Analysis Method for Harmonic Resonance Characteristics of a Multi - Converter Grid - Connected System

Abstract

The present invention discloses a method for analyzing harmonic resonance characteristics of a multi-converter grid-connected system based on double-order impedance modeling, comprising the following steps: S1. Construct a small-signal harmonic admittance model; S2. Combine the small-signal harmonic admittance model to construct a small-signal modal impedance matrix of the overall system, and analyze and predict the harmonic resonance frequency and harmonic amplitude value of the system through the small-signal modal impedance matrix.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to a method for analyzing harmonic resonance characteristics of a multi-converter grid-connected system. Background Art

[0002] In recent years, with the widespread application of new energy power generation technologies, distributed power generation technologies such as wind power and photovoltaics have been booming. As the interface for new energy grid connection, grid-connected converters play a key role in actual projects. Photovoltaic grid-connected converters have strong nonlinearity, and it is very easy for multiple photovoltaic converters and photovoltaic converters and distribution lines to interact, causing harmonic oscillations. Especially in more remote distribution networks, where the grid strength is reduced and the line impedance cannot be ignored, harmonic resonance will be more obvious.

[0003] In order to analyze the stability and harmonic resonance characteristics of the system, many scholars use impedance analysis and state space methods to analyze the internal dynamics of the converter and the harmonic resonance caused by its interaction with the power grid. Among them, the impedance analysis method establishes an equivalent impedance / admittance model of the converter-grid and uses the Nyquist stability criterion and the logarithmic frequency stability criterion or analyzes the resonant characteristics of the system. However, the dynamic characteristics of the phase-locked loop and other links were not considered in previous analyses, which may lead to inaccurate analysis results when performing resonance analysis. Summary of the invention

[0004] In view of this, the present invention provides a method for analyzing harmonic resonance characteristics of a multi-converter grid-connected system, so as to at least solve the problem that the method for obtaining the virtual series impedance parameters of the voltage source converter in the prior art is complex and inaccurate.

[0005] In order to achieve the above object, the present invention adopts the following technical solution:

[0006] A method for analyzing harmonic resonance characteristics of a multi-converter grid-connected system comprises the following steps:

[0007] S1. Construct a small perturbation harmonic admittance model:

[0008] S11. Inject positive sequence voltage disturbance at the PCC where the grid-connected converter GCC is connected to the grid and negative sequence voltage disturbances , respectively obtain the three-phase stationary coordinate system in the time domain and frequency domain and The voltage and current of the three phases at the PCC;

[0009] S12. Based on the voltage disturbance at PCC, the phase-locked loop outputs the phase angle With steady-state value There is a deviation angle , the transformation matrix between the three-phase stationary natural coordinate system and the dq coordinate system Perform linear decomposition to obtain the steady-state value matrix and the deviation angle matrix ;

[0010] S13. Convert the three-phase voltage in the time domain to the dq coordinate system through the steady-state value matrix to obtain the frequency-domain voltage in the dq coordinate system without considering the phase-locked loop deviation angle and the relationship between and ; Correspondingly obtain the frequency-domain voltage considering the phase-locked loop deviation angle and the relationship between and and ;

[0011] S14. Based on the relationship obtained in S13, further obtain the frequency-domain expression corresponding to the deviation angle and and , and then deduce the frequency-domain expressions of the disturbance response expressions and : and , and obtain the frequency-domain expression of and ; the frequency-domain expression of

[0012] S15. Use to convert the three-phase current in the time domain to the dq coordinate system to obtain and , and then obtain the corresponding current frequency-domain expressions: and , based on and obtain the modulation wave and corresponding to the GCC in the dq coordinate system: and , based on the inverse transformation of convert and to the three-phase stationary natural coordinate system to obtain the modulation wave in the three-phase stationary coordinates, and further obtain the frequency-domain expression of the modulation wave voltage according to the feedforward structure of the GCC: , and ;

[0013] S16. Based on the GCC average model, obtain , and the relationship with the inductive impedance , and then calculate the positive-sequence and negative-sequence harmonic admittances of GCC: and , thereby obtaining the harmonic admittance of GCC. Combine the harmonic admittances of the line and the grid impedance to construct a small-signal harmonic admittance model;

[0014] S2. Combine the small-signal harmonic admittance model to construct the small-signal modal impedance matrix of the overall system, and analyze and predict the system harmonic resonance frequency and harmonic amplitude value through the small-signal modal impedance matrix.

[0015] Preferably, in S11, the specific content of obtaining the three-phase voltages and currents at the PCC containing and in the three-phase stationary coordinate system in the time domain and frequency domain includes:

[0016] The three-phase voltages and currents at the PCC in the time domain are respectively:

[0017] ,

[0018] ,

[0019] wherein, corresponds to the fundamental voltage amplitude at the frequency of , and correspond to the amplitude and initial phase of the positive-sequence voltage perturbation at the frequency of , and correspond to the amplitude and initial phase of the negative-sequence voltage perturbation at the frequency of , and are respectively the amplitudes of the fundamental current, positive-sequence perturbation current response, and negative-sequence perturbation current response, and are respectively the initial phase angles of the fundamental current, positive-sequence perturbation current response, and negative-sequence perturbation current response; is the time;

[0020] Using the Fourier transform, the three-phase voltages and currents at the PCC in the frequency domain are:

[0021] ,

[0022] ,

[0023]

[0024] Wherein, ; ; , , , .

[0025] Preferably, the specific content of S12 includes:

[0026] The relationship between and is:

[0027] ,

[0028] In order to linearize the non - linear link in the coordinate transformation matrix, is decomposed into a steady - state value matrix and a deviation angle matrix in two parts:

[0029] ,

[0030] ,

[0031] .

[0032] Preferably, the specific content of S13 includes:

[0033] Without considering the deviation angle caused by the phase - angle perturbation of the phase - locked loop, using to transform the three - phase voltages and at the PCC from the three - phase stationary coordinate system to and in the dq coordinate system. After Fourier transform, the frequency - domain expressions and of and are respectively:

[0034] ,

[0035] ,

[0036] Wherein, is used to simulate the PWM delay, sampling delay and low - pass filtering link, is the complex frequency, represents the sampling period, is the cut - off frequency of the low - pass filter; dc is the DC component, that is, is 0;

[0037] Substitute The coordinate transformation matrix in the steady-state operating point is linearized near and is as follows:

[0038] .

[0039] Preferably, the specific content of S14 includes:

[0040] Assume that has a frequency-domain expression of:

[0041] ,

[0042] wherein and are the response functions of the positive-sequence voltage disturbance and the negative-sequence voltage disturbance respectively;

[0043] Based on the relational expression obtained in S13, the expression of is:

[0044] ,

[0045] According to the phase-locked loop principle, we have:

[0046] ,

[0047] Further, by simultaneously solving the assumed frequency-domain expression of , and the phase-locked loop principle expression, the expressions of , are solved:

[0048] ,

[0049] Then is specifically:

[0050] ,

[0051] wherein ; is the transfer function of the PI regulator of the phase-locked loop;

[0052] Combined with , we have:

[0053] ,

[0054] ,

[0055] ,

[0056] .

[0057] Preferably, the specific content of S15 includes:

[0058] Based on and and relationship, according to and obtain frequency domain expression of, using frequency domain expression of to convert the three-phase current at the PCC to the dq coordinate system to obtain and , and then obtain the corresponding current frequency domain expression:

[0059] ,

[0060] ,

[0061] In the formula, is the current sampling function, is used to simulate the sampling delay and the low-pass filter function, is the sampling period, is the cut-off frequency of the low-pass filter;

[0062] According to the feedforward decoupling control of the converter-side current, the modulation waves of GCC in the dq coordinate system and are:

[0063] ,

[0064] In the formula, is the current-loop PI regulator, , is the feedforward decoupling coefficient; and are the d-axis and q-axis grid-connected current reference values in the dq coordinate system respectively; are the d-axis and q-axis components of the converter-side current respectively; respectively represent the proportional coefficient and integral coefficient of the current-loop regulator;

[0065] ,

[0066] ,

[0067] Based on inverse transform of, convert and to the three-phase stationary natural coordinate system to obtain the modulation wave in the three-phase stationary coordinates, and further obtain the frequency domain expression of the modulation wave voltage according to the feedforward structure of GCC, where the feedforward structure expression of GCC is , where is the reference value of the converter's phase-A modulation voltage, is the phase-A modulation voltage without feedforward, is the voltage feedforward coefficient, is the phase-A voltage at the PCC, then there is:

[0068] ,

[0069] ,

[0070] .

[0071] Preferably, the specific content of S16 includes:

[0072] According to the topology of the GCC, the average model of the GCC is:

[0073] ,

[0074] In the formula, and are the phase-A, phase-B, and phase-C currents at the PCC, is the PWM gain, and are the grid-connected converter leg voltages, and are the phase-A, phase-B, and phase-C voltages at the PCC;

[0075] Combining the average model of the GCC with the frequency-domain expression of the modulation-wave voltage, the positive-sequence and negative-sequence harmonic admittances of the GCC are derived as:

[0076] ,

[0077] ,

[0078] In the formula, is the positive-sequence current perturbation, is the negative-sequence current perturbation; is the DC-side voltage;

[0079] The harmonic admittance of the GCC is:

[0080] ,

[0081] The expression of the harmonic admittance of the grid impedance is:

[0082] ,

[0083] The expression of the harmonic admittance of the line impedance is:

[0084] ,

[0085] In the formula, and are the line impedance and the equivalent inductance of the power grid, respectively.

[0086] Preferably, the specific content of S2 includes:

[0087] For a three-phase system with nodes at the operating point it can operate stably, where is the harmonic order, is the node voltage matrix of the th node under the th harmonic;

[0088] When positive and negative sequence small disturbance quantities are injected into the network nodes, the node voltage equation is expressed as:

[0089] ,

[0090] where and are the small disturbance harmonic impedance matrix of the network, the node small disturbance positive and negative sequence voltages, and the node small disturbance positive and negative sequence currents, respectively; are the elements of the matrix respectively, and are expressed as:

[0091] ,

[0092] The harmonic admittance matrix is decomposed into the following form:

[0093] ,

[0094] where and are the left and right eigenvector matrices respectively, ; is the diagonal eigenvalue matrix;

[0095] Substituting the decomposition form of the harmonic admittance matrix Y into the node voltage equation, we get:

[0096] ,

[0097] Defining as the modal current vector and as the modal voltage vector, the above equation is simplified to:

[0098] ,

[0099] Obtain the critical modes and their corresponding resonant frequencies according to the eigenvalues of the diagonal eigenvalue matrix, and complete the harmonic resonance analysis.

[0100] As can be seen from the above technical solutions, compared with the prior art, the present invention discloses a method for analyzing the harmonic resonance characteristics of a multi-converter grid-connected system, which has the following beneficial effects:

[0101] (1) The present invention proposes a method for analyzing the harmonic resonance characteristics of a multi-converter grid-connected system based on double-sequence impedance modeling. On the basis of the traditional resonance analysis method, the proposed resonance characteristic analysis method considers the d-axis and q-axis asymmetry dynamics caused by the PLL in the converter, and simultaneously analyzes the harmonic resonance characteristics of positive and negative sequence currents, greatly improving the analysis range and accuracy.

[0102] (2) Based on the harmonic resonance characteristic analysis method, the influences of key parameters such as filter parameters, line parameters, grid parameters, and PLL bandwidth on the harmonic resonance characteristics of the multi-converter grid-connected system are analyzed, verifying the application value of the proposed method in practical engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0104] Figure 1 Schematic diagram of the GCC topology structure of the photovoltaic conversion system provided by the embodiment of the present invention;

[0105] Figure 2 Schematic diagram of the control principle of the photovoltaic conversion system provided by the embodiment of the present invention;

[0106] Figure 3 Schematic diagram of the Norton equivalent circuit of the multi-photovoltaic converter parallel system provided by the embodiment of the present invention;

[0107] Figure 4 Schematic diagram of the system resonance characteristics under different filter inductance parameters provided by the embodiment of the present invention;

[0108] Figure 5 Schematic diagram of the system resonance characteristics under different grid inductance and line inductance parameters provided by the embodiment of the present invention; Figure 5 (a) Schematic diagram of the system resonance characteristics under different grid inductances; Figure 5 (b) Schematic diagram of the system resonance characteristics under different line inductances;

[0109] Figure 6Schematic diagram of the system resonance characteristics under different PLL bandwidth parameters provided by the embodiments of the present invention. Detailed implementation manners

[0110] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0111] The GCC topology of the photovoltaic conversion system is as Figure 1 shown. Figure 1 The meanings of the variables in it are: and are the arm voltages of the grid-connected converter; and are the PCC point voltages; and are the converter-side currents; and are the grid-connected currents; and are the grid voltages; is the DC-side voltage; and are the filter inductor, line impedance and grid equivalent inductor respectively; is the filter inductor and its damping resistor.

[0112] The control principle of the photovoltaic conversion system is as Figure 2 shown. The grid-connected converter adopts a current control method. Figure 2 In it, and are the d-axis and q-axis grid-connected current reference values in the dq coordinate system respectively; are the d-axis and q-axis components of the converter-side current respectively; are the d-axis and q-axis components of the PCC voltage respectively; is the feedforward decoupling coefficient; is the voltage feedforward coefficient; are the d-axis and q-axis modulation waves respectively; and are the modulation waves in the three-phase stationary coordinate system; and are the reference values of the converter modulation voltage; respectively represent the proportional coefficient and integral coefficient of the phase-locked loop regulator; respectively represent the proportional coefficient and integral coefficient of the current loop regulator. When operating stably, the voltage fluctuation on the DC side is very small, and the DC-side capacitor voltage is regarded as a constant value.

[0113] The present invention provides a method for analyzing the harmonic resonance characteristics of a multi-converter grid-connected system, comprising the following steps:

[0114] S1. Construct a small-signal harmonic admittance model:

[0115] S11. Inject positive-sequence voltage perturbation and negative-sequence voltage perturbation at the PCC where the grid-connected converter GCC is connected to the power grid, and obtain the three-phase voltages and currents at the PCC containing and in the three-phase stationary coordinate system in both the time domain and the frequency domain;

[0116] S12. Based on the voltage perturbation existing at the PCC, there is a deviation angle between the phase angle output by the phase-locked loop and the steady-state value . Linearly decompose the transformation matrix between the three-phase stationary natural coordinate system and the dq coordinate system to obtain the steady-state value matrix and the deviation angle matrix ;

[0117] S13. Convert the three-phase voltages in the time domain to the dq coordinate system through the steady-state value matrix to obtain the frequency-domain voltages in the dq coordinate system without considering the phase-locked loop deviation angle and and the relationship between and ; Correspondingly obtain the frequency-domain voltages considering the phase-locked loop deviation angle and and the relationship between and and through

[0118] S14. Based on the relationships obtained in S13, further obtain the frequency-domain expression corresponding to the deviation angle and the relationship between and , and then deduce the frequency-domain expressions of the perturbation response expressions and : and . According to and obtain the frequency-domain expression of ;

[0119] S15. Utilize Convert the three-phase current in the time domain to the dq coordinate system to obtain and , and then obtain the corresponding current frequency-domain expressions: and , based on and obtain the modulation waves of GCC in the dq coordinate system and corresponding frequency-domain expressions: and , based on inverse transform to and convert to the three-phase stationary natural coordinate system, obtain the modulation waves in the three-phase stationary coordinates, and further obtain the frequency-domain expression of the modulation wave voltage according to the feedforward structure of GCC: , and ;

[0120] S16. Based on the average model of GCC, obtain and the relationship with the inductance impedance , and then calculate the positive-sequence and negative-sequence harmonic admittances of GCC: and , thus obtaining the harmonic admittance of GCC, combining with the harmonic admittances of the line and the grid impedance, and constructing a small-signal harmonic admittance model;

[0121] S2. Combine the small-signal harmonic admittance model to construct the small-signal modal impedance matrix of the overall system, and analyze and predict the system harmonic resonance frequency and harmonic amplitude through the small-signal modal impedance matrix.

[0122] To further implement the above technical solution, the specific content of obtaining the three-phase voltages and currents at the PCC containing and in the three-phase stationary coordinate system in the time domain and frequency domain respectively includes:

[0123] The three-phase voltages and currents at the PCC in the time domain are respectively:

[0124] ,

[0125] ,

[0126] wherein, corresponds to the fundamental voltage amplitude at the frequency of , and correspond to the amplitude and initial phase of the positive-sequence voltage disturbance at the frequency of , and The amplitude and initial phase of the negative-sequence voltage disturbance corresponding to the frequency are and the amplitudes of the fundamental current, positive-sequence disturbance current response, and negative-sequence disturbance current response respectively, and the initial phase angles of the fundamental current, positive-sequence disturbance current response, and negative-sequence disturbance current response respectively; is time;

[0127] Using Fourier transform, the three-phase voltages and currents at the PCC in the frequency domain are:

[0128] ,

[0129] ,

[0130] ,

[0131] wherein, ; ; , , , .

[0132] To further implement the above technical solution, the specific content of S12 includes:

[0133] The relationship between and is:

[0134] ,

[0135] To linearize the non-linear link in the coordinate transformation matrix, is decomposed into a steady-state value matrix and a deviation angle matrix in two parts:

[0136] ,

[0137] ,

[0138] .

[0139] To further implement the above technical solution, the specific content of S13 includes:

[0140] When not considering the deviation angle caused by the phase angle disturbance of the phase-locked loop, using to transform the three-phase voltages at the PCC and Convert from three-phase stationary coordinate system to dq coordinate system and , after Fourier transformation, and Frequency domain expression of and They are:

[0141] ,

[0142] ,

[0143] In the formula, Used to simulate PWM delay, sampling delay and low-pass filtering. is the complex frequency, represents the sampling period, is the cut-off frequency of the low-pass filter; dc is the direct current, that is, is 0;

[0144] Will The coordinate transformation matrix in the steady-state operating point If linearized near and for:

[0145] .

[0146] In order to further implement the above technical solution, the specific contents of S14 include:

[0147] Assumptions The frequency domain expression of is:

[0148] ,

[0149] In the formula, and are the response functions of positive sequence voltage disturbance and negative sequence voltage disturbance respectively;

[0150] Based on the relational expression obtained in S13, we can obtain The expression is:

[0151] ,

[0152] According to the phase-locked loop principle:

[0153] ,

[0154] Further simultaneous hypothesis The frequency domain expression of And the principle expression of the phase-locked loop, solve , Expression:

[0155] ,

[0156] Then Specifically:

[0157] ,

[0158] In the formula, ; is the transfer function of the PI regulator of the phase-locked loop;

[0159] Combined with , then there is:

[0160] ,

[0161] ,

[0162] ,

[0163] .

[0164] It should be noted that:

[0165] In this embodiment, a phase-locked loop based on a synchronous rotating coordinate system is adopted, and the expression of the PI regulator of the phase-locked loop is: ;

[0166] To further implement the above technical solution, the specific content of S15 includes:

[0167] Based on and and relationship, according to and get frequency-domain expression, use frequency-domain expression to convert the three-phase current at the PCC to the dq coordinate system to obtain and , and then obtain the corresponding current frequency-domain expression:

[0168] ,

[0169] ,

[0170] In the formula, is the current sampling function, is used to simulate the sampling delay and low-pass filtering function, is the sampling period, is the cut-off frequency of the low-pass filter;

[0171] According to Figure 2 the converter - side current feed - forward decoupling control in and we can get the modulation waves of GCC in the dq coordinate system as follows:

[0172] ,

[0173] In the formula, is the PI regulator of the current loop, , is the feed - forward decoupling coefficient; and are the d - axis and q - axis grid - connected current reference values in the dq coordinate system respectively; are the d - axis and q - axis components of the converter - side current respectively; represent the proportional coefficient and integral coefficient of the current - loop regulator respectively;

[0174] ,

[0175] ,

[0176] Based on the inverse transformation of and are converted to the three - phase stationary natural coordinate system, and the modulation waves in the three - phase stationary coordinates are obtained. According to the feed - forward structure of GCC, the frequency - domain expression of the modulation - wave voltage is further obtained. The feed - forward structure expression of GCC is , where is the reference value of the converter A - phase modulation voltage, is the A - phase modulation voltage without feed - forward, is the voltage feed - forward coefficient, is the A - phase voltage at the PCC. As shown in Figure 2 , then we have:

[0177] ,

[0178] ,

[0179] ,

[0180] In order to further implement the above - mentioned technical solution, the specific content of S16 includes:

[0181] According to the topological structure of GCC, the average model of GCC is:

[0182] ,

[0183] In the formula, and The three-phase currents of A, B, and C at the PCC is the PWM gain and is the arm voltage of the grid-connected converter and is the three-phase voltages of A, B, and C at the PCC;

[0184] Combining the average model of the GCC and the frequency-domain expression of the modulation-wave voltage, the positive-sequence and negative-sequence harmonic admittances of the GCC are derived as:

[0185] ,

[0186] ,

[0187] where is the positive-sequence current perturbation is the negative-sequence current perturbation; is the DC-side voltage;

[0188] The harmonic admittance of the GCC is:

[0189] ,

[0190] The expression of the harmonic admittance of the grid impedance is:

[0191] ,

[0192] The expression of the harmonic admittance of the line impedance is:

[0193] ,

[0194] where and are the line impedance and the grid equivalent inductance, respectively.

[0195] To further implement the above technical solution, the specific content of S2 includes:

[0196] For a three-phase system with nodes, it can operate stably at the operating point , where is the harmonic order is the node voltage matrix of the th node at the , ; ;

[0197] When injecting positive- and negative-sequence small perturbation amounts into the network nodes, the node voltage equation is expressed as:

[0198] ,

[0199] Among them, and are the small disturbance harmonic impedance matrix of the network, the positive and negative sequence voltages of the node small disturbance, and the positive and negative sequence currents of the node small disturbance respectively; are respectively the elements of the matrix and are respectively expressed as:

[0200] ,

[0201] Harmonic admittance matrix is decomposed into the following form:

[0202] ,

[0203] Among them, and are respectively the left and right eigenvector matrices, ; is the diagonal eigenvalue matrix;

[0204] Substitute the decomposition form of the harmonic admittance matrix into the node voltage equation to obtain:

[0205] ,

[0206] Define as the modal current vector, Define

[0207] ,

[0208] Obtain the critical mode and its corresponding resonant frequency according to the eigenvalues of the diagonal eigenvalue matrix to complete the harmonic resonance analysis.

[0209] It should be noted that:

[0210] In S1, a small disturbance harmonic admittance model of each component of the system is constructed. In S2, the improved generalized modal analysis method is used to combine the small disturbance harmonic admittance models of each component to construct the small disturbance modal impedance matrix of the whole system. The small disturbance modal impedance matrix can be used to analyze and predict the harmonic resonance frequency and harmonic amplitude value of the system.

[0211] The inverse of the eigenvalue of the eigenmatrix shows impedance properties, and the inverse matrix of the diagonal eigenmatrix is defined as the modal impedance matrix . When tends to zero, its inverse tends to infinity at this time. Inject a very small modal current into the system, and the node will excite a very large modal voltage . Since the other modal voltages and modal currents are linearly independent, the other modal voltages are not affected. In addition, the smallest eigenvalue in the diagonal eigenmatrix is called the critical mode, and the corresponding frequency is the resonance frequency of the GCC system.

[0212] The harmonic resonance analysis of the distributed photovoltaic cluster access system will be carried out below:

[0213] Considering the grid impedance and line impedance of the system, based on the harmonic admittance model of the photovoltaic converter, the harmonic admittance model of the grid impedance, and the harmonic admittance model of the line impedance constructed above, the Norton equivalent circuit of the multi-converter parallel system is obtained as Figure 3 shown, and the system parameters are shown in Table 1:

[0214] Table 1

[0215] ,

[0216] According to the listed simulation parameters, the analysis results of the system harmonic resonance characteristics under different filter inductor parameters are as Figure 4 shown. There is a resonance peak in the system. As the value of the filter inductor increases, the resonance center of the resonance mode drops from 8.62 p.u. to 7.4 p.u., and the corresponding modal impedance amplitude also decreases. The obtained results show that increasing the filter parameter value can improve the filtering effect to a certain extent and suppress the resonance of the system.

[0217] The analysis results of the system harmonic resonance characteristics under different grid inductor and line inductor parameters are as Figure 5 shown in (a) and (b). As the value of the grid inductor increases, the resonance center of the resonance mode drops from 8.68 p.u. to 6.8 p.u., and the corresponding modal impedance amplitude also decreases. When the value of the line inductor increases, the center of the resonance mode remains almost unchanged, but the amplitude of the modal impedance decreases.

[0218] According to the definition of the PLL bandwidth, the relationship between the bandwidth and the natural frequency is:

[0219] ,

[0220] where:

[0221] ,

[0222] Considering the requirements of system stability and dynamic performance, the damping is generally taken as 0.707, is the PCC point voltage under the rated condition, which is about 310V. From the above bandwidth and the natural frequency Relationship establishment of PLL bandwidth The relational expressions with the proportional coefficient and integral coefficient of the PLL regulation. Substituting the PLL bandwidth into the harmonic admittance model of the converter, the harmonic resonance characteristics of the system under different PLL bandwidths can be analyzed, and the results are as Figure 6 shown.

[0223] It can be seen that as the PLL bandwidth increases, the resonance center drops from 8.7 p.u. to 6.16 p.u., and the corresponding modal impedance amplitude decreases significantly.

[0224] The above embodiments are only used to illustrate the technical solutions of the present application, rather than limiting them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A method for analyzing harmonic resonance characteristics of a multi-converter grid-connected system, characterized in that: The following steps are involved: S1. Construct a small perturbation harmonic admittance model: S11. Inject positive sequence voltage disturbance at the PCC where the grid-connected converter GCC is connected to the grid and negative sequence voltage disturbances , respectively obtain the three-phase stationary coordinate system in the time domain and frequency domain and The voltage and current of the three phases at the PCC; S12. Based on the voltage disturbance at PCC, the phase-locked loop outputs the phase angle With steady-state value There is a deviation angle , the transformation matrix between the three-phase stationary natural coordinate system and the dq coordinate system Perform linear decomposition to obtain the steady-state value matrix and the deviation angle matrix ; S13. Through the steady-state value matrix Convert the three-phase voltage in the time domain to the dq coordinate system and obtain the phase-locked loop deviation angle in the dq coordinate system without considering the phase-locked loop deviation angle. Frequency domain voltage and and and the relationship between Corresponding acquisition considering the phase-locked loop deviation angle Frequency domain voltage and and and the relationship between; S14. Based on the relationship obtained in S13, further obtain the deviation angle The corresponding frequency domain expression is and and The relationship between and The frequency domain expression of is: and ,according to and get Frequency domain expression of ; S15. Utilization Convert the three-phase current in the time domain to the dq coordinate system to obtain and , and then the corresponding current frequency domain expression is obtained: and ,based on and Get the modulation wave of GCC in the dq coordinate system and The corresponding frequency domain expression is: and ,based on The inverse transformation will be and Converted to the three-phase stationary natural coordinate system, the modulation wave under the three-phase stationary coordinate system is obtained. According to the feedforward structure of GCC, the frequency domain expression of the modulation wave voltage is further obtained: , and ; S16. Based on the GCC average model, we get , and With inductor impedance The relationship between and then calculates the positive and negative sequence harmonic admittance of GCC: and , thus obtaining the harmonic admittance of GCC, combining the harmonic admittance of line and grid impedance, and constructing a small disturbance harmonic admittance model; S2. Combined with the small perturbation harmonic admittance model, the small perturbation modal impedance matrix of the system as a whole is constructed, and the harmonic resonant frequency and resonance amplitude of the system are analyzed and predicted through the small perturbation modal impedance matrix.

2. A method for analyzing harmonic resonance characteristics of a multi-converter grid-connected system according to claim 1, characterized in that: In S11, the three-phase stationary coordinate system is obtained in the time domain and frequency domain respectively. and The specific contents of the three-phase voltage and current at the PCC include: The three-phase voltages and currents at the PCC in the time domain are: ， ， In the formula, The corresponding frequency is The fundamental voltage amplitude, and The corresponding frequency is The amplitude and initial phase of the positive sequence voltage disturbance, and The corresponding frequency is The amplitude and initial phase of the negative sequence voltage disturbance, and are the amplitudes of fundamental current, positive sequence disturbance current response and negative sequence disturbance current response, respectively. and They are the initial phase angles of fundamental current, positive sequence disturbance current response and negative sequence disturbance current response respectively; For time; Using Fourier transform, the three-phase voltage and current at PCC in the frequency domain are obtained as follows: ， ， ， In the formula, ; ; , , , .

3. A method for analyzing harmonic resonance characteristics of a multi-converter grid-connected system according to claim 1, characterized in that: The specific contents of S12 include: and and The relationship is: ， In order to linearize the nonlinear link in the coordinate transformation matrix, Decompose into a steady-state value matrix and the deviation angle matrix Two parts: ， ， 。 4. A method for analyzing harmonic resonance characteristics of a multi-converter grid-connected system according to claim 2, characterized in that: The specific contents of S13 include: The deviation angle caused by the phase angle disturbance of the phase-locked loop is not considered. When using The three-phase voltage at PCC and Convert from three-phase stationary coordinate system to dq coordinate system and , after Fourier transformation, and Frequency domain expression of and They are: ， ， In the formula, Used to simulate PWM delay, sampling delay and low-pass filtering. is the complex frequency, represents the sampling period, is the cut-off frequency of the low-pass filter; dc is the direct current, that is, is 0; Will The coordinate transformation matrix in the steady-state operating point If linearization is done near and for: 。 5. A method for analyzing harmonic resonance characteristics of a multi-converter grid-connected system according to claim 4, characterized in that: The specific contents of S14 include: Assumptions The frequency domain expression of is: ， In the formula, and are the response functions of positive sequence voltage disturbance and negative sequence voltage disturbance respectively; Based on the relational expression obtained in S13, we can obtain The expression is: ， According to the phase-locked loop principle: ， Further simultaneous hypothesis The frequency domain expression of And the principle expression of the phase-locked loop, solve , The expression is: ， but Specifically: ， In the formula, ; is the transfer function of the PI regulator of the phase-locked loop; Combination , then: ， ， ， 。 6. A method for analyzing harmonic resonance characteristics of a multi-converter grid-connected system according to claim 5, characterized in that: The specific contents of S15 include: based on and and relationship, according to and get The frequency domain expression of The frequency domain expression of the three-phase current at the PCC is converted to the dq coordinate system to obtain and , and then the corresponding current frequency domain expression is obtained: ， ， In the formula, is the current sampling function, Used to simulate sampling delay and low-pass filtering functions, is the sampling period, is the cutoff frequency of the low-pass filter; According to the current feedforward decoupling control on the converter side, the modulation wave of GCC in the dq coordinate system is and for: ， In the formula, is the current loop PI regulator, , is the feedforward decoupling coefficient; and are the d-axis and q-axis grid-connected current reference values ​​in the dq coordinate system respectively; They are the d-axis and q-axis components of the converter side current respectively; They represent the proportional coefficient and integral coefficient of the current loop regulator respectively; ， ， based on The inverse transformation will be and Transformed to the three-phase stationary natural coordinate system, the modulation wave under the three-phase stationary coordinate system is obtained. According to the feedforward structure of GCC, the frequency domain expression of the modulation wave voltage is further obtained, where the feedforward structure expression of GCC is: ,in is the reference value of the modulation voltage of phase A of the converter, is the A-phase modulation voltage without feedforward, is the voltage feed-forward coefficient, is the phase A voltage at PCC, then: ， ， 。 7. A method for analyzing harmonic resonance characteristics of a multi-converter grid-connected system according to claim 6, characterized in that: The specific contents of S16 include: According to the topological structure of GCC, the average model of GCC is: ， In the formula, and is the three-phase current of A, B and C at PCC, is the PWM gain, and is the bridge arm voltage of the grid-connected converter, and is the three-phase voltage of A, B and C at PCC; Combining the GCC average model with the frequency domain expression of the modulation wave voltage, the positive and negative sequence harmonic admittances of GCC are derived as follows: ， ， In the formula, is the positive sequence current disturbance, is the negative sequence current disturbance, is the DC side voltage; The harmonic admittance of GCC is: ， The expression of harmonic admittance of grid impedance is: ， The expression for the harmonic admittance of the line impedance is: ， In the formula, and are line impedance and grid equivalent inductance respectively.

8. The method for analyzing harmonic resonance characteristics of a multi-converter grid-connected system according to claim 1, characterized in that: The specific contents of S2 include: For those with The three-phase system with 10 nodes is at the working point It can run stably under is the harmonic order, for Subharmonic The node voltage matrix of nodes, ; When a small positive and negative sequence disturbance is injected into the network node When , the node voltage equation is expressed as: ， in, and They are the small disturbance harmonic impedance matrix of the network, the small disturbance positive and negative sequence voltage of the node, and the small disturbance positive and negative sequence current of the node; The matrices are The elements are represented as: ， Harmonic Admittance Matrix Decomposed into the following form: ， in, and are the left and right eigenvector matrices, ; is a diagonal eigenvalue matrix; Substituting the decomposed form of the harmonic admittance matrix Y into the node voltage equation, we get: ， Will Defined as the modal current vector, Defined as the modal voltage vector, the above equation is simplified to: ， The critical modes and their corresponding resonant frequencies are obtained according to the eigenvalues ​​of the diagonal eigenvalue matrix to complete the harmonic resonance analysis.

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