CN113489056B - Output component calculation method of indirect matrix converter of wind power generation system - Google Patents
Output component calculation method of indirect matrix converter of wind power generation system Download PDFInfo
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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
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/381—Dispersed generators
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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
- H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
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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
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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
- H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
- H02J2300/20—The dispersed energy generation being of renewable origin
- H02J2300/28—The renewable source being wind energy
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- 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
- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/70—Wind energy
- Y02E10/76—Power conversion electric or electronic aspects
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- 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]
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Abstract
The invention discloses a method for calculating output components of an indirect matrix converter of a wind power generation system, which is used for accurately obtaining the amplitudes of common-mode components and harmonic components of output voltages under different frequencies. The method is based on the triple Fourier series, the zero vector action time is considered, the analytic expressions of the output common-mode component and the harmonic component of the indirect matrix converter are established, and the influence of the zero vector action time on the output voltage common-mode component and the harmonic component is quantitatively analyzed.
Description
Technical Field
The invention relates to the technical field of power electronics, in particular to a method for calculating an output component of an indirect matrix converter of a wind power generation system.
Background
Wind power generation as a green renewable energy has the advantages of energy structure improvement, economy, environmental protection and the like, and is an important trend of future energy power development.
Matrix Converter (MC) is a direct AC-AC Converter developed on the basis of a cycle Converter, and has the advantages of controllable output voltage waveform, sinusoidal input and output current, controllable input power factor, no limitation of output power factor, high integration level, high energy density and the like, and becomes a new generation of electric energy conversion device with great potential. The Matrix Converter can be topologically divided into a Direct Matrix Converter (DMC) and an Indirect Matrix Converter (IMC). Compared with DMC, IMC needs fewer switching devices and has a more compact structure, so that IMC has a wide application prospect in the fields of wind power generation and the like.
In a wind power generation system, a grid-connected subsystem generates a large amount of harmonic interference in the past; when the indirect matrix converter is used as a converter of a wind power generation system, output voltage during working contains a large amount of common-mode components and harmonic components besides fundamental waves, and the output common-mode characteristics and the output harmonic characteristics of the matrix converter are important indexes for measuring the output performance of the converter. The part of harmonic components and the common-mode components are used as excitation sources and flow into a power grid together, and the harmonic waves have serious influence on the normal power supply environment of a power system and the normal operation of equipment.
The following are common effects: the generation of harmonic increases the possibility of power grid resonance, increases the accessory loss of electrical equipment, accelerates the insulation aging, shortens the service life, and solves the problems that a relay protection device and an automatic device can not operate correctly, a metering instrument is out of alignment, communication is abnormal and the like. At present, more and more wind turbine generators are in grid-connected operation, and the influence of wind power generation on the power quality of a power grid draws wide attention. Therefore, it is necessary to study the influence of the output harmonic correlation characteristics of the indirect matrix converter on the wind driven generator and the power system.
At present, common-mode components or harmonic components are mainly suppressed by changing a modulation strategy, and in the research on output characteristics, qualitative analysis is mainly performed, and the output characteristics are not calculated quantitatively. The method for quantitatively analyzing the output characteristics of the matrix converter mainly adopts Fourier transform to analyze an output waveform and obtain an output voltage frequency spectrum. The common method is FFT analysis, but FFT analysis requires sampling, windowing, and the like of signals in the process of processing waveforms, which may cause problems of spectrum leakage, aliasing, and the like, resulting in inaccurate FFT analysis results. Another commonly used research method is to obtain an analytic expression of an output waveform by using fourier series, and calculate the harmonic amplitude thereof to obtain a more accurate harmonic spectrum. In the quantitative analysis method for the output characteristics, the influence of the zero vector action time on the output common-mode component and harmonic component of the indirect matrix converter is not considered.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an analysis method based on a triple Fourier series, and a calculation method of output components of an indirect matrix converter of a wind power generation system under the condition of considering different zero vector action times. The method can obtain more accurate output component amplitude and harmonic spectrum.
The technical scheme of the invention is as follows:
a method for calculating output components of an indirect matrix converter of a wind power generation system comprises the following steps:
s1: setting three-phase output symmetry with input power factor of 1, in each sector of the rectifier stage, referring to the input current vector I ref From two adjacent active vectors I δ And I γ Synthesizing, respectively calculating duty ratio d of two effective current vectors δ 、d γ ；
S2: in each sector of the inverter stage, the output voltage vector V is referenced according to the vector synthesis principle ref From adjacent effective vectors V α And V β And zero vector V 0 And V 7 Synthesizing, respectively calculating two effective vector duty ratios d α ，d β Duty ratio d corresponding to zero vector 07 ；
S3: the effective vector of the rectifier stage is matched with the vector of the inverter stage to generate different output voltages, and the jump time m of different output voltage amplitudes is determined according to the duty ratio of the vector in a carrier period x1 、m x2 、m x3 (x = A, B, C); the output voltage amplitude jump time of half carrier period is
m A1 ＝d γ d NA π；m A2 ＝d γ π；m A3 ＝(1-d δ d NA )π
D is NA In order to output the duty ratio of the A-phase lower tube, the duty ratio d of the A-phase lower tube is adjusted according to the space vector modulation principle of the inverter stage NA As shown in the following table
S4: taking into account the input frequency f in Output frequency f out And carrier frequency f c Independent of each other, when k is not equal to 0, the amplitude of the output voltage jumps at the moment m A1 ，m A2 ，m A3 Carry over into triple Fourier integral expression pair F k，p，q Solving to obtain different frequenciesThe output component of each harmonic at a rate; h is com_L_n Is a low frequency common mode component, h com_H_n For high frequency common mode components, h har_n As harmonic components
Further, the duty ratio d of two effective current vectors of the rectifier stage δ 、d γ Respectively as follows:
at each inversion stage sector k out In, reference to output voltage vector V ref From two adjacent effective vectors V α And V β And zero vector V 0 And V 7 And synthesizing, wherein the duty ratios of the two effective vectors and the zero vector are as follows:
according to inverse-stage modulation, reference output voltage vector V ref Can be expressed as:
V ref ＝d α V α +d β V β +d 0 V 0 +d 7 V 7
in the formula, k in Inputting the sector number of the sector where the current vector is located for the IMC; v in Is the magnitude of the input phase voltage; input phase theta in ＝2πf in t，f in Is the input frequency; k is a radical of out Is the sector number where the output reference voltage vector is located; d α 、d β 、d 0 And d 7 Representing the effective vector V of the voltage of the inverter stage α And V β And zero vector V 0 And V 7 Duty ratio of V ref For outputting a voltage vector V as a reference ref Amplitude of, output phase of
f out In order to output the frequency of the frequency,
for the initial phase of the output voltage, 0 is assumed.
Further, in the step S2, a zero vector duty ratio coefficient i is defined k Is i k ＝d min_0 /d 07 ，i k The value of (2) determines the action time of two voltage zero vectors; when i is k When =0.5, small zero vector V min And a large zero vector V max The action time is equal; when i is k When the phase is not less than 1, the action time of the large zero vector is 0, and the inverter stage only selects the small zero vector for modulation; when i is k When the zero vector is not less than 0, the small zero vector action time is not less than 0, and the inverter stage only selects the large zero vector modulation.
Further, the S2 further includes:
s21: let k in For the number of the commutation sector, the virtual DC side voltage is not a constant value in different commutation sectors, and two different zero voltage vectors V 0 、V 7 The generated common mode amplitude values are different in size;
s22: when k is in V is 1,3,5 7 Corresponding common mode voltage amplitude greater than V 0 A corresponding common mode voltage amplitude; when k is in V is 2,4,6 0 Corresponding common mode voltage amplitude greater than V 7 A corresponding common mode voltage amplitude;
s23: redefining two voltage zero vectors of an inverter stage as a small zero vector V min_0 And a large zero vector V max_0 ：
S24: defining a zero vector duty cycle coefficient i k To assign the zero vector on-time to,i k representing small zero vectors V min_0 Ratio of the sum of two zero voltage vectors:
s25: the duty ratio of a small zero vector in the two zero voltage vectors is d min_0 The duty cycle of the large zero vector is d max_0 Wherein
Further, in S4, the triple fourier coefficient F of the output voltage of the indirect matrix converter under the space vector modulation k，p，q Is composed of
When k =0, jumping the amplitude of the output voltage at the moment m A1 ，m A2 ，m A3 Carry over into triple Fourier integral expression pair F k，p，q Solving for the Fourier coefficient of the output voltage of
In the formula, z 1 And z 2 Is an integer; m is voltage transmission ratio, m = V out /V in (ii) a f (p) is a function related to p, and f (p) is equal to 1,0.75,0.69,0.67,0.65,0.63 when p is 3,9,15,21,27 and 33, respectively;
when k is not equal to 0, jumping the amplitude of the output voltage at a moment m A1 ，m A2 ，m A3 Carry over into triple Fourier integral expression pair F k，p，q The solution is carried out to obtain
Wherein n represents the frequency of each component of the output voltage, and n = [ pf ] out ±qf in ±kf c |；F com_n (m，i k ) Is equal to m and i k Fourier coefficient, F, of the relevant output high-frequency common-mode voltage component har_n (m，i k ) Is equal to m and i k The fourier coefficients of the high-frequency harmonic components of the correlation output.
Further, the matrix converter outputs an A-phase voltage u Ag Is expressed as
Triple Fourier coefficient F of output voltage k，p，q
Wherein the carrier phase θ c ＝2πf c t, input phase θ in ＝2πf in t, output phase
k, p, q are carrier frequencies f c Input frequency f in Output frequency f out Coefficient of (A) k，p，q And B k，p，q Respectively the real part and the imaginary part of the triple Fourier coefficient; j denotes an imaginary unit, j 2 ＝-1。
Frequency of kf c ±pf in ±qf out Has harmonic component and common mode component of amplitudes
Further, the carrier of the space vector modulation is a triangular wave, the carrier function c (theta) c ) Is composed of
Further, the rectifier stage outputs a Fourier coefficient F of the voltage during one complete modulation cycle k， p ，q Is composed of
D kin A computational expression representing the output voltage over one carrier period:
the invention has the following technical effects:
in the method for calculating the output components of the indirect matrix converter of the wind power generation system, disclosed by the invention, in order to accurately obtain the amplitudes of the common-mode components and harmonic components under different frequencies, the common-mode components and the harmonic components of the output voltage are subjected to mathematical modeling by adopting a triple Fourier transform method.
The invention analyzes the influence of zero vector action time on the common-mode component and harmonic component of output voltage based on triple Fourier series quantization, and the following conclusion can be obtained by analyzing the common-mode component and the harmonic component of output voltage: on the basis of not changing the selection of the effective vector, only selecting a large zero vector or a small zero vector has the same influence on the high-frequency common-mode component, but has larger influence on the low-frequency common-mode component; under a space vector modulation strategy, the amplitude of the low-frequency common-mode voltage can be greatly reduced by adjusting the action time of two zero voltage vectors; when the voltage transmission ratio m is larger, i k Has little influence on the distortion of the output phase current, so that under high voltage transmission ratio, i can be changed k To reduce the magnitude of certain high frequency common mode components in the output phase voltages. The conclusion can provide theoretical basis and theoretical basis for the modulation strategy for improving the output performance of the indirect matrix converter.
Drawings
FIG. 1 is a schematic diagram of a topology of an indirect matrix converter
FIG. 2 illustrates the space vector modulation principle of an indirect matrix converter
FIG. 3a is k in ＝1，k out =1, the synthesized waveform of the A-phase output voltage under space vector modulation
FIG. 3b is k in ＝2，k out When =1, the synthesized waveform of the a-phase output voltage under space vector modulation
FIG. 4a, FIG. 4b, and FIG. 4c show the frequency 3f in 、(6Z 1 +3)f in 、3f out Low frequency common mode component of output voltage
FIG. 5a and FIG. 5b show the frequency of (3 z) 1 f in +kf c )、kf c High frequency common mode component of output voltage
FIGS. 6a, 6b, and 6c show harmonic components of output voltages at different frequencies
FIG. 7 is a theoretical output phase voltage spectrum calculated by a triple Fourier series
FIG. 8 is an experimental waveform and FFT analysis spectrum of output phase voltage
FIG. 9 is an IMC experiment hardware diagram of the present invention
FIG. 10 shows output phase currents i for m =0.2,0.5 and 0.8 A Experimental waveforms
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments.
As shown in fig. 1, from the topological point of view, an Indirect Matrix Converter (IMC) is divided into two stages: a rectification stage and an inverter stage. The structure of the rectifier stage is the same as that of a current-type rectifier, the structure of the inverter stage is the same as that of a voltage-type two-level inverter, three-phase output symmetry is set, and the input power factor is 1.
The IMC space vector modulation is divided into rectification-stage and inversion-stage modulation. The rectification stage adopts a space vector modulation method without zero vector, and in each rectification stage sector, a reference current vector I ref From two adjacent active vectors I δ And I γ The synthesis was as shown in FIG. 2 (a). Reference current vector I ref Comprises the following steps:
I ref ＝I δ d δ +I γ d γ (1)
according to the rectification level modulation, the average voltage of the direct current side in one period is as follows:
duty cycle d of two active current vectors of a rectifier stage δ 、d γ Respectively as follows:
the space vector modulation method of the inversion stage is shown in fig. 2 (b). At each inversion stage sector k out In, reference to output voltage vector V ref From two adjacent effective vectors V α And V β And zero vector V 0 And V 7 And synthesizing, wherein the duty ratios of the two effective vectors and the zero vector are as follows:
according to inverse-stage modulation, reference output voltage vector V ref Can be expressed as:
V ref ＝d α V α +d β V β +d 0 V 0 +d 7 V 7 (5)
in the formula, k in Inputting the sector number of the sector where the current vector is located for the IMC; v in Is the magnitude of the input phase voltage; transfusion systemInto phase theta in ＝2πf in t，f in Is the input frequency; k is a radical of out Is the sector number where the output reference voltage vector is located; d α 、d β 、d 0 And d 7 Representing the effective vector V of the voltage of the inverter stage α And V β And zero vector V 0 And V 7 Duty ratio of V ref For outputting a voltage vector V as a reference ref Amplitude of, output phase of
f out In order to output the frequency of the radio frequency,
for the initial phase of the output voltage, 0 is assumed.
Further, in the S2, a zero vector duty ratio coefficient i is defined k Is i k ＝d min_0 /d 07 ，i k The value of (A) determines the action time of two voltage zero vectors; when i is k When =0.5, small zero vector V min And a large zero vector V max The action time is equal; when i is k When the phase is not less than 1, the action time of the large zero vector is 0, and the inverter stage only selects the small zero vector for modulation; when i is k When the zero vector is not less than 0, the small zero vector action time is not less than 0, and the inverter stage only selects the large zero vector modulation.
Because the virtual direct current side voltage is not a constant value, the amplitude of the common mode voltage correspondingly generated by the two voltage zero vectors is different. When k is in V is 1,3,5 7 Corresponding common mode voltage amplitude greater than V 0 Corresponding common mode voltage amplitude: when k is in V is 2,4,6 0 Corresponding common mode voltage amplitude greater than V 7 Corresponding common mode voltage amplitude. Redefining two voltage zero vectors of an inverter stage as a small zero vector V min And a large zero vector V max And corresponding duty cycle is d min_0 And d max_0 。V min_0 、V max_0 And V 0 、V 7 In a relationship of
Defining two zero vector duty cycle coefficients i k Is composed of
i k ＝d min_0 /d 07 (7)
i k The value of (a) determines the action time of the two voltage zero vectors. When i is k When =0.5, the action time of the large and small zero vectors is equal, and the modulation method is a traditional space vector modulation method; when i is k When the modulation time is not less than 1, the action time of the large zero vector in the modulation method is 0, and only the small zero vector modulation is selected by the inverter stage. When i is k When the modulation method is not less than 0, the action time of the small zero vector is not less than 0, and the inverter stage only selects the large zero vector for modulation.
Taking the output phase A as an example, the voltage u of the output point A relative to the neutral point g of the input voltage Ag Defined as the output phase voltage
u Ag ＝u AN +u Ng (8)
Wherein u is AN For outputting the voltage of phase A to output ground N, u Ng Is the common mode voltage. To analyze the common mode and harmonic characteristics of the output voltage, u is selected Ag And (6) carrying out analysis.
The invention adopts the carrier wave modulated by space vector as triangular wave, and the carrier function c (theta) thereof c ) Is composed of
Carrier phase theta in formula c ＝2πf c t，f c Is the carrier frequency. According to the IMC rectification stage space vector modulation, when k is in =1,3,5, the a-phase voltage u is output Ag The waveform in one carrier period is synthesized from 5 segments of input voltage as shown in fig. 3 (a). When k is in =2,4,6, the a-phase voltage u is output Ag The waveform in one carrier period is synthesized by 7 segments of input voltage, and the output voltage waveform is shown in fig. 3 (b).
U in FIG. 3 (a) A1 ，u A2 And u A3 Are respectively as
U in FIG. 3 (b) A1_1 ，u A2_1 And u A3_1 Are respectively as
In the formula V in For the input voltage amplitude, it can be seen from fig. 3 that the voltage amplitude of each segment of the output voltage is determined by the modulation of the rectifier stage, and is not related to the modulation of the inverter stage, but the transition time of the output voltage amplitude is related to the duty ratio of the switching tube of the inverter stage. The output voltage amplitude jump time of half carrier period is
m A1 ＝d γ d NA π；m A2 ＝d γ π；m A3 ＝(1-d δ d NA )π (12)
d NA In order to output the duty ratio of the A-phase lower tube, the duty ratio d of the A-phase lower tube is adjusted according to the space vector modulation principle of the inverter stage NA As shown in table 1.
Table 1: d NA Expression formula
From equation (12) and table 1, it can be seen that the transition time m of the output voltage variation A1 、m A2 、m A3 Not only with the duty ratio of the voltage and current effective vectors, but also with the duty ratio coefficient i of the voltage zero vector k It is related.
Since the indirect matrix converter output waveform is related to and independent of the input, output frequency and carrier frequency. In order to accurately obtain the common-mode component and harmonic component amplitude of the output voltage under different frequencies, the invention adopts a triple Fourier transform method to carry out mathematical modeling on the common-mode component and the harmonic component of the output voltage.
The method for calculating the output common-mode component and the harmonic component of the indirect matrix converter comprises the following steps:
s1: in each sector of the rectifier stage, the input current vector I is referenced according to the vector synthesis principle ref From two adjacent active vectors I δ And I γ Synthesizing, respectively calculating duty ratio d of two effective current vectors δ 、d γ ；
S2: in each sector of the inverter stage, the output voltage vector V is referenced according to the vector synthesis principle ref From adjacent effective vectors V α And V β And zero vector V 0 And V 7 Synthesizing, respectively calculating two effective vector duty ratios d α ，d β Duty ratio d corresponding to zero vector 07 。
The step S2 specifically includes:
s21: let k in For the number of the commutation sector, the virtual DC side voltage is not a constant value in different commutation sectors, and two different zero voltage vectors V 0 、V 7 The generated common mode amplitude values are different in size;
s22: when k is in V is 1,3,5 7 Corresponding common mode voltage amplitude greater than V 0 A corresponding common mode voltage amplitude; when k is in V is 2,4,6 0 Corresponding common mode voltage amplitude greater than V 7 A corresponding common mode voltage amplitude;
s23: redefining two voltage zero vectors of an inverter stage as a small zero vector V min_0 And a large zero vector V max_0 ：
S24: defining zero vector dutyRatio coefficient i k To assign zero vector action time, i k Representing small zero vectors V min_0 Ratio of the sum of two zero voltage vectors:
s25: the duty ratio of a small zero vector in the two zero voltage vectors is d min_0 The duty cycle of the large zero vector is d max_0 Wherein
S3: the effective vector of the rectifier stage is matched with the vector of the inverter stage to generate different output voltages, and the jump time m of different output voltage amplitudes is determined according to the duty ratio of the vector in a carrier period x1 、m x2 、m x3 ，(x＝A、B、C)。
S4: taking into account the input frequency f in Output frequency f out And carrier frequency f c Independent of each other, and combined with triple Fourier series, calculating triple Fourier coefficient F k，p，q And obtaining the amplitude of each harmonic wave under different frequencies.
According to the principle of triple Fourier transform, an SVPWM-modulated indirect matrix converter outputs an A-phase voltage u Ag Is expressed as
Triple Fourier coefficient F of output voltage k，p，q
Wherein k, p and q are integers and are respectively carrier frequency f c Input frequency f in Output frequency f out The coefficient of (a) is determined,A k，p，q and B k，p，q The real and imaginary parts of the triplex fourier coefficients, respectively.
Frequency of kf c ±pf in ±qf out Each of the harmonic component and the common mode component has an amplitude of
A triple Fourier mathematical model of harmonic components and common-mode components in output voltage of the indirect matrix converter under space vector modulation is constructed, and because output voltage waveforms are different in different rectification sectors, fourier coefficients F of the output voltage of a rectification stage in a complete modulation period are calculated k， p ，q Is composed of
D kin A computational expression representing the output voltage over one carrier period:
the Fourier coefficients of the odd sectors and the even sectors in the rectification stage satisfy the relationship of
According to the IMC inversion level modulation principle, the inversion level modulation is also divided into 6 sectors, and the Fourier coefficient, F, of the output voltage of the inversion level in a complete modulation period is calculated k，p，q_kin Can be expressed as
Triple Fourier coefficient F of output voltage of indirect matrix converter under space vector modulation k，p，q Is composed of
When k =0, jumping the amplitude of the output voltage at the moment m A1 ，m A2 ，m A3 Bring-in triple Fourier integral expression pair F k，p，q Solving for the Fourier coefficient of the output voltage of
In the formula, z 1 And z 2 Is an integer; m is the voltage transfer ratio, equal to V out /V in . f (p) is a function related to p, and is equal to 1,0.75,0.69,0.67,0.65,0.63 when p is 3,9,15,21,27 and 33, respectively.
As can be seen from equation (23), the output voltage contains (6 z) in addition to the fundamental component in the low frequency band 1 +3)f in And (62) 2 +3)f out Of the common-mode component belonging to the low-frequency common-mode voltage.
When k is not equal to 0, jumping the amplitude of the output voltage at a moment m A1 ，m A2 ，m A3 Carry over into triple Fourier integral expression pair F k，p，q The solution is carried out to obtain
Where n denotes the frequency of each component of the output voltage, and n = | pf out ±qf in ±kf c |；F com_n (m，i k ) Is equal to m and i k Fourier coefficient of the relevant high-frequency common-mode component, F har_n (m，i k ) Is equal to m and i k Fourier coefficients of the associated high-frequency harmonic components.
According to the solving process, the voltage transmission ratio m and the zero vector duty ratio coefficient i k The frequency distribution is not changed and only its amplitude is affected. Per-unit transforming the Fourier coefficient of the common mode component and the Fourier coefficient of the harmonic component of the output voltage into h com_L_n Is the per unit value of the low frequency common mode component, h com_H_n Is a per unit value of the high frequency common mode component, h har_n Is a per-unit value of the harmonic component. The main common mode component and harmonic component of the output voltage can be obtained as
In order to further verify the influence rule of the zero vector action time on the common-mode component and harmonic component of the output voltage, fig. 4, 5 and 6 respectively show different voltage transmission ratios m and different zero vector action time coefficients i k And (4) obtaining a simulation result.
FIG. 4 shows a three-dimensional view of the low frequency common mode component, and FIG. 4 (a) shows the frequency 3f in The low-frequency common-mode amplitude under different voltage transmission ratios and different zero vector action time coefficients is 3f when m is more than 0and less than 0.68 in H of com_L_n With i being k Decreasing and then increasing, when m is more than 0.68 and less than 0.866, the frequency is 3f in H of com_L_n With i being k Is increased and decreased.
FIG. 4 (b) shows a low frequency of (62) 1 +3)f in Low frequency common mode amplitude at different voltage transfer ratios and different zero vector time coefficients of action, frequency is (62) 1 +3)f in H of com_L_n The basic trend is roughly as follows k And =0.5 is a symmetrical change rule of the symmetry axis. When i is k E (0,0.5), FIG. 4 (b)H of com_L_n And i k In an anti-growth relationship, so when i k The larger the higher the low frequency common mode component.
FIG. 4 (c) shows the low frequency common mode amplitude at 3fout with frequency of 3f at different voltage transfer ratios and different zero vector time coefficients of action out The common-mode component of (2) is independent of the zero vector action time and only linearly changes with m.
FIG. 5 shows a three-dimensional view of the high frequency common mode component, which is seen in FIGS. 5 (a) and 5 (b) with respect to i k =0.5 symmetry, the space vector modulation strategy only selects large zero vectors or small zero vectors without distinction in the influence of high-frequency common-mode components; in FIG. 5 (a), | i k -0.5| is inversely proportional to the amplitude of the high frequency common mode component; when the voltage transfer ratio m is smaller, i k The greater the effect on the high frequency common mode component. When m is larger, i k The smaller the influence on the change of the high-frequency common-mode component, when m is more than 0.8, i k Has substantially no effect on the common mode component. In FIG. 5 (b), i k E (0,0.5), when m < 0.4, with i k The variation trend of the high-frequency common-mode component is firstly increased, then decreased and then increased; when m is more than 0.4, the variation trend of the high-frequency common-mode component is along with i k Is increased by an increase of i k The maximum value is taken at = 0.5.
FIG. 6 shows a three-dimensional plot of the amplitude of the harmonic component of the output voltage, the principal harmonic component being represented by i k And =0.5 is a change rule with a symmetric axis, and the rule of the influence of the zero vector action time on the harmonic component can be classified as follows through calculation of triple fourier transform: 1) The space vector modulation strategy selects only the large or small zero vector to have no difference in the effect on the harmonic components. 2) When i is k K =0.5, frequency is kf c ±f out ±3f in The harmonic component of (k =1,2,3,4) is 0.
And (3) experimental verification:
as shown in fig. 9, in order to prove the correctness of the rule summary of the zero vector action time under the space vector modulation on the output voltage component, a set of IMC experimental prototype is built. The rectification stage comprises 12 IGBTs (FGL 40N120 AND); the inverter stage comprises 6 IGBTs (FGL 40N120 AND); the system employs a controller DSP (TMSF 28335). The experimental parameters are shown in table 2.
TABLE 2 Experimental parameters
When the FFT analysis is adopted, when the carrier frequency, the input frequency and the output voltage frequency are all integers, and the waveform corresponding time intercepted by the FFT analysis is just integral multiples of the carrier period, the input voltage period and the output voltage period, the result obtained by the FFT analysis is basically the same as the result obtained based on the triple Fourier transform. Based on the above conditions, the output voltage is FFT and compared with the output voltage spectrum obtained by the triple fourier series calculation, verifying the above analysis.
In order to verify the correctness of the influence analysis of the zero vector action time obtained by adopting the triple Fourier integral transformation on the output characteristic more intuitively, the output voltage u under the same parameters with the experiment is given Ag As a comparison graph of experimental verification. When f is in ＝50Hz、f out ＝25Hz、f c =5kHz, and m =0.2, the output voltage u was obtained by three-fold fourier transform Ag At a different i k The output spectrum of the lower band, the spectrum of its main common mode component and the spectrum of its harmonic component, are shown in fig. 7.
(a) Output phase voltage u Ag Common mode component and harmonic component of
Different i were obtained by experiment under the same conditions k Lower output voltage u A Waveform, FFT analysis of the output phase voltage waveform, and the output voltage waveform and the result of FFT analysis thereof are shown in fig. 8.
The main common-mode and harmonic components are extracted from the experimental results and theoretical calculation results, as shown in table 2 below:
table 2:
the shaded area data in table 2 represents the per unit value of the harmonic component in the output voltage, and the blank area represents the per unit value of the harmonic component in the output voltage. When m is constant, the action time i of the zero vector k The change changes the amplitude of common-mode component and harmonic component in the output voltage, and the influence rule is the same as that of theoretical analysis. The magnitude of most common mode components is given by i k And =0.5 is a symmetry axis and is symmetrically distributed. Frequency of kf c ±6z 1 f in (k＝1，2，3；z 1 =1,2,3) has a common mode component amplitude of i k Maximum value is obtained when = 0.5. The amplitude of the major harmonic component is set by i k =0.5 as axis of symmetry, symmetrically distributed, and having frequency kf c ±f out ±6f in (k＝2，3，4)、2f c ±f out For harmonic component amplitude at i k The maximum value is obtained when = 0.5.
Comparing the experimental value with the theoretical value, obtaining that the amplitudes of the main common-mode component and harmonic component of the experiment are approximately the same as the amplitudes of the common-mode component and harmonic component obtained by applying the triple Fourier transform theory through FFT analysis. The experimental results verify the correctness of the analysis of the influence rule of the zero vector action time on the common-mode component and the harmonic component.
(b) Output phase current distortion rate
As shown in fig. 10, output phase currents i of m =0.2,0.5 and 0.8 A Experimental waveforms. Output phase current i from FIG. 10 A The distortion rate is known, m is a constant, i k =0.2 and i k The output phase current total harmonic distortion rate under the condition of =0.8 is basically the same under the condition of the same m; under the same m, i k Output phase current total harmonic distortion rate of =0.5 is less than i k =0.2 and i k =0.8 output phase current total harmonic distortion rate. When m is smaller, i k The influence on the distortion rate of the output current is large, and as m increases, i k The influence on the distortion rate of the output current is gradually reduced; when m reaches 0.8, i k Almost has no influence on the distortion rate of the output current; the above experimental results verify the output current distortion rate by i k =0.5 is a symmetry axis and is symmetrically distributed; and isThe influence rule is consistent with the theoretical analysis.
According to the space vector modulation principle of the indirect matrix converter, the output voltage component of the indirect matrix converter is quantitatively calculated by utilizing a triple Fourier transform method, the amplitude and the frequency spectrum of the output voltage component are obtained, and the influence of zero vector action time on the common mode component and the harmonic component of the output voltage is analyzed. The following conclusions can be drawn by analyzing the common mode component and the harmonic component:
1) On the basis of not changing the selection of the effective vectors, only selecting large zero vectors or small zero vectors has the same influence on high-frequency common-mode components, but has larger influence on low-frequency common-mode components.
2) By varying the zero vector duty factor i k The amplitude of part of high-frequency components in the output phase voltage can be effectively reduced.
3) Zero voltage vector duty factor i k Has an influence on the output phase current distortion rate, with i k The increase in (c) is first reduced and then increased. And as the voltage transfer ratio m increases, i k The less influence on the distortion rate of the output current.
4) When the voltage transmission ratio m is larger, i k Has little influence on the distortion of the output phase current, so that under high voltage transmission ratio, i can be changed k To reduce the magnitude of certain high frequency common mode components in the output phase voltages.
The correctness of the output component of the indirect matrix converter calculated by the method is verified through experiments and simulation, meanwhile, the influence rule of the zero vector action time on the common-mode component and the harmonic component is analyzed, the correctness of the rule is verified, and the conclusion can provide theoretical basis and theoretical basis for the modulation strategy for improving the output performance of the indirect matrix converter.
It should be noted that the above-mentioned embodiments enable a person skilled in the art to more fully understand the invention, without restricting it in any way. Therefore, although the present invention has been described in detail with reference to the drawings and examples, it will be understood by those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention.
Claims (7)
1. A method for calculating output components of an indirect matrix converter of a wind power generation system comprises the following steps:
s1: setting three-phase output symmetry with input power factor of 1, in each sector of the rectifier stage, referring to the input current vector I ref From two adjacent effective current vectors I δ And I γ Synthesizing, respectively calculating duty ratio d of two effective current vectors δ 、d γ ；
S2: in each sector of the inverter stage, the output voltage vector V is referenced according to the vector synthesis principle ref From adjacent effective vectors V α And V β And zero vector V 0 And V 7 Synthesizing, respectively calculating two effective vector duty ratios d α ,d β Duty ratio d corresponding to zero vector 07 ；
S3: the effective vector of the rectifier stage is matched with the vector of the inverter stage to generate different output voltages, and the jump time m of different output voltage amplitudes is determined according to the duty ratio of the vector x1 、m x2 、m x3 X = A, B, C; the output voltage amplitude jump time of half carrier period is
m A1 ＝d γ d NA π；m A2 ＝d γ π；m A3 ＝(1-d δ d NA )π
D is NA To output the duty cycle of the A-phase down tube, the duty cycle of the A-phase down tube d NA As shown in the following table
Wherein k is in For the indirect matrix converter, the sector number k of the sector in which the current vector is present is input out For outputting the sector number, i, in which the reference voltage vector is located k Is zero vector duty ratio coefficient i k ＝d min_0 /d 07 ；
S4: taking into account the input frequency f in Output frequency f out And carrier frequency f c Independent of each other, the amplitude of the output voltage is jumped at the time m A1 ,m A2 ,m A3 Bring-in triple Fourier integral expression pair F k,p,q Solving to obtain output components of each harmonic wave under different frequencies; h is com_L_n Is a low frequency common mode component, h com_H_n For high frequency common mode components, h har_n As harmonic components
In S4, the triple Fourier coefficient F of the output voltage of the indirect matrix converter under the space vector modulation k,p,q Is composed of
When k =0, jumping the amplitude of the output voltage at the moment m A1 ,m A2 ,m A3 Carry over into triple Fourier integral expression pair F k,p,q Solving for the Fourier coefficient of the output voltage of
In the formula, z 1 And z 2 Is an integer; m is voltage transmission ratio, m = V out /V in (ii) a f (p) is a function related to p, and when p is 3,9,15,21,27 and 33 respectively, f (p) is equal to 1,0.75,0.69,0.67,0.65,0.63 respectively;
when k is not equal to 0, jumping the amplitude of the output voltage at a moment m A1 ,m A2 ,m A3 Bring-in triple Fourier integral expression pair F k,p,q The solution is carried out to obtain
Where n represents the frequency of each component of the output voltage, and n = | pf out ±qf in ±kf c |；F com_n (m,i k ) Is equal to m and i k Fourier coefficient of the relevant output high frequency common mode voltage component, F har_n (m,i k ) Is equal to m and i k The fourier coefficients of the correlated output high-frequency harmonic components.
2. A method of calculating the output components of an indirect matrix converter of a wind power system according to claim 1, wherein: duty ratio d of two effective current vectors of rectifier stage δ 、d γ Respectively as follows:
at each inversion stage sector k out In, reference to output voltage vector V ref From two adjacent effective vectors V α And V β And zero vector V 0 And V 7 And synthesizing, wherein the duty ratios of the two effective vectors and the zero vector are as follows:
according to inverse-stage modulation, reference output voltage vector V ref Can be expressed as:
V ref ＝d α V α +d β V β +d 0 V 0 +d 7 V 7
in the formula, k in Inputting the sector number of the sector where the current vector is located for the indirect matrix converter; v in Is the magnitude of the input phase voltage; input phase theta in ＝2πf in t，f in Is the input frequency; k is a radical of out The sector number where the output reference voltage vector is located; d α 、d β 、d 0 And d 7 Representing the effective vector V of the voltage of the inverter stage α And V β And zero vector V 0 And V 7 Duty cycle of (d), V ref Output phase with reference to magnitude of output voltage vector
f out In order to output the frequency of the radio frequency,
for the initial phase of the output voltage, 0 is assumed.
3. A method of calculating the output components of an indirect matrix converter of a wind power system according to claim 1, wherein: in S2, a zero vector duty ratio coefficient i is defined k Is i k ＝d min_0 /d 07 ，i k The value of (A) determines the action time of two voltage zero vectors; when i is k When =0.5, small zero vector V min_0 And a large zero vector V max_0 The action time is equal; when i is k When the phase is not less than 1, the action time of the large zero vector is 0, and the inverter stage only selects the small zero vector for modulation; when i is k When the phase is not less than 0, the action time of the small zero vector is 0, and the inverter stage only selects the large zero vector for modulation;
wherein d is min_0 Is a small zero vector V min_0 Corresponding duty cycle, d max_0 Is a large zero vector V max_0 The corresponding duty cycle.
4. A method of calculating the output components of an indirect matrix converter of a wind power system according to claim 1 or 3, characterized by: the S2 further comprises:
s21: let k in Inputting the sector number of the sector where the current vector is located for the indirect matrix converter, wherein in different rectification sectors, the virtual direct current side voltage is not a constant value, and two different zero voltage vectors V 0 、V 7 Generated common mode amplitudeThe values are different in size;
s22: when k is in V is 1,3,5 7 Corresponding common mode voltage amplitude greater than V 0 A corresponding common mode voltage amplitude; when k is in V is 2,4,6 0 Corresponding common mode voltage amplitude greater than V 7 A corresponding common mode voltage amplitude;
s23: redefining two voltage zero vectors of an inverter stage as a small zero vector V min_0 And a large zero vector V max_0 ：
S24: defining a zero vector duty cycle coefficient i k To assign zero vector action time, i k Representing small zero vectors V min_0 Ratio of the sum of two zero voltage vectors:
s25: the duty ratio of a small zero vector in the two zero voltage vectors is d min_0 The duty cycle of the large zero vector is d max_0 Wherein
5. A method of calculating the output components of an indirect matrix converter of a wind power system according to claim 1, wherein: matrix converter outputting A-phase voltage u Ag Is expressed as
Triple Fourier coefficient F of output voltage k,p,q
Wherein the carrier phase θ c ＝2πf c t, input phase θ in ＝2πf in t, output phase
k, p, q are carrier frequencies f c Input frequency f in Output frequency f out Coefficient of (A) k,p,q And B k,p,q Respectively the real part and the imaginary part of the triple Fourier coefficient; j denotes an imaginary unit, j 2 ＝-1；
Frequency of kf c ±pf in ±qf out Has harmonic component and common mode component of amplitudes
6. The method of claim 5 for calculating the output components of an indirect matrix converter of a wind power system, wherein: the space vector modulated carrier is a triangular wave, the carrier function c (theta) c ) Is composed of
7. A method of calculating the output components of an indirect matrix converter of a wind power system according to claim 1, wherein: fourier coefficient F of output voltage of rectifying stage in one complete modulation period k,p,q Is composed of
D kin A computational expression representing the output voltage over one carrier period:
wherein u is A1 ，u A2 And u A3 Are respectively as
u A1_1 ，u A2_1 And u A3_1 Are respectively as
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