An Algebraic Modulation Method for Three-Phase Current Source Converter

Abstract

An algebraic modulation method for a three-phase current source converter is to transform the distribution problem of the duty cycle into the problem of solving a non-homogeneous linear equation group. The specific steps of the method are as follows: first, according to the system mathematical model, a non-homogeneous linear equation group of the duty cycle is constructed, and the general solution of the duty cycle matrix is ​​obtained by means of the relevant linear algebra theory; secondly, according to the physical constraints of the duty cycle, the feasible solution range of the free variable is obtained by means of the geometric method; then, a point is selected in the feasible solution area as the value of the free variable 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.), the switch action sequence is reasonably arranged to obtain the driving pulse of each switch. The modulation method avoids trigonometric function calculations, saves system operation costs, and has the characteristics of easy implementation, high flexibility and strong versatility.

Description

Technical Field

[0001] The invention belongs to the technical field of AC power conversion devices and relates to an algebraic modulation method for a three-phase current type converter. Background Art

[0002] Current source converters have inherent short-circuit protection, adjustable power factor, and easy renewable features, which makes them very attractive in industrial applications such as medium voltage drives, distributed generation systems, and high voltage direct current (HVDC) systems. Especially for distributed generation system applications, current source converters only need one conversion to convert the DC voltage of distributed generation systems (such as solar and fuel cells) into grid-connected AC voltage. Therefore, the excellent characteristics of current source converters have attracted more and more attention.

[0003] The modulation strategy will directly affect the performance of the current source converter. At present, the mainstream modulation strategies in three-phase current source converters are space vector modulation (SVM) and carrier modulation (CBM). In space vector modulation, each vector has a clear physical meaning, so it is very flexible in performance optimization. By reasonably selecting the effective vector and the zero vector and arranging the switching sequence, the common mode voltage, DC current ripple and system efficiency can be optimized. However, since space vector modulation requires the calculation of trigonometric functions, its computational burden is greater than that of carrier modulation, so the duty cycle calculation in carrier modulation is simpler.

[0004] 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), two-stage carrier modulation (TS-CBM) and direct carrier modulation (DCBM). TPWM has the highest DC current utilization rate, but the AC current quality is poor. BTL-SPWM is derived from the duality of voltage-source converter modulation, but the DC current utilization rate of this method is less than 0.866, and the reference signal needs to be preprocessed to compensate for the advanced phase angle. SS-DPWM and DDPWM can overcome the above problems, but their switching modes cannot be flexibly adjusted. TS-CBM is proposed to improve the flexibility of the switching mode, and different performance index requirements are achieved by adjusting the voltage compensation of the second stage. DCBM reduces AC current switching harmonics and common-mode voltage by selecting different current references in different sectors. However, compared with space vector modulation, the above carrier modulation schemes are more complicated in terms of 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

[0005] In view of the above problems, the present invention proposes an algebraic modulation method for a three-phase current source converter. The method is to transform the duty cycle distribution problem into the problem of solving a non-homogeneous linear equation group. The specific steps of the method are as follows: first, according to the system mathematical model, a non-homogeneous linear equation group of the duty cycle is constructed, and the general solution of the duty cycle matrix is ​​obtained with the help of linear algebra related theories; secondly, according to the physical constraints of the duty cycle, the feasible solution range of the free variables is obtained with the help of geometric methods; then, a point is selected in the feasible solution area as the value of the free variable 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.), the switch action sequence is reasonably arranged to obtain the driving pulse of each switch. This modulation method avoids trigonometric function calculations, saves system operation costs, and has the characteristics of easy implementation, high flexibility and strong versatility.

[0006] The innovative features of the present invention are as follows:

[0007] 1) A new modulation framework, algebraic modulation, is proposed, which is simple and easy to implement;

[0008] 2) The proposed algebraic modulation method is highly flexible. It inherits the advantages of SVM and can flexibly adjust the allocation of valid vectors and zero vectors to achieve the optimization of different performance indicators.

[0009] 3) The proposed algebraic modulation method is highly versatile and can be easily extended to other power electronic converters.

[0010] To achieve the above object, the technical solution adopted by the present invention is:

[0011] An algebraic modulation method for a three-phase current source converter comprises the following steps, characterized in that:

[0012] S1, transform the duty cycle allocation problem into a non-homogeneous linear equation system and use linear algebra theory to find the general solution of the duty cycle matrix;

[0013] S2, based on the physical constraints of the duty cycle, the feasible solution region of the free variables is determined by geometric methods;

[0014] S3, select a point in the feasible solution region as the solution of the free variable to determine the final duty cycle matrix;

[0015] 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.

[0016] 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:

[0017] According to the ampere-second balance principle:

[0018]

[0019] Among them, d m , m=1,2,…,6 is a current source converter switch S i The duty cycle, i dc is the DC side current, i i , i = a, b, c is 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, we have:

[0020]

[0021] Combining equations (1) and (2), we get the following non-homogeneous linear equation:

[0022]

[0023] Among them, the three-phase expected input current is I m is the expected input current peak value, ω i is the input voltage angular frequency, is the phase angle of input voltage and input current;

[0024] From equation (3), we know that the equation has 4 unknown variables, the rank of matrix A is 2, and from the relevant linear algebra theory, we know that the free variable of this equation is 2, so the general solution is expressed as:

[0025] x=λ1h1+λ2h2+p (4)

[0026] Among them, λ1 and λ2 are free variables; h1 and h2 are four-dimensional column vectors, which are the general solutions of the homogeneous equation system Ax=0; the four-dimensional column vector p is the special solution of the non-homogeneous equation system Ax=b, taking h1=[110 0] T ,h2=[00 1 1] T ,p=[i a * / i dc 0i b * / i dc 0] T ;

[0027] Therefore, combining (2) to (4), the general solution of the duty cycle matrix D is:

[0028]

[0029] According to the above analysis, when the current source converter is expanded to N, N ≥ 3 phases, the general solution of D is expanded accordingly:

[0030]

[0031] As a further improvement of the present invention, the determination of the feasible solution region of the free variables of the general solution of the duty cycle matrix described in S2 is as follows:

[0032] The physically achievable duty cycle must satisfy the following constraints:

[0033] 0≤d m ≤1,(m=1,2,3,4,5,6) (7)

[0034] Therefore, substituting equation (5) into inequality (7), we can obtain the following constraints on free variables:

[0035]

[0036] It is worth noting that the positions of the six boundary values ​​of the inequality group are related to the polarity of the desired current. With λ1 as the horizontal coordinate and λ2 as the vertical coordinate, it can be deduced from the above formula that no matter how the current relationship changes, the feasible solution range of the free variables (λ1, λ2) is 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 l2 l3 The intersection point, point B is the straight line l1 The straight line l6 The intersection point, point C is l1 l3 Intersection.

[0037] 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, which is as follows:

[0038] The free variable feasible solution region is the interior and boundary of triangle ABC, and any point therein can be used as the value of the free variable.

[0039] The coordinates of points A, B, and C are expressed as:

[0040]

[0041] 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 select the vertices of triangle ABC as the solution of free variables to reduce the switching loss of the current source converter.

[0042] 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. The corresponding switching sequence is selected according to actual performance requirements such as common mode voltage, DC current ripple, etc., as follows:

[0043] Without loss of generality, the three-phase input voltage or input current is divided into 12 equal parts, namely sectors I to XII, assuming that the expected input current satisfies i a * >0>i b * >i c * , sector I, when three vertices are selected as the solution of free variables, the duty cycle matrix is ​​expressed as:

[0044]

[0045] Taking the reduction of 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 order is abcba; when vertex B is selected, the corresponding zero vector is The switching order is bacab; when vertex C is selected, the corresponding zero vector is The switching order is cbabc. Different vertices correspond to different zero vector selections, and the remaining sectors can be operated according to the same rules. In one power frequency cycle, one vertex can be selected all the time, or three vertices can be rotated;

[0046] Taking the reduction of common-mode voltage as an example, it is necessary to select a group of switches corresponding to the phase with the minimum absolute value of the input voltage as the zero vector in each modulation cycle. Therefore, the corresponding zero vector is selected according to the input voltage sector, thereby determining the corresponding free variable value and switch sequence arrangement;

[0047] The specific options are as follows:

[0048] When the input voltage satisfies u ca >u cb >u cc Or u cc >u cb >u ca When, that is, in sectors I, II VII, VIII, vertex B is selected as the solution of the free variable, the switching sequence is arranged as bacab, and the corresponding zero vector is When the input voltage satisfies u cb >u ca >u cc Or u cc >u ca >u cb When, that is, in sectors III, IV, IX, and X, vertex A is selected as the solution of the free variable, and the switching sequence is arranged as abcba, and the corresponding zero vector is When the input voltage satisfies u cb >u cc >u ca Or u ca >u cc >u cb When, that is, in sectors V, VI, XI, and XII, the top C is selected as the solution of the free variable, and the switching sequence is arranged as cbabc, and the corresponding zero vector is

[0049] The present invention proposes an algebraic modulation method for a three-phase current source converter, which converts the duty cycle allocation problem into a problem of solving a non-homogeneous linear equation group. The method is simple and easy to implement, and converts a complex modulation problem into a mathematical problem, reducing the complexity of modulation; the method is highly flexible, and can obtain an optimized modulation scheme that reduces power loss, common mode voltage and DC ripple by designing free variables in the general solution of the non-homogeneous linear equation group and arranging the switching sequence; the method is highly versatile and can be extended to other power electronic converters. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 Workflow diagram of an embodiment of the present invention;

[0051] Figure 2 Topological structure diagram of the bidirectional three-phase current source converter of the present invention;

[0052] Figure 3 DSP control block diagram of the control system of the embodiment of the present invention;

[0053] Figure 4 Schematic diagram of feasible solution area of ​​the embodiment of the present invention;

[0054] Figure 5 Input voltage and input current sector division diagram of an embodiment of the present invention;

[0055] Figure 6 A schematic diagram of an algebraic modulation method for reducing power loss according to an embodiment of the present invention;

[0056] Figure 7 A flow chart of an algebraic modulation method for reducing common mode voltage according to an embodiment of the present invention;

[0057] Figure 8 Experimental waveform diagram of the algebraic modulation method for reducing common mode voltage according to an embodiment of the present invention. DETAILED DESCRIPTION

[0058] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0059] The present invention provides an algebraic modulation method for a three-phase current source converter and proposes a novel algebraic modulation framework, which can optimize performance indicators by selecting free variables and arranging switch sequences, thereby solving the problems of complex performance optimization of existing carrier modulation and complex calculation of space vector modulation.

[0060] Figure 1 This is a working diagram of an algebraic modulation method for a three-phase current source converter of the present invention. Figure 2 The bidirectional three-phase current source converter topology structure of the present invention is as follows, including an input AC voltage source 1, an input inductor 2, an input capacitor 3, a switch network 4, a DC side inductor 5, a DC voltage source 6, and a load resistor 7; the input AC voltage source 1 and the input inductor 2 are connected in series and connected to the switch network 4 after passing through the input capacitor 3, and the DC side of the switch network 4 is connected to the DC side inductor 5 and then connected to the load DC voltage source 6 or resistor 7. The switch network 4 is composed of a combination of bidirectional switches, and the bidirectional switch is constructed as two IGBT emitters connected in series.

[0061] Figure 3 : is a control block diagram of the system, in which the main circuit includes the bidirectional three-phase current source converter topology structure of the embodiment of the present invention; the control circuit includes a sampling and conditioning circuit 8, a controller 9, and a drive circuit 10. The right part of the sampling circuit 8 is responsible for sampling and conditioning the inductor current on the DC side, and the left part 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 drive circuit 10, so as to achieve the purpose of controlling each switch.

[0062] Figure 4 This is a sector division diagram of input voltage and input current. According to the magnitude relationship of the three-phase input voltage or the three-phase input current, the voltage or current of one power frequency cycle is equally divided into 12 parts and named as I, II, III...XII.

[0063] Figure 5 Schematic diagram of the feasible solution area for free variables. The range of free variables is limited to the shaded area. Point A is l2 l3 The intersection point, point B is the straight line l1 The straight line l6 The intersection point, point C is l1 l3 Intersection.

[0064] Figure 6 It shows the switch PWM signal and the corresponding space vector arrangement of the three-phase current source converter under different free variable selections. It can be seen that the selection of three different vertices A, B, and C corresponds to three different switch sequences, and other sectors can also be arranged according to the above switch sequence. Among them, Figure 5 (a) is the switching sequence when vertex A is selected, using the commutation order of abcba, and the corresponding zero vector is Figure 5 (b) The figure shows the switching sequence when vertex B is selected, using the commutation sequence of bacab or bcacb. The corresponding zero vector is Figure 5 (c) The figure shows the switching sequence when vertex C is selected, using the commutation order of cbabc or cabac. The corresponding zero vector is Different vertices are selected, corresponding to three different space vector arrangement orders, and other sectors can also be arranged according to the above switching sequence. Generally, one vertex can be selected all the time during the modulation process, or three vertices can be rotated.

[0065] Figure 7 The flowchart of the algebraic modulation method for reducing the common-mode voltage. First, the desired input current is obtained through the outer loop control, and the input voltage and DC side current are sampled; then, the sector in which the input voltage 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 duty cycle matrix is ​​calculated; finally, the appropriate switch sequence is selected according to the corresponding vertex to generate the PWM pulse signal of the switch, as shown in the attached figure. Figure 5 It is not difficult to find that this method only requires simple mathematical calculations, without the need for trigonometric calculations, to obtain the final duty cycle. Therefore, compared with space vector modulation, this method reduces the computational burden.

[0066] Figure 8 This is the experimental waveform diagram of the algebraic modulation method to reduce the common mode voltage. Figure 8 The first half of (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 common-mode voltage peak of the proposed algebraic modulation method is greatly reduced. Figure 8 (b) is the experimental waveform on the AC side of the proposed algebraic modulation method for reducing the common-mode voltage. It can be seen that the input current is sinusoidal. Figure 8 (c) is 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 constant and the current is maintained near the reference value of 6 A. The above waveforms prove the correctness and effectiveness of the proposed algebraic modulation method.

[0067] The above description is only a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent change made based on the technical essence of the present invention still falls within the scope of protection required by the present invention.

Claims

1. An algebraic modulation method for a three-phase current source converter comprises the following steps, characterized in that: S1, transform the duty cycle allocation problem into a non-homogeneous linear equation system and use linear algebra theory to find the general solution of the duty cycle matrix; 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 ampere-second balance principle: Among them, d m , m=1,2,…,6 is a current source converter switch S i The duty cycle, i dc is the DC side current, i i , i=a,b,c is 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, we have: Combining equations (1) and (2), we get the following non-homogeneous linear equation: Among them, the three-phase expected input current is I m is the expected input current peak value, ω i is the input voltage angular frequency, is the phase angle of input voltage and input current; From equation (3), we know that the equation has 4 unknown variables, the rank of matrix A is 2, and from the relevant linear algebra theory, we know that the free variable of this equation is 2, so the general solution is expressed as: x=λ1h1+λ2h2+p (4) Among them, λ1 and λ2 are free variables; h1 and h2 are four-dimensional column vectors, which are the general solutions of the homogeneous equation system Ax=0; the four-dimensional column vector p is the special solution of the non-homogeneous equation system Ax=b, taking h1=[1 1 0 0] T ,h2=[0 0 1 1] T ,p=[i a * / i dc 0 i b * / i dc 0] T ; Therefore, combining (2) to (4), the general solution of the duty cycle matrix D is: According to the above analysis, when the current source converter is expanded to N, N ≥ 3 phases, the general solution of D is expanded accordingly: S2, based on the physical constraints of the duty cycle, the feasible solution region of the free variables is determined by means of geometric methods; the determination of the feasible solution region of the free variables 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, substituting equation (5) into inequality (7), we can obtain the following constraints on free variables: It is worth noting that the positions of the six boundary values ​​of the inequality group are related to the polarity of the desired current. With λ1 as the horizontal coordinate and λ2 as the vertical coordinate, it can be deduced from the above formula that no matter how the current relationship changes, the feasible solution range of the free variables (λ1, λ2) is 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 a straight line. of Intersection point, point B is a straight line The straight line The intersection point, point C is a straight line of Intersection S3, select a point in the feasible solution region as the solution of the free variable to determine the final duty cycle matrix; S4, determining a switching sequence and obtaining a switch driving pulse according to specific performance requirements, wherein the performance requirements include low switching loss, low common mode voltage, and low DC current ripple; The switching sequence action described in S4 is flexible and variable. Different switching sequences correspond to different performances. The corresponding switching sequence is selected according to the actual performance requirements. The actual performance requirements include common mode voltage and DC current ripple, as follows: Without loss of generality, the three-phase input voltage or input current is divided into 12 equal parts, namely sectors I to XII, assuming that the expected input current satisfies i a * >0>i b * >i c * , sector I, when three vertices are selected as the solution of free variables, the duty cycle matrix is ​​expressed as: Taking the reduction of 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 order is abcba; when vertex B is selected, the corresponding zero vector is The switching order is bacab; when vertex C is selected, the corresponding zero vector is The switching order is cbabc. Different vertices correspond to different zero vector selections. The remaining sectors can be operated according to the same rules. One vertex can be selected all the time in one power frequency cycle, or three vertices can be rotated. Taking the reduction of common-mode voltage as an example, it is necessary to select a group of switches corresponding to the phase with the minimum absolute value of the input voltage as the zero vector in each modulation cycle. Therefore, the corresponding zero vector is selected according to the input voltage sector, thereby determining the 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 When, that is, in sectors I, II VII, VIII, vertex B is selected as the solution of the free variable, the switching sequence is arranged as bacab, and the corresponding zero vector is When the input voltage satisfies u cb >u ca >u cc Or u cc >u ca >u cb When, that is, in sectors III, IV, IX, and X, vertex A is selected as the solution of the free variable, and the switching sequence is arranged as abcba, and the corresponding zero vector is When the input voltage satisfies u cb >u cc >u ca Or u ca >u cc >u cb When, that is, in sectors V, VI, XI, and XII, the top C is selected as the solution of the free variable, and the switching sequence is arranged as cbabc, and the corresponding zero vector is 2. The algebraic modulation method of a three-phase current source converter according to claim 1, characterized in that: The determination of the final duty cycle matrix described in S3 depends on the selection of free variables, as follows: The free variable feasible solution region is the interior and boundary of triangle ABC, and any point in it can be used as the value of the free variable; The coordinates of 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 triangle ABC are selected as the solution of the free variables.

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