CN103412221A - Transformer excitation surge current identification method based on time-frequency characteristic quantities - Google Patents

Abstract

的综合时频特征相关系数

。当ρ _{j,j+ 1} ρ _th 时，令ρ _{j,j+ 1}=1，否则ρ _{j,j+ 1}=0。利用相关系数表征差流信号的时频特性及其变化规律，并结合综合相关系数构成励磁涌流识别判据。本发明从差动电流时域和频域分析入手，有效寻找到不同滑动时窗内内部故障电流与励磁涌流的时频特征差异。有别于传统的仅利用单一特征量的涌流鉴别方法，融合了差流的幅值、相位、奇异性、频率分布等多重信息，具有更高的可靠性。The invention relates to a transformer excitation inrush current identification method based on time-frequency characteristic quantities, and belongs to the technical field of transformer relay protection. If the transformer differential current is greater than the set value, use discrete wavelet decomposition to decompose the data in N consecutive sliding time windows, and calculate the total energy E _j of the differential current and the energy sum Ed _i of each frequency band in each sliding time window, respectively, Calculate the energy percentage E _ij of each sub-band within a time window, and form the characteristic matrix W _TF . Compute the two adjacent time windows and

The comprehensive time-frequency characteristic correlation coefficient of

. When ρ _{j,j+ 1} ρ _th , let ρ _{j,j+ 1} =1, otherwise ρ _{j,j+ 1} =0. The correlation coefficient is used to characterize the time-frequency characteristics of the differential current signal and its changing law, and combined with the comprehensive correlation coefficient to form the identification criterion of inrush current. The present invention starts with differential current time domain and frequency domain analysis, and effectively finds the time-frequency characteristic difference of internal fault current and excitation inrush current in different sliding time windows. Different from the traditional inrush identification method that only uses a single characteristic quantity, it integrates multiple information such as the amplitude, phase, singularity, and frequency distribution of the differential current, and has higher reliability.

Description

A Discrimination Method of Transformer Exciting Inrush Current Based on Time-Frequency Feature Quantities

technical field

The invention relates to a transformer excitation inrush current identification method based on time-frequency characteristic quantities, and belongs to the technical field of transformer relay protection.

Background technique

Transformer is an indispensable and important equipment in the power system to connect networks with different voltage levels, and its safe operation is directly related to whether the entire power system can work stably and continuously. There are many types of transformer protection. Among many types of transformer protection, longitudinal differential protection can better meet the requirements of selectivity, quick action, sensitivity and reliability in relay protection, and is the main form of transformer main protection. The longitudinal difference protection uses the difference between the primary side current and the secondary side current of the transformer as the differential current, and if the differential current exceeds a certain setting value, it is judged as an internal fault. Theoretically, the longitudinal differential protection widely used at present can only be used for equipment composed of pure resistance. However, the transformer has completely different characteristics from the bus bar, generator, etc., and its two sides are saturable nonlinear devices that connect the primary side and the secondary side through the iron core electromagnetic field, rather than a pure circuit structure. The transformer is unloaded Kirchhoff's current law (KCL) is no longer established under the conditions of closing, over-excitation, external fault voltage recovery, etc., and the differential current on both sides of the transformer will cause differential protection to malfunction. Therefore, both the traditional analog differential protection and the current digital differential protection need to effectively identify the inrush current to ensure that the protection will not malfunction during no-load closing and voltage recovery after the external fault is eliminated.

The principle of second harmonic braking is mainly used on site to prevent the influence of inrush current on longitudinal differential protection. However, with the improvement of ferromagnetic materials of transformers, the second harmonic component is significantly reduced in saturation, and the differential protection may be wrong at this time. Action; Affected by the parallel capacitance and distributed capacitance of the ultra-high voltage long transmission line, when a serious fault occurs inside the transformer, the resonance between the inductance and capacitance can significantly increase the harmonic component in the short-circuit current, which may cause delay in differential protection. time action. When the current transformer is saturated, the inrush current transmitted to the secondary side generates a reverse current, the waveform is deformed, and the discontinuity angle of the inrush current disappears, which makes the inrush current identification technology relying on the characteristics of the discontinuity angle of the waveform invalid. In recent years, the sampling value difference principle, the waveform symmetry principle, the waveform superposition principle, the waveform correlation analysis method and the waveform fitting method have been proposed. Among them, the sampling value difference principle is a derivative of the discontinuous angle principle, the waveform symmetry principle is an improvement of the discontinuity angle principle, and the waveform superposition principle, waveform correlation analysis method and waveform fitting method are derivative improvements of the waveform symmetry principle. The protection setting of the above various principles is relatively difficult. In the application, the intelligence is set or corrected through experiments according to the actual situation, and there is a hidden danger of misjudgment. Therefore, there are many kinds of excitation inrush current identification methods, but the degree of perfection and applicability still need to be improved.

Contents of the invention

The technical problem to be solved by the invention is to improve the ability of the transformer to correctly and quickly identify the excitation inrush current, and propose a method for identifying the excitation inrush current of the transformer based on the time-frequency characteristic quantity.

和

的综合时频特征相关系数

。当ρ _j,j+1<ρ _th 时，令ρ _j,j+1=1，否则ρ _j,j+1=0。利用相关系数表征差流信号的时频特性及其变化规律，并结合综合相关系数构成励磁涌流识别判据。 The technical scheme of the present invention is: if the differential current of the transformer is greater than the set value, use discrete wavelet decomposition to decompose the data in its N consecutive sliding time windows, and calculate the total energy E _j and the total energy of the differential current in each sliding time window respectively Calculate the energy of each frequency band and E _ij , calculate the energy percentage E _ij of each sub-band within a time window, and form the characteristic matrix W _TF . Compute the two adjacent time windows

and

The comprehensive time-frequency characteristic correlation coefficient of

. When ρ _{j,j+ 1} < ρ _th , set ρ _{j,j+ 1} =1, otherwise ρ _{j,j+ 1} =0. The correlation coefficient is used to characterize the time-frequency characteristics of the differential current signal and its changing law, and combined with the comprehensive correlation coefficient to form the identification criterion of inrush current.

Specific steps are as follows:

(1) If the differential current of the transformer is greater than the set value, use discrete wavelet decomposition to decompose the data in N consecutive sliding time windows.

(2) Calculation of time-frequency feature matrix

Calculate the energy percentage of each frequency band in each sliding time window: first calculate the total energy E _j of the differential current in each sliding time window according to formula (1); secondly calculate the energy of each frequency band in each sliding time window according to formula (2) and Ed _i ; finally calculate the energy percentage E _ij of each sub-band within a time window according to formula (3).

                              （1）

(1)

(2)

                             （3）

(3)

为每个采样点的差动电流幅值；i=1…M、M=8为DWT分解层数，

为差动电流小波分解后第i层第n点的幅值。 In the formula, j =1... K , K =400, which are the sampling points in each time window;

is the differential current amplitude of each sampling point; i =1...M, M=8 is the number of DWT decomposition layers,

is the amplitude of the nth point in the i- th layer after the differential current wavelet decomposition.

The time-frequency feature quantity W _TF,j of each sliding time window is shown in formula (4), and the total time-frequency feature matrix W _TF is shown in formula (5)

                      （4）

(4)

                     （5）

(5)

(3) Calculate the comprehensive time-frequency characteristic correlation coefficient

           （6）

(6)

、

为时频特征量的均方差，其中D（W _TF,j ）= E（W ² _TF,j ）- E ²（W _TF,j ） ，D（W _TF,j+1）= E（W ² _TF,j+1）- E ²（W _TF,j+1）。 where Cov ( W _{TF , j} , W _{TF,j+ 1} ) is the covariance of the time-frequency special domain feature quantity W _{TF , j} , W _{TF,j+ 1} , Cov ( W _{TF , j} , W _{TF,j+ 1} ) = E （ W _{TF , j} · W _{TF,j+ 1} - E （ W _{TF , j} ） E （ W _{TF,j+ 1} ,

,

is the mean square error of the time-frequency feature quantity, where D ( W _{TF , j} ) = E ( W ² _{TF , j} ) - E ² ( W _{TF , j} ), D ( W _{TF,j+ 1} ) = E ( W ² _{TF ,j+ 1} ) - E ² ( W _{TF,j+ 1} ).

(4) When the comprehensive correlation coefficient ρ _{j,j+ 1} of adjacent time windows is smaller than the threshold value ρ _th , set ρ _{j,j+ 1} =1, otherwise ρ _{j,j+ 1} =0. Introduce normal distribution statistics to analyze it to form the final criterion.

(5) Identify whether it is an exciting inrush current according to the size of the expected value S;

If the expected value S<0.2, it is judged to be an internal fault current, and the protection outlet operates; otherwise, it is judged to be an excitation inrush current, and the differential protection of the transformer is blocked.

When measuring the differential current of the transformer, the time window length is 20 ms, the sampling frequency is 20 kHz, the number of sampling points in the sliding time window is 50, and the wavelet decomposition is divided into 8 layers.

Principle of the present invention is:

1. The basic theory of wavelet transform:

(1) Continuous wavelet transform

为一平方可积函数，若其傅里叶变换

满足可容许性条件，即： set up

is a square integrable function, if its Fourier transform

The admissibility conditions are met, namely:

                          （1）

(1)

为一个基本小波，或者小波母函数。 then called

is a basic wavelet, or wavelet mother function.

进行伸缩和平移，可以得到连续小波基函数

： wavelet mother function

By stretching and translating, the continuous wavelet basis function can be obtained

:

        

               （2）

(2)

In the formula: a is the scaling factor, or scale factor; b is the translation factor.

for any function The continuous wavelet transform of is:

          （3）

(3)

的共轭。 In the formula: express

the conjugate.

(2) Discrete wavelet transform

中的连续变量a和b取做整数离散形式，将

表示为： Known from the concept of continuous wavelet transform, the scale factor a and translation factor b of continuous wavelet transform are continuous variables. In practical applications, usually the

The continuous variables a and b in are taken as integer discrete forms, and the

Expressed as:

                         （4）

(4)

的离散小波变换可表示为： corresponding function

The discrete wavelet transform of can be expressed as:

                        （5）

(5)

是由小波函数

经整数倍放、缩和经整数k平移所生成的函数族

，

。因此，该离散后的小波序列一般称为离散二进小波序列。 Due to the discrete wavelet

is given by the wavelet function

through A family of functions generated by integer multiplication, scaling, and translation by integer k

,

. Therefore, the discrete wavelet sequence is generally called discrete binary wavelet sequence.

2. Correlation coefficient:

The strict definition of the cross-correlation function of signals f ( t ) and g ( t ) is as follows:

(6)

where T is the average time. The cross-correlation function characterizes the time average of the product of two signals.

If f ( t ) and g ( t ) are periodic signals with period T0 , the above formula can be _expressed as:

(7)

，其自相关函数可以表示为： The correlation function is discretized, and the influence of the signal amplitude is excluded, and the correlation operation is normalized. For discrete signals

, its autocorrelation function can be expressed as:

               （8）

(8)

、

为时频特征量的均方差，其中D（i（k））= E（i ²（k））- E ²（i（k）） ，D（i（k+ j））= E（i ²（k+ j））- E ²（i（k+ j））。ρ _k,k+j 的取值为0至1之间，当i（k）和i（k+j）越接近ρ值越大。 In the formula, Cov ( i ( k ), i ( k + 1)) is the covariance of time-frequency special domain feature quantities i ( k ), i ( k + j ), Cov ( i ( k ), i ( k + j )) = E ( i ( k ) i ( k + j ) - E ( i ( k )) E ( i ( k + j ),

,

is the mean square error of the time-frequency feature quantity, where D ( i ( k )) = E ( i ² ( k )) - E ² ( i ( k )), D ( i ( k + j )) = E ( i ² ( k + j ))- E2 ⁽ i ( k + j )). The value of ρ _k,k+j is between 0 and 1, when i ( k ) and i ( k + j ) are closer, the value of ρ is larger.

When j is 1, the above formula can be expressed as:

             （9）

(9)

In the formula, k=1, 2, 3... N, N is the sampling data length in the short time window, the range of autocorrelation coefficient ρ is [-1, +1], +1 means two A signal is 100% positively correlated, and -1 means that two signals are 100% negatively correlated.

3. Identification of transformer excitation inrush current based on time-frequency characteristic quantity:

In different sliding time windows, discrete wavelet transform is used to decompose the differential current shown in Figure 2. The moving process of the sliding time window is shown in Figure 3, and the length of each time window is one power frequency period (20ms). The time-frequency characteristic distribution diagrams of internal fault current and inrush current in different time windows shown in Fig. 4 and Fig. 5 are decomposed. In the figure, the x- axis is used to represent the time distribution, the y- axis frequency band distribution, and the z- axis represents the energy under the corresponding time frequency distributed.

Figure 4 ( a ) and (b) are the time-frequency characteristic distribution diagrams of the differential current in adjacent time windows under the same working condition, and (c) is the time-frequency characteristic of the differential current separated by 50 sliding time windows Distribution. From Figure 3-16, we know that after the transformer has an internal fault, the time-frequency characteristics of its differential current are distributed in different time windows basically the same: mainly concentrated in the low-frequency band, and the amplitude is basically unchanged. From Figure 3-17, in the first time window (figure a ) the excitation inrush frequency is mainly distributed on the 7th and 8th floors and the energy ratio is about 1:1; in the second time window (figure b) the frequency distribution changes , mainly on the 5th, 6th, 7th, and 8th floors, and its energy ratio is about 1:1:3:2; compared with the first two time windows, the frequency component of the inrush current in the 50th time window changes more drastically, It is mainly distributed on the 4th, 5th, 6th, 7th, and 8th floors, and the energy ratio is about 1:1:1:1:1.

In the process of transformer no-load closing or voltage recovery after fault removal, the excitation inrush current generated is a nonlinear and non-stationary signal composed of different frequency components; the fault differential current when the transformer is internally faulty is approximately a power frequency sinusoidal signal. Therefore, the differential current data of each sliding time window after the differential protection is started can be decomposed by wavelet and decomposed into different frequency bands, and then the time-frequency characteristic quantity obtained can fully reflect the time-frequency characteristics of the signal in the time-frequency window , according to which the identification criterion of excitation inrush current can be constituted.

The beneficial effects of the present invention are:

(1) The present invention starts from the time-domain and frequency-domain analysis of the differential current, and effectively finds the time-frequency characteristic difference between the internal fault current and the excitation inrush current in different sliding time windows.

(2) This patent does not simply use the single characteristic of the differential current, but comprehensively analyzes the sinusoidal characteristics of the internal fault current waveform, the waveform of the inrush current is biased to one side of the time axis, and the waveform has discontinuous angles. Multiple information such as the amplitude, phase, singularity, and frequency distribution of the flow, with higher reliability.

(3) The sampling frequency of the present invention is 20kHz, which meets the current hardware conditions and is easy to implement on site.

Description of drawings

Fig. 1 is a schematic diagram of patent simulation in this aspect;

Figure 2 Schematic diagram of window movement when sliding;

Figure 3 differential current waveform diagram, where (a) is the differential current waveform diagram when the transformer internal fault occurs, and (b) diagram is the excitation inrush current waveform diagram when the transformer is switched on with no load;

Figure 4 is the time-frequency characteristic distribution diagram of the internal fault current in different time windows, where ( a ) and (b) are the time-frequency characteristic distribution diagrams of the differential current in adjacent time windows under the same working condition, and (c) is the time-frequency characteristic distribution diagram of the differential current separated by 50 sliding time windows;

Figure 5 is the time-frequency characteristic distribution diagram of inrush current in different time windows, where ( a ) and (b) are the time-frequency characteristic distribution diagrams of differential current in adjacent time windows under the same working condition, and (c) is Distribution map of time-frequency characteristics of differential current separated by 50 sliding time windows.

Detailed ways

The present invention will be further described below in combination with the accompanying drawings and specific embodiments.

和的综合时频特征相关系数

。当ρ _j,j+1<ρ _th 时，令ρ _j,j+1=1，否则ρ _j,j+1=0。利用相关系数表征差流信号的时频特性及其变化规律，并结合综合相关系数构成励磁涌流识别判据。 An integrated transformer excitation inrush identification method based on time-frequency characteristic quantities is to use discrete wavelet decomposition to decompose the data in N consecutive sliding time windows when the differential current of the transformer is greater than the set value, and calculate the difference in each sliding time window respectively. The total energy E _j of the dynamic current and the energy sum E _i of each frequency band are calculated, and the energy percentage E _ij of each sub-band within a time window is calculated, and the characteristic matrix W _TF is formed. Calculate the two adjacent time windows

and The comprehensive time-frequency characteristic correlation coefficient of

. When ρ _{j,j+ 1} < ρ _th , set ρ _{j,j+ 1} =1, otherwise ρ _{j,j+ 1} =0. The correlation coefficient is used to characterize the time-frequency characteristics of the differential current signal and its changing law, and combined with the comprehensive correlation coefficient to form the identification criterion of inrush current.

Specific steps are as follows:

(1) If the differential current of the transformer is greater than the set value, use discrete wavelet decomposition to decompose the data in N consecutive sliding time windows.

(2) Calculation of time-frequency feature matrix

Calculate the energy percentage of each frequency band in each sliding time window: first calculate the total energy E _j of the differential current in each sliding time window according to formula (1); secondly calculate the energy of each frequency band in each sliding time window according to formula (2) and Ed _i ; finally calculate the energy percentage E _ij of each sub-band within a time window according to formula (3).

                              （1）

(1)

(2)

(3)

为每个采样点的差动电流幅值；i=1…M、M=8为DWT分解层数，

为差动电流小波分解后第i层第n点的幅值。 In the formula, j =1... K , K =400, which are the sampling points in each time window;

is the differential current amplitude of each sampling point; i =1...M, M=8 is the number of DWT decomposition layers,

is the amplitude of the nth point in the i- th layer after the differential current wavelet decomposition.

The time-frequency feature quantity W _TF,j of each sliding time window is shown in formula (4), and the total time-frequency feature matrix W _TF is shown in formula (5)

(4)

                     （5）

(5)

(3) Calculate the comprehensive time-frequency characteristic correlation coefficient

           （6）

(6)

为时频特征量的均方差，其中D（W _TF,j ）= E（W ² _TF,j ）- E ²（W _TF,j ） ，D（W _TF,j+1）= E（W ² _TF,j+1）- E ²（W _TF,j+1）。 where Cov ( W _{TF , j} , W _{TF,j+ 1} ) is the covariance of the time-frequency special domain feature quantity W _{TF , j} , W _{TF,j+ 1} , Cov ( W _{TF , j} , W _{TF,j+ 1} ) = E （ W _{TF , j} · W _{TF,j+ 1} - E （ W _{TF , j} ） E （ W _{TF,j+ 1} , ,

is the mean square error of the time-frequency feature quantity, where D ( W _{TF , j} ) = E ( W ² _{TF , j} ) - E ² ( W _{TF , j} ), D ( W _{TF,j+ 1} ) = E ( W ² _{TF ,j+ 1} ) - E ² ( W _{TF,j+ 1} ).

(4) When the comprehensive correlation coefficient ρ _{j,j+ 1} of adjacent time windows is smaller than the threshold value ρ _th , set ρ _{j,j+ 1} =1, otherwise ρ _{j,j+ 1} =0. Introduce normal distribution statistics to analyze it to form the final criterion.

(5) Identify whether it is an exciting inrush current according to the size of the expected value S;

If the expected value S<0.2, it is judged to be an internal fault current, and the protection outlet operates; otherwise, it is judged to be an excitation inrush current, and the differential protection of the transformer is blocked.

When measuring the differential current of the transformer, the time window length is 20 ms, the sampling frequency is 20 kHz, the number of sampling points in the sliding time window is 50, and the wavelet decomposition is divided into 8 layers.

Embodiment 1: In the simulation system shown in Fig. 1, the transformers are three single-phase three-winding transformers, which adopt the Yd11 connection method. The high-voltage winding connected to the 110kV system is the primary side of the transformer, and the medium-voltage winding and the low-voltage winding are cascaded to form the secondary side of the transformer. The transmission line is simulated by 5 sections of π-type equivalent circuit, each section is 4km long. The parameters of the transformer simulation system are shown in Table 1, and the parameters of the magnetization curve are shown in Table 2.

Table 1 Simulation system parameters

Table 2 Magnetization parameters

 

When a 30% turn-to-turn fault occurs inside the transformer:

(1) The differential current of the transformer is greater than the set value, and the data in the continuous 400 sliding time windows are decomposed by discrete wavelet decomposition.

(2) Calculate the time-frequency feature matrix W _TF in different sliding time windows

，当相邻时窗的综合相关系数ρ _j,j+1小于门槛值ρ _th 时，令ρ _j,j+1=1，否则ρ _j,j+1=0。 (3) Calculate the comprehensive time-frequency feature correlation coefficient in adjacent time windows

, when the comprehensive correlation coefficient ρ _{j,j+ 1} of the adjacent time window is less than the threshold value ρ _th , set ρ _{j,j+ 1} =1, otherwise ρ _{j,j+ 1} =0.

(4) Use the normal distribution to reset the Carry out analysis, expect S=0.01<0.2, it is judged as an internal fault, and the protection exit action.

Embodiment 2: The simulation system and transformer parameters are the same as Embodiment 1.

The transformer is closed with no load, and the closing angle is 45°. The calculation and statistics are carried out in the same way as in Embodiment 1. The expected value S=0.43>0.2, the excitation inrush current is correctly identified, and the protection is blocked. .

The specific embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned embodiments. Change accordingly.

Claims (3)

1. discrimination method of the transformer excitation flow based on the time-frequency characteristics amount, it is characterized in that: if the transformer differential electric current is greater than setting valve, utilize discrete wavelet to decompose the data in its N continuous sliding window are decomposed, calculate respectively difference current gross energy in each sliding window E _j With each frequency band energy and Ed _i , each sub-band energy percentage in window while asking for E _Ij , and form eigenmatrix W _TF Calculate in two windows when adjacent

With

Comprehensive time-frequency characteristics related coefficient

When ρ _{J, j+1} < ρ _Th The time, order ρ _{J, j+1} =1, otherwise ρ _{J, j+1} =0, utilize the integrated correlation coefficient of normal distribution counterweight postpone to add up, according to the size of expectation value S, differentiate excitation surge current.

2. the discrimination method of the transformer excitation flow based on the time-frequency characteristics amount according to claim 1, is characterized in that, concrete steps are as follows:

(1), if the transformer differential electric current is greater than setting valve, utilizes discrete wavelet to decompose the data in its N continuous sliding window are decomposed;

(2) time-frequency characteristics matrix computations:

Ask for each frequency band energy number percent in each sliding window: at first according to formula (1), calculate difference current gross energy in each sliding window E _j Secondly according to formula (2) calculate in each sliding window each frequency band energy and Ed _i Each sub-band energy percentage in window while finally asking for one according to formula (3) E _Ij

（1）

（2）

（3）

In formula j=1 K, K=400, sampled point in window during for each;

Difference current amplitude for each sampled point; i=1 ... M, M=8 are that DWT decomposes the number of plies,

For after the difference current wavelet decomposition iLayer the nThe amplitude of point;

The time-frequency characteristics amount of each sliding window W _{TF, j} As the formula (4), total time-frequency characteristics matrix W _TF As the formula (5)

（4）

（5）

(3) calculate comprehensive time-frequency characteristics related coefficient:

（6）

In formula Cov( W _{TF, j} , W _{TF, j+1} ) be the special characteristic of field amount of time-frequency W _{TF, j} , W _{TF, j+1} Covariance, Cov( W _{TF, j} , W _{TF, j+1} )= E( W _{TF, j} W _{TF, j+1} - E( W _{TF, j} ) E( W _{TF, j+1} ,

,

For the mean square deviation of time-frequency characteristics amount, wherein D( W _{TF, j} )= E( W ² _{TF, j} )- E ²( W _{TF, j} ), D( W _{TF, j+1} )= E( W ² _{TF, j+1} )- E ²( W _{TF, j+1} );

(4) integrated correlation coefficient of window when adjacent ρ _{J, j+1} Be less than threshold value ρ _Th The time, order ρ _{J, j+1} =1, otherwise ρ _{J, j+1} =0, introduce the normal distribution statistics it is analyzed and forms final criterion;

(5) according to expectation value S size, differentiate whether be excitation surge current:

If its expectation value S<0.2, be judged to be internal fault current, protection outlet action; Otherwise be judged to be excitation surge current, the locking transformer differential protection.

3. the discrimination method of the transformer excitation flow based on the time-frequency characteristics amount according to claim 1, it is characterized in that: during the difference current of described measuring transformer, time window is 20ms, and sample frequency is 20kHz, in sliding window, the sampled point number is 50, and wavelet decomposition is 8 layers.

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