CN114564821A - Grid-connected inverter impedance modeling method based on single-phase disturbance injection - Google Patents

Grid-connected inverter impedance modeling method based on single-phase disturbance injection Download PDF

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CN114564821A
CN114564821A CN202210091536.3A CN202210091536A CN114564821A CN 114564821 A CN114564821 A CN 114564821A CN 202210091536 A CN202210091536 A CN 202210091536A CN 114564821 A CN114564821 A CN 114564821A
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frequency
omega
phase
grid
connected inverter
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赵静波
马俊鹏
王顺亮
刘天琪
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Sichuan University
Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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Sichuan University
Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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    • 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
    • H02J3/38—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
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/493—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode the static converters being arranged for operation in parallel
    • 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
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/40—Arrangements for reducing harmonics

Abstract

The invention discloses a grid-connected inverter impedance modeling method based on single-phase disturbance injection, which specifically comprises the following steps: the method comprises the steps of considering phase-locked loop frequency coupling response, and analyzing harmonic response frequency generated after single-phase disturbance is injected into an alternating current power grid; expressing positive and negative sequence harmonic responses at the PCC by using a fast Fourier transform and an alpha beta coordinate system; and optimizing the frequency point selection value and the number of the single-phase disturbance injection according to different coupling harmonic conditions. The impedance modeling method based on single-phase disturbance injection provided by the invention reduces the complexity and required capacity of impedance measurement equipment, reduces the equipment volume and improves the impedance modeling accuracy.

Description

Grid-connected inverter impedance modeling method based on single-phase disturbance injection
Technical Field
The invention belongs to the field of converter modeling, and particularly relates to a grid-connected inverter impedance modeling method based on single-phase disturbance injection.
Background
Impedance modeling has become an important means for analyzing the stability of the converter-grid interconnection system. The impedance model of the grid-connected inverter is established by measuring the impedance values of the grid-connected inverter under different frequencies through a mathematical method, however, the traditional three-phase impedance measurement method requires impedance measurement to have large capacity and volume, which brings higher cost and energy consumption. The single-phase disturbance injection method only needs to carry out frequency sweep once, frequency sweep times are reduced, the single-phase disturbance injection only needs to inject harmonic waves into the single-phase inverter, the complexity of the harmonic wave generating device is reduced, single energy consumption is reduced, and economy and practicability are improved. The existing impedance calculation method considering frequency coupling needs to change the impedance of a power grid, and the operation is likely to change the operating point of the system and is complex, thus being not beneficial to practical use.
Disclosure of Invention
In order to reduce the volume and energy consumption of a grid-connected inverter impedance measuring device and ensure the correctness of a measuring result, the invention provides a grid-connected inverter impedance modeling method based on single-phase disturbance injection.
The invention discloses a grid-connected inverter impedance modeling method based on single-phase disturbance injection, which comprises the following steps of:
step 1: and calculating the harmonic frequency generated by three phases after single-phase injection disturbance at the alternating-current side of the grid-connected inverter.
After voltage disturbance is injected into the A phase of the alternating current side of the grid-connected inverter, a three-phase alternating voltage signal is expressed as:
Figure BDA0003489242070000011
wherein, V1For the amplitude of the mains voltage, VpFor disturbing the voltage amplitude, omega0For grid voltage angular frequency, omegapTo disturb the voltageAngular frequency, thetapIs the initial phase of the disturbance voltage.
The three-phase ac voltage signal is dq converted into:
Figure BDA0003489242070000012
wherein, thetasThe phase is output for the phase locked loop.
Expression (2) is expressed as a complex variable form:
Figure BDA0003489242070000021
form ejxThe method is characterized in that cos x + jsin x is Euler transformation, a dq transformed small disturbance voltage signal is obtained, and only a q-axis component causes an output phase theta of a phase-locked loopsThe disturbance amount of Δ θ is generated, and the transfer function of the phase-locked loop is:
Figure BDA0003489242070000022
wherein k isppIs a phase-locked loop proportionality coefficient, kpiFor the integral coefficient of the phase-locked loop, after introducing phase angle disturbance due to the influence of the phase-locked loop and Park transformation:
θ＝ω0t+Δθ (5)
Substituting the formula (5) into the formula (3) and carrying out linearization to obtain:
Figure BDA0003489242070000023
equation (6) translates to:
Figure BDA0003489242070000024
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003489242070000025
has an imaginary part of-jV1Delta theta, complex variable
Figure BDA0003489242070000026
Combining equation (4) and equation (5) yields:
Figure BDA0003489242070000027
obtained according to equations (6), (7) and (8):
Figure BDA0003489242070000028
as can be seen from equation (9), due to the influence of the phase-locked loop, a frequency ω is inputpThe single-phase voltage disturbance of (2) generates four frequency responses in the dq coordinate system, wherein the four frequency responses are respectively (omega)p-ω0)、(ω0-ωp)、(ω0+ωp) And (-omega)0-ωp) Converting to three-phase coordinate system, the four frequencies become omegap、(2ω0-ωp)、(2ω0+ωp) And-omegapThis is a single input multiple output phenomenon due to frequency coupling caused by the phase locked loop.
Step 2: injecting voltage (or current) disturbance with different frequencies into any phase of the AC side of the grid-connected inverter, extracting the voltage and the current at a common Point (PCC), and obtaining the harmonic amplitudes of the positive sequence and the negative sequence of the three phases by Fast Fourier Transform (FFT).
Extracting three-phase voltage and current signals at the PCC after single-phase injection voltage disturbance, and obtaining voltage and current signals v under an alpha-beta coordinate system through Clark transformationα、vβ，iα、iβAnd obtaining voltage and current positive and negative sequence harmonics through FFT analysis:
Figure BDA0003489242070000031
Figure BDA0003489242070000032
Figure BDA0003489242070000033
wherein v isp、ipIs a positive sequence voltage, current harmonic, v n、inIs a negative sequence voltage and a current harmonic,
Figure BDA0003489242070000034
representing the component with a fourier transform back angle frequency of ω.
And step 3: according to the obtained amplitude of each harmonic wave, the self impedance and the mutual impedance of the frequency coupling are obtained;
the self-impedance expression of the grid-connected inverter is as follows:
Figure BDA0003489242070000035
wherein Z issFor self-impedance of the grid-connected inverter, ZaFor grid-connected inverter transimpedance, YsFor grid-connected inverters self-admittance, YaIs the mutual admittance of the grid-connected inverter.
YsAnd YaCalculated from equation (12):
Figure BDA0003489242070000036
wherein, Ys(ωp) Representing the frequency of the grid-connected inverter as the injection disturbance frequency omegapSelf-admittance of time, Ya(ωc) Representing the coupling frequency omega of the grid-connected inverter at the frequency of the injection disturbance frequencycMutual admittance of time, Ya(ωp)*Representing the frequency of the grid-connected inverter as the injection disturbance frequency omegapMutual conductance of timeConjugation of sodium, Ys(ωc)*Representing the coupling frequency omega of the grid-connected inverter at the frequency of the injection disturbance frequencycThe self-admittance during the time of the operation,
Figure BDA0003489242070000037
representing the injection frequency omegapThe response current of the port of the grid-connected inverter after the single-phase disturbance is in omegapThe component (b) of (a) is,
Figure BDA0003489242070000038
representing the injection frequency omegapThe response current of the port of the grid-connected inverter after the single-phase disturbance of the coupling frequency is in omegapThe component (b) of (a) is,
Figure BDA0003489242070000039
representing the injection frequency omegapThe response current of the port of the grid-connected inverter after the single-phase disturbance is in omega pOf coupling frequency omegacThe conjugate of the components is determined by the conjugate of the components,
Figure BDA00034892420700000310
representing the injection frequency omegapThe response current of the port of the grid-connected inverter after the single-phase disturbance of the coupling frequency is in omegacThe component (b) of (a) is,
Figure BDA00034892420700000311
representing the injection frequency omegapThe response voltage of the grid-connected inverter port after single-phase disturbance is in omegapThe component (b) of (a) is,
Figure BDA00034892420700000312
representing the injection frequency omegapThe response voltage of the port of the grid-connected inverter after the single-phase disturbance of the coupling frequency is in omegapThe component (b) of (a) is,
Figure BDA0003489242070000041
representing the injection frequency omegapThe response voltage of the grid-connected inverter port after single-phase disturbance is in omegapOf coupling frequency omegacThe conjugate of the components is determined by the conjugate of the components,
Figure BDA0003489242070000042
representing the injection frequency omegapThe response voltage of the port of the grid-connected inverter after the single-phase disturbance of the coupling frequency is in omegacThe component (c).
When the frequency of the injected disturbance is omegapLess than 2 omega0The coupling frequency harmonic should be 2 ω in the positive sequence component0-ωpA component; when the frequency of the injected disturbance is omegapGreater than 2 omega0The coupling frequency harmonic should be 2 ω in the negative sequence component0-ωpA component;
during the impedance scan, the frequency of the injection is required to be omegapAnd its coupling frequency |2 ω0-ωpI, extracting a frequency omega from the obtained voltage current at the PCCpAnd its corresponding harmonic component of the coupling frequency.
The concrete classification is as follows:
when the predetermined frequency is ω pLess than 2 omega0The method comprises the following steps:
(1) the injection frequency of any phase to the AC side of the grid-connected inverter is omegapSmall perturbation signals of (2);
(2) extracting the frequency at PCC as omegapAnd 2 omega0-ωpPositive sequence voltage, current harmonic components;
(3) the injection frequency of any phase to the AC side of the grid-connected inverter is 2 omega0-ωpSmall perturbation signals of (2);
(4) extracting the frequency at PCC as omegapAnd 2 omega0-ωpPositive sequence voltage, current harmonic components.
When the predetermined frequency is ωpGreater than 2 omega0The method comprises the following steps:
(1) the injection frequency of any phase to the AC side of the grid-connected inverter is omegapSmall perturbation signals of (2);
(2) extracting the frequency at PCC as omegapPositive sequence voltage, current harmonic component and frequency of omegap-2ω0Negative sequence voltage, current harmonic components;
(3) to the AC side of the grid-connected inverterThe injection frequency of any one phase is omegap-2ω0Small perturbation signals of (2);
(4) extracting the frequency at PCC as omegapPositive sequence voltage, current harmonic component and frequency of omegap-2ω0Negative sequence voltage, current harmonic components.
The beneficial technical effects of the invention are as follows:
the invention provides a modeling method capable of reducing the volume of an impedance measuring device without changing the impedance of a power grid under the condition of considering the frequency coupling of a phase-locked loop, analyzes the response harmonic condition of single-phase injection disturbance generated in a three-phase system, explains the extraction method of harmonic components when the injection disturbance frequencies are different, reduces the disturbance injection times, reduces the energy consumption during impedance measurement and improves the modeling precision.
Drawings
FIG. 1 is a block diagram of the impedance measurement system of the grid-connected inverter of the present invention;
fig. 2 is a comparison graph of the self-impedance and transadmittance modeling result and the frequency sweep result of the grid-connected inverter of the invention.
Detailed Description
The invention is described in further detail below with reference to the drawings and the detailed description.
The impedance measurement operation structure of the grid-connected inverter is shown in fig. 1, an alternating current power grid is simulated by impedance and an ideal three-phase power supply, a direct current side is equivalent to a direct current voltage source, three-phase voltage and current responses are extracted from a PCC, three-phase voltage and current information of harmonic components with required frequency is calculated through a data preprocessing module, and a grid-connected inverter impedance model is obtained through a data calculating module.
The invention discloses a grid-connected inverter impedance modeling method based on single-phase disturbance injection, which comprises the following steps of:
step 1: and calculating the harmonic frequency generated by three phases after single-phase injection disturbance at the alternating-current side of the grid-connected inverter.
After voltage disturbance is injected into the A phase of the alternating current side of the grid-connected inverter, a three-phase alternating voltage signal is expressed as:
Figure BDA0003489242070000051
wherein, V1For the amplitude of the mains voltage, VpFor disturbing the voltage amplitude, omega0For grid voltage angular frequency, omegapTo perturb the voltage angular frequency, theta pIs the initial phase of the disturbance voltage.
After the three-phase alternating current voltage signal is subjected to dq conversion, the three-phase alternating current voltage signal is:
Figure BDA0003489242070000052
wherein, thetasThe phase is output for the phase locked loop.
Expression (2) is expressed as a complex variable form:
Figure BDA0003489242070000053
wherein, form ejxThe method is characterized in that cos x + jsin x is Euler transformation, a dq transformed small disturbance voltage signal is obtained, and only a q-axis component causes an output phase theta of a phase-locked loopsThe disturbance amount of Δ θ is generated, and the transfer function of the phase-locked loop is:
Figure BDA0003489242070000054
wherein k isppIs a phase-locked loop proportionality coefficient, kpiFor the integral coefficient of the phase-locked loop, after introducing phase angle disturbance due to the influence of the phase-locked loop and Park transformation:
θ＝ω0t+Δθ (5)
substituting the formula (5) into the formula (3) and linearizing to obtain:
Figure BDA0003489242070000061
equation (6) translates to:
Figure BDA0003489242070000062
wherein the content of the first and second substances,
Figure BDA0003489242070000063
has an imaginary part of-jV1Delta theta, complex variable
Figure BDA0003489242070000064
Combining equation (4) and equation (5) yields:
Figure BDA0003489242070000065
obtained according to equations (6), (7) and (8):
Figure BDA0003489242070000066
as can be seen from equation (9), due to the influence of the phase-locked loop, a frequency ω is inputpThe single-phase voltage disturbance of (2) generates four frequency responses in the dq coordinate system, wherein the four frequency responses are respectively (omega)p-ω0)、(ω0-ωp)、(ω0+ωp) And (-omega)0-ωp) Converting to three-phase coordinate system, the four frequencies become omegap、(2ω0-ωp)、(2ω0+ωp) And-omegapThis is a single input multiple output phenomenon due to frequency coupling caused by the phase locked loop.
Step 2: injecting voltage (or current) disturbance with different frequencies into any phase of the AC side of the grid-connected inverter, extracting the voltage and the current at a common Point (PCC), and obtaining the harmonic amplitudes of the positive sequence and the negative sequence of the three phases by Fast Fourier Transform (FFT).
Extracting three-phase voltage and current signals at the PCC after single-phase injection voltage disturbance, and obtaining alpha beta through Clark transformationVoltage and current signals v under coordinate systemα、vβ，iα、iβAnd obtaining voltage and current positive and negative sequence harmonics through FFT analysis:
Figure BDA0003489242070000067
Figure BDA0003489242070000068
Figure BDA0003489242070000069
wherein v isp、ipIs a positive sequence voltage, current harmonic, vn、inNegative sequence voltage, current harmonics.
And step 3: according to the obtained amplitude of each harmonic wave, the self impedance and the mutual impedance of the frequency coupling are obtained;
the self-impedance expression of the grid-connected inverter is as follows:
Figure BDA0003489242070000071
wherein Z issFor self-impedance of the grid-connected inverter, ZaFor grid-connected inverter transimpedance, YsFor grid-connected inverters self-admittance, YaIs the mutual admittance of the grid-connected inverter.
YsAnd YaCalculated from equation (12):
Figure BDA0003489242070000072
wherein, Ys(ωp) Representing the frequency of the grid-connected inverter as the injection disturbance frequency omegapSelf-admittance of time, Ya(ωc) Representing the coupling frequency omega of the grid-connected inverter at the frequency of the injection disturbance frequencycMutual admittance of time, Ya(ωp)*Representing the frequency of the grid-connected inverter as the injection disturbance frequency omegapConjugation of transadmittance of time, Ys(ωc)*Representing the coupling frequency omega of the grid-connected inverter at the frequency of the injection disturbance frequencycThe self-admittance during the time of the operation,
Figure BDA0003489242070000073
representing the injection frequency omegapThe response current of the port of the grid-connected inverter after the single-phase disturbance is in omegapThe component (b) of (a) is,
Figure BDA0003489242070000074
Representing the injection frequency omegapThe response current of the port of the grid-connected inverter after the single-phase disturbance of the coupling frequency is in omegapThe component (b) of (a) is,
Figure BDA0003489242070000075
representing the injection frequency omegapThe response current of the port of the grid-connected inverter after the single-phase disturbance is in omegapOf coupling frequency omegacThe conjugate of the components is determined by the conjugate of the components,
Figure BDA0003489242070000076
representing the injection frequency omegapThe response current of the port of the grid-connected inverter after the single-phase disturbance of the coupling frequency is in omegacThe component (b) of (a) is,
Figure BDA0003489242070000077
representing the injection frequency omegapThe response voltage of the grid-connected inverter port after single-phase disturbance is in omegapThe component (b) of (a) is,
Figure BDA0003489242070000078
representing the injection frequency omegapThe response voltage of the port of the grid-connected inverter after the single-phase disturbance of the coupling frequency is in omegapThe component (b) of (a) is,
Figure BDA0003489242070000079
representing the injection frequency omegapAfter single-phase disturbance ofThe response voltage of the grid-connected inverter port is in omegapOf coupling frequency omegacThe conjugate of the components is determined by the conjugate of the components,
Figure BDA00034892420700000710
representing the injection frequency omegapThe response voltage of the port of the grid-connected inverter after the single-phase disturbance of the coupling frequency is in omegacThe component (c).
When the frequency of the injected disturbance is omegapLess than 2 omega0The coupling frequency harmonic should be 2 ω in the positive sequence component0-ωpA component; when the frequency of the injected disturbance is omegapGreater than 2 omega0The coupling frequency harmonic should be 2 ω in the negative sequence component0-ωpA component;
during the impedance scan, the frequency of the injection is required to be omegapAnd its coupling frequency |2 ω 0-ωpA small disturbance signal with the frequency of omega is extracted from the obtained voltage and current at the PCCpAnd its corresponding harmonic component of the coupling frequency.
The concrete classification is as follows:
when the predetermined frequency is ωpLess than 2 omega0The method comprises the following steps:
(1) the injection frequency of any phase to the AC side of the grid-connected inverter is omegapSmall perturbation signals of (2);
(2) extracting the frequency at PCC as omegapAnd 2 omega0-ωpPositive sequence voltage, current harmonic components;
(3) the injection frequency of any phase to the AC side of the grid-connected inverter is 2 omega0-ωpSmall perturbation signals of (2);
(4) extracting the frequency at PCC as omegapAnd 2 omega0-ωpPositive sequence voltage, current harmonic components.
When the predetermined frequency is ωpGreater than 2 omega0The method comprises the following steps:
(1) the injection frequency of any phase to the AC side of the grid-connected inverter is omegapSmall perturbation signals of (2);
(2) extracting the frequency at PCC as omegapPositive sequence voltage, current harmonic components ofAnd a frequency of ωp-2ω0Negative sequence voltage, current harmonic components;
(3) the injection frequency of any phase to the AC side of the grid-connected inverter is omegap-2ω0Small perturbation signals of (2);
(4) extracting the frequency at PCC as omegapPositive sequence voltage, current harmonic component and frequency of omegap-2ω0Negative sequence voltage, current harmonic components.
Fig. 2 is a comparison graph of the calculated values and the measured values of the amplitude and the phase of the self-admittance and the mutual admittance of the grid-connected inverter according to the scheme of the present invention, where the graphs (a) and (d) are comparison graphs of the amplitude and the phase of the self-admittance, the graphs (b) and (c) are comparison graphs of the amplitude and the phase of the mutual admittance, a solid line is a theoretical value admittance curve calculated according to an admittance expression, and a scatter point is an admittance value corresponding to each frequency obtained by actual measurement, so that it can be seen that the measured values and the calculated values of the grid-connected inverter are consistent, and the accuracy of the proposed method is high.

Claims (2)

1. A grid-connected inverter impedance modeling method based on single-phase disturbance injection is characterized by comprising the following steps:
step 1: calculating harmonic frequency generated by three phases after single-phase injection disturbance at the alternating-current side of the grid-connected inverter;
after voltage disturbance is injected into the A phase of the alternating current side of the grid-connected inverter, a three-phase alternating voltage signal is expressed as:
Figure FDA0003489242060000011
wherein, V1For the amplitude of the mains voltage, VpFor disturbing the voltage amplitude, omega0For grid voltage angular frequency, omegapTo perturb the voltage angular frequency, thetapThe initial phase of the disturbance voltage is t is time;
the three-phase ac voltage signal is dq converted into:
Figure FDA0003489242060000012
wherein, thetasOutputting the phase for the phase locked loop;
expression (2) is expressed as a complex variable form:
Figure FDA0003489242060000013
wherein, form ejxThe euler transformation is performed on cosx + jsinx, the small disturbance voltage signal is subjected to dq transformation, and only q-axis component causes output phase theta of the phase-locked loopsThe disturbance amount of Δ θ is generated, and the transfer function of the phase-locked loop is:
Figure FDA0003489242060000014
wherein k isppIs a phase-locked loop proportionality coefficient, kpiFor the integral coefficient of the phase-locked loop, after introducing phase angle disturbance due to the influence of the phase-locked loop and Park transformation:
θ＝ω0t+Δθ (5)
substituting the formula (5) into the formula (3) and carrying out linearization to obtain:
Figure FDA0003489242060000015
equation (6) translates to:
Figure FDA0003489242060000016
wherein the content of the first and second substances,
Figure FDA0003489242060000021
has an imaginary part of-jV1Delta theta, complex variable
Figure FDA0003489242060000022
Combining equation (4) and equation (5) yields:
Figure FDA0003489242060000023
obtained according to equations (6), (7) and (8):
Figure FDA0003489242060000024
as can be seen from equation (9), due to the influence of the phase-locked loop, a frequency ω is inputpThe single-phase voltage disturbance of (2) generates four frequency responses in the dq coordinate system, wherein the four frequency responses are respectively (omega)p-ω0)、(ω0-ωp)、(ω0+ωp) And (-omega)0-ωp) Converting to three-phase coordinate system, the four frequencies become omegap、(2ω0-ωp)、(2ω0+ωp) And-omegap；
Step 2: injecting voltage disturbance with different frequencies into any phase of the alternating current side of the grid-connected inverter, extracting the voltage and current at the PCC, and obtaining the harmonic amplitudes of the three phases of positive and negative sequences by adopting fast Fourier transform;
extracting three-phase voltage and current signals at the PCC after single-phase injection voltage disturbance, and obtaining voltage and current signals v under an alpha-beta coordinate system through Clark transformationα、vβ，iα、iβAnd obtaining voltage and current positive and negative sequence harmonics through FFT analysis:
Figure FDA0003489242060000025
wherein v isp、ipIs a positive sequence voltage, current harmonic, vn、inIs the negative sequence voltage and the current harmonic wave,
Figure FDA0003489242060000026
a component representing a fourier transform back angle frequency ω;
and step 3: according to the obtained amplitude of each harmonic wave, the self impedance and the mutual impedance of the frequency coupling are obtained;
the self-impedance expression of the grid-connected inverter is as follows:
Figure FDA0003489242060000027
wherein Z issFor self-impedance of the grid-connected inverter, ZaFor grid-connected inverter transimpedance, Y sFor grid-connected inverters self-admittance, YaIs the mutual admittance of the grid-connected inverter;
Ysand YaCalculated from equation (12):
Figure FDA0003489242060000031
wherein, Ys(ωp) Representing the frequency of the grid-connected inverter as the injection disturbance frequency omegapSelf-admittance of time, Ya(ωc) Representing the coupling frequency omega of the grid-connected inverter at the frequency of the injection disturbance frequencycMutual admittance of time, Ya(ωp)*Representing the frequency of the grid-connected inverter as the injection disturbance frequency omegapConjugation of transadmittance of time, Ys(ωc)*Representing the coupling frequency omega of the grid-connected inverter at the frequency of the injection disturbance frequencycThe self-admittance during the time of the operation,
Figure FDA0003489242060000032
representing the injection frequency omegapThe response current of the port of the grid-connected inverter after the single-phase disturbance is in omegapThe component (b) of (a) is,
Figure FDA0003489242060000033
representing the injection frequency omegapOf a coupled frequency ofThe response current of the port of the grid-connected inverter after the operation is in omegapThe component (b) of (a) is,
Figure FDA0003489242060000034
representing the injection frequency omegapThe response current of the port of the grid-connected inverter after the single-phase disturbance is in omegapOf coupling frequency omegacThe conjugate of the components is determined by the conjugate of the components,
Figure FDA0003489242060000035
representing the injection frequency omegapThe response current of the port of the grid-connected inverter after the single-phase disturbance of the coupling frequency is in omegacThe component (b) of (a) is,
Figure FDA0003489242060000036
representing the injection frequency omegapThe response voltage of the grid-connected inverter port after single-phase disturbance is in omegapThe component (b) of (a) is,
Figure FDA0003489242060000037
representing the injection frequency omegapThe response voltage of the port of the grid-connected inverter after the single-phase disturbance of the coupling frequency is in omega pThe component (c) of (a) is,
Figure FDA0003489242060000038
representing the injection frequency omegapThe response voltage of the port of the grid-connected inverter after single-phase disturbance is omegapOf coupling frequency omegacThe conjugate of the components is determined by the conjugate of the components,
Figure FDA0003489242060000039
representing the injection frequency omegapThe response voltage of the port of the grid-connected inverter after the single-phase disturbance of the coupling frequency is in omegacA component of (a);
when the frequency of the injected disturbance is omegapLess than 2 omega0The coupling frequency harmonic should be 2 ω in the positive sequence component0-ωpA component; when the frequency of the injected disturbance is omegapGreater than 2 omega0The coupling frequency harmonic should be 2 ω in the negative sequence component0-ωpA component;
during the impedance scan, the frequency of the injection is required to be omegapAnd its coupling frequency |2 ω0-ωpI, extracting a frequency omega from the obtained voltage current at the PCCpAnd its corresponding harmonic component of the coupling frequency.
2. The grid-connected inverter impedance modeling method based on single-phase disturbance injection as claimed in claim 1, wherein the impedance modeling method is required according to 2 ω0And ωpThe magnitude relationship of (a) injects and extracts different signals, and is classified as follows:
when the predetermined frequency is ωpLess than 2 omega0The method comprises the following steps:
(1) the injection frequency of any phase to the AC side of the grid-connected inverter is omegapSmall perturbation signals of (2);
(2) extracting the frequency at PCC as omegapAnd 2 omega0-ωpPositive sequence voltage, current harmonic components;
(3) The injection frequency of any phase to the AC side of the grid-connected inverter is 2 omega0-ωpSmall perturbation signals of (2);
(4) extracting the frequency at PCC as omegapAnd 2 omega0-ωpPositive sequence voltage, current harmonic components;
when the predetermined frequency is ωpGreater than 2 omega0The method comprises the following steps:
(1) the injection frequency of any phase to the AC side of the grid-connected inverter is omegapSmall perturbation signals of (2);
(2) extracting the frequency at PCC as omegapPositive sequence voltage, current harmonic component and frequency of omegap-2ω0Negative sequence voltage, current harmonic components;
(3) the injection frequency of any phase to the AC side of the grid-connected inverter is omegap-2ω0Small perturbation signals of (2);
(4) extracting the frequency at PCC as omegapPositive sequence voltage, current harmonic component and frequency of omegap-2ω0Negative sequence voltage, current harmonic components.
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Cited By (3)

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Publication number Priority date Publication date Assignee Title
CN114935692A (en) * 2022-07-25 2022-08-23 国网浙江省电力有限公司经济技术研究院 Converter impedance measuring method and device
CN116418049A (en) * 2023-06-08 2023-07-11 四川大学 Accurate admittance modeling method for sagging-controlled three-phase grid-connected inverter
CN116699248A (en) * 2023-08-01 2023-09-05 中国电力科学研究院有限公司 Broadband impedance measurement method and system for new energy power generation unit

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114935692A (en) * 2022-07-25 2022-08-23 国网浙江省电力有限公司经济技术研究院 Converter impedance measuring method and device
CN114935692B (en) * 2022-07-25 2022-11-08 国网浙江省电力有限公司经济技术研究院 Method and device for measuring impedance of converter
CN116418049A (en) * 2023-06-08 2023-07-11 四川大学 Accurate admittance modeling method for sagging-controlled three-phase grid-connected inverter
CN116418049B (en) * 2023-06-08 2023-08-11 四川大学 Accurate admittance modeling method for sagging-controlled three-phase grid-connected inverter
CN116699248A (en) * 2023-08-01 2023-09-05 中国电力科学研究院有限公司 Broadband impedance measurement method and system for new energy power generation unit
CN116699248B (en) * 2023-08-01 2023-12-15 中国电力科学研究院有限公司 Broadband impedance measurement method and system for new energy power generation unit

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