CN110752604A - MMC alternating current and direct current side harmonic coupling transfer analysis method and system - Google Patents

MMC alternating current and direct current side harmonic coupling transfer analysis method and system Download PDF

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CN110752604A
CN110752604A CN201911120904.7A CN201911120904A CN110752604A CN 110752604 A CN110752604 A CN 110752604A CN 201911120904 A CN201911120904 A CN 201911120904A CN 110752604 A CN110752604 A CN 110752604A
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CN110752604B (en
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樊丽娟
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Maintenance and Test Center of Extra High Voltage Power Transmission Co
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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
    • 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
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • 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
    • H02M1/00—Details of apparatus for conversion
    • H02M1/12—Arrangements for reducing harmonics from ac input or output
    • 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
    • H02M7/483—Converters with outputs that each can have more than two voltages levels
    • 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
    • H02M7/53—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 using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/537—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 using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
    • H02M7/5387—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 using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration
    • H02M7/53871—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 using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration with automatic control of output voltage or current
    • 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
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • H02J2003/365—Reducing harmonics or oscillations in HVDC
    • 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
    • H02M1/00—Details of apparatus for conversion
    • H02M1/12—Arrangements for reducing harmonics from ac input or output
    • H02M1/123—Suppression of common mode voltage or current
    • 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
    • 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
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/60—Arrangements for transfer of electric power between AC networks or generators via a high voltage DC link [HVCD]

Abstract

The invention discloses an MMC (modular multilevel converter) AC-DC side harmonic coupling transfer analysis method and system, and relates to the technical field of converter harmonic coupling and modulationdiffjAnd the common mode voltage fluctuation model delta ucomjSubstituting into an equivalent circuit model at the AC side and the DC side of the MMC to obtain harmonic current i at the AC side and the DC side when the bridge arm parameters after the modulation process are symmetrical and asymmetricalhAnd ikAnd (4) a transfer relation on the AC/DC side of the MMC. System masterThe harmonic current detection unit, the first analysis processing unit and the second analysis processing unit are included. The invention establishes an MMC alternating current side and direct current side equivalent circuit model, can qualitatively analyze the internal coupling process of each phase sequence harmonic in the modular multilevel converter and the alternating current-direct current side harmonic transmission rule thereof, and can be applied to analyzing and solving the problem of harmonic instability of the modular multilevel converter.

Description

MMC alternating current and direct current side harmonic coupling transfer analysis method and system
Technical Field
The invention relates to the technical field of converter harmonic coupling and modulation, in particular to an MMC alternating current and direct current side harmonic coupling transfer analysis method and system.
Background
The Modular Multilevel Converter (MMC) has the characteristics of low switching loss, high equivalent switching frequency, good output waveform, low harmonic content, easy expansion of modular design, capacity increase and the like. In recent years, it has gained more and more attention in the field of High Voltage Direct Current (HVDC). However, due to the non-linear characteristic of the inverter device, harmonic waves are generated in the alternating current and direct current system, and the harmonic waves even affect the stability of the system. Therefore, the method has very important significance for researching the harmonic instability of the MMC-HVDC by analyzing the harmonic coupling relation in the MMC and the harmonic transformation rule at the AC side and the DC side.
At present, research on the MMC at home and abroad mainly focuses on the aspects of bridge arm circulation generation mechanism and inhibition, sub-module capacitor voltage balance, control strategy, bridge arm voltage coupling mechanism and the like of the MMC. Harmonic research on a two-level and three-level Voltage Source Converter (VSC) is mature at home and abroad, but the research on the alternating current-direct current side harmonic conversion of the MMC is still insufficient. Therefore, the MMC ac/dc side harmonic transfer law with universal applicability needs further research.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides an MMC alternating current and direct current side harmonic coupling transmission analysis method and system, which can qualitatively analyze the internal coupling process of each phase sequence harmonic in a modular multilevel converter and the alternating current and direct current side harmonic transmission rule thereof, and can be applied to analyzing and solving the problem of harmonic instability of the modular multilevel converter.
In order to achieve the purpose, the technical scheme of the invention is as follows:
step 1: obtaining harmonic current i at alternating current side of MMC (Modular multilevel converter)hOr harmonic current i on the DC sidek；
Step 2: establishing a general model of j phase difference mode voltage fluctuation and common mode voltage fluctuation;
and step 3: respectively establishing the harmonic current i of the alternating current side on the basis of a common model of j phase difference mode voltage fluctuation and common mode voltage fluctuationhOr the harmonic current i on the DC sidekDifferential mode voltage fluctuation model of time Δ udiffjWith common-mode voltage fluctuation model Delautcomj；
And 4, step 4: establishing an equivalent circuit model of an MMC alternating current side and a direct current side, and enabling the differential mode voltage fluctuation model delta udiffjAnd the common mode voltage fluctuation model delta ucomjSubstituting into an equivalent circuit model at the AC side and the DC side of the MMC to obtain harmonic current i at the AC side and the DC side when the bridge arm parameters after the modulation process are symmetrical and asymmetricalhAnd ikAnd (4) a transfer relation on the AC/DC side of the MMC.
The method for analyzing the harmonic coupling transfer on the ac-dc side of the MMC as described above further obtains a general model of the j phase difference mode voltage fluctuation and the common mode voltage fluctuation in step 2 by the following method:
according to the operating principle of the MMC, the voltage fluctuation of the upper and lower bridge arms of the MMC can be represented as:
Figure BDA0002275446140000021
wherein S ispjAnd SnjRespectively are the switching functions of the upper and lower bridge arms; i.e. ipjAnd injRespectively the upper and lower bridge arm currents; n is the total number of the bridge arm sub-modules; c is the sub-module capacitance value;
the j-phase upper and lower bridge arm currents can be expressed as:
Figure BDA0002275446140000022
wherein ijA cross-current side current of j; i.e. icomjIs j phase direct side current;
the j-phase upper and lower bridge arm switching function can be expressed as:
Figure BDA0002275446140000023
wherein m is0,ω0,γj0The modulation degree, the angular frequency (fundamental frequency) and the phase angle of the j-phase modulation wave are respectively;
let the phase difference voltage fluctuation and the common mode voltage fluctuation of j be:
Figure BDA0002275446140000024
Δucomj＝Δupj+Δunj.
then the general model of the j phase difference mode voltage fluctuation and the common mode voltage fluctuation can be obtained as follows:
wherein S isj＝m0cos(ω0t+γj0)。
The MMC AC-DC side harmonic coupling transfer analysis method further comprises the following steps,
in step 1, obtaining harmonic current i on the AC side of MMChOr harmonic current i on the DC sidekAnd are respectively expressed as:
ih＝Ihcos(ωht+θh)
ik＝Ikcos(ωkt+θk)
wherein, Ih,ωh,θhThe amplitude, angular frequency and phase angle of the harmonic current at the alternating current side are respectively; i isk,ωk,θkThe amplitude, angular frequency and phase angle of the harmonic current at the direct current side are respectively;
in step 3: when harmonic i exists on the AC sidehWhen is making ij＝ihThen the harmonic i can be obtainedhThe relevant common mode voltage and differential mode voltage models:
Figure BDA0002275446140000031
Figure BDA0002275446140000032
when harmonic i exists on the AC sidekWhen is making icomj＝ikThen the harmonic i can be obtainedkThe relevant common mode voltage and differential mode voltage models:
Figure BDA0002275446140000033
Figure BDA0002275446140000034
the MMC AC-DC side harmonic coupling transfer analysis method further comprises the following steps,
in step 4, according to the MMC topological structure, analyzing by using a KCL kirchhoff current law and a KVL kirchhoff voltage law, obtaining equivalent circuit models of the ac side and the dc side of the MMC, respectively:
Figure BDA0002275446140000035
Figure BDA0002275446140000036
the above equation can be equated as:
Figure BDA0002275446140000041
Figure BDA0002275446140000042
wherein u isjAnd UdcThe voltage of the alternating current side phase and the voltage of the direct current side are respectively; l isSpAnd LSnUpper and lower bridge arm inductors respectively; rSpAnd RSnRespectively an upper bridge arm resistor and a lower bridge arm resistor.
The MMC AC-DC side harmonic coupling transfer analysis method further comprises the following steps,
fluctuating the differential mode voltage by DeltaudiffjWith common mode voltage fluctuation DeltaucomjSubstituting an equivalent circuit model of an AC side and a DC side of an MMC (Modular multilevel converter), and obtaining harmonic current i of the AC side and the DC side when the bridge arm parameters after a modulation process are symmetrical and asymmetricalhAnd ikThe transmission relation on the AC/DC side of the MMC is as follows:
a. when the bridge arm parameters are symmetrical, the current harmonic waves on the alternating current side cannot be directly transmitted to the direct current side, and the current harmonic waves on the direct current side cannot be directly transmitted to the alternating current side; the current harmonic frequency and common mode voltage fluctuation delta u newly generated at the DC sidecomjThe harmonic frequencies of (A) are the same; the newly generated current harmonic frequency and differential mode voltage fluctuation delta u on the AC sidediffjThe harmonic frequencies of (A) are the same;
①, when harmonic current i exists on the AC sidehIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegah±2ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegah±ω0；
②, when harmonic current i exists on the DC sidekIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegak±ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegak±2ω0；
b. When the bridge arm parameters are asymmetric, the current harmonic waves on the alternating current side can be directly transmitted to the direct current side, and the current harmonic waves on the direct current side can also be directly transmitted to the alternating current side; harmonic frequency of current generated at DC side and common mode voltage fluctuation DelautcomjThe harmonic frequency of the alternating current is the same as the harmonic frequency of the alternating current side current; the newly generated current harmonic frequency and differential mode voltage fluctuation delta u on the AC sidediffjThe harmonic frequency of the direct current side current is the same as the harmonic frequency of the direct current side current;
①, when harmonic current i exists on the AC sidehWhen the current on the AC side is newly generated through a modulation processThe harmonic frequencies are: omegah±2ω0，ωh±ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegah±ω0，ωh±2ω0，ωh；
②, when harmonic current i exists on the DC sidekIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegak±ω0，ωk±2ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegak±2ω0，ωk±ω0，ωk。
The method for analyzing the harmonic coupling transmission on the ac-dc side of the MMC as described above further includes determining whether the phase sequence of the common mode current harmonic frequency newly generated by the MMC modulation process is zero sequence, if so, the zero sequence common mode harmonic current will enter the dc line,
j-phase upper bridge arm switching function SpjAnd bridge arm submodule uSMjWhen all three phases are symmetrical, the angular frequencies obtained by the product are omega respectively1+ω2、ω1－ω2Voltage u of(ω1+ω2)、u(ω1－ω2)Phase sequence and Spj、uSMjThe phase sequence relation of (1) is as follows:
①、Spj、uSMjone of which is zero sequence, u(ω1+ω2)The phase sequence is the same as the other phase sequence, u(ω1－ω2)The phase sequence is opposite to the other phase sequence;
②、Spj、uSMjthe phase sequence is the same, u(ω1+ω2)Phase sequence and Spj、uSMjThe phase sequence is the same, u(ω1－ω2)Is zero sequence;
③、Spj、uSMjopposite phase sequence, u(ω1+ω2)Is zero sequence u(ω1－ω2)Phase sequence and uSMjThe phase sequence is the same.
According to the MMC alternating current-direct current side harmonic coupling transmission analysis method, further, the harmonic current newly generated at the alternating current-direct current side of the MMC obtained through the MMC modulation process is used as the input quantity in the step 1 to carry out the next modulation process, and therefore the harmonic wave newly generated at the alternating current-direct current side in the next modulation process can be obtained.
An MMC AC/DC side harmonic coupling transfer analysis system comprises
A harmonic current detection unit for obtaining the harmonic current i at the AC side of the MMChOr harmonic current i on the DC sidek；
The first analysis processing unit is used for establishing a general model of j phase difference mode voltage fluctuation and common mode voltage fluctuation, and establishing the harmonic current i of the alternating current side when the alternating current side exists on the basis of the general model of the j phase difference mode voltage fluctuation and the common mode voltage fluctuationhOr the harmonic current i on the DC sidekDifferential mode voltage fluctuation model of time Δ udiffjWith common-mode voltage fluctuation model Delautcom；
The second analysis processing unit is used for establishing an equivalent circuit model of an MMC alternating current side and an MMC direct current side and enabling the differential mode voltage fluctuation model delta u to be useddiffjAnd the common mode voltage fluctuation model delta ucomjSubstituting into an equivalent circuit model at the AC side and the DC side of the MMC to obtain harmonic current i at the AC side and the DC side when the bridge arm parameters after the modulation process are symmetrical and asymmetricalhAnd ikThe transmission relation at the AC/DC side of the MMC;
the display unit is used for displaying the harmonic frequency of the AC side and the DC side of the MMC;
in the first analysis processing unit, a common model of j phase difference mode voltage fluctuation and common mode voltage fluctuation is as follows:
wherein S isj＝m0cos(ω0t+γj0)；
When harmonic i exists on the AC sidehWhen is making ij＝ihThen the harmonic i can be obtainedhThe relevant common mode voltage and differential mode voltage models:
Figure BDA0002275446140000052
Figure BDA0002275446140000053
when harmonic i exists on the AC sidekWhen is making icomj＝ikThen the harmonic i can be obtainedkThe relevant common mode voltage and differential mode voltage models:
Figure BDA0002275446140000061
Figure BDA0002275446140000062
in the second analysis processing unit, equivalent circuit models from the AC side to the MMC and from the DC side to the MMC are respectively as follows:
Figure BDA0002275446140000063
wherein u isjAnd UdcThe voltage of the alternating current side phase and the voltage of the direct current side are respectively; l isSpAnd LSnUpper and lower bridge arm inductors respectively; rSpAnd RSnRespectively an upper bridge arm resistor and a lower bridge arm resistor.
The MMC AC/DC side harmonic coupling transfer analysis system further comprises an AC/DC side harmonic current ihAnd ikThe transfer relationship at the AC/DC side of the MMC is as follows:
fluctuating the differential mode voltage by DeltaudiffjWith common mode voltage fluctuation DeltaucomjSubstituting an equivalent circuit model of an AC side and a DC side of an MMC (Modular multilevel converter), and obtaining harmonic current i of the AC side and the DC side when the bridge arm parameters after a modulation process are symmetrical and asymmetricalhAnd ikThe transmission relation on the AC/DC side of the MMC is as follows:
a. when the bridge arm parameters are symmetrical, the current harmonic wave on the alternating current side can not be directlyThe harmonic wave of the current on the direct current side can not be directly transmitted to the alternating current side; the current harmonic frequency and common mode voltage fluctuation delta u newly generated at the DC sidecomjThe harmonic frequencies of (A) are the same; the newly generated current harmonic frequency and differential mode voltage fluctuation delta u on the AC sidediffjThe harmonic frequencies of (A) are the same;
①, when harmonic current i exists on the AC sidehIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegah±2ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegah±ω0；
②, when harmonic current i exists on the DC sidekIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegak±ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegak±2ω0；
b. When the bridge arm parameters are asymmetric, the current harmonic waves on the alternating current side can be directly transmitted to the direct current side, and the current harmonic waves on the direct current side can also be directly transmitted to the alternating current side; harmonic frequency of current generated at DC side and common mode voltage fluctuation DelautcomjThe harmonic frequency of the alternating current is the same as the harmonic frequency of the alternating current side current; the newly generated current harmonic frequency and differential mode voltage fluctuation delta u on the AC sidediffjThe harmonic frequency of the direct current side current is the same as the harmonic frequency of the direct current side current;
①, when harmonic current i exists on the AC sidehIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegah±2ω0，ωh±ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegah±ω0，ωh±2ω0，ωh；
②, when harmonic current i exists on the DC sidekIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegak±ω0，ωk±2ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegak±2ω0，ωk±ω0，ωk。
The MMC AC/DC side harmonic coupling transmission analysis system further comprises a common mode current harmonic frequency judgment unit, wherein the common mode current harmonic frequency judgment unit is used for judging whether the phase sequence of the common mode current harmonic frequency newly generated in the MMC modulation process is zero sequence or not, if the phase sequence is zero sequence, the zero sequence common mode harmonic current enters a DC circuit,
j-phase upper bridge arm switching function SpjAnd bridge arm submodule uSMjWhen all three phases are symmetrical, the angular frequencies obtained by the product are omega respectively1+ω2、ω1－ω2Voltage u of(ω1+ω2)、u(ω1－ω2)Phase sequence and Spj、uSMjThe phase sequence relation of (1) is as follows:
①、Spj、uSMjone of which is zero sequence, u(ω1+ω2)The phase sequence is the same as the other phase sequence, u(ω1－ω2)The phase sequence is opposite to the other phase sequence;
②、Spj、uSMjthe phase sequence is the same, u(ω1+ω2)Phase sequence and Spj、uSMjThe phase sequence is the same, u(ω1－ω2)Is zero sequence;
③、Spj、uSMjopposite phase sequence, u(ω1+ω2)Is zero sequence u(ω1－ω2)Phase sequence and uSMjThe phase sequence is the same.
Compared with the prior art, the invention has the beneficial effects that: the invention establishes an MMC alternating current side and direct current side equivalent circuit model, can qualitatively analyze the internal coupling process of each phase sequence harmonic in the modular multilevel converter and the alternating current-direct current side harmonic transmission rule thereof, and can be applied to analyzing and solving the problem of harmonic instability of the modular multilevel converter.
Drawings
FIG. 1 is a flow chart of an MMC AC/DC side harmonic coupling transfer analysis method according to the present invention;
FIG. 2 is a flowchart of an MMC AC/DC side harmonic coupling transfer analysis method according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of an MMC AC/DC side harmonic coupling transfer analysis system according to an embodiment of the present invention;
FIG. 4 shows the simulation results of harmonic conversion from AC to DC;
FIG. 5 shows the simulation result of harmonic conversion from DC to AC side when the bridge arm parameters are symmetric;
fig. 6 shows the simulation result of the harmonic conversion from the dc side to the ac side when the bridge arm parameters are asymmetric.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and detailed description.
Example (b):
step 1: obtaining harmonic current i at alternating current side of MMC (Modular multilevel converter)hOr harmonic current i on the DC sidek。
In step 1, obtaining harmonic current i on the AC side of MMChOr harmonic current i on the DC sidekAnd are respectively expressed as:
ih＝Ihcos(ωht+θh) (1)
ik＝Ikcos(ωkt+θk) (2)
wherein, Ih,ωh,θhThe amplitude, angular frequency and phase angle of the harmonic current at the alternating current side are respectively; i isk,ωk,θkThe amplitude, angular frequency and phase angle of the harmonic current on the direct current side are respectively.
Step 2: and establishing a general model of the j phase difference mode voltage fluctuation and the common mode voltage fluctuation.
According to the operating principle of the MMC, the voltage fluctuation of the upper and lower bridge arms of the MMC can be represented as:
Figure BDA0002275446140000081
wherein S ispjAnd SnjRespectively are the switching functions of the upper and lower bridge arms; i.e. ipjAnd injRespectively the upper and lower bridge arm currents; n is the total number of the bridge arm sub-modules; c is the sub-module capacitance value;
the j-phase upper and lower bridge arm currents can be expressed as:
Figure BDA0002275446140000082
wherein ijA cross-current side current of j; i.e. icomjIs j phase direct side current;
the j-phase upper and lower bridge arm switching function can be expressed as:
Figure BDA0002275446140000083
wherein m is0,ω0,γj0The modulation degree, the angular frequency (fundamental frequency) and the phase angle of the j-phase modulation wave are respectively;
let the phase difference voltage fluctuation and the common mode voltage fluctuation of j be:
Figure BDA0002275446140000084
Δucomj＝Δupj+Δunj. (7)
then the general model of the j phase difference mode voltage fluctuation and the common mode voltage fluctuation can be obtained as follows:
Figure BDA0002275446140000085
wherein S isj＝m0cos(ω0t+γj0)。
And step 3: respectively establishing the harmonic current i of the alternating current side on the basis of a common model of j phase difference mode voltage fluctuation and common mode voltage fluctuationhOr the harmonic current i on the DC sidekDifferential mode voltage fluctuation model of time Δ udiffjWith common-mode voltage fluctuation model Delautcomj。
In step 3:
when harmonic i exists on the AC sidehWhen is making ij＝ihThen the harmonic i can be obtainedhThe relevant common mode voltage and differential mode voltage models:
Figure BDA0002275446140000092
when harmonic i exists on the AC sidekWhen is making icomj＝ikThen the harmonic i can be obtainedkThe relevant common mode voltage and differential mode voltage models:
Figure BDA0002275446140000093
Figure BDA0002275446140000094
and 4, step 4: establishing an equivalent circuit model of an MMC alternating current side and a direct current side, and enabling the differential mode voltage fluctuation model delta udiffjAnd the common mode voltage fluctuation model delta ucomjSubstituting into an equivalent circuit model at the AC side and the DC side of the MMC to obtain harmonic current i at the AC side and the DC side when the bridge arm parameters after the modulation process are symmetrical and asymmetricalhAnd ikAnd (4) a transfer relation on the AC/DC side of the MMC.
According to the MMC topological structure, by adopting a KCL kirchhoff current law and a KVL kirchhoff voltage law method for analysis, the MMC alternating-current side equivalent circuit model and the MMC direct-current side equivalent circuit model are respectively as follows:
Figure BDA0002275446140000095
Figure BDA0002275446140000096
equation (13) (14) can be equated with:
Figure BDA0002275446140000101
Figure BDA0002275446140000102
wherein u isjAnd UdcThe voltage of the alternating current side phase and the voltage of the direct current side are respectively; l isSpAnd LSnUpper and lower bridge arm inductors respectively; rSpAnd RSnRespectively an upper bridge arm resistor and a lower bridge arm resistor.
Fluctuating the differential mode voltage by DeltaudiffjWith common mode voltage fluctuation DeltaucomjSubstituting an equivalent circuit model of an AC side and a DC side of an MMC (Modular multilevel converter), and obtaining harmonic current i of the AC side and the DC side when the bridge arm parameters after a modulation process are symmetrical and asymmetricalhAnd ikThe transmission relation on the AC/DC side of the MMC is as follows:
a. when the bridge arm parameters are symmetrical, the current harmonic waves on the alternating current side cannot be directly transmitted to the direct current side, and the current harmonic waves on the direct current side cannot be directly transmitted to the alternating current side; the current harmonic frequency and common mode voltage fluctuation delta u newly generated at the DC sidecomjThe harmonic frequencies of (A) are the same; the newly generated current harmonic frequency and differential mode voltage fluctuation delta u on the AC sidediffjThe harmonic frequencies of (A) are the same;
①, when harmonic current i exists on the AC sidehIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegah±2ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegah±ω0；
②, when harmonic current i exists on the DC sidekIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegak±ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegak±2ω0；
b. When the bridge arm parameters are asymmetric, the current harmonic waves on the alternating current side can be directly transmitted to the direct current side, and the current harmonic waves on the direct current side can also be directly transmitted to the alternating current side; harmonic frequency of current generated at DC side and common mode voltage fluctuation DelautcomjThe harmonic frequency of the alternating current is the same as the harmonic frequency of the alternating current side current; the newly generated current harmonic frequency and differential mode voltage fluctuation delta u on the AC sidediffjHarmonic frequency ofThe frequency is the same as the harmonic frequency of the direct current side current;
①, when harmonic current i exists on the AC sidehIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegah±2ω0，ωh±ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegah±ω0，ωh±2ω0，ωh；
②, when harmonic current i exists on the DC sidekIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegak±ω0，ωk±2ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegak±2ω0，ωk±ω0，ωk。
And (3) taking the newly generated harmonic current at the AC/DC side of the MMC obtained through the MMC modulation process as the input quantity in the step (1) to carry out the next modulation process, thus obtaining the newly generated harmonic at the AC/DC side in the next modulation process.
The method also comprises the steps of judging whether the phase sequence of the common-mode current harmonic frequency newly generated in the MMC modulation process is zero sequence or not, if so, enabling the zero-sequence common-mode harmonic current to enter a direct-current circuit, and the specific method comprises the following steps:
setting j-phase upper bridge arm switch function SpjAnd bridge arm submodule uSMjRespectively expressed as:
Figure BDA0002275446140000111
wherein A is1And A2Respectively, the switching function and the amplitude of the voltage; omega1And omega2Respectively angular frequency α1(m ═ 1, 2; j ═ a, B, C) are the voltage phase angles, respectively.
If the voltage is three-phase symmetry, the phase angle of the three-phase voltage satisfies the relationship:
Figure BDA0002275446140000112
wherein when the three phases are zero sequence, positive sequence and negative sequence, gamma ismThe values of (A) are respectively: 0. 2 pi/3 and-2 pi/3.
Will SpjAnd uSMjMultiplication is obtained according to the sum and difference formula:
Figure BDA0002275446140000113
from which ω is obtained1+ω2And omega1－ω2α, respectively1j+α2j，α1j－α2j。
According to the formula, the three-phase angle relationship of the new voltage is as follows:
Figure BDA0002275446140000114
when S is compared with the formulapjAnd uSMjWhen the two voltages are three-phase symmetrical, the two new voltages obtained by the product still meet the three-phase symmetrical relationship, but the phase sequence can be changed.
For angular frequency ω1+ω2Voltage of (d) three-phase angular difference gamma of1+γ2The following relationship is satisfied:
thus, gamma can be obtained1And gamma2The solution of (a) is:
Figure BDA0002275446140000116
for angular frequency ω1－ω2The phase angle analysis of the voltage of (1) is similar.
Therefore, the phase sequence determination method comprises the following steps:
j-phase upper bridge arm switching function SpjAnd bridge arm submodule uSMjWhen all three phases are symmetrical, the angular frequencies obtained by the product are omega respectively1+ω2、ω1－ω2Voltage u of(ω1+ω2)、u(ω1－ω2)Phase sequence and Spj、uSMjThe phase sequence relation of (1) is as follows:
①、Spj、uSMjone of which is zero sequence, u(ω1+ω2)The phase sequence is the same as the other phase sequence, u(ω1－ω2)The phase sequence is opposite to the other phase sequence;
②、Spj、uSMjthe phase sequence is the same, u(ω1+ω2)Phase sequence and Spj、uSMjThe phase sequence is the same, u(ω1－ω2)Is zero sequence;
③、Spj、uSMjopposite phase sequence, u(ω1+ω2)Is zero sequence u(ω1－ω2)Phase sequence and uSMjThe phase sequence is the same.
The simulation is performed by taking a two-end MMC-HVDC system as an example. At 3.5s, a positive sequence harmonic voltage with the content of 10% and the frequency of 130Hz is added on the AC side, and according to the analysis, after the first modulation action, the voltage fluctuation of 80Hz is generated on the DC side, and after the second modulation action, the voltage fluctuation of a small amount of 160Hz is generated on the DC side. The current harmonic with the content of 10% and the frequency of 1050Hz is added at the direct current side within 3.5s, and the analysis shows that when the bridge arm parameters are symmetrical, 1000Hz and 1100Hz harmonic waves are generated in the alternating current side phase voltage through the first modulation action, and a small amount of 900Hz and 1200Hz harmonic waves are generated in the alternating current side phase voltage through the second modulation action. When the bridge arm parameters are asymmetric, there will also be a 1050Hz harmonic in the ac side phase voltage. And building models at two ends of MMC-HVDC on the PSCAD simulation platform, and carrying out FFT on-line analysis on the direct current side voltage, wherein the analysis results are shown in fig. 4 to fig. 6.
An MMC AC/DC side harmonic coupling transfer analysis system comprises
A harmonic current detection unit for obtaining the harmonic current i at the AC side of the MMChOr harmonic current i on the DC sidek；
A first analysis processing unit for establishing a common model of j phase difference mode voltage fluctuation and common mode voltage fluctuation, and based on the j phase difference mode voltage fluctuation and the common mode voltageA general model of fluctuation is established when the harmonic current i of the alternating current side exists on the alternating current sidehOr the harmonic current i on the DC sidekDifferential mode voltage fluctuation model of time Δ udiffjWith common-mode voltage fluctuation model Delautcom；
The second analysis processing unit is used for establishing an equivalent circuit model of an MMC alternating current side and an MMC direct current side and enabling the differential mode voltage fluctuation model delta u to be useddiffjAnd the common mode voltage fluctuation model delta ucomjSubstituting into an equivalent circuit model at the AC side and the DC side of the MMC to obtain harmonic current i at the AC side and the DC side when the bridge arm parameters after the modulation process are symmetrical and asymmetricalhAnd ikThe transmission relation at the AC/DC side of the MMC;
and the display unit is used for displaying the harmonic frequency of the AC side and the DC side of the MMC.
Obtaining harmonic current i at alternating current side of MMC (Modular multilevel converter)hOr harmonic current i on the DC sidekAnd are respectively expressed as:
ih＝Ihcos(ωht+θh) (1)
ik＝Ikcos(ωkt+θk) (2)
wherein, Ih,ωh,θhThe amplitude, angular frequency and phase angle of the harmonic current at the alternating current side are respectively; i isk,ωk,θkThe amplitude, angular frequency and phase angle of the harmonic current on the direct current side are respectively.
And establishing a general model of the j phase difference mode voltage fluctuation and the common mode voltage fluctuation.
According to the operating principle of the MMC, the voltage fluctuation of the upper and lower bridge arms of the MMC can be represented as:
Figure BDA0002275446140000131
wherein S ispjAnd SnjRespectively are the switching functions of the upper and lower bridge arms; i.e. ipjAnd injRespectively the upper and lower bridge arm currents; n is the total number of the bridge arm sub-modules; c is the sub-module capacitance value;
the j-phase upper and lower bridge arm currents can be expressed as:
Figure BDA0002275446140000132
wherein ijA cross-current side current of j; i.e. icomjIs j phase direct side current;
the j-phase upper and lower bridge arm switching function can be expressed as:
Figure BDA0002275446140000133
wherein m is0,ω0,γj0The modulation degree, the angular frequency (fundamental frequency) and the phase angle of the j-phase modulation wave are respectively;
let the phase difference voltage fluctuation and the common mode voltage fluctuation of j be:
Δucomj＝Δupj+Δunj. (7)
by substituting the formula (4) and the formula (5) into the formula (3) and combining the formula (6) and the formula (7), the general model of the j phase difference mode voltage fluctuation and the common mode voltage fluctuation can be obtained as follows:
Figure BDA0002275446140000135
wherein S isj＝m0cos(ω0t+γj0)。
Respectively establishing the harmonic current i of the alternating current side on the basis of a common model of j phase difference mode voltage fluctuation and common mode voltage fluctuationhOr the harmonic current i on the DC sidekDifferential mode voltage fluctuation model of time Δ udiffjWith common-mode voltage fluctuation model Delautcomj。
When harmonic i exists on the AC sidehWhen is making ij＝ihThen the harmonic i can be obtainedhThe relevant common mode voltage and differential mode voltage models:
Figure BDA0002275446140000142
when harmonic i exists on the AC sidekWhen is making icomj＝ikThen the harmonic i can be obtainedkThe relevant common mode voltage and differential mode voltage models:
Figure BDA0002275446140000143
Figure BDA0002275446140000144
establishing an equivalent circuit model of an MMC alternating current side and a direct current side, and enabling the differential mode voltage fluctuation model delta udiffjAnd the common mode voltage fluctuation model delta ucomjSubstituting into an equivalent circuit model at the AC side and the DC side of the MMC to obtain harmonic current i at the AC side and the DC side when the bridge arm parameters after the modulation process are symmetrical and asymmetricalhAnd ikAnd (4) a transfer relation on the AC/DC side of the MMC.
According to the MMC topological structure, by adopting a KCL kirchhoff current law and a KVL kirchhoff voltage law method for analysis, the MMC alternating-current side equivalent circuit model and the MMC direct-current side equivalent circuit model are respectively as follows:
Figure BDA0002275446140000145
Figure BDA0002275446140000146
equation (13) (14) can be equated with:
Figure BDA0002275446140000147
Figure BDA0002275446140000148
wherein u isjAnd UdcThe voltage of the alternating current side phase and the voltage of the direct current side are respectively; l isSpAnd LSnUpper and lower bridge arm inductors respectively; rSpAnd RSnRespectively an upper bridge arm resistor and a lower bridge arm resistor.
Fluctuating the differential mode voltage by DeltaudiffjWith common mode voltage fluctuation DeltaucomjSubstituting into MMC AC side and DC side equivalent circuit model (namely formula (15) and formula (16)), obtaining AC DC side harmonic current i when bridge arm parameter after modulation process is symmetrical and asymmetricalhAnd ikThe transmission relation on the AC/DC side of the MMC is as follows:
a. when the bridge arm parameters are symmetrical, the current harmonic waves on the alternating current side cannot be directly transmitted to the direct current side, and the current harmonic waves on the direct current side cannot be directly transmitted to the alternating current side; the current harmonic frequency and common mode voltage fluctuation delta u newly generated at the DC sidecomjThe harmonic frequencies of (A) are the same; the newly generated current harmonic frequency and differential mode voltage fluctuation delta u on the AC sidediffjThe harmonic frequencies of (A) are the same;
①, when harmonic current i exists on the AC sidehIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegah±2ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegah±ω0；
②, when harmonic current i exists on the DC sidekIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegak±ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegak±2ω0；
b. When the bridge arm parameters are asymmetric, the current harmonic waves on the alternating current side can be directly transmitted to the direct current side, and the current harmonic waves on the direct current side can also be directly transmitted to the alternating current side; harmonic frequency of current generated at DC side and common mode voltage fluctuation DelautcomjThe harmonic frequency of the alternating current is the same as the harmonic frequency of the alternating current side current; the newly generated current harmonics on the AC sideWave frequency and differential mode voltage fluctuation DeltaudiffjThe harmonic frequency of the direct current side current is the same as the harmonic frequency of the direct current side current;
①, when harmonic current i exists on the AC sidehIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegah±2ω0，ωh±ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegah±ω0，ωh±2ω0，ωh；
②, when harmonic current i exists on the DC sidekIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegak±ω0，ωk±2ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegak±2ω0，ωk±ω0，ωk。
And (3) taking the newly generated harmonic current at the AC/DC side of the MMC obtained through the MMC modulation process as the input quantity in the step (1) to carry out the next modulation process, thus obtaining the newly generated harmonic at the AC/DC side in the next modulation process.
The method also comprises the steps of judging whether the phase sequence of the common-mode current harmonic frequency newly generated in the MMC modulation process is zero sequence or not, if so, enabling the zero-sequence common-mode harmonic current to enter a direct-current circuit, and the specific method comprises the following steps:
setting j-phase upper bridge arm switch function SpjAnd bridge arm submodule uSMjRespectively expressed as:
wherein A is1And A2Respectively, the switching function and the amplitude of the voltage; omega1And omega2Respectively angular frequency α1(m ═ 1, 2; j ═ a, B, C) are the voltage phase angles, respectively.
If the voltage is three-phase symmetry, the phase angle of the three-phase voltage satisfies the relationship:
Figure BDA0002275446140000161
wherein when the three phases are zero sequence, positive sequence and negative sequence, gamma ismThe values of (A) are respectively: 0. 2 pi/3 and-2 pi/3.
Will SpjAnd uSMjMultiplication is obtained according to the sum and difference formula:
omega is obtained from the formula (19)1+ω2And omega1－ω2α, respectively1j+α2j，α1j－α2j。
According to equation (18), the three-phase angle relationship of the new voltage is:
Figure BDA0002275446140000163
when S is found by comparing the formula (18) with the formula (20)pjAnd uSMjWhen the two voltages are three-phase symmetrical, the two new voltages obtained by the product still meet the three-phase symmetrical relationship, but the phase sequence can be changed.
For angular frequency ω1+ω2Voltage of (d) three-phase angular difference gamma of1+γ2The following relationship is satisfied:
Figure BDA0002275446140000164
thus, gamma can be obtained1And gamma2The solution of (a) is:
Figure BDA0002275446140000165
for angular frequency ω1－ω2The phase angle analysis of the voltage of (1) is similar.
Therefore, the phase sequence determination method comprises the following steps:
j-phase upper bridge arm switching function SpjAnd bridge arm submodule uSMjWhen all three phases are symmetrical, the angular frequencies obtained by the product are omega respectively1+ω2、ω1－ω2Voltage u of(ω1+ω2)、u(ω1－ω2)Phase sequence and Spj、uSMjThe phase sequence relation of (1) is as follows:
①、Spj、uSMjone of which is zero sequence, u(ω1+ω2)The phase sequence is the same as the other phase sequence, u(ω1－ω2)The phase sequence is opposite to the other phase sequence;
②、Spj、uSMjthe phase sequence is the same, u(ω1+ω2)Phase sequence and Spj、uSMjThe phase sequence is the same, u(ω1－ω2)Is zero sequence;
③、Spj、uSMjopposite phase sequence, u(ω1+ω2)Is zero sequence u(ω1－ω2)Phase sequence and uSMjThe phase sequence is the same.
The above embodiments are only for illustrating the technical concept and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the contents of the present invention and implement the present invention accordingly, and not to limit the protection scope of the present invention accordingly. All equivalent changes or modifications made in accordance with the spirit of the present disclosure are intended to be covered by the scope of the present disclosure.

Claims (10)

1. An MMC AC/DC side harmonic coupling transfer analysis method is characterized by comprising the following steps:
step 1: obtaining harmonic current i at alternating current side of MMC (Modular multilevel converter)hOr harmonic current i on the DC sidek；
Step 2: establishing a general model of j phase difference mode voltage fluctuation and common mode voltage fluctuation;
and step 3: respectively establishing the harmonic current i of the alternating current side on the basis of a common model of j phase difference mode voltage fluctuation and common mode voltage fluctuationhOr the harmonic current i on the DC sidekDifferential mode voltage fluctuation model of time Δ udiffjWith common-mode voltage fluctuation model Delautcomj；
And 4, step 4: establishing equivalence of an MMC alternating current side and a direct current sideA circuit model for modeling the differential mode voltage fluctuation Δ udiffjAnd the common mode voltage fluctuation model delta ucomjSubstituting into an equivalent circuit model at the AC side and the DC side of the MMC to obtain harmonic current i at the AC side and the DC side when the bridge arm parameters after the modulation process are symmetrical and asymmetricalhAnd ikAnd (4) a transfer relation on the AC/DC side of the MMC.
2. The MMC alternating current-direct current side harmonic coupling transfer analysis method of claim 1, wherein in step 2, a general model of j phase difference mode voltage fluctuation and common mode voltage fluctuation is obtained by:
according to the operating principle of the MMC, the voltage fluctuation of the upper and lower bridge arms of the MMC can be represented as:
Figure FDA0002275446130000011
wherein S ispjAnd SnjRespectively are the switching functions of the upper and lower bridge arms; i.e. ipjAnd injRespectively the upper and lower bridge arm currents; n is the total number of the bridge arm sub-modules; c is the sub-module capacitance value;
the j-phase upper and lower bridge arm currents can be expressed as:
Figure FDA0002275446130000012
wherein ijA cross-current side current of j; i.e. icomjIs j phase direct side current;
the j-phase upper and lower bridge arm switching function can be expressed as:
Figure FDA0002275446130000013
wherein m is0,ω0,γj0The modulation degree, the angular frequency (fundamental frequency) and the phase angle of the j-phase modulation wave are respectively;
let the phase difference voltage fluctuation and the common mode voltage fluctuation of j be:
Δucomj＝Δupj+Δunj.
then the general model of the j phase difference mode voltage fluctuation and the common mode voltage fluctuation can be obtained as follows:
Figure FDA0002275446130000021
wherein S isj＝m0cos(ω0t+γj0)。
3. The MMC AC-DC side harmonic coupling transfer analysis method of claim 2,
in step 1, obtaining harmonic current i on the AC side of MMChOr harmonic current i on the DC sidekAnd are respectively expressed as:
ih＝Ihcos(ωht+θh)
ik＝Ikcos(ωkt+θk)
wherein, Ih,ωh,θhThe amplitude, angular frequency and phase angle of the harmonic current at the alternating current side are respectively; i isk,ωk,θkThe amplitude, angular frequency and phase angle of the harmonic current at the direct current side are respectively;
in step 3:
when harmonic i exists on the AC sidehWhen is making ij＝ihThen the harmonic i can be obtainedhThe relevant common mode voltage and differential mode voltage models:
Figure FDA0002275446130000022
when harmonic i exists on the AC sidekWhen is making icomj＝ikThen the harmonic i can be obtainedkThe relevant common mode voltage and differential mode voltage models:
Figure FDA0002275446130000024
4. the MMC AC-DC side harmonic coupling transfer analysis method of claim 3,
in step 4, according to the MMC topological structure, analyzing by using a KCL kirchhoff current law and a KVL kirchhoff voltage law, obtaining equivalent circuit models of the ac side and the dc side of the MMC, respectively:
Figure FDA0002275446130000032
the above equation can be equated as:
Figure FDA0002275446130000034
wherein u isjAnd UdcThe voltage of the alternating current side phase and the voltage of the direct current side are respectively; l isSpAnd LSnUpper and lower bridge arm inductors respectively; rSpAnd RSnRespectively an upper bridge arm resistor and a lower bridge arm resistor.
5. The MMC AC-DC side harmonic coupling transfer analysis method of claim 4,
fluctuating the differential mode voltage by DeltaudiffjWith common mode voltage fluctuation DeltaucomjSubstituting an equivalent circuit model of an AC side and a DC side of an MMC (Modular multilevel converter), and obtaining harmonic current i of the AC side and the DC side when the bridge arm parameters after a modulation process are symmetrical and asymmetricalhAnd ikThe transmission relation on the AC/DC side of the MMC is as follows:
a. when the bridge arm parameters are symmetrical, the current harmonic waves on the alternating current side cannot be directly transmitted to the direct current side, and the current harmonic waves on the direct current side cannot be directly transmitted to the alternating current side; the current harmonic frequency and common mode voltage fluctuation delta u newly generated at the DC sidecomjThe harmonic frequencies of (A) are the same; the newly generated current harmonic frequency and differential mode voltage fluctuation delta u on the AC sidediffjThe harmonic frequencies of (A) are the same;
①, when harmonic current i exists on the AC sidehIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegah±2ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegah±ω0；
②, when harmonic current i exists on the DC sidekIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegak±ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegak±2ω0；
b. When the bridge arm parameters are asymmetric, the current harmonic waves on the alternating current side can be directly transmitted to the direct current side, and the current harmonic waves on the direct current side can also be directly transmitted to the alternating current side; harmonic frequency of current generated at DC side and common mode voltage fluctuation DelautcomjThe harmonic frequency of the alternating current is the same as the harmonic frequency of the alternating current side current; the newly generated current harmonic frequency and differential mode voltage fluctuation delta u on the AC sidediffjThe harmonic frequency of the direct current side current is the same as the harmonic frequency of the direct current side current;
①, when harmonic current i exists on the AC sidehIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegah±2ω0，ωh±ω0(ii) a Direct currentThe newly generated harmonic frequencies in the side common mode current are: omegah±ω0，ωh±2ω0，ωh；
②, when harmonic current i exists on the DC sidekIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegak±ω0，ωk±2ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegak±2ω0，ωk±ω0，ωk。
6. The MMC AC-DC side harmonic coupling transmission analysis method of claim 5, further comprising determining if the phase sequence of the common mode current harmonic frequency newly generated by the MMC modulation process is zero sequence, if zero sequence, the zero sequence common mode harmonic current will enter the DC line,
the phase sequence judging method comprises the following steps:
j-phase upper bridge arm switching function SpjAnd bridge arm submodule uSMjWhen all three phases are symmetrical, the angular frequencies obtained by the product are omega respectively1+ω2、ω1－ω2Voltage u of(ω1+ω2)、u(ω1－ω2)Phase sequence and Spj、uSMjThe phase sequence relation of (1) is as follows:
①、Spj、uSMjone of which is zero sequence, u(ω1+ω2)The phase sequence is the same as the other phase sequence, u(ω1－ω2)The phase sequence is opposite to the other phase sequence;
②、Spj、uSMjthe phase sequence is the same, u(ω1+ω2)Phase sequence and Spj、uSMjThe phase sequence is the same, u(ω1－ω2)Is zero sequence;
③、Spj、uSMjopposite phase sequence, u(ω1+ω2)Is zero sequence u(ω1－ω2)Phase sequence and uSMjThe phase sequence is the same.
7. The MMC alternating current-direct current side harmonic coupling transfer analysis method of claim 6, wherein the next modulation process is performed by taking the obtained newly generated harmonic current at the AC-DC side of the MMC after the MMC modulation process as the input quantity in step 1, so as to obtain the newly generated harmonic at the AC-DC side in the next modulation process.
8. An MMC AC/DC side harmonic coupling transfer analysis system is characterized by comprising
A harmonic current detection unit for obtaining the harmonic current i at the AC side of the MMChOr harmonic current i on the DC sidek；
The first analysis processing unit is used for establishing a general model of j phase difference mode voltage fluctuation and common mode voltage fluctuation, and establishing the harmonic current i of the alternating current side when the alternating current side exists on the basis of the general model of the j phase difference mode voltage fluctuation and the common mode voltage fluctuationhOr the harmonic current i on the DC sidekDifferential mode voltage fluctuation model of time Δ udiffjWith common-mode voltage fluctuation model Delautcom；
The second analysis processing unit is used for establishing an equivalent circuit model of an MMC alternating current side and an MMC direct current side and enabling the differential mode voltage fluctuation model delta u to be useddiffjAnd the common mode voltage fluctuation model delta ucomjSubstituting into an equivalent circuit model at the AC side and the DC side of the MMC to obtain harmonic current i at the AC side and the DC side when the bridge arm parameters after the modulation process are symmetrical and asymmetricalhAnd ikThe transmission relation at the AC/DC side of the MMC;
the display unit is used for displaying the harmonic frequency of the AC side and the DC side of the MMC;
in the first analysis processing unit, a common model of j phase difference mode voltage fluctuation and common mode voltage fluctuation is as follows:
Figure FDA0002275446130000041
wherein S isj＝m0cos(ω0t+γj0)；
When harmonic i exists on the AC sidehWhen is making ij＝ihThen the harmonic i can be obtainedhThe relevant common mode voltage and differential mode voltage models:
Figure FDA0002275446130000051
Figure FDA0002275446130000052
when harmonic i exists on the AC sidekWhen is making icomj＝ikThen the harmonic i can be obtainedkThe relevant common mode voltage and differential mode voltage models:
Figure FDA0002275446130000053
Figure FDA0002275446130000054
in the second analysis processing unit, the equivalent circuit models of the MMC AC side and the DC side are respectively as follows:
Figure FDA0002275446130000056
wherein u isjAnd UdcThe voltage of the alternating current side phase and the voltage of the direct current side are respectively; l isSpAnd LSnUpper and lower bridge arm inductors respectively; rSpAnd RSnRespectively an upper bridge arm resistor and a lower bridge arm resistor.
9. The MMC AC-DC side harmonic coupling transfer analysis system of claim 1, wherein an AC-DC side harmonic current ihAnd ikThe transfer relationship at the AC/DC side of the MMC is as follows:
fluctuating the differential mode voltage by DeltaudiffjWith common mode voltage fluctuation DeltaucomjSubstituted MMC AC side and DC side, etcAn effective circuit model for obtaining harmonic current i at AC/DC side when the bridge arm parameters are symmetrical and asymmetrical after modulationhAnd ikThe transmission relation on the AC/DC side of the MMC is as follows:
a. when the bridge arm parameters are symmetrical, the current harmonic waves on the alternating current side cannot be directly transmitted to the direct current side, and the current harmonic waves on the direct current side cannot be directly transmitted to the alternating current side; the current harmonic frequency and common mode voltage fluctuation delta u newly generated at the DC sidecomjThe harmonic frequencies of (A) are the same; the newly generated current harmonic frequency and differential mode voltage fluctuation delta u on the AC sidediffjThe harmonic frequencies of (A) are the same;
①, when harmonic current i exists on the AC sidehIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegah±2ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegah±ω0；
②, when harmonic current i exists on the DC sidekIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegak±ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegak±2ω0；
b. When the bridge arm parameters are asymmetric, the current harmonic waves on the alternating current side can be directly transmitted to the direct current side, and the current harmonic waves on the direct current side can also be directly transmitted to the alternating current side; harmonic frequency of current generated at DC side and common mode voltage fluctuation DelautcomjThe harmonic frequency of the alternating current is the same as the harmonic frequency of the alternating current side current; the newly generated current harmonic frequency and differential mode voltage fluctuation delta u on the AC sidediffjThe harmonic frequency of the direct current side current is the same as the harmonic frequency of the direct current side current;
①, when harmonic current i exists on the AC sidehIn the process, through a modulation process, the newly generated harmonic frequency in the alternating current side current is as follows: omegah±2ω0，ωh±ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegah±ω0，ωh±2ω0，ωh；
②, when harmonic current i exists on the DC sidekWhen passing throughIn the secondary modulation process, the newly generated harmonic frequency in the alternating-current side current is as follows: omegak±ω0，ωk±2ω0(ii) a The newly generated harmonic frequencies in the common mode current on the direct current side are as follows: omegak±2ω0，ωk±ω0，ωk。
10. The MMC alternating current/direct current side harmonic coupling transmission analysis system of claim 1, further comprising a common mode current harmonic frequency determination unit for determining whether a phase sequence of a common mode current harmonic frequency newly generated by the MMC modulation process is zero sequence, if so, the zero sequence common mode harmonic current will enter the direct current circuit,
j-phase upper bridge arm switching function SpjAnd bridge arm submodule uSMjWhen all three phases are symmetrical, the angular frequencies obtained by the product are omega respectively1+ω2、ω1－ω2Voltage u of(ω1+ω2)、u(ω1－ω2)Phase sequence and Spj、uSMjThe phase sequence relation of (1) is as follows:
①、Spj、uSMjone of which is zero sequence, u(ω1+ω2)The phase sequence is the same as the other phase sequence, u(ω1－ω2)The phase sequence is opposite to the other phase sequence;
②、Spj、uSMjthe phase sequence is the same, u(ω1+ω2)Phase sequence and Spj、uSMjThe phase sequence is the same, u(ω1－ω2)Is zero sequence;
③、Spj、uSMjopposite phase sequence, u(ω1+ω2)Is zero sequence u(ω1－ω2)Phase sequence and uSMjThe phase sequence is the same.
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