CN112034251B - Method for evaluating parallel resonance excitation capability of Nonton type inter-harmonic source access point - Google Patents
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Abstract
The invention provides a method for evaluating the parallel resonance excitation capability of a Noton inter-harmonic source access point, which comprises the following steps of: step 1, establishing a fundamental frequency node admittance matrix of a power distribution network; step 2, correcting a fundamental frequency node admittance matrix of the power distribution network; step 3, solving a modified power distribution network fundamental frequency node impedance matrix; step 4, solving the parallel resonance frequency and the resonance mode impedance; step 5, obtaining node excitation parallel resonance capability evaluation impedance; and 6, evaluating the node excitation parallel resonance capability according to the amplitude of the node excitation parallel resonance capability evaluation impedance. The method for evaluating the parallel resonance excitation capacity of the inter-Norton harmonic source access point is built under the condition that the node impedance matrix needs to be corrected when the inter-Norton harmonic source is accessed to different positions of the power distribution network.
Description
Technical Field
The invention relates to the field of electric power, in particular to a method for evaluating parallel resonance excitation capability of a Nonton type inter-harmonic source access point.
Background
Inter-harmonics refer to signals present in the voltage or current signal at frequencies between the harmonic frequencies and not integral multiples of the fundamental frequency. The source of the inter-harmonic wave in the power grid is wide, and the fluctuating nonlinear loads such as power electronic devices and industrial arc furnaces can emit the inter-harmonic wave.
Since the power grid contains both inductive and capacitive elements, the power distribution network is susceptible to parallel resonance at inter-harmonic frequencies. When parallel resonance occurs, inter-harmonic current flowing through high impedance causes inter-harmonic voltage at the same frequency at some nodes to be high. When the parallel resonance causes the inter-harmonic voltage to be abnormally amplified, the power quality at some locations in the network will be significantly deteriorated.
When the inter-harmonic source is connected to the power distribution network, no access point of any inter-harmonic source can cause serious parallel resonance problem, and the problem of parallel resonance can be effectively avoided by connecting the inter-harmonic source to a node with weak excitation parallel resonance capability.
At present, a modal analysis method is a method capable of evaluating the capability of an inter-harmonic source access point for exciting parallel resonance. The method effectively judges the capability of each node of the network to excite the parallel resonance of the harmonic source access point through the amplitude of the resonance mode right eigenvector element corresponding to the node of the power distribution network. However, this method has been practiced only under the condition that the source of the inter-harmonics is an ideal current source.
When an ideal current source is taken as a harmonic source, the node impedance matrix at each frequency does not change along with the harmonic source access point. However, when a norton type inter-harmonic source is connected to the power distribution network, the node impedance matrix at each frequency changes depending on the position where the inter-harmonic source is connected.
Because the node impedance matrix of each frequency changes along with the harmonic source access position, each harmonic source access point corresponds to different parallel resonance frequencies, resonance mode impedance and resonance mode right eigenvector elements. Under the conditions, the original mode analysis method needs to be improved appropriately, and a new method is proposed to evaluate the parallel resonance exciting capability of the Noton interharmonic source access point.
Disclosure of Invention
Aiming at the problem that the original modal analysis method can not evaluate the parallel resonance exciting capability of the Noton interharmonic source access point, the invention improves the original modal analysis method and provides a novel method for evaluating the parallel resonance exciting capability of the Noton interharmonic source access point, and the invention adopts the following technical scheme to realize the following steps: which comprises the following steps:
Establishing a power distribution network fundamental frequency node admittance matrix Y by adopting the prior art according to the structure of the power distribution network and the fundamental frequency branch parameters; the number of the nodes of the power distribution network is n, so that the fundamental frequency node admittance matrix Y of the power distribution network is n x n matrix;
Defaults that only one Norton inter-harmonic source is connected into the power distribution network, and the fundamental frequency impedance of parallel branches of the Norton inter-harmonic sources is set to be ZLTaking the power distribution network node i as the inter-harmonic source access position to obtain a modified power distribution network fundamental frequency node admittance matrix YL(ii) a Because there are n distribution network nodes, there are n different modified distribution network fundamental frequency node admittance matrixes YL；
When the Nonton type inter-harmonic source uses a power distribution network node i as an inter-harmonic source access position, carrying out inversion operation on the modified power distribution network fundamental frequency node admittance matrix to obtain a power distribution network fundamental frequency node impedance matrix Z; because there are n different modified fundamental frequency node admittance matrixes Y of the distribution networkLTherefore, n corresponding distribution network fundamental frequency node impedance matrixes Z exist;
The method comprises the steps of taking a fundamental frequency node impedance matrix Z of the power distribution network as a reference, obtaining node impedance matrixes of the power distribution network under different frequencies through a frequency scanning method, carrying out diagonalization decomposition on the node impedance matrixes of the power distribution network under different frequencies to obtain a modal impedance matrix, a left eigenvector matrix and a right eigenvector matrix, obtaining a critical mode modal impedance amplitude-frequency characteristic curve according to the amplitude of the modal impedance of each frequency critical mode, determining the parallel resonance frequency as f, and determining the resonance modal impedance as lambdakk(fmax)And the resonance mode is k; sequentially obtaining parallel resonance frequency, resonance mode impedance and resonance mode for n distribution network fundamental frequency node impedance matrixes Z;
When a norton inter-harmonic source takes a power distribution network node i as an inter-harmonic source access position, the resonant mode voltage phasor can be expressed as:
wherein,
representing the modal voltage phasor when the parallel resonance frequency is f and the resonance mode is k;
representing the modal current phasor when the parallel resonance frequency is f and the resonance mode is k; lambda [ alpha ]kk(fmax)Represents the resonant mode impedance, R, when the parallel resonant frequency is f and the resonant mode is kki(f)When the parallel resonance frequency is f and the resonance mode is k, the coordinate ki element in the right eigenvector matrix,
representing the inter-harmonic current phasor injected into the network at a node i when the parallel resonance frequency is f and the resonance mode is k;
evaluation of impedance lambda using node-excited parallel resonance capability is determined according to equation (11)kk(fmax)Rki(f)Evaluating the capability of the node to excite the parallel resonance, and calculating the evaluation impedance lambda of the node excitation parallel resonance capability of each node in the power distribution networkkk(fmax)Rki(f)；
Calculating to obtain node excitation parallel resonance capability evaluation impedance according to the step 5, wherein the larger the amplitude of the node excitation parallel resonance capability evaluation impedance is, the stronger the node excitation parallel resonance capability is; the smaller the magnitude of the node-excited parallel resonance capability evaluation impedance, the weaker the node-excited parallel resonance capability.
Preferably, the fundamental frequency node admittance matrix Y of the power distribution network in the step 1 is specifically:
wherein Y is a distribution network fundamental frequency node admittance matrix, n is the number of distribution network nodes, and Y is used for each rowijThe current injected by the node i into the grid when the unit voltage is added to the node j and other nodes are grounded is equal in value, wherein i is 1, 2. j is 1, 2.
Preferably, the modified fundamental frequency node admittance matrix Y of the power distribution network in the step 2LThe method specifically comprises the following steps:
wherein i is an access node label of a Nonton type interharmonic source in the power distribution network, and ZLThe impedance of the fundamental frequency of the parallel branch of the Nonton type interharmonic source.
Preferably, the power distribution network fundamental frequency node impedance matrix Z in step 3 specifically is:
and Z represents a power distribution network fundamental frequency node impedance matrix taking a power distribution network node i as a Norton inter-harmonic source access position.
Preferably, in the step 4, diagonalization decomposition is performed on the node impedance matrix of the power distribution network at different frequencies to obtain a modal impedance matrix, a left eigenvector matrix and a right eigenvector matrix, an amplitude-frequency characteristic curve of the modal impedance of the key mode is obtained according to the amplitude of the modal impedance of the key mode of each frequency, and it is determined that the parallel resonance frequency is f and the resonance modal impedance is λkk(fmax)And the resonance mode is k, specifically:
wherein Z is(h)A node impedance matrix, λ, representing the frequency h obtained by frequency scanning(h)Is a modal impedance matrix, L(h)Is a left eigenvector matrix, R(h)As a matrix of right eigenvectors, a matrix of modal impedances λ(h)For the feature root diagonal matrix, the left eigenvector matrix L(h)And the right eigenvector matrix R(h)Is in a reciprocal relationship;
modal impedance matrix lambda(h)The middle diagonal element is modal impedance, a mode with the maximum modal impedance amplitude is selected as a key mode in the modal impedance matrix, and a key mode modal impedance amplitude-frequency characteristic curve is obtained according to the amplitude of the modal impedance of each frequency key mode;
the parallel resonance frequency f is the frequency at the peak of the amplitude-frequency characteristic curve of the key mode modal impedance, and the key mode modal impedance corresponding to the parallel resonance frequency f is the resonance modal impedance lambdakk(fmax)，λkk(fmax)Is a modal impedance matrix lambda with a parallel resonance frequency f(f)The element with the largest modal impedance amplitude is determined according to the resonant modal impedance lambdakk(fmax)The resonance mode corresponding to the parallel resonance frequency f is referred to as a resonance mode k.
Preferably, the specific steps for obtaining formula (11) in step 5 are as follows:
according to the prior art, when a norton type inter-harmonic source uses a node i of a power distribution network as an inter-harmonic source access position, a relational expression of a node voltage vector and a node injection current vector is known, and then a decomposition expression of a node impedance matrix is substituted to obtain the following relational expression:
wherein Z is(h)Representing the node impedance matrix at frequency h of the distribution network,
represents the node voltage vector at frequency h,
representing the node injected current vector, λ, at frequency h(h)Representing the modal impedance matrix at frequency h, L(h)And R(h)Respectively representing a left eigenvector matrix and a right eigenvector matrix at a frequency h;
the right eigenvector matrix is multiplied by the left side of the equal sign of the above equation, and the relation (5) between the node voltage vector and the node injection current vector can be further rewritten as:
then, define
Is a modal voltage vector
Is a modal current vector
Obtaining a relation (7) of the modal voltage vector and the modal current vector as follows:
according to the step 4, when the parallel resonance frequency is f and the resonance mode is k, the relational expression (7) of the modal voltage phasor and the modal current phasor is embodied as follows:
wherein,
representing the modal voltage phasor when the parallel resonance frequency is f and the resonance mode is k;
representing the modal current phasor when the parallel resonance frequency is f and the resonance mode is k; lambda [ alpha ]kk(fmax)Representing the impedance of the resonance mode when the parallel resonance frequency is f and the resonance mode is k;
when the parallel resonance frequency is f and the resonance mode is k, the modal current phasor can be expressed as:
wherein,
represents the modal current phasor R when the parallel resonance frequency is f and the resonance mode is kkj(f)The parallel resonance frequency is f, the resonance mode is k, and the coordinate kj element R in the right eigenvector matrix iskj(f)Capable of reflecting inter-harmonic current injected into network at node j versus resonant mode currentDegree of contribution, j ═ 1,2, …, n;
representing the inter-harmonic current phasor injected into the network by the node j at the parallel resonant frequency f;
according to the formulas (8) and (9), the relation between the resonant mode voltage phasor and the resonant mode current phasor is obtained as follows:
at this time, only the norton-type inter-harmonic source is connected to the node i, and the resonant mode voltage phasor of equation (10) can be expressed as equation (11).
Compared with the prior art, the invention has the following beneficial effects:
the method for evaluating the excitation parallel resonance capability of the Nonton inter-harmonic source access point is established under the condition that node impedance matrixes need to be corrected at different positions of the Nonton inter-harmonic source access distribution network, and a theoretical basis is provided for selecting the inter-harmonic source access point for avoiding the parallel resonance problem.
Drawings
FIG. 1 is a schematic diagram of a Nonton type inter-harmonic source provided by the present invention;
FIG. 2 is a flow chart of the present invention for evaluating the ability of an access point to excite parallel resonance in a Nonton inter-harmonic source;
FIG. 3 is a block diagram of an exemplary power distribution network provided by the present invention;
fig. 4 is a graph of amplitude-frequency characteristics of modal impedance in a critical mode when node No. 15 in an exemplary power distribution network is a inter-harmonic source access point; and
fig. 5 is a diagram illustrating an impedance magnitude distribution for evaluating the ability of each node to excite parallel resonance in an exemplary power distribution network according to the present invention.
Detailed Description
Exemplary embodiments, features and aspects of the present invention will be described in detail below with reference to the accompanying drawings. In the drawings, like reference numbers can indicate functionally identical or similar elements. While the various aspects of the embodiments are presented in drawings, the drawings are not necessarily drawn to scale unless specifically indicated.
A schematic diagram of a norton interharmonic source accessing a power distribution network is shown in fig. 1.
The invention provides a method for evaluating the parallel resonance excitation capability of a Noton inter-harmonic source access point, which comprises the following steps as shown in figure 2:
The condition that a Norton inter-harmonic source is accessed into the power distribution network is not considered, a power distribution network fundamental frequency node admittance matrix can be established by adopting the prior art according to the structure and fundamental frequency branch parameters of the power distribution network, so that the power distribution network fundamental frequency node admittance matrix Y is as follows:
wherein Y is a distribution network fundamental frequency node admittance matrix, n is the number of distribution network nodes (excluding system power supply access points), and for each column YijThe current injected by the node i into the grid when the unit voltage is added to the node j and other nodes are grounded is equal in value, wherein i is 1, 2. j is 1, 2.
When a norton inter-harmonic source is considered to be connected into a power distribution network, the norton inter-harmonic source contains internal impedance, so that a power distribution network fundamental frequency node admittance matrix needs to be corrected according to the access position of the norton inter-harmonic source and the fundamental frequency impedance parameters of parallel branches of the norton inter-harmonic source. Because the Norton type inter-harmonic source access power distribution network is only provided with one impedance branch between the inter-harmonic source access position and the ground, the fundamental frequency admittance matrix of the power distribution network only needs to correct the self impedance of the inter-harmonic source access position.
Only one Nonton inter-harmonic source is connected into the power distribution network by default, and the Nonton inter-harmonic source is assumed andthe fundamental frequency impedance of the branch is ZLTaking the power distribution network node i as the inter-harmonic source access position as an example, obtaining the modified power distribution network fundamental frequency node admittance matrix YLComprises the following steps:
and correcting the node admittance matrix according to the access position of the Nonton type inter-harmonic source to obtain a corrected distribution network fundamental frequency node admittance matrix corresponding to the access position of the inter-harmonic source. Because there are n distribution network nodes, there are n different modified distribution network fundamental frequency node admittance matrixes YL。
When the power distribution network node i is used as a harmonic source access position for a Norton type harmonic source, inverse operation is carried out on the modified power distribution network fundamental frequency node admittance matrix, and the power distribution network fundamental frequency node impedance matrix Z is obtained as follows:
and the distribution network fundamental frequency node impedance matrix Z represents a distribution network fundamental frequency node impedance matrix taking a distribution network node i as a Norton inter-harmonic source access position.
Because there are n different modified fundamental frequency node admittance matrixes Y of the distribution networkLTherefore, there are n corresponding distribution network fundamental frequency node impedance matrixes Z.
By taking the fundamental frequency node impedance matrix Z of the power distribution network as a reference, the node impedance matrix under different frequencies of the power distribution network can be obtained by a frequency scanning method, and the node impedance matrix Z(h)A nodal impedance matrix representing the frequency h obtained by the frequency sweep. Then carrying out diagonalization decomposition on the node impedance matrix of the power distribution network under different frequencies to obtain a modal impedance matrix, a left eigenvector matrix and a right eigenvector matrixAnd (5) arraying. In particular, for the node impedance matrix Z(h)Carrying out diagonalization decomposition to obtain a modal impedance matrix lambda(h)Left eigenvector matrix L(h)And a right eigenvector matrix R(h)。
According to the definition of linear algebra, the modal impedance matrix lambda(h)For characteristic root diagonal matrices, i.e. modal impedance matrices lambda(h)Is a matrix with the diagonal as an eigenvalue and the other elements as 0; left eigenvector matrix L(h)Is a feature vector matrix; and left eigenvector matrix L(h)And the right eigenvector matrix R(h)The relationship between them is shown in formula (4) as reciprocal relationship:
the diagonal elements in the modal impedance matrix are defined as modal impedances, the mode with the largest modal impedance amplitude is selected as a key mode modal impedance in the same frequency, namely the same modal impedance matrix, and the mode corresponding to the key mode modal impedance is defined as a key mode.
For each power distribution network node, according to the amplitude of each frequency key mode modal impedance, an amplitude-frequency characteristic curve of the key mode modal impedance corresponding to each inter-harmonic source access point condition can be drawn, wherein the frequency of the amplitude-frequency characteristic curve is taken as an X axis, and the amplitude of the modal impedance is taken as a Y axis. And taking the frequency at the peak of the amplitude-frequency characteristic curve of the modal impedance of the key mode as the parallel resonance frequency f. Meanwhile, a key mode corresponding to the parallel resonance frequency f is defined as a resonance mode, and a key mode modal impedance corresponding to the parallel resonance frequency f is defined as a resonance modal impedance lambdakk(fmax)，λkk(fmax)Is a modal impedance matrix lambda with a parallel resonance frequency f(f)The element with the largest modal impedance amplitude is determined according to the resonant modal impedance lambdakk(fmax)The resonance mode corresponding to the parallel resonance frequency f is referred to as a resonance mode k. Namely, when the node i of the power distribution network is the Nonton type inter-harmonic source access position, the parallel resonance frequency of the power distribution network is f, and the resonance modal impedance is lambdakk(fmax)The resonance mode is k.
As can be seen from the above description, when a norton inter-harmonic source is connected to a power distribution network, a node admittance matrix of the power distribution network needs to be modified according to an inter-harmonic source access point, a node impedance matrix of the power distribution network changes, and different inter-harmonic source access positions correspond to different parallel resonance frequencies and resonance modal impedances of the power distribution network. If n distribution network nodes exist, the distribution network has n inter-harmonic source access positions, n inter-harmonic source access conditions need to be considered in the process of solving the parallel resonance frequency and the resonance modal impedance, and then the parallel resonance frequency and the resonance modal impedance corresponding to each inter-harmonic source access position are sequentially obtained according to the amplitude-frequency characteristic curve of the n key mode modal impedances.
According to the prior art, when a norton type inter-harmonic source uses a node i of a power distribution network as an inter-harmonic source access position, a decomposition expression of a node impedance matrix is substituted into a relational expression of a node voltage vector and a node injection current vector, and the relational expression can be written as follows:
wherein Z is(h)Representing the node impedance matrix at frequency h of the distribution network,
represents the node voltage vector at frequency h,
representing the node injected current vector, λ, at frequency h(h)Representing the modal impedance matrix at frequency h, L(h)And R(h)Respectively representing a left eigenvector matrix and a right eigenvector matrix at a frequency h.
The right eigenvector matrix is multiplied by the left side of the equal sign of the above equation, and the relation between the node voltage vector and the node injection current vector can be further rewritten as follows:
will be provided with
Defined as a modal voltage vector
Will be provided with
Defined as the modal current vector
The relation between the modal voltage vector and the modal current vector can be obtained as follows:
in step 4, when the node i of the power distribution network is the norton inter-harmonic source access position, the parallel resonance frequency f and the resonance modal impedance lambda of the power distribution network can be obtainedkk(fmax)And a resonance mode k, then when the parallel resonance frequency is f and the resonance mode is k, the relation (7) of the modal voltage phasor and the modal current phasor can be embodied as follows:
wherein,
representing the modal voltage phasor when the parallel resonance frequency is f and the resonance mode is k;
which represents a parallel resonance frequency of f,the mode current phasor when the resonance mode is k; lambda [ alpha ]kk(fmax)The resonant mode impedance is shown when the parallel resonant frequency is f and the resonant mode is k.
According to the definition of modal current phasor and linear algebra, when the parallel resonance frequency is f and the resonance mode is k, the modal current phasor can be expressed as:
wherein,
represents the modal current phasor R when the parallel resonance frequency is f and the resonance mode is kkj(f)A coordinate k in a right eigenvector matrix when the parallel resonance frequency is f and the resonance mode is kjElement, Rkj(f)The contribution degree of the inter-harmonic current injected into the network at the node j to the harmonic mode current can be reflected, wherein j is 1, 2.
Representing the inter-harmonic current phasor injected into the network at node j at the parallel resonant frequency f.
According to the formulas (8) and (9), the relation between the resonant mode voltage phasor and the resonant mode current phasor is obtained as
At this time, if the norton-type inter-harmonic source is accessed only at the node i, the resonant mode voltage phasor of equation (10) can be expressed as:
wherein R iski(f)F is the parallel resonance frequency, K is the resonance mode, i is the access noroThe nodes of the sources of the harmonic waves between the bowden type,
indicating that the inter-harmonic current injected into the network at node i at the parallel resonant frequency f and the resonant mode k.
According to the steps 1-4, when a norton type inter-harmonic source is connected to the power distribution network, the inter-harmonic source access point can affect the resonance modal impedance. Further, from the formula (11), λkk(fmax)Rki(f)The amplitude of the harmonic source access point can reflect the amplification degree of the resonance mode voltage to the injection current of the harmonic source access point, and the parallel resonance exciting capability of the harmonic source access point is reflected. Thus will bekk(fmax)Rki(f)An evaluation impedance, defined as the ability of a node to excite parallel resonance, for evaluating the ability of a node to excite parallel resonance, where λkk(fmax)Is the resonant mode impedance, Rki(f)And f is the element of the coordinate ki in the right eigenvector matrix when the parallel resonance frequency is f and the resonance mode is k. Evaluation impedance lambda for calculating node excitation parallel resonance capability of each node in power distribution networkkk(fmax)Rki(f)。
And 5, calculating to obtain the node excitation parallel resonance capability evaluation impedance according to the step 5, and if the amplitude of the node excitation parallel resonance capability evaluation impedance is larger, considering that the node excitation parallel resonance capability is stronger. Accordingly, the ability of each node to excite parallel resonance is evaluated based on the result of the node excitation parallel resonance ability evaluation impedance.
An example of practical application:
the method disclosed by the invention is applied to the power distribution network shown in figure 3, and the node 0 in the power distribution network is a system power supply access point, so that the condition that the node 0 is accessed to an inter-harmonic source is not considered, and the capability of exciting parallel resonance of 32 power distribution network nodes is only required to be evaluated.
And 2, 32 Norton inter-harmonic source access positions are in the power distribution network, so that 32 times of correction needs to be carried out on the power distribution network fundamental frequency node admittance matrix to form a power distribution network fundamental frequency node admittance matrix corresponding to the 32 inter-harmonic source access points.
And 3, performing inversion calculation on the power distribution network fundamental frequency node admittance matrixes corresponding to the 32 inter-harmonic source access points one by one to obtain power distribution network fundamental frequency node impedance matrixes corresponding to the 32 inter-harmonic source access points.
And 4, respectively carrying out frequency scanning and matrix diagonalization decomposition processing on each distribution network fundamental frequency node impedance matrix according to the distribution network fundamental frequency node impedance matrixes corresponding to the 32 inter-harmonic source access points to obtain an amplitude-frequency characteristic curve of the key mode modal impedance corresponding to the 32 inter-harmonic source access points. The power frequency is 50Hz, the frequency scanning range is 0-12.5p.u., and the frequency scanning step is 5 Hz. Taking node No. 15 as an inter-harmonic source access point as an example, an amplitude-frequency characteristic curve of the modal impedance of the key mode is shown in fig. 4.
And respectively obtaining the parallel resonance frequency and the resonance mode impedance corresponding to the 32 inter-harmonic source access points, the resonance mode left eigenvector and the resonance mode right eigenvector according to the amplitude-frequency characteristic curve of the key mode modal impedance of each inter-harmonic source access point. The specific results of the parallel resonance frequency and resonance mode impedance table corresponding to the 32 inter-harmonic source access points are shown in table 1:
TABLE 1
| Inter-harmonic source access point | Parallel resonant frequency/p.u. | Resonant mode impedance/Ω | Inter-harmonic source access point | Parallel resonant frequency/p.u. | Resonant mode impedance/ |
| 1 | 9.5 | 3764.31 | 17 | 10.9 | 4367.48 |
| 2 | 9.5 | 3770.39 | 18 | 9.5 | 3764.31 |
| 3 | 9.5 | 3781.01 | 19 | 9.5 | 3764.31 |
| 4 | 9.5 | 3796.54 | 20 | 9.5 | 3764.31 |
| 5 | 9.6 | 3868.16 | 21 | 9.5 | 3764.30 |
| 6 | 9.7 | 3874.72 | 22 | 9.5 | 3770.34 |
| 7 | 10 | 4028.91 | 23 | 9.5 | 3770.12 |
| 8 | 10.2 | 4143.10 | 24 | 9.5 | 3769.82 |
| 9 | 10.4 | 4274.28 | 25 | 9.6 | 3870.23 |
| 10 | 10.4 | 4308.43 | 26 | 9.6 | 3872.42 |
| 11 | 10.4 | 4360.01 | 27 | 9.7 | 3877.73 |
| 12 | 10.6 | 4474.40 | 28 | 9.7 | 3881.91 |
| 13 | 10.8 | 4492.71 | 29 | 9.7 | 3883.00 |
| 14 | 10.8 | 4498.05 | 30 | 9.7 | 3880.49 |
| 15 | 10.9 | 4502.06 | 31 | 9.7 | 3878.41 |
| 16 | 10.9 | 4405.92 | 32 | 9.7 | 3874.39 |
And 5, calculating the impedance of the node excitation parallel resonance capability evaluation.
Computing node excitation parallel resonance capability evaluation impedance lambdakk(fmax)Rki(f)Wherein λ iskk(fmax)Is the resonant mode impedance, Rki(f)Is a coordinate ki element in the right eigenvector matrix, and table 2 gives the excitation parallel resonance capability evaluation impedance amplitude results corresponding to 32 inter-harmonic source access points:
TABLE 2
| Inter-harmonic source access point | Node excitation parallel resonance capability evaluation impedance/omega | Inter-harmonic source access point | Node excitation parallel resonance capability evaluation impedance/ |
| 1 | 5.8551 | 17 | 1255.4928 |
| 2 | 70.0079 | 18 | 5.8602 |
| 3 | 116.2610 | 19 | 5.7536 |
| 4 | 163.8352 | 20 | 5.6726 |
| 5 | 332.8040 | 21 | 5.4540 |
| 6 | 443.1269 | 22 | 69.5031 |
| 7 | 688.2698 | 23 | 67.5985 |
| 8 | 845.4352 | 24 | 65.3610 |
| 9 | 1007.1515 | 25 | 335.7838 |
| 10 | 1026.1613 | 26 | 338.3846 |
| 11 | 1056.7685 | 27 | 350.9120 |
| 12 | 1228.4524 | 28 | 353.8891 |
| 13 | 1298.8322 | 29 | 353.5244 |
| 14 | 1330.3915 | 30 | 347.4071 |
| 15 | 1343.5353 | 31 | 343.6863 |
| 16 | 1290.8394 | 32 | 336.7320 |
The impedance magnitude distribution diagram for the evaluation of the parallel resonance ability of each node is shown in fig. 5.
And 6, evaluating the node excitation parallel resonance capability according to the amplitude of the node excitation parallel resonance capability evaluation impedance.
As can be seen from table 2 and fig. 5, the amplitude of the impedance for evaluating the parallel resonance exciting capability of node No. 15 in the power distribution network is the largest, so that the inter-harmonic source access point has the strongest parallel resonance exciting capability. In the power distribution network, the excitation parallel resonance capability evaluation impedance amplitudes corresponding to the No. 1 node, the No. 18 node, the No. 19 node, the No. 20 node and the No. 21 node are far smaller than the excitation parallel resonance capability evaluation impedance amplitudes corresponding to the No. 15 node, so that the inter-harmonic source access points have weak capability of exciting parallel resonance.
Finally, it should be noted that: the above-mentioned embodiments are only used for illustrating the technical solution of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill 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 (4)
1. A method for evaluating parallel resonance excitation capability of a Nonton type inter-harmonic source access point is characterized by comprising the following steps: which comprises the following steps:
step 1, establishing a fundamental frequency node admittance matrix of a power distribution network
Establishing a power distribution network fundamental frequency node admittance matrix Y by adopting the prior art according to the structure of the power distribution network and the fundamental frequency branch parameters; the number of the nodes of the power distribution network is n, so that the fundamental frequency node admittance matrix Y of the power distribution network is n x n matrix;
step 2, correcting the fundamental frequency node admittance matrix of the power distribution network
Defaults that only one Norton inter-harmonic source is connected into the power distribution network, and the fundamental frequency impedance of parallel branches of the Norton inter-harmonic sources is set to be ZLTaking the power distribution network node i as the inter-harmonic source access position to obtain a modified power distribution network fundamental frequency node admittance matrix YL(ii) a Because there are n distribution network nodes, there are n different modified distribution network fundamental frequency node admittance matrixes YL；
Step 3, solving the modified power distribution network fundamental frequency node impedance matrix
When the Nonton type inter-harmonic source uses a power distribution network node i as an inter-harmonic source access position, carrying out inversion operation on the modified power distribution network fundamental frequency node admittance matrix to obtain a power distribution network fundamental frequency node impedance matrix Z; because there are n different modified fundamental frequency node admittance matrixes Y of the distribution networkLTherefore, there are n corresponding distribution network fundamental frequency node impedance matrices Z, which specifically are:
z represents a power distribution network fundamental frequency node impedance matrix taking a power distribution network node i as a Norton inter-harmonic source access position;
step 4, calculating the parallel resonance frequency and the resonance mode impedance
The method comprises the steps of taking a fundamental frequency node impedance matrix Z of the power distribution network as a reference, obtaining node impedance matrixes of the power distribution network under different frequencies through a frequency scanning method, carrying out diagonalization decomposition on the node impedance matrixes of the power distribution network under different frequencies to obtain a modal impedance matrix, a left eigenvector matrix and a right eigenvector matrix, obtaining a critical mode modal impedance amplitude-frequency characteristic curve according to the amplitude of the modal impedance of each frequency critical mode, determining the parallel resonance frequency as f, and determining the resonance modal impedance as lambdakk(fmax)And the resonance mode is k; sequentially obtaining parallel resonance frequency, resonance mode impedance and resonance mode for n distribution network fundamental frequency node impedance matrixes Z;
step 5, obtaining the evaluation impedance of the node excitation parallel resonance capability
When the Nonton type inter-harmonic source uses a node i of the power distribution network as an inter-harmonic source access position, the relational expression of the node voltage vector and the node injection current vector is known, and then the decomposition expression of the node impedance matrix is substituted to obtain the following relational expression:
wherein Z is(h)Representing the node impedance matrix at frequency h of the distribution network,
represents the node voltage vector at frequency h,
representing the node injected current vector, λ, at frequency h(h)Representing the modal impedance matrix at frequency h, L(h)And R(h)Respectively representing a left eigenvector matrix and a right eigenvector matrix at a frequency h;
the right eigenvector matrix is multiplied by the left side of the equal sign of the above equation, and the relation (5) between the node voltage vector and the node injection current vector can be further rewritten as:
then, define
Is a modal voltage vector
Is a modal current vector
Obtaining a relation (7) of the modal voltage vector and the modal current vector as follows:
according to the step 4, when the parallel resonance frequency is f and the resonance mode is k, the relational expression (7) of the modal voltage phasor and the modal current phasor is embodied as follows:
wherein,
representing the modal voltage phasor when the parallel resonance frequency is f and the resonance mode is k;
representing the modal current phasor when the parallel resonance frequency is f and the resonance mode is k; lambda [ alpha ]kk(fmax)Representing the impedance of the resonance mode when the parallel resonance frequency is f and the resonance mode is k;
when the parallel resonance frequency is f and the resonance mode is k, the modal current phasor can be expressed as:
wherein,
represents the modal current phasor R when the parallel resonance frequency is f and the resonance mode is kkj(f)The parallel resonance frequency is f, the resonance mode is k, and the coordinate kj element R in the right eigenvector matrix iskj(f)The degree of contribution of the inter-harmonic current injected into the network at node j to the resonant mode current can be reflected, j being 1,2, …, n;
representing the inter-harmonic current phasor injected into the network by the node j at the parallel resonant frequency f;
according to the formulas (8) and (9), the relation between the resonant mode voltage phasor and the resonant mode current phasor is obtained as follows:
when a Nonton type inter-harmonic source takes a power distribution network node i as an inter-harmonic source access position, the resonant mode voltage phasor is expressed as follows:
wherein,
representing the modal voltage phasor when the parallel resonance frequency is f and the resonance mode is k;
representing the modal current phasor when the parallel resonance frequency is f and the resonance mode is k; lambda [ alpha ]kk(fmax)Represents the resonant mode impedance, R, when the parallel resonant frequency is f and the resonant mode is kki(f)When the parallel resonance frequency is f and the resonance mode is k, the coordinate ki element in the right eigenvector matrix,
representing the inter-harmonic current phasor injected into the network at a node i when the parallel resonance frequency is f and the resonance mode is k;
according to the steps 1-4, when the Nonton type inter-harmonic source is connected to the power distribution network, the inter-harmonic source access point can affect the resonance modal impedance, and then according to the formula (11), the lambda is knownkk(fmax)Rki(f)The amplitude of the intermediate harmonic source access point can reflect the amplification degree of the resonance mode voltage to the injection current of the intermediate harmonic source access point, and the parallel resonance exciting capability of the intermediate harmonic source access point is reflected, so that lambda is converted into the amplitude of the intermediate harmonic source access pointkk(fmax)Rki(f)The evaluation impedance is defined as the node excitation parallel resonance capability evaluation impedance and is used for evaluating the node excitation parallel resonance capability and calculating the node excitation parallel resonance capability evaluation impedance lambda of each node in the power distribution networkkk(fmax)Rki(f)；
Step 6, evaluating the parallel resonance capability of the node excitation according to the amplitude of the impedance evaluated by the parallel resonance capability of the node excitation
Calculating to obtain node excitation parallel resonance capability evaluation impedance according to the step 5, wherein the larger the amplitude of the node excitation parallel resonance capability evaluation impedance is, the stronger the node excitation parallel resonance capability is; the smaller the magnitude of the node-excited parallel resonance capability evaluation impedance, the weaker the node-excited parallel resonance capability.
2. The method of claim 1, wherein the method comprises the following steps: the power distribution network fundamental frequency node admittance matrix Y in the step 1 specifically comprises the following steps:
wherein Y is a distribution network fundamental frequency node admittance matrix, n is the number of distribution network nodes, and Y is used for each rowijThe current injected into the grid by node i when the unit voltage is added to node j and the other nodes are grounded, i is 1,2, …, n; j is 1,2, …, n.
3. The method of claim 2, wherein the method comprises the following steps: the modified fundamental frequency node admittance matrix Y of the power distribution network in the step 2LThe method specifically comprises the following steps:
wherein i is an access node label of a Nonton type interharmonic source in the power distribution network, and ZLThe impedance of the fundamental frequency of the parallel branch of the Nonton type interharmonic source.
4. A method as claimed in claim 3The method for evaluating the parallel resonance excitation capability of the Noton inter-harmonic source access point is characterized by comprising the following steps: in the step 4, diagonalization decomposition is performed on the node impedance matrix of the power distribution network under different frequencies to obtain a modal impedance matrix, a left eigenvector matrix and a right eigenvector matrix, a critical mode modal impedance amplitude-frequency characteristic curve is obtained according to the amplitude of the modal impedance of each frequency critical mode, the parallel resonance frequency is determined to be f, and the resonance modal impedance is determined to be lambdakk(fmax)And the resonance mode is k, specifically:
wherein Z is(h)A node impedance matrix, λ, representing the frequency h obtained by frequency scanning(h)Is a modal impedance matrix, L(h)Is a left eigenvector matrix, R(h)As a matrix of right eigenvectors, a matrix of modal impedances λ(h)For the feature root diagonal matrix, the left eigenvector matrix L(h)And the right eigenvector matrix R(h)Is in a reciprocal relationship;
modal impedance matrix lambda(h)The middle diagonal element is modal impedance, a mode with the maximum modal impedance amplitude is selected as a key mode in the modal impedance matrix, and a key mode modal impedance amplitude-frequency characteristic curve is obtained according to the amplitude of the modal impedance of each frequency key mode;
the parallel resonance frequency f is the frequency at the peak of the amplitude-frequency characteristic curve of the key mode modal impedance, and the key mode modal impedance corresponding to the parallel resonance frequency f is the resonance modal impedance lambdakk(fmax)，λkk(fmax)Is a modal impedance matrix lambda with a parallel resonance frequency f(f)The element with the largest modal impedance amplitude is determined according to the resonant modal impedance lambdakk(fmax)The resonance mode corresponding to the parallel resonance frequency f is referred to as a resonance mode k.
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