CN108092523B - Harmonic calculation method of ultra-sparse matrix converter based on triple Fourier series - Google Patents

Harmonic calculation method of ultra-sparse matrix converter based on triple Fourier series Download PDF

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CN108092523B
CN108092523B CN201810025693.8A CN201810025693A CN108092523B CN 108092523 B CN108092523 B CN 108092523B CN 201810025693 A CN201810025693 A CN 201810025693A CN 108092523 B CN108092523 B CN 108092523B
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CN108092523A (en
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史婷娜
吴玲玲
阎彦
夏长亮
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Tianjin University
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    • 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
    • H02M5/00—Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases
    • H02M5/40—Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc
    • H02M5/42—Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc by static converters
    • H02M5/44—Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc by static converters using discharge tubes or semiconductor devices to convert the intermediate dc into ac
    • H02M5/453—Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc by static converters using discharge tubes or semiconductor devices to convert the intermediate dc into ac using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M5/458—Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc by static converters using discharge tubes or semiconductor devices to convert the intermediate dc into ac using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
    • H02M5/4585—Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc by static converters using discharge tubes or semiconductor devices to convert the intermediate dc into ac using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only having a rectifier with controlled elements
    • 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

Abstract

The invention discloses a harmonic calculation method of an ultra-sparse matrix converter based on triple Fourier series, which sets three-phase output symmetry and is carried out under a space vector modulation strategy and mainly comprises the steps of (1) solving the conduction duty ratio of each bridge arm switching tube of a rectifier stage; (2) solving the conduction duty ratio of each bridge arm switching tube of the inverter stage; (3) 36 different combinations are arranged between sectors where input current reference vectors and output voltage reference vectors are located, the waveforms of the switching tubes of the rectification stage and the inversion stage under each combination are determined according to the action sequence of the rectification stage effective vectors, the inversion stage effective vectors and the inversion stage zero vectors under each combination, and the output voltage pulse waveforms of each phase of the three-phase-three-phase ultra-sparse matrix converter are obtained; (4) solving the trip point of the three-phase output voltage pulse in the next carrier wave period of each sector combination; (5) solving the triple Fourier coefficient of the output voltage; and finally, solving the amplitude of each harmonic of the output voltage.

Description

Harmonic calculation method of ultra-sparse matrix converter based on triple Fourier series
Technical Field
The invention belongs to the technical field of power conversion, and particularly relates to a method for calculating harmonic waves of output voltage of an ultra-sparse matrix converter based on triple Fourier series.
Background
The ultra-sparse matrix converter is a derivative structure of the traditional matrix converter, not only has the excellent characteristics of the traditional matrix converter, such as compact structure, no intermediate energy storage link, sine input and output currents, adjustable input power factor and the like, but also overcomes the defects of complex commutation, large switch number and the like of the traditional matrix converter, and is a novel matrix converter with development potential at present.
As an AC-AC power converter, the ultra-sparse matrix converter has the primary task of obtaining an output waveform with high sine degree, but under the influence of the characteristics and the modulation method of power electronic devices, the output waveform inevitably contains harmonic components, and has adverse effect in practical application. Therefore, it is very important to accurately analyze harmonic components in the output waveform of the ultra-sparse matrix converter.
Although the harmonic characteristics of the ultra-sparse matrix converter are less researched at present, the harmonic analysis method of the traditional converter can be used for analyzing the harmonic of the ultra-sparse matrix converter. The common harmonic analysis method of the power converter includes the following aspects:
(1) the waveform is subjected to FFT analysis, the method is simple and easy to implement, and a harmonic spectrum is obtained by carrying out a series of processing such as sampling and windowing on a signal. However, FFT analysis is very sensitive to the periodicity and frequency resolution of the waveform, and in some cases, for example, when the input, output or carrier frequency of the converter is non-integer, FFT has more serious problems of spectrum leakage, aliasing and the like, and the obtained harmonic spectrum has larger deviation from the actual situation.
(2) And calculating a harmonic analytic expression of the waveform by utilizing Fourier series. It is more common to study the input or output harmonic characteristics of a converter using harmonic analytic expressions of the double fourier series calculated waveform. As with conventional matrix converters, the output waveform of the ultra-sparse matrix converter is related to both the input and output frequencies, and the carrier frequency, and these three frequencies are independent of each other. If a common double Fourier series analysis method is adopted to consider at most two frequencies, the obtained spectrum analysis result is not accurate.
In order to solve the above problems, researchers have attempted to analyze the output waveform harmonic of the conventional matrix converter under the "AV method" by using a triple fourier series to obtain an output voltage harmonic spectrum. However, compared with the traditional matrix converter, the ultra-sparse matrix converter has the difference in topological structure and control performance, and compared with the AV method, the space vector modulation not only improves the maximum voltage transmission ratio from 0.5 to 0.866, but also is convenient for digital realization, and is very widely applied. However, no mature harmonic analysis theory is applied to space vector modulation of the ultra-sparse matrix converter at present.
Disclosure of Invention
The invention provides a harmonic calculation method of an ultra-sparse matrix converter based on triple Fourier series aiming at the ultra-sparse matrix converter under space vector modulation, so as to obtain more accurate harmonic spectrum.
In order to solve the technical problems, the invention provides a harmonic calculation method of an ultra-sparse matrix converter based on a triple Fourier series, wherein the three-phase-three-phase ultra-sparse matrix converter comprises a rectification stage and an inversion stage, each phase of bridge arm of the rectification stage consists of a switch tube and four diodes, each phase of bridge arm of the inversion stage consists of two switch tubes and two diodes, firstly, three-phase output symmetry is set, and the three-phase output symmetry is carried out under a space vector modulation strategy, and the method specifically comprises the following steps:
step one, the space is divided into 6 sectors by the effective vector of the rectifier stage, and a phase current amplitude value is always maintained to be maximum in each sector; when a current reference vector I is inputrefAt a certain sector, solving and synthesizing the input current reference vector I by the sine theoremrefThe duty ratio of two adjacent effective vectors is dmAnd dnThen, by duty ratio dmAnd dnSolving the conduction duty ratio of each bridge arm switching tube of the rectifier stage, and respectively recording the conduction duty ratios as da、dbAnd dc；
Step two, the space is divided into 6 sectors by the effective vector of the inverter stage, and when the voltage reference vector V is outputrefLocated in a certain sector, solving and synthesizing the output voltage reference vector V by the sine theoremrefThe duty ratio of two adjacent effective vectors and zero vector is d1、d2And d0Then, by duty ratio d1、d2And d0Solving the conduction duty ratio of each bridge arm switching tube of the inverter stage, and respectively recording the conduction duty ratios as dPA、dPB、dPC；dNA、dNBAnd dNC；
Step three, inputting a current reference vector IrefThe sector and the output voltage reference vector Vref36 different combination forms are shared among the sectors, the waveforms of the switching tubes of the rectification stage and the inversion stage under each combination are determined according to the action sequence of the rectification stage effective vector, the inversion stage effective vector and the inversion stage zero vector under each combination, and the output voltage pulse waveform of each phase of the three-phase-three-phase ultra-sparse matrix converter is obtained;
step four, solving the trip point of the three-phase output voltage pulse in the next carrier period of each sector combination by using a formula (2) according to a carrier function c (x) expression shown in the formula (1);
Figure BDA0001544283090000021
Figure BDA0001544283090000022
in the formula (2), α1、α2、α3For the trip point of the phase a output voltage pulse,
step five, solving a triple Fourier coefficient F of the A-phase output voltage according to the output voltage pulse waveform obtained in the step three and the jump point of the output voltage pulse under each sector combination obtained in the step fourA_kpq；
Triple Fourier coefficient F of A-phase output voltageA_kpq：
Figure BDA0001544283090000023
In the formula (3), uAIs an A-phase output voltage pulse, k, p and q are integers,
Figure BDA0001544283090000024
wherein f isc、foutAnd finRespectively the carrier frequency, the output voltage frequency and the input voltage frequency of the ultra-sparse matrix converter,
Figure BDA0001544283090000025
is the initial phase of the carrier signal,
Figure BDA0001544283090000031
in order to input the power factor angle,
Figure BDA0001544283090000032
for the initial phase of the output voltage,
Figure BDA0001544283090000033
zr、zf、yr、yfare all integral limits;
according to the space vector modulation principle, the voltage pulse output by the A phase has a trip point alpha1、α2、α3Determining the range of integration interval, and recording the output voltage pulses of different integration intervals as uA1、uA2、uA3、uA4、uA5、uA6、uA7；
Figure BDA0001544283090000034
Figure BDA0001544283090000035
In the formulas (3) to (5), the vector I is referenced according to the input currentrefLocated sector kinDifference of (2), limit of integration zr、zfAnd the output voltage pulse takes the following values:
according to the output voltage reference vector VrefLocated sector koutDifference of (2), integration limit yr、yfThe values are as follows:
Figure BDA0001544283090000037
step six, obtaining triple Fourier coefficients F of A-phase output voltage in step fiveA_kpqFormula (6) is substituted to solve amplitude U of each harmonic of A-phase output voltageA_kpq，
UA_kpq＝2|FA_kpq| (6)
Further, the invention relates to a harmonic calculation method of an ultra-sparse matrix converter based on triple Fourier series, wherein the amplitude U of each harmonic of A-phase output voltage of the three-phase-three-phase ultra-sparse matrix converterA_kpqAmplitude U of each harmonic of B-phase output voltageB_kpqAmplitude U of each harmonic of phase C output voltageC_kpqIn the same way, any two-phaseAnd subtracting the voltage harmonics to obtain the line voltage harmonics between the two phases.
According to the amplitude U of each harmonic wave of the A-phase output voltageA_kpqAmplitude U of each harmonic of B-phase output voltageB_kpqAmplitude U of each harmonic of phase C output voltageC_kpqAnd respectively obtaining an A-phase output voltage spectrogram, a B-phase output voltage spectrogram and a C-phase output voltage spectrogram.
Compared with the prior art, the invention has the beneficial effects that:
according to the method for solving the output voltage harmonic wave under the space vector modulation strategy of the ultra-sparse matrix converter based on the triple Fourier series, the input frequency, the output frequency and the carrier frequency are all considered, the output voltage low-frequency-band harmonic wave is effectively described, the high-frequency-band harmonic wave component is effectively described, and the result obtained by the method is more accurate than that obtained by the double Fourier series. Meanwhile, the harmonic generation source can be determined by each subharmonic frequency expression. The method can obtain more accurate harmonic spectrum no matter what the input, output and carrier frequency are, and has wider application range than FFT. In addition, the harmonic distribution rule is easily seen from the output voltage harmonic spectrum, the harmonic analysis theory of the matrix converter is perfected, and a theoretical basis is provided for the design of a filter and the like. In addition, harmonic analysis can be performed in a similar manner for a conventional matrix converter or other improved space vector modulation method.
Drawings
FIG. 1 is a basic structure diagram of a three-phase-three-phase ultra-sparse matrix converter;
FIG. 2(a) is a schematic diagram of space vector modulation of a rectification stage of an ultra-sparse matrix converter;
FIG. 2(b) is a schematic diagram of the inverse level space vector modulation of the ultra-sparse matrix converter;
FIG. 3 is a modulation process when the reference vectors of both the rectification stage and the inversion stage are in the first sector;
FIG. 4(a) shows the voltage transfer ratio m is 0.5, fc＝5kHz，fin＝50Hz，foutOutputting a theoretical calculation result of a phase voltage frequency spectrum when the frequency is 70 Hz;
FIG. 4(b) is a voltageTransmission ratio m is 0.5, fc＝5kHz，fin＝50Hz，foutOutputting a line voltage frequency spectrum theoretical calculation result when the frequency spectrum is 70 Hz;
fig. 5(a) shows that the voltage transfer ratio m is 0.5, fc＝5kHz，fin＝50Hz，foutOutputting a phase voltage waveform and an FFT analysis result thereof when the frequency is 70 Hz;
fig. 5(b) shows that the voltage transfer ratio m is 0.5, fc＝5kHz，fin＝50Hz，foutOutputting the voltage waveform of the line and the FFT analysis result when the voltage waveform is 70 Hz;
FIG. 6 is a flow chart of solving harmonic waves of output voltage of the ultra-sparse matrix converter based on a triple Fourier series.
Detailed Description
The technical method of the present invention will be described in further detail with reference to the accompanying drawings and specific examples.
The design idea of the ultra-sparse matrix converter harmonic calculation method based on the triple Fourier series is as follows: based on a triple Fourier series correlation theory, and in combination with a three-phase-three-phase ultra-sparse matrix converter traditional space vector modulation strategy principle, an output voltage harmonic analytic expression is solved.
In the invention, the topological structure of the three-phase-three-phase ultra-sparse matrix converter is shown in figure 1 and comprises a rectification stage and an inverter stage, wherein each phase of bridge arm of the rectification stage consists of one switching tube and four diodes, and the structure of the inverter stage is the same as that of a traditional two-level inverter, namely each phase of bridge arm consists of two switching tubes and two diodes.
The space vector modulation strategy involved in the invention is a traditional space vector modulation strategy, no zero vector is inserted in the modulation process of a rectifier stage, and the reference input current is referred to as a reference vector IrefSynthesized by two adjacent effective vectors, and the inverter stage refers to the output voltage reference vector VrefIs composed of two adjacent effective vectors and a zero vector.
Firstly, three-phase output symmetry is set and performed under a space vector modulation strategy, as shown in fig. 6, the method specifically includes the following steps:
step (ii) ofFirst, the rectification stage space vector modulation method is as shown in fig. 2(a), the space is divided into 6 sectors by the effective vector, and a phase current amplitude is always maintained to be maximum in each sector. I in FIG. 2(a)1(a, c) equal 6 current space vectors divide the space into 6 sectors, denoted I1(a, c) are examples, I1(a, c) corresponding to rectifier stage switch SaAnd ScConduction, SbAnd (6) turning off. The modulation process of the rectifier stage has no insertion of zero vectors. When a current reference vector I is inputrefAt a certain sector, solving and synthesizing the input current reference vector I by the sine theoremrefRequired duty cycle d of two adjacent effective vectorsmAnd dnAre respectively as
Figure BDA0001544283090000051
Wherein a current reference vector k is inputinThe number of the sector in which the sector is located,
Figure BDA0001544283090000052
finis the input voltage frequency of the three-phase-three-phase ultra-sparse matrix converter,
Figure BDA0001544283090000053
for input power factor angle, matrix converter unity power factor operation is required in most applications to achieve maximum voltage transfer ratio, and so
Figure BDA0001544283090000054
By duty cycle dmAnd dnSeparately solving the input current reference vector IrefThe conduction duty ratio d of the switching tube of each bridge arm of the rectifier stage in different sectorsa、db、dcAnd the average value u of the DC voltage in one carrier perioddcAs shown in Table 1
TABLE 1 input Current reference vector IrefIn different sectors Sa、Sb、ScDuty cycle sum u ofdcValue of (A)
Figure BDA0001544283090000055
Step two, the inverse space vector modulation method is shown in fig. 2(b), the effective vector divides the space into 6 sectors, and V is used1(1,0,0) for example, "1" represents only S in the A-phase upper arm switchPAIn the on state, the 2 nd bit and the 3 rd bit are '0' respectively representing the S in the B phase and the C phase lower bridge arm switchesNBAnd SNCIs in an on state. When outputting the voltage reference vector VrefLocated in a certain sector, solving and synthesizing the output voltage reference vector V by the sine theoremrefTwo adjacent valid vectors d required1、d2And duty ratio d of zero vector0Are respectively as
Figure BDA0001544283090000056
Wherein k isoutTo output the sector number where the reference voltage is located,
Figure BDA0001544283090000057
foutfor the output voltage frequency of the ultra-sparse matrix converter,is the initial phase of the output voltage.
By duty cycle d1、d2And d0Solving the output voltage reference vector VrefWhen the inverter stage is positioned in different sectors, the switching tube of each phase upper bridge arm of the inverter stage
Figure BDA0001544283090000059
The on duty ratios of (μ ═ a, B, and C) are respectively denoted by dPA、dPB、dPCAs shown in Table 2, A, B, C the three-phase lower arm switch and the in-phase upper arm switch are in complementary relationship, so the power tube
Figure BDA0001544283090000061
Duty cycle
Figure BDA0001544283090000062
And
Figure BDA0001544283090000063
duty cycle
Figure BDA0001544283090000064
Satisfy the requirement of
Figure BDA0001544283090000065
TABLE 2VrefLocated in different sectors
Figure BDA0001544283090000066
Figure BDA0001544283090000067
Step three, inputting a current reference vector IrefThe sector and the output voltage reference vector Vref36 different combination forms are shared among the sectors, the waveforms of the switching tubes of the rectification stage and the inversion stage under each combination are determined according to the action sequence of the rectification stage effective vector, the inversion stage effective vector and the inversion stage zero vector under each combination, and the output voltage pulse waveform of each phase of the three-phase-three-phase ultra-sparse matrix converter is obtained;
the following analysis is given for phase a, since the three-phase output is symmetrical. When the reference vectors of the rectifying side and the inverting side are both in the 1 st sector, the waveforms of the switching tubes of the rectifying stage and the inverting stage and the instantaneous values of the a-phase output voltage in one carrier period can be obtained according to the distribution of the rectifying-stage direct-current voltage and the switching state of the inverting stage, as shown in fig. 3. The carrier function c (x) adopted in the modulation process has the expression of
Figure BDA0001544283090000068
Wherein the content of the first and second substances,
Figure BDA0001544283090000069
fcis the carrier frequency of the ultra-sparse matrix transformer,
Figure BDA00015442830900000610
is the initial phase of the carrier signal.
Step four, solving the jumping point of the A-phase output voltage pulse in the next carrier period of each sector combination by using the formula (2) according to the carrier function c (x) expression shown in the formula (1) and the waveform of each switch in the graph 3:
Figure BDA00015442830900000611
and in the same way, the waveforms of the switching tubes of the reference vectors of the rectifying side and the inverting side in other sectors and the output voltage pulse waveform of each phase of the three-phase-three-phase ultra-sparse matrix converter can be obtained. Through analysis, the result shows thatrefAnd VrefThe formula for calculating each trip point of the A-phase output voltage pulse in different sectors is the same as the formula (2), only d in the formulaPA、dmAnd dnThe specific values of (a) are changed in combination with tables 1 and 2.
Step five, solving a triple Fourier coefficient F of the A-phase output voltage according to the output voltage pulse waveform obtained in the step three and the jump point of the output voltage pulse under each sector combination obtained in the step fourA_kpq；
According to the Fourier transform theory, the A-phase output voltage is a triple Fourier coefficient FA_kpqThe expression is as follows:
Figure BDA0001544283090000071
in the formula (3), uAOutputting voltage pulse for phase A, wherein k, p and q are integers; z is a radical ofr、zf、yr、yfAre all integral limits;
according to the space vector modulation principle, the voltage pulse output by the A phase has a trip point alpha1、α2、α3Determining the range of integration interval, and recording the output voltage pulses of different integration intervals as uA1、uA2、uA3、uA4、uA5、uA6、uA7；
Figure BDA0001544283090000072
Figure BDA0001544283090000073
In the formulas (3) to (5), the vector I is referenced according to the input currentrefLocated sector kinDifference of (2), limit of integration zr、zfAnd the output voltage pulse values are shown in table 3:
TABLE 3 different kinZ ofr、zfAnd uAλ(λ＝1～7)
Figure BDA0001544283090000074
According to the output voltage reference vector VrefLocated sector koutDifference of (2), integration limit yr、yfThe values are shown in table 4:
TABLE 4 different koutY offAnd yr
Figure BDA0001544283090000075
From the following equations (3) to (5), F was obtained under matlabA_kpqThe analytical solution of (2).
Step six, obtaining triple Fourier coefficients F of A-phase output voltage in step fiveA_kpqFormula (6) is substituted to solve amplitude U of each harmonic of A-phase output voltageA_kpq，
UA_kpq＝2|FA_kpq| (6)
In the invention, the amplitude U of each harmonic of the A-phase output voltage of the three-phase-three-phase ultra-sparse matrix converterA_kpqAmplitude U of each harmonic of B-phase output voltageB_kpqAmplitude U of each harmonic of phase C output voltageC_kpqThe solving method is the same, and the line voltage harmonic between any two phases is obtained by subtracting the phase voltage harmonic of the two phases.
According to the amplitude U of each harmonic of A-phase output voltageA_kpqAmplitude U of each harmonic of B-phase output voltageB_kpqAmplitude U of each harmonic of phase C output voltageC_kpqAnd respectively obtaining an A-phase output voltage spectrogram, a B-phase output voltage spectrogram and a C-phase output voltage spectrogram.
When the voltage transfer ratio m is 0.5, the frequency f of the input voltageinIs 50Hz, output frequency foutIs 70Hz, carrier frequency fcAt 5kHz, the phase voltage u is outputAAnd line voltage uABThe results of the theoretical calculation of the spectrum of (a) are shown in FIGS. 4(a) and 4(b), and h in FIG. 4(a)AAnd h in FIG. 4(b)ABThe normalized phase voltage and line voltage harmonic amplitudes are respectively represented, the frequency and amplitude of each harmonic can be known from 4(a) and 4(b), and the main harmonic component and the harmonic distribution rule are analyzed. To verify the accuracy and effectiveness of the research method of the present invention, fig. 5(a) and 5(b) show the phase voltage u measured by experimentAAnd line voltage uABTime domain waveform and its FFT analysis result. By comparison, the harmonic frequency obtained by the analytic calculation and the FFT analysis result is the same, the amplitude is slightly different, but the difference is only 3.91 percent at most. The voltage transmission ratio, the carrier frequency and the output frequency are respectively changed, and the output voltage frequency spectrum obtained based on the triple Fourier series calculation is compared with the FFT analysis result, so that the conclusion can still be obtained.
While the present invention has been described with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments, which are illustrative only and not restrictive, and various modifications which do not depart from the spirit of the present invention and which are intended to be covered by the claims of the present invention may be made by those skilled in the art.

Claims (3)

1. A harmonic calculation method of an ultra-sparse matrix converter based on a triple Fourier series is disclosed, wherein a three-phase-three-phase ultra-sparse matrix converter comprises a rectification stage and an inversion stage, each phase of bridge arm of the rectification stage consists of a switch tube and four diodes, each phase of bridge arm of the inversion stage consists of two switch tubes and two diodes, and the harmonic calculation method is characterized in that:
firstly, setting three-phase output symmetry and performing under a space vector modulation strategy, specifically comprising the following steps:
step one, the space is divided into 6 sectors by the effective vector of the rectifier stage, and a phase current amplitude value is always maintained to be maximum in each sector; when a current reference vector I is inputrefAt a certain sector, solving and synthesizing the input current reference vector I by the sine theoremrefThe duty ratio of two adjacent effective vectors is dmAnd dnThen, by duty ratio dmAnd dnSolving the conduction duty ratio of each bridge arm switching tube of the rectifier stage, and respectively recording the conduction duty ratios as da、dbAnd dc；
Step two, the space is divided into 6 sectors by the effective vector of the inverter stage, and when the voltage reference vector V is outputrefLocated in a certain sector, solving and synthesizing the output voltage reference vector V by the sine theoremrefThe duty ratio of two adjacent effective vectors and zero vector is d1、d2And d0Then, by duty ratio d1、d2And d0Solving the conduction duty ratio of each bridge arm switching tube of the inverter stage, and respectively recording the conduction duty ratios as dPA、dPB、dPC；dNA、dNBAnd dNC；
Step three, inputting a current reference vector IrefThe sector and the output voltage reference vector Vref36 different combination forms are shared among the sectors, the waveforms of the switching tubes of the rectification stage and the inversion stage under each combination are determined according to the action sequence of the rectification stage effective vector, the inversion stage effective vector and the inversion stage zero vector under each combination, and the output voltage pulse waveform of each phase of the three-phase-three-phase ultra-sparse matrix converter is obtained;
step four, solving the trip point of the three-phase output voltage pulse in the next carrier period of each sector combination by using a formula (2) according to a carrier function c (x) expression shown in the formula (1);
Figure FDA0001544283080000011
Figure FDA0001544283080000012
in the formula (2), α1、α2、α3For the trip point of the phase a output voltage pulse,
step five, solving a triple Fourier coefficient F of the A-phase output voltage according to the output voltage pulse waveform obtained in the step three and the jump point of the output voltage pulse under each sector combination obtained in the step fourA_kpq；
Triple Fourier coefficient F of A-phase output voltageA_kpq：
Figure FDA0001544283080000013
In the formula (3), uAIs an A-phase output voltage pulse, k, p and q are integers,
Figure FDA0001544283080000014
wherein f isc、foutAnd finRespectively the carrier frequency, the output voltage frequency and the input voltage frequency of the ultra-sparse matrix converter,
Figure FDA0001544283080000015
is the initial phase of the carrier signal,in order to input the power factor angle,
Figure FDA0001544283080000017
for the initial phase of the output voltage,
Figure FDA0001544283080000018
zr、zf、yr、yfare all integral limits;
according to the space vector modulation principle, the voltage pulse output by the A phase has a trip point alpha1、α2、α3Determining the range of integration interval, and recording the output voltage pulses of different integration intervals as uA1、uA2、uA3、uA4、uA5、uA6、uA7；
Figure FDA0001544283080000021
In the formulas (3) to (5), the vector I is referenced according to the input currentrefLocated sector kinDifference of (2), limit of integration zr、zfAnd the output voltage pulse takes the following values:
according to the output voltage reference vector VrefLocated sector koutDifference of (2), integration limit yr、yfThe values are as follows:
Figure FDA0001544283080000024
step six, obtaining triple Fourier coefficients F of A-phase output voltage in step fiveA_kpqFormula (6) is substituted to solve amplitude U of each harmonic of A-phase output voltageA_kpq，
UA_kpq＝2|FA_kpq| (6)。
2. The triple Fourier series based ultra-sparse matrix converter harmonic of claim 1The wave calculation method is characterized in that the amplitude U of each harmonic of the A-phase output voltage of the three-phase-three-phase ultra-sparse matrix converterA_kpqAmplitude U of each harmonic of B-phase output voltageB_kpqAmplitude U of each harmonic of phase C output voltageC_kpqThe solving method is the same, and the line voltage harmonic between any two phases is obtained by subtracting the phase voltage harmonic of the two phases.
3. The harmonic calculation method of the triple Fourier series-based ultra-sparse matrix converter according to claim 1 or 2, wherein the amplitude U of each harmonic is calculated according to the amplitude U of the A-phase output voltageA_kpqAmplitude U of each harmonic of B-phase output voltageB_kpqAmplitude U of each harmonic of phase C output voltageC_kpqAnd respectively obtaining an A-phase output voltage spectrogram, a B-phase output voltage spectrogram and a C-phase output voltage spectrogram.
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