CN104901554B

CN104901554B - Multimode Modulation Strategy of Matrix Converter based on Mathematics structural

Info

Publication number: CN104901554B
Application number: CN201510266720.7A
Authority: CN
Inventors: 粟梅; 朱奇; 孙尧; 但汉兵; 杨建�; 柳张杰; 易梅杰; 彭涛; 韩华; 王春生
Original assignee: Central South University
Current assignee: Central South University
Priority date: 2015-05-22
Filing date: 2015-05-22
Publication date: 2017-10-24
Anticipated expiration: 2035-05-22
Also published as: CN104901554A

Abstract

The invention discloses a kind of multimode Modulation Strategy of Matrix Converter based on Mathematics structural, for three modular matrix converter MMMC I, in order to maximize input voltage utilization rate, amount of bias x is superimposed respectively to each row of low frequency modulations matrix, y, z, according to the physical constraint condition of switch, obtains the span of amount of bias；By choosing, different amount of bias can obtain the modulator approach of different performance；For the multi-module structure MMMC II cascaded by N number of MMMC I, to obtain more output-voltage levels, each MMMC I desired output voltage is equal, and the method that on off state uses cyclic shift.Modulator approach based on Mathematics structural eliminates the calculating to sector in conventional modulation strategy, and algorithm is simple, it is easy to understands and realizes.Moreover, the building method of the modulation strategy has versatility, there is directive function to the proposition of other converters modulation strategies.

Description

Multimode Modulation Strategy of Matrix Converter based on Mathematics structural

Technical field

The invention belongs to mesohigh AC energy converting means technical field, and in particular to the frequency conversion of mesohigh three-phase alternating current is led The Mathematics structural modulator approach of the multimode matrix converter in domain.

Background technology

Mesohigh high power AC motor is the major impetus in current industry, and its energy consumed accounts for motor total energy More than the 70% of consumption, the application of medium-high voltage frequency converter device causes the motor electricity saving rates such as blower fan, pump class to reach 30%- 60%, energy-saving effect is quite obvious.Meanwhile, medium-high voltage frequency converter realizes stepless speed regulation, meets industrial processes to electricity The speed adjusting performance requirement of machine, improves the yield and quality of product.

Multimode matrix converter as it is currently the only be commercially used be suitable for mesohigh application matrix converter, no The energy in bidirectional flow, sinusoidal input and output, the input power factor that only possess matrix converter are controllable, output voltage amplitude phase It is adjustable, without intermediate energy storage link the characteristics of, and its high modularization structure make it possess hardware design easily, scalability By force, the features such as software portability is strong, maintainable high, failure tolerant scheme is easily designed.

Modulator approach for multi-module cascade type matrix converter mainly has：Direct transfer function method, two voltage Method and space vector modulation method etc..Direct transfer function method is directly solved according to system mathematic model by input/output relation Modulation matrix；Two voltage method synthesizes what is needed using the maximum line voltage and time big line voltage of input by calculating Output voltage and the input power factor requirement for meeting setting；Space vector modulation method is by three modular matrix converter subsystems etc. Effect is transformed into virtual rectification stage and inversion level structure, and uses space vector modulating method to rectification stage and inverse cascade respectively.Before Both modulator approaches, according to common transformer structure, its maximum voltage transfer ratio is only capable of reaching 1.5；According to phase shift transformation Device structure, equivalent maximum voltage transfer ratio increases with the increase of cascade module number.Although the latter can expand voltage transfer ratio Greatly to 1.732, but equivalent process is complicated, computationally intensive.

The content of the invention

The technical problems to be solved by the invention are：A kind of general mathematics of multimode matrix converter MMMC-II is provided Modulator approach is constructed, different amount of bias obtains the modulation strategy of different performance by choosing.Modulation methods based on Mathematics structural Method eliminates the calculating to sector in conventional modulation strategy, and algorithm is simple, it is easy to understands and realizes.

The present invention is adopted the following technical scheme that：

A kind of multimode Modulation Strategy of Matrix Converter based on Mathematics structural, the multimode matrix converter MMM-II Including multiwinding transformer, power model unit；The multiwinding transformer is common transformer, each secondary side three-phase windings point Independent current source is not provided for each power model unit, the power model unit includes input filter capacitor and six groups of bidirectional powers Switch, realizes that three-phase-single-phase direct friendship alternation is changed, each power model unit provides amplitude, frequency by cascade system for load The three-phase symmetrical power of rate and phase-adjustable, for three modular matrix converter MMMC-I, is utilized to maximize input voltage Each row of low frequency modulations matrix are superimposed amount of bias x, y, z, according to the constraints of switch, obtain amount of bias by rate respectively Span, chooses the modulator approach that different amount of bias obtain different performance, takes the switching mode of bilateral symmetry；For by The multi-module structure MMMC-II, each MMMC-I of N number of MMMC-I cascades on off state use cyclic shift technique, export Amplitude, frequency, the three-phase symmetric voltage of phase-adjustable.

The solution of MMMC-I low frequency modulations matrix is obtained according to input and output voltage current relationship, and detailed process is such as Under：

(1) row write input/output relation formula

Assuming that the leakage inductance very little of transformer, is approximately considered filter capacitor voltage and voltage on line side is equal, then it is defeated for inputting Go out voltage, after taking away pass averagely, there is following relation：

Wherein, u_AN,u_BN,u_CNPhase voltage, u are exported for MMMC-I_a,u_b,u_cFor net side phase voltage, N_s/N_pFor the change of transformer Than,The dutycycle of each two-way switch is represented, M is low frequency modulations matrix

It can similarly obtain, the relation of input and output electric current is：

Wherein subscript T represents transposition,Respectively net side input current vector and load-side current phasor, i.e.,：

According to input can not short circuit, output end can not open circuit requirement and physics realization limitation, low frequency modulations matrix M Need to meet following constraints：

(2) solution of low frequency modulations matrix

The relation of above-mentioned input and output Current Voltage, can regard the process that experienced virtual rectification and virtual inversion as, because This low frequency modulations matrix M one group of solution can be described as：

Wherein,Respectively virtual rectification stage and virtual inverse cascade modulating vector, expression formula is such as Under：

Wherein, k is the index of modulation, it can be seen from the constraints of modulation matrix, 0≤k≤1, ω_i,ω_oRespectively input Output voltage angular frequency, φ_iFor input power factor angle,To input the initial phase angular difference with output voltage；

By above-mentioned modulation matrix and input and output voltage relation, k and input voltage peak value U can obtain_imAnd output electricity Voltage crest value U_omRelation be：

It is the ratio between MMMC-1 output phase voltages and Circuit Fault on Secondary Transformer phase voltage peak value to define voltage transfer ratio q, then has：

Preferably, the modulation matrix M' of described superposition amount of bias is：

Preferably, the span of amount of bias is：

According to the constraints of modulation matrix, x, y, z restrictive condition is as follows：

X+y+z=0

Wherein,

In order to more intuitively describe the span of amount of bias, above-mentioned restrictive condition is plotted in x, y plane and obtains x, y Feasible value region；

Amount of bias x, y, z is set to have solution, then must be fulfilled for following formula：

Assuming that e_AThe ＞ e of ＞ 0_B＞ e_C, r_a＞ r_bThe ＞ r of ＞ 0_c, then have:

Therefore, the condition that amount of bias x, y, z have solution is：

Due to now | r_a|≤1,|r_b|≤1,|r_c|≤1,Therefore k span needs to meet：

So as to as long as biasing selection meets constraints, you can it is 1.732 to realize maximum voltage transfer ratio.

Preferably, the modulator approach that different amount of bias obtain different performance is chosen, building method the simplest is as follows：

X, y are taken, z is the center of its boundary value, i.e.,：

Simplified processing further to above formula can be obtained：

Preferably, cyclic shift modulator approach is：N number of MMMC-I cascaded topologies MMMC-II, from top to bottom adjacent two The on off state difference staggering time T of three modular matrix converters_s/N.。

Preferably, bilateral symmetry modulating mode is：

By taking A phase modules as an example, the dutycycle in its corresponding modulating matrix M ' is：

Above formula is handled：First, m is found out_A1+x,m_A2+ y and m_A3Maximum absolute value value in+z, it is assumed that m_A1+ x is absolute Value is maximum, and m_A1+ x ＞ 0, order：

If m_A1+ x ＞ 0, then have：

Bilateral symmetry switching mode is：In a switch periods, the order of the size of module output voltage is：Minimum- It is secondary big-maximum-secondary big-minimum, and on T_s/ 2 is symmetrical；Assuming that input voltage is：u_aThe ＞ u of ＞ 0_b＞ u_c, with above-mentioned m_A1+ x ＞ 0 Exemplified by, the action situation of switch is：Upper switchIt is constantly on,Turn off always；In time, switchConducting, output voltage is 0；In time, switch is switched toConducting, output voltage is u_ab；In time, switch is switched toConducting, output voltage is u_ac； In time, switch is back switched toConducting, output voltage is u_ab；Finally, switch is switched toOutput voltage is 0.

Modulator approach of the invention based on Mathematics structural eliminates the calculating in conventional modulation strategy to sector, algorithm letter It is single, it is easy to understand and realize.Moreover, the building method of the modulation strategy has versatility, other converters are adjusted The proposition of system strategy has directive function.

Brief description of the drawings

Fig. 1 is the topological schematic diagrames of multimode matrix converter of embodiment of the present invention MMMC-II.

Fig. 2 is the topological schematic diagrames of the modular matrix converter MMMC-1 of the embodiment of the present invention three.

Fig. 3 is bilateral symmetry switching mode schematic diagram of the embodiment of the present invention.

Fig. 4 is that the embodiment of the present invention is based on cyclic shift technique module output voltage waveforms schematic diagram.

Fig. 5 system construction drawings of the embodiment of the present invention.

Fig. 6 is present example in q=3.0, f_oExperimental waveform during=60HZ.

Fig. 7 is present example in q=5.2, f_oExperimental waveform during=60HZ.

Fig. 8 is present example in q=3.0, f_oExperimental waveform during=30HZ.

Embodiment

The present invention will be done further specifically with reference to accompanying drawing and specific implementation case by taking the building method as an example below It is bright：

As shown in Figure 1 and Figure 2, multimode matrix converter MMMC-II is considered as by N number of three modular matrixs converter MMMC- I cascades are formed.Multimode matrix converter MMM-II includes multiwinding transformer 1, power model unit 2；The Multiple coil becomes Depressor is common transformer (non-phase-shifting transformer), and each secondary side three-phase windings are respectively that each power model unit provides independent electrical Source, the power model unit includes input filter capacitor 3 and six groups of two-way power switch 4, realizes three-phase-single-phase direct friendship Conversion, each power model unit provides the three-phase symmetrical power of amplitude, frequency and phase-adjustable by cascade system for load.

For MMMC-I, in order to maximize input voltage utilization rate, amount of bias is superimposed to each row of low frequency modulations matrix X, y, z, according to the constraints of switch, obtain the span and building method of amount of bias；For MMMC-II, each MMMC-I On off state use cyclic shift technique, output amplitude, frequency, the three-phase symmetric voltage of phase-adjustable.Describe in detail as follows.

Step one：Input voltage, reference input power factor (PF) and the reference output voltage obtained according to detection, calculates low frequency Modulation matrix, i.e.,

Wherein,Expression formula is as follows respectively：

Wherein, k is the index of modulation, it can be seen from the constraints of modulation matrix, 0≤k≤1, ω_i,ω_oRespectively input Output voltage angular frequency, φ_iFor input power factor angle,To input the initial phase angular difference with output voltage.Wherein, k with Input voltage peak value U_imAnd output voltage peak value U_omRelation be：

Due to k≤1, therefore the maximum voltage transfer ratio that above-mentioned modulation matrix is obtained is 1.5.

Step 2, solves the amount of bias of modulation matrix.

In order to maximize input voltage utilization rate, maximum voltage transfer ratio is improved, low frequency modulations matrix M each row are folded respectively Plus amount of bias x, y, a z, obtaining final modulation matrix M' is：

Obviously, bias matrix M₀Addition only change output phase voltage zero-sequence component, without change output line voltage, Load current and input current.

X+y+z=0

Wherein,

According to above-mentioned it is assumed that amount of bias x, y, the condition that z has solution is：

Due to now | r_a|≤1,|r_b|≤1,|r_c|≤1,Therefore k span is extended to：

By above-mentioned analysis, the selection of amount of bias x, y, z in restriction range have countless, choose different inclined The amount of putting can obtain the modulator approach of different performance, and the maximum voltage transfer ratio that MMMC-I can be achieved is 1.732.

Building method：Work as x, y, z takes the center of boundary value, the value that can obtain one group of amount of bias is：

Simplified processing further to above formula can be obtained：

Step 3：The generation of duty cycle of switching.

Element representation in the modulation matrix that above-mentioned different building method is obtained is upper switch and lower duty cycle of switching Only poor, by taking A phase modules as an example, the dutycycle in its corresponding modulating matrix M ' is：

If m_A1+ x ＞ 0, then have：

As shown in figure 3, bilateral symmetry switching mode is：In a switch periods, the size of module output voltage it is suitable Sequence is：It is minimum-secondary big-maximum-secondary big-minimum, and on T_s/ 2 is symmetrical；Assuming that input voltage is：u_aThe ＞ u of ＞ 0_b＞ u_c, the above State m_A1Exemplified by+x ＞ 0, the action situation of switch is：Upper switchIt is constantly on,Turn off always；When In, switchConducting, output voltage is 0；In time, switch is switched toConducting, Output voltage is u_ab；In time, switch is switched toConducting, output voltage is u_ac；In time, switch is back switched toConducting, output voltage is u_ab；Finally, switch is cut Shift toOutput voltage is 0.

For the multi-module structure MMMC-II cascaded by N number of MMMC-I, using cyclic shift technique, it thinks substantially Want for：In N number of MMMC-I cascade systems, the on off state of two adjacent MMMC-I distinguishes staggering time T from top to bottom_s/ N.As N=3, phase voltage waveform schematic diagram such as Fig. 4 institutes are exported using cyclic shift modulation technique module output voltage and system Show.

Illustrated below with a case.

In order to verify the validity of put forward Mathematics structural modulator approach, the experiment of 9 modular matrix converters (N=3) is built flat Platform, the parameter of system is as shown in the table,

Parameter	Value
		Input phase voltage virtual value (V_inRMS)	60V
Input voltage frequency (f_in)	50Hz
		Transformer voltage ratio (N_p/N_s)	380/100

Switching frequency (f_s)	2kHz
		Input filter capacitor (C_f)	66uF
Load resistor value (R)	8.33Ω
		Load inductance value (L_o)	6mH

System uses master ＆ slave control structure, and by a central controller controls, central controller is realized by fiber optic communication To the overall control of 9 unit modules, and the working condition of monitoring unit module and system in real time, as shown in Figure 5.

Central controller is read by host computer and used by gathering the information such as transformer primary side input voltage, load current Family control is required, determines system output reference voltage, input power factor, by DSP be responsible for modules low frequency modulations matrix M and The calculating of amount of bias, FPGA realizes distribution, completion and the communication of unit module of each module dutycycle etc., unit module according to The break-make of six two-way switch of Duty ratio control arrived.

Fig. 6, Fig. 7 are respectively that building method is q=3.0 and q=5.2 in voltage transfer ratio, and output frequency is f_o= 60Hz experimental waveform figure, is input voltage, input current, output line voltage, output current wave respectively in (a), is divided in (b) Phase voltage, output line voltage and output current wave Wei not exported, it is known that output line voltage is constituted and approached by multiple level Sine, input current and output current are sine, have reached maximum voltage transfer ratio, and voltage transmission is higher, output line electricity The level number of pressure is more, closer to sine.

Fig. 8 is that building method is q=3.0 in voltage transfer ratio, and output frequency is f_oExperimental waveform under=30Hz, from upper To it is lower be respectively input voltage, input current, output line voltage, output current wave, it is seen that in this case input current and Output current is sine, and shows that multimode matrix converter can realize the output less than incoming frequency.

Claims

1. a kind of multimode Modulation Strategy of Matrix Converter based on Mathematics structural, the multimode matrix converter MMM-II bags Include multiwinding transformer, power model unit；The multiwinding transformer is common transformer, each secondary side three-phase windings difference Independent current source is provided for each power model unit, the power model unit includes input filter capacitor and six groups of bidirectional powers are opened Close, realize that three-phase-single-phase direct friendship alternation is changed, each power model unit provides amplitude, frequency by cascade system for load And the three-phase symmetrical power of phase-adjustable, it is characterised in that：For three modular matrix converter MMMC-I, in order to maximize input Each row of low frequency modulations matrix are superimposed amount of bias x, y, z by voltage utilization respectively, according to the physical constraint condition of switch, The span of amount of bias is obtained, the modulator approach that different amount of bias obtain different performance is chosen, is modulated using bilateral symmetry Pattern；Moved for the on off state by N number of MMMC-I multi-module structure MMMC-II, each MMMC-I cascaded using circulation Position modulation, output amplitude, frequency, the three-phase symmetric voltage of phase-adjustable；Described MMMC-I is by three power model unit groups Into realizing the AC/AC (alternating current) variable-frequency of three-phase-three-phase；The solution of described MMMC-I low frequency modulations matrix is according to input and output voltage electricity What flow relation was obtained, detailed process is as follows：

(1) row write input/output relation formula

Assuming that the leakage inductance very little of transformer, is approximately considered filter capacitor voltage and voltage on line side is equal, then for input and output electricity Pressure, after taking away pass averagely, there is following relation：

<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>A</mi> <mi>N</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>B</mi> <mi>N</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>C</mi> <mi>N</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfrac> <msub> <mi>N</mi> <mi>s</mi> </msub> <msub> <mi>N</mi> <mi>p</mi> </msub> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>1</mn> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>4</mn> </mrow> <mi>k</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>2</mn> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>5</mn> </mrow> <mi>k</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>3</mn> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>6</mn> </mrow> <mi>k</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>B</mi> <mn>1</mn> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>d</mi> <mrow> <mi>B</mi> <mn>4</mn> </mrow> <mi>k</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>B</mi> <mn>2</mn> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>d</mi> <mrow> <mi>B</mi> <mn>5</mn> </mrow> <mi>k</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>B</mi> <mn>3</mn> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>d</mi> <mrow> <mi>B</mi> <mn>6</mn> </mrow> <mi>k</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>C</mi> <mn>1</mn> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>d</mi> <mrow> <mi>C</mi> <mn>4</mn> </mrow> <mi>k</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>C</mi> <mn>2</mn> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>d</mi> <mrow> <mi>C</mi> <mn>5</mn> </mrow> <mi>k</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>C</mi> <mn>3</mn> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>d</mi> <mrow> <mi>C</mi> <mn>6</mn> </mrow> <mi>k</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>&CenterDot;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>u</mi> <mi>a</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mi>b</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mi>c</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfrac> <msub> <mi>N</mi> <mi>s</mi> </msub> <msub> <mi>N</mi> <mi>p</mi> </msub> </mfrac> <mo>&CenterDot;</mo> <mi>M</mi> <mo>&CenterDot;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>u</mi> <mi>a</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mi>b</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mi>c</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>

Wherein, u_AN,u_BN,u_CNPhase voltage, u are exported for MMMC-I_a,u_b,u_cFor net side phase voltage, N_s/N_pFor the no-load voltage ratio of transformer,I=A, B, C；J=1,2 ... 6；K=1,2 ... N represent the dutycycle of each two-way switch, and M is low frequency modulations matrix

Similarly, the relation of input and output electric current is：

<mrow> <msub> <mover> <mi>i</mi> <mo>&RightArrow;</mo> </mover> <mi>s</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>N</mi> <mi>s</mi> </msub> <msub> <mi>N</mi> <mi>p</mi> </msub> </mfrac> <msup> <mi>M</mi> <mi>T</mi> </msup> <msub> <mover> <mi>i</mi> <mo>&RightArrow;</mo> </mover> <mi>L</mi> </msub> </mrow>

According to input can not short circuit, output end can not open circuit requirement and physics realization limitation, low frequency modulations matrix M need Meet following constraints：

(2) solution of low frequency modulations matrix

The relation of above-mentioned input and output Current Voltage, regards the process that experienced virtual rectification and virtual inversion as, therefore low frequency is adjusted Matrix M processed one group of solution is described as：

Wherein, M_rec(ω_i,φ_i),Respectively virtual rectification stage and virtual inverse cascade modulating vector, expression formula is such as Under：

<mrow> <msub> <mi>M</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>c</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&phi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>r</mi> <mi>a</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>r</mi> <mi>b</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>r</mi> <mi>c</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>cos</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mi>t</mi> <mo>-</mo> <msub> <mi>&phi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>cos</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mi>t</mi> <mo>-</mo> <msub> <mi>&phi;</mi> <mi>i</mi> </msub> <mo>-</mo> <mn>2</mn> <mi>&pi;</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>cos</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mi>t</mi> <mo>-</mo> <msub> <mi>&phi;</mi> <mi>i</mi> </msub> <mo>+</mo> <mn>2</mn> <mi>&pi;</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

Wherein, k is the index of modulation, it can be seen from the constraints of modulation matrix, 0≤k≤1, ω_i,ω_oRespectively input and output Voltage angular frequency, φ_iFor input power factor angle, it is operated under unity power factor, i.e. φ_i=0,To input and exporting electricity The initial phase angular difference of pressure；

By above-mentioned modulation matrix and input and output voltage relation, k and input voltage peak value U are obtained_imAnd output voltage peak value U_omRelation be：

2. the multimode Modulation Strategy of Matrix Converter according to claim 1 based on Mathematics structural, it is characterised in that institute The modulation matrix M' for the superposition amount of bias stated is：

3. the multimode Modulation Strategy of Matrix Converter according to claim 2 based on Mathematics structural, it is characterised in that institute The span for the amount of bias stated is：

X+y+z=0

Wherein,

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>m</mi> <mi>i</mi> <msub> <mi>n</mi> <mi>x</mi> </msub> <mo>&le;</mo> <mn>1</mn> <mo>-</mo> <mi>m</mi> <mi>a</mi> <msub> <mi>x</mi> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>min</mi> <mi>y</mi> </msub> <mo>&le;</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>max</mi> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>min</mi> <mi>z</mi> </msub> <mo>&le;</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>min</mi> <mi>z</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>min</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>min</mi> <mi>y</mi> </msub> <mo>&le;</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>min</mi> <mi>z</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>max</mi> <mi>x</mi> </msub> <mo>+</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>max</mi> <mi>y</mi> </msub> <mo>&GreaterEqual;</mo> <msub> <mi>max</mi> <mi>z</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced>

Therefore, the condition that amount of bias x, y, z have solution is：

Due to now | r_a|≤1,|r_b|≤1,|r_c|≤1,Therefore k span needs to meet：

So as to which as long as biasing x, y, z meets constraints, that is, realizes maximum voltage transfer ratio 1.732.

4. the multimode Modulation Strategy of Matrix Converter according to claim 3 based on Mathematics structural, it is characterised in that institute That states chooses the modulator approach that different amount of bias obtain different performance, wherein, the easiest building method is as follows：

X, y, z take the 1/2 of its boundary value sum respectively, i.e.,：

Obvious such a obtaining value method meets x, and y, z restrictive condition is handled the further simplification of above formula：

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mo>=</mo> <mo>-</mo> <mn>0.5</mn> <mi>k</mi> <mo>&CenterDot;</mo> <msub> <mi>r</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mo>(</mo> <mrow> <msub> <mi>e</mi> <mi>A</mi> </msub> <mo>,</mo> <msub> <mi>e</mi> <mi>B</mi> </msub> <mo>,</mo> <msub> <mi>e</mi> <mi>C</mi> </msub> </mrow> <mo>)</mo> <mo>+</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mo>(</mo> <mrow> <msub> <mi>e</mi> <mi>A</mi> </msub> <mo>,</mo> <msub> <mi>e</mi> <mi>B</mi> </msub> <mo>,</mo> <msub> <mi>e</mi> <mi>C</mi> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> <mo>=</mo> <mo>-</mo> <mn>0.5</mn> <mi>k</mi> <mo>&CenterDot;</mo> <msub> <mi>r</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mo>(</mo> <mrow> <msub> <mi>e</mi> <mi>A</mi> </msub> <mo>,</mo> <msub> <mi>e</mi> <mi>B</mi> </msub> <mo>,</mo> <msub> <mi>e</mi> <mi>C</mi> </msub> </mrow> <mo>)</mo> <mo>+</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mo>(</mo> <mrow> <msub> <mi>e</mi> <mi>A</mi> </msub> <mo>,</mo> <msub> <mi>e</mi> <mi>B</mi> </msub> <mo>,</mo> <msub> <mi>e</mi> <mi>C</mi> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>z</mi> <mo>=</mo> <mo>-</mo> <mn>0.5</mn> <mi>k</mi> <mo>&CenterDot;</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mo>(</mo> <mrow> <msub> <mi>e</mi> <mi>A</mi> </msub> <mo>,</mo> <msub> <mi>e</mi> <mi>B</mi> </msub> <mo>,</mo> <msub> <mi>e</mi> <mi>C</mi> </msub> </mrow> <mo>)</mo> <mo>+</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mo>(</mo> <mrow> <msub> <mi>e</mi> <mi>A</mi> </msub> <mo>,</mo> <msub> <mi>e</mi> <mi>B</mi> </msub> <mo>,</mo> <msub> <mi>e</mi> <mi>C</mi> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow>

5. the multimode Modulation Strategy of Matrix Converter according to claim 4 based on Mathematics structural, it is characterised in that institute The cyclic shift modulator approach stated is：N number of MMMC-I cascades constitute topology MMMC-II, from top to bottom two adjacent three modules The on off state difference staggering time T of matrix converter_s/N.。

6. the multimode Modulation Strategy of Matrix Converter according to claim 5 based on Mathematics structural, it is characterised in that institute The bilateral symmetry modulating mode stated is：

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>1</mn> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>4</mn> </mrow> <mi>k</mi> </msubsup> <mo>=</mo> <msub> <mi>m</mi> <mrow> <mi>A</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>x</mi> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>2</mn> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>5</mn> </mrow> <mi>k</mi> </msubsup> <mo>=</mo> <msub> <mi>m</mi> <mrow> <mi>A</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>3</mn> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>6</mn> </mrow> <mi>k</mi> </msubsup> <mo>=</mo> <msub> <mi>m</mi> <mrow> <mi>A</mi> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mi>z</mi> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>1</mn> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>2</mn> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>3</mn> </mrow> <mi>k</mi> </msubsup> <mo>=</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>4</mn> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>5</mn> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>6</mn> </mrow> <mi>k</mi> </msubsup> <mo>=</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> <mo>&le;</mo> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mi>j</mi> </mrow> <mi>k</mi> </msubsup> <mo>&le;</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>&Element;</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mn>6</mn> <mo>}</mo> </mtd> </mtr> </mtable> </mfenced>

Above formula is handled：First, m is found out_A1+x,m_A2+ y and m_A3Maximum absolute value value in+z, it is assumed that m_A1+ x absolute values are most Greatly, and m_A1+ x ＞ 0, order：

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>1</mn> </mrow> <mi>k</mi> </msubsup> <mo>=</mo> <mn>1</mn> <mo>;</mo> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>4</mn> </mrow> <mi>k</mi> </msubsup> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mrow> <mi>A</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>2</mn> </mrow> <mi>k</mi> </msubsup> <mo>=</mo> <mn>0</mn> <mo>;</mo> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>5</mn> </mrow> <mi>k</mi> </msubsup> <mo>=</mo> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mrow> <mi>A</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi>y</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>3</mn> </mrow> <mi>k</mi> </msubsup> <mo>=</mo> <mn>0</mn> <mo>;</mo> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>A</mi> <mn>6</mn> </mrow> <mi>k</mi> </msubsup> <mo>=</mo> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mrow> <mi>A</mi> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> 3

If m_A1+ x ＞ 0, then have：

In a switch periods, the order of the size of module output voltage is：It is minimum-secondary big-maximum-secondary big-minimum, and close In T_s/ 2 is symmetrical；Assuming that input voltage is：u_aThe ＞ u of ＞ 0_b＞ u_c, with above-mentioned m_A1Exemplified by+x ＞ 0, the action situation of switch is：On SwitchIt is constantly on,Turn off always；In time, switchConducting, output voltage is 0；In time, switch is switched toConducting, output voltage is u_ab； In time, switch is switched toConducting, output voltage is u_ac；In time, switch weight Newly switch toConducting, output voltage is u_ab；Finally, switch is switched toOutput voltage is 0.