CN117269604B - Multi-harmonic source responsibility quantification method and system considering impedance change - Google Patents

Multi-harmonic source responsibility quantification method and system considering impedance change Download PDF

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CN117269604B
CN117269604B CN202311210965.9A CN202311210965A CN117269604B CN 117269604 B CN117269604 B CN 117269604B CN 202311210965 A CN202311210965 A CN 202311210965A CN 117269604 B CN117269604 B CN 117269604B
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impedance
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CN117269604A (en
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徐方维
王川
郭凯
郑鸿儒
舒勤
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Sichuan University
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Abstract

The invention discloses a multi-harmonic source responsibility quantification method and system considering impedance change, relates to the technical field of multi-harmonic source responsibility quantification, and solves the problem that the calculated harmonic responsibility is inaccurate because the existing multi-harmonic source responsibility quantification method does not consider the change characteristic of impedance. The key points of the technical scheme are as follows: s1, constructing an objective function equation for simultaneously solving a plurality of variable impedances based on bus harmonic voltage data and harmonic current data of interest; s2, solving background harmonic voltage and network harmonic impedance based on an objective function equation, constructing a weight matrix according to a solving result, obtaining a new objective function equation, updating weight parameters based on the new objective function equation, obtaining an updated objective function equation, and calculating a responsibility value of each harmonic source to the harmonic of the bus of interest based on the updated objective function equation; by simultaneously solving for the change in the multiple harmonic transfer impedances, the quantified harmonic responsibility is more accurate and reasonable.

Description

Multi-harmonic source responsibility quantification method and system considering impedance change
Technical Field
The invention relates to the technical field of multi-harmonic source responsibility quantification, in particular to a multi-harmonic source responsibility quantification method and system considering impedance change.
Background
The multi-harmonic source responsibility quantification method is mainly used for quantifying harmonic responsibility of each harmonic source on bus harmonic problems, and the quantification result can guide the establishment of a harmonic treatment scheme. The key of the multi-harmonic source responsibility quantification is to accurately solve the transfer impedance between the concerned bus and each harmonic source, and the harmonic responsibility of each harmonic source can be quantified by using a projection index after the transfer impedance is obtained. The existing method mainly comprises the following steps: binary linear regression, multiple linear regression, covariance, independent component analysis, and hierarchical harmonic contribution assessment. The binary linear regression method and the multiple linear regression method have the advantages that harmonic responsibility is quantized only by using harmonic voltage and current amplitude, phase information is not needed, but the background harmonic voltage fluctuation has larger influence on the accuracy of an estimation result because the phase information is not used; the covariance method can reduce the adverse effect of background harmonic waves on the result to a certain extent; the independent component analysis rule has better background harmonic interference resistance, but the stability of the estimation result is poor; the layered harmonic contribution assessment method may divide the harmonic responsibilities of each harmonic source in the radial power distribution network layer by layer.
However, all the above methods assume that the harmonic transfer impedance for evaluating the harmonic responsibility is constant over the period of interest, which may not be true when the grid operation mode changes, for example, maintenance of the power line, switching of the filter, switching of the capacitor, and fluctuation of the high power load may cause a large change in the harmonic transfer impedance, resulting in unreliable harmonic responsibility estimation results of the existing methods.
Based on the above, the invention provides a multi-harmonic source responsibility quantification method and a multi-harmonic source responsibility quantification system considering impedance change.
Disclosure of Invention
The application aims to provide a multi-harmonic source responsibility quantification method and system considering impedance change, and solves the problem that the calculated harmonic responsibility is inaccurate because the existing multi-harmonic source responsibility quantification method does not consider the change characteristic of impedance. By simultaneously solving for the change in the multiple harmonic transfer impedances, the quantified harmonic responsibility is more accurate and reasonable.
The application first provides a multi-harmonic source responsibility quantification method considering impedance variation, which comprises the following steps:
s1, constructing an objective function equation for simultaneously solving a plurality of variable impedances based on bus harmonic voltage data and harmonic current data of interest;
S2, solving background harmonic voltage and network harmonic impedance based on an objective function equation, constructing a weight matrix according to a solving result, obtaining a new objective function equation, updating weight parameters based on the new objective function equation, obtaining an updated objective function equation, and calculating the responsibility value of each harmonic source to the harmonic of the bus of interest based on the updated objective function equation.
By adopting the technical scheme, a plurality of objective function equations with variable impedance are constructed, background harmonic voltage and network harmonic impedance are solved through the objective function equations, a weight matrix is constructed, weight parameters are updated, responsibility values of all harmonic sources to bus harmonic concerned are solved based on the final objective function equations, and the result is more accurate and reasonable. The objective function equation considers the average transfer impedance of adjacent harmonic sources, and can be applied to a scene that a plurality of harmonic transfer impedances change simultaneously.
In one possible implementation, step S1, constructing an objective function equation for simultaneously solving a plurality of variable impedances based on the bus harmonic voltage data and the harmonic current data of interest, includes:
S11, writing a harmonic measurement equation based on a multi-harmonic source system column, and converting the equation into a matrix form;
S12, calculating average transfer impedance of adjacent M harmonic sources to replace harmonic transfer impedance in a harmonic measurement equation, so as to obtain a new harmonic measurement equation;
S13, solving a variable impedance equation based on a new harmonic measurement equation, and constructing an objective function equation for simultaneously solving a plurality of variable impedances according to the variable impedance equation;
Step S2, solving background harmonic voltage and network harmonic impedance based on an objective function equation, constructing a weight matrix according to a solving result, obtaining a new objective function equation, updating weight parameters based on the new objective function equation, obtaining an updated objective function equation, and calculating a responsibility value of each harmonic source to the harmonic of a bus of interest based on the updated objective function equation, wherein the method comprises the following steps:
s21, solving background harmonic voltage and harmonic transfer impedance based on an objective function equation;
S22, constructing weight matrixes W 1 and W 2 according to the background harmonic voltage and the harmonic transfer impedance of the step S21, substituting the weight matrixes W 1 and W 2 into an objective function equation to obtain a new objective function equation, and solving the background harmonic voltage and the harmonic transfer impedance based on the new objective function equation;
S23, updating weight parameters according to the background harmonic voltage and the harmonic transfer impedance in the step S22, bringing the updated weight parameters into a new objective function equation to obtain an updated objective function equation, and solving the background harmonic voltage and the harmonic transfer impedance based on the updated objective function equation;
S24, calculating the responsibility value of each harmonic source to the harmonic wave of the bus concerned according to the background harmonic voltage and the harmonic transfer impedance obtained in the step S23.
In one possible implementation, step S11, writing a harmonic measurement equation based on a multi-harmonic source system column and converting it into a matrix form, includes:
And writing a harmonic measurement equation based on a multi-harmonic source system:
Where V x represents the harmonic voltage of the bus of interest x; m represents the number of harmonic sources, M is more than or equal to 2; v m represents the harmonic voltage contribution of harmonic source m on bus of interest x; v 0 denotes the background harmonic voltage at the bus of interest x; z m,x represents the harmonic transfer impedance between the busbar of interest x and the harmonic source m; i m represents the harmonic current of the harmonic source m;
Converting the harmonic measurement equation into a matrix form:
vx＝Iz+v0
Where v x denotes the harmonic voltage matrix of the bus of interest x, For a matrix formed by the harmonic voltages of the attention bus x at time T 1-tN, the superscript T represents the transpose, T 1-tN represents the sample time of the harmonic data, and N represents the total number of samples; i represents a harmonic current matrix of the harmonic source, I= [ I 1 I2 … IM ] is a matrix formed by harmonic currents of harmonic sources 1-M, and I/(A diagonal matrix formed by harmonic currents of the harmonic source m at the time t 1-tN; z represents the harmonic transfer impedance vector of the harmonic source,/>Vector formed by harmonic transfer impedance of harmonic source 1-M,/>A vector formed by harmonic transfer impedance of the concerned bus x and the harmonic m at time t 1-tN; v 0 denotes the background harmonic voltage matrix,/>A matrix of background harmonic voltages at time t 1-tN.
In one possible implementation, step S12, calculating the average transferred impedance of the adjacent M harmonic sources to replace the harmonic transferred impedance in the harmonic measurement equation, to obtain a new harmonic measurement equation includes:
Calculating the average transfer impedance vector z' of adjacent M harmonic sources:
z'＝Laz
Wherein, Representing a parameter matrix,/>All elements of l are 1;
The average transfer impedance is distributed to the adjacent M harmonic sources to obtain a new impedance vector z new:
znew＝Lbz'
Wherein, Representing a parameter matrix, the new impedance vector z new being approximately the true harmonic transfer impedance vector z when N is an integer multiple of M;
Bringing the new impedance vector into a harmonic measurement equation to obtain a new harmonic measurement equation:
vx≈ILbz′+v0。
In one possible implementation manner, step S13, solving a variable impedance equation based on a new harmonic measurement equation, constructs an objective function equation for simultaneously solving a plurality of variable impedances according to the variable impedance equation, including:
And (3) solving a variable impedance equation based on the new harmonic measurement equation:
z′≈B(vx-v0)
Where z 'represents the average transfer impedance vector, z' = [ (z 1')T (z2')T … (zM')T]T is the vector of harmonic average transfer impedance between the bus of interest x and the harmonic sources 1-M, An average transfer impedance between the bus x and the harmonic source m is concerned; b represents a process matrix, b= (IL b)-1;
Constructing an objective function equation for simultaneously solving a plurality of variable impedances according to the variable impedance equation:
Wherein min </is the minimum; the 2 represents a 2-norm; ||g 1z1′||2 denotes the sum of squares of the M average transfer impedance changes; λ represents a weight parameter; QG 2v0||2/(N-1) represents the variance of v 0 variance; g 1,G2,G3, Q represents a parameter matrix.
In one possible implementation, step S21, solving the background harmonic voltage and the harmonic transfer impedance based on the objective function equation includes:
Let d=qg 2, replace λ/(N-1) with λ, and rewrite the objective function equation to:
min<||b-Av0||2+λ||Dv0||2>
wherein, b=g 1Bvx,A＝G1 B,
The objective function equation is developed, and the method comprises the following steps:
Wherein H represents a conjugate transpose, b HA(AHA+λDTD)-1AHb+bH b is a constant term ,||(AHA+λDTD)1/2v0-(AHA+λDTD)-1/2AHb||2≥0 is a positive term;
Setting positive number term in objective function equation to zero, solving background harmonic voltage And harmonic transfer impedance/>
Wherein the harmonic transfer impedanceIs an estimate of the average transfer impedance z' = [ (z 1′)T(z2′)T...(zM′)T]T).
In one possible implementation, step S22, constructing weight matrices W 1 and W 2 according to the background harmonic voltage and the harmonic transfer impedance of step S21, substituting the weight matrices W 1 and W 2 into the objective function equation to obtain a new objective function equation, and solving the background harmonic voltage and the harmonic transfer impedance based on the new objective function equation, including:
Constructing weight matrices W 1 and W 2 according to the background harmonic voltages and harmonic transfer impedances of step S21:
W1＝diag(w1),w1＝(w1,1,w1,2,...,w1,M),W2＝diag(w2),
wherein diag represents transforming a vector into a diagonal matrix; w 1 represents a vector in the weight matrix W 1; Representing column vectors in vector w 1; /(I) Representing the vector in the weight matrix W 2; [ n ] represents the nth element of the vector; r 1,m,/> Representing intermediate variables that construct a weight matrix;
Wherein, All are intermediate variables for constructing a weight matrix; max represents the maximum value of the vector; mean represents the average value of the vector,/>Estimated value of harmonic transfer impedance representing mth harmonic source,/>Representing a background harmonic voltage estimate;
substituting the weight matrices W 1 and W 2 into the objective function equation to obtain a new objective function equation:
Solving background harmonic voltage based on new objective function equation And harmonic transfer impedance/>
In one possible implementation manner, step S23, updating the weight parameter according to the background harmonic voltage and the harmonic transfer impedance of step S22, and bringing the updated weight parameter into a new objective function equation to obtain an updated objective function equation, and solving the background harmonic voltage and the harmonic transfer impedance based on the updated objective function equation, including:
The weight parameter λ is updated according to the following formula:
wherein argmin represents a function minimum; ρ represents P=10; a 1、a2 represents a process parameter; std (x) represents the standard deviation of the vector;
Substituting the obtained weight parameter lambda into a new objective function equation to obtain an updated objective function equation and solving the background harmonic voltage and the harmonic transfer impedance.
In one possible implementation, step S24 calculates a harmonic source harmonic responsibility value for the bus concerned according to the background harmonic voltage and the harmonic transfer impedance obtained in step S23, where the harmonic source harmonic responsibility value is shown by the following formula:
Wherein, Representing harmonic responsibility values of the harmonic source m concerning the bus x; /(I)A harmonic voltage of the concerned bus x at time t n is shown; /(I)Representing the harmonic voltage of harmonic source m at time t n, α is the angular difference between V m and V x.
The application also provides a multi-harmonic source responsibility quantification system considering impedance variation, which executes any one of the multi-harmonic source responsibility quantification methods considering impedance variation, and comprises the following steps:
The objective function construction module is used for constructing an objective function equation for simultaneously solving a plurality of variable impedances based on the bus harmonic voltage data and harmonic current data;
The harmonic responsibility value calculation module is used for solving background harmonic voltage and network harmonic impedance based on the objective function equation, constructing a weight matrix according to the solving result, obtaining a new objective function equation, updating weight parameters based on the new objective function equation, obtaining an updated objective function equation, and calculating the responsibility value of each harmonic source to the harmonic waves of the bus concerned based on the updated objective function equation.
Compared with the prior art, the application has the following beneficial effects: the application considers that the harmonic transfer impedance can be changed due to the maintenance of a power line, the switching of a filter, the switching of a capacitor and the fluctuation of a high-power load, and discloses a multi-harmonic source responsibility quantification method and a multi-harmonic source responsibility quantification system considering the impedance change. According to the scheme, by constructing objective function equations of multiple variable impedances, the change conditions of multiple harmonic transfer impedances can be calculated at the same time, and quantized harmonic responsibility is more accurate and reasonable. The method solves the problem that the traditional method does not consider the change characteristic of impedance, and can be applied to a scene that a plurality of harmonic transfer impedances change simultaneously.
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The accompanying drawings, which are included to provide a further understanding of embodiments of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the principles of the application. In the drawings:
FIG. 1 is a flow chart of a multi-harmonic source responsibility quantification method taking into account impedance variations according to the present invention;
FIG. 2 is a step-by-step flow chart of a multi-harmonic source responsibility quantification method taking into account impedance variations in accordance with the present invention;
FIG. 3 is a diagram of a multi-harmonic source system for a multi-harmonic source responsibility quantification method that accounts for impedance variations in accordance with the present invention;
FIG. 4 is a diagram of an IEEE13 node system of a multi-harmonic source responsibility quantification method taking into account impedance variations in accordance with the present invention;
FIG. 5 is a graph of the harmonic responsibility calculation error of a multi-harmonic source responsibility quantification method taking into account impedance variations according to the present invention;
FIG. 6 is a schematic diagram of a multi-harmonic source responsibility quantification system considering impedance variation according to the present invention.
Detailed Description
For the purpose of making apparent the objects, technical solutions and advantages of the present application, the present application will be further described in detail with reference to the following examples and the accompanying drawings, wherein the exemplary embodiments of the present application and the descriptions thereof are for illustrating the present application only and are not to be construed as limiting the present application.
A multi-harmonic source responsibility quantification method considering impedance variation of embodiment 1, please refer to fig. 1, includes:
s1, constructing an objective function equation for simultaneously solving a plurality of variable impedances based on bus harmonic voltage data and harmonic current data of interest;
S2, solving background harmonic voltage and network harmonic impedance based on an objective function equation, constructing a weight matrix according to a solving result, obtaining a new objective function equation, updating weight parameters based on the new objective function equation, obtaining an updated objective function equation, and calculating the responsibility value of each harmonic source to the harmonic of the bus of interest based on the updated objective function equation.
Compared with the prior art, the method constructs a plurality of objective function equations with variable impedance, and the objective function equations take into consideration that the harmonic transfer impedance is possibly changed due to the conditions of maintenance of a power line, switching of a filter, switching of a capacitor, fluctuation of a high-power load and the like, and construct the objective function equations based on the change quantity. The responsibility values of all harmonic sources solved based on the objective function equation to the harmonic waves of the bus concerned are more accurate and reasonable, and the method can be applied to a scene that a plurality of harmonic transfer impedances change simultaneously.
Referring to fig. 2, in one possible implementation, S1, constructing an objective function equation for simultaneously solving a plurality of variable impedances based on bus harmonic voltage data and harmonic current data of interest includes:
S11, writing a harmonic measurement equation based on a multi-harmonic source system column, and converting the equation into a matrix form;
The harmonic measurement equation is written based on the multi-harmonic source system column shown in fig. 3:
Where V x represents the harmonic voltage of the bus of interest x; m represents the number of harmonic sources, M is more than or equal to 2; v m represents the harmonic voltage contribution of harmonic source m on bus of interest x; v 0 denotes the background harmonic voltage at the bus of interest x; z m,x represents the harmonic transfer impedance between the busbar of interest x and the harmonic source m; i m represents the harmonic current of the harmonic source m;
Converting the harmonic measurement equation into a matrix form:
vx＝Iz+v0
Where v x denotes the harmonic voltage matrix of the bus of interest x, For a matrix formed by the harmonic voltages of the attention bus x at time T 1-tN, the superscript T represents the transpose, T 1-tN represents the sample time of the harmonic data, and N represents the total number of samples; i represents a harmonic current matrix of the harmonic source, I= [ I 1 I2 … IM ] is a matrix formed by harmonic currents of harmonic sources 1-M, and I/(A diagonal matrix formed by harmonic currents of the harmonic source m at the time t 1-tN; z represents the harmonic transfer impedance vector of the harmonic source,/>Vector formed by harmonic transfer impedance of harmonic source 1-M,/>A vector formed by harmonic transfer impedance of the concerned bus x and the harmonic m at time t 1-tN; v 0 denotes the background harmonic voltage matrix,/>A matrix of background harmonic voltages at time t 1-tN.
S12, calculating average transfer impedance of adjacent M harmonic sources to replace harmonic transfer impedance in a harmonic measurement equation, and obtaining a new harmonic measurement equation:
Calculating the average transfer impedance vector z' of adjacent M harmonic sources:
z'＝Laz
Wherein, Representing a parameter matrix,/>All elements of l are 1;
the average transferred impedance z' is distributed to the adjacent M harmonic sources to obtain a new impedance vector z new:
znew＝Lbz'
Wherein, Representing a parameter matrix, the new impedance vector z new being approximately the true harmonic transfer impedance vector z when N is an integer multiple of M;
Replacing the harmonic transfer impedance vector z in the harmonic measurement equation with the new impedance vector z new to obtain a new harmonic measurement equation:
vx≈ILbz′+v0。
S13, solving a variable impedance equation based on a new harmonic measurement equation, and constructing an objective function equation for simultaneously solving a plurality of variable impedances according to the variable impedance equation:
Based on the new harmonic measurement equation, the estimated transferred impedance z is converted into an average transferred impedance z' of M adjacent harmonic sources, and a variable impedance equation can be obtained:
z′≈B(vx-v0)
Where z 'represents the average transfer impedance vector, z' = [ (z 1')T (z2')T … (zM')T]T is the vector of harmonic average transfer impedance between the bus of interest x and the harmonic sources 1-M, An average transfer impedance between the bus x and the harmonic source m is concerned; b represents a process matrix, b= (IL b)-1;
Constructing an objective function equation for simultaneously solving a plurality of variable impedances according to the variable impedance equation:
Wherein min </is the minimum; the 2 represents a 2-norm; ||g 1z1′||2 denotes the sum of squares of the M average transfer impedance changes; λ represents a weight parameter; QG 2v0||2/(N-1) represents the variance of v 0 variance; g 1,G2,G3, Q represents a parameter matrix.
Referring to fig. 2, in one possible implementation, S2, solving the background harmonic voltage and the network harmonic impedance based on the objective function equation, constructing a weight matrix according to the solving result, obtaining a new objective function equation, updating the weight parameter based on the new objective function equation, obtaining an updated objective function equation, and calculating the responsibility value of each harmonic source to the bus of interest harmonic based on the updated objective function equation, including:
S21, solving background harmonic voltage and harmonic transfer impedance based on an objective function equation:
Let d=qg 2, replace λ/(N-1) with λ, and rewrite the objective function equation to:
min<||b-Av0||2+λ||Dv0||2>
wherein, b=g 1Bvx,A＝G1 B,
The objective function equation is developed, and the method comprises the following steps:
Wherein H represents a conjugate transpose, b HA(AHA+λDTD)-1AHb+bH b is a constant term ,||(AHA+λDTD)12v0-(AHA+λDTD)-12AHb||2≥0 is a positive term;
Setting the positive number term in the objective function equation to be zero, and solving the background harmonic voltage with the minimum value of the objective function And harmonic transfer impedance/>
Wherein the harmonic transfer impedanceIs an estimate of the average transfer impedance z' = [ (z 1′)T(z2′)T...(zM′)T]T;
the value of the weight parameter lambda can be determined according to the following formula:
Wherein argmin represents a function minimum; ρ represents an estimated value of harmonic transfer impedance of the mth harmonic source P=10; a 1、a2 represents a process parameter; mean (x) and std (x) represent the mean and standard deviation of the vector, respectively.
S22, constructing weight matrixes W 1 and W 2 according to the background harmonic voltage and the harmonic transfer impedance in the step S21, substituting the weight matrixes W 1 and W 2 into an objective function equation to obtain a new objective function equation, and solving the background harmonic voltage and the harmonic transfer impedance based on the new objective function equation:
Constructing weight matrices W 1 and W 2 according to the background harmonic voltages and harmonic transfer impedances of step S21:
W1＝diag(w1),w1＝(w1,1,w1,2,...,w1,M),W2＝diag(w2),
wherein diag represents transforming a vector into a diagonal matrix; w 1 represents a vector in the weight matrix W 1; Representing column vectors in vector w 1; /(I) Representing the vector in the weight matrix W 2; [ n ] represents the nth element of the vector; /(I) Representing intermediate variables that construct a weight matrix;
/>
Wherein, All are intermediate variables for constructing a weight matrix; max represents the maximum value of the vector; mean represents the average value of the vector,/>Estimated value of harmonic transfer impedance representing mth harmonic source,/>Representing a background harmonic voltage estimate;
substituting the weight matrices W 1 and W 2 into the objective function equation to obtain a new objective function equation:
min<||W1(b-Av0)||2+λ||W2Dv0||2>,
simplifying a new objective function equation and solving background harmonic voltage And harmonic transfer impedance/>
S23, updating weight parameters according to the background harmonic voltage and the harmonic transfer impedance in the step S22, bringing the updated weight parameters into a new objective function equation to obtain an updated objective function equation, and solving the background harmonic voltage and the harmonic transfer impedance based on the updated objective function equation:
Updating the weight value lambda according to the following formula, substituting the calculated weight value into a new objective function equation to obtain an updated objective function equation:
wherein argmin represents a function minimum; ρ represents P=10; a 1、a2 represents a process parameter; std (x) represents the standard deviation of the vector;
Substituting the obtained weight parameter lambda into a new objective function equation to obtain an updated objective function equation and solving the background harmonic voltage and the harmonic transfer impedance.
S24, calculating the responsibility value of each harmonic source to the harmonic wave of the bus concerned according to the background harmonic voltage and the harmonic transfer impedance obtained in the step S23:
By means of And/>Find the final harmonic transfer impedance vector/>Calculating each harmonic source harmonic responsibility based on the calculated harmonic transfer impedance:
Wherein, Representing harmonic responsibility values of the harmonic source m concerning the bus x; /(I)A harmonic voltage of the concerned bus x at time t n is shown; /(I)Representing the harmonic voltage of harmonic source m at time t n, α is the angular difference between V m and V x.
According to the method, through setting the steps and constructing an objective function equation based on the variable quantity, the responsibility of each harmonic source harmonic can be effectively solved.
To further illustrate the effects produced by this embodiment, simulations were performed based on the IEEE13 node system in fig. 4 to verify the effectiveness of the proposed method and to compare the analysis with the following methods: method 1 is covariance method, method 2 is multiple linear regression method, method 3 is independent component analysis method, and method 4 is the method of the invention. The loads of the bus bars 3, 12 and 13 in fig. 4 are harmonic source loads, named as harmonic source 1, harmonic source 2 and harmonic source 0, respectively, wherein the harmonic source 0 is a background harmonic source. To simulate the ramp and abrupt change in impedance, the capacitance value of the capacitor at bus 3 was changed as shown in table 1. According to the above arrangement, 900 sets of 7 th harmonic sample data are generated.
TABLE 1 capacitor switching conditions
Since methods 1-3 assume that the harmonic impedance is constant throughout the time interval, to reduce the impact of impedance changes on existing methods, the harmonic data is divided equally into 10 parts. By performing 50 simulations on each piece of data, an estimated error value for 7 th harmonic responsibilities is calculated, as shown in fig. 5. According to fig. 5, since the harmonic impedance is relatively constant at segments 1,2, 3, 5 and 6, the harmonic duty calculation error of methods 1,2,4 at these data segments is much smaller than at other data segments. And the harmonic impedance of the 4 th, 7 th, 8 th and 9 th sections is greatly changed, so that the errors of the methods 1 to 3 are obviously increased. In contrast, the error value of the harmonic responsibilities calculated by method 4, whether or not the impedance is constant, is less than 10%, demonstrating the superiority of the proposed method.
Referring to fig. 6, a multi-harmonic source responsibility quantification system considering impedance variation in embodiment 2 is shown, and the system includes:
The objective function construction module is used for constructing an objective function equation for simultaneously solving a plurality of variable impedances based on the bus harmonic voltage data and harmonic current data;
The harmonic responsibility value calculation module is used for solving background harmonic voltage and network harmonic impedance based on the objective function equation, constructing a weight matrix according to the solving result, obtaining a new objective function equation, updating weight parameters based on the new objective function equation, obtaining an updated objective function equation, and calculating the responsibility value of each harmonic source to the harmonic waves of the bus concerned based on the updated objective function equation.
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the invention, and is not meant to limit the scope of the invention, but to limit the invention to the particular embodiments, and any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the invention are intended to be included within the scope of the invention.

Claims (3)

1. A multi-harmonic source responsibility quantification method considering impedance variation, comprising:
s1, constructing an objective function equation for simultaneously solving a plurality of variable impedances based on bus harmonic voltage data and harmonic current data of interest;
S2, solving background harmonic voltage and network harmonic impedance based on an objective function equation, constructing a weight matrix according to a solving result, obtaining a new objective function equation, updating weight parameters based on the new objective function equation, obtaining an updated objective function equation, and calculating a responsibility value of each harmonic source to the harmonic of the bus of interest based on the updated objective function equation;
step S1, constructing an objective function equation for simultaneously solving a plurality of variable impedances based on bus harmonic voltage data and harmonic current data of interest, wherein the objective function equation comprises the following steps:
S11, writing a harmonic measurement equation based on a multi-harmonic source system column, and converting the equation into a matrix form;
S12, calculating average transfer impedance of adjacent M harmonic sources to replace harmonic transfer impedance in a harmonic measurement equation, so as to obtain a new harmonic measurement equation;
S13, solving a variable impedance equation based on a new harmonic measurement equation, and constructing an objective function equation for simultaneously solving a plurality of variable impedances according to the variable impedance equation;
Step S2, solving background harmonic voltage and network harmonic impedance based on an objective function equation, constructing a weight matrix according to a solving result, obtaining a new objective function equation, updating weight parameters based on the new objective function equation, obtaining an updated objective function equation, and calculating a responsibility value of each harmonic source to the harmonic of a bus of interest based on the updated objective function equation, wherein the method comprises the following steps:
s21, solving background harmonic voltage and harmonic transfer impedance based on an objective function equation;
S22, constructing weight matrixes W 1 and W 2 according to the background harmonic voltage and the harmonic transfer impedance of the step S21, substituting the weight matrixes W 1 and W 2 into an objective function equation to obtain a new objective function equation, and solving the background harmonic voltage and the harmonic transfer impedance based on the new objective function equation;
S23, updating weight parameters according to the background harmonic voltage and the harmonic transfer impedance in the step S22, bringing the updated weight parameters into a new objective function equation to obtain an updated objective function equation, and solving the background harmonic voltage and the harmonic transfer impedance based on the updated objective function equation;
s24, calculating the responsibility value of each harmonic source to the harmonic wave of the bus concerned according to the background harmonic voltage and the harmonic transfer impedance obtained in the step S23;
The step S11, writing a harmonic measurement equation based on a multi-harmonic source system column, and converting the equation into a matrix form, includes:
And writing a harmonic measurement equation based on a multi-harmonic source system:
Where V x represents the harmonic voltage of the bus of interest x; m represents the number of harmonic sources, M is more than or equal to 2; v m represents the harmonic voltage contribution of harmonic source m on bus of interest x; v 0 denotes the background harmonic voltage at the bus of interest x; z m,x represents the harmonic transfer impedance between the busbar of interest x and the harmonic source m; i m represents the harmonic current of the harmonic source m;
Converting the harmonic measurement equation into a matrix form:
vx＝Iz+v0
Where v x denotes the harmonic voltage matrix of the bus of interest x, For a matrix formed by the harmonic voltages of the attention bus x at time T 1-tN, the superscript T represents the transpose, T 1-tN represents the sample time of the harmonic data, and N represents the total number of samples; i represents a harmonic current matrix of the harmonic source, I= [ I 1 I2 … IM ] is a matrix formed by harmonic currents of harmonic sources 1-M, and I/(A diagonal matrix formed by harmonic currents of the harmonic source m at the time t 1-tN; z represents the harmonic transfer impedance vector of the harmonic source,/>Vector formed by harmonic transfer impedance of harmonic source 1-M,/>A vector formed by harmonic transfer impedance of the concerned bus x and the harmonic m at time t 1-tN; v 0 denotes the background harmonic voltage matrix,/>A matrix formed by the background harmonic voltages at the time t 1-tN;
Step S12, calculating the average transfer impedance of the adjacent M harmonic sources to replace the harmonic transfer impedance in the harmonic measurement equation to obtain a new harmonic measurement equation, wherein the step comprises the following steps:
Calculating the average transfer impedance vector z' of adjacent M harmonic sources:
z'＝Laz
Wherein, Representing a parameter matrix,/>All elements of l are 1;
The average transfer impedance is distributed to the adjacent M harmonic sources to obtain a new impedance vector z new:
znew＝Lbz'
Wherein, Representing a parameter matrix, the new impedance vector z new being approximately the true harmonic transfer impedance vector z when N is an integer multiple of M;
Bringing the new impedance vector into a harmonic measurement equation to obtain a new harmonic measurement equation:
vx≈ILbz′+v0；
step S13, a variable impedance equation is obtained based on a new harmonic measurement equation, an objective function equation for simultaneously solving a plurality of variable impedances is constructed according to the variable impedance equation, and the method comprises the following steps:
And (3) solving a variable impedance equation based on the new harmonic measurement equation:
z′≈B(vx-v0)
where z 'represents the average transfer impedance vector, z' = [ (z 1')T (z2')T ... (zM')T]T is the vector of harmonic average transfer impedance between the bus of interest x and the harmonic sources 1-M, An average transfer impedance between the bus x and the harmonic source m is concerned; b represents a process matrix, b= (IL b)-1;
Constructing an objective function equation for simultaneously solving a plurality of variable impedances according to the variable impedance equation:
wherein min </is the minimum; the 2 represents a 2-norm; ||gz 1′||2 denotes the sum of squares of M average transfer impedance changes; λ represents a weight parameter; QG 2v0||2/(N-1) represents the variance of v 0 variance; g 1,G2,G3, Q represents a parameter matrix;
step S21, solving background harmonic voltage and harmonic transfer impedance based on an objective function equation, wherein the step comprises the following steps:
Let d=qg 2, replace λ/(N-1) with λ, and rewrite the objective function equation to:
min<||b-Av0||2+λ||Dv0||2>
wherein, b=g 1Bvx,A＝G1 B,
The objective function equation is developed, and the method comprises the following steps:
Wherein H represents a conjugate transpose, b HA(AHA+λDTD)-1AHb+bH b is a constant term ,||(AHA+λDTD)1/2v0-(AHA+λDTD)-1/2AHb||2≥0 is a positive term;
Setting positive number term in objective function equation to zero, solving background harmonic voltage And harmonic transfer impedance/>
Wherein the harmonic transfer impedanceIs an estimate of the average transfer impedance z' = [ (z 1′)T(z2′)T ... (zM′)T]T;
Step S22, constructing weight matrixes W 1 and W 2 according to the background harmonic voltage and the harmonic transfer impedance of the step S21, substituting the weight matrixes W 1 and W 2 into an objective function equation to obtain a new objective function equation, and solving the background harmonic voltage and the harmonic transfer impedance based on the new objective function equation, wherein the method comprises the following steps:
Constructing weight matrices W 1 and W 2 according to the background harmonic voltages and harmonic transfer impedances of step S21:
W1＝diag(w1),w1＝(w1,1,w1,2,...,w1,M),W2＝diag(w2),
wherein diag represents transforming a vector into a diagonal matrix; w 1 represents a vector in the weight matrix W 1; Representing column vectors in vector w 1; /(I) Representing the vector in the weight matrix W 2; [ n ] represents the nth element of the vector; /(I) Representing intermediate variables that construct a weight matrix;
r1,m＝rz,m+rzv,r2＝rv+rvz,
Wherein, All are intermediate variables for constructing a weight matrix; max represents the maximum value of the vector; mean represents the average value of the vector,/>Estimated value of harmonic transfer impedance representing mth harmonic source,/>Representing a background harmonic voltage estimate;
substituting the weight matrices W 1 and W 2 into the objective function equation to obtain a new objective function equation:
min<||W1(b-Av0)||2+λ||W2Dv0||2>,
Solving background harmonic voltage based on new objective function equation And harmonic transfer impedance/>
Step S23, updating the weight parameters according to the background harmonic voltage and the harmonic transfer impedance of the step S22, bringing the updated weight parameters into a new objective function equation to obtain an updated objective function equation, and solving the background harmonic voltage and the harmonic transfer impedance based on the updated objective function equation, wherein the step S23 comprises the following steps:
The weight parameter λ is updated according to the following formula:
wherein argmin represents a function minimum; ρ represents P=10; a 1、a2 represents a process parameter; std (x) represents the standard deviation of the vector;
Substituting the obtained weight parameter lambda into a new objective function equation to obtain an updated objective function equation and solving the background harmonic voltage and the harmonic transfer impedance.
2. The method for quantifying multi-harmonic source responsibility taking into account impedance variation according to claim 1, wherein step S24 calculates harmonic source-to-bus-of-interest harmonic responsibility values according to the background harmonic voltage and the harmonic transfer impedance obtained in step S23, wherein each harmonic source harmonic responsibility value is represented by the following formula:
Wherein, Representing harmonic responsibility values of the harmonic source m concerning the bus x; /(I)A harmonic voltage of the concerned bus x at time t n is shown; Representing the harmonic voltage of harmonic source m at time t n, α is the angular difference between V m and V x.
3. A multi-harmonic source responsibility quantification system taking into account impedance variations, characterized in that a multi-harmonic source responsibility quantification method taking into account impedance variations as defined in any of claims 1-2 is performed comprising:
The objective function construction module is used for constructing an objective function equation for simultaneously solving a plurality of variable impedances based on the bus harmonic voltage data and harmonic current data;
The harmonic responsibility value calculation module is used for solving background harmonic voltage and network harmonic impedance based on the objective function equation, constructing a weight matrix according to the solving result, obtaining a new objective function equation, updating weight parameters based on the new objective function equation, obtaining an updated objective function equation, and calculating the responsibility value of each harmonic source to the harmonic waves of the bus concerned based on the updated objective function equation.
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