CN108268999A - For more pivot modal analysis methods of electric power networks node Harmonic characteristic analysis - Google Patents
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Abstract
The present invention provides more pivot modal analysis methods for electric power networks node Harmonic characteristic analysis, include the following steps：1st, the bus admittance matrix of electric power networks is built, feature decomposition is carried out to bus admittance matrix；2nd, the Nodal admittance equation of electric power networks is built, obtains the mode impedance of electric power networks node；3rd, it sorts to the characteristic root of mode impedance matrix, according to the number for the characteristic root that the index of cumulative proportion in ANOVA determines to retain；4th, the index of the harmonic distortion level of power grid is calculated；5th, the harmonic wave risk assessment index of electric power networks node is calculated.The present invention is on the basis of traditional modal analysis method, the number of the mode retained is determined using the index of cumulative proportion in ANOVA, avoid the harmonic wave containing the disresonance frequency in the abundant harmonic components in injection electric power networks, the condition of single mode amount in the highest flight is destroyed, and the problem of the precision of electric power networks node Harmonic characteristic analysis is caused not reach requirement.
Description
Technical field
The present invention relates to electric power networks frequency analysis fields, and in particular to for electric power networks node Harmonic characteristic analysis
More pivot modal analysis methods.
Background technology
With the popularization of power electronic equipment in electric power networks, the particularly increase of nonlinear-load, D.C. high voltage transmission
The application of technology, the harmonic problem of electric power networks become increasingly severe.Therefore, the harmonic characterisitic of system is assessed very
It is necessary.
Existing harmonic analysis method can be divided into Time Domain Analysis and frequency-domain analysis method.
Time Domain Analysis is primarily referred to as electromagnetic transient simulation, and this method does real-time analysis to electric power networks branch scape, though
Right accuracy is relatively good, but this method is higher to the parameter request of element, and time-consuming, and it is non-of overall importance to analyze.
Frequency-domain analysis method mainly includes harmonic trend program, frequency sweep method etc.；Wherein harmonic flow calculation is most base
This harmonic analysis method, this method is also to divide scene analysis to electric power networks, has of overall importance, and component parameters are required not
Height, but calculate and be related to matrix inversion, it takes longer；Frequency sweep method is fundamentally based on harmonic flow calculation, is mainly used for
The identification of electric power networks resonance point and the design of wave filter, this method need successively to sweep the input impedance of busbar into line frequency
It retouches, needs to traverse all busbares and all interested frequencies.More than each method is all there are the drawbacks of oneself, and they all can not
Degree of participation of each busbar in harmonic problem is assessed, in other words the size of each busbar influence from harmonic degree.
Modal analysis method is a kind of effective ways for analyzing electric power networks harmonic resonance characteristic, and this method is based on leading system
It receives the feature decomposition of matrix, by the relationship between the voltage of each busbar of electric power networks, electric current in mode domain " decoupling ", resonance is asked
The analysis of topic is converted into the analysis of resonance mode, compared with frequency sweep method, modal analysis method can not only identifying system resonance
Frequency, moreover it is possible to assess the degree that each busbar in electric power networks participates in harmonic resonance, resonance problems are administered with important
Meaning.
But traditional modal analysis method is directed to the resonance problems of electric power networks, i.e., when electric power networks generation is in parallel humorous
When shaking, the admittance matrixs of electric power networks carries out some characteristic root that feature decomposition obtains and levels off to zero, which is to cause
The basic reason of electric power networks resonance problems, therefore we only retain this feature root and its corresponding mode voltage and mode electricity
Stream.But into the harmonic source of electric power networks harmonic often containing abundant harmonic components, such as the excitation surge current of transformer
Deng；For the harmonic wave of the disresonance frequency, the applicable elements of traditional modal analysis method no longer meet, i.e. admittance matrix feature decomposition
It obtains no longer being that only some characteristic root levels off to zero in characteristic root, in such cases, if being continuing with traditional mode
Analytic approach does not reach requirement the precision for leading to electric power networks node Harmonic characteristic analysis.
Invention content
The purpose of the present invention is to provide more pivot modal analysis methods for electric power networks node Harmonic characteristic analysis, energy
Enough solve the problems of traditional Time Domain Analysis and frequency-domain analysis method described in background technology, additionally it is possible to solve
Traditional modal analysis method can only analyze the harmonic wave of the resonance frequency, and the problem of the harmonic wave of the disresonance frequency cannot be analyzed.
To achieve these goals, the present invention uses following technical scheme：
For more pivot modal analysis methods of electric power networks node Harmonic characteristic analysis, include the following steps：
Step 1, the bus admittance matrix that electric power networks are built according to the parameter of electric power networks node, and to node admittance square
Battle array carries out feature decomposition, obtains the feature decomposition result of bus admittance matrix；
Step 2, the Nodal admittance equation that electric power networks are formed according to the parameter of electric power networks node, by bus admittance matrix
Feature decomposition result substitute into Nodal admittance equation, obtain the mode impedance of electric power networks node；
Step 3 sorts from big to small to the characteristic root of the mode impedance matrix of electric power networks node, according to cumulative variance tribute
The index for offering rate determines the number of the characteristic root retained, that is, the number of mode amount retained；
Step 4, the voltage that each node of electric power networks is represented by the mode voltage that step 3 retains, and only injected in node j single
Position harmonic currentWhen, calculate the index of the harmonic distortion level of power grid
The horizontal evaluation index of step 5, the mains by harmonics distortion in step 4Result of calculation obtain electric power
The harmonic wave risk assessment index of network node.
The feature decomposition result of the step 1 interior joint admittance matrix is：
The bus admittance matrix for defining electric power networks is Y, according to the resolution theory of matrix it is found that bus admittance matrix Y can
In the form of being decomposed into left eigenvector matrix, characteristic root matrix and right eigenvectors matrix three product, i.e.,：
Y=LDT；
Wherein, L is left eigenvector matrix, and T is right eigenvectors matrix, and D is characterized root matrix, λ1, λ2…λnFor D's
Characteristic root.
The method that the mode impedance of electric power networks node is obtained in the step 2 is：
The Nodal admittance equation of electric power networks is：
Wherein,To inject the electric current column vector of electric power networks via node,ForUnder the action of electric power networks node
Column voltage vector；
The feature decomposition result of bus admittance matrix is substituted into above-mentioned Nodal admittance equation, is obtained：
Further, it can obtain：
DefinitionFor mode voltage,For mode electric current, D-1For mode impedance matrix, by mode voltageMode electric currentBetween relational expression be written as matrix form, i.e.,：
Wherein, λ1 -1, λ2 -1…λn -1For mode impedance matrix D-1Characteristic root, be defined as mode impedance.
Determine that the method for the number of characteristic root retained is according to the index of cumulative proportion in ANOVA in the step 3：
To n characteristic root of mode impedance matrix by being ranked sequentially from big to small, m characteristic root before reservation, the m
The proportion that the sum of characteristic root accounts for the sum of total characteristic root is cumulative proportion in ANOVA, i.e.,：
As CPV (m)>M values when 0.9 are the number of the characteristic root of the mode impedance matrix retained.
The index of the harmonic distortion level of power grid is calculated in the step 4Method be：
BecauseUnder the action of electric power networks node column voltage vectorWith mode voltageBetween meet with ShiShimonoseki
System：
It willIt is unfolded：
Assuming that only unit harmonic current is injected in node jThe then horizontal evaluation index of mains by harmonics distortionFor：
The harmonic wave risk assessment that electric power networks node is calculated in the step 5 refers to calibration method and is：
DefinitionWhat it is due to electric power networks node j injections is unit harmonic currentSo power network
The harmonic wave risk assessment index PF of network node j(j)It can be denoted as：
For the electric power networks of n nodes, the harmonic wave risk assessment index expression of each node is that matrix form is：
Beneficial effects of the present invention：
More pivot modal analysis methods of the present invention for electric power networks node Harmonic characteristic analysis are directed to power network
Harmonic characterisitic problem in network, on the basis of traditional modal analysis method, it is proposed that more pivot modal analysis methods utilize accumulation
The index of variance contribution ratio come determine retain mode number, avoid injection electric power networks in abundant harmonic components in
Harmonic wave containing the disresonance frequency, the condition of single mode amount in the highest flight is destroyed, and leads to electric power networks node harmonic wave
Not the problem of precision of specificity analysis does not reach requirement；More leading for electric power networks node Harmonic characteristic analysis of the present invention
First modal analysis method also constructs the harmonic wave degree of each busbar in characterization electric power networks using the multiple mode amounts remained
Index, us can both have been made intuitively to obtain which busbar is influenced bigger by harmonic wave, be also us to electric power networks
Harmonic wave control provides guidance.
Description of the drawings
It, below will be to specific in order to illustrate more clearly of the specific embodiment of the invention or technical solution of the prior art
Embodiment or attached drawing needed to be used in the description of the prior art are briefly described, it should be apparent that, in being described below
Attached drawing is some embodiments of the present invention, for those of ordinary skill in the art, before not making the creative labor
It puts, can also be obtained according to these attached drawings other attached drawings.
Fig. 1 is flow chart of the method for the present invention.
Specific embodiment
Technical scheme of the present invention is clearly and completely described below in conjunction with attached drawing, it is clear that described implementation
Example is part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, ordinary skill
Personnel's all other embodiments obtained without making creative work, shall fall within the protection scope of the present invention.
As shown in Figure 1：More pivot modal analysis methods of the present invention for electric power networks node Harmonic characteristic analysis,
Include the following steps：
Step 1, the bus admittance matrix that electric power networks are built according to the parameter of electric power networks node, and to node admittance square
Battle array carries out feature decomposition, obtains the feature decomposition of bus admittance matrix as a result, specific method is：
The bus admittance matrix for defining electric power networks is Y, according to the resolution theory of matrix it is found that bus admittance matrix Y can
In the form of being decomposed into left eigenvector matrix, characteristic root matrix and right eigenvectors matrix three product, i.e.,：
Y=LDT；
Wherein, L is left eigenvector matrix, and T is right eigenvectors matrix, and D is characterized root matrix, λ1, λ2…λnFor D's
Characteristic root；Since bus admittance matrix is usually symmetrical matrix, so left eigenvector matrix and right eigenvectors matrix are reciprocal, i.e.,
L=T-1。
Step 2, the Nodal admittance equation that electric power networks are formed according to the parameter of electric power networks node, by bus admittance matrix
Feature decomposition result substitute into Nodal admittance equation, obtain the mode impedance of electric power networks node, specific method is；
The Nodal admittance equation of electric power networks is：
Wherein,To inject the electric current column vector of electric power networks via node,ForUnder the action of electric power networks node
Column voltage vector；
The feature decomposition result of bus admittance matrix is substituted into above-mentioned Nodal admittance equation, is obtained：
Further, it can obtain：
DefinitionFor mode voltage,For mode electric current, D-1For mode impedance matrix, by mode voltageMode electric currentBetween relational expression be written as matrix form, i.e.,：
Wherein, λ1 -1, λ2 -1…λn -1For mode impedance matrix D-1Characteristic root, be defined as mode impedance.
Because mode impedance matrix D-1For diagonal matrix, so, mode voltageOnly with the mode electric current under corresponding modeRelated, i.e., voltage, electric current realize " decoupling " in mode domain.It is well known that for the harmonic wave of the resonance frequency, some mode
Impedance can be much larger than other mode impedances, our this mode impedance is referred to as crucial mode impedance, and other mode impedances are non-pass
Key mode impedance, we only retain crucial mode impedance, by other mode impedance zero setting.But for the humorous of the disresonance frequency
For wave, this condition no longer meets.
Step 3 sorts from big to small to the characteristic root of the mode impedance matrix of electric power networks node, according to cumulative variance tribute
The index for offering rate determines the number of the characteristic root retained, that is, the number of mode amount retained, and specific method is；
To n characteristic root λ of mode impedance matrix1 -1, λ2 -1…λn -1By being ranked sequentially from big to small, m spy before reservation
The proportion that sign the sum of root, the m characteristic root accounts for the sum of total characteristic root is cumulative proportion in ANOVA CPV (m), i.e.,：
Since the perunit value of voltage floating lower limit in electric power networks is ordinarily selected to 0.9, the present invention is by accumulation side
The critical value setting of poor contribution rate CPV (m) is 0.9, that is, is thought as cumulative proportion in ANOVA CPV (m)>When 0.9, the mode of reservation
The number m of impedance matrix characteristic root meets the requirement of precision.
After the characteristic root of mode impedance matrix that reservation is determined, while the characteristic root for retaining these mode impedances is corresponding
Mode voltage and mode electric current.
Step 4, the voltage that each node of electric power networks is represented by the mode voltage that step 3 retains, and only injected in node j single
Position harmonic currentWhen, calculate the index of the harmonic distortion level of power gridSpecific method is：
BecauseUnder the action of electric power networks node column voltage vectorWith mode voltageBetween meet with ShiShimonoseki
System：
It willIt is unfolded：
Assuming that only unit harmonic current is injected in node jThe then horizontal evaluation index of mains by harmonics distortionFor：
The horizontal evaluation index of step 5, the mains by harmonics distortion in step 4Result of calculation obtain electric power
The harmonic wave risk assessment index of network node；
DefinitionWhat it is due to electric power networks node j injections is unit harmonic currentSo power network
The harmonic wave risk assessment index PF of network node j(j)It can be denoted as：
For the electric power networks of n nodes, the harmonic wave risk assessment index expression of each node is that matrix form is：
More pivot modal analysis methods of the present invention for electric power networks node Harmonic characteristic analysis are directed to power network
Harmonic characterisitic problem in network, on the basis of traditional modal analysis method, it is proposed that more pivot modal analysis methods utilize accumulation
The index of variance contribution ratio come determine retain mode number, avoid injection electric power networks in abundant harmonic components in
Harmonic wave containing the disresonance frequency, the condition of single mode amount in the highest flight is destroyed, and leads to electric power networks node harmonic wave
Not the problem of precision of specificity analysis does not reach requirement；More leading for electric power networks node Harmonic characteristic analysis of the present invention
First modal analysis method also constructs the harmonic wave degree of each busbar in characterization electric power networks using the multiple mode amounts remained
Index, us can both have been made intuitively to obtain which busbar is influenced bigger by harmonic wave, be also us to electric power networks
Harmonic wave control provides guidance.
Finally it should be noted that：The above embodiments are only used to illustrate the technical solution of the present invention., rather than its limitations；To the greatest extent
Pipe is described in detail the present invention with reference to foregoing embodiments, it will be understood by those of ordinary skill in the art that：Its according to
Can so modify to the technical solution recorded in foregoing embodiments either to which part or all technical features into
Row equivalent replacement；And these modifications or replacement, various embodiments of the present invention technology that it does not separate the essence of the corresponding technical solution
The range of scheme.
Claims (6)
1. for more pivot modal analysis methods of electric power networks node Harmonic characteristic analysis, which is characterized in that include the following steps：
Step 1, according to the parameter of electric power networks node build electric power networks bus admittance matrix, and to bus admittance matrix into
Row feature decomposition obtains the feature decomposition result of bus admittance matrix；
Step 2, the Nodal admittance equation that electric power networks are formed according to the parameter of electric power networks node, by the spy of bus admittance matrix
It levies decomposition result and substitutes into Nodal admittance equation, obtain the mode impedance of electric power networks node；
Step 3 sorts from big to small to the characteristic root of the mode impedance matrix of electric power networks node, according to cumulative proportion in ANOVA
Index determine retain characteristic root number, that is, the number of mode amount retained；
Step 4, the voltage that each node of electric power networks is represented by the mode voltage that step 3 retains, and it is only humorous in node j injections unit
Wave electric currentWhen, calculate the index of the harmonic distortion level of power grid
The horizontal evaluation index of step 5, the mains by harmonics distortion in step 4Result of calculation obtain electric power networks
The harmonic wave risk assessment index of node.
2. more pivot modal analysis methods according to claim 1 for electric power networks node Harmonic characteristic analysis, special
Sign is：The feature decomposition result of the step 1 interior joint admittance matrix is：
The bus admittance matrix for defining electric power networks is Y, according to the resolution theory of matrix it is found that bus admittance matrix Y can divide
The form for left eigenvector matrix, characteristic root matrix and right eigenvectors matrix three product is solved, i.e.,：
Y=LDT；
Wherein, L is left eigenvector matrix, and T is right eigenvectors matrix, and D is characterized root matrix, λ1, λ2…λnFeature for D
Root.
3. more pivot modal analysis methods according to claim 1 for electric power networks node Harmonic characteristic analysis, special
Sign is：The method that the mode impedance of electric power networks node is obtained in the step 2 is：
The Nodal admittance equation of electric power networks is：
Wherein,To inject the electric current column vector of electric power networks via node,ForUnder the action of electric power networks node electricity
Press column vector；
The feature decomposition result of bus admittance matrix is substituted into above-mentioned Nodal admittance equation, is obtained：
Further, it can obtain：
DefinitionFor mode voltage,For mode electric current, D-1For mode impedance matrix, by mode voltage
Mode electric currentBetween relational expression be written as matrix form, i.e.,：
Wherein, λ1 -1, λ2 -1…λn -1For mode impedance matrix D-1Characteristic root, be defined as mode impedance.
4. more pivot modal analysis methods according to claim 1 for electric power networks node Harmonic characteristic analysis, special
Sign is：Determine that the method for the number of characteristic root retained is according to the index of cumulative proportion in ANOVA in the step 3：
To n characteristic root of mode impedance matrix by being ranked sequentially from big to small, m characteristic root before reservation, the m feature
The proportion that the sum of root accounts for the sum of total characteristic root is cumulative proportion in ANOVA, i.e.,：
As CPV (m)>M values when 0.9 are the number of the characteristic root of the mode impedance matrix retained.
5. more pivot modal analysis methods according to claim 1 for electric power networks node Harmonic characteristic analysis, special
Sign is：The index of the harmonic distortion level of power grid is calculated in the step 4Method be：
BecauseUnder the action of electric power networks node column voltage vectorWith mode voltageBetween meet following relationship：
It willIt is unfolded：
Assuming that only unit harmonic current is injected in node jThe then horizontal evaluation index of mains by harmonics distortionFor：
6. more pivot modal analysis methods according to claim 1 for electric power networks node Harmonic characteristic analysis, special
Sign is：The harmonic wave risk assessment that electric power networks node is calculated in the step 5 refers to calibration method and is：
DefinitionWhat it is due to electric power networks node j injections is unit harmonic currentSo electric power networks node
The harmonic wave risk assessment index PF of j(j)It can be denoted as：
For the electric power networks of n nodes, Ge Gejie
The harmonic wave risk assessment index expression of point is that matrix form is：
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| CN112034251A (en) * | 2020-08-28 | 2020-12-04 | 武汉大学 | Method for evaluating parallel resonance excitation capability of Nonton type inter-harmonic source access point |
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| CN112034251A (en) * | 2020-08-28 | 2020-12-04 | 武汉大学 | Method for evaluating parallel resonance excitation capability of Nonton type inter-harmonic source access point |
| CN112072662A (en) * | 2020-08-28 | 2020-12-11 | 武汉大学 | Method for avoiding inter-harmonic parallel resonance of one frequency band |
| CN112034251B (en) * | 2020-08-28 | 2021-11-23 | 武汉大学 | Method for evaluating parallel resonance excitation capability of Nonton type inter-harmonic source access point |
| CN112072662B (en) * | 2020-08-28 | 2022-02-22 | 武汉大学 | Method for avoiding inter-harmonic parallel resonance of one frequency band |
| CN112701689A (en) * | 2020-12-16 | 2021-04-23 | 深圳供电局有限公司 | Wide-area resonance evaluation and early warning method based on limited distribution points |
| CN112701689B (en) * | 2020-12-16 | 2023-01-20 | 深圳供电局有限公司 | Wide-area resonance evaluation and early warning method based on limited distribution points |
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