CN110221168B - Method for positioning leading harmonic source and tracking harmonic pollution propagation path - Google Patents
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Abstract
The invention belongs to the technical field of harmonic source positioning of an electric power system, and particularly relates to a method for positioning a leading harmonic source and tracking a pollution propagation path of the harmonic source, which comprises the following steps: forming a harmonic node impedance matrix according to the parameters of the distribution network and the load data, and performing row-column normalization to generate an atom library; after detecting the higher harmonics, acquiring voltage data measured by each node of the distribution network, calculating harmonic voltage amplitude to form a harmonic voltage amplitude vector, searching atoms which are most matched with the harmonic voltage amplitude vector from an atom library, calculating a weighting coefficient according to a least square method, calculating a residual vector, continuously performing the searching operation on the residual, continuously iterating until an error value is smaller than a threshold value, indicating the position of a leading harmonic source by using the weighting coefficient, and multiplying the normalized harmonic position indication vector by a harmonic node impedance matrix to obtain a pollution propagation path of the leading harmonic source. The invention can further solve the responsibility dispute of harmonic pollution and improve the power quality management level.
Description
Technical Field
The invention belongs to the technical field of harmonic source positioning of an electric power system, and particularly relates to a method for positioning a leading harmonic source and tracking a pollution propagation path of the harmonic source.
Background
With the rapid development of technologies such as flexible direct current transmission and new energy power generation, power electronic rectifying equipment is increasingly connected to a power distribution network except for traditional nonlinear loads such as an electric arc furnace and an electrified railway, so that the problem of harmonic pollution in a power system is increasingly serious. The method is important for effectively treating harmonic pollution in a power system, ensuring economic operation of a power distribution network and safe power utilization of users, and leading accurate positioning of a harmonic source and tracking of harmonic pollution responsibility. At present, methods for positioning leading harmonic sources at home and abroad are roughly classified into two types: the positioning method based on the equivalent circuit model and the positioning method based on the wide area measurement. The positioning method based on the equivalent circuit model is used for calculating and analyzing the electric quantity at the public coupling point, and the side where the leading harmonic source is located can be judged only at a certain node, such as a harmonic power flow direction method, a method based on harmonic impedance and the like, so that the positioning method is easy to realize in practical application but needs to check all nodes, and is relatively complicated; the positioning method based on wide area measurement collects harmonic measurement data from multiple nodes, and realizes leading harmonic source positioning by means of an intelligent algorithm, so that the method can avoid one-by-one inspection of all nodes, has engineering research value and practical significance, and is concerned by more and more relevant learners. However, most of the existing positioning methods based on wide-area measurement need to extract harmonic voltage phasor or current phasor as input, and the degree of dependence on the synchronous phasor measurement device is high, but the popularization of the synchronous phasor measurement device in high and medium voltage distribution networks in many areas is still limited by economic conditions, so the implementation of the existing positioning methods still suffers from certain resistance. In consideration of the actual situation that synchronous acquisition of harmonic voltage amplitude in daily power quality monitoring data of a power grid is realized, a leading harmonic source positioning method based on the harmonic voltage amplitude is necessary to be designed, and harmonic pollution propagation path tracking is realized on the basis.
Disclosure of Invention
In order to solve the problems, the invention provides a method for positioning a leading harmonic source and tracking a pollution propagation path of the harmonic source, which has the following specific technical scheme:
a method for positioning a dominant harmonic source comprises the following steps:
s1: when the situation that higher harmonics appear in the power distribution network is monitored, load harmonic impedance is calculated according to power distribution network line parameters and user load data in a power generation plan, so that a harmonic node impedance matrix of the power distribution network is obtained, each row of the harmonic node impedance matrix is subjected to normalization processing, and an atom library moment is obtainedArraying; let the column vector of the atom library be [ a ]1,a2,…,aN]Each column vector in the atom library is 1 atom;
s2: after the situation that the power distribution network is polluted by higher harmonics is monitored, carrying out Fourier decomposition on three-phase voltage data measured at each node, extracting amplitude data of harmonic voltage components, and forming a multi-dimensional harmonic voltage amplitude column vector;
s3: searching an atom which is most matched with the harmonic voltage amplitude column vector obtained in the step S2 from the atom library matrix obtained in the step S1 through the dot product operation of the vectors;
s4: calculating a weighting coefficient corresponding to the most matched atom obtained in the step S3 by using a least square method, and subtracting the product of the most matched atom obtained in the step S3 and the corresponding weighting coefficient from the harmonic voltage amplitude column vector obtained in the step S2 to obtain a residual vector;
s5: continuously searching the optimal matching atoms and the corresponding weighting coefficients for the residual vector obtained in the step S4 according to the step S3 and the step S4, updating the residual, and continuously iterating until the modulus of the residual vector is smaller than the allowable error, so that the sum of the products of all the matching atoms and the corresponding weighting coefficients can approximately represent the harmonic voltage amplitude column vector obtained in the step 2; and arranging the weighting coefficients according to the corresponding positions to obtain a position indication vector of the leading harmonic source, wherein the nonzero elements of the position indication vector correspond to the node numbers accessed by the leading harmonic source, so that the leading harmonic source is positioned.
Preferably, the formula for calculating the load harmonic impedance in step S1 is as follows:
ZhL＝RhL+jXhL； (2)
wherein R ishLIs the equivalent harmonic resistance of the load, XhLIs h order equivalent harmonic reactance, Z, corresponding to the loadhLH harmonic equivalent impedance corresponding to the load, and the unit is ohm; u shapeLIs the nominal operating voltage of the load in kilovolts; pLAnd QLThe unit is megawatt and megavar respectively; h represents the harmonic order and j is an imaginary unit.
Preferably, in step S1, the generated harmonic node impedance matrix is normalized by dividing each column vector element in the harmonic node impedance matrix by a module value of the column vector:
wherein, bijIs an element of the ith row and j column in the atom library matrix, zijThe element of the ith row and the j column in the harmonic node impedance matrix, and the square root of the square sum of the element of the jth column on the denominator is the module value of the column.
Preferably, the calculation formula for calculating the harmonic voltage by fourier decomposition in step S2 is:
wherein,
is the h-th harmonic voltage component obtained by calculation, M is the number of data points for Fourier decomposition, v (n) is the discrete voltage data measured, and j is an imaginary unit; and respectively taking the amplitudes of the h-th harmonic voltage calculated by all the nodes, and forming an N-dimensional harmonic voltage amplitude column vector according to the node numbers, wherein N is the total number of the nodes in the distribution network, and the N-dimensional harmonic voltage amplitude column vector is expressed as follows:
Vh＝[V1 V2 … VN]T (5)。
preferably, the calculation manner of finding the atom which is the closest match to the harmonic voltage amplitude column vector obtained in step S2 from the atom library matrix obtained in step S1 in step S3 is:
wherein, aiIs an atom in the atom library, i.e. each column vector of the atom library matrix, i ═ 1,2, …, N;
is the transpose of the harmonic voltage amplitude column vector;
represents a vector VhAnd aiPerforming dot product operation;
means to find a that maximizes the dot product calculationiThe operation of (1); a isnIs a column vector V of voltage amplitude of harmonic in a single iterationhThe closest matching atom.
Preferably, the calculation formula of the weighting coefficient corresponding to the best matching atom in the step S4 according to the least square method is:
wherein, cnIs a weighting coefficient corresponding to an atom obtained by the least square method, and is a scalar or scalar quantity, and V can be calculated by calculating the weighting coefficienthAnd cn·anThe sum of the squares of the errors is minimal; vhRepresenting the harmonic voltage amplitude column vector, anIs a column vector V of voltage amplitude of harmonic in a single iterationhThe closest matching atom.
Preferably, the calculation formula for calculating the residual vector in step S4 is as follows:
R＝Vh-cn·an； (8)
wherein, VhRepresenting a harmonic voltage amplitude column vector; a isnIs a column vector V of harmonic voltage amplitudehThe most matched atom; r is the residual vector, dimension and Vh、anThe same is N; c. CnIs an atom a obtained by the least square methodnThe corresponding weighting coefficients.
Preferably, in step 5, the error is calculated as follows:
wherein R is an error value corresponding to the error vector R, | R | | Y2Is the 2-norm of the vector, which is the square of the sum of the squares of all the elements of the vector.
Preferably, the harmonic voltage amplitude column vector in step S5 is approximately the sum of products of all matching atoms and corresponding weighting coefficients, which is specifically expressed as:
wherein, VhRepresenting the harmonic voltage amplitude column vector, cnIs a weighting coefficient corresponding to an atom obtained by the least square method, and is a scalar or scalar quantity, anIs a column vector V corresponding to the amplitude of the harmonic voltage in a single iterationhThe atoms that are the best match are,
and
k in the lower middle right-hand subscript denotes the kth iteration, nkIndicating the position of the atom retrieved at the k-th time in the atom library.
Preferably, the method for arranging the weighting coefficients to obtain the position indication vector of the dominant harmonic source in step S5 includes:
cnis a weighting coefficient corresponding to an atom obtained by a least square method,
i in the lower right-hand corner denotes the i-th iteration, niRepresenting the position of the ith retrieved atom in the atom library; vhRepresenting the harmonic voltage amplitude column vector, anIs a column vector V corresponding to the amplitude of the harmonic voltage in a single iterationhThe most matched atom;
in accordance with its right subscript niIs ordered from small to large, atoms not being retrieved
Corresponding to
Set to 0, vector IhDimension of and harmonic voltage magnitude column vector Vh、anThe same is N.
The method for tracking the harmonic pollution propagation path based on the leading harmonic source positioning comprises the following steps:
s6: according to the position indication vector of the leading harmonic source obtained in the step S5, carrying out normalization processing on the vector, and multiplying the normalized vector by the atom library matrix obtained in the step S1 to obtain the contribution degree of the leading harmonic source to the voltage distortion of each node, namely tracking the harmonic pollution propagation path of the leading harmonic source; the calculation formula of the contribution degree of the dominant harmonic source to the voltage distortion of each node is as follows:
V'h＝Zh·I'h； (12)
wherein, V'hIs the degree of contribution of the dominant harmonic source to the voltage distortion of each node, I'hIs a position indication vector I of the dominant harmonic source after normalization processinghThe normalization processing is the same as the normalization processing of the array vector of the harmonic node impedance matrix in step S1.
The invention has the beneficial effects that: the method can realize the positioning of the leading harmonic source and the tracking of the pollution propagation path only by acquiring the harmonic voltage amplitude data on the basis of the conventional power quality monitoring system, and has important significance for further solving the responsibility dispute of harmonic pollution and improving the power quality management level.
Drawings
Fig. 1 is a schematic diagram of a distribution network structure of IEEE14 nodes in an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating the results of the algorithm positioning when the dominant harmonic source is connected at node 12 in an embodiment of the present invention;
fig. 3 is a schematic diagram of a calculation result of the contribution degree of the dominant harmonic source to the voltage distortion of each node of the distribution network in the embodiment of the present invention.
Detailed Description
For a better understanding of the present invention, reference is made to the following detailed description taken in conjunction with the accompanying drawings in which:
specific parameters of the distribution network system model with the IEEE14 nodes used in the embodiment can be seen in tables 1-3, the voltage reference is 18kV, the rated power is 100MW, and the schematic diagram of the topological structure of the system is shown in FIG. 1. The 12 nodes of the distribution network are connected with a dominant harmonic current source with the amplitude of 1A and the frequency of 250Hz (5 times of power frequency), and the 11 nodes and the 14 nodes are respectively connected with two small-amplitude harmonic sources with the amplitude of 0.25A and the frequency of 250Hz so as to simulate background harmonics in the distribution network. In order to simulate the noise effect in practical engineering, the measured voltage data is added in the embodiment
White gaussian noise. In practice, the collected measured voltage data is processed in steps 2 to 6 in real time, and the processing procedure at a certain time is taken as an example.
TABLE 1 IEEE-14 distribution network simulation system branch parameters
TABLE 2 IEEE-14 distribution network Transformer parameters
TABLE 3 IEEE-14 distribution network load parameters
A method for positioning a dominant harmonic source comprises the following steps:
s1: before the situation that higher harmonics appear in the power distribution network is monitored, load harmonic impedance is calculated according to power distribution network line parameters and user load data in a power generation plan, so that a harmonic node impedance matrix of the power distribution network is obtained, and each column of the harmonic node impedance matrix is subjected to normalization processing, so that an atom library matrix is obtained; let the column vector of the atom library be [ a ]1,a2,…,aN]Each column vector in the atom library is 1 atom. The formula for calculating the load harmonic impedance is as follows:
ZhL＝RhL+jXhL； (2)
wherein R ishLIs the equivalent harmonic resistance of the load, XhLIs h order equivalent harmonic reactance, Z, corresponding to the loadhLH harmonic equivalent impedance corresponding to the load, and the unit is ohm; u shapeLIs the nominal operating voltage of the load in kilovolts; pLAnd QLThe unit is megawatt and megavar respectively; h represents the harmonic order and j is an imaginary unit.
The line and load parameters such as line impedance, charging admittance, load equivalent impedance and the like stored in the general distribution network database are numerical values under power frequency. In the present invention, it is necessary to calculate the research by converting these parametersFor each impedance parameter at harmonic, i.e. the resistance value, is constant, the reactance value is multiplied by the corresponding harmonic order (e.g. for a harmonic of 5 th, the reactance value of the parameter is multiplied by 5). Taking the circuit 1-2 as an example, it can be seen from Table 1 that the fundamental frequency impedance of the circuit 1-2 is z1-2Then the impedance of the 5 th harmonic is converted to z1-2(5)：
z1-2＝0.01938+j0.05917； (3)
z1-2(5)＝0.01938+j0.05917×5＝0.01938+j0.29585； (4)
And (3) converting the harmonic values of all network parameters according to the method to form a harmonic impedance matrix of the distribution network, and obtaining the amplitude of the elements of the harmonic impedance matrix to obtain a matrix Z:
all the columns of Z are normalized, namely each element is divided by the module value of the column to obtain an atom library B, and the calculation formula is as follows:
wherein, bijIs an element of the ith row and j column in the atom library matrix, zijThe element of the ith row and the j column in the harmonic node impedance matrix, and the square root of the square sum of the element of the jth column on the denominator is the module value of the column. The following can be obtained:
s2: after the situation that the power distribution network is polluted by higher harmonics is monitored, Fourier decomposition is carried out on three-phase voltage data measured at each node, amplitude data of 5-order harmonic voltage components are extracted, and a multi-dimensional harmonic voltage amplitude column vector is formed. The calculation formula for calculating the harmonic voltage by fourier decomposition is:
wherein,
is the h-th harmonic voltage component obtained by calculation, M is the number of data points for Fourier decomposition, v (n) is the discrete voltage data measured, and j is an imaginary unit; and respectively taking the amplitudes of the h-th harmonic voltage calculated by all the nodes, and forming an N-dimensional harmonic voltage amplitude column vector according to the node numbers, wherein N is the total number of the nodes in the distribution network, and the N-dimensional harmonic voltage amplitude column vector is expressed as follows:
Vh＝[V1 V2 … VN]T (9)。
in the simulation example, the sampling frequency is 4000Hz, 80 sampling points are taken from the recorded wave data for fast fourier processing, and the complex frequency domain form of the 5 th harmonic voltage at each node at the moment is obtained as follows:
where j is an imaginary unit. Obtaining the amplitude column vector of the harmonic voltage by taking the amplitudes of all the elements in the vector and reserving 3 decimal places:
s3: through the dot product operation of the vectors, the atom which is most matched with the harmonic voltage amplitude column vector obtained in the step S2 is searched from the atom library matrix obtained in the step S1, and the calculation method is as follows:
wherein, aiIs an atom in the atom library, i.e. each column vector of the atom library matrix, i ═ 1,2, …, N;
is the transpose of the harmonic voltage amplitude column vector;
represents a vector VhAnd aiPerforming dot product operation;
means to find a that maximizes the dot product calculationiThe operation of (1); a isnIs a column vector V of voltage amplitude of harmonic in a single iterationhThe closest matching atom.
With the 1 st atom (column 1 of the atom library matrix) and VhThe dot product operation of (a) is explained as an example:
the results of all dot product operations are: 0.2757,0.6182,0.6756,1.4227,1.0036,2.0090,1.8618,1.8233,2.5823,2.0583,0.9994,18.8515,7.4226,4.6207. The maximum corresponding atom is the 12 th atom a12I.e., column 12 of the atom pool matrix B.
S4: and calculating the weighting coefficient corresponding to the best matched atom obtained in the step S3 by using a least square method, and subtracting the product of the best matched atom obtained in the step S3 and the corresponding weighting coefficient from the harmonic voltage amplitude column vector obtained in the step S2 to obtain a residual vector. The calculation formula for calculating the weighting coefficient corresponding to the best matching atom by the least squares method is:
wherein, cnIs a weighting coefficient corresponding to an atom obtained by the least square method, and is a scalar or scalar quantity, and V can be calculated by calculating the weighting coefficienthAnd cn·anThe sum of the squares of the errors is minimal; vhRepresenting the harmonic voltage amplitude column vector, anIs harmonic in a single iterationWave voltage amplitude column vector VhThe closest matching atom.
Preferably, the calculation formula for calculating the residual vector in step S4 is as follows:
R＝Vh-cn·an； (15)
wherein, VhRepresenting a harmonic voltage amplitude column vector; a isnIs a column vector V of harmonic voltage amplitudehThe most matched atom; r is the residual vector, dimension and Vh、anThe same is N; c. CnIs an atom a obtained by the least square methodnThe corresponding weighting coefficients.
The calculation corresponds to the atom a12Weighting coefficient c of12：
By harmonic voltage amplitude column vector VhMinus c12·a12And calculating a residual vector R:
s5: continuously searching the optimal matching atoms and the corresponding weighting coefficients for the residual vector obtained in the step S4 according to the step S3 and the step S4, updating the residual, and continuously iterating until the modulus of the residual vector is smaller than the allowable error, so that the sum of the products of all the matching atoms and the corresponding weighting coefficients can approximately represent the harmonic voltage amplitude column vector obtained in the step 2; and arranging the weighting coefficients according to the corresponding positions to obtain a position indication vector of the leading harmonic source, wherein the nonzero elements of the position indication vector correspond to the node numbers accessed by the leading harmonic source, so that the leading harmonic source is positioned.
The error is calculated as follows:
wherein R is an error value corresponding to the error vector R, | R | | Y2Is the 2-norm of the vector, which is the square of the sum of the squares of all the elements of the vector.
The harmonic voltage amplitude column vector is approximated by the sum of the products of all matching atoms and the corresponding weighting coefficients, which is specifically expressed as:
wherein, VhRepresenting the harmonic voltage amplitude column vector, cnIs a weighting coefficient corresponding to an atom obtained by the least square method, and is a scalar or scalar quantity, anIs a column vector V corresponding to the amplitude of the harmonic voltage in a single iterationhThe atoms that are the best match are,
and
k in the lower middle right-hand subscript denotes the kth iteration, nkIndicating the position of the atom retrieved at the k-th time in the atom library.
The method for obtaining the position indication vector of the leading harmonic source by arranging the weighting coefficients comprises the following steps:
cnis a weighting coefficient corresponding to an atom obtained by a least square method,
i in the lower right-hand corner denotes the i-th iteration, niRepresenting the position of the ith retrieved atom in the atom library; vhRepresenting the harmonic voltage amplitude column vector, anIs a column vector V corresponding to the amplitude of the harmonic voltage in a single iterationhThe most matched atom;
in accordance with its right subscript niIs ordered from small to large, atoms not being retrieved
Corresponding to
Set to 0, vector IhDimension of and harmonic voltage magnitude column vector Vh、anThe same is N.
It should be noted that in this embodiment, the error after the first iteration is smaller than the allowable error range. Therefore, the iterative process of step S5 is not embodied, which does not affect that step S5 still has significance in other application cases.
Calculating a modulus value, i.e., an error, of the residual vector R obtained in step S4:
in the present embodiment, the error threshold is set to 0.5, which means that when the calculated error is less than 0.5, the resolution of the harmonic voltage amplitude vector is considered to satisfy the error requirement. At this time, the error calculation value | | | R | non-woven phosphor2＝||Vh-c12·a12||2The iteration stops when 0.3099 < 0.5. Neglecting errors, harmonic voltage magnitude vector VhCan be approximated by the retrieved atoms and corresponding coefficients:
Vh≈c12·a12 (22)。
arranging the weighting coefficients to obtain a position indication vector of the dominant harmonic source is as follows:
from the indication vector IhThe positions of the non-negative elements can intuitively obtain that the leading harmonic source is connected to the 12 nodes of the distribution network, and the judgment result is correct.
The method for tracking the harmonic pollution propagation path based on the leading harmonic source positioning comprises the following steps:
s6: according to the position indication vector of the leading harmonic source obtained in the step S5, carrying out normalization processing on the vector, and multiplying the normalized vector by the atom library matrix obtained in the step S1 to obtain the contribution degree of the leading harmonic source to the voltage distortion of each node, namely tracking the harmonic pollution propagation path of the leading harmonic source; the calculation formula of the contribution degree of the dominant harmonic source to the voltage distortion of each node is as follows:
V'h＝Zh·I'h； (24)
wherein, V'hIs the degree of contribution of the dominant harmonic source to the voltage distortion of each node, I'hIs a position indication vector I of the dominant harmonic source after normalization processinghThe normalization processing is the same as the normalization processing of the array vector of the harmonic node impedance matrix in step S1.
According to the position indication vector of the leading harmonic source obtained in the step 5, carrying out normalization processing on the vector:
I'h＝[0 0 0 0 0 0 0 0 0 0 0 1 0 0]T； (25)
will ZhAnd l'hMultiplying to obtain the degree V 'of contribution of the dominant harmonic source to distortion of each node voltage'h：
It can be seen that the dominant harmonic source has the greatest effect on the distortion of the voltage at node 12, and the distortion effect on the voltage of each node can be according to V'hThe numerical values of the corresponding elements in the sequence are sorted, so that the propagation path of the harmonic pollution is obtained.
It can be seen that the calculation results are reasonable, and from the calculation process, the method is easy to apply in engineering practice.
The present invention is not limited to the above-described embodiments, which are merely preferred embodiments of the present invention, and the present invention is not limited thereto, and any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (11)
1. A method for positioning a leading harmonic source is characterized by comprising the following steps: the method comprises the following steps:
s1: before the situation that higher harmonics appear in the power distribution network is monitored, load harmonic impedance is calculated according to power distribution network line parameters and user load data in a power generation plan, so that a harmonic node impedance matrix of the power distribution network is obtained, and each column of the harmonic node impedance matrix is subjected to normalization processing, so that an atom library matrix is obtained; let the column vector of the atom library be [ a ]1,a2,…,aN]Each column vector in the atom library is 1 atom;
s2: after the situation that the power distribution network is polluted by higher harmonics is monitored, carrying out Fourier decomposition on three-phase voltage data measured at each node, extracting amplitude data of harmonic voltage components, and forming a multi-dimensional harmonic voltage amplitude column vector;
s3: searching an atom which is most matched with the harmonic voltage amplitude column vector obtained in the step S2 from the atom library matrix obtained in the step S1 through the dot product operation of the vectors;
s4: calculating a weighting coefficient corresponding to the most matched atom obtained in the step S3 by using a least square method, and subtracting the product of the most matched atom obtained in the step S3 and the corresponding weighting coefficient from the harmonic voltage amplitude column vector obtained in the step S2 to obtain a residual vector;
s5: continuously searching the optimal matching atoms and the corresponding weighting coefficients for the residual vector obtained in the step S4 according to the step S3 and the step S4, updating the residual, and continuously iterating until the modulus of the residual vector is smaller than the allowable error, so that the sum of the products of all the matching atoms and the corresponding weighting coefficients can approximately represent the harmonic voltage amplitude column vector obtained in the step 2; and arranging the weighting coefficients according to the corresponding positions to obtain a position indication vector of the leading harmonic source, wherein the nonzero elements of the position indication vector correspond to the node numbers accessed by the leading harmonic source, so that the leading harmonic source is positioned.
2. The method of claim 1, wherein the method comprises: the formula for calculating the load harmonic impedance in step S1 is as follows:
ZhL＝RhL+jXhL； (2)
wherein R ishLIs the equivalent harmonic resistance of the load, XhLIs h order equivalent harmonic reactance, Z, corresponding to the loadhLH harmonic equivalent impedance corresponding to the load, and the unit is ohm; u shapeLIs the nominal operating voltage of the load in kilovolts; pLAnd QLThe unit is megawatt and megavar respectively; h represents the harmonic order and j is an imaginary unit.
3. The method of claim 1, wherein the method comprises: in step S1, the generated harmonic node impedance matrix is normalized by dividing each column vector element in the harmonic node impedance matrix by the modulus of the column vector:
wherein, bijIs an element of the ith row and j column in the atom library matrix, zijThe element of the ith row and the j column in the harmonic node impedance matrix, and the square root of the square sum of the element of the jth column on the denominator is the module value of the column.
4. The method of claim 1, wherein the method comprises: the calculation formula for calculating the harmonic voltage by fourier decomposition in step S2 is:
wherein,
is the h-th harmonic voltage component obtained by calculation, M is the number of data points for Fourier decomposition, v (n) is the discrete voltage data measured, and j is an imaginary unit; and respectively taking the amplitudes of the h-th harmonic voltage calculated by all the nodes, and forming an N-dimensional harmonic voltage amplitude column vector according to the node numbers, wherein N is the total number of the nodes in the distribution network, and the N-dimensional harmonic voltage amplitude column vector is expressed as follows:
Vh＝[V1 V2...VN]T (5)。
5. the method of claim 1, wherein the method comprises: the calculation method for finding the atom which is most matched with the harmonic voltage amplitude column vector obtained in the step S2 from the atom library matrix obtained in the step S1 in the step S3 is as follows:
wherein, aiIs an atom in the atom library, i.e. each column vector of the atom library matrix, i ═ 1,2, …, N;
is the transpose of the harmonic voltage amplitude column vector;
represents a vector VhAnd aiPerforming dot product operation;
means to find a that maximizes the dot product calculationiThe operation of (1); a isnIs a column vector V of voltage amplitude of harmonic in a single iterationhThe closest matching atom.
6. The method of claim 1, wherein the method comprises: the calculation formula of the weighting coefficient corresponding to the best matching atom in the step S4 by the least square method is:
wherein, cnIs a weighting coefficient corresponding to an atom obtained by the least square method, and is a scalar or scalar quantity, and V can be calculated by calculating the weighting coefficienthAnd cn·anThe sum of the squares of the errors is minimal; vhRepresenting the harmonic voltage amplitude column vector, anIs a column vector V of voltage amplitude of harmonic in a single iterationhThe closest matching atom.
7. The method of claim 1, wherein the method comprises: the calculation formula for calculating the residual vector in step S4 is as follows:
R＝Vh-cn·an； (8)
wherein, VhRepresenting a harmonic voltage amplitude column vector; a isnIs a column vector V of harmonic voltage amplitudehThe most matched atom; r is the residual vector, dimension and Vh、anThe same is N; c. CnIs an atom a obtained by the least square methodnThe corresponding weighting coefficients.
8. The method of claim 1, wherein the method comprises: in step 5, the residual error is calculated as follows:
wherein R is a residual value corresponding to the residual vector R, | R | | Y2Is the 2-norm of the vectorI.e. the square of the sum of the squares of all the elements of the vector.
9. The method of claim 1, wherein the method comprises: in step S5, the harmonic voltage amplitude column vector is approximated by the sum of products of all matching atoms and corresponding weighting coefficients, which is specifically expressed as:
wherein, VhRepresenting the harmonic voltage amplitude column vector, cnIs a weighting coefficient corresponding to an atom obtained by the least square method, and is a scalar or scalar quantity, anIs a column vector V corresponding to the amplitude of the harmonic voltage in a single iterationhThe atoms that are the best match are,
and
k in the lower middle right-hand subscript denotes the kth iteration, nkIndicating the position of the atom retrieved at the k-th time in the atom library.
10. The method of claim 1, wherein the method comprises: the method for obtaining the position indication vector of the dominant harmonic source by arranging the weighting coefficients in step S5 includes:
cnis a weighting coefficient corresponding to an atom obtained by a least square method,
i in the lower right-hand corner denotes the i-th iteration, niRepresents the atom of the ith search inA position in the atom library; vhRepresenting the harmonic voltage amplitude column vector, anIs a column vector V corresponding to the amplitude of the harmonic voltage in a single iterationhThe most matched atom;
in accordance with its right subscript niIs ordered from small to large, atoms not being retrieved
Corresponding to
Set to 0, vector IhDimension of and harmonic voltage magnitude column vector Vh、anThe same is N.
11. The method of claim 1, wherein the method comprises: the method comprises the following steps:
s6: according to the position indication vector of the leading harmonic source obtained in the step S5, carrying out normalization processing on the vector, and multiplying the normalized vector by the atom library matrix obtained in the step S1 to obtain the contribution degree of the leading harmonic source to the voltage distortion of each node, namely tracking the harmonic pollution propagation path of the leading harmonic source; the calculation formula of the contribution degree of the dominant harmonic source to the voltage distortion of each node is as follows:
V'h＝Zh·I'h； (12)
wherein, V'hIs the degree of contribution of the dominant harmonic source to the voltage distortion of each node, I'hIs a position indication vector I of the dominant harmonic source after normalization processinghThe normalization processing is the same as the normalization processing of the array vector of the harmonic node impedance matrix in step S1.
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