Three-level pwm rectifier fast modulation and neutral point potential balance control method

Abstract

The application discloses a three-level PWM rectifier fast modulation and neutral point potential balance control method, which comprises the following steps: 1) according to a mathematical model of the three-level PWM rectifier, a modulation model of the three-level PWM rectifier is established based on the mathematical model and constraint conditions of duty ratios of nine switch tubes; 2) a basic solution system and a special solution of a linear equation set are utilized to decompose free components of a modulation process, and different modulation strategies are obtained by appropriately selecting different free components; and 3) a control strategy that AC components of duty ratios of three zero potential switches should be in-phase with three-phase currents is proposed, and solving of an inequality with four degrees of freedom is reduced to one, and finally a value range of one degree of freedom is determined. According to the inequality constraint, the modulation result is solved, and the calculation workload is small and the speed is fast; the proposed neutral point balance control strategy reduces the duty ratio fluctuation range of the three zero position switches, thereby providing a larger space for voltage or current control of the three-level PWM rectifier.

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 method for rapid modulation and midpoint potential balance control of a three-level PWM rectifier. Background Technology

[0002] Multilevel pulse-width modulation (PWM) rectifiers / inverters are widely used in high-voltage, high-power applications, such as active power filters, static var compensators (SVCs), and high-capacity high-voltage variable frequency drives (VFDs). The corresponding pulse width modulation (PWM) control method is one of the core issues in the research field of multilevel inverters. Currently, the two most widely researched and applied methods are sinusoidal carrier-based modulation (SPWM) and space vector pulse width modulation (SVPWM). If the essential relationship between SPWM and SVPWM can be found, and the modulation effect of SVPWM can be achieved through a simple and easy-to-implement SPWM modulation method, the application of SVPWM can be extended to arbitrary levels, fully utilizing the advantages of SVPWM modulation. However, the intrinsic relationship between these two modulation methods has not yet been thoroughly analyzed and understood.

[0003] Existing SPWM carrier modulation methods are simple to operate, easy to implement, and convenient for multi-module cascading, but their DC-side voltage utilization is low, and they cannot control the DC-side voltage. SVPWM switching models are simple, convenient for real-time microcomputer control, and have the characteristics of low torque ripple, low noise, and high voltage utilization. Furthermore, they can utilize the redundant states of the voltage vector to control the DC-side voltage and reduce switching losses. However, when the number of voltage levels in the main circuit exceeds 5, the algorithm becomes overly complex due to the increased redundancy of the voltage vector, resulting in less frequent use. Conventional three-level PWM rectifier modulation techniques mainly include SPWM and SVPWM. Three-level SPWM is simple to implement, but neutral point potential control is more difficult. Three-level SVPWM involves a large computational workload due to the large number of synthesized vectors. Summary of the Invention

[0004] The purpose of this invention is to overcome the defects of the prior art and provide a fast modulation and midpoint potential balance control method for a three-level PWM rectifier. Based on the analysis of the mathematical model of the three-level PWM rectifier, a modulation model for the three-level PWM rectifier is proposed, which greatly reduces the calculation time compared with the SVPWM modulation technology of the three-level converter.

[0005] The objective of this invention is achieved as follows: a method for fast modulation and midpoint potential balance control of a three-level PWM rectifier, comprising the following steps:

[0006] 1) Based on the mathematical model of the three-level PWM rectifier, and the constraints of the duty cycle of the nine switching transistors, a modulation model of the three-level PWM rectifier is established. The resulting modulation model is a set of five equations.

[0007] 2) By using the fundamental solution set and particular solutions of the linear equation system, the free components of the modulation process can be decomposed, and different modulation strategies can be obtained by appropriately selecting different free components;

[0008] 3) A control strategy was proposed that the AC component of the duty cycle of the three zero-potential switches should be in phase with the three-phase current; the solution of the inequality with four degrees of freedom was reduced to one, and the range of values ​​for one degree of freedom was finally determined.

[0009] As a further limitation of the present invention, step 1) specifically includes: obtaining the constraint relationship between duty cycle and control voltage by the relationship between the duty cycle of the three switches of the three-level system and the control voltage; obtaining the constraint condition of duty cycle by ensuring that the switch on each phase bridge arm can only be in one position at a certain time, while the duty cycle satisfies the condition of changing from 0 to 1.

[0010] Based on the control voltage constraints and the constraints of the three switches in the same bridge arm, the modulation model is obtained as a set of five equations (1):

[0011]

[0012] Among them, S α S is the modulation coefficient in the α coordinate system. β S is the modulation coefficient in the β coordinate system. ap S bp S cp S an S bn S cn S a0 S b0 S c0 Let be the duty cycle of the positive level switch of bridge arm a, the duty cycle of the positive level switch of bridge arm b, the duty cycle of the positive level switch of bridge arm c, the duty cycle of the negative level switch of bridge arm a, the duty cycle of the negative level switch of bridge arm b, the duty cycle of the negative level switch of bridge arm c, the duty cycle of the zero level switch of bridge arm a, the duty cycle of the zero level switch of bridge arm b, and the duty cycle of the zero level switch of bridge arm c.

[0013] As a further limitation of the present invention, step 2) specifically includes: 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 shown in equation (2), where c1, c2, c3, and c4 are free variables; the first four terms on the right side of the equation are the general solution, and the fifth term on the right side is the particular solution;

[0014]

[0015] make The duty cycle equations for the nine switches are obtained (3), and the free variables should satisfy (4):

[0016]

[0017]

[0018] Among them, S x S y According to S α S β Intermediate variables defined.

[0019] As a further limitation of the present invention, the control strategy proposed in step 3) that the AC component of the duty cycle of the three zero-potential switches should be in phase with the three-phase current specifically includes: S a0 S b0 S c0 Used for neutral point voltage control, the difference Δu between the upper and lower capacitors on the DC side. c It should satisfy (5), and S a0 S b0 S c0 The value of the neutral point voltage is obtained by converting it into an AC quantity, i.e., equation (6). After PI regulation using equation (7), the control value of the neutral point voltage is obtained, i.e., equation (8).

[0020]

[0021]

[0022]

[0023]

[0024] Thus, S' was obtained. a0 S' b 0S' c In practical applications, it needs to be converted to S a0 S b 0S c ; where S' a0 S b '0、S c '0 is the duty cycle S of the zero-level switch a0 Sb0 S c0 intermediate variables that satisfy S' a0 =1-S a0 S b '0 = 1 - S b0 S c '0 = 1 - S c0 S a0 S b0 S c0 The duty cycle of the zero-level switch, i a i b i c For the three-phase inductor current, Δu c i represents the voltage difference across the upper and lower capacitors on the DC side. Δc The current controlled by the neutral point voltage, k pc k is the proportional control coefficient for neutral point voltage control. ic I is the integral regulation coefficient for neutral point voltage control. m This represents the amplitude of the three-phase inductor current.

[0025] As a further limitation of the present invention, step 3) of reducing the solution of the inequality with four degrees of freedom to one, and finally determining the value range of one degree of freedom, specifically includes: after obtaining S a0 S b0 S c0 Then, the formula for finding the range of c1 is modified, and the constraint condition that c1 should satisfy is (9):

[0026]

[0027] According to equation (9), the variable S represented by equation (10) is defined. L S H Thus, the range of c1 is obtained, i.e., equation (11).

[0028]

[0029] S L ≤c1≤S H (11)

[0030] Where S L For, S H Let c1 be the lower and upper bounds of the free variable.

[0031] Compared with the prior art, the present invention adopts the above technical solution and has the following advantages: The present invention directly solves the duty cycle modulation process from the mathematical model, without targeting any specific modulation algorithm. Therefore, the present invention has universality and can unify common modulation strategies; The present invention solves the modulation result based on inequality constraints, which reduces the computational workload and speed; The neutral point balance control strategy proposed in the present invention reduces the duty cycle fluctuation range of the three zero-position switches, thereby providing more space for the control of the voltage or current of the three-level PWM rectifier. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the main circuit structure of the three-level PWM rectifier described in the embodiment.

[0033] Figure 2 S in the embodiment a0 S b0 S c0 The waveform diagram.

[0034] Figure 3 The waveform diagram shows the duty cycle of the nine switches in the embodiment.

[0035] Figure 4 This diagram illustrates the effect of the VIENNA rectifier in suppressing neutral point potential fluctuations in the embodiment. Detailed Implementation

[0036] The embodiment discloses a method for fast modulation and midpoint potential balance control of a three-level PWM rectifier, including the following steps:

[0037] 1) The three-level circuit topology can be simplified as follows: Figure 1 As shown, the definitions of each variable and their positive directions are also marked in the figure; the switch on each phase arm can only be in one position at a certain time, that is, each arm switch is a single-pole three-throw switch, so the switch in the figure should satisfy equation (1):

[0038]

[0039] Among them, S ap S bp S cp S an S bn S cn S a0 S b0 S c0Let be the duty cycle of the positive level switch of bridge arm a, the duty cycle of the positive level switch of bridge arm b, the duty cycle of the positive level switch of bridge arm c, the duty cycle of the negative level switch of bridge arm a, the duty cycle of the negative level switch of bridge arm b, the duty cycle of the negative level switch of bridge arm c, the duty cycle of the zero level switch of bridge arm a, the duty cycle of the zero level switch of bridge arm b, and the duty cycle of the zero level switch of bridge arm c.

[0040] Figure 1 The voltages of points A, B, and C relative to the DC neutral point M can be expressed as:

[0041]

[0042] By applying the differential equation to the inductor, we can obtain:

[0043]

[0044] Among them, u a =u AM +u MO u b =u BM +u MO u c =u CM +u MO ;u MO The voltage between the DC-side capacitor center point M and the power supply center point O; u a u b u c This is the three-phase modulated output voltage; utilizing the symmetry of the three-phase system, and since the AC side uses a connection without a neutral line, the existence of zero-sequence voltage is not considered. For three-phase symmetry, u... a +u b +u c =0, therefore:

[0045]

[0046] Where u c1 The voltage across the upper capacitor on the DC side, u c2 This is the voltage across the capacitor on the lower side of the DC side.

[0047] 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 A unified representation of (i = a, b, c). Combining equations (2), (3), and (4), we can obtain:

[0048]

[0049] For now, we will disregard the DC voltage deviation across the upper and lower capacitors, assuming that the voltage u across capacitors C1 and C2 is... c1 u c2 Equal, that is u a u b u c It can be represented as:

[0050]

[0051] For nodes P, M, and N, the following relationships can be obtained using Kirchhoff's laws:

[0052]

[0053]

[0054]

[0055] To find the differential equation for the DC-side output voltage, assume C1 = C2 = C and use u dc =u c1 +u c2 Adding equations (7) and (8) together, we get:

[0056]

[0057] To ensure that the voltages across capacitors C1 and C2 are equal, Δu is defined. c =u c1 -u c2 Subtracting equations (7) and (8) gives:

[0058]

[0059] 2) The three-level PWM rectifier uses a control strategy similar to that of the two-level PWM rectifier to obtain the control voltage u. α u β ,use u α =S α u dc u β =S β u dc Combining equation (6), we can obtain S. α S β With S ap S an S bp S bn S cp S cnThe relationship between them can be represented as:

[0060]

[0061] Among them, S α S is the modulation coefficient in the α coordinate system. β The modulation coefficient is in the β coordinate system.

[0062] Based on the constraints of equation (1) and equation (12), a system of equations can be formed to obtain the modulation model, which consists of five equations. Let the vector composed of the solution variables be: [S ap S bp S cp S an S bn S cn S a0 S b0 S c0 ] T The system of simultaneous equations can be represented in matrix form as follows:

[0063]

[0064] It is easy to verify that the coefficient matrix and the augmented matrix of the system of equations represented by equation (13) both have a rank of 5. Using linear algebra, the system of equations (13) has a solution. Since there are nine unknowns in the system of equations, and the rank of both the coefficient matrix and the augmented matrix is ​​5, the system of equations has infinitely many solutions, and the dimension of the solution is 4. The solution of the system of equations consists of a general solution and a particular solution. The general structure of the solution is as follows:

[0065]

[0066] In the equation, the first four terms on the right-hand side are the general solution, with c1, c2, c3, and c4 being free variables; the fifth term on the right-hand side is the particular solution. For ease of description, let: S x S y for S x S y According to S α S β When the intermediate variable is defined, equation (14) can be transformed into:

[0067]

[0068] Due to [S] ap S bp S cp S an S bn S cn S a0 S b0 S c0 ]T The range of each variable in the equation is 0 to 1. From (15), we can obtain:

[0069]

[0070] If [S] ap S bp S cp S an S bn S cn S a0 S b0 S c0 ] T All variables in the equation are greater than or equal to 0. From equation (1), we can see that [S] ap S bp S cp S an S bn S cn S a0 S b0 S c0 ] T The variables in the equation naturally satisfy the condition that each variable is less than or equal to 1, and equation (16) can be simplified to:

[0071]

[0072] This transforms the modulation problem into solving a system of linear inequalities for the free variables c1, c2, c3, and c4.

[0073] 3) However, in actual operation, due to the inconsistency of component characteristics and measurement and control errors, the voltages on capacitors C1 and C2 are not equal. This will result in a worse control effect and may even lead to damage to some components. Therefore, neutral point voltage control must be performed in actual operation.

[0074] according to Because i a +i b +i c = 0 always holds true, so the constant 1 on the right-hand side of the formula applies to Δu c Since the control is ineffective, the above equation becomes:

[0075]

[0076] Due to Δu c The polarity of the control variable S is different. a0 S b0 S c0 The polarity of S can be positive or negative, therefore S a0 S b0 S c0It is not suitable to use it directly as a control variable; that is, the control variable should have communication characteristics. Because S a0 S b0 S c0 Adding a certain value to a variable will not change the control effect, therefore, a variable is defined. For S 0a , 0b S 0c The average value of S S 0a , 0b S 0c Subtracting S0 from each of S yields an AC quantity, i.e. This style (18) can be transformed into style (19):

[0077]

[0078] Let i in the formula ΔC =-S' a0 i a -S b '0i b -S c '0i c i ΔC For Δu c Total control quantity. ΔC Usually by Δu c The result obtained after PI adjustment is shown in equation (20):

[0079]

[0080] In the formula k pC k iC These are the proportional and integral coefficients, respectively. When i is obtained using equation (20)... ΔC Then, in order to solve S' a0 S b '0、S c There are many possible outcomes with '0'.

[0081] The strategy adopted in this invention is to achieve the same effect by making S' a0 S' b0 S' c0 The range of variation is minimized, thus making S ap S an S bp S bn S cp S cn It has a wider adjustment range and can adjust the DC side DC voltage u dc . from i ΔC =-S' a0 i a -S'b0 i b -S'i c0 It can be seen that if [S'] a0 S' b0 S c '0] 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 certain time, when [S' a0 S' b0 S c '0] T with[i a i b i c ] T When the directions are the same, that is, when they are parallel, [S' a0 S b '0、S c '0] T The length is minimized, so [S'] a0 S b '0、S c '0] T It can be expressed as equation (21):

[0082]

[0083] Substituting equation (21) 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 (21) yields:

[0084]

[0085] Thus, S was obtained. a '0、S b '0、S c '0' needs to be converted to S in practical applications. a0 S b0 S c0 Because S a0 S b0 S c0 It is a variable greater than 0, so S' needs to be... a0 S' b0 S c'0 Add a positive number to each of the three variables to ensure S a0 S b0 S c0 ≥0.

[0086] Based on the foregoing analysis, S a0 S b0 S c0 and S' a0 S' b0 S c The relationship between '0' is: Represented in matrix form:

[0087]

[0088] It is not difficult to verify that the rank of the coefficient matrix in equation (23) is 2, that is, from S' a0 S b '0、S c Solve for S with 0 a0 S b0 S c0 The result is not unique; in this case, the equations should be transformed into an independent system of second-order equations, and the three-phase system should be transformed into a stationary two-phase system, i.e.

[0089]

[0090] Define S' x S' y The variables are as follows:

[0091]

[0092] Let S c0 If the variables are free variables, then equation (25) can be simplified to:

[0093]

[0094] Assume S a0 S b0 S c0 The maximum value is S 0max , by S a0 S b0 S c0 The constraints are:

[0095]

[0096] From equation (27), we can obtain S c0 The constraints are as follows:

[0097]

[0098] definition: Where S' L S' H Free variable S c0 The lower and upper limits of S can be obtained from this. c0 The conditions that must be met are:

[0099] S' L ≤S c0 ≤S' H (30)

[0100] Pick Substituting into formula (26), the desired result can be obtained.

[0101] Figure 2 For S 0m The result of this method when = 0.1 Figure 2 (a) is S' L S' H Curve waveform diagram Figure 2 (b) is S a0 S b0 S c0 The curve waveform diagram shows that S at this time a0 S b0 S c0 The limit value S 0max Reduce to That is, S can be a0 S b0 S c0 The dynamic range is reduced to 0.866 times that of Method 1.

[0102] In obtaining S a0 S b0 S c0 Then, the formula for finding the range of c1 should also be modified. At this time, equation (17) can be changed to:

[0103]

[0104] According to equation (31), S is defined. L S H for:

[0105]

[0106] According to S L ≤c1≤S H After finding c1 under the given conditions, substitute it into equation (15) to find S. ap S an S bp S bn S cp S cn Thus, the duty cycles of the nine switches can be obtained.

[0107] Figure 3 This is a waveform diagram of nine duty cycles of a three-level PWM rectifier when the neutral point voltage is balanced. Figure 3 (a) is S ap S bp S cp waveform diagram, Figure 3 (b) is S an S bn S cn waveform diagram, Figure 3 (c) is S a0 S b0 S c0 The waveform diagram, where S a0 S b0 S c0 It fluctuates around 0.1, caused by the ripple voltage of the capacitor voltage, with an average value of 0.1 for Δu. c Overall, it has no controlling effect.

[0108] After applying the neutral point voltage balance control algorithm of this invention, the waveform is as follows: Figure 4 As shown in Figure (a). Figure (a) shows the waveforms of the capacitor voltage and the total DC voltage. It can be seen from Figure (a) that after 0.02s, the voltages across the two capacitors are equal. Figure (b) shows the voltage across S. a0 S b0 S c0 Waveform diagram.

[0109] This invention utilizes a mathematical model of a three-level PWM rectifier and a control algorithm similar to that of a two-level PWM rectifier to obtain the required voltage. Based on this mathematical model and the constraints of the duty cycles of the nine switches, a modulation model of the three-level PWM rectifier is established, resulting in a set of inequalities for solving the duty cycle with four free variables. Methods for solving these inequalities are established considering both neutral point voltage balance and imbalance. For neutral point voltage imbalance, a control strategy is proposed where the AC component of the duty cycle of the three zero-potential switches should be in phase with the three-phase current. Under the condition of the same control effect, this reduces the variation range of the duty cycle of the three zero-potential switches.

[0110] 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 method for fast modulation and midpoint potential balance control of a three-level PWM rectifier, characterized in that, Includes the following steps: 1) Based on the mathematical model of the three-level PWM rectifier, and the constraints of the duty cycle of the nine switching transistors, a modulation model of the three-level PWM rectifier is established. The resulting modulation model is a set of five equations. Step 1) specifically includes: obtaining the constraint relationship between duty cycle and control voltage by the relationship between the duty cycle of the three switches of the three-level system and the control voltage; obtaining the constraint condition of duty cycle by ensuring that the switch on each phase bridge arm can only be in one position at a certain time, while the duty cycle satisfies the condition of changing from 0 to 1. Based on the control voltage constraints and the constraints of the three switches in the same bridge arm, the modulation model is obtained as a set of five equations (1): (1)； in, for Modulation coefficient in coordinate system for Modulation coefficient in coordinate system, S ap S bp S cp S an S bn S cn S a0 S b0 S c0 Let A be the duty cycle of the positive level switch of bridge arm A, the duty cycle of the positive level switch of bridge arm B, the duty cycle of the positive level switch of bridge arm C, the duty cycle of the negative level switch of bridge arm A, the duty cycle of the negative level switch of bridge arm B, the duty cycle of the negative level switch of bridge arm C, the duty cycle of the zero level switch of bridge arm A, the duty cycle of the zero level switch of bridge arm B, and the duty cycle of the zero level switch of bridge arm C. 2) By using the fundamental solution set and particular solutions of the linear equation system, the free components of the modulation process can be decomposed, and different modulation strategies can be obtained by appropriately selecting different free components; Step 2) specifically includes: the solution of the system of equations consists of a general solution and a particular solution, and the structure of the solution is as shown in equation (2), where c1, c2, c3, and c4 are free variables; the first four terms on the right side of the equation are the general solution, and the fifth term on the right side is the particular solution; (2)； make We obtain the duty cycle equations (3) for the nine switches, while the free variables should satisfy (4): (3) ； (4)； Among them, S x S y According to Intermediate variables defined; 3) A control strategy was proposed that the AC component of the duty cycle of the three zero-potential switches should be in phase with the three-phase current; the solution of the inequality with four degrees of freedom was reduced to one, and the range of values ​​for one degree of freedom was finally determined. Step 3) describes a control strategy where the AC components of the three zero-potential switches' duty cycles are in phase with the three-phase current. This strategy specifically includes: Used for neutral point voltage control, the difference between the upper and lower capacitors on the DC side. It should satisfy (5), The value of the neutral point voltage is obtained by converting it into an AC quantity, i.e., equation (6). After PI regulation using equation (7), the control value of the neutral point voltage is obtained, i.e., equation (8). (5)； (6)； (7)； (8)； Thus obtained In practical applications, it needs to be converted into ;in, Zero-level switch duty cycle intermediate variables that satisfy , The duty cycle of the zero-level switch, i a i b i c For three-phase inductor current, This represents the voltage difference across the upper and lower capacitors on the DC side. The current controlled by the neutral point voltage, k pc k is the proportional control coefficient for neutral point voltage control. ic I is the integral regulation coefficient for neutral point voltage control. m This represents the amplitude of the three-phase inductor current; for The average value; Step 3) describes reducing the solution of the inequality with four degrees of freedom to one, ultimately determining the range of values ​​for one degree of freedom. Specifically, this includes obtaining... Afterwards, regarding the request The range formula needs to be modified. The constraint condition to be satisfied is (9): (9)； The variable represented by equation (10) is defined according to equation (9). ,get The range, i.e., equation (11). (10)； (11) ； Where S L S is the lower limit value of the free variable c1. H This represents the upper limit of the free variable c1.

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