CN114640260A - An Algebraic Modulation Method of Three-phase Current-Mode Converter - Google Patents

Abstract

An algebraic modulation method of a three-phase current-mode converter is to transform the assignment problem of the duty cycle into a solution problem of an inhomogeneous linear equation system. The specific steps of the method are as follows: first, according to the mathematical model of the system, construct the inhomogeneous linear equation system of the duty cycle, and obtain the general solution of the duty cycle matrix with the help of linear algebra correlation theory; secondly, according to the physical constraints of the duty cycle , obtain the feasible solution range of the free variables by means of geometric methods; then, select a point in the feasible solution region as the value of the free variables to determine the final duty cycle matrix; finally, according to the specific performance requirements (low loss, low common mode voltage, Low DC current ripple, etc.) reasonably arrange the switching action sequence to obtain the driving pulse of each switch. The modulation method avoids trigonometric function calculation, saves system operation cost, and has the characteristics of easy implementation, high flexibility and strong versatility.

Description

An Algebraic Modulation Method of Three-phase Current-Mode Converter

technical field

The invention belongs to the technical field of AC power conversion devices, and relates to an algebraic modulation method of a three-phase current-mode converter.

Background technique

The inherent short-circuit protection, adjustable power factor, and ease of regeneration of current-mode converters also make them attractive in industrial applications such as medium-voltage drives, distributed generation systems, and high-voltage direct current (HVDC) systems. Especially for the application of distributed power generation system, the current-mode converter only needs one conversion to convert the DC voltage of the distributed power generation system (such as solar energy and fuel cells) to the grid-connected AC voltage. Therefore, the excellent characteristics of the current source type converter make it attract more and more attention.

The modulation strategy directly affects the performance of the current-mode converter. The current mainstream modulation strategies in three-phase current-mode converters are space vector modulation (SVM) and carrier modulation (CBM). Each vector in the space vector modulation has a clear physical meaning, so it is very flexible in terms of performance optimization. By selecting the effective vector and zero vector reasonably, and arranging the switching sequence reasonably, the common mode voltage and DC current ripple can be realized. and optimization of system efficiency. However, since space vector modulation needs to calculate trigonometric functions, its computational burden is larger than that of carrier modulation, so the duty cycle calculation in carrier modulation is simpler.

There are many carrier modulation methods for three-phase current source converters, such as trapezoidal wave PWM modulation (TPWM), two-three logic SPWM modulation (BTL-SPWM), six-step direct modulation (SS-DPWM), direct duty cycle PWM modulation (DDPWM), dual-level carrier modulation (TS-CBM) and direct carrier modulation (DCBM), etc. TPWM has the highest utilization of DC current, but the quality of AC current is poor. BTL-SPWM is derived from the duality of voltage-type converter modulation, but the DC current utilization of this method is less than 0.866, and the reference signal needs to be preprocessed to compensate for the leading phase angle. SS-DPWM and DDPWM can overcome the above problems, but their switching modes cannot be adjusted flexibly. TS-CBM is proposed to improve the flexibility of the switch mode, by adjusting the voltage compensation of the second stage to achieve different performance index requirements. DCBM reduces AC current switching harmonics and reduces common mode voltage by selecting different current references in different sectors. However, compared with space vector modulation, the above carrier modulation scheme is more complicated in performance optimization. Therefore, it is urgent to propose a modulation strategy that can ensure flexible arrangement of switching modes and simple calculation of duty cycle.

SUMMARY OF THE INVENTION

In view of the above problems, the present invention proposes an algebraic modulation method for a three-phase current-mode converter. The purpose of this method is to transform the assignment problem of duty cycle into a solution problem of inhomogeneous linear equations. The specific steps of the method are as follows: first, according to the mathematical model of the system, construct the inhomogeneous linear equation system of the duty cycle, and obtain the general solution of the duty cycle matrix with the help of linear algebra correlation theory; secondly, according to the physical constraints of the duty cycle , obtain the feasible solution range of free variables by means of geometric methods; then, select a point in the feasible solution region as the value of free variables to determine the final duty cycle matrix; finally, according to specific performance requirements (low loss, low common mode voltage, Low DC current ripple, etc.) reasonably arrange the switching action sequence to obtain the driving pulse of each switch. The modulation method avoids trigonometric function calculation, saves system operation cost, and has the characteristics of easy implementation, high flexibility and strong versatility.

The innovation of the present invention is as follows:

1) A new modulation framework, algebraic modulation, is proposed, which is simple and easy to implement;

2) The proposed algebraic modulation method has high flexibility, it inherits the advantages of SVM well, and can flexibly adjust the allocation of effective vectors and zero vectors to achieve optimization of different performance indicators;

3) The proposed algebraic modulation method has strong versatility and can be easily extended to other power electronic converters.

For realizing the above-mentioned purpose, the technical scheme that the present invention takes is:

An algebraic modulation method for a three-phase current-mode converter, comprising the following steps, characterized in that:

S1, transform the assignment problem of duty cycle into a non-homogeneous linear equation system to solve, and use linear algebra theory to find the general solution of the duty cycle matrix;

S2, based on the physical constraints of the duty cycle, determine the feasible solution region of the free variables with the help of geometric methods;

S3, select a point in the feasible solution area as the solution of the free variable, and determine the final duty cycle matrix;

S4, according to specific performance requirements, the performance requirements include low switching loss, low common mode voltage and low DC current ripple, etc., determine the switching sequence, and obtain the driving pulse of the switch.

As a further improvement of the present invention, the general solution of the duty cycle matrix described in S1 contains two free variables, and the specific process is as follows:

According to the principle of ampere-second balance:

where d _m , m=1,2,...,6 is the duty cycle of a current-mode converter switch S _i , i _dc is the DC side current, i _i , i=a, b, c are the input

Current; since the input side of the three-phase current source converter cannot be short-circuited and the DC side cannot be open-circuited, there are:

Combining equations (1) and (2), the following inhomogeneous linear equation is obtained:

I_m为期望输入电流峰值，ω_i为输入电压角频率，

为输入电压和输入电流的相位角；Among them, the three-phase expected input current is

_Im is the expected peak value of the input current, ω _i is the angular frequency of the input voltage,

is the phase angle of input voltage and input current;

According to formula (3), the equation has 4 unknown variables, the rank of matrix A is 2, and the free variable of this equation is 2 according to the correlation theory of linear algebra, so the general solution is expressed as:

x=λ ₁ h ₁ +λ ₂ h ₂ +p (4)

Among them, λ ₁ and λ ₂ are free variables; h ₁ , h ₂ are four-dimensional column vectors, which are the general solutions of the homogeneous system of equations Ax=0; the four-dimensional column vector p is the special solution of the inhomogeneous system of equations Ax=b, take h ₁ =[1100] ^T , h ₂ =[0011] ^T , p=[i _a ^* /i _dc 0i _b ^* /i _dc 0] ^T ;

Therefore, by combining (2) to (4), the general solution of the duty cycle matrix D is:

According to the above analysis, when the current-mode converter is extended to N, N≥3 phases, the general solution of D is correspondingly extended as:

As a further improvement of the present invention, the determination of the free variable feasible solution region of the general solution of the duty cycle matrix described in S2 is as follows:

The physically achievable duty cycle must satisfy the following constraints:

0≤d _m ≤1,(m=1,2,3,4,5,6) (7)

Therefore, by substituting equation (5) into inequality (7), the following constraints on free variables can be obtained:

的l₃

交点，点B是直线l₁

的直线l₆

交点，点C是l₁

的l₃

交点。It is worth noting that the positions of the six boundary values of the inequality group are related to the polarity of the expected current. Taking λ ₁ as the abscissa and λ ₂ as the ordinate, it can be derived from the above formula. No matter how the current relationship changes, the free variable ( The feasible solution range of λ ₁ , λ ₂ ) is all within a triangle, and the position of the vertex changes with the change of boundary conditions, the range of free variables is limited to the interior and boundary of triangle ABC, point A is l ₂

l ₃

The point of intersection, point B is the straight line l ₁

straight line l ₆

intersection, point C is l ₁

l ₃

intersection.

As a further improvement of the present invention, the determination of the final duty cycle matrix described in S3 depends on the selection of free variables, specifically as follows:

The free variable feasible solution region is the interior and boundary of the triangle ABC, and any point in it can be used as the value of the free variable.

The coordinates of the three points A, B, and C are expressed as:

Observing equations (5) and (9), when the three vertices of the triangle are selected, there are always two switches in the off state. Therefore, we can choose the vertex of the triangle ABC as the solution of the free variable to reduce the switching loss of the current-mode converter.

As a further improvement of the present invention, the switching action sequence described in S4 is flexible and variable, different switching sequences correspond to different performances, and corresponding switching sequences are selected according to actual performance requirements such as common mode voltage, DC current ripple, etc. details as follows:

Without loss of generality, it is divided into 12 equal parts according to the magnitude relationship of the three-phase input voltage or input current, namely sectors I ~ XII, assuming that the expected input current satisfies i _a ^* >0>i _b ^* > _ic ^* , Sector I, when three vertices are chosen as the solution for the free variables, the duty cycle matrix is expressed as:

开关换流次序为a-b-c-b-a；当选择顶点B时，对应零矢量为

开关换流次序为b-a-c-a-b；当选择顶点C时，对应零矢量为

开关换流次序为c-b-a-b-c。不同的顶点对应着不同的零矢量选择，其余各扇区均可按照相同的规则进行操作，一个工频周期内可以一直选择一个顶点，也可三个顶点之间进行轮换；Taking reducing switching loss as an example, a bilaterally symmetrical switching mode is adopted, and the zero vector is arranged at the beginning and end of the modulation period. When vertex A is selected, the corresponding zero vector is

The switching commutation sequence is abcba; when vertex B is selected, the corresponding zero vector is

The switching commutation order is bacab; when vertex C is selected, the corresponding zero vector is

The switching commutation sequence is cbabc. Different vertices correspond to different zero vector selections, and the rest of the sectors can be operated according to the same rules. One vertex can always be selected in one power frequency cycle, or it can be rotated among the three vertices;

Taking reducing the common-mode voltage as an example, it is necessary to select a group of switches corresponding to the phase with the smallest absolute value of the input voltage to be turned on as the zero vector in each modulation cycle. Therefore, the corresponding zero vector is selected according to the input voltage sector to determine Corresponding free variable value and switch sequence arrangement;

The specific options are as follows:

当输入电压满足u_cb>u_ca>u_cc或者u_cc>u_ca>u_cb时，即在扇区III,IV,IX,X时，选择顶点A作为自由变量的解，开关序列安排为a-b-c-b-a，对应零矢量为

当输入电压满足u_cb>u_cc>u_ca或者u_ca>u_cc>u_cb时，即在扇区V,VI,XI,XII时，选择顶C作为自由变量的解，开关序列安排为c-b-a-b-c，对应零矢量为

When the input voltage satisfies u _ca >u _cb >u _cc or u _cc >u _cb >u _ca , that is, in sectors I, II VII, VIII, vertex B is selected as the solution of the free variable, and the switching sequence is arranged as bacab, The corresponding zero vector is

When the input voltage satisfies u _cb >u _ca >u _cc or u _cc >u _ca >u _cb , that is, in sectors III, IV, IX, X, vertex A is selected as the solution of the free variable, and the switching sequence is arranged as abcba , the corresponding zero vector is

When the input voltage satisfies u _cb >u _cc >u _ca or u _ca >u _cc >u _cb , that is, in sectors V, VI, XI, XII, select IM C as the solution of the free variable, and the switching sequence is arranged as cbabc , the corresponding zero vector is

The invention proposes an algebraic modulation method for a three-phase current-mode converter, which transforms the assignment problem of the duty cycle into a solution problem of an inhomogeneous linear equation system. The method is simple and easy to implement, converts complex modulation problems into mathematical problems, and reduces the modulation complexity; the method is highly flexible, and can obtain reduced power by designing free variables in the general solution of inhomogeneous linear equations and arranging switching sequences Optimized modulation scheme for losses, common-mode voltage, and DC ripple; the method is versatile and can be extended to other power electronic converters.

Description of drawings

Fig. 1 is a working flow chart of an embodiment of the present invention;

Fig. 2 topological structure diagram of bidirectional three-phase current source converter of the present invention;

Fig. 3 control system DSP control block diagram of the embodiment of the present invention;

4 is a schematic diagram of a feasible solution area according to an embodiment of the present invention;

FIG. 5 is an input voltage and input current sector division diagram according to an embodiment of the present invention;

6 is a schematic diagram of an algebraic modulation method for reducing power loss according to an embodiment of the present invention;

7 is a flowchart of an algebraic modulation method for reducing common-mode voltage according to an embodiment of the present invention;

FIG. 8 is an experimental waveform diagram of an algebraic modulation method for reducing common mode voltage according to an embodiment of the present invention.

Detailed ways

The present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments:

The invention provides an algebraic modulation method for a three-phase current-mode converter, and proposes a new type of algebraic modulation framework, which can realize the optimization of performance indicators through the selection of free variables and the arrangement of switching sequences, and solves the problem of complex optimization of the existing carrier modulation performance. , space vector modulation computationally complex problems.

Fig. 1 is a working flow chart of an algebraic modulation method of a three-phase current-mode converter of the present invention, and Fig. 2 is a topology structure of a bidirectional three-phase current-mode converter of the present invention, the details are as follows, including an input AC voltage source 1, an input inductor 2, Input capacitor 3, switch network 4, DC side inductor 5, DC voltage source 6, load resistor 7; input AC voltage source 1 and input inductor 2 are connected in series and connected to switch network 4 after input capacitor 3, and the DC side of switch network 4 After the DC side inductor 5 is connected, the load DC voltage source 6 or the resistor 7 is connected. The switch network 4 is composed of two bidirectional switches, and the bidirectional switches are constructed as two IGBT emitters connected in series.

3 is a control block diagram of the system. The main circuit in the figure includes the bidirectional three-phase current source converter topology structure of the implementation object of the present invention; the control circuit includes a sampling conditioning circuit 8 , a controller 9 and a driving circuit 10 . The sampling circuit on the right side of the sampling circuit 8 is responsible for sampling and conditioning the inductor current on the DC side, and the sampling circuit on the left side of the sampling circuit 8 is responsible for sampling and conditioning the capacitor voltage on the AC side. The controller 9 is responsible for important tasks such as control and modulation, and transmits each PWM switch signal to the driving circuit 10, so as to achieve the purpose of controlling each switch.

Figure 4 is the sector division diagram of input voltage and input current. According to the magnitude relationship of three-phase input voltage or three-phase input current, the voltage or current of one power frequency cycle is divided into 12 equal parts, and named as I, II, III...XII.

的l₃

交点，点B是直线l₁

的直线l₆

交点，点C是l₁

的l₃

交点。Figure 5 is a schematic diagram of the feasible solution area of free variables, the range of free variables is limited to the shaded area, and point A is l ₂

l ₃

The point of intersection, point B is the straight line l ₁

straight line l ₆

intersection, point C is l ₁

l ₃

intersection.

图6(b)图为选用顶点B时的开关序列，采用b-a-c-a-b或b-c-a-c-b的换流顺序，对应的零矢量为

图6(c)图为当选用顶点C时的开关序列，采用c-b-a-b-c或c-a-b-a-c的换流顺序，对应的零矢量为

选择不同的顶点，分别对应着三种不同的空间矢量安排顺序，其他扇区也可以按照上述开关序列来排列。一般地，在调制过程中可以一直选择一个顶点，也可以三个顶点进行轮换。Figure 6 shows the switching PWM signals of the three-phase current-mode converter and the corresponding space vector arrangement under different free variable selections. It can be seen that the selection of three different vertices A, B and C correspond to three different switching sequences respectively, and other sectors can also be arranged according to the above switching sequences. Among them, Figure 6(a) is the switching sequence when vertex A is selected, the commutation sequence of abcba is adopted, and the corresponding zero vector is

Figure 6(b) shows the switching sequence when vertex B is selected. The commutation sequence of bacab or bcacb is used, and the corresponding zero vector is

Figure 6(c) shows the switching sequence when vertex C is selected, and the commutation sequence of cbabc or cabac is used, and the corresponding zero vector is

Selecting different vertices corresponds to three different order of space vector arrangement, and other sectors can also be arranged according to the above switch sequence. Generally, during the modulation process, one vertex can be selected all the time, or three vertices can be rotated.

FIG. 7 is a flowchart of an algebraic modulation method for reducing common mode voltage. First, the expected input current is obtained through the outer loop control, and the input voltage and DC side current are sampled; then, the sector where it is located is determined according to the input voltage value; secondly, the corresponding vertex is selected as the solution of the free variable according to the input voltage sector, and the accounting space ratio matrix; finally, select the appropriate switching sequence according to the corresponding vertex to generate the PWM pulse signal of the switch, see Figure 5 for details. It is not difficult to find that this method only needs to perform simple mathematical calculations, and does not require trigonometric function calculations to obtain the final duty cycle. Therefore, this method reduces the computational burden relative to space vector modulation.

FIG. 8 is an experimental waveform diagram of the algebraic modulation method for reducing the common mode voltage. Among them, the first half of Figure 8(a) is the waveform of the traditional space vector modulation method, and the second half is the waveform of the proposed algebraic modulation method. It is not difficult to find that the peak value of the common mode voltage of the proposed algebraic modulation method is greatly reduced. Figure 8(b) is the experimental waveform of the AC side of the proposed algebraic modulation method to reduce the common-mode voltage. It can be seen that the input current is sinusoidal. Figure 8(c) shows the DC side experimental waveform of the proposed algebraic modulation method for reducing the common mode voltage. It can be seen that the DC side voltage is a constant value and the current is maintained near the reference value of 6A. The above waveforms demonstrate the correctness and effectiveness of the proposed algebraic modulation method.

The above are only preferred embodiments of the present invention, and are not intended to limit the present invention in any other form, and any modifications or equivalent changes made according to the technical essence of the present invention still fall within the scope of protection of the present invention. .

Claims (5)

1. an algebraic modulation method of a three-phase current-type converter, comprising the steps, is characterized in that: S1, transform the assignment of duty cycle into a non-homogeneous linear equation system to solve, and use linear algebra theory to find the general solution of the duty cycle matrix; S2, based on the physical constraints of the duty cycle, determine the feasible solution region of the free variables with the help of geometric methods; S3, select a point in the feasible solution area as the solution of the free variable, and determine the final duty cycle matrix; S4, according to specific performance requirements, the performance requirements include low switching loss, low common mode voltage and low DC current ripple, determine the switching sequence, and obtain the driving pulse of the switch. 2. the algebraic modulation method of a kind of three-phase current mode converter according to claim 1, is characterized in that: The general solution of the duty cycle matrix described in S1 contains two free variables, and the specific process is as follows: According to the principle of ampere-second balance:

Among them, d _m , m=1,2,...,6 is the duty cycle of a current-mode converter switch S _i , i _dc is the DC side current, i _i , i=a, b, c are the input currents; Since the input side of the three-phase current source converter cannot be short-circuited, and the DC side cannot be open-circuited, there are:

Combining equations (1) and (2), the following inhomogeneous linear equation is obtained:

Among them, the three-phase expected input current is

_Im is the expected peak value of the input current, ω _i is the angular frequency of the input voltage,

is the phase angle of input voltage and input current; According to formula (3), the equation has 4 unknown variables, the rank of matrix A is 2, and the free variable of this equation is 2 according to the correlation theory of linear algebra, so the general solution is expressed as: x=λ ₁ h ₁ +λ ₂ h ₂ +p (4) Among them, λ ₁ and λ ₂ are free variables; h ₁ , h ₂ are four-dimensional column vectors, which are the general solutions of the homogeneous system of equations Ax=0; the four-dimensional column vector p is the special solution of the inhomogeneous system of equations Ax=b, take h ₁ =[1 1 0 0] ^T , h ₂ =[0 0 1 1] ^T , p=[i _a ^* /i _dc 0 i _b ^* /i _dc 0] ^T ; Therefore, by combining (2) to (4), the general solution of the duty cycle matrix D is:

According to the above analysis, when the current-mode converter is extended to N, N≥3 phases, the general solution of D is correspondingly extended as:

3. the algebraic modulation method of a kind of three-phase current mode converter according to claim 1, is characterized in that: The determination of the free variable feasible solution region of the general solution of the duty cycle matrix described in S2 is as follows: The physically achievable duty cycle must satisfy the following constraints: 0≤d _m ≤1,(m=1,2,3,4,5,6) (7) Therefore, by substituting equation (5) into inequality (7), the following constraints on free variables can be obtained:

It is worth noting that the positions of the six boundary values of the inequality group are related to the polarity of the expected current. Taking λ ₁ as the abscissa and λ ₂ as the ordinate, it can be derived from the above formula. No matter how the current relationship changes, the free variable ( The feasible solution range of λ ₁ , λ ₂ ) is all within a triangle, and the position of the vertex changes with the change of boundary conditions. The range of free variables is limited to the interior and boundary of triangle ABC, and point A is a straight line.

of

point of intersection, point B is a straight line

straight line

The point of intersection, point C is the straight line l ₁

of

intersection. 4. the algebraic modulation method of a kind of three-phase current source converter according to claim 1, is characterized in that: the determination of the final duty cycle matrix described in S3 depends on the selection of free variables, and is specifically as follows: The free variable feasible solution area is the interior and boundary of the triangle ABC, and any point in it can be used as the value of the free variable; The coordinates of the three points A, B, and C are expressed as:

Observing equations (5) and (9), when the three vertices of the triangle are selected, there are always two switches in the off state. Therefore, the vertices of the triangle ABC are selected as the solution of the free variable. 5. The algebraic modulation method of a three-phase current-mode converter according to claim 1, characterized in that: the switching action sequence described in S4 is flexible and variable, and different switching sequences correspond to different performances, Select the corresponding switching sequence according to the actual performance requirements such as common mode voltage, DC current ripple, etc. The details are as follows: Without loss of generality, it is divided into 12 equal parts according to the magnitude relationship of the three-phase input voltage or input current, namely sectors I ~ XII, assuming that the expected input current satisfies i _a ^* >0>i _b ^* > _ic ^* , Sector I, when three vertices are chosen as the solution for the free variables, the duty cycle matrix is expressed as:

Taking reducing switching loss as an example, a bilaterally symmetrical switching mode is adopted, and the zero vector is arranged at the beginning and end of the modulation period. When vertex A is selected, the corresponding zero vector is

The switching commutation sequence is abcba; when vertex B is selected, the corresponding zero vector is

The switching commutation order is bacab; when vertex C is selected, the corresponding zero vector is

The switching commutation sequence is cbabc; different vertices correspond to different zero vector selections, and the rest of the sectors can be operated according to the same rules. One vertex can always be selected in one power frequency cycle, or it can be performed between three vertices. rotation; Taking reducing the common-mode voltage as an example, it is necessary to select a group of switches corresponding to the phase with the smallest absolute value of the input voltage to be turned on as the zero vector in each modulation cycle. Therefore, the corresponding zero vector is selected according to the input voltage sector to determine Corresponding free variable value and switch sequence arrangement; The specific options are as follows: When the input voltage satisfies u _ca >u _cb >u _cc or u _cc >u _cb >u _ca , that is, in sectors I, II VII, VIII, vertex B is selected as the solution of the free variable, and the switching sequence is arranged as bacab, The corresponding zero vector is

When the input voltage satisfies u _cb >u _ca >u _cc or u _cc >u _ca >u _cb , that is, in sectors III, IV, IX, X, vertex A is selected as the solution of the free variable, and the switching sequence is arranged as abcba , the corresponding zero vector is

When the input voltage satisfies u _cb >u _cc >u _ca or u _ca >u _cc >u _cb , that is, in sectors V, VI, XI, XII, select IM C as the solution of the free variable, and the switching sequence is arranged as cbabc , the corresponding zero vector is

Images