CN116633161B - Algebraic modulation method without function of input of expansion matrix converter - Google Patents
Algebraic modulation method without function of input of expansion matrix converter Download PDFInfo
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Classifications
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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
- H02M5/02—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 without intermediate conversion into dc
- H02M5/04—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 without intermediate conversion into dc by static converters
-
- 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
- H02M1/0003—Details of control, feedback or regulation circuits
- H02M1/0012—Control circuits using digital or numerical techniques
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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
- H02M5/02—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 without intermediate conversion into dc
- H02M5/04—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 without intermediate conversion into dc by static converters
- H02M5/22—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 without intermediate conversion into dc by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
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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
- H02M5/02—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 without intermediate conversion into dc
- H02M5/04—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 without intermediate conversion into dc by static converters
- H02M5/22—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 without intermediate conversion into dc by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
- H02M5/275—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 without intermediate conversion into dc by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
- H02M5/293—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 without intermediate conversion into dc by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
- H02M5/2932—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 without intermediate conversion into dc by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage, current or power
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Abstract
An algebraic modulation method for expanding the input nonfunctional of matrix converter is disclosed, which features that the complex modulation problem is converted into a solution problem of mathematical equation, and the reactive power of matrix converter is expanded by reasonably choosing the free variables. The method comprises the following steps: 1. based on the input and output relation of the matrix converter, constructing a non-homogeneous linear equation of the input voltage, the expected output voltage and the modulation matrix, and solving the general solution of the modulation matrix; 2. with the aim of maximizing the input reactive power, designing an analytical expression of the modulation degree of freedom, and providing a specific parameter calculation method; 3. according to the physical constraint of the duty ratio in the modulation matrix, obtaining the feasible solution range of the offset matrix by a geometric method, thereby determining the final modulation matrix; 4. in order to optimize the output current quality and the common mode voltage characteristic, the switching action sequence is reasonably arranged, and the driving pulse signals of all the switching tubes are obtained. The method has the characteristics of easiness in implementation, high flexibility and strong universality, and perfects the modulation theory of the matrix converter.
Description
Technical Field
The invention relates to the technical field of alternating current electric energy conversion devices, in particular to an algebraic modulation method without functional power for input of an expansion matrix converter.
Background
Matrix Converter (MC) is an ac-ac direct power conversion device that can implement any m-phase input to any n-phase output. Among the structures of matrix converters, the three-phase input-three-phase output structure (m=3, n=3) is widely used due to its simple topology and advantages. The three-phase-three-phase matrix converter is formed by connecting 9 bidirectional switches in a matrix form, and can realize connection of any one phase on an input side and any one phase on an output side. Typical topologies for matrix converters are stand-alone matrix converters (Direct Matrix Converter, DMC) and dual stage matrix converters (Indirect Matrix Converter, IMC).
The matrix converter is used as a green frequency converter, and can provide a certain reactive power for the power grid at the input side of the matrix converter while driving the load. However, the reactive power characteristics and control laws of matrix converters are very complex, which are related to factors such as converter topology, modulation strategy, voltage transfer ratio and load properties. For single-stage matrix transformation topology, a learner puts forward a direct modulation strategy based on space vector description and a generalized modulation strategy based on a singular value decoupling technology, so that the input nonfunctional of the matrix transformer can be expanded, but the two schemes are complex in calculation and difficult to understand and realize. Aiming at the two-stage matrix converter, a scholars put forward a mixed modulation strategy based on indirect space vector modulation, and the synthesis process of decoupling output voltage and input reactive current is realized, but the scheme is complex. Therefore, the reactive power expansion scheme of the matrix converter, which is simple and easy to realize, has certain theoretical value and engineering practice significance.
Disclosure of Invention
In order to solve the technical problems, the invention provides an algebraic modulation method for expanding the input nonfunctional of the matrix converter, which converts the complex modulation problem into a mathematical equation solving problem and expands the reactive power capability of the matrix converter by reasonably selecting the free variable. The method comprises the following specific implementation steps: firstly, constructing a non-homogeneous linear equation of an input voltage, an expected output voltage and a modulation matrix based on an input and output relation of a matrix converter, and solving a general solution of the modulation matrix; secondly, with the aim of maximizing the input reactive power, designing an analytical expression of the modulation degree of freedom, and providing a specific parameter calculation method; then, according to the physical constraint of the duty ratio in the modulation matrix, obtaining the feasible solution range of the offset matrix by a geometric method, thereby determining the final modulation matrix; and finally, reasonably arranging a switching action sequence to optimize the quality of output current and the common mode voltage characteristic, and obtaining the driving pulse signals of all the switching tubes. The modulation method has the characteristics of easy implementation, high flexibility and strong universality, and perfects the modulation theory of the matrix converter.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
an algebraic modulation method for extending matrix converter input nonfunctional includes the following steps:
s1, constructing a non-homogeneous linear equation of an input voltage, an expected output voltage and a modulation matrix according to a relational expression of the input voltage and the output voltage of a matrix converter, and solving a modulation matrix general solution by utilizing a linear algebraic correlation theory;
s2, designing analysis expressions of six free variables of the general solution of the modulation matrix with the aim of maximizing the input reactive power of the matrix converter, and explaining a specific parameter calculation method;
s3, obtaining a feasible region of the offset matrix through a geometric method according to physical constraints of the duty ratio in the modulation matrix, and further determining a final modulation matrix;
s4, in order to optimize the output current quality and the common-mode voltage characteristic, the switching sequence and the offset item are selected and adjusted according to different actual performance requirements, and the switching action sequence is reasonably arranged to obtain the driving pulse signals of all switching tubes.
Further, the non-homogeneous linear equation of the input voltage, the desired output voltage and the modulation matrix described in S1 is as follows:
obtaining the relation between input voltage/current and output voltage/current according to the topological structure of the matrix converter:
wherein d ij (i=a, B, C; j=a, B, C) is the duty cycle S of each switch ij ,i j And u j Input current and voltage respectively, according to the input end unable short circuit, the output end unable open circuit, obtain the restriction condition as follows:
d ia +d ib +d ic ＝1 (3)
the simultaneous expression (1) and expression (3) yields the following non-homogeneous linear equation:
in the middle ofFor three-phase desired output voltage, equation (4) is a non-homogeneous equation with 9 unknown variables and rank 3, and the general solution expression is derived from six corresponding homogeneous equation sets (ax=0) based on line agents And the free variable lambda m A special solution of the product of (a) and a non-homogeneous equation (ax=b)The composition, general solution expression is as follows:
the special solution is selected as follows:
dividing the duty cycle into two parts, namely an initial modulation matrix and an offset term, wherein the initial modulation matrix is used for synthesizing the reference voltage, and the offset term is used for ensuring that the final duty cycle can meet the physical constraint:
D＝D′+D 0 (7)
initial modulation matrix general solution D' and offset term D 0 The expression of (2) is as follows:
d 'in the formula' ij For the initial modulation matrix, X, Y, Z are three offset terms.
Further, the analytical expressions of the six free variables of the modulation matrix general solution described in S2 are specifically as follows:
the switching duty ratio should satisfy the composition of the output current, and substituting the duty ratio into equation (2) yields:
wherein p is o Is output power, andin the case of three-wire wiring and three-phase balancing, the zero sequence current is zero, and for facilitating the subsequent analysis, the parameter k is set to 0:
based on the instantaneous power (pq) theory, the input instantaneous active and reactive power of the MC is expressed as:
substituting (10) into (12) to obtain
From (13), it was found that the free variable lambda 1 、λ 2 And lambda (lambda) 3 For adjusting the input reactive power, for facilitating the adjustment of the input reactive power, the following is explained:
according to the above selection, the input reactive power is calculated as:
from (15), it is known that the first part is related to active power and the second part is related to load reactive power, thus, by adjusting k 1 Effectively regulating the input reactive power, the reactive power of a matrix converter employing the proposed algebraic modulation strategy depends on k 1 And k 2 Is a viable range of (2);
thus, the active currentAnd reactive current->The amplitude of (c) is expressed as:
where q is the voltage transmission ratio q=u om /U im ，Is the load power factor angle, U im To input voltage amplitude, I om To output the current amplitude, U om For output voltage amplitude, the matrix converter input current amplitude should meet the following condition:
the optimization objective is to enlarge the reactive power input capacity of the converter, and the parameter k is selected to maximize the reactive power input by the matrix converter 2 The method comprises the following steps:
substituting formula (20) into formula (18), reactive currentThe expression of (2) translates into:
let theObtaining:
when the input reactive current takes the maximum value, the input reactive power reaches the maximum value according to the output impedance angleParameter k 1 And k 2 The values of (2) are as follows:
selecting a suitable parameter k 1 And k 2 Six free variables in the initial modulation matrix are determined, and the input reactive power, the I-type current source load and the output current amplitude I are aimed at I-type and II-type loads om The type II resistive load comprises a resistor R and an inductor L, and the amplitude I of the output current is fixed and independent of the output voltage om As the load changes, the impedance angle of the load changesThen, depending on the load itself, the maximum voltage transmission ratio q of the matrix converter when the matrix converter adopts the extended reactive power modulation strategy described above max =0.866, calculating the maximum reactive power |q of class I load respectively imax | I And class II load maximum reactive power |q imax | II The following are provided:
further, in S3, according to the physical constraint of the duty ratio in the modulation matrix, a feasible solution range of the offset matrix is obtained through a geometric method, and offset terms X, Y and Z are selected in the feasible domain, so as to determine a final modulation matrix, and the specific process is as follows:
the final modulation matrix needs to add an offset term to satisfy physical constraints on the basis of determining the initial modulation matrix, and according to the physical constraints that the duty cycle should satisfy, the following inequality is obtained:
0≤d ij ≤1(i＝A,B,C；j＝a,b,c) (27)
according to the above inequality, the resulting offset needs to satisfy the following inequality:
with X as the horizontal axis and Y as the vertical axis, the six boundary lines of the feasible region of the offset term depend on the initial modulation matrix, and it is noted that the feasible solution of the free variable always falls within triangle ABC regardless of the variation of the desired voltage and the input voltage, and the vertex varies with the boundary line, which is defined as follows:
the triangle vertex A is the boundary line l 1 And l 6 The point of intersection of (B) and the vertex B is the boundary line l 1 And l 3 The point of intersection of (C) and the vertex C is the boundary line l 3 And l 6 The expressions of the offset items X, Y and Z corresponding to the vertexes are as follows:
further, the switching sequence and the offset items in S4 are selected and adjusted according to different actual performance requirements, different offset items X, Y and Z and the switching sequence are selected to generate different modulation effects, the three-phase voltage on the input side is divided into 6 sectors according to the magnitude relation between the three-phase voltage on the input side, namely, sectors I to VI, and different offset items are selected to overlap the initial modulation matrix to synthesize a final modulation matrix.
Further, the actual performance is the power quality and the common mode voltage is reduced, the offset term is taken from the boundary point ABC of the feasible region, so that in the I sector, the input three-phase voltage magnitude relation is u a >u b >u c Selecting the point A as an offset item; and when the voltage is positioned in the II th sector, the input voltage magnitude relation is u b >u a >u c Selecting point C as offset term, in this mode, the maximum and minimum phases of three phases perform switching operation for 2 times in one carrier period, so as to reduce switching loss, and limit common-mode voltage peak value lower thanIn order to reduce harmonic distortion of input and output waveforms of the matrix converter, the switching sequences are arranged according to a bilateral symmetry mode, and finally PWM signals for driving the switches are obtained;
in the sectors I, IV, the three-phase input voltage has a magnitude relation of u a >u b >u c And u c >u b >u a When the three-phase input voltage is in the sectors II and V, the three-phase input voltage has the magnitude relation of u b >u a >u c And u c >u a >u b When the switching operation is performed, the vertex C is selected as an offset item, and the switching operation sequences are b-a-C-a-b and C-a-b-a-C respectively. When in the sectors III, VI, the three-phase input voltage has the magnitude relation of u b >u c >u a And u a >u c >u b When the vertex B is selected as the offset item, the switching sequence is B-c-a-c-B and a-c-B-c-a respectively. Notably, "a-b" refers to the corresponding switch S ia (i=a, B, C) is turned on first, and then turned off S ia Open S ib ；
The generalization is as follows: the three-phase input voltage can be greatly calculated according to the valueDivided into a maximum phase, an intermediate phase and a minimum phase, and denoted by the symbol p max ，p mid And p min To indicate that when the bilateral symmetry mode is adopted, the switching action sequence is p max -p mid -p min -p mid -p max . The algebraic modulation strategy for expanding the reactive power of the matrix converter converts the determination problem of the modulation strategy into the structure of the solution of the non-homogeneous linear equation, reduces the modulation complexity, and realizes the optimization of the input reactive power of the matrix converter by designing the free variable in the general solution of the non-homogeneous linear equation. Finally, to optimize the output current quality and common mode voltage characteristics, the switch action sequence and the offset term are reasonably arranged, and the driving pulse of each switch is obtained. The modulation method has the characteristics of easiness in implementation, high flexibility and strong universality.
Drawings
FIG. 1 is a flowchart of the control algorithm of an embodiment of the present invention;
FIG. 2 is a diagram of the topology of the subject matrix converter of the present invention;
FIG. 3 is a block diagram of a control algorithm of a control system according to an embodiment of the present invention;
FIG. 4 is a diagram of a feasible region of an offset term according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of a symmetrical double-sided switch switching mode according to the present invention;
FIG. 6 is a flow chart of an embodiment of the invention extending the algebraic modulation strategy of the input reactive power;
FIG. 7 is a schematic diagram of the maximum reactive power achievable under different loads for an embodiment of the invention;
FIG. 8 is a waveform diagram of an algebraic modulation strategy simulation experiment for expanding input reactive power according to the embodiment of the invention;
FIG. 9 is a waveform diagram of a simulation experiment of a general algebraic modulation strategy according to an embodiment of the present invention;
FIG. 10 is a waveform diagram of an algebraic modulation strategy simulation experiment of the input reactive power of the expansion matrix converter under the low-voltage transmission ratio working condition in the embodiment of the invention;
fig. 11 is a waveform diagram of algebraic modulation strategy simulation experiment of the input reactive power of the expansion matrix converter when the low-voltage transmission ratio is changed.
Detailed Description
The invention is described in further detail below with reference to the attached drawings and detailed description:
the invention provides an algebraic modulation method without functional input of an expansion matrix converter, which aims at solving the problems of complex optimization of the current carrier modulation performance and high calculation difficulty of space vector modulation, and provides a novel algebraic modulation framework, wherein the optimization of different performances can be realized by adjusting free variables and a switching sequence, and the algebraic modulation framework is simple and easy to realize.
Fig. 1 is a flowchart of an algebraic modulation method of a matrix converter according to the present invention, and fig. 2 is a topology of the matrix converter, specifically, the method includes a grid-side ac voltage source 1, an input filter inductor 2, an input filter capacitor 3, a switching network 4, and an RL load 5. Wherein the switching network 4 is formed by a two-way switch formed by connecting two IGBT emitters in series.
FIG. 3 is a control block diagram of a system in which the main circuit includes an implementation object matrix converter topology of the present invention; the control circuit part is a sampling circuit 6, a controller 7 and a driving circuit 8. The left sampling circuit of the sampling circuit 6 is responsible for sampling and conditioning the input voltage and current at the power grid side, and the right sampling circuit samples the output voltage. The controller 7 is responsible for important operations such as modulation and control, and transmits PWM switching signals to the driving circuit 8, thereby controlling the switching actions.
FIG. 4 is a schematic diagram of a possible domain of the offset term, the range of the offset term being limited to the shaded area, and the boundary point A being l 1 (X＝-min{d' Aa ,d' Ba ,d' Ca }) l 5 (X+Y＝max{d' Ac ,d' Bc ,d' Cc }) intersection point, boundary point B is straight line l 1 (X＝-min{d' Aa ,d' Ba ,d' Ca }) straight line l 3 (Y＝-min{d' Ab ,d' Bb ,d' Cb }) intersection point, boundary point C is l 3 (Y＝-min{d' Ab ,d' Bb ,d' Cb }) l 5 (X+Y＝max{d' Ac ,d' Bc ,d' Cc }) intersection points.
The performance of the power converter of fig. 5 is determined by both duty cycle allocation and switching order. In order to improve the input current quality, a symmetrical bilateral switching mode is used, and a visual example of the symmetrical bilateral switching mode is shown in fig. 5.
Fig. 6 is a flow chart of an algebraic modulation method for extending matrix converter input non-functionality. Sampling the input voltage of the power grid side, obtaining a rotation angle through a phase-locked loop, and judging the sector where the rotation angle is located; secondly, taking the input maximum reactive power as an optimization target to solve a free variable in a general solution of the non-homogeneous equation set; then, corresponding vertexes are selected as offset items according to the input voltage sector, and the duty ratio in the modulation matrix is synthesized; and finally, arranging the action sequence of the switching tubes by adopting a bilateral symmetry switching mode to generate PWM pulse signals of the switches. It is easy to find that the final duty ratio can be obtained by performing simple mathematical calculation, and the calculation complexity is reduced.
Fig. 7 is a schematic diagram of maximum reactive power achievable under different loads for an example extended matrix converter input non-functional algebraic modulation strategy of the present invention. Maximum input reactive power |Q under two types of loads imax I corresponds to different voltage transmission ratios q, load impedance anglesThe three-dimensional perspective view of the (a) extended reactive power modulation strategy of fig. 7 under class I load and the (b) extended reactive power modulation strategy of fig. 7 under class II load are shown.
FIG. 8 is a waveform diagram of an example extended matrix converter of the present invention with input non-functional algebraic modulation strategy simulation experiments. FIG. 8 (a) shows experimental waveforms on the input and output sides of the proposed modulation method, including a-phase grid voltage u sa A-phase grid current i sa Output line voltage u AB Wherein the output current is sinusoidal and the output line voltage is five levels. FIG. 8 (b) is the input active power P of the matrix converter with algebraic modulation of the proposed extended input reactive power i And input reactive power Q i FIG. 8 (c) shows the output common-mode voltage V of the proposed algebraic modulation method cm The modulation strategy can stably outputCommon mode voltage is limited toThe following is given.
FIG. 9 shows a general algebraic modulation method (k 1 ＝k 2 =0), fig. 9 (a) shows experimental waveforms of input and output sides of a general modulation method, output current is sinusoidal, output line voltage is five level, fig. 9 (b) shows input active and reactive power of a general modulation strategy, and input reactive power Q of a matrix converter is not expanded in the case of input reactive power of the matrix converter i Lower.
Fig. 10 (a) is a waveform diagram of an algebraic modulation method simulation experiment for the input nonfunctional of the extended matrix converter proposed at a low voltage transmission ratio q=0.3, and fig. 10 (b) is an active power P input to the matrix converter at a voltage transmission ratio q=0.3 i And reactive power Q i At low voltage transmission ratios, the input reactive power is reduced, but still has some reactive compensation capability.
T in FIG. 11 1 A transition instant for switching to a high voltage transmission ratio (q=0.79) for a low voltage transmission ratio (q=0.3). As the dynamic response of the graph is fast enough and has no large fluctuation in the transition process, the developed strategy has strong dynamic performance.
The above description is only of the preferred embodiment of the present invention, and is not intended to limit the present invention in any other way, but is intended to cover any modifications or equivalent variations according to the technical spirit of the present invention, which fall within the scope of the present invention as defined by the appended claims.
Claims (1)
1. An algebraic modulation method for extending matrix converter input nonfunctional includes the following steps:
s1, constructing a non-homogeneous linear equation of an input voltage, an expected output voltage and a modulation matrix according to a relational expression of the input voltage and the output voltage of a matrix converter, and solving a modulation matrix general solution by utilizing a linear algebraic correlation theory;
the non-homogeneous linear equation of the input voltage, the desired output voltage and the modulation matrix described in S1 is specifically as follows:
obtaining the relation between input voltage/current and output voltage/current according to the topological structure of the matrix converter:
wherein d ij (i=a, B, C; j=a, B, C) is the duty cycle S of each switch ij ,i j And u j Input current and voltage respectively, according to the input end unable short circuit, the output end unable open circuit, obtain the restriction condition as follows:
d ia +d ib +d ic ＝1 (3)
the simultaneous expression (1) and expression (3) yields the following non-homogeneous linear equation:
in the middle ofFor three-phase desired output voltage, equation (4) is a non-homogeneous equation with 9 unknown variables and rank 3, and the general solution expression is derived from six corresponding homogeneous equation sets (ax=0) based on line agents And the free variable lambda m A special solution of the product of (a) and a non-homogeneous equation (ax=b)The composition, general solution expression is as follows:
the special solution is selected as follows:
dividing the duty cycle into two parts, namely an initial modulation matrix and an offset term, wherein the initial modulation matrix is used for synthesizing the reference voltage, and the offset term is used for ensuring that the final duty cycle can meet the physical constraint:
D＝D′+D 0 (7)
initial modulation matrix general solution D' and offset term D 0 The expression of (2) is as follows:
D 0 ＝[X Y Z X Y Z X Y Z] T (9)
d 'in the formula' ij For the initial modulation matrix, X, Y and Z are three offset terms;
s2, designing analysis expressions of six free variables of the general solution of the modulation matrix with the aim of maximizing the input reactive power of the matrix converter, and explaining a specific parameter calculation method;
the analytical expressions of six free variables of the modulation matrix general solution described in S2 are specifically as follows:
the switching duty ratio should satisfy the composition of the output current, and substituting the duty ratio into equation (2) yields:
wherein the method comprises the steps ofp o Is output power, andin the case of three-wire wiring and three-phase balancing, the zero sequence current is zero, and for facilitating the subsequent analysis, the parameter k is set to 0:
based on the instantaneous power (pq) theory, the input instantaneous active and reactive power of the MC is expressed as:
substituting (10) into (12) to obtain
From (13), it was found that the free variable lambda 1 、λ 2 And lambda (lambda) 3 For adjusting the input reactive power, for facilitating the adjustment of the input reactive power, the following is explained:
according to the above equation (14), the input reactive power is calculated as:
from (15), it is known that the first part is related to active power and the second part is related to load reactive power, thus, by adjusting k 1 Matrix converter with effective regulation of input reactive power employing proposed algebraic modulation strategyThe non-functional force depends on k 1 And k 2 Is a viable range of (2);
thus, the active currentAnd reactive current->The amplitude of (c) is expressed as:
where q is the voltage transmission ratio q=u om /U im ，Is the load power factor angle, U im To input voltage amplitude, I om To output the current amplitude, U om For output voltage amplitude, the matrix converter input current amplitude should meet the following condition:
the optimization objective is to enlarge the reactive power input capacity of the converter, and the parameter k is selected to maximize the reactive power input by the matrix converter 2 The method comprises the following steps:
substituting formula (20) into formula (18), reactive currentThe expression of (2) translates into:
let theObtaining:
when the input reactive current takes the maximum value, the input reactive power reaches the maximum value according to the output impedance angleParameter k 1 And k 2 The values of (2) are as follows:
selecting a suitable parameter k 1 And k 2 Six free variables in the initial modulation matrix are determined, and the input reactive power, the I-type current source load and the output current amplitude I are aimed at I-type and II-type loads om The type II resistive load comprises a resistor R and an inductor L, and the amplitude I of the output current is fixed and independent of the output voltage om As the load changes, the impedance angle of the load changesThen, depending on the load itself, the maximum voltage transmission ratio q of the matrix converter when the matrix converter adopts the extended reactive power modulation strategy described above max =0.866, calculating the maximum reactive power |q of class I load respectively imax | I And class II load maximum reactive power |q imax | II The following are provided:
s3, obtaining a feasible region of the offset matrix through a geometric method according to physical constraints of the duty ratio in the modulation matrix, and further determining a final modulation matrix;
s3, according to the physical constraint of the duty ratio in the modulation matrix, obtaining a feasible solution range of the offset matrix by a geometric method, selecting offset items X, Y and Z in the feasible domain, and further determining a final modulation matrix, wherein the specific process is as follows:
the final modulation matrix needs to add an offset term to satisfy physical constraints on the basis of determining the initial modulation matrix, and according to the physical constraints that the duty cycle should satisfy, the following inequality is obtained:
0≤d ij ≤1(i＝A,B,C；j＝a,b,c) (27)
according to the above inequality, the resulting offset needs to satisfy the following inequality:
with X as the horizontal axis and Y as the vertical axis, the six boundary lines of the feasible region of the offset term depend on the initial modulation matrix, and it is noted that the feasible solution of the free variable always falls within triangle ABC regardless of the variation of the desired voltage and the input voltage, and the vertex varies with the boundary line, which is defined as follows:
the triangle vertex A is the boundary line l 1 And l 6 The point of intersection of (B) and the vertex B is the boundary line l 1 And l 3 The point of intersection of (C) and the vertex C is the boundary line l 3 And l 6 The expressions of the offset items X, Y and Z corresponding to the vertexes are as follows:
s4, for optimizing the quality of output current and the common-mode voltage characteristic, selecting a switching sequence and an offset item to adjust according to different actual performance requirements, and reasonably arranging a switching action sequence to obtain driving pulse signals of each switching tube;
s4, selecting a switching sequence and an offset term to adjust according to different actual performance requirements, selecting different offset terms X, Y and Z and the switching sequence to generate different modulation effects, dividing the three-phase voltage on the input side into 6 sectors according to the magnitude relation between the three-phase voltages, namely, sectors I to VI, and selecting different offset terms to superimpose an initial modulation matrix on different sectors to synthesize a final modulation matrix;
the practical performance is the power quality and the common mode voltage reduction, the offset term is taken from the boundary point ABC of the feasible region, so that in the I sector, the input three-phase voltage magnitude relation is u a >u b >u c Selecting the point A as an offset item; and when the voltage is positioned in the II th sector, the input voltage magnitude relation is u b >u a >u c Selecting point C as offset term, in this mode, the maximum and minimum phases of three phases perform switching operation for 2 times in one carrier period, so as to reduce switching loss, and limit common-mode voltage peak value lower thanIn order to reduce harmonic distortion of input and output waveforms of the matrix converter, the switching sequences are arranged according to a bilateral symmetry mode, and finally PWM signals for driving the switches are obtained;
in the sectors I, IV, the three-phase input voltage has a magnitude relation of u a >u b >u c And u c >u b >u a When the three-phase input voltage is in the sectors II and V, the three-phase input voltage has the magnitude relation of u b >u a >u c And u c >u a >u b When in the sectors III, VI, the three-phase input voltage magnitude relation is u b >u c >u a And u a >u c >u b When the vertex B is selected as the offset term, the switching sequences are B-c-a-c-B and a-c-B-c-a, respectively, it is noted that "a-B" refers to the corresponding switch S ia (i=a, B, C) is turned on first, and then turned off S ia Open S ib ；
The generalization is as follows: the three-phase input voltage can be divided into a maximum phase, an intermediate phase and a minimum phase according to the value, and the symbol p is used max ，p mid And p min To indicate that when the bilateral symmetry mode is adopted, the switching action sequence is p max -p mid -p min -p mid -p max 。
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