CN113612231B - Impedance adapter addressing method based on modal analysis method - Google Patents

Impedance adapter addressing method based on modal analysis method Download PDF

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CN113612231B
CN113612231B CN202110862034.1A CN202110862034A CN113612231B CN 113612231 B CN113612231 B CN 113612231B CN 202110862034 A CN202110862034 A CN 202110862034A CN 113612231 B CN113612231 B CN 113612231B
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CN113612231A (en
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李飞
许珂
张永新
刘洋
张兴
马铭遥
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Hefei University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/01—Arrangements for reducing harmonics or ripples
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/002—Flicker reduction, e.g. compensation of flicker introduced by non-linear load
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381—Dispersed generators
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/04—Power grid distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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Abstract

The invention provides an impedance adapter address selection method based on a modal analysis method, and belongs to the technical field of distributed grid-connected power generation. The address selection method comprises the following steps: obtaining the output impedance of each grid-connected inverter in an offline impedance measurement mode; respectively writing node admittance matrixes under all frequencies of the system in a row mode and respectively decomposing characteristic values; the potential parallel harmonic resonance frequency of the system and the leading node causing the frequency to resonate are judged, and an impedance adapter is installed at the leading node to achieve the optimal harmonic resonance suppression effect. The method is simple to implement, for a multi-inverter grid-connected system, the parallel resonance frequency and the leading node of the system can be judged without establishing a complex inverter transfer function expression, and the selection of the optimal installation position of the impedance adapter is completed.

Description

Impedance adapter address selecting method based on modal analysis method
Technical Field
The invention relates to an impedance adapter site selection method based on a modal analysis method, and belongs to the technical field of distributed grid-connected power generation.
Background
With the rapid development of new energy power generation technology, a large number of distributed power supplies are connected to a power grid, and meanwhile, a large number of harmonic waves are injected into a system, so that harmonic pollution is caused. In order to inhibit harmonic interaction in a system and avoid harmonic resonance, the academic world proposes a device of an impedance adapter, which is essentially to inhibit harmonic resonance caused by the combined action of the power grid impedance and an inverter by virtualizing a resistor in a resonant frequency section through an additional inverter. The impedance adapter is typically selected to fit on the PCC, however, the fitting position of the impedance adapter changes in consideration of the presence of the collector line impedance. For a large-scale new energy power station, ideal lines are not arranged between each inverter unit node and a grid-connected point any more, certain collecting line impedance exists, and the collecting line impedance can also participate in harmonic resonance of a grid-connected system, so that the resonance condition of the system is more complex. Because the impedances of the collecting lines from each unit node to the grid-connected point are different, and the contribution degrees of different nodes to system harmonic resonance are also different, the optimal adaptation position of the impedance adapter is not limited to the PCC point, and can be any node in the grid-connected system. How to select the optimal adaptive position of the impedance adapter has certain research value;
among the related studies, document 1, "Harmonic Resonance Investigation of a Multi-Inverter Grid-Connected System Using Resonance analog Analysis [ J ]. IEEE Transactions on Power Delivery,2019, 34 (1): 63-72. (multiple inverter grid-connected system harmonic resonance research based on resonance mode analysis); document 2 application of down poetry modal analysis in harmonic analysis and treatment of electrified railways [ D ]. University of southwest traffic, 2017,; document 3 "Jia L, ruan X, ZHao W, et al, an Adaptive Active speaker for Improving the Stability of Grid-Connected Inverters Under Weak Grid [ J ]. IEEE Transactions on Power Electronics,2018:1-1 (an adaptive active damper for improving the stability of a grid-connected inverter under a weak power grid) researches related problems;
document 1 applies a modal analysis method to harmonic resonance characteristic analysis of a multi-inverter grid-connected system, but only considers the influence of grid impedance, line impedance and inverter parameters on harmonic resonance frequency, and does not make deeper research on resonance suppression, participation factors and the like, and an article adopts single-inverter transfer function modeling and then popularizes the method to the multi-inverter system, so that the analysis process is complicated, the node admittance matrix dimension is high, characteristic value decomposition is not facilitated, and the calculation efficiency is low. Document 2 identifies a leading node where a system resonates by using a participation factor, but only a passive filter is connected in parallel to the node to filter a harmonic wave, and an active device such as an impedance adapter is not selected, so that the harmonic wave stability of the new energy power generation system cannot be improved, and the introduction of the filter causes a change in the system structure, which may cause new harmonic resonance. Document 3 connects an impedance adapter in parallel to the PCC point, and does not consider the influence of the collector line impedance in the system. The impedance of a collecting line between each unit node and a grid-connected point can cause harmonic resonance to occur not only between the power grid impedance and the system impedance but also possibly generated in the system, so that the optimal adaptation position of the impedance adapter is not limited to the PCC point;
in summary, the existing impedance adapter addressing research has the following disadvantages:
1. the node admittance matrix of the multi-inverter system established by the transfer function method is too complex, and the calculation efficiency is low in practical application;
2. the influence of the resistance of a current collecting circuit on the stability of the system is not considered during modeling of the multi-machine system, harmonic resonance may occur in the system, and the resistance adapter installed on the PCC point may not achieve the optimal harmonic resonance suppression effect;
3. under the condition of considering the impedance of the current collecting line, the installation position of the impedance adapter has no clear selection strategy;
disclosure of Invention
The invention aims to select the optimal adaptation position for the impedance adapter and improve the capability of inhibiting the harmonic resonance of a system. The impedance adapter addressing method based on the modal analysis method provided by the invention not only adopts a mode based on impedance measurement to obtain the system node admittance matrix, reduces the modeling complexity and improves the calculation efficiency, but also considers the influence of the current collection circuit impedance on the installation position of the impedance adapter, and installs the impedance adapter at the selected node to achieve the optimal harmonic resonance suppression effect.
In order to solve the technical problem, the invention provides an impedance adapter site selection method based on a modal analysis method, which relates to a system consisting of a plurality of inverters, wherein the topological structure of the system comprises n identical direct-current power supplies, n identical grid-connected inverters, a power supply system and a power supply system,n identical LC filters, n identical three-phase collector line impedances, a network impedance X g And a power grid; any one of the n DC power supplies is recorded as a DC power supply V dcj And any one grid-connected inverter of the n grid-connected inverters is marked as an inverter A j Any one of the n LC filters is denoted as filter B j And any one of the n collector line impedances is recorded as a collector line impedance X Dj J =1,2, \ 8230;, n; wherein, the grid-connected inverter A j Input terminal and DC power supply V dcj Connected, grid-connected inverter A j Output terminal of (1) and filter B j Is connected to the input terminal of the filter B j Is connected with the collector line impedance X through a node j Dj Connected, n collector line impedances X Dj The other end of the grid-connected point is connected in parallel with a grid-connected point PCC followed by a power-connected impedance X g Grid impedance X g The other end of the switch is connected to a power grid;
the site selection method comprises the steps of obtaining the output impedance of each grid-connected inverter, judging the resonance frequency section of the parallel resonance of a plurality of grid-connected inverter systems, and guiding an impedance adapter to be installed at a leading node inducing resonance, and specifically comprises the following steps:
step 1, the system carries out m times of circulation in the process of site selection, and the frequency of operation in any circulation is recorded as operation frequency f a A =1,2, \8230;, m; setting the initial frequency f 0 Iteration step Δ f, i.e. f 1 ＝f 0 ，f a+1 ＝f a +Δf；
Step 2, obtaining the operation frequency f through off-line impedance measurement a Each grid-connected inverter A j Output impedance X of aj ；
Step 3, based on the output impedance X obtained in step 2 aj Known grid impedance X g Known collector line impedance X Dj Frequency of column write operation f a Time node admittance matrix Y fa And a node voltage equation;
will operate at frequency f a Nodal admittance matrix Y of time fa Is inversely described as
Figure BDA0003183891140000041
The expression is as follows:
Figure BDA0003183891140000042
the expression of the node voltage equation is as follows:
Figure BDA0003183891140000051
wherein, U fa To operate the frequency f a Node voltage matrix of time, I fa To operate the frequency f a The expressions of the node current matrix are respectively as follows:
Figure BDA0003183891140000052
in the formula of U aj For a grid-connected inverter A j Output voltage of V g For the grid voltage, I aj For a grid-connected inverter A j Output current of I g Is the current of the power grid;
step 4, calculating the frequency f obtained in the step 3 a Inverse of the nodal admittance matrix of time
Figure BDA0003183891140000058
Eigenvalue decomposition was performed and expressed as:
Figure BDA0003183891140000053
wherein the content of the first and second substances,
Figure BDA0003183891140000054
is the operating frequency f a A diagonal feature matrix of time, wherein the diagonal contains i elements, and one of the i elementsAny one element is marked as an operation frequency f a Modal impedance value of time
Figure BDA0003183891140000055
Ordered from top left to bottom right, i =1,2, \8230;, n, n +1, whose expressions are as follows:
Figure BDA0003183891140000056
L a as a diagonal feature matrix
Figure BDA0003183891140000057
Left eigenvector matrix of (3), R a As a diagonal feature matrix
Figure BDA0003183891140000061
A right eigenvector matrix of, and
Figure BDA0003183891140000062
the expressions are respectively as follows:
Figure BDA0003183891140000063
R a ＝(y a1 y a2 … y az … y a(n+1) )
in the formula, x az Is a left eigenvector, x az ＝(c z1 c z2 … c zz … c zn c z(n+1) )，c zz Is an irregular natural number; y is az Is a right eigenvector, y az ＝(e 1z ，e 2z ，…e zz …e zn e z(n+1) ) T ，e zz Is an irregular natural number, z =1,2, \ 8230;, n +1; right eigenvector y az Should satisfy the formula
Figure BDA0003183891140000064
Left eigenvector x az Satisfy the formula
Figure BDA0003183891140000065
Calculating to obtain the operation frequency f according to the three matrixes a I modal impedance values of time
Figure BDA0003183891140000066
Step 5, firstly, calculating m × i modal impedance values at m operation frequencies according to the method from step 2 to step 4
Figure BDA0003183891140000067
Secondly, the number set formed by the ith element on the diagonal of the diagonal feature matrix obtained in the calculation process of all the operation frequencies is recorded as a mode M i I.e. by
Figure BDA0003183891140000068
Modal impedance value
Figure BDA0003183891140000069
Redefined as the same mode M i Corresponding modal impedance values, a =1,2, \8230;, m, i =1,2, \8230;, n, n +1;
step 6, for each mode M i Judging whether the mode is a key mode, wherein the method comprises the following steps:
if it satisfies
Figure BDA00031838911400000610
And is provided with
Figure BDA00031838911400000611
Then the mode M is identified i Modal impedance value of
Figure BDA00031838911400000612
In which there is at least one modal impedance maximum, defining the mode M i Is a key modality;
if not satisfied with
Figure BDA00031838911400000613
And is provided with
Figure BDA00031838911400000614
Identify the mode M i No modal impedance maxima exist, i.e. they do not participate in the addressing of the impedance adapter;
step 7, comparing the modal impedance maximum values in the key modes obtained in the step 6, finding out the maximum value, and recording the operation frequency of the maximum value of the modal impedance as the parallel resonance frequency f of the system in the key modes b ；
Step 8, defining a participation point d, wherein the participation point d comprises n nodes j and 1 point-to-point PCC (d =1,2, \8230); n +1 and n +1 correspond to a point-to-point user CC;
writing a participation factor matrix F of n +1 participation points d in a key mode, wherein the matrix is a (n + 1) x (n + 1) matrix, and the d-th element on the diagonal line of the matrix is the participation factor of the participation point d;
the expression of the participation factor matrix F is as follows:
Figure BDA0003183891140000071
wherein x is bz To a parallel resonance frequency f b Corresponding left eigenvector, y bz To the parallel resonance frequency f b A corresponding right eigenvector;
and comparing the n +1 participation factors, finding out the maximum value of the participation factors, and marking the participation point corresponding to the maximum value as a leading node, wherein the leading node is the optimal installation position of the impedance adapter in the key mode.
Compared with the prior art, the invention has the following beneficial effects:
1) The invention uses the system model obtained based on the off-line impedance measurement to carry out modal analysis, can effectively solve the complexity of the resonance characteristic analysis of the multi-inverter grid-connected system, and improves the calculation efficiency;
2) The invention considers the current collecting line impedance X Dj In the case of (2), the resonant frequency can be determined quickly by using the participation factorAnd the generated leading node provides guidance for selecting the adaptive position of the impedance adapter.
Drawings
Fig. 1 is a topology structure diagram of a multi-inverter grid-connected system according to the present invention;
FIG. 2 is a flow chart of the method for selecting the optimal mounting position of the impedance adapter according to the present invention;
FIG. 3 is a grid-connected inverter A obtained by offline impedance measurement according to an embodiment of the present invention 1 Output impedance X of a1 Amplitude-frequency and phase diagrams of;
FIG. 4 is a diagram of modal impedance values of the system obtained after modal analysis in an embodiment of the present invention;
FIG. 5 is a voltage FFT analysis result of a point-on-grid PCC when an impedance adapter is not connected in parallel to any node after harmonic current with a frequency of 503Hz and an amplitude of 1A is injected into a node 2 in the embodiment of the present invention;
fig. 6 is a result of FFT analysis of PCC voltages at grid-connected points when an impedance adapter is connected in parallel to the PCC at the grid-connected point after a harmonic current with a frequency of 503Hz and an amplitude of 1A is injected at a node 2 in the embodiment of the present invention;
FIG. 7 is a FFT analysis result of the PCC voltage at the grid-connected point when the impedance adapter is connected in parallel to the node 1 after the harmonic current with the frequency of 503Hz and the amplitude of 1A is injected into the node 2 in the embodiment of the present invention;
FIG. 8 is a graph showing FFT analysis results of a point-on-grid PCC voltage when an impedance adapter is connected in parallel to node 2 after harmonic current with frequency 503Hz and amplitude 1A is injected into node 2.
Detailed Description
The example takes a double-inverter grid-connected system containing one impedance adapter in simulation software Matlab/Simulink as an example, and illustrates a method for selecting the optimal installation position of the impedance adapter.
Fig. 1 is a topology structural diagram of a multi-inverter grid-connected system according to the present invention. It can be seen from the figure that the impedance adapter addressing method based on the modal analysis method of the invention relates to a system consisting of a plurality of inverters, and the topological structure of the system comprises n identical direct current power supplies, n identical grid-connected inverters, n identical LC filters, n identical three-phase current collection line impedances and a power grid impedance X g And a power grid.
Any one of the n DC power supplies is recorded as a DC power supply V dcj And any one grid-connected inverter in the n grid-connected inverters is marked as an inverter A i And any one LC filter of the n LC filters is marked as a filter B j And any one of the n collector line impedances is recorded as a collector line impedance X Dj J =1,2, \ 8230;, n. Wherein, the grid-connected inverter A j Input terminal and DC power supply V dcj Connected, grid-connected inverter A j Output terminal of and filter B j Is connected to the input terminal of the filter B j Is connected with the collector line impedance X through a node j Dj Connected, n collector line impedances X Dj The other end of the grid-connected point is connected in parallel with a grid-connected point PCC followed by a power-connected impedance X g Grid impedance X g And the other end of the power grid is connected to the power grid.
In addition, as can be seen from fig. 1, filter B j Comprising a filter inductance L j And a filter capacitor C j 。
In the present embodiment, n =2, that is, 2 inverters are provided, and each inverter is denoted as inverter a 1 Inverter A 2 . Other specific parameters are as follows: the effective value of the grid line voltage is 380V, and the rated frequency f is 50Hz. X g ＝50mΩ+j0.014mH，X D1 ＝0.08mΩ+j0.174mH，X D2 =0.17m omega +0.347mH, filter inductance L 1 ＝L 2 =3mH, filter capacitance C 1 ＝C 2 =274uF. The used 1 impedance adapter comprises a direct current bus capacitor, a three-phase full bridge and an LC filter, wherein the three-phase full bridge is connected with a node of a grid-connected system through the LC filter.
Fig. 2 is a flowchart of a method for selecting an optimal installation position of an impedance adapter according to the present invention, and it can be seen from the flowchart that the method for selecting an address of an impedance adapter based on a modal analysis method according to the present invention includes obtaining an output impedance of each grid-connected inverter, determining a resonant frequency band of a parallel resonance of a plurality of grid-connected inverter systems, and guiding the impedance adapter to be installed at a leading node causing the resonance, and the specific steps are as follows:
step 1, in the address selection process, the systemM cycles are performed in total, and the frequency of operation in any cycle is recorded as an operation frequency f a A =1,2, \8230;, m; setting an initial frequency f 0 Iteration step Δ f, i.e. f 1 ＝f 0 ，f a+1 ＝f a +Δf。
In the present embodiment, m =3000.
Step 2, obtaining the operation frequency f through off-line impedance measurement a Each grid-connected inverter A j Output impedance X of aj 。
In the present embodiment, the output impedance X of the grid-connected inverter a1 ＝X a2 And output impedance X aj The output impedance X is determined by the impedance amplitude and the impedance phase aj The magnitude of the impedance phase determines the output impedance X aj Magnitude of phase, output impedance X aj The impedance magnitude and impedance phase of (a) are shown in fig. 3.
Step 3, based on the output impedance X obtained in step 2 aj Known grid impedance X g Known collector line impedance X Dj Frequency of column write operation f a Time node admittance matrix Y fa And a node voltage equation.
Will operate at frequency f a Nodal admittance matrix Y of time fa Is inversely expressed as
Figure BDA0003183891140000101
The expression is as follows:
Figure BDA0003183891140000111
the expression of the node voltage equation is as follows:
Figure BDA0003183891140000112
wherein, U fa To operate the frequency f a Node voltage matrix of time, I fa To operate the frequency f a Node current of timeMatrix, the expression is respectively:
Figure BDA0003183891140000113
in the formula of U aj For grid-connected inverter A j Output voltage of V g For the mains voltage, I aj For grid-connected inverter A j Output current of I g Is the grid current.
In the present embodiment of the present invention,
Figure BDA0003183891140000114
step 4, calculating the frequency f obtained in the step 3 a Inverse of nodal admittance matrix of time
Figure BDA0003183891140000115
Eigenvalue decomposition was performed and expressed as:
Figure BDA0003183891140000116
wherein the content of the first and second substances,
Figure BDA0003183891140000121
is the operating frequency f a The diagonal feature matrix of the time contains i elements on the diagonal, and any one element in the i elements is recorded as the operation frequency f a Modal impedance value of time
Figure BDA0003183891140000122
Ordered from top left to bottom right, i =1,2, \ 8230;, n, n +1, whose expression is as follows:
Figure BDA0003183891140000123
L a is a diagonal feature matrix
Figure BDA0003183891140000124
Left eigenvector matrix of (1), R a As a diagonal feature matrix
Figure BDA0003183891140000125
A right eigenvector matrix of, and
Figure BDA0003183891140000126
the expressions are respectively as follows:
Figure BDA0003183891140000127
R a ＝(y A1 y a2 … y az … y a(n+1) )
in the formula, x az Is a left eigenvector, x az ＝(c z1 c z2 … c zz … c zn c z(n+1) )，c zz Is an irregular natural number; y is az Is a right eigenvector, y az ＝(e 1z ，e 2z ，…e zz …e zn e z(n+1) ) T ，e zz Is an irregular natural number, z =1,2, \ 8230;, n +1; right eigenvector y az Should satisfy the formula
Figure BDA0003183891140000128
Left eigenvector x az Satisfy the formula
Figure BDA0003183891140000129
Calculating to obtain the operation frequency f according to the three matrixes a I modal impedance values of time
Figure BDA00031838911400001210
In this embodiment, i =3, resulting in a total of 3 modal impedance values
Figure BDA00031838911400001211
Step 5, firstly, calculating m × i modal impedance values at m operation frequencies according to the method of step 2 to step 4
Figure BDA0003183891140000131
Secondly, the number set formed by the ith element on the diagonal of the diagonal feature matrix obtained in the calculation process of all the operation frequencies is recorded as a mode M i I.e. by
Figure BDA0003183891140000132
Modal impedance value
Figure BDA0003183891140000133
Redefined as the same mode M i Corresponding modal impedance values, a =1,2, \8230;, m, i =1,2, \8230;, n, n +1.
In this embodiment, 9000 modal impedance values are obtained by calculation, and are divided into three modes: modality
Figure BDA0003183891140000134
Modality
Figure BDA0003183891140000135
Modality
Figure BDA0003183891140000136
Wherein a =1,2, \8230, 3000,i =1,2,3;
calculating 3 modes according to the method from step 2 to step 4 to obtain 9000 modal impedance values in total under 3000 operation frequencies
Figure BDA0003183891140000137
Step 6, for each mode M i Judging whether the mode is a key mode, wherein the method comprises the following steps:
if it satisfies
Figure BDA0003183891140000138
And is
Figure BDA0003183891140000139
Then the mode M is identified i Modal impedance value of
Figure BDA00031838911400001310
In which there is at least one modal impedance maximum, defining the mode M i Is a key modality;
if not satisfied
Figure BDA00031838911400001311
And is
Figure BDA00031838911400001312
Identify the mode M i There are no modal impedance maxima, i.e. they do not participate in the addressing of the impedance adapter.
In the present embodiment, the three modalities are determined separately, and the determination results are shown in fig. 4. As can be seen in FIG. 4, the mode M 1 Absence of maxima, mode M 2 And mode M 3 Has a maximum value, so that the mode M is 2 And mode M 3 All are recorded as key modalities.
Step 7, comparing the modal impedance maximum values in the key modes obtained in the step 6, finding out the maximum value, and recording the operation frequency of the maximum value of the modal impedance as the parallel resonance frequency f of the system in the key modes b 。
The mode M is visible from FIG. 4 2 Has a maximum modal impedance of 13.33 Ω and at a frequency of 703Hz, so that the mode M is 2 Parallel resonant frequency f b Is 703Hz. Mode M 3 Has a maximum modal impedance of 17.2 omega, mode M 3 Parallel resonant frequency f b Is 503Hz;
step 8, defining a participation point d, wherein the participation point d comprises n nodes j and 1 point-to-point PCC, i.e. d =1,2, \ 8230;, n +1, and n +1 th participation point correspond to the point-to-point PCC.
Writing out an engagement factor matrix F of n +1 engagement points d in the key mode, wherein the matrix is an (n + 1) × (n + 1) matrix, and the d-th element on the diagonal is the engagement factor of the engagement point d.
The expression of the participation factor matrix F is as follows:
Figure BDA0003183891140000141
wherein x is bz To a parallel resonance frequency f b Corresponding left eigenvector, y bz To the parallel resonance frequency f b A corresponding right eigenvector;
and comparing the n +1 participation factors, finding out the maximum value of the participation factors, and marking a participation point corresponding to the maximum value as a leading node, wherein the leading node is the optimal installation position of the impedance adapter in the key mode.
In the present embodiment, the participating points d are 3, including 2 nodes and 1 point-to-grid PCC, d =1,2,3, and f is calculated respectively b Participation factor sum f of 3 participation points at =703Hz b Participation factor of 3 participation points at =503 Hz.
With f b =503Hz calculation at f b The participation factor matrix F expression at 503Hz is as follows:
Figure BDA0003183891140000151
from f b The participation factor matrix F is known at the parallel resonance frequency F when =503Hz b The point where the participation factor is the largest at =503Hz is the participation point 2, i.e., the node 2, and therefore, the impedance adapter is connected in parallel to the node 2, and the optimum resonance suppression effect can be achieved at the parallel resonance frequency.
In order to prove the beneficial effects of the invention, the invention is simulated.
FIG. 3 shows a grid-connected inverter A obtained by impedance measurement 1 Output impedance curve X 1 . Fig. 4 is a diagram of the modal impedance of the system, showing two maxima, 503Hz and 703Hz, respectively, which illustrate the susceptibility of the system to parallel resonance at these two frequencies.
FIG. 5 illustrates impedance adaptation after node 2 injects harmonic current with frequency 503Hz and amplitude 1AThe FFT analysis result of the grid-connected point PCC voltage is obtained when the device is not connected in parallel with any node, wherein the abscissa is the operation frequency f a The ordinate is the harmonic content THD (percentage of the fundamental voltage), and the smaller the harmonic content, the better the resonance suppression effect.
FIG. 6 is a FFT analysis result of the voltage of the PCC when the impedance adapter is connected in parallel to the PCC, wherein the abscissa is the operation frequency f a The ordinate is the harmonic content THD (in percent of the fundamental voltage).
FIG. 7 is a graph of FFT analysis results of point-on-point PCC voltages when an impedance adapter is connected in parallel to node 2 after injecting harmonic current, where the abscissa is the operating frequency f a The ordinate is the harmonic content THD (in percent of the fundamental voltage).
FIG. 8 is a graph of FFT analysis results of the point-on-grid PCC voltage when the impedance adapter is connected in parallel to node 2 after injecting the harmonic current, wherein the abscissa is the operating frequency f a The ordinate is the harmonic content THD (in percent of the fundamental voltage).
It can be known from comparison of fig. 5 to 8 that, for the parallel resonance of 503Hz, the impedance adapter is assembled in the multi-inverter grid-connected system to suppress the harmonic resonance of the system to a certain extent, and the suppression effect when the impedance adapter is connected in parallel to the node 2 is obviously better than that when the impedance adapter is connected in parallel to the node 1 and the grid-connected point PCC, so that the impedance adapter assembling position selected by the method is the best position, and the correctness of the method is verified.
In summary, the method is simple to implement, and under the condition that the internal parameters of the inverter are unknown, the output impedance X of the inverter is obtained by using impedance measurement j And a known collector line impedance X Dj And the known grid impedance X g The optimal installation position of the impedance adapter can be judged, and certain feasibility is achieved.

Claims (1)

1. An impedance adapter addressing method based on a modal analysis method relates to a system consisting of a plurality of inverters, and the topological structure of the system comprises n identical direct-current power supplies, n identical grid-connected inverters, n identical LC filters, n identical three-phase current collection line impedances and one inverterImpedance of power grid X g And a power grid; any one of the n DC power supplies is recorded as a DC power supply V dcj And any one grid-connected inverter in the n grid-connected inverters is marked as an inverter A j And any one LC filter of the n LC filters is marked as a filter B j And any one of the n collector line impedances is recorded as a collector line impedance X Dj J =1,2, \8230;, n; wherein, the grid-connected inverter A j Input terminal and DC power supply V dcj Connected, grid-connected inverter A j Output terminal of and filter B j Is connected to the input terminal of filter B j Is connected with the collector line impedance X through a node j Dj Connected, n collector line impedances X Dj The other end of the grid-connected point is connected with a power grid impedance X in parallel after PCC g Grid impedance X g The other end of the switch is connected to a power grid;
the method is characterized by comprising the following steps of obtaining the output impedance of each grid-connected inverter, judging the resonance frequency section of the parallel resonance of a plurality of grid-connected inverter systems, and guiding an impedance adapter to be installed at a leading node inducing resonance, wherein the method comprises the following specific steps:
step 1, the system carries out m times of circulation in the process of site selection, and the frequency of operation in any circulation is recorded as operation frequency f a A =1,2, \8230;, m; setting an initial frequency f 0 Iteration step Δ f, i.e. f 1 ＝f 0 ，f a+1 ＝f a +Δf；
Step 2, obtaining the operation frequency f through off-line impedance measurement a Each grid-connected inverter A j Output impedance X of aj ；
Step 3, based on the output impedance X obtained in step 2 aj Known grid impedance X g Known collector line impedance X Dj Frequency of column write operation f a Time node admittance matrix Y fa And a node voltage equation;
will operate the frequency f a Time node admittance matrix Y fa Is inversely expressed as
Figure FDA0003183891130000021
The expression is as follows:
Figure FDA0003183891130000022
the expression of the node voltage equation is as follows:
Figure FDA0003183891130000023
wherein, U fa To operate the frequency f a Node voltage matrix of time, I fa To operate the frequency f a The expressions of the node current matrix are respectively as follows:
Figure FDA0003183891130000024
in the formula of U aj For grid-connected inverter A j Output voltage of V g For the mains voltage, I aj For grid-connected inverter A j Output current of I g Is the current of the power grid;
step 4, calculating the frequency f obtained in the step 3 a Inverse of the nodal admittance matrix of time
Figure FDA0003183891130000025
Eigenvalue decomposition was performed and expressed as:
Figure FDA0003183891130000026
wherein the content of the first and second substances,
Figure FDA0003183891130000031
is the operating frequency f a A diagonal feature matrix of time having common inclusion on the diagonalsi elements, and recording any one of the i elements as an operation frequency f a Modal impedance value of time
Figure FDA0003183891130000032
Ordered from top left to bottom right, i =1,2, \8230;, n, n +1, whose expressions are as follows:
Figure FDA0003183891130000033
L a as a diagonal feature matrix
Figure FDA00031838911300000310
Left eigenvector matrix of (1), R a As a diagonal feature matrix
Figure FDA0003183891130000034
A right eigenvector matrix of, and
Figure FDA0003183891130000035
the expressions are respectively as follows:
Figure FDA0003183891130000036
R a ＝(y A1 y a2 …y az …y a(n+1) )
in the formula, x az Is a left eigenvector, x az ＝(c z1 c z2 …c zz …c zn c z(n+1) )，c zz Is an irregular natural number; y is az Is a right eigenvector, y az ＝(e 1z ，e 2z ，…e zz …e zn e z(n+1) ) T ，e zz Is an irregular natural number, z =1,2, \8230, n +1; right eigenvector y az Should satisfy the formula
Figure FDA0003183891130000037
Left eigenvector x az Satisfy the formula
Figure FDA0003183891130000038
Calculating to obtain the operation frequency f according to the three matrixes a I modal impedance values of time
Figure FDA0003183891130000039
Step 5, firstly, calculating m × i modal impedance values at m operation frequencies according to the method from step 2 to step 4
Figure FDA0003183891130000041
Secondly, the number set formed by the ith element on the diagonal of the diagonal feature matrix obtained in the calculation process of all the operation frequencies is recorded as a mode M i I.e. by
Figure FDA0003183891130000042
Modal impedance value
Figure FDA0003183891130000043
Redefined as the same mode M i Corresponding modal impedance values, a =1,2, \8230;, m, i =1,2, \8230;, n, n +1;
step 6, for each mode M i Judging whether the mode is a key mode, wherein the method comprises the following steps:
if it satisfies
Figure FDA0003183891130000044
And is provided with
Figure FDA0003183891130000045
Then the mode M is identified i Modal impedance value of
Figure FDA0003183891130000046
In which at least one modal impedance pole is presentLarge value, define the mode M i Is a key modality;
if not satisfied with
Figure FDA0003183891130000047
And is provided with
Figure FDA0003183891130000048
Identify the mode M i No modal impedance maxima exist, i.e. they do not participate in the addressing of the impedance adapter;
step 7, comparing the modal impedance maximum values in the key modes obtained in the step 6, finding out the maximum value, and recording the operation frequency of the maximum value of the modal impedance as the parallel resonance frequency f of the system in the key mode b ；
Step 8, defining a participation point d, wherein the participation point d comprises n nodes j and 1 point-to-point PCC (d =1,2, \ 8230); n +1 and n +1 correspond to the point-to-point PCC;
writing a participation factor matrix F of n +1 participation points d in a key mode, wherein the matrix is a (n + 1) x (n + 1) matrix, and the d-th element on the diagonal line of the matrix is the participation factor of the participation point d;
the expression of the participation factor matrix F is as follows:
Figure FDA0003183891130000049
wherein x is bz To a parallel resonance frequency f b Corresponding left eigenvector, y bz To the parallel resonance frequency f b A corresponding right eigenvector;
and comparing the n +1 participation factors, finding out the maximum value of the participation factors, and marking a participation point corresponding to the maximum value as a leading node, wherein the leading node is the optimal installation position of the impedance adapter in the key mode.
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