A Universal Fast Modulation Method for VIENNA Rectifiers

Abstract

This invention discloses a general fast modulation method for a VIENNA rectifier, comprising: 1) establishing a mathematical model of nine switches based on the mathematical model of the VIENNA rectifier, obtaining the equality constraints between the duty cycle of the nine switches and the modulation wave; 2) establishing two equations satisfying the control voltage constraint through newly defined variables, and providing a general solution satisfying the equality constraint conditions; 3) obtaining six states based on the different directions of the three-phase current; obtaining inequality constraints under different states based on these six states; and obtaining the upper and lower limits of the free variables based on the inequality constraints under the six states; 4) solving for the compensation amount for neutral point potential balance control starting from the control equation for the capacitor neutral point potential control of the VIENNA rectifier. The modulation model and solution process of the VIENNA rectifier disclosed in this invention have a small computational workload, significantly reducing the computation time compared to the SVPWM modulation technology of three-level converters.

Description

Technical Field

[0001] This invention relates to the field of power electronic and electrical equipment and electrical engineering technology, and in particular to a universal fast modulation method for VIENNA rectifiers. Background Technology

[0002] The VIENNA rectifier is a two-quadrant midpoint clamped three-level PWM rectifier topology. In applications where bidirectional energy flow is not required, the VIENNA rectifier offers several advantages. Firstly, compared to the traditional two-level structure, the increased number of levels reduces the harmonic distortion (THD) of the current and the voltage stress on the power switches. Secondly, compared to a three-level PWM rectifier, the required number of power switches is reduced from 12 to 6, lowering switching losses, cost, and control complexity. Furthermore, when the power switches are on, the diodes connected to the DC bus can block the shoot-through current, eliminating the output voltage bridge arm shoot-through problem and eliminating the need for a drive dead time, thus further improving the rectifier's reliability.

[0003] The control strategies of VIENNA rectifiers are mainly divided into single-cycle control and vector control. Single-cycle control is a nonlinear control technique that does not require multipliers or input voltage detection. It uses a reset integrator to make the controlled variable track the control reference value within one switching cycle. Single-cycle control also has advantages such as constant switching frequency, fast response speed, and simple control. However, the single-cycle control of VIENNA rectifiers ignores the dynamic process of the current inner loop, directly obtaining the duty cycle of the fully controlled switch from the absolute value of the sampled current. Because there is no current inner loop, current control is in an open-loop state, making the current susceptible to interference. Vector control consists of a voltage outer loop and a current inner loop. Its control output is the control voltage in a two-phase coordinate system, which needs to be modulated to obtain the actual switching duty cycle. Currently, the two most widely researched and applied methods are sinusoidal carrier-based modulation (SPWM) and space vector pulse width modulation (SVPWM). Carrier modulation is simple to operate, easy to implement, and convenient for multi-module cascading, but it has low DC-side voltage utilization and cannot control the DC-side voltage. SVPWM switching models are simple, facilitating real-time microcomputer control, and feature low torque ripple, low noise, and high voltage utilization. Furthermore, the redundancy of the voltage vector can be used to control the DC-side voltage and reduce switching losses. However, due to the increased redundancy, the algorithm becomes overly complex, limiting its use. If the essential relationship between SPWM and SVPWM could be identified, and the modulation effect of SVPWM could be achieved using a simple and easily implemented SPWM modulation method, SVPWM applications could be extended to arbitrary voltage levels, fully utilizing its advantages. However, the intrinsic relationship between these two modulation methods remains poorly understood.

[0004] In existing technologies, the VIENNA rectifier is a three-level rectifier with low ripple, widely used in high-voltage, high-power applications. Its control strategies mainly include single-cycle control and vector control. Single-cycle control is a publicly available, simple method for achieving unity power factor, but it results in third-harmonic pulsations in the voltage across the DC-side capacitors. Vector control's SVPWM modulation is computationally complex due to the large number of synthesized vectors. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a fast modulation method for VIENNA rectifiers that considers midpoint potential balance control. The modulation model and solution process of VIENNA rectifiers have a small computational workload, which greatly reduces the calculation time compared with the SVPWM modulation technology of three-level converters.

[0006] The objective of this invention is achieved as follows: a universal fast modulation method for VIENNA rectifiers, comprising the following steps:

[0007] 1) Using the mathematical model of the VIENNA rectifier, establish a mathematical model of nine switches, establish the relationship between the nine switches and the actual three switches and the current direction, and obtain the equation constraint between the duty cycle of the nine switches and the modulation wave.

[0008] 2) By defining new variables, establish two equations that satisfy the control voltage constraints, and give a general solution that satisfies the equality constraint conditions;

[0009] 3) Based on the different directions of the three-phase current, six states are obtained; based on these six states, inequality constraints under different states are obtained; based on the inequality constraints under the six states, the upper and lower limits of the free variables are obtained, and finally the duty cycle of the three bidirectional switching transistors is determined.

[0010] 4) Starting from the control equation of the capacitor neutral point potential control of the VIENNA rectifier, the compensation amount of the neutral point potential balance control is solved.

[0011] As a further limitation of the present invention, step 1) specifically includes: assuming the VIENNA rectifier control voltage is u α u β ,use u α =S α u dc u β =S β u dc , obtain S α S β With S ap S an S bp S bn S cp S cn The relationship between them is shown in equation (1):

[0012]

[0013] Because of the three switches S ip ,S in ,S i0 It depends on the direction of the current, let S i (i = a, b, c) represents the duty cycle of the three-phase switch. For simplicity, let S' i =1-S i i = a, b, c, S' i (i = a, b, c) are intermediate variables for the duty cycle of the three-phase switch. Then the modulation equality constraint equation is obtained:

[0014]

[0015] Where, sign is the sign function, u a u b u c To modulate the output phase voltage, S α S β The modulation coefficients are in the α and β coordinate system; i a i b i c The current in the three-phase inductor; S ap S an S bp S bn S cp S cn These are the duty cycles of the positive-level switch (phase a), the negative-level switch (phase a), the positive-level switch (phase b), the negative-level switch (phase b), the positive-level switch (phase c), and the negative-level switch (phase c); S apn S bpn S cpn S′ represents the intermediate variables of the three-phase modulation coefficients a, b, and c. a S′ b S′ c Duty cycle S a S b S c Intermediate variables.

[0016] As a further limitation of the present invention, step 2) specifically includes: the constraint equation (3) has one free variable, and the general structure of the solution is as follows:

[0017]

[0018] Where S x S y for S cpn The variable is a free variable, and the free variable is related to the direction of the current; S x S y According to S α S β Intermediate variables defined.

[0019] As a further limitation of the present invention, step 3) specifically includes: determining six possible current directions and S. apn S bpn S cpn The range of variation is shown in Table 1:

[0020] Table 1i a ib i c Direction and S apn S bpn S cpn Scope correspondence

[0021]

[0022]

[0023] Based on the six cases in Table 1 and by modification, the free variable S is obtained. cpn The constraints to be satisfied are shown in Table 2:

[0024] Table 2i a i b i c Direction and S cpn Constraints

[0025]

[0026] S obtained from Table 2 cpn To satisfy the constraints of three inequalities, a common interval of inequalities should be chosen. Therefore, a lower bound S of the common interval is defined. L and upper limit S H The corresponding S in Table 2 L S H See Table 3:

[0027] Table 3i a i b i c Direction and S L S H Definition

[0028]

[0029] Therefore, S is obtained. cpn The conditions that must be met are:

[0030] S L ≤S cpn ≤S H (5)

[0031] Determine S using equation (5) cpn According to equation (4), S is obtained. apn S bpn S cpn Transforming equation (2) yields:

[0032]

[0033] The preceding definition S′ i =1-Si The final duty cycle obtained by i = a, b, c is:

[0034]

[0035] As a further limitation of the present invention, step 4) specifically includes: the compensation amount of the capacitor neutral point control of the VIENNA rectifier satisfies:

[0036] ΔS' a i a +ΔS' b i b +ΔS' c i c =i ΔC (8)

[0037] Where i ΔC The neutral point control current of the capacitor that satisfies (9), ΔS' a , ΔS' b , ΔS' c i is the compensation amount for capacitor neutral point control of the switching transistor's duty cycle. a i b i c This represents the three-phase current in the inductor.

[0038]

[0039] (9) In the formula k pC k iC For the proportional and integral coefficients of the capacitor neutral point control, Δu c Given the voltage difference between the upper and lower capacitors on the DC side, the final compensation amount is:

[0040]

[0041] Where I m For i a i b i c The amplitude.

[0042] Compared with the prior art, the beneficial effects of the above technical solution adopted by the present invention are as follows: 1) The present invention directly starts from mathematics to find the general solution of the equality constraint and the upper and lower limits of the free variables, and the method has universality;

[0043] 2) It is implemented directly using mathematical methods, which reduces the amount of calculation in the intermediate steps and greatly reduces the calculation time.

[0044] 3) Starting directly from the control equations of neutral point potential control, the compensation amount for neutral point potential balance control is solved, resulting in a significant control effect;

[0045] 4) The proposed strategy of parallel compensation amount with three-phase current amount minimizes the required duty cycle compensation amount, thus allowing the duty cycle of the three switches to have a larger adjustment range to adjust the DC voltage on the DC side. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the main circuit structure of the VIENNA rectifier described in the embodiment.

[0047] Figure 2 This is an equivalent schematic diagram of a portion of the main circuit structure of the VIENNA rectifier in the embodiment.

[0048] Figure 3 The modulation waveform of the VIENNA rectifier is shown in the example without considering neutral point voltage balance.

[0049] Figure 4 The simulation results of the compensation modulation method for the VIENNA rectifier in the embodiment are shown. Detailed Implementation

[0050] like Figure 1 As shown in the embodiment, a general fast modulation method for a VIENNA rectifier is disclosed, including the following steps:

[0051] like Figure 2 As shown, due to the three switches S ip ,S in ,S i0 Related to the direction of the current, S ip For S ap S bp S cp The unified representation of (i = a, b, c), S in For S an S bn S cn The unified representation of (i = a, b, c), S i0 For S a0 S b0 S c0 A unified representation of (i = a, b, c); let S i '=1-S i i = a, b, c, S ip ,S in ,S i0 with i i The relationship between them can be represented as:

[0052]

[0053] Where sign is the sign function, i i The three-phase current in the inductor; the VIENNA rectifier control voltage uα u β ,use u α =S α u dc u β =S β u dc S can be obtained α S β With S ap S an S bp S bn S cp S cn The relationship between them is shown in equation (2):

[0054]

[0055] Among them, u a u b u c To modulate the output phase voltage, S α S β S represents the modulation coefficients in the α and β coordinate systems; ap S an S bp S bn S cp S cn These are the duty cycles of the positive-level switch in phase a, the negative-level switch in phase a, the positive-level switch in phase b, the negative-level switch in phase b, the positive-level switch in phase c, and the negative-level switch in phase c, respectively.

[0056] The expression can be represented by a matrix, as shown in equation (3):

[0057]

[0058] Equation (1) can be expressed as a matrix:

[0059]

[0060] Among them, i a i b i c This refers to the current in the three-phase inductor.

[0061] Substituting equation (4) into equation (3), we get:

[0062]

[0063] The coefficient matrix in equation (5) can be represented as the product of two matrices, i.e.:

[0064]

[0065] If defined:

[0066]

[0067] S apn S bpn S cpn S′ represents the intermediate variables of the three-phase modulation coefficients a, b, and c. a S′ b S′ c For: duty cycle S a S b S c intermediate variables that satisfy S' a =1-S a S′ b =1-S b S′ c =1-S c Thus, equation (6) becomes a more concise form:

[0068]

[0069] Thus, the modulation process of the VIENNA rectifier becomes solving the equation represented by equation (8), which has multiple solutions.

[0070] When the modulation at neutral point voltage balance is not considered, when solving equation (8), since there is one free variable in the equation, the dimension of the solution is 1; the solution of the system of equations consists of a general solution and a particular solution, and the general structure of the solution is as follows:

[0071]

[0072] In the equation, the first term on the right-hand side is the general solution, where c is any number; the second term on the right-hand side is a particular solution. For ease of description, let:

[0073]

[0074] From the third term of equation (9), we can obtain S. cpn =c, for a more intuitive description, let c = S cpn Then equation (9) can be simplified to:

[0075]

[0076] From equation (7), we get S' a S' b S′ c The range of variation is 0 to 1, although S apn S bpn S cpnThe range of variation is -1 to 1, but their signs are determined by the direction of the current, that is, S apn S bpn S cpn Not every time point satisfies -1≤S ipn ≤1i=a,b,c, but 0≤S is satisfied during the positive half-cycle of the current. ipn ≤1i=a,b,c, but satisfies -1≤S during the negative half-cycle of the current. ipn For i ≤ 0, i = a, b, c, the condition to be satisfied within one period is:

[0077] 0≤sign(i i )S ipn ≤1i=a,b,c (12)

[0078] Therefore, to determine S apn S bpn S cp The range of change of i needs to be determined. a i b i c The direction, due to i a i b i c The current direction cannot be both positive and both negative simultaneously, resulting in six possible combinations. Table 1 lists the six possible current directions and S. apn S bpn S cpn The range of variation.

[0079] Table 1i a i b i c Direction and S apn S bpn S cpn Scope correspondence

[0080]

[0081]

[0082] Substituting equation (11) into the six cases in Table 1 and transforming them, we can obtain S. cpn The constraints that must be met are shown in Table 2.

[0083] Table 2i a i b i c Direction and S cpn Constraints

[0084]

[0085]

[0086] S obtained from Table 2 cpn To satisfy the constraints of three inequalities, a common interval of inequalities should be chosen. Therefore, a lower bound S of the common interval is defined. L and upper limit S H The corresponding S in Table 2 L S H See Table 3.

[0087] Table 3i a i b i c Direction and S L S H Definition

[0088]

[0089] From this, we can obtain S. cpn The conditions that must be met are:

[0090] S L ≤S cpn ≤S H (13)

[0091] Thus, S is determined using equation (13). cpn According to equation (11), S can be obtained. apn S bpn S cpn However, this is not the final duty cycle. Transforming equation (7) yields:

[0092]

[0093] The preceding definition S' i =1-S i The final duty cycle obtained by i = a, b, c is:

[0094]

[0095] Figure 3 To obtain S at time L S H i a i b i c S apn S bpn S cpn and S a S b S c Waveform diagrams. In (a), the free variable S is shown. cpn The lower limit S Land upper limit S H (a) is the curve of the three-phase current in the inductor, and (b) is the waveform of the intermediate variable S. apn S bpn S cpn The waveform diagram is shown in (d), where S is the duty cycle of the three switching transistors. a S b S c Waveform diagram.

[0096] The capacitor neutral point control equation for the VIENNA rectifier is equation (16):

[0097]

[0098] Because the control variables in this formula are defined differently from those in formula (8), formula (16) needs to be transformed. Using S... ip +S in =S' i i = a, b, c, so equation (16) becomes:

[0099]

[0100] To account for neutral point voltage balance, a compensation S needs to be added to equation (17). a '、S b '、S c ', let the compensation of S' a S' b S' c For ΔS' a , ΔS' b , ΔS' c .set up iΔC For Δu c Total control quantity, i ΔC From Δu c The result obtained after PI adjustment is shown in equation (18):

[0101]

[0102] In the formula k pC k iC These are the proportional and integral coefficients, respectively. Thus, the compensation amount ΔS' a , ΔS' b , ΔS' c with i ΔC The relationship is:

[0103] ΔS' a i a +ΔS' b i b +ΔS' c i c =iΔC (19)

[0104] Since equation (19) cannot uniquely determine the compensation amount, the strategy adopted by this invention is to make ΔS' so that, in order to achieve the same effect, ΔS' a , ΔS' b , ΔS' c The range of variation is minimized, thus making S' a S' b S' c It has a wider adjustment range and can adjust the DC side DC voltage u dc From ΔS' a i a +ΔS' b i b +ΔS' c i c =i ΔC It can be seen that if [ΔS'] a , ΔS' b , ΔS' c ] T and[i a i b i c ] T Viewed as two vectors, i ΔC This can be viewed as the dot product of these two vectors. In i ΔC At a given time, when [ΔS'] a , ΔS' b , ΔS' c ] T with[i a i b i c ] T When the directions are the same, that is, when they are parallel, [S' a0 S' b0 S' c0 ] T The length is minimized, so [ΔS'] a , ΔS' b , ΔS' c ] T It can be expressed as equation (20):

[0105]

[0106] Substituting equation (20) into equation (19), we get This formula assumes [i] a i b i c ] T Given a sinusoidal alternating current, and simplified using the formula for the square of the sine function, we obtain... Substituting k into equation (20) yields:

[0107]

[0108] Thus, the compensation amount ΔS' for neutral point voltage balance control is obtained from equation (21). a , ΔS' b , ΔS' c , and equation (14)S' a S' b S' c Add them together and then use formula (15) to obtain the required control quantity.

[0109] Figure 4 To simulate the waveforms of the compensation modulation method considering neutral point voltage balance, Figure (a) shows the three-phase grid voltage waveform, and Figure (b) shows the three-phase current waveform. Comparing Figure (b) and Figure (c), the phase voltage and phase current waveforms are in phase, achieving a power factor of 1. Figure (c) shows the voltage u across the upper and lower capacitors. c1 u c2 The waveform diagram shows u when the neutral point voltage is balanced. c1 u c2 The curves coincided and finally stabilized at 400V, with a total voltage u. dc The voltage stabilized at 800V. When a load was suddenly applied at 0.04s, all voltages briefly dropped before stabilizing at the set value of 400V. After the load was applied, the three-phase current increased to twice the current before the load was applied, compensating for the load current and thus maintaining the voltage. dc Constant.

[0110] This invention starts from the working principle of the VIENNA rectifier and establishes a mathematical model of nine switches. However, the VIENNA rectifier actually only has three switches, thus establishing the relationship between the nine switches and the actual three switches and the current direction. Based on this relationship, two equations satisfying the control voltage constraint are established through the definition of new variables, and a general solution satisfying the equality constraint conditions is given. Since the free variables in the general solution are related to the current direction, this invention establishes constraint conditions for variables in six states with different directions of the three-phase current, thereby obtaining the upper and lower limits of the free variables under different current states, and finally obtaining the general expression for the modulation output. This invention directly utilizes mathematical methods, reducing the amount of calculation in the entire process through intermediate links and fewer logical judgments, greatly reducing the calculation time.

[0111] This invention is not limited to the above embodiments. Based on the technical solutions disclosed in this invention, those skilled in the art can make some substitutions and modifications to some of the technical features without creative effort, and all such substitutions and modifications are within the protection scope of this invention.

Claims

1. A universal fast modulation method for VIENNA rectifiers, characterized in that, Includes the following steps: 1) Using the mathematical model of the VIENNA rectifier, establish a mathematical model of nine switches, establish the relationship between the nine switches and the actual three switches and the current direction, and obtain the equation constraint between the duty cycle of the nine switches and the modulation wave. Step 1) specifically includes: assuming the VIENNA rectifier control voltage is... ,use , , , ,get and The relationship between them is shown in equation (1): (1) Because of three switches It depends on the direction of the current, let's assume Let be the duty cycle of the three-phase switch. , This is an intermediate variable for the duty cycle of a three-phase switch. (2), then the modulation equality constraint equation is obtained: (3) Where, sign is the sign function, u a u b u c To modulate the output phase voltage, for Modulation coefficient in coordinate system; This refers to the current in the three-phase inductor. These are the duty cycles of the positive-level switch (phase a), the negative-level switch (phase a), the positive-level switch (phase b), the negative-level switch (phase b), the positive-level switch (phase c), and the negative-level switch (phase c); S apn S bpn S cpn These are intermediate variables for the three-phase modulation coefficients a, b, and c; Duty cycle intermediate variables; 2) By defining new variables, establish two equations that satisfy the control voltage constraints, and give a general solution that satisfies the equality constraint conditions; Step 2) specifically includes: the constraint equation (3) has one free variable, and the general structure of the solution is as follows: (4) in for S apn S bpn S cpn The three-phase modulation coefficients a, b, and c are intermediate variables; at this time, the free variable S cpn Related to the direction of the current; S x S y According to Intermediate variables defined; 3) Based on the different directions of the three-phase current, six states are obtained; based on these six states, inequality constraints under different states are obtained; based on the inequality constraints under the six states, the upper and lower limits of the free variables are obtained, and finally the duty cycle of the three bidirectional switching transistors is determined. 4) Starting from the control equation of the capacitor neutral point potential control of the VIENNA rectifier, solve for the compensation amount of the neutral point potential balance control.

2. The universal fast modulation method for a VIENNA rectifier according to claim 1, characterized in that, Step 3) specifically includes: determining six possible current directions and The range of variation is shown in Table 1: Table 1 direction and Scope correspondence ； Based on the six cases in Table 1 and by modification, the free variables are obtained. The constraints to be satisfied are shown in Table 2: Table 2 direction and Constraints ； The results obtained from Table 2 To satisfy the constraints of three inequalities, a common interval of inequalities should be chosen. Therefore, a lower bound of this common interval is defined. and upper limit The corresponding table 2 , See Table 3: Table 3 direction and , Definition ； Therefore, we obtain The conditions that must be met are: (5) Determine using equation (5) According to equation (4), we get Transforming equation (2) yields: (6) The preceding definition The final duty cycle is: (7)。 3. The universal fast modulation method for a VIENNA rectifier according to claim 1, characterized in that, Step 4) specifically includes: the compensation amount for the capacitor neutral point control of the VIENNA rectifier satisfies: （8） in The capacitor neutral point control current that satisfies (9) This is the compensation amount for capacitor neutral point control of the switching transistor's duty cycle. The three-phase current in the inductor; （9） (9) These are the proportional and integral coefficients for capacitor neutral point control. Given the voltage difference between the upper and lower capacitors on the DC side, the final compensation amount is: （10） in for The amplitude.

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