CN111751671A - VMD-DTW cluster-based low-current grounding system fault line selection method - Google Patents
VMD-DTW cluster-based low-current grounding system fault line selection method Download PDFInfo
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Abstract
The fault line selection method of the small current grounding system based on VMD-DTW clustering comprises the steps of taking zero sequence currents of different lines as samples, extracting and enhancing original signals of the zero sequence currents by adopting a VMD decomposition method, and decomposing the original signals of the zero sequence currents into modal components of three frequency bands, namely high, middle and low; then, calculating the similarity of modal components of different lines by using a DTW method to realize the similarity measurement of zero sequence currents of different lines; updating the center of the HAC cluster according to the similarity measurement result to realize clustering of the zero-sequence current characteristics; and distinguishing a fault line and a healthy line according to the clustering result, and finally realizing the purpose of fault line selection of the low-current grounding system. The method can avoid a series of problems caused by distinguishing the fault line by using a pull method by power grid dispatching monitoring personnel, assist the monitoring personnel to find the fault line in time and ensure the safe and stable operation of the power distribution network.
Description
Technical Field
The invention relates to the technical field of power grid dispatching intelligence, in particular to a fault line selection method of a low-current grounding system based on VMD-DTW clustering.
Background
With the annual increase of electricity consumption in China, the system of the power distribution network is also larger and larger so as to ensure that the increasing electricity demand is met. The distribution network acts as the last ring in the power supply, and its operating state will directly affect the reliability of the power supply. However, due to the fact that the communication and the matched construction of automation equipment are relatively backward, the dispatching data private network cannot realize the full coverage of the power distribution network, and therefore when a single-phase ground fault occurs in the power distribution network, a dispatching department cannot find information of a fault line at the first time, and the fault cannot be timely eliminated.
In the practical engineering, the power distribution network is allowed to still run for 1-2 hours under the condition of single-phase ground fault for guaranteeing the power supply reliability. At this time, the magnitude and phase of the line voltage are unchanged, but the voltage of the non-fault phase-to-ground voltage is increased by 1.732 times, which poses a threat to insulation weak points in the system. In addition, before the fault is effectively treated, the grounding point may generate intermittent arc discharge due to poor contact, and generate resonant overvoltage under certain condition excitation, which may cause great damage to the insulation system. Therefore, timely troubleshooting is required. In order to eliminate faults, at present, power grid dispatching personnel can break outlet circuit breakers in a transformer substation one by one through a circuit pulling method to distinguish fault circuits. However, the high-voltage circuit breaker has more operation steps, and the method can lead to the existence of the ground fault for a longer time, so that the potential safety hazard of the power grid is increased. Therefore, the method for rapidly identifying the fault line is researched, the workload of power grid dispatching personnel can be reduced, the fault can be timely eliminated, and the complete reliability of the power grid is ensured.
Disclosure of Invention
The invention provides a VMD-DTW cluster-based fault line selection method for a low-current grounding system, which is used for searching a single-phase grounding fault line of a power distribution network. A series of problems caused by distinguishing fault lines by using a pull method by power grid dispatching monitoring personnel can be avoided, the monitoring personnel are assisted to find the fault lines in time, and the safe and stable operation of the power distribution network is guaranteed.
The technical scheme adopted by the invention is as follows:
the VMD-DTW cluster-based low-current grounding system fault line selection method comprises the following steps:
step 1: taking zero sequence currents of different lines as samples, extracting and enhancing a zero sequence current original signal by adopting a VMD decomposition method, and decomposing the zero sequence current original signal into modal components of three frequency bands of high, middle and low;
step 2: then, calculating the similarity of modal components of different lines by using a DTW method to realize the similarity measurement of zero sequence currents of different lines;
and step 3: updating the center of the HAC cluster according to the similarity measurement result to realize clustering of the zero-sequence current characteristics;
and 4, step 4: and distinguishing a fault line and a healthy line according to the clustering result, and finally realizing the purpose of fault line selection of the low-current grounding system.
In the step 1, extracting and enhancing the zero sequence current original signal by adopting a VMD decomposition method, comprising the following steps of: and (3) giving the number of modal components, taking the sum of the modal components equal to the total signal as a constraint condition and the minimum bandwidth of the modal components as an optimization target, constructing a modal component solving model, and completing the adaptive decomposition of a signal frequency domain through iterative solution to obtain a plurality of narrowband decomposed signals.
In step 2, calculating the similarity of modal components of different lines by using a DTW method, and realizing the similarity measurement of zero sequence currents of different lines, wherein the similarity measurement comprises the following steps: on the basis of modal components obtained by decomposing each zero sequence current, similarity of each line in high, middle and low frequency bands is calculated based on the DTW principle, so that a similarity matrix of the zero sequence currents (namely different cluster centers) of each line is obtained.
In step 3, updating the center of the HAC cluster according to the similarity measure result, comprising: and clustering the zero sequence current by adopting an HAC method, wherein the cluster center of the cluster is updated according to a similarity matrix obtained based on a DTW method.
The invention relates to a VMD-DTW cluster-based fault line selection method for a low-current grounding system, which has the advantages that: the method comprises the steps of firstly decomposing zero-sequence currents of different lines by using a VMD method, decomposing the zero-sequence currents into three components of high, medium and low frequency bands, then measuring the similarity of each modal component of the different zero-sequence currents by using a DTW method, and finally dividing samples with high similarity into several types by using an HAC method, thereby completing the distinguishing of healthy lines and fault lines, and achieving the purposes of improving the efficiency of dispatching and monitoring personnel in distinguishing the fault lines and ensuring the safe and stable operation of a power distribution network.
The method can avoid a series of problems caused by distinguishing the fault line by using a pull method by power grid dispatching monitoring personnel, assist the monitoring personnel to find the fault line in time and ensure the safe and stable operation of the power distribution network.
Drawings
Fig. 1 is an equivalent circuit diagram of a single-phase fault.
Fig. 2 is a comparison diagram of zero-sequence currents of fault lines from scene 1 to scene 3.
Fig. 3(a) is an exploded view of a zero-sequence current VMD of a fault line in scenario 1;
fig. 3(b) is an exploded view of a zero-sequence current VMD of a fault line in scenario 2;
fig. 3(c) is an exploded view of the zero sequence current VMD of the fault line in scenario 2.
Fig. 4 is a VMD decomposition flow chart.
Fig. 5 is a flow chart of similarity measurement of zero sequence currents of different lines.
Fig. 6 is a flow chart of clustering analysis based on the HAC method.
Detailed Description
The VMD-DTW cluster-based low-current grounding system fault line selection method comprises the following steps:
step 1: taking zero sequence currents of different lines as samples, extracting and enhancing a zero sequence current original signal by adopting a VMD decomposition method, and decomposing the zero sequence current original signal into modal components of three frequency bands of high, middle and low;
step 2: then, calculating the similarity of modal components of different lines by using a DTW method to realize the similarity measurement of zero sequence currents of different lines;
and step 3: updating the center of the HAC cluster according to the similarity measurement result to realize clustering of the zero-sequence current characteristics;
and 4, step 4: and distinguishing a fault line and a healthy line according to the clustering result, and finally realizing the purpose of fault line selection of the low-current grounding system.
In the step 1, extracting and enhancing the zero sequence current original signal by adopting a VMD decomposition method, comprising the following steps of: and (3) giving the number of modal components, taking the sum of the modal components equal to the total signal as a constraint condition and the minimum bandwidth of the modal components as an optimization target, constructing a modal component solving model, and completing the adaptive decomposition of a signal frequency domain through iterative solution to obtain a plurality of narrowband decomposed signals.
In step 2, calculating the similarity of modal components of different lines by using a DTW method, and realizing the similarity measurement of zero sequence currents of different lines, wherein the similarity measurement comprises the following steps: on the basis of modal components obtained by decomposing each zero sequence current, similarity of each line in high, middle and low frequency bands is calculated based on the DTW principle, so that a similarity matrix of the zero sequence currents (namely different cluster centers) of each line is obtained.
In step 3, updating the center of the HAC cluster according to the similarity measure result, comprising: and clustering the zero sequence current by adopting an HAC method, wherein the cluster center of the cluster is updated according to a similarity matrix obtained based on a DTW method.
The VMD-DTW cluster-based low-current grounding system fault line selection method specifically comprises the following steps:
step one, signal decomposition based on VMD:
step 1.1: acquisition of the original signal: obtaining zero sequence current [ I ] of N lines by measurement1,I2,…IN]。
Step 1.2: a mathematical model of Variational Modal Decomposition (VMD) is constructed.
And (3) establishing an optimization model taking the formula (1) as a target and constraint according to the VMD decomposition principle.
Wherein f (t) is an initial signal, ui(t) is the i-th eigenmode component, ω, obtained by decompositioniIs the ith eigenmode component ui(t) the center frequency of (t), which is the Dirac function, i ∈ [0, M]M is the total number of modal components corresponding to each zero sequence current, and is set to 3, j represents an imaginary number, and e represents the base number of a natural logarithm.
In the specific solving process, the center frequency of each modal component is obtained through iterative calculation according to the principle that the sum of modal bandwidths is minimum, so that the separation of each modal component is realized.
In order to facilitate the solution, a Lagrange multiplier is introduced, and an augmented Lagrange expression L is constructed on the basis of a VMD decomposition optimization target, wherein the augmented Lagrange expression L is shown in the following formula (2):
wherein, λ is Lagrange multiplier, α is secondary penalty factor. And converting the optimization problem containing the constraint conditions into the solution of the unconstrained variational problem through the transformation.
Iterative optimization is carried out on the augmented Lagrange expression by adopting a multiplicative operator alternating direction method, and u is solved according to arg { minL }kCenter frequency ω of modal componentkThe calculation method is shown in the following formulas (3) and (4):
wherein u (ω) and f (ω) are the result of fourier transform of the corresponding modal component and the initial signal. k is the number of iterations and i is the modal component number.
Step 1.3: initializing model parameters u1、ω1、λ1And maximum iteration times, respectively calculating zero sequence current [ I ] according to formulas (3) and (4)1,I2,…IN]Of the kth iteration of (a).
Step 1.4: judging the termination of iteration according to the zero sequence current [ I ]1,I2,…IN]Difference feedback update λ with its modal componentkUntil an iteration end condition is reached. Equation (5) below is the λ update equation in the k +1 th iteration:
in the formula, λk+1(omega) represents the Lagrangian multiplier obtained by the (k + 1) th iteration solution, lambdak(omega) represents a Lagrange multiplier obtained by the kth iteration solution, f (omega) is a result of Fourier transform of the initial signal,
the ith modal component obtained by the (k + 1) th iteration solution is represented, and tau represents a noise tolerance parameter.
Equation (6) is an iteration termination judgment equation, and if equation (6) is satisfied, the iteration is stopped and the modal component set { u } obtained by decomposition is outputi(t) }, if equation (6) does not hold, then go to step 3 to repeat the above steps, generally set to 1.0 × 10-6。
In the formula (I), the compound is shown in the specification,
represents the ith modal component obtained by the (k + 1) th iterative solution,
the ith modal component obtained by the kth iteration solution,
presentation pair
And 2 norm calculation.
Step two, similarity measurement based on DTW:
step 2.1: and (3) normalization of each component, namely after finding out the maximum value and the minimum value of each component, performing normalization processing according to an equation (7):
in the formula uijmin(t) is the minimum value of the jth component of the ith sample, uijmax(t) is the maximum value of the jth component of the ith sample, uij(t) is the jth component of the ith sample.
Step 2.2: establishing a DTW similarity measurement model: modal component data X ═ X for any two samples1…xn}、Y＝{y1…ymAnd (4) corresponding relation exists in the two sets of modal component data: p ═ P1,1,…pi,j…pn,m}, wherein: p is a radical ofi,j＝(xi,yj) Representing the ith element X in the X sequence for the correspondence between the two sequencesiTo the jth element Y in the Y sequencejThe path of (2). Then the mathematical model of the DTW similarity measure is as follows (8):
in the formula IPLength of DTW path P, d (P)i,j) Is pi,jTwo points x in the correspondenceiAnd yjGenerally, euclidean distance is taken as a distance measure criterion, and W represents a set of paths consisting of all paths.
Step 2.3: the method comprises the following steps of carrying out line numbering {1,2, …, N } based on DTW line zero-sequence current similarity calculation, measuring the similarity of each line in high, medium and low frequency bands by adopting a formula (8), and obtaining a similarity matrix R of each line zero-sequence current:
wherein r isij∈[0,1]And (3) representing the similarity measurement result of the zero sequence currents of the i and j of the line, namely the Euclidean distance of the zero sequence currents in high and low and attenuation direct current frequency bands, wherein the smaller the numerical value, the better the similarity is represented. The calculation formula is shown in the following formula (10):
where hi (i) represents the high-frequency modal component of line i, hi (j) represents the high-frequency modal component of line j, mi (i) represents the mid-frequency modal component of line i, mi (j) represents the mid-frequency modal component of line j, li (i) represents the low-frequency modal component of line i, and li (j) represents the low-frequency modal component of line j.
Step three, cluster analysis based on the HAC method:
step 3.1: expressing the cluster center by using 3 modal components of the zero-sequence current of the line to form an initial cluster set comprising N samples, namely { [ HI { [1,MI1,LI1],…,[HIN,MIN,LIN]}。
Step 3.2: calculating the distance between the samples by adopting a formula (9), namely similarity;
step 3.3: and according to the obtained similarity matrix, selecting two samples a and b with highest similarity, namely the two samples a and b with the smallest element values in the similarity matrix, merging the two samples a and b, and updating the cluster center according to the formula (11).
Wherein, [ HIi,MIi,LIi]To the updated cluster center, PH、PM、PLAnd respectively representing DTW paths of mode components of the a object and the b object in each frequency band after decomposition. When the cluster center is updated, the mean value between the two merged modal components is obtained according to the DTW paths of the modal components of the zero-sequence currents of the two lines a and b to serve as the updated cluster center.
And 4, step 4: and repeating the steps 3.2 and 3.3 until the convergence condition shown in the formula (12) is met, and taking the cluster with less samples as a fault line cluster, wherein the line corresponding to the sample is taken as a fault line selection result.
min[Rlast]>μ×max[R0](12)
Wherein R islast、R0Respectively the last updated and the initial correlation matrix, max [ R ]]Is the value of the largest element in the correlation matrix μ ∈ [0,1 ]]In order to stop the threshold value of iteration, if the threshold value is set too low, the healthy line can be judged as a fault line by mistake, and if the threshold value is set too high, the iteration process of clustering is difficult to converge, so that the efficiency of fault line selection is reduced.
Example (b):
referring to fig. 4, the embodiment of the invention discloses a fault line selection method of a low-current grounding system based on VMD-DTW clustering. The implementation steps are as follows:
s11, obtaining zero sequence currents [ I ] of different lines through measurement1,I2,…IN]。
S12, establishing a VDM mathematical model according to the preset component number and the VDM principle, optimizing a target model by constructing an augmented Lagrangian function, and finally performing iterative optimization on the augmented Lagrangian function by adopting a multiplicative operator alternating direction method, wherein the calculation method is shown as formulas (3) and (4).
S13, initializing model parameters, and solving zero sequence current [ I ] according to the formula (3) and the formula (4)1,I2,…IN]Of the kth iteration of (a).
And S14, judging whether the modal components which are continuously processed twice satisfy an iteration convergence condition, namely, an expression (6). If yes, ending iteration, otherwise, updating lambda according to equation (5)kAnd returning to the previous step.
Referring to fig. 5, the similarity of each zero sequence current is calculated, and the specific steps include:
and S21, performing normalization processing on the modal component obtained by VMD decomposition, and obtaining a normalization formula shown in formula (7).
S22, establishing a mathematical model based on the DTW principle, as shown in the formula (8).
And S23, based on the formula (8), solving a similarity matrix R of each zero sequence current sample according to the formula (9), wherein the similarity between any two zero sequence current samples can be obtained by calculation according to the formula (10).
Referring to fig. 6, the cluster analysis based on the HAC algorithm includes:
s31, representing the cluster center by 3 modal components of the zero sequence current of the line, and forming an initial cluster set comprising N samples, namely { [ HI ]1,MI1,LI1],…,[HIN,MIN,LIN]}。
And S32, calculating a similarity matrix of each sample in the initial cluster set according to the formula (9).
And S33, updating the cluster center according to the formula (11) based on the similarity matrix obtained in the previous step.
S34, judging whether the convergence condition shown in the formula (12) is satisfied, and if so, finishing clustering; if not, the process returns to step S32. And after clustering is finished, taking the clustering cluster with less samples as a fault line cluster, wherein the line corresponding to the sample is taken as a fault line selection result.
Analysis by calculation example:
the simulation system used in the invention is an 110/10kV substation with 7 lines, the transformer is △/Y0 wiring, the equivalent circuit of the single-phase earth fault of the distribution network is shown in figure 1, and the parameter of the overhead line is r1＝0.147Ω/km，l1＝0.43Ω/km，c1＝0.0093μF/km，r0＝0.514Ω/km，l0＝1.3885Ω/km，c00.006 μ F/km. The arc suppression coil adopts a 5% overcompensation mode. The line length is 10 km.
To verify the validity of the method of the invention, the validity of the method of the invention is checked by setting fault conditions according to the scenario described in table 1 below:
table 1 fault scene setting table
In Table 1, phi is the phase angle at the time of failure, RfTo ground resistance of the fault, DfDistance from fault point to bus, PascThe compensation degree of the arc suppression coil is obtained. Fig. 2 is a comparison result of zero sequence currents of a fault line under three scenarios. As can be seen from fig. 2, the zero sequence current is affected by the ground resistance and the ground arc suppression coil, and thus there is a difference. And in the scene 3, the fault time phase angle is 20 degrees, the grounding resistance and the reactance of the arc suppression coil are the maximum, the amplitude of the zero sequence current of the corresponding fault line in the initial transient state and the steady state is smaller, and the attenuation of the fault current is quicker. Therefore, in the three scenarios, the faulty line characteristic of scenario 1 is the most obvious, and the faulty line characteristic of scenario 3 is the weakest, and the difficulty of faulty line selection is greater.
Subsequently, VMD decomposition and normalization processing are performed on the initial zero-sequence current signal, and the result is shown in fig. 3(a), 3(b), and 3 (c). Comparing fig. 2, fig. 3(a), fig. 3(b), fig. 3(c), it can be found that the zero sequence current changes greatly with the change of the fault phase angle, the grounding resistance and the reactance of the arc suppression coil, especially the amplitude of the high-frequency oscillation component for distinguishing the fault line from the healthy line changes greatly. After VMD decomposition and normalization processing, the method can better separate high, middle and low frequency band components in the zero sequence current and better reserve the characteristics of high frequency band signals, and lays a foundation for subsequent fault line selection.
Finally, the method provided by the invention is adopted to carry out similarity measurement and fault line selection. And (4) iteratively updating the healthy clusters and the fault clusters under different scenes according to the formulas (9) to (11), and classifying the results into corresponding clusters according to the similarity measurement results of the modal characteristics of each line and the cluster center to complete fault line selection. The results are shown in table 2 below:
table 2 table of similarity measurement results of each line
As can be seen from the results in Table 2, the method provided by the invention can accurately divide the zero sequence current samples into two types in all scenes, and correctly distinguish the healthy line from the fault line. In the scene 3, the fault characteristics are weak under the influence of factors such as fault time phase angles and the like, but the characteristics can still be effectively extracted after VMD decomposition and normalization processing, so that accurate fault line selection is realized.
In conclusion, the zero sequence currents of different lines of the power distribution network are used as data samples, and the clustering rule of the zero sequence currents of the lines is analyzed by adopting a clustering method to obtain the fault line when the single-phase earth fault occurs in the power distribution network. When the distribution network has single-phase earth fault, the data samples are identified and classified through VMD decomposition and similarity calculation based on DTW, and intelligent identification and classification of the healthy line and the fault line of the distribution network are realized. The method can greatly reduce the burden of power grid dispatching monitoring personnel, assist the monitoring personnel in finding out the fault line of the power distribution network in time and keep the safe and stable operation of the power distribution network.
Claims (5)
1. The fault line selection method of the low-current grounding system based on VMD-DTW clustering is characterized by comprising the following steps of:
step 1: taking zero sequence currents of different lines as samples, extracting and enhancing a zero sequence current original signal by adopting a VMD decomposition method, and decomposing the zero sequence current original signal into modal components of three frequency bands of high, middle and low;
step 2: then, calculating the similarity of modal components of different lines by using a DTW method to realize the similarity measurement of zero sequence currents of different lines;
and step 3: updating the center of the HAC cluster according to the similarity measurement result to realize clustering of the zero-sequence current characteristics;
and 4, step 4: and distinguishing a fault line and a healthy line according to the clustering result, and finally realizing the purpose of fault line selection of the low-current grounding system.
2. The VMD-DTW cluster-based low-current grounding system fault line selection method of claim 1, wherein: in the step 1, extracting and enhancing the zero sequence current original signal by adopting a VMD decomposition method, comprising the following steps of: and (3) giving the number of modal components, taking the sum of the modal components equal to the total signal as a constraint condition and the minimum bandwidth of the modal components as an optimization target, constructing a modal component solving model, and completing the adaptive decomposition of a signal frequency domain through iterative solution to obtain a plurality of narrowband decomposed signals.
3. The VMD-DTW cluster-based low-current grounding system fault line selection method of claim 1, wherein: in step 2, calculating the similarity of modal components of different lines by using a DTW method, and realizing the similarity measurement of zero sequence currents of different lines, wherein the similarity measurement comprises the following steps: and calculating the similarity of each line in high, middle and low frequency bands based on the DTW principle on the basis of the modal component obtained by decomposing each zero sequence current, thereby obtaining the similarity matrix of each line zero sequence current.
4. The VMD-DTW cluster-based low-current grounding system fault line selection method of claim 1, wherein: in step 3, updating the center of the HAC cluster according to the similarity measure result, comprising: and clustering the zero sequence current by adopting an HAC method, wherein the cluster center of the cluster is updated according to a similarity matrix obtained based on a DTW method.
5. The fault line selection method of the low-current grounding system based on VMD-DTW clustering is characterized by comprising the following steps of:
step one, signal decomposition based on VMD:
step 1.1: acquisition of the original signal: obtaining zero sequence current [ I ] of N lines by measurement1,I2,…IN]；
Step 1.2: constructing a mathematical model of Variational Mode Decomposition (VMD); establishing an optimization model taking the formula (1) as a target and constraint according to a VMD decomposition principle;
wherein f (t) is an initial signal, ui(t) is the i-th eigenmode component, ω, obtained by decompositioniIs the ith eigenmode component ui(t) the center frequency of (t), which is the Dirac function, i ∈ [0, M]M is the total number of modal components corresponding to each zero sequence current, and is set to be 3; in the specific solving process, the center frequency of each modal component is obtained through iterative calculation according to the principle that the sum of modal bandwidths is minimum, so that the separation of each modal component is realized;
in order to facilitate the solution, a Lagrange multiplier is introduced, and an augmented Lagrange expression L is constructed on the basis of a VMD decomposition optimization target, wherein the augmented Lagrange expression L is shown in the following formula (2):
wherein, λ is Lagrange multiplier, α is secondary punishment factor; converting the optimization problem containing constraint conditions into the solution of the unconstrained variational problem through the transformation;
iterative optimization is carried out on the augmented Lagrange expression by adopting a multiplicative operator alternating direction method, and u is solved according to arg { minL }kCenter frequency ω of modal componentkThe calculation method is shown in the following formulas (3) and (4):
wherein u (omega) and f (omega) are results of Fourier transform of the corresponding modal components and the initial signals; k is iteration times, and i is a modal component number;
step 1.3: initializing model parameters u1、ω1、λ1And maximum iteration times, respectively calculating zero sequence current [ I ] according to formulas (3) and (4)1,I2,…IN]3 modal components at the kth iteration of (a);
step 1.4: judging the termination of iteration according to the zero sequence current [ I ]1,I2,…IN]Difference feedback update λ with its modal componentkUntil an iteration termination condition is reached; equation (5) below is the λ update equation in the k +1 th iteration:
equation (6) is an iteration termination judgment equation, and if equation (6) is satisfied, the iteration is stopped and the modal component set { u } obtained by decomposition is outputi(t), if formula (6) does not hold, then go to step 3 to repeat the above steps, and set to 1.0 × 10-6；
Step two, similarity measurement based on DTW:
step 2.1: and (3) normalization of each component, namely after finding out the maximum value and the minimum value of each component, performing normalization processing according to an equation (7):
in the formula uijmin(t) is the minimum value of the jth component of the ith sample, uijmax(t) is the maximum value of the jth component of the ith sample, uij(t) is the jth component of the ith sample;
step 2.2: establishing a DTW similarity measurement model: modal scoring of any two samplesQuantity data X ═ { X ═ X1…xn}、Y＝{y1…ymAnd (4) corresponding relation exists in the two sets of modal component data: p ═ P1,1,…pi,j…pn,m}, wherein: p is a radical ofi,j＝(xi,yj) Representing the ith element X in the X sequence for the correspondence between the two sequencesiTo the jth element Y in the Y sequencejA path of (a); then the mathematical model of the DTW similarity measure is as follows (8):
in the formula IPLength of DTW path P, d (P)i,j) Is pi,jTwo points x in the correspondenceiAnd yjGenerally, the Euclidean distance is taken as a distance measurement standard;
step 2.3: the method comprises the following steps of carrying out line numbering {1,2, …, N } based on DTW line zero-sequence current similarity calculation, measuring the similarity of each line in high, medium and low frequency bands by adopting a formula (8), and obtaining a similarity matrix R of each line zero-sequence current:
wherein r isij∈[0,1]The similarity measurement result of the zero sequence currents of the lines i and j is represented, namely the Euclidean distance between the zero sequence currents in high and low and attenuation direct current frequency bands, the smaller the numerical value is, the better the similarity is represented, and the calculation formula is shown as the following formula (10):
in the formula, HI, MI and LI are modal components of high, middle and low frequency bands obtained by VMD decomposition of each zero sequence current respectively;
step three, cluster analysis based on the HAC method:
step 3.1: the cluster center is expressed by 3 modal components of the zero sequence current of the line, and the cluster center is formed by N samplesInitial set of clusters of this, i.e., { [ HI ]1,MI1,LI1],…,[HIN,MIN,LIN]}；
Step 3.2: calculating the distance between the samples by adopting a formula (9), namely similarity;
step 3.3: according to the obtained similarity matrix, selecting two samples a and b with highest similarity, namely the two samples a and b with the smallest element values in the similarity matrix, merging the two samples a and b, and updating the cluster center according to a formula (11);
wherein, [ HIi,MIi,LIi]To the updated cluster center, PH、PM、PLDTW paths respectively representing the modal components of the a and b objects in each frequency band after decomposition; when the cluster center is updated, the mean value between the two merged modal components is obtained according to the DTW paths of the modal components of the zero-sequence currents of the two lines a and b and is used as the updated cluster center;
and 4, step 4: repeating the steps 3.2 and 3.3 until the convergence condition shown in the formula (12) is satisfied, and taking the cluster with less samples as a fault line cluster, wherein the line corresponding to the sample is taken as a fault line selection result;
min[Rlast]>μ×max[R0](12)；
wherein R islast、R0Respectively the last updated and the initial correlation matrix, max [ R ]]Is the value of the largest element in the correlation matrix, μ ∈ [0,1 [ ]]A threshold to stop the iteration.
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