comprises a time domain method and a traveling wave method, wherein the time domain method mainly utilizes double-end fault information to realize fault location according to the principle that calculated voltages along the line are distributed at fault points equally, and the distance measurement precision is influenced to a certain extent due to the fact that transient transmission characteristics of transmitting equipment corresponding to the voltages and the currents are inconsistent. The traveling wave method is mainly divided into a double-end traveling wave method and a single-end traveling wave method, wherein: the accurate measurement of the double-end traveling wave method is based on the accurate capture of the arrival time of the first traveling wave head, but because of the existence of elements such as a smoothing reactor and a direct current filter in a direct current power transmission system, the high-frequency and low-frequency components of the traveling wave present different frequency characteristics, which brings difficulty to the identification of the traveling wave head and the accurate capture of the arrival time; in addition, the double-end method has relatively high ranging cost and relatively few application scenes. The single-ended traveling wave method has higher requirements for accurately identifying the traveling wave head, and not only needs to capture the precision of the arrival of the first traveling wave head, but also needs to accurately identify the second traveling wave head reflected again by a fault point, and particularly has difficulty in accurately identifying the reflected wave head when a high-resistance grounding fault or a line form is changed.

Aiming at the problems, the method for extracting the inherent main frequency of the traveling wave for ranging at the initial fault stage of the conventional direct current system is provided in the field, and the strict requirement of the ranging method on the capturing of the traveling wave head is effectively avoided. However, the boundary structure and the operation mode of the flexible dc power grid are greatly different from those of the conventional dc power grid, and therefore, it is necessary to further study the method for measuring the distance of the flexible dc power grid by using the natural frequency to ensure that the fault of the flexible dc power grid is accurately located.

When the traveling wave natural frequency is used for ranging, the frequency characteristics need to be analyzed, namely the natural frequency component of the fault traveling wave needs to be effectively and accurately extracted, so that the fast and accurate frequency measurement method becomes the key of research. The methods proposed at present have respective advantages and disadvantages. For example, the FFT algorithm can reduce the problems of frequency spectrum leakage and barrier effect when FFT is applied independently, improve the detection precision of harmonic parameters, but cannot detect inter-harmonics near integer harmonics; the continuous wavelet transform can realize the detection of inter/sub harmonics, but wavelet functions with different scales have mutual interference in a frequency domain, and when detected signals contain harmonic components with similar frequencies, the detection method is invalid. In addition, there is currently a research on applying a modern spectrum estimation method to power harmonic analysis for frequency analysis, wherein the method for extracting natural frequency by using MUSIC algorithm is most representative, that is, the frequency of a real signal is determined by constructing a pseudo spectrum and scanning a signal to obtain the frequency corresponding to a pseudo spectrum peak. However, when frequency measurement is performed by using the MUSIC algorithm, the number of frequency signals, that is, the dimension N of the signal subspace cannot be determined, and thus, only subjective judgment and adjustment are performed without accurate judgment basis. In the process of determining the number N of the information sources, the value N is selected too much, false spectral peaks appear on the frequency spectrum obtained by frequency scanning, and the maximum deviation of inherent frequency searching is caused; if the value of N is too small, the spectral peaks may be lost. Therefore, it is necessary to improve the ranging method based on the MUSIC algorithm to improve the objectivity and accuracy of the frequency and distance measuring algorithm.

The invention is to solve the problem by analyzing the characteristic relation between the traveling wave natural frequency and the fault distance in the process of breaking the fault of the circuit breaker and exploring the applicable stage of the fault handling natural process of the distance measurement method based on the traveling wave natural frequency.

Disclosure of Invention

Aiming at a flexible direct-current power transmission system based on a hybrid direct-current circuit breaker, the invention provides a flexible direct-current power grid fault location method based on clustering and iterative algorithms, and improves a location method based on an MUSIC algorithm.

The invention discloses a flexible direct current power grid fault location improvement method based on clustering and iterative algorithm, which comprises the following steps:

step 1, measuring the positive voltage U of the line after the RCB is tripped_pAnd negative electrode voltage U_nThen calculating the line mode voltage U_mode；

Step 2, obtaining a series of linear mode voltage spectrums when the signal dimension N takes different values by utilizing an MUSIC algorithm, and extracting the frequencies corresponding to all spectrum peaks;

and 3, setting a category number K by using a K-means clustering method, and clustering all the spectrum peak frequencies obtained in the step 2. Fitting the density functions of all categories, and regarding the frequency corresponding to the peak value of the obtained density function as the natural frequency f_f1,f_f2,f_f3…；

Step 4, assuming the first natural frequency f obtained in step 3_f1Is an inherent main frequency f₁According to formula (I)Calculating the fault distance d₁；

Step 5, according to the formulaEstimating the natural frequency f₂' and a third frequency f₃'；

Step 6, searching the natural frequency obtained in step 3, and respectively selecting the nearest f₂'，f₃' as the true second natural frequency f₂And a true third natural frequency f₃. Then by f₂，f₃Calculating the fault distance d₂And d₃；

Step 7, according to the formulaCalculating d₁、d₂、d₃Standard deviation of (std). If std<std_setThen average fault distance d is taken_mean＝(d₁+d₂+d₃) (ii)/3 as the final failure distance; but if std>std_setThen the frequency f is adjusted_f1Regarded as a spurious frequency, and then the next natural frequency f obtained in step 4 is taken_f2As f₁And 4, repeating the steps 4 to 7.

Compared with the prior art, the flexible direct-current power grid fault location improvement method based on the clustering and iterative algorithm can achieve the following beneficial effects:

1) the fault distance measurement method does not depend on additional distance measurement operation or equipment, is only based on the inherent frequency characteristic of the residual voltage of the line after the RCB is tripped, and improves the distance measurement method based on the MUSIC algorithm; 2) a fault location method capable of accurately calculating a DC fault distance.

Drawings

FIG. 1 is a frequency domain two-port model diagram of a fault loop of a single-conductor transmission system of a flexible direct-current power grid;

FIG. 2 is a corresponding equivalent circuit diagram of a fault handling process and system of a flexible DC power grid based on a hybrid DC breaker;

FIG. 3 is a diagram of an equivalent model of the parameters in the set of free discharge lines after the RCB trips;

FIG. 4 is an overall flow chart of the flexible direct current power grid fault location method based on clustering and iterative algorithm.

Detailed Description

The technical solution of the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

In order to realize the fault positioning method without depending on additional distance measurement operation or equipment and realize accurate measurement of fault distance and accurate fault positioning by utilizing the natural frequency characteristics of fault traveling waves,

the theoretical basis of the fault positioning method based on the inherent frequency characteristic of the residual voltage of the line after the RCB of the direct-current circuit breaker is tripped is as follows:

FIG. 1 is a frequency domain two-port model diagram of a fault loop of a flexible DC power grid single-conductor transmission system, wherein Z is_CSAnd Z_CRepresenting the equivalent impedance of the converter station (including that of the MMC station, of the current-limiting reactors and of the circuit breakers) and the line impedance, E_CSRepresenting an ideal voltage source with negligible frequency characteristics, E_CON1、E_CON2Representing a controlled voltage source, is commonly used to characterize traveling fault waves transmitted from the other side of the line. Line terminal voltage U_PExpressed as:

thus, U_PNatural frequency characteristic of (E) and_CON1have the same natural frequency characteristics. The fault distance and the natural frequency of the traveling wave have the following relationship:

wherein, theta₁、θ₂The phase angle of the reflection coefficient (travelling wave reflection angle) at the converter station and at the fault point, respectively, v is the wave speed, f_nIs the natural frequency. Through analysis, the above formula is still suitable for a flexible direct current power grid, but compared with a traditional direct current power grid, the boundary states at the converter stations of the two systems have larger difference (namely, the traveling wave reflection angles are different). Therefore, the characteristic relation between the natural frequency of the traveling wave and the fault distance in the on-off fault process of the circuit breaker is analyzed, and the characteristic relation is shown in figure 2. When the current flows through the current branch of the breaker (path a in the diagram (a)) or is transferred to the commutation branch (path b) at the initial stage of the fault occurrence, the equivalent circuit of the system is as shown in the diagram (b), and the reflection coefficient at the converter station in the above two stages can be expressed by the formula (3); when the fault current is transferred to the RCD buffer branch of the converter branch to charge the buffer capacitor (path c), the equivalent circuit of the system is as shown in a graph (c), and the reflection coefficient at the converter station can be represented by an expression (4); when the fault current is transferred to the energy absorption branch (path d) for energy consumption, the equivalent circuit of the system is shown as a graph (d), and the reflection coefficient can be expressed as an expression (5).

Through analysis, the natural frequency of the path a, the path b and the path d is too small (only dozens of Hz) to meet the frequency measurement requirement; the available time window for path c is too short (only a few tens of microseconds) and the use of the natural frequency ranging method is not suitable at this stage.

However, after the residual current switch (RCB) trips, the line will be free to discharge to ground through the fault point due to the effects of the line distributed inductance, capacitance and the line stored energy, which means that the line terminals will develop an oscillating voltage. As shown in fig. 3, a lumped parameter model of the system when the oscillation process occurs includes:

can be further written as:

according to equation (7), the corresponding solution can be expressed as:

i_dis＝e^-αt(K₁cosωdt+K₂sinωdt) (8)

wherein α ═ R + R_f) 2L, represents i_dis(t) the attenuation coefficient of the light beam,represents i_dis(t) angular frequency of oscillation. K₁And K₂Is a constant determined by initial conditions.

Thus, the line termination voltage U_PCan be calculated as

WhereinK₄＝L(K₁ω_d-K₂α), attenuation coefficient U_P(t) may be represented by the formula α ═ R + R_f) Calculated as/2L, U_PThe decay time constant of (t) can be expressed as τ 1/α. It is generally considered that the decaying signal decays completely after 5 τ time, i.e. the voltage U is within 5 τ time after RCB has tripped_P(t) can be measured and utilized. It has been analyzed that in the case of typical line lengths, the damping coefficient of the oscillating voltage after the RCB has tripped is sufficiently small, which means that the available measurement time window is sufficiently long.

At this stage, the converter station side line corresponds to an open state (Z)₁Infinite), i.e. the reflection coefficient is expressed as:

therefore, the relationship between the fault distance and the natural frequency at this time can be further expressed as:

the principle of frequency measurement by using the MUSIC algorithm is to perform characteristic decomposition on an array output covariance matrix according to the theory of matrix characteristic decomposition, decompose a signal space into a noise subspace and a signal subspace, and construct a spatial spectrum function P by using the orthogonal property of the noise subspace and a column vector of a signal receiving array matrix_MUSICAnd spectral peak search is performed to estimate signal frequency information. Spatial spectral function P_MUSICThe expression is as follows:

wherein u is a noise feature vector, a is a signal guide vector, N is the number of signal sources, and m is the number of feature values. In the ideal case u and a are orthogonal to each other, i.e. when sweeping to the frequency point of the signal, there is P_MUSIC(f) Denominator 0, i.e. P_MUSIC(f) Infinity, but in practice the value is not strictly 0, but is a very small value, so that P_MUSIC(f) The value at the signal frequency point is larger, shown as P_MUSIC(f) Peak of the spectrum.

In actual conditions, the fault distance is unknown, and the frequency signals are unknown, so that the number N of the signal sources is unknown. When the frequency measurement is carried out by utilizing the MUSIC algorithm, N is required to be selected as a parameter, and improper selection of the value of N can cause the frequency spectrum to generate false spectral peaks and the like. Therefore, the method firstly adopts a K-means clustering method to determine the inherent frequency (all spectrum peak frequencies of all MUSIC frequency spectrums in different N are taken as clustering objects, and the peak value corresponding frequency of the density function fitted by each class of frequency objects is taken as the inherent frequency), so that the subjective dependence on N value selection is reduced; and then, adopting a method of range iteration of the inherent main frequency, the secondary frequency and the third frequency to avoid the influence of false frequency on the fault distance estimation.

When the spectral peak frequencies are clustered by using a K-means clustering algorithm, data are divided into K groups in advance, and K frequency objects are randomly selected as initial clustering centers. Then, the distance between the cluster center frequency and each frequency object is calculated as:

wherein C is a clustering center, x is each frequency object, and dis represents the distance between the two.

According to the formula, the object is allocated to the nearest clustering center, the clustering center is recalculated according to the existing frequency object in the cluster when the frequency sample is allocated each time, and finally, the average value of all the objects in the cluster on each dimension is taken as the clustering center, and the clustering center is expressed as follows:

s is the number of samples per category.

Based on the principle, the invention provides an overall flow chart of the flexible direct-current power grid fault location method based on clustering and iterative algorithm as shown in fig. 4. The method comprises the following specific steps:

step 1, measuring the positive voltage U of the line after the RCB is tripped_pAnd negative electrode voltage U_nThen calculating the line mode voltage U_mode；

Step 2, obtaining a series of linear mode voltage spectrums when the signal dimension N takes different values by utilizing an MUSIC algorithm, and extracting the frequencies corresponding to all spectrum peaks;

and 3, setting one class number K (K is 0,1,2 …) by using a K-means clustering method, and clustering all the spectrum peak frequencies obtained in the step 2. Fitting the density functions of all categories, and regarding the frequency corresponding to the peak value of the obtained density function as the natural frequency f_f1,f_f2,f_f3…；

Step 4, assuming the first natural frequency f obtained in step 3_f1Is, the inherent main frequency f₁According to formula (I)Calculating the fault distance d₁Wherein k is 0;

step 5, according to the formulaEstimating the natural frequency f₂' (corresponding to k taking the value 1) and a third frequency f₃' (corresponding to a k value of 2);

step 6, searching the natural frequency obtained in step 3, and respectively selecting the nearest f₂'，f₃' as the true second natural frequency f₂And a true third natural frequency f₃. Then by f₂，f₃Calculating the fault distance d₂And d₃；

Step 7, according to the formulaCalculating d₁、d₂、d₃Is markedThe standard deviation std. If std<std_setThen average fault distance d is taken_mean＝(d₁+d₂+d₃) (ii)/3 as the final failure distance; if std>std_setThen the frequency f is adjusted_f1Regarded as a spurious frequency, and then the next natural frequency f obtained in step 4 is taken_f2As an inherent main frequency f₁And 4, repeating the steps 4 to 7.

(1) Under the condition that the actual fault distance and the number N of signal sources are unknown, the values of the natural frequencies are determined by using a clustering algorithm (all spectrum peak frequencies of all MUSIC frequency spectrums in different N are taken as clustering objects, and the frequencies corresponding to the peak values of the density functions fitted by the frequency objects of various categories are taken as the natural frequencies), so that the subjective dependence on the N value selection is reduced. The feasibility and the practicability of the MUSIC algorithm in the application of frequency measurement are increased.

(2) The influence of false frequency on the estimation of the fault distance is avoided by using the method of iterative verification of the ranging results of the inherent main frequency, the secondary frequency and the third frequency; because the distance measurement error is larger when the frequency is lower, when an iteration method is adopted, the distance measurement precision is improved by introducing a higher frequency layer, and the average value is taken as a final distance measurement result, so that the reliability of the distance measurement result is improved.

The technical scheme of the invention or the similar technical scheme designed under the invention can achieve the technical effects and fall into the protection scope of the invention.