A hybrid multi-level rectifier and a control method thereof
By adopting phase-cascaded rectifier and H-bridge unit structure and model predictive control in the multi-level converter, the control complexity and voltage balance problems of the multi-level converter are solved, and the output level is increased and the waveform quality is improved.
Patent Information
- Application Number
- CN202210390036.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-04-14
- Publication Date
- 2025-09-05
- Estimated Expiration
- 2042-04-14
AI Technical Summary
Multilevel converters have problems with coupled control methods, difficulty in capacitor voltage balancing, and an increased number of switching devices, leading to increased costs and low efficiency.
A phase-cascaded rectifier and H-bridge unit structure is adopted, combined with a Vienna rectifier and an H-bridge unit. The midpoint voltage balance and suspended capacitor voltage stability are achieved through voltage stabilization control. The model predictive control method is used to optimize the switching state and eliminate the voltage vector that causes current distortion.
The output level is improved, the number of switching tubes is reduced, the balance between the midpoint voltage and the floating capacitor voltage is ensured, the waveform quality and the simplicity of control are improved, and the amount of calculation is reduced.
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Figure CN114977851B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of power electronic converters, and in particular relates to a hybrid multi-level rectifier and a control method thereof. Background Art
[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.
[0003] As the "bridge" between the power grid and equipment, how to improve the performance and efficiency of power electronic converters is an urgent problem that needs to be solved.
[0004] Multilevel converters have garnered widespread attention in recent years due to their advantages, such as improved waveform quality, increased power density, and reduced electromagnetic interference. However, they also face a series of challenges, such as the coupling of control methods due to the combination of different topologies, making control scheme design difficult, capacitor voltage balancing difficulties, and increased costs due to the increased number of switching devices. Summary of the Invention
[0005] In order to overcome the above-mentioned deficiencies in the prior art, the present invention provides a hybrid multi-level rectifier, which achieves an increase in output level with fewer switching tubes.
[0006] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:
[0007] In a first aspect, a hybrid multi-level rectifier is disclosed, comprising:
[0008] A rectifier and an H-bridge unit are cascaded, wherein the rectifier outputs three levels to the H-bridge unit, and the H-bridge unit outputs seven levels per phase;
[0009] The voltages of the upper and lower capacitors on the DC side of the rectifier are kept equal to balance the midpoint voltage. The voltage of the floating capacitor in the H-bridge unit is controlled at a stable value through voltage stabilization control.
[0010] As a further technical solution, the rectifier is a Vienna rectifier, which includes two switching tubes and two diodes per phase, and the DC side voltage is u dc , according to different switch states and current directions, output u dc / 2,0,-u dc / 2 three levels.
[0011] As a further technical solution, each phase of the H-bridge unit includes four switching tubes and a capacitor. The capacitor works in a suspended state. By performing voltage regulation control on it, its voltage is controlled at the E value without adding an additional DC source, and three output levels are achieved: -E, 0, E;
[0012] The upper and lower switching tubes on the same bridge arm of the H-bridge unit operate in a complementary state.
[0013] In a second aspect, a control method for a hybrid multi-level rectifier is disclosed, comprising:
[0014] Establish a mathematical model of the hybrid multi-level rectifier, discretize the mathematical model, and predict the reference voltage value at the next moment based on the discretized model;
[0015] By coordinate rotation, the reference voltage vectors of different sectors are unified to the first sector;
[0016] In the first sector, the optimal space voltage vector that minimizes the current tracking cost function is obtained in the space voltage vector diagram to perform optimal current tracking;
[0017] Restoring the redundant switch state corresponding to the obtained optimal voltage vector to the initial sector of the reference voltage;
[0018] The redundant switch state corresponding to the optimal space voltage vector is substituted into the midpoint voltage and floating capacitor voltage balance value function to obtain the optimal switch state for achieving voltage balance.
[0019] As a further technical solution, it also includes:
[0020] Obtaining three-phase sampled current and three-phase grid-side sampled voltage of the hybrid multilevel rectifier;
[0021] Clark transformation is performed on the above current and voltage respectively to obtain the current value and voltage value in the two-phase stationary coordinate system.
[0022] As a further technical solution, a seven-level spatial voltage vector diagram in an αβ coordinate system is obtained based on the current and voltage values in a two-phase stationary coordinate system;
[0023] According to the current polarity, the spatial voltage vector diagram is divided into multiple sectors.
[0024] As a further technical solution, the current at the next moment is obtained based on a mathematical model of the hybrid multi-level rectifier.
[0025] As a further technical solution, optimal current tracking is performed in the first sector, specifically including:
[0026] Delete the voltage vector and switch state that cause current distortion;
[0027] Substitute the coordinates corresponding to the remaining voltage vector into the current tracking value function for calculation;
[0028] The voltage vector that minimizes the current tracking cost function is calculated as the voltage vector that achieves the optimal current tracking performance.
[0029] As a further technical solution, the current tracking value function is specifically:
[0030] g1=(u ref_αr (k+1)-u α ) 2 +(u ref_βr (k+1)-u β ) 2
[0031] Among them, the reference voltage u ref (u ref_α ,u ref_β ),
[0032] As a further technical solution, the value function of the balance between the midpoint voltage and the floating capacitor voltage is expressed as:
[0033]
[0034] λ1,λ2 are weight factors, and the midpoint voltage deviation is Δu dc , floating capacitor voltage u fx ,
[0035] One or more of the above technical solutions have the following beneficial effects:
[0036] The disclosed technical solution achieves an increase in output level with fewer switching tubes by cascading a Vienna rectifier and an H-bridge unit.
[0037] The technical solution disclosed in the present invention effectively achieves midpoint voltage balance.
[0038] The technical solution disclosed in the present invention controls the voltage of the floating capacitor in the H-bridge unit to a stable value through voltage stabilization control, without adding an additional DC source.
[0039] The technical solution disclosed in the present invention reduces the amount of calculation by rotating all voltage vectors to the same sector.
[0040] The technical solution disclosed in the present invention performs a qualitative analysis on the voltage vector and the switch state, removes the voltage vector and the switch state that cause current distortion, and ensures the quality of the output waveform.
[0041] The technical solution disclosed in the present invention is simple to implement, has strong scalability for parallel systems, is simple to apply, and is highly practical.
[0042] Advantages of additional aspects of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS
[0043] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.
[0044] Figure 1 is a topology diagram of a hybrid multi-level rectifier;
[0045] Figure 2 The current paths st1-st9 corresponding to different switching states of the hybrid multi-level rectifier;
[0046] Figure 3 It is a seven-level space voltage vector diagram;
[0047] Figure 4 This is an analysis diagram of the voltage vector and switch state that cause current distortion;
[0048] Figure 5 It is the voltage vector rotation process diagram;
[0049] Figure 6 This is the process diagram for restoring the switch state;
[0050] Figure 7 is the schematic diagram of midpoint voltage and suspended capacitor voltage;
[0051] Figure 8 is the three-phase current i of the hybrid multilevel rectifier a ,i b ,i c waveform;
[0052] Figure 9 is the phase current i of the hybrid multilevel rectifier a FFT analysis diagram of
[0053] Figure 10 is the DC side voltage u of the hybrid multilevel rectifier dc , upper capacitor voltage u P , lower capacitor voltage u N Waveform graph;
[0054] Figure 11 is the three-phase floating capacitor voltage u of the hybrid multilevel rectifier fa ,u fb ,u fc Waveform graph;
[0055] Figure 12 is the hybrid multilevel rectifier line voltage u ab Waveform graph;
[0056] Figure 13 Schematic diagram of hybrid multilevel rectifier control. DETAILED DESCRIPTION
[0057] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.
[0058] It should be noted that the terms used herein are for describing particular embodiments only and are not intended to limit the exemplary embodiments according to the present invention.
[0059] In the absence of conflict, the embodiments of the present invention and the features thereof may be combined with each other.
[0060] Example 1
[0061] This embodiment discloses a novel hybrid multi-level rectifier, comprising: a Vienna rectifier and an H-bridge circuit. The Vienna rectifier outputs three voltage levels, which are cascaded with the H-bridge circuit to achieve seven voltage levels per phase. Each phase H-bridge circuit includes four switching tubes and a floating capacitor.
[0062] Among them, the voltages of the upper and lower capacitors on the DC side of the Vienna rectifier should be kept equal to ensure the balance of the midpoint voltage.
[0063] The Vienna rectifier contains two switching tubes and two diodes per phase, and the DC side voltage is u dc (4E), according to different switch states and current directions, the output u dc / 2,0,-u dc Compared with the traditional T-type three-level rectifier, the Vienna rectifier saves 6 switching tubes, reducing equipment cost and power loss.
[0064] Each phase of the H-bridge unit contains four switching transistors and a capacitor. The capacitor operates in a suspended state. Voltage regulation controls its voltage at E, eliminating the need for an additional DC source. Three output levels are achieved: -E, 0, and E. The upper and lower switching transistors in the same arm of the H-bridge unit operate in a complementary state.
[0065] The Vienna rectifier's three phases share two DC-side capacitors, with each H-bridge unit having a floating capacitor. The technical solution in this example eliminates current distortion by analyzing the relationship between switch state and current polarity. By designing a value function, it achieves current tracking, midpoint voltage balance, and floating capacitor voltage balance.
[0066] Specifically, Figure 1It is a three-phase hybrid multi-level rectifier topology, which consists of a three-phase Vienna rectifier and three H-bridge units in cascade. Each phase of the Vienna rectifier contains two IGBT tubes S x5 、S x6 and 2 diodes D x1 、D x2 , S x5 With S x6 The working state is the same. By designing a control scheme, the DC side load voltage is controlled to u dc , the upper and lower capacitance values of the DC side are C dc , the voltage of the upper and lower capacitors on the DC side should be controlled to u dc / 2, so the voltage u x’o Can output -u dc / 2,0,u dc / 2 three levels, the three-phase H-bridge suspension capacitance value is C f , S x1 With S x2 , S x3 With S x4 Working in complementary state, the floating capacitor voltage u fx Should be controlled as u dc / 4, therefore, combined with different switching states and current directions, the entire hybrid multilevel rectifier can achieve u xo Generate 7 levels: -3u dc / 4, -2u dc / 4, -1u dc / 4,0,1u dc / 4,2u dc / 4,3u dc / 4, see Table 1 for details, where 1 corresponds to the switch being on and 0 corresponds to the switch being off. The simulation experiment parameters are set as follows: peak voltage of the grid e x =110V(x=a,b,c), grid voltage frequency f=50Hz, filter resistance R=0.2Ω, filter inductance L=4.5mH, load resistance R load =24Ω, DC side capacitance C d1 =C d2 =2350μF, H-bridge floating capacitor C fx =3300μF, DC side voltage u dc =200V, sampling period T S =100μS. The DC side does not contain a voltage source, but instead introduces a PI controller to achieve R load The voltage at both ends is controlled at u dc .
[0067] Table 1
[0068]
[0069] Figure 2 Figure 2 shows the current paths corresponding to different switching states of the mixed multi-level rectifier. It can be seen that the switching states of states st1 and st7 are the same, but the different current polarities result in different levels.
[0070] At the same time, due to the unidirectional conductivity of the diodes in the hybrid multilevel rectifier, some voltage vectors cannot function. If these voltage vectors are used in the control process, current distortion will occur, seriously affecting the normal operation of the hybrid multilevel rectifier.
[0071] Example 2
[0072] See attached Figure 13 As shown, based on the hybrid multi-level rectifier in Example 1, the purpose of this embodiment is to provide a control method for the hybrid multi-level rectifier, including:
[0073] The three-phase sampling current is transformed by Clark to obtain the current in the two-phase stationary coordinate system;
[0074] The three-phase grid-side sampling voltage is transformed by Clark to obtain the voltage value in the two-phase stationary coordinate system;
[0075] A mathematical model of the hybrid multi-level rectifier is established based on Kirchhoff's voltage law. The current at the next moment is obtained by Lagrangian extrapolation. Combined with the transformed current and voltage values, the reference voltage value at the next moment is calculated by discretized model predictive control.
[0076] By coordinate rotation, the reference voltage vectors of different sectors are unified into the first sector, which reduces the amount of calculation.
[0077] By designing a current tracking value function and finding the optimal space voltage vector that minimizes the value function in the space voltage vector diagram, optimal current tracking can be achieved.
[0078] Different from the traditional multi-level space voltage vector diagram, some vectors in the hybrid multi-level space voltage vector diagram need to be eliminated to prevent current distortion.
[0079] The redundant switch state corresponding to the obtained optimal voltage vector is restored to the initial sector of the reference voltage.
[0080] By designing the cost function of midpoint voltage and suspended capacitor voltage balance and substituting the redundant switch state corresponding to the optimal space voltage vector into the cost function, the optimal switch state for achieving voltage balance is obtained.
[0081] Specifically, Figure 3 The calculation formula for converting the abc three-phase coordinate system to the αβ coordinate system is:
[0082]
[0083] Where u ao ,u bo ,u co is the three-phase voltage of the hybrid multilevel rectifier, u α ,u β are the corresponding coordinates of the three-phase voltage of the hybrid multilevel rectifier converted to the αβ coordinate system.
[0084] The space voltage vector diagram includes 343(7 3 ) voltage vectors and 729(9 3 ) switch states, (2,3,3) represents the voltage of phases a, b, and c are 2u dc / 4,3u dc / 4,3u dc / 4, the unit length of the α axis represents u dc / 12, the unit length of the β axis represents According to the current polarity, the space voltage vector diagram can be divided into 6 sectors, see Table 2.
[0085] Table 2
[0086]
[0087] Figure 4 This is an analysis diagram of the voltage vector and switching state that cause current distortion. Taking the first sector as an example, the polarity of the three-phase current of abc is (+--). Combined with Table 1, the switching state of phase a must be limited to st4-st8, and the switching state st4-st6 cannot be used. Similarly, the switching state of phases b and c must be limited to st1-st6, and the switching state st7-st9 cannot be used. Figure 4 Taking the coordinate (0, 2E / 3) as an example, we analyze the switch states that cause current distortion. Table 3 categorizes the switch states corresponding to the coordinate (0, 2E / 3) into two categories: normal switch states and those that cause current distortion.
[0088] Table 3
[0089]
[0090]
[0091] Model predictive control has received extensive attention in the field of power electronics in recent years due to its advantages such as rapidity and ease of calculation. Therefore, the present invention adopts a model predictive control scheme to achieve current tracking, midpoint voltage balance, and suspended capacitor voltage balance. According to Kirchhoff's voltage law, a mathematical model of a hybrid multi-level rectifier is constructed.
[0092]
[0093] Where u xo (x=a,b,c) is the three-phase voltage, e x is the grid voltage, u on is the common mode voltage. Since the sum of the three-phase currents abc is 0, the common mode voltage is calculated as
[0094]
[0095] Define the coefficient k vx for
[0096]
[0097] Phase voltage u xo It can be calculated as
[0098]
[0099] By Clarke transformation, (5) can be calculated as
[0100]
[0101] The current can be calculated as
[0102]
[0103] Substituting (10) into (9), we can obtain
[0104]
[0105] In actual application, in order to compensate for the delay caused by sampling, (11) is moved forward by one time period to obtain the reference voltage u ref (u ref_α ,u ref_β ) in (k+1)T S Calculation expression of time
[0106]
[0107] Figure 5 Figure 1 is a schematic diagram of voltage vector rotation. Since the entire spatial voltage vector diagram contains 343 voltage vectors, it will bring a huge computational burden. Therefore, the vectors of sectors 2-5 are rotated to the first sector so that the current tracking calculation process is only completed in the first sector, which can reduce the computational burden. ref (u ref_α ,u ref_β ) is rotated to the first sector and recorded as u refr (u ref_αr ,u ref_βr), the calculation formula for the rotation process is
[0108]
[0109] Where S is u ref (u ref_α ,u ref_β )The sector it was in before rotation.
[0110] In order to achieve the optimal current tracking effect, the value function g1 is designed
[0111] g1=(u ref_αr (k+1)-u α ) 2 +(u ref_βr (k+1)-u β ) 2 (14)
[0112] Where u refr (u ref_αr ,u ref_βr ) represents the predicted reference voltage vector coordinates at the current moment, (u α ,u β ) represents the coordinates of the candidate space vector in the space voltage vector diagram.
[0113] In the first sector, the voltage vector and the switch state that cause current distortion are first deleted, and the coordinates (u α ,u β ) is substituted into the value function g1 for calculation, and the voltage vector that minimizes g1 is calculated as the voltage vector u to achieve the optimal current tracking performance. opt (u opt_α ,u opt_β ). From the space voltage vector diagram and Table 1, we can see that the optimal voltage vector u opt It usually includes several voltage vectors, and each voltage vector often includes several switching states. The redundant switching states provide control options for achieving midpoint voltage balance and suspended capacitor voltage balance.
[0114] Figure 6 This is the process diagram of the switch state restoration. It should be noted that after the rotation sector, the optimal voltage vector u obtained based on the value function g1 opt Only located in the first sector, if you continue to use u opt The switching state in the corresponding first sector acts on the hybrid multi-level rectifier, which will cause the switching state to be inconsistent with the original sector of the reference voltage. Therefore, the optimal voltage vector u opt The corresponding switch state is restored to the original reference voltage u ref (u ref_α ,uref_β ) is located in the sector. Assume that u opt The corresponding redundant switch state is (sta stb stc), which is restored to the original reference voltage u ref (u ref_α ,u ref_β ) is located in the sector is shown in Table 4.
[0115] Table 4
[0116]
[0117] Figure 7 is the DC side midpoint voltage and H-bridge suspension capacitor voltage flow path diagram. From the above analysis, we can know that the optimal voltage vector u opt It often corresponds to multiple switch states. By designing the value function of midpoint voltage balance and suspension capacitor voltage balance, the redundant switch states are substituted into the value function calculation to obtain the switch state that is most favorable to achieve midpoint voltage balance and suspension capacitor voltage balance. Define the midpoint current as i o , the current flowing through the upper capacitor on the DC side is i p , voltage is u P , the current flowing through the capacitor at the lower end of the DC side is i N , voltage is u N , the DC side midpoint voltage difference is Δu dc , we can get
[0118] i o +i P =i N (15)
[0119]
[0120]
[0121] Δu dc =u P -u N (18)
[0122] Combining the above formula, we can get the midpoint current i o Expression
[0123]
[0124] Using Euler's forward formula, the midpoint voltage deviation Δu dc The predicted value of is further calculated as
[0125]
[0126] The current i flowing through the floating capacitor fx Calculated as
[0127]
[0128] By using Euler's forward formula, the predicted value u of the suspended capacitor voltage can be obtained: fx Calculated as
[0129]
[0130] In order to achieve the midpoint voltage deviation Δu dc Control it to 0 as much as possible, the floating capacitor voltage u fx Control u as much as possible dc / 4, design value function g2
[0131]
[0132] Where λ1 and λ2 are weight factors for controlling the midpoint voltage balance and the floating capacitor voltage balance, Δudc is the midpoint voltage deviation, and ufx (x = a, b, c) is the voltage of the three-phase floating capacitor. This value can be flexibly adjusted according to actual conditions. By substituting the aforementioned redundant switch states into the value function g2, the switch state that minimizes g2 is calculated and applied to the hybrid multilevel rectifier to achieve midpoint voltage balance and floating capacitor voltage balance.
[0133] Figure 8 is the three-phase current i of the hybrid multilevel rectifier a ,i b ,i c Waveform,From the current waveform, we can see that, due to the elimination of inappropriate voltage vectors and switching states, the current waveform presents a good sine curve.
[0134] Figure 9 is the phase current i of the hybrid multilevel rectifier a From the FFT analysis chart, we can see that the current THD = 3.09%, which meets the requirement of less than 5%.
[0135] Figure 10 is the DC side voltage u of the hybrid multilevel rectifier dc , upper capacitor voltage u P , lower capacitor voltage u N Waveform diagram, we can see that the DC side voltage u dc Controlled at 200V, the upper and lower capacitor voltages are both 100V (u dc / 2), which proves the effectiveness of the control strategy for midpoint voltage balance.
[0136] Figure 11 is the three-phase floating capacitor voltage u of the hybrid multilevel rectifier fa ,u fb ,u fcWaveform, you can see that u fa ,u fb ,u fc All are controlled at 50V(u dc / 4), which proves the effectiveness of the control strategy for the voltage balance of the suspended capacitor. Figure 12 is the hybrid multilevel rectifier line voltage u ab waveform.
[0137] Although the above describes the specific embodiments of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without any creative work are still within the scope of protection of the present invention.
Claims
1. A control method for a hybrid multi-level rectifier, based on a hybrid multi-level rectifier, characterized in that: The hybrid multi-level rectifier comprises: A rectifier and an H-bridge unit are cascaded, wherein the rectifier outputs three levels to the H-bridge unit, and the H-bridge unit outputs seven levels per phase; The voltages of the upper and lower capacitors on the DC side of the rectifier are kept equal to balance the midpoint voltage, and the voltage of the floating capacitor in the H-bridge unit is controlled at a stable value through voltage stabilization control; The rectifier is a Vienna rectifier, which includes two switching tubes and two diodes per phase. The DC side voltage is u dc , according to different switch states and current directions, output u dc / 2,0,- u dc / 2 three levels; Each phase of the H-bridge unit includes four switching tubes and a capacitor. The capacitor works in a suspended state and its voltage is controlled by voltage regulation. E-value , no additional DC source is required, and three output levels are achieved:- E ,0, E ; The upper and lower switching tubes on the same bridge arm of the H-bridge unit operate in a complementary state; Control methods include: Establish a mathematical model of the hybrid multi-level rectifier, discretize the mathematical model, and predict the reference voltage value at the next moment based on the discretized model; By coordinate rotation, the reference voltage vectors of different sectors are unified to the first sector; In the first sector, the optimal space voltage vector that minimizes the current tracking cost function is obtained in the space voltage vector diagram to perform optimal current tracking; Restoring the redundant switch state corresponding to the obtained optimal space voltage vector to the initial sector of the reference voltage; The redundant switch state corresponding to the optimal space voltage vector is substituted into the midpoint voltage and floating capacitor voltage balance value function to obtain the optimal switch state for achieving voltage balance.
2. A control method for a hybrid multi-level rectifier according to claim 1, characterized in that: include: Obtaining three-phase sampled current and three-phase grid-side sampled voltage of the hybrid multilevel rectifier; Clark transformation is performed on the above current and voltage respectively to obtain the current value and voltage value in the two-phase stationary coordinate system.
3. A control method for a hybrid multi-level rectifier according to claim 2, characterized in that: Obtained based on the current and voltage values in the two-phase stationary coordinate system αβ Seven-level spatial voltage vector diagram in the coordinate system; According to the current polarity, the spatial voltage vector diagram is divided into multiple sectors.
4. A control method for a hybrid multi-level rectifier according to claim 1, characterized in that: The current at the next moment is obtained based on the mathematical model of the hybrid multi-level rectifier.
5. A control method for a hybrid multi-level rectifier according to claim 1, characterized in that In the first sector, optimal current tracking is performed, including: Delete the space voltage vector and switch state that cause current distortion; Substitute the coordinates corresponding to the remaining space voltage vector into the current tracking value function for calculation; The spatial voltage vector that minimizes the current tracking value function is calculated as the spatial voltage vector that achieves the optimal current tracking performance.
6. A control method for a hybrid multi-level rectifier according to claim 1, characterized in that: The current tracking value function is specifically: Among them, u refr ( u ref_αr , u ref_βr ) represents the predicted reference voltage vector coordinates at the current moment, ( u α , u β ) represents the coordinates of the candidate space vector in the space voltage vector diagram.
7. A control method for a hybrid multi-level rectifier according to claim 1, characterized in that: The value function of the balance between the midpoint voltage and the floating capacitor voltage is expressed as: λ 1, λ 2 is the weight factor, and the DC side voltage is u dc , the midpoint voltage deviation is Δ u dc , the floating capacitor voltage is u fx .
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