Method for distinguishing internal and external faults of flexible HVDC transmission line based on S-transform

Abstract

The application discloses a flexible DC transmission line intra-zone and extra-zone fault discrimination method based on S transform, a method of waveform continuation is used to cover the subsequent wave with the wave tail of the first wave, the influence of the subsequent wave head on the frequency characteristics is reduced, the S transform is used to make the modulus time frequency matrix of the continued waveform, the row vectors of the modulus time frequency matrix are integrated, the corresponding amplitude-frequency curve is obtained, the energy operator is used to weight the amplitude-frequency curve to improve the proportion of high-frequency components, the energy accumulation of different frequency bands is constructed, the ratio of the high-frequency band energy accumulation and the total frequency band energy accumulation is taken as the intra-zone and extra-zone fault recognition criterion, when the ratio is greater than the threshold value, the intra-zone fault is determined, otherwise, the extra-zone fault is determined. The method meets the rapidity requirement of the flexible DC transmission line protection, has high sensitivity, and has important reference value for the development of the flexible DC transmission protection.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power systems, and relates to a flexible DC transmission line internal and external fault discrimination method based on S transform. BACKGROUND

[0002] Under the background of the country proposing to achieve the "double carbon" target construction, new energy power generation technology is developing rapidly. However, compared with traditional hydropower and thermal power, new energy such as wind energy and solar energy has the characteristics of intermittency and randomness, and the AC power grid has limited capacity for consumption. Flexible DC transmission technology is widely considered as one of the effective technical means to solve the problem of flexible consumption of large-scale renewable energy due to its strong controllability, fast power regulation speed and flexible operation mode.

[0003] After the flexible DC transmission line fault occurs, the fault current amplitude increases rapidly, which will affect the entire DC system in a very short time, so the protection is required to complete the fault discrimination within 3ms after the fault. At present, the research on the main protection of the flexible DC transmission line is mainly single-ended protection, one of which uses the transient frequency domain characteristics as the protection criterion. The basic principle is based on the high impedance characteristics of the line boundary element to high-frequency components, which causes the high-frequency components of external faults to attenuate, so most protections use the ratio of high-frequency and low-frequency energy to distinguish. However, the selection method of high and low frequency lacks theoretical basis, and cannot maximize the difference between high and low frequencies. At the same time, the protection criterion threshold value is often dependent on experience or simulation, which is difficult to adapt to the flexible changes of the flexible DC power grid structure and operation mode. In addition, the frequent reflection of near-end fault traveling waves will affect the frequency characteristics of the traveling waves, which is not conducive to the correct discrimination of line faults. SUMMARY

[0004] The purpose of the present application is to provide a flexible DC transmission line internal and external fault discrimination method based on S transform, which can accurately judge the internal and external faults of the flexible DC transmission line.

[0005] The technical solution adopted by the present application is a flexible DC transmission line internal and external fault discrimination method based on S transform, which specifically includes the following processes: the first wave after the traveling wave is covered with the tail of the first wave by the waveform continuation method, the S transform is used to make the modulus time frequency matrix of the continued waveform, the row vectors of the modulus time frequency matrix are integrated to obtain the corresponding amplitude-frequency curve, then the energy operator is used to weight the amplitude-frequency curve to improve the proportion of high-frequency components, and the energy accumulation of different frequency bands is constructed. The ratio of high-frequency band energy accumulation to total frequency band energy accumulation is used as the internal and external fault recognition criterion. When the ratio is greater than the threshold value, it is judged as an internal fault, otherwise it is judged as an external fault.

[0006] The present application has the following characteristics:

[0007] Specifically includes the following steps:

[0008] Step 1, after the protection starting element is started, a protection time window is selected, voltage and current data in the time window are read, and line mode voltage fault component Δu1(t) and line mode current fault component Δi1(t) in the time window are calculated;

[0009] Step 2, according to the amplitude ratio K of the backward wave and the forward wave d , the fault direction is judged, if the amplitude ratio of the backward wave and the forward wave is less than 1, it is judged as an opposite direction external fault, and the protection returns; if the amplitude ratio of the backward wave and the forward wave is greater than 1, it is judged as a positive direction fault, and step 3 is entered;

[0010] Step 3, the wave head of the line mode voltage forward wave in the time window is extracted by using the wavelet mode maximum value, db4 wavelet is taken as the wavelet base, the line mode voltage forward wave is decomposed by four layers, the first layer decomposition data is taken, the wave head in the time window is marked by the wavelet mode maximum value, if there is only one wave head in the time window, the original line mode voltage backward wave data in the time window is reserved; if there is more than one wave head in the time window, the second wave head is taken as the extension point, denoted as h, and all data from h point to the end of the time window is replaced by the data of h point;

[0011] Step 4, the line mode voltage backward wave in the time window processed in step 3 is subjected to discrete S transform, the corresponding mode time frequency matrix is obtained, the row vector of the mode time frequency matrix is integrated, the corresponding amplitude frequency curve is obtained, and the energy operator is weighted, and the weighted amplitude frequency curve is obtained;

[0012] Step 5, the high frequency band energy accumulation E h , the total frequency band energy accumulation E all are calculated, the ratio K of E h and E all is obtained, the energy accumulation ratio K is compared with the set threshold value K set , and the fault is judged according to the comparison result.

[0013] The specific process of step 1 is: the positive electrode voltage u p (t), the negative electrode voltage u n (t), the positive electrode current i p (t), and the negative electrode current i n (t) are read, and are subtracted from the positive electrode voltage average u p0 , the negative electrode voltage average u n0 , the positive electrode current average i p0 , and the negative electrode current average i n0 before the protection is started, respectively, to obtain the positive electrode voltage fault component Δu p (t), the negative electrode voltage fault component Δu n(t), positive electrode current fault component Δi p (t) and negative electrode current fault component Δi n (t), and the calculation formula is shown in formula (1):

[0014]

[0015] The line mode voltage fault component Δu1(t) and the line mode current fault component Δi1(t) in the time window are calculated according to the calculation result of formula (1), and the calculation formula is shown in formula (2):

[0016]

[0017] The specific process of step 2 is as follows:

[0018] Step 2.1, sampling the line mode voltage back wave u b (t) and the line mode voltage forward wave u f (t) in the time window according to the following formula (3):

[0019]

[0020] In the formula, Z c1 is the line mode wave impedance of the line;

[0021] Step 2.2, using the amplitude ratio K d of the fault back wave and the fault forward wave to judge the fault direction, K d The calculation formula is shown in formula (4):

[0022]

[0023] In the formula, t represents the sampling point in the time window, and N is the total number of sampling points in the time window;

[0024] When the ratio K d is less than 1, it is judged as a reverse direction fault, and the protection returns; when the ratio is greater than 1, it is judged as a positive direction fault, and step 3 is entered.

[0025] The specific process of step 3 is as follows:

[0026] Step 3.1, discrete wavelet transform is performed on the line mode voltage back wave in the time window, and the process of extracting the wave head of the wavelet transform mode maximum value is as follows:

[0027] Taking db4 wavelet as the wavelet base function, taking the scale factor equal to 2 and the translation factor equal to 1, the discrete wavelet transform of the function f(t) is as follows:

[0028]

[0029] In formula (5), p is the transform scale, and q is the translation amount;

[0030] Step 3.2, the time window within the line mode voltage backward wave into f(t), select the highest layer in the four-layer decomposition, that is, the first layer wavelet coefficient, that is, p = 1 to get WT f (1, q), the modulus maximum point of the signal in the time window is obtained, if all q in the neighborhood of q0 satisfy formula (6), then q0 is the wavelet transform modulus maximum value:

[0031] |WT f (1, q)|≤|WT f (1, q0)| (6)

[0032] Step 3.3, using the wavelet transform modulus maximum value, starting from the first sampling point to calibrate the wave head in the time window, according to formula (6) to obtain the wavelet modulus maximum value q0 in the time window, which is the wave head, if there is only one wave head in the time window, the line mode voltage backward wave data in the original time window is retained; if there is more than one wave head in the time window, take the point before the second wave head as the continuation point h, replace all data from h point to the end of the time window with the data of h point, and the continuation formula is as follows:

[0033] u b (h+i)=u b (h) (7)

[0034] In the formula, i = 1, 2, 3, …, N-h; h point is the continuation point.

[0035] The specific process of step 4 is as follows:

[0036] Step 4.1, the line mode voltage backward wave obtained in step 3 is denoted as Where t = 1, 2, 3, …, N, the discrete S transform is performed on to obtain the complex time-frequency matrix of (N / 2+1) × N The discrete S transform calculation formula is shown in formula (8):

[0037]

[0038] In the formula, 1≤k≤N; T is the sampling time interval; m is the discrete time point, which takes the value: 0≤m≤N-1; n is the frequency serial number, which takes the value: 1≤n≤N / 2; n / NT represents the corresponding frequency; Indicates: the discrete expression of the data in the time window after continuation The discrete signal obtained by Fourier transform;

[0039] Step 4.2, the modulus value of each element in the complex time-frequency matrix is calculated to obtain the modulus time-frequency matrix ​

[0040] Step 4.3, integrate the row vector of the modal time-frequency matrix to get the discrete amplitude-frequency curve Multiply the amplitude-frequency curve with the energy operator L(f), the discrete expression of the energy operator is where n / NT is the discrete form of f, get the weighted amplitude-frequency curve The expression is shown in equation (9):

[0041]

[0042] The specific process of step 5 is as follows:

[0043] Step 5.1, calculate the weighted amplitude-frequency curve The energy accumulation of different frequency bands, select 1-10 kHz as the full frequency band, the calculation formula is as follows:

[0044]

[0045]

[0046] In the formula, b is the total number of sampling points in the frequency range of 1-10 kHz, E h is the energy accumulation of the full frequency band; E all is the energy accumulation of the high frequency band; λ1 is the lower boundary of the energy accumulation of the high frequency band;

[0047] Calculate the ratio K of the energy accumulation of the high frequency band to the total frequency band, as the identification criterion, the calculation formula of the energy accumulation ratio K is:

[0048]

[0049] The specific setting method of λ1 in equation (11) is as follows:

[0050] Theoretical frequency domain expression of faults in the area:

[0051]

[0052] A(s)=e -γ(s)l (14)

[0053] In the formula, U1(s) is the frequency domain expression of faults in the area, l is the distance from the fault point to the protection measuring point, γ(s) is the line attenuation constant, U0 is the normal operating voltage of the transmission line; Z C1 and Z C0 are the modal wave impedance and zero modal wave impedance; R f is the transition resistance;

[0054] ​The out-of-zone fault attenuates on the line boundary compared with the in-zone fault, so the out-of-zone fault expression should be multiplied by the boundary element transfer function H(s) on the basis of formula (13), and the expression is as follows:

[0055]

[0056]

[0057] In the formula, U2(s) is the frequency domain expression of the out-of-zone fault, the parameter of the current limiting reactor is L dc ;

[0058] Bring s = jω, ω = 2πf into formula (13) and formula (16), the amplitude-frequency relationship of the in-zone fault and the out-of-zone fault with frequency f can be obtained respectively, take a sampling point every 100 Hz, take to 10 kHz cutoff, a total of 100 sampling points, calculate the amplitude size under each sampling point, and get the discrete amplitude-frequency curve, denoted as the in-zone fault amplitude-frequency curve and the out-of-zone fault amplitude-frequency curve and the discrete energy operator are multiplied respectively to obtain the weighted amplitude-frequency curve and The curve K(λ) of the energy accumulation ratio changing with λ is calculated, and the calculation formula is shown in formula (17):

[0059]

[0060] In the formula, λ = 1, 2, 3, …, 100, s is a complex frequency, ω is an angular frequency, and f is a frequency;

[0061] The weighted two amplitude-frequency curves are brought into formula (17), that is, and

[0062]

[0063]

[0064] K1(λ) represents the curve of the energy accumulation ratio of the in-zone fault changing with λ, and K2(λ) represents the curve of the energy accumulation ratio of the out-of-zone fault changing with λ, K1(λ) and K2(λ) are brought into formula (20), and the maximum point of the difference value between them is calculated:

[0065] ΔK(λ) = |K1(λ)-K2(λ)| (20)

[0066] According to the above formula, the λ corresponding to the maximum value of ΔK(λ) is obtained, denoted as λ1, and λ1 is the lower boundary value of the high frequency band energy accumulation.​​

[0067] Step 5.2, compare the result obtained in step 5.1 with the set threshold value K set , determine whether K satisfies formula (21), and determine the fault location according to the judgment result, if formula (21) is satisfied, it is judged as an intra-zone fault, if formula (21) is not satisfied, it is judged as an out-of-zone fault, and the discrimination formula is as follows:

[0068] K>K set (21)。

[0069] Step 5.2, the threshold value K set is set, and the specific steps are as follows:

[0070] The value of λ1 obtained in step 5.1 is brought into formula (18) and (19) to obtain K1(λ1) and K2(λ1), according to formula (22), the threshold value K set can be obtained:

[0071]

[0072] The beneficial effects of the present application are that the present application is a kind of out-of-zone fault identification method for flexible DC transmission line, according to the frequency domain characteristic difference of line mode voltage anti-traveling wave after S transformation, compared with other methods, different frequency bands can be flexibly divided, and the energy operator method is used to amplify the frequency domain characteristics, and the frequency band below 10kHz is taken to analyze. The size of the energy accumulation ratio K is calculated to distinguish the intra-zone and out-of-zone faults. Secondly, the method of time window extension is used to filter the wave heads except the first wave head, which reduces the interference of the wave head. The method is simple in principle, high in sensitivity, strong in reliability and strong in noise resistance. It does not need to be set according to experience or simulation results, and meets the requirements of engineering practice. BRIEF DESCRIPTION OF DRAWINGS

[0073] Figure 1 It is the flow chart of the intra-zone and out-of-zone fault discrimination method of the flexible DC transmission line based on S transformation of the present application;

[0074] Figure 2 It is the flexible DC transmission line topology structure diagram adopted in the intra-zone and out-of-zone fault discrimination method of the flexible DC transmission line based on S transformation of the present application;

[0075] Figures 3(a) to 3(c) It is the image before and after extension and the amplitude-frequency curve after S transformation and energy operator weighting of the 100km positive polarity metallic short circuit grounding fault in the simulation verification stage using the intra-zone and out-of-zone fault discrimination method of the flexible DC transmission line based on S transformation of the present application;

[0076] Figures 4(a) to 4(c)It is the image before and after the continuation of the positive pole 100Ω transition resistance grounding fault at 400km of the flexible DC transmission line using the S transform-based flexible DC transmission line internal and external fault discrimination method in the simulation verification stage and the amplitude-frequency curve after the S transform and energy operator weighting.

[0077] Figures 5(a) to 5(c) It is the image before and after the continuation of the positive pole 100Ω transition resistance grounding fault at 400km of the flexible DC transmission line using the S transform-based flexible DC transmission line internal and external fault discrimination method in the simulation verification stage and the amplitude-frequency curve after the S transform and energy operator weighting.

[0078] Figures 6(a) to 6(c) It is the image before and after the continuation of the positive pole 100Ω transition resistance grounding fault at 400km of the flexible DC transmission line using the S transform-based flexible DC transmission line internal and external fault discrimination method in the simulation verification stage and the amplitude-frequency curve after the S transform and energy operator weighting. DETAILED DESCRIPTION

[0079] The application will be described in detail below in combination with the drawings and specific embodiments.

[0080] The S transform-based flexible DC transmission line internal and external fault discrimination method covers the subsequent wave head with the wave tail of the first wave by the method of waveform continuation, reduces the influence of the subsequent wave head on the frequency characteristics, uses the S transform to make the modulus time-frequency matrix of the continued waveform, integrates the row vectors of the modulus time-frequency matrix to obtain the corresponding amplitude-frequency curve, then uses the energy operator to weight the amplitude-frequency curve to improve the proportion of high-frequency components, constructs the energy accumulation of different frequency bands, takes the ratio of the high-frequency band energy accumulation and the total frequency band energy accumulation as the internal and external fault recognition criterion, and determines the internal fault when the ratio is greater than the threshold value, and determines the external fault otherwise. The method meets the rapidity requirement of the flexible DC transmission line protection, has high sensitivity, and has important reference value for the development of the flexible DC transmission protection.

[0081] The S transform-based flexible DC transmission line internal and external fault discrimination method of the application has the flow as shown in the figure, and specifically includes the following steps: Figure 1

[0082] Step 1, after the protection starting element is started, take 1ms before starting and 1.5ms after starting as the protection time window, and read the voltage and current data in the data window. Read the positive voltage u p (t) of the protection installation, the negative voltage u n (t), the positive current i p (t), the negative current i n (t), respectively, and the average value of the positive voltage u p0 , the average value of the negative voltage u n0 ​, positive electrode current average i p0 , negative electrode current average i n0 Subtraction, positive electrode voltage fault component Δu p (t), negative electrode voltage fault component Δu n (t), positive electrode current fault component Δi p (t) and negative electrode current fault component Δi n (t), the calculation formula is shown in formula (1):

[0083]

[0084] The line mode voltage fault component Δu1(t) and the line mode current fault component Δi1(t) in the calculation time window are calculated, and the calculation formula is shown in formula (2):

[0085]

[0086] Step 2, the line mode voltage forward wave and the line mode voltage backward wave are calculated, and the amplitude ratio K of the backward wave to the forward wave is made d , the size of K d is judged, if the amplitude ratio K d of the backward wave to the forward wave is less than 1, it is judged as an out-of-direction fault, and the protection returns; if the amplitude ratio K d of the backward wave to the forward wave is greater than 1, it is judged as a positive direction fault, and step 3 is entered, and the specific process of step 2 is:

[0087] Step 2.1, the line mode voltage backward wave u b (t) and the line mode voltage forward wave u f (t) in the time window are calculated, and the calculation formula is shown in formula (3):

[0088]

[0089] In the formula, Z c1 is the line mode wave impedance of the line.

[0090] Step 2.2, the amplitude ratio K d of the fault backward wave to the fault forward wave is used to judge the fault direction, and the calculation formula of K d is shown in formula (4):

[0091]

[0092] In the formula, t represents the sampling point in the time window, and N is the total number of sampling points in the time window.

[0093] When the ratio K d is less than 1, it is judged as a reverse direction fault, and the protection returns; when the ratio is greater than 1, it is judged as a positive direction fault, and step 3 is entered.

[0094] Step 3, the wave head of the line mode voltage forward wave in the time window is extracted by using wavelet modulus maximum, db4 wavelet is taken as the wavelet base, the line mode voltage forward wave is decomposed for four layers, the wave head in the time window is marked by using wavelet modulus maximum, if there is only one wave head in the time window, the original line mode voltage reverse wave data in the time window is reserved; if there is more than one wave head in the time window, the first sampling point before the second wave head is taken as the continuation point, recorded as h, the data from h point to the end of the time window is replaced by the data of h point.

[0095] The specific process of step 3 is as follows:

[0096] Firstly, the discrete wavelet transform is performed on the line mode voltage reverse wave in the time window, and the process of extracting the wave head by using wavelet transform modulus maximum is as follows:

[0097] db4 wavelet is taken as the wavelet base function, the scale factor is equal to 2, and the translation factor is equal to 1, and the discrete wavelet transform of the function f(t) is as follows:

[0098]

[0099] In formula (5), p is the transform scale, and q is the translation.

[0100] The line mode voltage reverse wave in the time window is brought into f(t), the highest layer in the four-layer decomposition is selected, that is, the first layer wavelet coefficient is taken, that is, p=1, WT f (1, q) is obtained, the modulus maximum point of the signal in the time window is solved, if all q in the neighborhood of q0 satisfy formula (6), q0 is the wavelet transform modulus maximum:

[0101] |WT f (1, q) |≤ |WT f (1, q0) | (6)

[0102] The wave head in the time window is marked from the first sampling point by using the wavelet transform modulus maximum, the wave head in the time window is solved according to formula (6), if there is only one wave head in the time window, the original line mode voltage reverse wave data in the time window is reserved; if there is more than one wave head in the time window, the point before the second wave head is taken as the continuation point h, the data from h point to the end of the time window is replaced by the data of h point, and the influence of the subsequent wave head is reduced. The continuation formula is as follows:

[0103] u b (h+i)=u b (h) (7)

[0104] In the formula, i=1, 2, 3, …, N-h; h point is the continuation point.

[0105] Step 4, the discrete S transform is performed on the line mode voltage traveling wave in the time window processed in step 3, to obtain a corresponding mode time-frequency matrix, the row vectors of the mode time-frequency matrix are integrated to obtain a corresponding amplitude-frequency curve, and the amplitude-frequency curve is weighted with an energy operator to obtain a weighted amplitude-frequency curve.

[0106] The specific process of step 4 is as follows:

[0107] Step 4.1, let the line mode voltage traveling wave obtained in step 3 be denoted as where t = 1, 2, 3, …, N.

[0108] The discrete S transform is performed on to obtain a complex time-frequency matrix, and the discrete S transform calculation formula is shown in formula (8):

[0109]

[0110] In the formula, 1≤k≤N; T is a sampling time interval; N is a sampling point number; m is a discrete time point, and the value is: 0≤m≤N-1; n is a frequency serial number, and the value is: 1≤n≤N / 2; n / NT represents the corresponding frequency; represents the discrete expression of the data in the extended time window after the Fourier transform is performed.

[0111] Step 4.2, the modulus of each element in the complex time-frequency matrix is calculated to obtain a mode time-frequency matrix

[0112] Step 4.3, the row vectors of the mode time-frequency matrix are integrated to obtain a discrete amplitude-frequency curve The amplitude-frequency curve is multiplied by an energy operator L(f), and the discrete expression of the energy operator is where n / NT is the discrete form of f, to obtain a weighted amplitude-frequency curve The expression is shown in formula (9):

[0113]

[0114] Step 5, the high-frequency band energy accumulation E h and the total frequency band energy accumulation E all are calculated, the ratio K of E h to E all is obtained, the energy accumulation ratio K is compared with a set threshold value K set , and the fault is judged according to the comparison result. ​

[0115] The specific process of step 5 is as follows:

[0116] Step 5.1, calculate the weighted amplitude-frequency curve The energy accumulation amount of different frequency bands is selected as the full frequency band of 1-10 kHz, and the calculation formula is as follows:

[0117]

[0118]

[0119] In the formula, b is the total number of sampling points in the frequency range of 1-10 kHz, E h is the energy accumulation amount of the full frequency band; E all is the energy accumulation amount of the high frequency band; λ1 is the lower boundary of the energy accumulation amount of the high frequency band;

[0120] Calculate the ratio K of the energy accumulation amount of the high frequency band to the total frequency band as the identification criterion, and the calculation formula of the energy accumulation amount ratio K is as follows:

[0121]

[0122] The specific setting method of λ1 in formula (11) is as follows:

[0123] Theoretical frequency domain expression of zone fault:

[0124]

[0125] A(s)=e -γ(s)l (14)

[0126] In the formula, U1(s) is the frequency domain expression of the zone fault, l is the distance from the fault point to the protection measuring point, γ(s) is the line attenuation constant, U0 is the normal operating voltage of the transmission line; Z C1 and Z C0 are the line mode wave impedance and zero mode wave impedance; R f is the transition resistance;

[0127] The out-of-zone fault attenuates on the line boundary compared with the in-zone fault, so the expression of the out-of-zone fault needs to be multiplied by the boundary element transfer function H(s) based on formula (13), and the expression is as follows:

[0128]

[0129]

[0130] In the formula, U2(s) is the frequency domain expression of the out-of-zone fault, and the parameter of the current limiting reactor is L dc ;

[0131] Substitute s = jω, ω = 2πf into equation (13) and equation (16), the amplitude-frequency relationship of in-zone fault and out-zone fault can be obtained respectively, take a sample point every 100Hz, to 10kHz cutoff, a total of 100 sample points, calculate the amplitude at each sample point, get the discrete amplitude-frequency curve, denoted as in-zone fault amplitude-frequency curve and out-zone fault amplitude-frequency curve and discrete energy operator respectively, to get the weighted amplitude-frequency curve

[0132]

[0133] In the formula, λ = 1, 2, 3, …, 100, s is a complex frequency, ω is an angular frequency, and f is a frequency;

[0134] Substitute the two weighted amplitude-frequency curves into equation (17), that is, Get:

[0135]

[0136]

[0137] Wherein, K1(λ) represents the curve of the ratio of energy accumulation of in-zone fault to λ, K2(λ) represents the curve of the ratio of energy accumulation of out-zone fault to λ, substitute K1(λ) and K2(λ) into equation (20), calculate the maximum value point ΔK(λ) between them:

[0138] ΔK(λ) = |K1(λ)-K2(λ)| (20)

[0139] According to the above formula, the λ corresponding to the maximum value of ΔK(λ) is obtained, denoted as λ1, λ1 is the lower boundary value of high frequency band energy accumulation;

[0140] Step 5.2, compare the result obtained in step 5.1 with the set threshold value K set , judge whether K satisfies equation (21) or not, according to the judgment result to determine the fault location, if equation (21) is satisfied, it is judged as in-zone fault, if equation (21) is not satisfied, it is judged as out-zone fault, the judgment formula is as follows:

[0141] K > K set (21).

[0142] The threshold value K set ​​​​The setting is as follows:

[0143] The value of λ1 obtained in step 5.1 is brought into equations (18) and (19) to obtain K1(λ1) and K2(λ1), and according to equation (22), the threshold value K can be obtained set :

[0144]

[0145] As shown in the accompanying Figure 2 , it is a simulation model diagram of a certain double-ended flexible HVDC transmission system. In the diagram, L dc is a line boundary current limiting reactor L dc = 0.2H, MMC is a modular converter, R1 and R2 are two measuring points of line boundary protection, f1 and f2 are two positions where faults occur, L is the distance of the fault distance protection measuring point, the system rated voltage is ±500kV, the rated transmission capacity is 3000MVA, the total length of the transmission line is 500km, the overhead line frequency-varying parameter model is used, and the line wave impedance is Z c0 = 320Ω and Z c1 = 260Ω. During system simulation, the sampling frequency is 100kHz, and through the setting process of the threshold value K set , the threshold value K set = 0.50 can be obtained. At this time, the total length of the line L = 500km is identified according to the identification process shown in the accompanying Figure 1 , and the external fault is identified.

[0146] Example 1

[0147] A positive metallic short-circuit grounding fault occurs at 100km from the protection installation, the protection element is started, the voltage and current data of 100 sampling points before starting and 150 sampling points after starting are read, the line mode voltage reverse traveling wave is calculated. Fig. 3(a) shows the line mode voltage reverse traveling wave of the positive metallic short-circuit grounding fault at 100km before extension, Fig. 3(b) shows the line mode voltage reverse traveling wave of the positive metallic short-circuit grounding fault at 100km after extension, the second wave head exists at the 167th sampling point by using wavelet modulus maximum value detection, and therefore the 166th sampling point is defined as the extension point h, the data in the extended time window is subjected to S transform, energy operator weighting, and row vector integration to obtain the weighted amplitude-frequency characteristic curve of the metallic grounding fault at 100km as shown in Fig. 3(c), and the energy accumulation amount K is 0.65; K is greater than the setting threshold value K set = 0.50, and it is determined as an internal fault.

[0148] Example 2

[0149] In the protected installation 400 km positive pole through 100 Ω transition resistance grounding fault, protection element starts, reads 100 sampling points before starting, 150 sampling points voltage, current data after starting, calculates line mode voltage reverse wave. Figure 4 (a) extends the line mode voltage reverse wave of 400 km positive pole through 100 Ω transition resistance grounding fault, figure 4 (b) extends the line mode voltage reverse wave of 400 km positive pole through 100 Ω transition resistance grounding fault, detects the second wave head existing in the 163th sampling point by wavelet modulus maximum value, therefore defines the 162th sampling point as extension point h, carries out S transform to the data in the extended time window, energy operator weights, after row vector integration, obtains the weighted amplitude-frequency characteristic curve of 400 km positive pole through 100 Ω transition resistance grounding fault as shown in figure 4 (c), calculates the accumulation K as 0.64; K is greater than the setting threshold value K set =0.50, judges as internal fault.

[0150] Example 3

[0151] In the protected installation 50 km positive pole metallic short circuit grounding fault under 30 db noise interference, protection element starts, reads 100 sampling points before starting, 150 sampling points voltage, current data after starting, calculates line mode voltage reverse wave. Figure 5 (a) extends the line mode voltage reverse wave of 50 km positive pole metallic grounding fault under 30 db noise, figure 5 (b) extends the line mode voltage reverse wave of 50 km positive pole metallic grounding fault under 30 db noise, detects the second wave head existing in the 118th sampling point by wavelet modulus maximum value, therefore defines the 117th sampling point as extension point h, carries out S transform to the data in the extended time window, energy operator weights, after row vector integration, obtains the weighted amplitude-frequency characteristic curve of 50 km positive pole metallic grounding under 30 db noise as shown in figure 5 (c), calculates the accumulation K as 0.66; K is greater than the setting threshold value K set =0.50, judges as internal fault.

[0152] Example 4

[0153] In the protected installation, positive pole metallic short circuit grounding fault occurs outside the area, protection element starts, reads 100 sampling points before starting, 150 sampling points voltage, current data after starting, calculates line mode voltage reverse wave. Figure 6 (a) extends the line mode voltage reverse wave of positive pole metallic grounding fault outside the area, figure 6 (b) extends the line mode voltage reverse wave of positive pole metallic grounding fault outside the area, detects a wave head in the time window by wavelet modulus maximum value, therefore retains the original data, carries out S transform to the data in the extended time window, energy operator weights, after row vector integration, obtains the weighted amplitude-frequency characteristic curve of positive pole metallic grounding fault outside the area as shown in 6 (c), calculates the accumulation K as 0.27; K is less than the setting threshold value Kset = 0.50, determined as an out-of-zone fault.

[0154] In order to comprehensively verify the influence of fault distance, transition resistance and noise on the judgment result, the in-zone grounding fault and the out-of-zone grounding fault are respectively set at 50km, 100km, 200km, 300km, 400km and 450km, and the transition resistance is set to 0Ω, 100Ω and 500Ω. The out-of-zone fault and lightning interference identification method is verified according to the simulation results. The verification results are shown in Tables 1 and 2 as follows:

[0155] Table 1 Energy accumulation calculation results of different transition resistances

[0156]

[0157] Table 2 Energy accumulation calculation results after adding noise

[0158]

Claims

1. A method for identifying faults inside and outside a flexible DC transmission line based on S-transform, characterized in that, Specifically, the steps include the following: Step 1: After the protection starting element is activated, select the protection time window, read the voltage and current data within the time window, and calculate the line-mode voltage fault component within the time window. Linear current fault component ; The specific process of step 1 is as follows: Read the positive voltage at the protection installation point. Negative voltage Positive current Negative current , respectively compared with the average positive voltage before protection activation Average negative electrode voltage Average positive current Average negative current Subtracting them yields the positive voltage fault component. Negative voltage fault component Positive current fault component With negative current fault component The calculation formula is shown in equation (1): （1） The line-mode voltage fault component within the time window is calculated based on the results of formula (1). Linear current fault component The calculation formula is shown in equation (2): （2） Step 2, based on the amplitude ratio of the reverse traveling wave to the forward traveling wave. K d The magnitude of the wave determines the direction of the fault. If the ratio of the amplitude of the reverse traveling wave to that of the forward traveling wave is less than 1, it is determined to be a fault outside the reverse direction zone, and the protection returns. If the ratio of the amplitude of the reverse traveling wave to that of the forward traveling wave is greater than 1, it is determined to be a fault in the forward direction, and proceed to step 3. The specific process of step 2 is as follows: Step 2.1, sample the following formula (3) to calculate the line-mode voltage reverse traveling wave within the time window. and line mode voltage traveling wave : （3） In the formula, The line-mode impedance; Step 2.2, using the amplitude ratio of the fault reverse traveling wave to the fault forward traveling wave. K d Determine the direction of the fault. K d The calculation formula is shown in equation (4): （4） In the formula, t Representative sampling points within the time window, N This represents the total number of sampling points within the time window; When the ratio K d When the ratio is less than 1, it is judged as a reverse direction fault, and the protection returns; when the ratio is greater than 1, it is judged as a forward direction fault, and proceed to step 3. Step 3: Extract the wavefront of the line-mode voltage traveling wave within the time window using wavelet modulus maxima. Using the db4 wavelet as the wavelet basis, perform a four-level decomposition on the line-mode voltage traveling wave. Take the first-level decomposition data and use the wavelet modulus maxima to calibrate the wavefronts within the time window. If only one wavefront exists within the time window, retain the original line-mode voltage reverse traveling wave data within the time window; if more than one wavefront exists within the time window, take the sampling point preceding the second wavefront as the extension point, denoted as... h ,Will h All data up to the end of the time window. h Replace the data at the points; The specific process of step 3 is as follows: Step 3.1: Perform discrete wavelet transform on the inverse traveling wave of the line-mode voltage within the time window. The process of extracting the wavefront from the modulus maxima of the wavelet transform is as follows: Using the db4 wavelet as the wavelet basis function, with a scaling factor of 2 and a translation factor of 1, for the function... f ( t The discrete wavelet transform of ) is: （5） In equation (5), p To change the scale, q This is the translation amount; Step 3.2, introduce the inverse traveling wave of the line-mode voltage within the time window. In the process, the highest level of the four-level decomposition is selected, that is, the wavelet coefficients of the first level are taken. p =1 Find the maximum modulus of the signal within the time window. If it exists... q All in a certain neighborhood of 0 q If all satisfy equation (6), then q 0 represents the maximum value of the wavelet transform modulus: （6） Step 3.3: Using the wavelet transform modulus maxima, the wavefront within the time window is calibrated starting from the first sampling point, and the wavelet modulus maxima within the time window are calculated according to equation (6). q 0 represents the wavefront. If only one wavefront exists within the time window, the original line-mode voltage reverse wave data within the time window is retained. If more than one wavefront exists within the time window, the point preceding the second wavefront is taken as the extension point. h ,Will h All data up to the end of the time window. h The data at each point is replaced, and the extension formula is as follows: （7） In the formula, i =1, 2, 3, ... a - h ; h Point is an extension point; Step 4: Perform a discrete S-transform on the inverse traveling wave of the line-mode voltage within the time window processed in Step 3 to obtain the corresponding modal time-frequency matrix. Integrate the row vectors of the modal time-frequency matrix to obtain the corresponding amplitude-frequency curve, and then compare it with the energy operator. Weighting yields the weighted amplitude-frequency curve; The specific process of step 4 is as follows: Step 4.1, denote the inverse traveling wave of the line-mode voltage obtained in step 3 as... ,in t =1, 2, 3, ..., N, pairs Perform a discrete S-transform to obtain Complex time-frequency matrix The formula for calculating the discrete S-transform is shown in formula (8): （8） In the formula, 1≤ k ≤ N T is the sampling time interval; m For discrete time points, the value is: 0 ≤ m ≤ N -1; n The frequency index has a value of 1 ≤ n ≤ N / 2; n / NT represents the corresponding frequency; Indicates: Data within the extended time window Discrete expression Discrete signals obtained by performing Fourier transform; Step 4.2, for the complex time-frequency matrix The modulus of each element in the matrix is ​​calculated to obtain the modulus-time frequency matrix. ; Step 4.3, adjust the modulus time-frequency matrix. Integrating the row vectors yields discrete amplitude-frequency curves. , the amplitude-frequency curve With energy operator L ( f Multiplying, the discrete expression of the energy operator is: In the formula n / NT is f The discrete form is used to obtain the weighted amplitude-frequency curve. Its expression is shown in formula (9): （9） Step 5: Calculate the energy accumulation in the high-frequency band. E h Total frequency band energy accumulation E all Find E h and E all ratio K The ratio of energy accumulation K With the set threshold value K set The comparison is performed, and the fault is determined based on the comparison results; the specific process of step 5 is as follows: Step 5.1: Calculate the weighted amplitude-frequency curve. The energy accumulation in different frequency bands, taking 1~10kHz as the full frequency band, is calculated using the following formula: （10） （11） In the formula, b This represents the total number of sampling points within the frequency range of 1 to 10 kHz. E h This refers to the total energy accumulation across the entire frequency band. E all This refers to the amount of energy accumulated in the high-frequency band. This represents the lower boundary of energy accumulation in the high-frequency band. Calculate the ratio of energy accumulation in the high-frequency band to the total frequency band. K As an identification criterion, the ratio of energy accumulation K The calculation formula is: （12）； In formula (11) The specific tuning method is as follows: The theoretical frequency domain expression for faults within the zone: （13） （14） In the formula, The frequency domain expression for faults within the area. l The distance from the fault point to the protection measuring point. The line attenuation constant is... U 0 represents the normal operating voltage of the transmission line; Z C1 and Z C0 For line-mode impedance and zero-mode impedance; R f For transition resistance; External faults are attenuated at the line boundary compared to internal faults. Therefore, the expression for external faults should be multiplied by the boundary element transfer function based on equation (13). H ( s The expression is as follows: （15） （16） In the formula, The frequency domain expression for the fault outside the zone is given, and the parameters of the current-limiting reactor are: L dc ; Will , Substituting into equations (13) and (16), we can obtain the amplitude and frequency of faults within and outside the area, respectively. f The relation will f A sampling point is taken every 100Hz, up to a cutoff of 10kHz, for a total of 100 sampling points. The amplitude at each sampling point is calculated to obtain a discrete amplitude-frequency curve, which is denoted as the fault amplitude-frequency curve within the area. Compared with the amplitude-frequency curve of faults outside the area ,Will , With discrete energy operators Multiplying them separately yields the weighted amplitude-frequency curve. and The ratio of energy accumulation varies with Changing curve The calculation formula is shown in (17): （17） In the formula, s is the complex frequency. Here, f is the angular frequency; Substituting the two weighted amplitude-frequency curves into equation (17) yields... and ,get: （18） （19） in, The ratio of the amount of fault energy accumulated in the area varies with The changing curve, The ratio of the amount of fault energy accumulated outside the zone increases with The changing curve will and Substitute into equation (20) to calculate the maximum point of the difference between the two. : （20） The above formula yields the result. The maximum value corresponding to , recorded as , This represents the lower boundary value for the energy accumulation in the high-frequency band. Step 5.2: Compare the result obtained in Step 5.1 with the set threshold value. K set Compare and distinguish K Whether equation (21) is satisfied is used to determine the fault location. If equation (21) is satisfied, the fault is judged to be within the zone; if equation (21) is not satisfied, the fault is judged to be outside the zone. The judgment formula is as follows: （21） in, K set This is the threshold value.

2. The method for determining faults inside and outside the area of ​​flexible DC transmission lines based on S-transform according to claim 1, characterized in that, For the threshold value in step 5.2 K set The tuning is performed as follows: The result obtained in step 5.1 Substituting the values ​​into equations (18) and (19) yields and According to equation (22), the threshold value can be obtained. K set : （22） in, The ratio of the amount of fault energy accumulated in the area varies with The changing curve, The ratio of the amount of fault energy accumulated outside the zone increases with A changing curve.

Images