CN112083271A - 10kV cable online distance measurement method based on sheath current traveling wave time-frequency composite analysis - Google Patents
10kV cable online distance measurement method based on sheath current traveling wave time-frequency composite analysis Download PDFInfo
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Abstract
The invention relates to a 10kV cable online distance measurement method based on sheath current traveling wave time-frequency composite analysis, and belongs to the technical field of force system relay protection. Firstly, extracting three-phase sheath current and I after phase-mode conversion by an expanded Clarke matrix∑As a fault ranging signal; secondly, the fault distance measurement signal I is processed by an FFT-MUSIC algorithm∑Carrying out frequency spectrum transformation, extracting each frequency component in the traveling wave signal, and calculating by using a frequency difference formula to obtain a fault rough measurement distance x; finally, time domain analysis is carried out on the signals according to the primary fault position obtained by the frequency domain analysis method and the improved lumped empirical mode decomposition algorithm, and the secondary reflection wave head of the fault line is accurately judgedAnd when the time arrives, the accurate fault distance measurement is realized by utilizing the time difference between the fault point reflected wave and the opposite end reflected wave and the initial wave head. The invention fully considers the electromagnetic effect of the cable sheath, utilizes the sheath current as the fault characteristic quantity, and improves the feasibility of on-line distance measurement.
Description
Technical Field
The invention relates to a 10kV cable online distance measurement method based on sheath current traveling wave time-frequency composite analysis, and belongs to the technical field of force system relay protection.
Background
The power cable is an important component of the urban power grid, and along with the transformation and development of the urban power grid by the country, the power cable has the advantages of small floor area, no external influence, simple operation and the like, and is widely applied. However, the cable feeder has many branches and complicated distribution, and is influenced by artificial external force, environmental factors, and backward technology and equipment, and once a fault occurs, the power supply quality of a user and the operation efficiency of an urban power grid are seriously influenced. At present, about 80% of fault types of power distribution network cables are single-phase earth faults, and after the single-phase earth faults, a system can operate with the faults for a period of time, but due to the fact that the non-fault phase-to-earth voltage rises, the insulation of lines and the normal operation of equipment can be seriously threatened by the long-time fault operation of the system. Therefore, the fault position can be found quickly and accurately, and the fault can be removed quickly, which has important significance for maintaining the safe and stable operation of the power distribution network.
Disclosure of Invention
The invention aims to solve the technical problem of providing a 10kV cable online distance measurement method based on sheath current traveling wave time-frequency composite analysis, which is used for solving the problem.
The technical scheme of the invention is as follows: a10 kV cable online distance measurement method based on sheath current traveling wave time-frequency composite analysis comprises the steps of firstly, extracting the sum I of three-phase sheath currents after phase-mode conversion is carried out on an expanded Clarke matrix∑As a fault ranging signal; secondly, the FFT-MUSIC algorithm is used for the faultObstacle ranging signal I∑Carrying out frequency spectrum transformation, extracting each frequency component in the traveling wave signal, and calculating by using a frequency difference formula to obtain a fault rough measurement distance x; and finally, performing time domain analysis on the signal according to the primary fault position obtained by the frequency domain analysis method and an improved lumped empirical mode decomposition (MEEMD) algorithm, accurately judging the arrival time of the secondary reflection wave head of the fault line, and further realizing accurate fault distance measurement by utilizing the time difference between the fault point reflected wave, the opposite end reflected wave and the initial wave head.
The method comprises the following specific steps:
step 1: obtaining three-phase sheath current and I∑As the fault ranging signal:
in the practical engineering, a Clarke transformation matrix is commonly used for decoupling signals of a three-phase conductor system, and the decoupling matrix is as follows:
in order to realize the phase-mode transformation of the three-phase cable six-conductor system, a Clarke matrix needs to be expanded, and the expanded voltage transformation matrix S and current transformation matrix Q are as follows:
the three-phase core current and the sheath current are decoupled into six independent moduli through phase-mode transformation, and analysis on the characteristics of each modulus of a cable system can find that the external moduli ( moduli 1, 2 and 3) are not main components of fault traveling waves, and because the external moduli are closely connected with the ground, the traveling waves are quickly attenuated in the transmission process, stable traveling wave transient signals cannot be obtained, and the traveling waves are difficult to apply to cable fault location, which is similar to the ground mode of an overhead line. And the three internal moduli (4, 5 and 6) are similar to the overhead line mode, and the traveling wave signal mutation characteristic of the modulus 4 is obvious and stable, so that the method can be used for cable fault location. However, in the tunnel or channel-laid system, since the three-phase sheath includes three internal moduli and the propagation velocities of the moduli 5 and 6 are higher than the modulus 4, the three internal moduli interfere with each other.
In the above formula (3), Ia、Ib、IcRespectively three-phase sheath current i1～i6Six modulus currents. Adding the three phase sheath currents as described above, it can be seen that the outer mold quantities 2, 3 and the inner moduli 5, 6 cancel each other out, and the final formula contains only modulus 1 and modulus 4, i.e.:
step 2: utilizing FFT-MUSIC algorithm to carry out fault ranging on signal I in Step1∑Carrying out frequency spectrum transformation to extract each frequency component in the traveling wave signal, and the specific method is as follows:
1. multiple signal classification (MUSIC)
Let the time series y (n) be a complex sinusoidal signal with noise signals, i.e.:
in the formula (5), w (n) is the added noise signal, which is the random initial phase, wiFor the signal frequency to be estimated, aiIs the complex harmonic signal amplitude.
For the (M +1) -dimensional observation signal vector y (n), if:
y(n)＝[y(0),y(1)…y(M)]T (6)
y(n)＝[1,eiwj,ei2wj,…,eiMwj]T (7)
from the formulas (6) and (7), a (M +1) × (M +1) -dimensional correlation matrix can be obtained:
for matrix Ry(τ) singular value decomposition to give:
Ry(τ)＝VAUH (9)
in the formula (9), A is a diagonal matrix composed of frequency energy, the upper corner H in the formula is expressed by a unitary matrix, and V and U are respectively RyA unitary matrix of left and right singular vectors of (τ), the expression being as follows:
let R ═ E (R)yRy H)＝HA2VHFrom this, it can be seen that the singular vector V is a feature vector of R, and V is made to be [ V ]s,VN]And thus may be represented by matrix RySingular value decomposition of (τ) to obtain a signal subspace VsSum noise subspace VNThe spatial spectrum constructed by the MUSIC principle is as follows:
therefore, the precise frequency of each group of components of the signal can be obtained according to the peak position of the MUSIC pseudo spectrum, and the normalized frequency is as follows:
according to research, the MUSIC algorithm can be used for extracting the real frequency aiming at the traveling wave signals with short signal length and high attenuation speed. However, the MUSIC algorithm has the disadvantages of being over-dependent on parameters, and the MUSIC requires a spectral peak search in the whole frequency domain, which takes a long time, and the application of the MUSIC algorithm in practice is seriously influenced due to the existence of a pseudo-spectrum.
Therefore, the invention adopts the frequency estimation combining the FFT and the MUSIC algorithm, firstly, the FFT is used for pre-estimating the frequency, the search domain is reduced, and then the MUSIC is used for frequency refinement.
2. Frequency estimation method of FFT-MUSIC
The FFT algorithm is a spectral analysis performed in one signal period, which is expressed as:
in the equation (13), the sampling sequence and its corresponding harmonic coefficients are x (n) and x (k), respectively, and in practical applications, nonlinear, non-periodic, and unsteady signals with limited length are usually encountered. To apply equation (13) to the signal to be analyzed for fourier transformation, the data needs to be truncated into N, and then the N-point sequence is treated as a periodic sequence of a periodic signal.
Satisfying the sampling theorem f when performing the MUSIC algorithms≥2fmaxIn the case of (2), the data row vector is sampled N times, and the entire spectrum of the signal can be obtained in principle. However, when the spectrum transform is performed by using equation (5), since the period of the signal cannot be accurately obtained, performing the FFT transform on the N samples directly can only obtain an approximate value of the signal spectrum. It proved to be as follows:
suppose that when performing a MUSIC analysis, the sampling data of a certain signal is N0The data sequence is x (n). If the sampled data in one signal period is N0N is (r + m) N0Wherein m is a non-negative integer, and r is more than or equal to 0 and less than 1. According to the periodicity of the signal: x (N) ═ x (N + N)0) Then, FFT is performed using data with length N, and the spectrum is:
in the formula (14), the second part can be regarded as N formed by zero padding after being cut by the window0The DFT of the point data has certain leakage; mx (k) is the exact spectrum of the signal. Therefore, the equation (14) includes a frequency spectrum of the periodic signal and a pseudo spectrum due to leakage. On the other hand, formula (5)In the k-th spectral line, the corresponding frequency is fk＝k/N0. The frequency of the (r + m) th line of equation (14) is given by:
as can be seen from the above equation (15), the FFT can directly perform spectrum transformation on the data sequence of any signal length, so as to obtain an approximate value of the corresponding frequency. By the spectral analysis combining the FFT and the MUSIC algorithm, the spectral peak searching time can be shortened in the whole frequency domain range, the frequency of the fault transient signal can be extracted more accurately and effectively, and the frequency leakage phenomenon is avoided.
Step 3: according to each frequency component extracted at Step2, fault location is carried out by using a frequency difference method, which specifically comprises the following steps:
the initial traveling wave generated by the fault propagates to both sides along the line, and the measuring end senses the superposition of the measuring end M and the traveling waves reflected by the fault point and the tail end for multiple times, and the superposition shows that the frequency is a series of high-frequency components with natural frequency.
For the measurement end M, the natural frequency of the fault transient traveling wave is determined by the characteristic formula of formula (16):
1-M(s)F(s)p2(s)＝0 (16)
by solving the equation using the euler equation, equation (15) can be transformed into:
this is obtained by the following equation (17):
according to the physical meaning of the pole of the laplace function, the imaginary part of the equation (18) is the oscillation degree of the fault traveling wave frequency, and the real part represents the attenuation degree of the fault traveling wave frequency. From equation (18), considering the non-negativity of the actual frequency, the frequency of the fault traveling wave can be obtained as:
in the formula (19), θFAnd thetaMThe reflection angles of the fault point and the measuring end are shown, and therefore, the frequency spectrum of the fault traveling wave is related to the reflection angle of the fault point, the reflection angle of the system measuring end and the fault distance. Changing tau to xfThe calculation formula of the fault distance obtained by substituting/v into the above formula is as follows:
as can be seen from equation (20), when the power cable is subjected to the fault location using equation (20), the fault distance is not only related to the traveling wave frequency but also related to the fault point reflection angle θFAnd the measurement end reflection angle thetaMIt is related. Therefore, the travelling wave natural frequency ranging needs to accurately extract natural frequency components and accurately estimate the fault point reflection angle and the measurement end reflection angle. Therefore, the frequency method is difficult to find the fault distance, a high-precision frequency spectrum analysis technology is needed, and the practicability is not high. Therefore, the invention changes the angle consideration and utilizes the frequency difference delta f between adjacent frequency components in the frequency domain to carry out fault distance measurement. According to the natural frequency ranging formula (20), the frequency difference Δ f between adjacent frequency components is:
step 4: the basic formula for travelling wave ranging from a single-ended fault is as follows:
in the formula (22), x is the distance between the fault point and the measuring end, and L is the fault lineFull length, Δ t1＝tFf-t0Reflecting the wave t for the fault pointFfWith the initial travelling wave head t0Time difference of (1), Δ t2＝tFd-t0Reflecting waves t for opposite end of faulty lineFdWith the initial travelling wave head t0The time difference of (a). The relationship of 2 wave head arrival times can be derived from equation (22):
v(Δt1+Δt2)＝2L (23)
step 5: substituting the distance x measured by the frequency difference method into the formula to calculate the reflected wave t of the fault pointFfWith the initial travelling wave head t0Time difference Δ t of1Reflected wave t from opposite end of faulty lineFdWith the initial travelling wave head t0Time difference Δ t of2. Detecting the time t when the initial traveling wave head reaches the measuring end by using an improved lumped mean empirical mode decomposition (MEEMD)0Then mark t0+Δt1、t0+Δt2And observing whether the wave head corresponds to the corresponding moment or not at the moment. Since x is not the exact distance to failure, at t0+Δt1、 t0+Δt2At that moment, no corresponding wave front will generally appear.
Step 6: let t in Step50+Δt1、t0+Δt2The wave head information appearing in the time range is taken as an object to be analyzed, and the wave head time is marked as A1、A2、A3、…、AkAnd a1、a2、a3、…ak. Respectively combining different combinations [ Ai，ai]Verifying in place of equation (23) until finding the combination closest to satisfying the condition, at which time the corresponding time A is recordedxAnd ax。
Step 7: reflecting wave A from fault point satisfying conditionsxAnd the opposite end reflected wave axReplacing the formula (22) again, and calculating to obtain the fault distance x by using a single-ended traveling wave method1、x2And then taking the average of the two as the finally determined fault distance.
The invention has the beneficial effects that:
1. the invention gives consideration to 2 single-ended distance measurement methods, the distance measurement algorithm of the natural frequency difference method is easy to realize and has larger error, the traditional time domain method has high distance measurement precision but is difficult to realize, the two methods are effectively combined and mutually compensated, and a new thought is opened up for the single-ended distance measurement method.
2. Simulation experiments show that the time-frequency composite analysis method has higher precision, and the single-ended distance measurement method is more feasible.
3. The invention fully considers the electromagnetic effect of the cable sheath, utilizes the sheath current as the fault characteristic quantity, and improves the feasibility of on-line distance measurement.
Drawings
FIG. 1 is a diagram of a 10kV cable simulation model according to the present invention;
FIG. 2 is a diagram of a Thevenin equivalent model of a transmission system fault attachment network and two-terminal systems thereof according to the present invention;
FIG. 3 shows branch L of FIG. 1 in embodiment 1 of the present invention1Middle 3km fault ranging signal I∑A spectrogram;
FIG. 4 is the sum I of currents of three-phase sheath with a fault of 13km in the embodiment 1 of the present invention∑Signal IFM1Component(s) of
FIG. 5 shows branch L of FIG. 1 in embodiment 2 of the present invention1Middle 5km fault ranging signal I∑A spectrogram;
FIG. 6 is the sum I of currents of three-phase sheath at 5km fault in embodiment 2 of the present invention∑Signal IFM1Component(s) of
FIG. 7 shows branch L of FIG. 1 in embodiment 3 of the present invention1Middle 10km fault ranging signal I∑A spectrogram;
FIG. 8 is the sum I of currents of three-phase sheath at 10km fault in embodiment 3 of the present invention∑Signal IFM1Component(s) of
FIG. 9 shows branch L of FIG. 1 in embodiment 4 of the present invention1Middle 13km fault ranging signal I∑A spectrogram;
FIG. 10 is the sum I of currents of three-phase sheath with a fault of 13km in the embodiment 4 of the present invention∑Signal IFM1And (4) components.
Detailed Description
The invention is further described with reference to the following drawings and detailed description.
Example 1: as shown in FIG. 1, a 10kV power distribution network cable simulation model is provided with a branch L1The single-phase earth fault occurs at the position 3km away from the head end of the line, the total length of the line is 15km, the transition resistance is 0.01 omega, the sampling frequency is 800kHz, and due to the occurrence of the earth fault, the duration time of the traveling wave is 0.5-0.7 power frequency periods, so that the time window data of 10ms after the fault occurs is taken as an analysis signal. Fault ranging signal I using FFT-MUSIC algorithm∑(sum of three-phase cable sheath currents) is subjected to spectrum analysis, and the corresponding spectrum is shown in fig. 3.
From the spectrum analysis, the stable Δ f is approximately 3.125 × 104Hz,. DELTA.f can be initially isolated by substituting formula (21) as:
3.152 km. Substituting the frequency difference method ranging result as a preliminary fault distance into formula (22) to calculate a fault point reflected wave tFfWith the initial travelling wave head t0Time difference Δ t of132 mus and the reflected wave t from opposite end of fault lineFdWith the initial travelling wave head t0Time difference Δ t of2120.284 μ s; detecting the time t when the initial traveling wave head reaches the measuring end by utilizing an improved lumped mean empirical mode decomposition (MEEMD) method for the signals obtained by the measuring end of the bus015.228 μ s, label t0+Δt1、t0+Δt2The corresponding time points are shown in fig. 4.
By marking t0+Δt1、t0+Δt2The corresponding time mark can see that there is no wave head corresponding to the dotted line, and there are wave heads A near the dotted line1、A2And a1、a2、a3And occurs. The time difference between each wave head and the initial traveling wave head is shown in table 1 below.
Table 1: time difference between each wave head and initial travelling wave
The above 5 mutation wave heads can have 6 combinations: [ A ]1，a1]、[A1，a2]、[A1，a3]；[A2，a1]、[A2，a2]、[A2， a3](ii) a Each of the above combination methods is respectively substituted into formula (23), and a combination satisfying the equation is found. Will combine [ A ]1，a1]Substitution in equation (23) gives the equation to the left: 197m/μ s × (29.98+116.75) μ s ═ 28.906 km; for combination [ A1，a2]Can be substituted into the formula (23): 197m/μ s × (29.98+121.72) μ s ═ 29.885 km; for combination [ A1，a3]Can be substituted into the formula (23): 197m/μ s × (29.98+134.22) μ s ═ 32.347 km; for combination [ A2，a1]、[A2，a2]、[A2，a3]Substituting (23) respectively can obtain the equation on the left as: 31.573 km; 32.552 km; 35.014 km. The results of the various combined calculations are shown in table 2 with the error table for the right-hand side of the equation, 2L-30 km:
table 2: time difference between each wave head and initial travelling wave
From Table 2 above, see the combination [ A ]1，a2]Equation (23) is best satisfied, i.e. the fault point reflects a wave A1(45.21 μ s), the reflected wave at the end of the line is a2(136.95 μ s), and the rest wave heads are reflected waves at the end of the non-fault line or interference wave heads. Thus, the combination [ A1，a2]With the initial travelling wave t0Transmission time difference Δ t corresponding to 15.228 μ s1＝29.98μs、Δt2Formula (22) was substituted for 121.72 μ s, yielding the fault distance:
x1＝(197m/μs×29.98μs)/2＝2.953km
x2＝(30km-197m/μs×121.72μs)/2＝3.01km
x＝(x1+x2)/2＝2.980km
the final fault distance was 2.980km, the absolute error was 0.02km, and the relative error was 0.13%. The distance measurement error is small, the actual line patrol requirement is met, the identification of the traveling wave secondary reflection wave head is effective, and the distance measurement result of the time-frequency composite analysis method is accurate and effective.
Example 2: as shown in FIG. 1, a 10kV power distribution network cable simulation model is provided with a branch L1The single-phase earth fault occurs at the position 5km away from the head end of the line, the total length of the line is 15km, the transition resistance is 10 omega, the sampling frequency is 800kHz, and due to the occurrence of the earth fault, the duration time of the traveling wave is 0.5-0.7 power frequency periods, so that the time window data of 10ms after the fault occurs are taken as analysis signals. Fault ranging signal I using FFT-MUSIC algorithm∑(sum of three-phase cable sheath currents) is subjected to spectrum analysis, and the corresponding spectrum is shown in fig. 5.
From the spectrum analysis, the stability Δ f is approximately 1.875 × 104Hz,. DELTA.f can be initially isolated by substituting formula (21) as: 5.253 km. Substituting the frequency difference method ranging result as a preliminary fault distance into formula (22) to calculate the reflected wave t of the opposite end of the fault lineFdWith the initial travelling wave head t0Time difference Δ t of298.954 mus and the fault point reflected wave tFfWith the initial travelling wave head t0Time difference Δ t of153.33 μ s; signal I obtained from bus measuring end∑Detecting the time t when the initial traveling wave head reaches the measuring end by using an improved lumped mean empirical mode decomposition (MEEMD)025.40. mu.s, mark t0+Δt1、t0+Δt2The corresponding time points are shown in fig. 6.
By marking t0+Δt1、t0+Δt2The corresponding time mark can see that there is no wave head corresponding to the dotted line, and there are wave heads A near the dotted line1、A2And a1、a2、a3、a4And occurs. The time difference between each wave front and the initial traveling wave front is shown in table 3.
Table 3: time difference between each wave head and initial travelling wave
The above 6 mutation wave heads can have 8 combinations: [ A ]1，a1]、[A1，a2]、[A1，a3]、[A1，a4]；[A2，a1]、[A2， a2]、[A2，a3]、[A2，a4](ii) a Each of the above combinations was substituted into the equations (4-21), respectively, to find a combination satisfying the equations. Will combine [ A ]1，a1]Substitution in equation (23) gives the equation to the left: 197m/μ s × (50.85+80.85) μ s ═ 25.945 km; for combination [ A1，a2]Can be substituted into the formula (23): 197m/μ s × (50.85+100.85) μ s 29.885 km; for combination [ A1， a3]Can be substituted into the formula (23): 197m/μ s × (50.85+120.85) μ s 33.825 km; for combination [ A1，a4]Can be substituted into the formula (23): 197m/μ s × (50.85+129.60) μ s 35.549 km; for combination [ A2，a1]、[A2，a2]、[A2， a3]Substituting (23) respectively can obtain the equation on the left as: 27.176 km; 31.118 km; 35.056 km; 36.780 km. The results of the various combined calculations are shown in table 4 with the error table for the right-hand side of the equation, 2L-30 km:
table 4: time difference between each wave head and initial travelling wave
From Table 4 above, see combination [ A ]1，a2]Equation (23) is best satisfied, i.e. the fault point reflects a wave A1(76.25 μ s), the reflected wave at the end of the line is a2(126.25 mus), the rest wave heads are the reflected waves of the non-fault line end or the interference wave heads. Thus, the combination [ A1，a2]With the initial travelling wave t025.40 μ sCorresponding transmission time difference Δ t1＝50.85μs、Δt2Formula (22) was substituted for 100.85 μ s, yielding the fault distance:
x1＝(197m/μs×50.85μs)/2＝5.009km
x2＝(30km-197m/μs×100.85μs)/2＝5.066km
x＝(x1+x2)/2＝5.038km
the final fault distance is 5.038km, the absolute error is 0.038km, and the relative error is 0.25%. The distance measurement error is small, the actual line patrol requirement is met, the identification of the traveling wave secondary reflection wave head is effective, and the distance measurement result of the time-frequency composite analysis method is accurate and effective.
Example 3: as shown in FIG. 1, a 10kV power distribution network cable simulation model is provided with a branch L1The single-phase earth fault occurs at a position 10km away from the head end of the line, the total length of the line is 15km, the transition resistance is 30 omega, the sampling frequency is 800kHz, and due to the occurrence of the earth fault, the duration time of the traveling wave is 0.5-0.7 power frequency periods, so that time window data of 10ms after the fault occurs are taken as analysis signals. Fault ranging signal I using FFT-MUSIC algorithm∑(sum of three-phase cable sheath currents) is subjected to spectrum analysis, and the corresponding spectrum is shown in fig. 7.
From the spectrum analysis, the stable Δ f is approximately 0.974 × 104Hz,. DELTA.f can be initially isolated by substituting formula (21) as: 10.113 km. Substituting the frequency difference method ranging result as a preliminary fault distance into formula (22) to calculate a fault point reflected wave tFfWith the initial travelling wave head t0Time difference Δ t of1102.67 mus and the reflected wave t from opposite end of fault lineFdWith the initial travelling wave head t0Time difference Δ t of249.614 μ s; signal I obtained from bus measuring end∑Detecting the time t when the initial traveling wave head reaches the measuring end by using an improved lumped mean empirical mode decomposition (MEEMD)051.25. mu.s, mark t0+Δt1、t0+Δt2The corresponding time points are shown in fig. 8.
By marking t0+Δt1、t0+Δt2The corresponding time mark can be seen in a dotted lineThere is no wave head corresponding to it, and there are wave heads A near it respectively1、A2、A3And a1、a2And occurs. The time difference between each wave front and the initial traveling wave front is shown in table 5.
Table 5: time difference between each wave head and initial travelling wave
The above 5 mutation wave heads can have 6 combinations: [ A ]1，a1]、[A1，a2]；[A2，a1]、[A2，a2]；[A3，a1]、[A3， a2](ii) a Each of the above combinations is substituted into formula (23), respectively, and a combination satisfying the equation is found. Will combine [ A ]1，a1]Substitution in equation (23) gives the equation to the left: 197m/μ s × (101.95+50.40) μ s 30.012 km; for combination [ A1，a2]Can be substituted into the formula (23): 197m/μ s × (101.95+56.25) μ s ═ 31.165 km; for combination [ A2，a1]、[A2，a2]、[A3，a1]、 [A3，a2]Substituting (23) respectively can obtain the equation on the left as: 33.569 km; 34.721 km; 35.293 km; 36.445 km. The results of the various combined calculations are shown in table 6 with the error table for the right-hand side of the equation, 2L-30 km:
table 6: time difference between each wave head and initial travelling wave
From Table 6 above, see combination [ A ]1，a1]Equation (23) is best satisfied, i.e. the fault point reflects a wave A1(153.20 μ s), the reflected wave at the end of the line is a1(101.65Mus), and the rest wave heads are the reflected waves at the end of the non-fault line or interference wave heads. Thus, the combination [ A1，a1]With the initial travelling wave t0Transmission time difference Δ t corresponding to 51.25 μ s1＝101.95μs、Δt2Formula (22) was substituted for 50.40 μ s, yielding the fault distance:
x1＝(197m/μs×101.95μs)/2＝10.042km
x2＝(30km-197m/μs×50.30)/2＝10.036km
x＝(x1+x2)/2＝10.039km
the final fault distance was 10.039km, the absolute error was 0.039km, and the relative error was 0.26%. The distance measurement error is small, the actual line patrol requirement is met, the identification of the traveling wave secondary reflection wave head is effective, and the distance measurement result of the time-frequency composite analysis method is accurate and effective.
Example 4: as shown in FIG. 1, a 10kV power distribution network cable simulation model is provided with a branch L1The single-phase earth fault occurs at the position 13km away from the head end of the line, the total length of the line is 15km, the transition resistance is 50 omega, the sampling frequency is 800kHz, and due to the occurrence of the earth fault, the duration time of the traveling wave is 0.5-0.7 power frequency periods, so that time window data of 10ms after the fault occurs are taken as analysis signals. Fault ranging signal I using FFT-MUSIC algorithm∑(sum of three-phase cable sheath currents) is subjected to spectrum analysis, and the corresponding spectrum is shown in fig. 9.
From the spectrum analysis, the stable Δ f is approximately 0.974 × 104Hz,. DELTA.f can be initially isolated by substituting formula (21) as: 13.116 km. Substituting the frequency difference method ranging result as a preliminary fault distance into formula (22) to calculate a fault point reflected wave tFfWith the initial travelling wave head t0Time difference Δ t of1133.157 mus and the reflected wave t from opposite end of fault lineFdWith the initial travelling wave head t0Time difference Δ t of219.127 μ s; signal I obtained from bus measuring end∑Detecting the time t when the initial traveling wave head reaches the measuring end by using an improved lumped mean empirical mode decomposition (MEEMD)066.25 mus and then labeled t0+Δt1、t0+Δt2Corresponding time, knotAs shown in fig. 10.
By marking t0+Δt1、t0+Δt2The corresponding time mark can see that there is no wave head corresponding to the dotted line, and there are wave heads A near the dotted line1、A2、A3And a1、a2And occurs. The time difference between each wave front and the initial traveling wave front is shown in table 7.
Table 7: time difference between each wave head and initial travelling wave
The above 5 mutation wave heads can have 6 combinations: [ A ]1，a1]、[A1，a2]；[A2，a1]、[A2，a2]；[A3，a1]、[A3， a2](ii) a Each of the above combinations is substituted into formula (23), respectively, and a combination satisfying the equation is found. Will combine [ A ]1，a1]The left side of the equation is obtained by substituting in equation (4-21): 197m/μ s × (126.25+20) μ s ═ 28.811 km; for combination [ A1，a2]Can be substituted into the formula (23): 197m/μ s × (126.25+27.50) μ s 30.289 km; for combination [ A2，a1]、[A2，a2]、[A3，a1]、 [A3，a2]Substituting (23) respectively can obtain the equation on the left as: 30.043 km; 31.520 km; 31.028 km; 32.505 km. The results of the various combined calculations are shown in table 8 with the error table for the right-hand side of the equation, 2L-30 km:
table 8: time difference between each wave head and initial travelling wave
From Table 8 above, see combination [ A ]2，a1]Equation (23) is best satisfied, i.e. the fault point reflects a wave A1(198.75 μ s), the reflected wave at the end of the line is a1(86.25. mu.s), the rest wave heads areThe reflected wave at the end of the non-faulty line is either an interference wave header. Thus, the combination [ A1，a1]With the initial travelling wave t0Transmission time difference Δ t corresponding to 66.25 μ s1＝132.50μs、Δt2Formula (22) was substituted for 20 μ s, yielding the fault distance:
x1＝(197m/μs×132.50μs)/2＝13.051km
x2＝(30km-197m/μs×20μs)/2＝13.030km
x＝(x1+x2)/2＝13.041km
the final fault distance is 13.041km, the absolute error is 0.041km, and the relative error is 0.27%. The distance measurement error is small, the actual line patrol requirement is met, the identification of the traveling wave secondary reflection wave head is effective, and the distance measurement result of the time-frequency composite analysis method is accurate and effective.
While the present invention has been described in detail with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, and various changes can be made without departing from the spirit and scope of the present invention.
Claims (2)
1. A10 kV cable online distance measurement method based on sheath current traveling wave time-frequency composite analysis is characterized by comprising the following steps: firstly, extracting the sum I of three-phase sheath currents after phase-mode conversion by an expanded Clarke matrix∑As a fault ranging signal; secondly, the fault distance measurement signal I is processed by an FFT-MUSIC algorithm∑Carrying out frequency spectrum transformation, extracting each frequency component in the traveling wave signal, and calculating by using a frequency difference formula to obtain a fault rough measurement distance x; and finally, performing time domain analysis on the signal according to the primary fault position obtained by the frequency domain analysis method and an improved lumped empirical mode decomposition algorithm, accurately judging the arrival time of a secondary reflection wave head of the fault line, and further realizing accurate fault distance measurement by utilizing the time difference between the reflected wave of the fault point, the reflected wave of the opposite terminal and the initial wave head.
2. The 10kV cable online distance measurement method based on sheath current traveling wave time-frequency composite analysis according to claim 1, which is characterized by comprising the following specific steps:
step 1: obtaining the sum I of three-phase sheath currents∑As a fault ranging signal;
firstly, decoupling a three-phase conductor system signal by using a Clarke transformation matrix, wherein the decoupling matrix is as follows:
the expanded Clarke matrix is used for phase-mode transformation, and the expanded voltage transformation matrix S and the expanded current transformation matrix Q are as follows:
decoupling three-phase core current and sheath current into six independent moduli after phase-mode conversion:
in the formula (3), Ia、Ib、IcRespectively three-phase sheath current i1～i6Current of six moduli;
adding the three-phase sheath currents to obtain a fault distance measurement signal I∑：
Step 2: utilizing FFT-MUSIC algorithm to carry out fault ranging on signal I in Step1∑Performing frequency spectrum transformation, and extracting each frequency component in the traveling wave signal, specifically:
firstly, the frequency is pre-estimated by using an FFT algorithm, and FFT spectrum analysis is carried out in a signal period, which is expressed as:
in the formula (5), x (n) and x (k) are respectively a sampling sequence and a corresponding harmonic coefficient thereof;
and then, frequency refinement is carried out by using MUSIC, and the spatial spectrum constructed by the MUSIC principle is as follows:
obtaining the precise frequency of each component of the signal according to the position of the spectrum peak, wherein the normalized frequency is as follows:
step 3: and (3) fault location is carried out by using a frequency difference method according to each frequency component extracted in Step2, wherein the frequency of the fault traveling wave is as follows:
in the formula (8), θFAnd thetaMThe reflection angles at the fault point and the measuring end are obtained;
changing tau to xfThe calculation formula of the fault distance obtained by substituting/v into the above formula is as follows:
step 4: the formula of the single-end fault traveling wave distance measurement is as follows:
in the formula (10), x is the distance between the fault point and the measuring end, and L is the total number of the fault linesLong, Δ t1＝tFf-t0Reflecting the wave t for the fault pointFfWith the initial travelling wave head t0Time difference of (1), Δ t2＝tFd-t0Reflecting waves t for opposite end of faulty lineFdWith the initial travelling wave head t0The time difference of (a);
the relationship of 2 wave head arrival times is obtained by the following equation (10):
v(Δt1+Δt2)＝2L (11)
step 5: using frequency difference method to measure distance xfSubstituting the above formula to calculate the reflected wave t at the fault pointFfWith the initial travelling wave head t0Time difference Δ t of1Reflected wave t from opposite end of faulty lineFdWith the initial travelling wave head t0Time difference Δ t of2；
Detecting the time t when the initial traveling wave head reaches the measuring end by using an improved lumped average empirical mode decomposition method0Then mark t0+Δt1、t0+Δt2Observing whether a wave head corresponds to the corresponding moment at the moment;
step 6: let t in Step50+Δt1、t0+Δt2The wave head information appearing in the time range is taken as an object to be analyzed, and the wave head time is marked as A1、A2、A3、…、AkAnd a1、a2、a3、…ak；
Respectively combining different combinations [ Ai，ai]The verification is performed in place of equation (11) until the combination closest to the satisfying condition is found, at which time the corresponding time A is recordedxAnd ax；
Step 7: reflecting wave A from fault point satisfying conditionsxAnd the opposite end reflected wave axReplacing the formula (10) again, and calculating by using a single-ended traveling wave method to obtain a fault distance x1、x2And then taking the average of the two as the finally determined fault distance.
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