CN108268999B - Multi-principal-element modal analysis method for harmonic characteristic analysis of power network nodes - Google Patents
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Abstract
The invention provides a multi-principal-element modal analysis method for harmonic characteristic analysis of a power network node, which comprises the following steps: 1. constructing a node admittance matrix of the power network, and performing characteristic decomposition on the node admittance matrix; 2. constructing a node admittance equation of the power network to obtain modal impedance of the power network node; 3. sorting the characteristic roots of the modal impedance matrix, and determining the number of the reserved characteristic roots according to the index of the cumulative variance contribution rate; 4. calculating an index of a harmonic distortion level of the power grid; 5. and calculating the harmonic risk evaluation index of the power network node. According to the invention, on the basis of a traditional mode analysis method, the number of reserved modes is determined by using the index of the cumulative variance contribution rate, so that the problem that the harmonic characteristic analysis precision of the power network node cannot meet the requirement due to the fact that abundant harmonic components injected into the power network contain harmonic waves with non-resonant frequency and the condition that a single mode quantity occupies the main position is damaged is solved.
Description
Technical Field
The invention relates to the field of power network harmonic analysis, in particular to a multi-principal-element modal analysis method for power network node harmonic characteristic analysis.
Background
With the popularization of power electronic equipment in a power network and the increase of nonlinear loads, particularly the application of a high-voltage direct-current transmission technology, the harmonic problem of the power network becomes more and more serious. Therefore, it is necessary to evaluate the harmonic characteristics of the system.
Existing harmonic analysis methods can be classified into time domain analysis methods and frequency domain analysis methods.
The time domain analysis method mainly refers to electromagnetic transient simulation, the method carries out real-time analysis on power network sub-scenes, although the accuracy is good, the method has high requirements on parameters of elements and long time consumption, and the analysis is non-global.
The frequency domain analysis method mainly comprises a harmonic tide program, a frequency scanning method and the like; the harmonic current calculation is the most basic harmonic analysis method, the method is also used for analyzing the power network in different scenes, the method has globality and low requirements on element parameters, but the calculation involves matrix inversion and consumes long time; the frequency scanning method is essentially based on harmonic load flow calculation and is mainly used for identification of a resonance point of a power network and design of a filter. All the above methods have their own disadvantages, and they cannot evaluate the participation degree of each bus in the harmonic problem, or the degree of the harmonic influence on each bus.
The modal analysis method is an effective method for analyzing harmonic resonance characteristics of the power network, and is based on characteristic decomposition of a system admittance matrix, the relation between voltage and current of each bus of the power network is decoupled in a modal domain, analysis of resonance problems is converted into analysis of resonance modes, and compared with a frequency scanning method, the modal analysis method not only can identify the resonance frequency of the system, but also can evaluate the degree of participation of each bus in harmonic resonance in the power network, and has important significance for resonance problem treatment.
However, the conventional modal analysis method aims at the resonance problem of the power network, that is, when the power network generates parallel resonance, a certain characteristic root obtained by performing characteristic decomposition on an admittance matrix of the power network approaches to zero, and the zero characteristic root is a root cause of the resonance problem of the power network, so that only the characteristic root and a modal voltage and a modal current corresponding to the characteristic root are reserved. However, harmonic sources injecting harmonics into the power network often contain rich harmonic components, such as magnetizing inrush current of a transformer; for the harmonic wave of the non-resonant frequency, the application condition of the traditional modal analysis method is not satisfied any more, that is, only one characteristic root in the characteristic roots obtained by the characteristic decomposition of the admittance matrix approaches to zero, under the condition, if the traditional modal analysis method is continuously used, the accuracy of the harmonic wave characteristic analysis of the power network node cannot meet the requirement.
Disclosure of Invention
The invention aims to provide a multi-principal-element modal analysis method for analyzing harmonic characteristics of a power network node, which can solve the problems of the traditional time domain analysis method and the traditional frequency domain analysis method in the background art and can also solve the problem that the traditional modal analysis method can only analyze harmonic waves of resonant frequencies but can not analyze harmonic waves of non-resonant frequencies.
In order to achieve the purpose, the invention adopts the following technical scheme:
a multi-principal-element modal analysis method for harmonic characteristic analysis of power network nodes comprises the following steps:
step 1, constructing a node admittance matrix of the power network according to parameters of nodes of the power network, and performing characteristic decomposition on the node admittance matrix to obtain a characteristic decomposition result of the node admittance matrix;
step 2, forming a node admittance equation of the power network according to parameters of the power network nodes, and substituting a characteristic decomposition result of the node admittance matrix into the node admittance equation to obtain modal impedance of the power network nodes;
step 3, sorting the characteristic roots of the modal impedance matrix of the power network nodes from large to small, and determining the number of the reserved characteristic roots, namely the number of reserved modal quantities according to the index of the cumulative variance contribution rate;
step 4, representing the voltage of each node of the power network by the mode voltage reserved in the step 3, and injecting unit harmonic current only in the node j
Calculating an indicator of a harmonic distortion level of the power grid
Step 5, evaluating indexes according to power grid harmonic distortion levels in step four
And obtaining the harmonic risk evaluation index of the power network node according to the calculation result.
The characteristic decomposition result of the node admittance matrix in the step 1 is as follows:
defining a node admittance matrix of the power network as Y, wherein the node admittance matrix Y can be decomposed into a product form of a left eigenvector matrix, a feature root matrix and a right eigenvector matrix according to a matrix decomposition theory, namely:
Y＝LDT；
where L is the left eigenvector matrix, T is the right eigenvector matrix, D is the radix matrix, λ1，λ2…λnIs the characteristic root of D.
The method for obtaining the modal impedance of the power network node in the step 2 comprises the following steps:
the node admittance equation of the power network is:
wherein the content of the first and second substances,
for a current column vector injected into the power network via a node,
is at the same time
Voltage column vectors of the power network nodes under the action of (1);
substituting the characteristic decomposition result of the node admittance matrix into the node admittance equation to obtain:
further, it is possible to obtain:
definition of
In the form of a modal voltage,
is a modal current, D-1As a modal impedance matrix, applying a modal voltage
Modal current
The relation between them is written in matrix form, i.e.:
wherein λ is1 -1，λ2 -1…λn -1Is a modal impedance matrix D-1Is defined as the modal impedance.
The method for determining the number of the reserved feature roots according to the index of the cumulative variance contribution rate in the step 3 comprises the following steps:
arranging n characteristic roots of the modal impedance matrix from big to small, reserving the first m characteristic roots, wherein the proportion of the sum of the m characteristic roots in the sum of the total characteristic roots is the cumulative variance contribution rate, namely:
the value of m when cpv (m) >0.9 is the number of characteristic roots of the reserved modal impedance matrix.
Calculating the index of harmonic distortion level of the power grid in the step 4
The method comprises the following steps:
because of the fact that
Voltage column vector of power network node under action of
And modal voltage
Satisfies the following relationship:
will be provided with
Unfolding to obtain:
suppose that unity harmonic current is injected only at node j
Evaluation index of harmonic distortion level of power grid
Comprises the following steps:
the method for calculating the harmonic risk assessment index of the power network node in the step 5 comprises the following steps:
definition of
Since the power network node j injects unit harmonic current
So harmonics of power network node jRisk assessment index PF(j)Can be written as:
for an n-node power network, the harmonic risk assessment indexes of each node are expressed in a matrix form as follows:
the invention has the beneficial effects that:
aiming at the problem of harmonic characteristics in the power network, the multi-principal-element modal analysis method for analyzing the harmonic characteristics of the power network nodes is provided on the basis of the traditional modal analysis method, the number of reserved modes is determined by utilizing indexes of accumulated variance contribution rate, and the problem that the harmonic characteristics of the power network nodes cannot meet the requirement due to the fact that abundant harmonic components injected into the power network contain harmonic waves with non-resonant frequency and the condition that single modal quantity occupies the main position is damaged is avoided; the multi-principal-element modal analysis method for harmonic characteristic analysis of the power network nodes also constructs indexes representing the harmonic degree of each bus in the power network by utilizing the reserved multiple modal quantities, so that the influence of harmonic on which bus is obtained visually is larger, and guidance is provided for harmonic treatment of the power network.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1: the invention relates to a multi-principal-element modal analysis method for harmonic characteristic analysis of power network nodes, which comprises the following steps:
step 1, constructing a node admittance matrix of the power network according to parameters of nodes of the power network, and performing characteristic decomposition on the node admittance matrix to obtain a characteristic decomposition result of the node admittance matrix, wherein the specific method comprises the following steps:
defining a node admittance matrix of the power network as Y, wherein the node admittance matrix Y can be decomposed into a product form of a left eigenvector matrix, a feature root matrix and a right eigenvector matrix according to a matrix decomposition theory, namely:
Y＝LDT；
where L is the left eigenvector matrix, T is the right eigenvector matrix, D is the radix matrix, λ1，λ2…λnIs the characteristic root of D; since the node admittance matrix is usually a symmetric matrix, the left eigenvector matrix and the right eigenvector matrix are reciprocal, i.e., L ═ T-1。
Step 2, forming a node admittance equation of the power network according to parameters of the power network nodes, substituting characteristic decomposition results of the node admittance matrix into the node admittance equation to obtain modal impedance of the power network nodes, wherein the specific method comprises the following steps of;
the node admittance equation of the power network is:
wherein the content of the first and second substances,
for a current column vector injected into the power network via a node,
is at the same time
Voltage column vectors of the power network nodes under the action of (1);
substituting the characteristic decomposition result of the node admittance matrix into the node admittance equation to obtain:
further, it is possible to obtain:
definition of
In the form of a modal voltage,
is a modal current, D-1As a modal impedance matrix, applying a modal voltage
Modal current
The relation between them is written in matrix form, i.e.:
wherein λ is1 -1，λ2 -1…λn -1Is a modal impedance matrix D-1Is characterized byRoot, defined as the modal impedance.
Because of the modal impedance matrix D-1Is a diagonal matrix, so the modal voltage
Corresponding to modal current only
The voltage and the current realize the decoupling in the mode domain. As is known, for harmonics of the resonant frequency, one modal impedance is much larger than other modal impedances, which is called as a critical modal impedance, and the other modal impedances are non-critical modal impedances, and we only reserve the critical modal impedance and set the other modal impedances to zero. But for harmonics of non-resonant frequencies this condition is no longer satisfied.
Step 3, sorting the characteristic roots of the modal impedance matrix of the power network nodes from large to small, and determining the number of the reserved characteristic roots, namely the number of reserved modal quantities according to the index of the cumulative variance contribution rate, wherein the specific method is as follows;
for n characteristic roots lambda of modal impedance matrix1 -1，λ2 -1…λn -1Arranging the characteristic roots in the order from big to small, reserving the first m characteristic roots, wherein the proportion of the sum of the m characteristic roots in the sum of the total characteristic roots is the accumulated variance contribution rate CPV (m), namely:
since the per unit value of the voltage fluctuation lower limit in the power network is usually selected to be 0.9, the present invention sets the critical value of the cumulative variance contribution rate cpv (m) to 0.9, i.e., it is considered that the number m of characteristic roots of the modal impedance matrix that is retained satisfies the requirement of accuracy when the cumulative variance contribution rate cpv (m) > 0.9.
After the characteristic roots of the reserved modal impedance matrix are determined, the modal voltages and modal currents corresponding to the characteristic roots of the modal impedances are reserved at the same time.
Step 4, representing the voltage of each node of the power network by the mode voltage reserved in the step 3, and injecting unit harmonic current only in the node j
Calculating an indicator of a harmonic distortion level of the power grid
The specific method comprises the following steps:
because of the fact that
Voltage column vector of power network node under action of
And modal voltage
Satisfies the following relationship:
will be provided with
Unfolding to obtain:
suppose that unity harmonic current is injected only at node j
Evaluation index of harmonic distortion level of power grid
Comprises the following steps:
step 5, evaluating indexes according to power grid harmonic distortion levels in step four
Obtaining harmonic risk evaluation indexes of the power network nodes according to the calculation result;
definition of
Since the power network node j injects unit harmonic current
Harmonic risk assessment index PF of power network node j(j)Can be written as:
for an n-node power network, the harmonic risk assessment indexes of each node are expressed in a matrix form as follows:
aiming at the problem of harmonic characteristics in the power network, the multi-principal-element modal analysis method for analyzing the harmonic characteristics of the power network nodes is provided on the basis of the traditional modal analysis method, the number of reserved modes is determined by utilizing indexes of accumulated variance contribution rate, and the problem that the harmonic characteristics of the power network nodes cannot meet the requirement due to the fact that abundant harmonic components injected into the power network contain harmonic waves with non-resonant frequency and the condition that single modal quantity occupies the main position is damaged is avoided; the multi-principal-element modal analysis method for harmonic characteristic analysis of the power network nodes also constructs indexes representing the harmonic degree of each bus in the power network by utilizing the reserved multiple modal quantities, so that the influence of harmonic on which bus is obtained visually is larger, and guidance is provided for harmonic treatment of the power network.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (1)
1. The multi-principal-element modal analysis method for harmonic characteristic analysis of the power network nodes is characterized by comprising the following steps of:
step 1, constructing a node admittance matrix of the power network according to parameters of nodes of the power network, and performing characteristic decomposition on the node admittance matrix to obtain a characteristic decomposition result of the node admittance matrix;
specifically, a node admittance matrix of the power network is defined as Y, and according to a decomposition theory of the matrix, the node admittance matrix Y can be decomposed into a form of a product of a left eigenvector matrix, a feature root matrix, and a right eigenvector matrix, that is:
Y＝LDT；
where L is the left eigenvector matrix, T is the right eigenvector matrix, D is the radix matrix, λ1，λ2…λnIs the characteristic root of D;
step 2, forming a node admittance equation of the power network according to parameters of the power network nodes, and substituting a characteristic decomposition result of the node admittance matrix into the node admittance equation to obtain modal impedance of the power network nodes;
specifically, the node admittance equation of the power network is:
wherein the content of the first and second substances,
for a current column vector injected into the power network via a node,
is at the same time
Voltage column vectors of the power network nodes under the action of (1);
substituting the characteristic decomposition result of the node admittance matrix into the node admittance equation to obtain:
further, it is possible to obtain:
definition of
In the form of a modal voltage,
is a modal current, D-1As a modal impedance matrix, applying a modal voltage
Modal current
The relation between them is written in matrix form, i.e.:
wherein λ is1 -1，λ2 -1…λn -1Is a modal impedance matrix D-1Is defined as the modal impedance;
step 3, sorting the characteristic roots of the modal impedance matrix of the power network nodes from large to small, and determining the number of the reserved characteristic roots, namely the number of reserved modal quantities according to the index of the cumulative variance contribution rate;
specifically, n characteristic roots of the modal impedance matrix are arranged in a descending order, the first m characteristic roots are reserved, and the proportion of the sum of the m characteristic roots in the sum of the total characteristic roots is the cumulative variance contribution rate, namely:
when CPV (m) is more than 0.9, the m value is the number of characteristic roots of the reserved modal impedance matrix;
step 4, representing the voltage of each node of the power network by the mode voltage reserved in the step 3, and injecting unit harmonic current only in the node j
Calculating an indicator of a harmonic distortion level of the power grid
In particular, because of
Voltage column vector of power network node under action of
And modal voltage
Satisfies the following relationship:
will be provided with
Unfolding to obtain:
suppose that unity harmonic current is injected only at node j
Evaluation index of harmonic distortion level of power grid
Comprises the following steps:
step 5, evaluating indexes according to power grid harmonic distortion levels in step four
Obtaining harmonic risk evaluation indexes of the power network nodes according to the calculation result;
in particular, define
Since the power network node j injects unit harmonic current
Harmonic risk assessment index PF of power network node j(j)Can be written as:
for an n-node power network, the harmonic risk assessment indexes of each node are expressed in a matrix form as follows:
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