Three-cell energy storage power flow regulator control method and system

CN122801795APending Publication Date: 2026-09-22CHINA UNIV OF PETROLEUM (EAST CHINA)
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Patent Information

Application Number
CN202611281453.5
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-08-24
Publication Date
2026-09-22

AI Technical Summary

Technical Problem

尽管SiC MOSFET的开关损耗较低,但在高开关频率时的总开关损耗仍然非常大,需要进行改进优化,以降低总开关损耗和提升效率

Benefits of technology

(1)本申请提供的三电池储能空调整流器控制方法及系统,基于三电池储能空调整流器的三相指令电流和三相调制波指令电压生成叠加信号,根据三相调制波指令电压和叠加信号生成三相初始调制波,对三相初始调制波进行分裂生成形状存在明显钳位区间的三相分裂调制波,根据三相分裂调制波与载波的大小生成驱动信号,在钳位区间内控制SiCMOSFET功率开关器件不进行开关动作,能够有效减小开关损耗,提高效率。

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Abstract

The application belongs to the technical field of power electronics, and relates to a three-battery energy storage air regulator control method and system. A superimposed signal is generated based on three-phase instruction currents of a three-battery energy storage air regulator and three-phase modulation wave instruction voltages. Three-phase initial modulation waves are generated according to the three-phase modulation wave instruction voltages and the superimposed signal. The three-phase initial modulation waves are split to generate three-phase split modulation waves with obvious clamping intervals in shape. A driving signal is generated according to the size of the three-phase split modulation waves and a carrier wave. The SiC MOSFET power switching device is not controlled to perform switching action in the clamping interval, so that switching loss can be effectively reduced and efficiency can be improved.
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Description

Technical Field

[0001] This application belongs to the field of power electronics technology and relates to air conditioning regulator technology. Specifically, it relates to a control method and system for a three-battery energy storage air conditioning regulator. Background Technology

[0002] Energy storage air conditioners demonstrate irreplaceable value in three aspects: power supply and demand regulation, cost savings, and emergency support. Firstly, from the perspective of grid operation, energy storage air conditioners can store cheaper electricity during periods of low demand, releasing it for cooling during peak hours. This effectively alleviates the peak-valley difference in grid load, reduces the peak-shaving pressure on thermal power plants, and provides a storage method for surplus electricity from unstable renewable energy sources such as wind and solar power, facilitating their more efficient grid integration. Secondly, from a user perspective, energy storage air conditioners can fully utilize peak-valley electricity prices, significantly reducing the overall operating cost of air conditioning, making them particularly suitable for locations with high cooling demands and high power consumption, such as shopping malls and data centers. Thirdly, in emergency scenarios involving sudden power outages or grid interruptions due to extreme weather, energy storage air conditioners used in conjunction with energy storage batteries can operate independently of the public grid, continuously providing stable cooling for critical areas such as medical treatment and communication transmission.

[0003] The core function of an energy storage air conditioner dynamometer is to achieve efficient conversion and adaptation of electrical energy. It converts AC power from the grid into DC power to supply loads such as air conditioner compressors, and can also store electrical energy in energy storage batteries during off-peak hours. It is a key power management unit connecting the grid, energy storage system, and air conditioning loads. The grid transmits reactive power, which generates line losses, and some industrial electricity is charged separately based on reactive power. Therefore, the operation of an energy storage air conditioner dynamometer should aim to improve the power factor, i.e., reduce reactive power during operation, to reduce line losses and lower user electricity costs. Meanwhile, traditional air conditioner dynamometers use silicon insulated gate bipolar transistors (Si IGBTs), which have relatively high switching losses, limiting efficiency improvements. Newer silicon carbide metal-oxide-semiconductor field-effect transistors (SiC MOSFETs) with low switching losses can be used instead to improve efficiency. Although SiC MOSFETs have low switching losses, their total switching losses remain very high at high switching frequencies, necessitating improvements and optimizations to reduce total switching losses and increase efficiency. Therefore, there is an urgent need for an optimized control method and system for energy storage air conditioning current regulators that offers high power factor and high efficiency. Summary of the Invention

[0004] This application addresses the aforementioned problems in the existing technology by providing a control method and system for a three-battery energy storage air conditioning regulated current converter. Based on the three-phase command current and three-phase modulation wave command voltage of the three-battery energy storage air conditioning regulated current converter, a three-phase split modulation wave with a clear clamping interval is generated. Within the clamping interval, the SiC MOSFET power switching device does not perform switching action, which can effectively reduce switching losses and improve efficiency.

[0005] In a first aspect, this application provides a control method for a three-battery energy storage air conditioning regulator, comprising: Acquisition steps: Acquire the three-phase command current and three-phase modulation wave command voltage of the three-battery energy storage air conditioning regulated current unit; The superimposed signal generation steps are as follows: Take the maximum and minimum current values ​​from the three-phase command currents, add them together to obtain a first intermediate value, generate a second intermediate value k0 based on the magnitude of the first intermediate value, multiply the second intermediate value k0 by a first set coefficient and add a first constant to obtain a first signal; Take the maximum and minimum voltage values ​​from the three-phase modulation wave command voltages, subtract the second intermediate value k0 from the first constant, multiply the difference by the minimum voltage value to obtain a second signal, multiply the second intermediate value k0 by the maximum voltage value to obtain a third signal; Multiply the sum of the first, second, and third signals by a second set coefficient to obtain the superimposed signal; Modulation wave generation steps: Generate a three-phase initial modulation wave based on the three-phase modulation wave command voltage and the superimposed signal; Modulation wave splitting step: Multiply the difference obtained by subtracting the first constant from the initial modulation wave of phase i by the third set coefficient, and then perform amplitude limiting to obtain the first modulation wave of phase i. Let i = a, b, c; the sum of the initial modulation wave of phase i and the first constant is multiplied by the third set coefficient, and then the second modulation wave of phase i is obtained by amplitude limiting. The sum of the initial modulation wave of phase i and the second constant is multiplied by the third set coefficient, and then subjected to amplitude limiting to obtain the third modulation wave of phase i. ; Drive signal generation steps: Based on the first modulation wave of phase i With carrier The size generates the i-phase drive signal S i1 and i-phase drive signal S i2 According to the second modulation wave of phase i With carrier The size generates the i-phase drive signal S i3 and i-phase drive signal S i4 According to the i-phase third modulation wave With carrier The size generates the i-phase drive signal S i5 and i-phase drive signal Si6 ; Control steps: Discard the i-phase drive signal S i1 and i-phase drive signal S i6 Driven by i-phase signal S i3 Drive i-phase SiC MOSFET power switching device Q i1 Driven by i-phase signal S i2 Drive i-phase SiC MOSFET power switching device Q i2 Driven by i-phase signal S i5 Drive i-phase SiC MOSFET power switching device Q i3 Driven by i-phase signal S i4 Drive i-phase SiCMOSFET power switching device Q i4 .

[0006] In conjunction with the first aspect, in some embodiments, the method for generating a second intermediate value k0 based on the magnitude of the first intermediate value in the superimposed signal generation step includes: Determine if the first intermediate value is greater than 0; If yes, assign 1 to the second intermediate value k0; otherwise, assign 2 to the second intermediate value k0.

[0007] In conjunction with the first aspect, in some embodiments, the method for generating the three-phase initial modulation wave in the modulation wave generation step includes: adding the i-phase modulation wave command voltage to the superimposed signal, and then multiplying it by a fourth set coefficient to obtain the i-phase initial modulation wave.

[0008] In conjunction with the first aspect, in some embodiments, during the modulation wave splitting step, the limiting process employs a limiting module with a limiting value of 0 to 1 for limiting.

[0009] In conjunction with the first aspect, in some embodiments, in the drive signal generation step, an i-phase drive signal S is generated. i1 and i-phase drive signal S i2 The methods include: Compare the first modulation wave of phase i With carrier Size; If the first modulation wave of phase i Greater than or equal to carrier Then the i-phase drive signal S is obtained. i1 It is high level; if the first modulation wave of phase i is high. Less than carrier Then the i-phase drive signal S is obtained. i1 Low level; for i-phase drive signal S i1 Inverting the signal yields the i-phase drive signal S. i2 .

[0010] In conjunction with the first aspect, in some embodiments, in the drive signal generation step, an i-phase drive signal S is generated. i3 and i-phase drive signal S i4 The methods include: Compare the second modulation wave of phase i With carrier Size; If the second modulation wave of phase i Greater than or equal to carrier Then the i-phase drive signal S is obtained. i3 It is high level; if the second modulation wave of phase i is high. Less than carrier Then the i-phase drive signal S is obtained. i3 Low level; for i-phase drive signal S i3 Inverting the signal yields the i-phase drive signal S. i4 .

[0011] In conjunction with the first aspect, in some embodiments, in the drive signal generation step, an i-phase drive signal S is generated. i5 and i-phase drive signal S i6 The methods include: Compare the third modulation wave of phase i With carrier Size; If the third modulation wave of phase i Greater than or equal to carrier Then the i-phase drive signal S is obtained. i5 It is high level; if the third modulation wave of phase i is high. Less than carrier Then the i-phase drive signal S is obtained. i5 Low level; for i-phase drive signal S i5 Inverting the signal yields the i-phase drive signal S. i6 .

[0012] A second aspect of this application provides a control system for a three-battery energy storage air conditioning regulator, used to implement the control method for a three-battery energy storage air conditioning regulator described in the first aspect of this application, including: The acquisition module is used to acquire the three-phase command current and three-phase modulated wave command voltage of the three-battery energy storage air conditioning regulated current device; The setting module is used to set the carrier wave, the first setting coefficient, the second setting coefficient, the third setting coefficient, and the fourth setting coefficient. The superimposed signal generation module takes the maximum and minimum current values ​​from the three-phase command currents, adds them together to obtain a first intermediate value, generates a second intermediate value k0 based on the magnitude of the first intermediate value, multiplies the second intermediate value k0 by a first set coefficient and adds a first constant to obtain a first signal; it takes the maximum and minimum voltage values ​​from the three-phase modulation wave command voltages, subtracts the second intermediate value k0 from the first constant, multiplies the difference by the minimum voltage value to obtain a second signal, multiplies the second intermediate value k0 by the maximum voltage value to obtain a third signal; and multiplies the sum of the first, second, and third signals by a second set coefficient to obtain a superimposed signal. The modulation wave generation module generates a three-phase initial modulation wave based on the three-phase modulation wave command voltage and the superimposed signal. The modulation wave splitting module multiplies the difference between the initial modulation wave of phase i and the first constant by a third set coefficient, and then performs amplitude limiting to obtain the first modulation wave of phase i. Let i = a, b, c; the sum of the initial modulation wave of phase i and the first constant is multiplied by the third set coefficient, and then the second modulation wave of phase i is obtained by amplitude limiting. The sum of the initial modulation wave of phase i and the second constant is multiplied by the third set coefficient, and then subjected to amplitude limiting to obtain the third modulation wave of phase i. ; The drive signal generation module, based on the i-phase first modulation wave With carrier The size of the driving signal S is generated i1 and drive signal S i2 According to the second modulation wave of phase i With carrier The size of the driving signal S is generated i3 and drive signal S i4 According to the i-phase third modulation wave With carrier The size of the driving signal S is generated i5 and drive signal S i6 ; The control module is configured to: drive signal S i3 Drive i-phase SiC MOSFET power switching device Q i1 Through the drive signal S i2 Drive i-phase SiC MOSFET power switching device Q i2 Through the drive signal S i5 Drive i-phase SiC MOSFET power switching device Q i3 Through the drive signal S i4 Drive i-phase SiC MOSFET power switching device Q i4 .

[0013] In conjunction with the second aspect, in some embodiments, the superimposed signal generation module includes: The first comparison submodule is used to compare the magnitudes of the three-phase command currents to obtain the maximum and minimum current values. The second comparison submodule is used to compare the magnitudes of the three-phase modulated wave command voltages to obtain the maximum and minimum voltage values. The first adder is used to add the maximum current value and the minimum current value to obtain the first intermediate value; A selector is used to generate a second intermediate value k0 based on the size of a first intermediate value; The first calculation submodule is used to multiply the second intermediate value k0 by the first set coefficient and add the first constant to obtain the first signal; The second calculation submodule is used to multiply the difference obtained by subtracting the second intermediate value k0 from the first constant by the minimum voltage value to obtain the second signal. The first multiplier multiplies the second intermediate value k0 by the maximum voltage value to obtain the third signal; The third calculation submodule adds the first signal, the second signal, and the third signal together, multiplies the sum by a second set coefficient to obtain the superimposed signal.

[0014] In conjunction with the second aspect, in some embodiments, the modulation wave splitting module includes: The fourth calculation submodule is used to multiply the difference obtained by subtracting the first constant from the initial modulation wave of phase i by the third set coefficient to obtain the first intermediate wave of phase i. The first amplitude limiting submodule is used to perform amplitude limiting processing on the first intermediate wave of phase i to obtain the first modulated wave of phase i. ; The fifth calculation submodule is used to multiply the sum of the initial modulation wave of phase i and the first constant by the third set coefficient to obtain the second intermediate wave of phase i; The second amplitude limiting submodule is used to perform amplitude limiting processing on the second intermediate wave of phase i to obtain the second modulated wave of phase i. ; The sixth calculation submodule is used to multiply the sum of the initial modulation wave of phase i and the second constant by the third set coefficient to obtain the third intermediate wave of phase i; The third amplitude limiting submodule is used to perform amplitude limiting processing on the third intermediate wave of phase i to obtain the third modulation wave of phase i. .

[0015] Compared with the prior art, the advantages and positive effects of this application are as follows: (1) The control method and system for the three-battery energy storage air conditioning regulator provided in this application generates a superimposed signal based on the three-phase command current and the three-phase modulation wave command voltage of the three-battery energy storage air conditioning regulator. It generates a three-phase initial modulation wave based on the three-phase modulation wave command voltage and the superimposed signal. It splits the three-phase initial modulation wave to generate a three-phase split modulation wave with a clear clamping interval. It generates a drive signal based on the magnitude of the three-phase split modulation wave and the carrier wave. It controls the SiCMOSFET power switching device not to perform switching action within the clamping interval, which can effectively reduce switching losses and improve efficiency.

[0016] (2) The three-battery energy storage air conditioning regulated current control method and system provided in this application achieve a unity power factor with voltage and current out of phase and a high operating power factor. Attached Figure Description

[0017] Figure 1 This is the main circuit topology diagram of the battery energy storage air conditioning regulator in Embodiment 3 of this application; Figure 2 This is a flowchart of the three-battery energy storage air conditioning regulator control method described in the embodiments of this application; Figure 3 This is a schematic diagram illustrating the principle of signal superposition generation in an embodiment of this application; Figure 4 This is a schematic diagram illustrating the principle of modulated wave generation in an embodiment of this application; Figure 5 This is a schematic diagram illustrating the modulation wave splitting and driving signal generation in an embodiment of this application. Figure 6 This is a structural block diagram of the three-battery energy storage air conditioning regulator control system described in the embodiments of this application; Figure 7 This is a structural block diagram of the superimposed signal generation module described in an embodiment of this application; Figure 8 This is a structural block diagram of the modulation wave splitting module described in the embodiments of this application; Figure 9 This is a schematic diagram of the waveform of the first modulation wave of the three phases in an embodiment of this application; Figure 10 This is a schematic diagram of the waveform of the third-phase second modulation wave in an embodiment of this application; Figure 11 This is a schematic diagram of the waveform of the third modulation wave of the three phases in an embodiment of this application; Figure 12 A schematic diagram of the three-phase grid current waveforms using the three-battery energy storage air conditioning current regulator control method and system described in this application; Figure 13 The diagram shows the three-phase grid voltage and current waveforms for the control method and system of the three-battery energy storage air conditioning regulated current device described in this application. Detailed Implementation

[0018] The present application will now be described in detail with reference to the accompanying drawings through exemplary embodiments. However, it should be understood that, without further description, elements, structures, and features in one embodiment may be advantageously incorporated into other embodiments.

[0019] Figure 1 The diagram shows the topology of the main circuit for a three-battery energy storage air conditioning regulated circuit. (See also...) Figure 1 In the main circuit of the three-battery energy storage air conditioner regulated circuit, E1, E2, and E3 are DC-side batteries, C1, C2, and C3 are DC bus capacitors, and Q... a1 Q a2 Q a3 Q a4 For phase a, SiC MOSFET power switching devices, D a1 D a2 This is a SiC Schottky diode for phase a; Q b1 Q b2 Q b3 Q b4 For b-phase SiCMOSFET power switching devices, D b1 D b2 This is a SiC Schottky diode with phase b; Q c1 Q c2 Q c3 Q c4 For c-phase SiC MOSFET power switching devices, D c1 D c2 A SiC Schottky diode with c-phase; L a L b L c For a three-phase filter inductor, i a i b i c The three-phase current E generated by the main topology circuit a E b E c R is the three-phase grid voltage; R is the load resistance of the simulated air conditioner inverter and compressor.

[0020] Since the three-phase (a, b, c) bridge arms in the main circuit of the three-battery energy storage air conditioner regulated circuit are completely symmetrical, the connection method of the main circuit of the three-battery energy storage air conditioner regulated circuit will be explained using phase a as an example. See also... Figure 1DC-side battery E1 has its positive terminal connected to point P and its negative terminal connected to point O1; DC-side battery E2 has its positive terminal connected to point O1 and its negative terminal connected to point O2; DC-side battery E3 has its positive terminal connected to point O2 and its negative terminal connected to point N. The load resistor R is connected between points P and N. One end of the DC bus capacitor C1 is connected to point P and the other end to point O1; one end of the DC bus capacitor C2 is connected to point O1 and the other end to point O2; one end of the DC bus capacitor C3 is connected to point O2 and the other end to point N. Power switching device Q... a1 The source pole and X A1 Point connection, power switching device Q a1 The drain and power switching device Q a2 The drain of X A2 Point connection, power switching device Q a2 The source of the capacitor is connected to the DC bus capacitor C2 through point O1; the power switching device Q a3 The source pole and X A1 Point connection, power switching device Q a3 The drain and power switching device Q a4 The drain of X A3 Point connection, power switching device Q a4 The source of the SiC Schottky diode is connected to the DC bus capacitor C2 through point O2; a1 The cathode and DC bus capacitor C1 are connected through point P, and the SiC Schottky diode D... a1 anode and X A1 Point connection; SiC Schottky diode D a2 The cathode and DC bus capacitor C3 are connected through point N, and the SiC Schottky diode D... a2 anode and X A1 Point connection; Phase a filter inductor L a One end and X A1 One end is connected, and the other end is connected to the voltage E of phase a of the power grid. a Direct connection. The connection method of phase b and phase c bridge arms is the same as that of phase a bridge arm, and will not be described again here.

[0021] Regarding the aforementioned three-battery energy storage air conditioner regulated current converter, this application provides a control method and system for a three-battery energy storage air conditioner regulated current converter. The method generates a superimposed signal based on the three-phase command current and three-phase modulation wave command voltage of the three-battery energy storage air conditioner regulated current converter. It then generates a three-phase initial modulation wave based on the three-phase modulation wave command voltage and the superimposed signal. The method further splits the three-phase initial modulation wave to generate a three-phase split modulation wave with a clear clamping interval. Finally, it generates a drive signal based on the magnitude of the three-phase split modulation wave and the carrier wave. Within the clamping interval, the method controls the SiC MOSFET power switching device to not perform switching operations, effectively reducing switching losses and improving efficiency.

[0022] The following describes in detail the control method and system for the three-battery energy storage air conditioning regulator of this application, with reference to the accompanying drawings and embodiments.

[0023] See Figure 2 The first aspect of this application provides a control method for a three-battery energy storage air conditioning regulator, including: S1. Data acquisition steps: Acquire the three-phase command current and three-phase modulated wave command voltage of the three-battery energy storage air conditioning regulated current unit.

[0024] S2. Steps for generating superimposed signals: See [link / details] Figure 3 Take the command current of phase a. b-phase command current c-phase command current The maximum and minimum current values ​​are calculated, and the sum of these values ​​is used to obtain a first intermediate value. A second intermediate value k0 is generated based on this first intermediate value. The second intermediate value k0 is multiplied by a first set coefficient and then added to a first constant to obtain the first signal m1. The modulated wave command voltage of phase a is then taken. b-phase modulated wave command voltage c-phase modulated wave command voltage The maximum and minimum voltage values ​​are used to obtain the second signal m2 by multiplying the difference between the first constant and the second intermediate value k0 by the minimum voltage value. The second signal m3 is obtained by multiplying the second intermediate value k0 by the maximum voltage value. The sum of the first signal m1, the second signal m2, and the third signal m3 is multiplied by a second set coefficient to obtain the superimposed signal m. zs .

[0025] Specifically, the first constant is set to 1, the first set coefficient is set to -2, and the second set coefficient is set to -1. It should be noted that the first constant, the first set coefficient, and the second set coefficient can be set according to actual needs.

[0026] In this embodiment, a second intermediate value k0 is obtained by extracting the maximum and minimum values ​​of the three-phase command current. This is then combined with the maximum and minimum values ​​of the three-phase modulated wave command voltage, and a superimposed signal is generated using set coefficients and constants. The injected superimposed signal is obtained by coupling the amplitude characteristics of the three-phase command current on the current side with the characteristics of the modulated wave command voltage on the voltage side. The superimposed signal is no longer generated based on the three-phase modulated wave command voltage itself, but rather incorporates the actual operating conditions reflected by the maximum and minimum values ​​of the three-phase command current. The superimposed signal is adaptively adjusted according to the peak and valley characteristics of the three-phase command current, mitigating output voltage and current waveform distortion in the overmodulation region, reducing output harmonic content, minimizing current ripple caused by harmonics, and improving load stability.

[0027] Specifically, in one embodiment of this application, see also: Figure 3The method for generating a second intermediate value k0 based on the magnitude of the first intermediate value includes: Use the selector Switch1 to determine if the first intermediate value is greater than 0; If yes, assign 1 to the second intermediate value k0; otherwise, assign 2 to the second intermediate value k0.

[0028] In this embodiment, the first intermediate value is obtained by superimposing the maximum and minimum values ​​of the three-phase command current. It can intuitively reflect the overall amplitude reference and positive and negative operating status of the three-phase current. By determining whether the first intermediate value is greater than 0, it is possible to accurately and quickly distinguish whether the three-phase current is in a positive or negative operating condition. The accurate division of the working mode can be completed without complex calculations, providing an accurate basis for the differential adjustment of voltage and current coupling calculations in the future.

[0029] S3. Modulation wave generation steps: Generate the three-phase initial modulation wave based on the three-phase modulation wave command voltage and the superimposed signal.

[0030] Specifically, in one embodiment of this application, the method for generating a three-phase initial modulation wave includes: adding the i-phase modulation wave command voltage to the superimposed signal, and then multiplying it by a fourth set coefficient to obtain the i-phase initial modulation wave.

[0031] In this embodiment, on the one hand, a superimposed signal obtained by coupling current and voltage extrema is superimposed on the original modulation wave command voltage of each phase. This is equivalent to performing neutral point potential offset processing on the three-phase modulation wave, which can dynamically adjust the neutral point offset according to the output current condition. It no longer uses fixed zero-sequence component injection, and adapts to the modulation requirements under different load currents and unbalanced conditions. On the other hand, a third setting coefficient is introduced to perform amplitude scaling on the superimposed voltage. This can constrain the overall amplitude of the modulation wave, including the original modulation wave command voltage and the injected superimposed signal, to prevent the modulation wave amplitude from exceeding the maximum amplitude of the carrier wave and prematurely entering deep overmodulation. This avoids modulation wave clipping and ensures that the modulation wave always works within a controllable range, balancing voltage output capability and waveform distortion.

[0032] Specifically, see Figure 4 The method for generating the initial modulation wave of phase a includes: converting the command voltage of phase a modulation wave into the voltage of phase a. With superimposed signal m zs After addition, multiply by the fourth set coefficient to obtain the initial modulation wave of phase a. .

[0033] Specifically, see [link to relevant documentation] Figure 4 The method for generating the initial modulation wave of phase b includes: converting the phase b modulation wave command voltage... With superimposed signal m zs After addition, multiply by the fourth set coefficient to obtain the initial modulation wave of phase b. .

[0034] Specifically, see [link to relevant documentation] Figure 4 The method for generating the initial modulation wave of phase c includes: converting the command voltage of phase c modulation wave into a voltage of phase c. With superimposed signal m zs After addition, multiply by the fourth set coefficient to obtain the initial modulation wave of phase c. .

[0035] Specifically, the fourth setting coefficient is set to 3. It should be noted that the fourth setting coefficient can be set according to actual needs.

[0036] S4. Modulation wave splitting step: Multiply the difference obtained by subtracting the first constant from the initial modulation wave of phase i by the third set coefficient, and then perform amplitude limiting to obtain the first modulation wave of phase i. Let i = a, b, c; the sum of the initial modulation wave of phase i and the first constant is multiplied by the third set coefficient, and then the second modulation wave of phase i is obtained by amplitude limiting. The sum of the initial modulation wave of phase i and the second constant is multiplied by the third set coefficient, and then subjected to amplitude limiting to obtain the third modulation wave of phase i. .

[0037] In this embodiment, multi-dimensional offset reconstruction of the three-phase modulated wave is achieved through multi-constant differential and summation operations, constructing three differentiated modulated waves. By applying post-amplitude limiting processing to constrain the boundaries of the three sets of modulated waves, the amplitude of each modulated wave can be strictly limited to the effective operating range of the carrier, thereby preventing problems such as over-range modulation, deep over-modulation, and waveform clipping distortion.

[0038] Since the splitting process of each phase's initial modulation wave is exactly the same in the three-phase initial modulation waves, the splitting process is explained using the initial modulation wave of phase a as an example. For details, see [link to documentation]. Figure 5 The difference obtained by subtracting the first constant from the initial modulated wave of phase a is multiplied by the third set coefficient, and then the first modulated wave of phase a is obtained by the first limiting module Saturation1 with a limiting range of 0 to 1. The sum of the initial modulated wave of phase a and the first constant is multiplied by the third set coefficient, and then the sum is subjected to amplitude limiting processing by the second amplitude limiting module Saturation2, which limits the amplitude to 0 to 1, to obtain the second modulated wave of phase a. The sum of the initial modulated wave of phase a and the second constant is multiplied by the third set coefficient, and then the sum is subjected to the third limiting module Saturation3, which limits the amplitude to 0 to 1, to obtain the third modulated wave of phase a. .

[0039] Specifically, the second constant is set to 3, and the third coefficient is set to 1 / 2. It should be noted that the second constant and the third coefficient can be set according to actual needs.

[0040] S5. Drive signal generation steps: Based on the first modulation wave of phase i... With carrier The size generates the i-phase drive signal S i1 and i-phase drive signal S i2 According to the second modulation wave of phase i With carrier The size generates the i-phase drive signal S i3 and i-phase drive signal S i4 According to the i-phase third modulation wave With carrier The size generates the i-phase drive signal S i5 and i-phase drive signal S i6 .

[0041] In this embodiment, the three modulated waves obtained from each phase split are compared with the same carrier wave to generate six independent drive signals S. i1 -S i6 This method generates multiple drive pulses based on a single-carrier unified comparison logic. Compared to schemes using multiple staggered carriers, this eliminates additional harmonic disturbances introduced by phase differences between multiple carriers, ensuring coordinated and unified timing of each drive pulse. The three modulated waves independently participate in carrier comparison, enabling separate control of the on / off timing of power switching devices at different levels of the bridge arm. This accurately achieves three-level operating mode switching and avoids shoot-through risks caused by bridge arm switching timing errors. Furthermore, this pulse generation method has well-structured logic, is easy to programmatically implement with a digital controller, facilitates unified control of the modulation interval, effectively suppresses overmodulation, stabilizes the AC side output waveform quality, and is suitable for the operation requirements of a three-level rectifier powered by three series-connected batteries.

[0042] Specifically, in one embodiment of this application, an i-phase drive signal S is generated. i1 and i-phase drive signal S i2 The methods include: Compare the first modulation wave of phase i With carrier Size; If the first modulation wave of phase i Greater than or equal to carrier Then the i-phase drive signal S is obtained. i1 It is high level; if the first modulation wave of phase i is high. Less than carrier Then the i-phase drive signal S is obtained. i1 Low level; for i-phase drive signal S i1 Inverting the signal yields the i-phase drive signal S. i2 .

[0043] Specifically, in one embodiment of this application, an i-phase drive signal S is generated. i3and i-phase drive signal S i4 The methods include: Compare the second modulation wave of phase i With carrier Size; If the second modulation wave of phase i Greater than or equal to carrier Then the i-phase drive signal S is obtained. i3 It is high level; if the second modulation wave of phase i is high. Less than carrier Then the i-phase drive signal S is obtained. i3 Low level; for i-phase drive signal S i3 Inverting the signal yields the i-phase drive signal S. i4 .

[0044] Specifically, in one embodiment of this application, an i-phase drive signal S is generated. i5 and i-phase drive signal S i6 The methods include: Compare the third modulation wave of phase i With carrier Size; If the third modulation wave of phase i Greater than or equal to carrier Then the i-phase drive signal S is obtained. i5 It is high level; if the third modulation wave of phase i is high. Less than carrier Then the i-phase drive signal S is obtained. i5 Low level; for i-phase drive signal S i5 Inverting the signal yields the i-phase drive signal S. i6 .

[0045] Since the generation process of each phase drive signal in the three-phase drive signal is the same, the generation process of the drive signal is explained by taking the generation process of phase a drive signal as an example.

[0046] Specifically, see [link to relevant documentation] Figure 5 Generate phase a driving signal S a1 and phase a drive signal S a2 The methods include: Compare the first modulation wave of phase a With carrier Size; If phase a is the first modulation wave Greater than or equal to carrier Then the a-phase driving signal S is obtained. a1 It is a high level; if the first modulation wave of phase a is high. Less than carrier Then the a-phase driving signal S is obtained. a1 It is at a low level; for phase a drive signal Sa1 Inverting the signal yields the a-phase drive signal S. a2 .

[0047] Specifically, see [link to relevant documentation] Figure 5 Generate phase a driving signal S a3 and phase a drive signal S a4 The methods include: Compare the second modulation wave of phase a With carrier Size; If phase a is the second modulation wave Greater than or equal to carrier Then the a-phase driving signal S is obtained. a3 It is high level; if the second modulation wave of phase a is high level. Less than carrier Then the a-phase driving signal S is obtained. a3 It is at a low level; for phase a drive signal S a3 Inverting the signal yields the a-phase drive signal S. a4 .

[0048] Specifically, see [link to relevant documentation] Figure 5 Generate phase a driving signal S a5 and phase a drive signal S a6 The methods include: Compare the third modulation wave of phase a With carrier Size; If phase a is the third modulation wave Greater than or equal to carrier Then the a-phase driving signal S is obtained. a5 It is high level; if the third modulation wave of phase a is high level. Less than carrier Then the a-phase driving signal S is obtained. a5 It is at a low level; for phase a drive signal S a5 Inverting the signal yields the a-phase drive signal S. a6 .

[0049] S6, Drive Control Steps: Discard drive signal S i1 and drive signal S i6 Through the drive signal S i3 Drive i-phase SiCMOSFET power switching device Q i1 Through the drive signal S i2 Drive i-phase SiC MOSFET power switching device Q i2 Through the drive signal S i5 Drive i-phase SiC MOSFET power switching device Q i3 Through the drive signal S i4Drive i-phase SiC MOSFET power switching device Q i4 .

[0050] In this embodiment, the present invention innovatively employs differentiated driving logic that generates multiple drive signals and discards redundant signals. After generating multiple drive signals for the three modulated waves, it accurately selects the effective drive signal that matches the SiC MOSFET power switching device and discards the invalid redundant drive signal S. i1 S i6 To realize the Q of each phase power switching device i1 Q i2 Q i3 Q i4 The one-to-one precise drive. This group drive matching method perfectly matches the multi-tube topology of the three-battery energy storage air conditioning regulator, avoiding the defects of device drive misalignment and switch coordination disorder in traditional unified drive logic, and greatly improving the collaborative control accuracy of multi-switch topologies.

[0051] Since the three-phase bridge arms abc are completely symmetrical in the main circuit of the three-battery energy storage air conditioner regulated current device, the specific method of driving the power switching device with the drive signal is explained by taking the power switching device of phase a as an example.

[0052] Specifically, discard the drive signal S a1 and drive signal S a6 Through the drive signal S a3 Drive a-phase SiC MOSFET power switching device Q a1 Through the drive signal S a2 Drive a-phase SiC MOSFET power switching device Q a2 Through the drive signal S a5 Drive a-phase SiC MOSFET power switching device Q a3 Through the drive signal S a4 Drive a-phase SiC MOSFET power switching device Q a4 .

[0053] The second aspect of this application provides a control system for a three-battery energy storage air conditioner regulated flow, used to implement the three-battery energy storage air conditioner regulated flow control method described in the first aspect of this application.

[0054] See Figure 6 The three-battery energy storage air conditioning regulator control system includes: The acquisition module 100 is used to acquire the three-phase command current and three-phase modulated wave command voltage of the three-battery energy storage air conditioning regulated current device; The setting module 200 is used to set the carrier wave, the first setting coefficient, the second setting coefficient, the third setting coefficient, and the fourth setting coefficient; The superimposed signal generation module 300 takes the maximum and minimum current values ​​from the three-phase command currents, adds the maximum and minimum current values ​​to obtain a first intermediate value, generates a second intermediate value k0 based on the magnitude of the first intermediate value, multiplies the second intermediate value k0 by a first set coefficient and adds a first constant to obtain a first signal; it takes the maximum and minimum voltage values ​​from the three-phase modulation wave command voltages, subtracts the second intermediate value k0 from the first constant and multiplies the minimum voltage value to obtain a second signal, multiplies the second intermediate value k0 by the maximum voltage value to obtain a third signal; and multiplies the sum of the first signal, second signal, and third signal by a second set coefficient to obtain a superimposed signal. The modulation wave generation module 400 generates a three-phase initial modulation wave based on the three-phase modulation wave command voltage and the superimposed signal. The modulation wave splitting module 500 multiplies the difference between the initial modulation wave of phase i and the first constant by a third set coefficient, and then performs amplitude limiting processing to obtain the first modulation wave of phase i. Let i = a, b, c; the sum of the initial modulation wave of phase i and the first constant is multiplied by the third set coefficient, and then the second modulation wave of phase i is obtained by amplitude limiting. The sum of the initial modulation wave of phase i and the second constant is multiplied by the third set coefficient, and then subjected to amplitude limiting to obtain the third modulation wave of phase i. ; The drive signal generation module 600 generates a signal based on the first modulation wave of phase i. With carrier The size generates the i-phase drive signal S i1 and i-phase drive signal S i2 According to the second modulation wave of phase i With carrier The size generates the i-phase drive signal S i3 and i-phase drive signal S i4 According to the i-phase third modulation wave With carrier The size generates the i-phase drive signal S i5 and i-phase drive signal S i6 ; Control module 700 is configured to: drive the i-phase signal S i3 Drive i-phase SiC MOSFET power switching device Q i1 Driven by i-phase signal S i2 Drive i-phase SiC MOSFET power switching device Q i2 Driven by i-phase signal S i5 Drive i-phase SiC MOSFET power switching device Q i3 Driven by i-phase signal S i4 Drive i-phase SiC MOSFET power switching device Q i4 .

[0055] In this embodiment, the neutral point offset correction (superimposed signal) is constructed by extracting the extreme values ​​of the three-phase current. The original modulation wave is then superimposed with a unified zero-sequence component. The single-channel modulation wave is then split into three-channel modulation waveforms. The single carrier wave is compared with the multi-channel modulation wave to generate a multi-channel drive pulse. The SiC MOSFET power transistors of each phase are driven according to a preset mapping relationship to achieve stable operation of the three-level rectifier of the three-battery series energy storage air conditioner. This balances the DC-side series battery balance, AC-side current waveform quality, SiC device switching losses, and overall energy efficiency.

[0056] Specifically, see Figure 7 The superimposed signal generation module 300 includes: The first comparison submodule 301 is used to compare the magnitudes of the three-phase command currents to obtain the maximum and minimum current values. The second comparison submodule 302 is used to compare the magnitudes of the three-phase modulated wave command voltages to obtain the maximum and minimum voltage values. The first adder 303 is used to add the maximum current value and the minimum current value to obtain the first intermediate value; Selector 304 is used to generate a second intermediate value k0 based on the size of the first intermediate value; The first calculation submodule 305 is used to multiply the second intermediate value k0 by the first set coefficient and add the first constant to obtain the first signal; The second calculation submodule 306 is used to multiply the difference obtained by subtracting the second intermediate value k0 from the first constant by the minimum voltage value to obtain the second signal. The first multiplier 307 multiplies the second intermediate value k0 by the maximum voltage value to obtain the third signal; The third calculation submodule 308 adds the first signal, the second signal, and the third signal together and multiplies the sum by a second set coefficient to obtain the superimposed signal.

[0057] Specifically, see Figure 8 The modulation wave splitting module 500 includes: The fourth calculation submodule 501 is used to multiply the difference obtained by subtracting the first constant from the initial modulation wave of phase i by the third set coefficient to obtain the first intermediate wave of phase i. The first amplitude limiting submodule 502 is used to perform amplitude limiting processing on the i-phase first intermediate wave to obtain the i-phase first modulation wave. ; The fifth calculation submodule 503 is used to multiply the sum of the initial modulation wave of phase i and the first constant by the third set coefficient to obtain the second intermediate wave of phase i. The second amplitude limiting submodule 504 is used to perform amplitude limiting processing on the second intermediate wave of phase i to obtain the second modulation wave of phase i. ; The sixth calculation submodule 505 is used to multiply the sum of the initial modulation wave of phase i and the second constant by the third set coefficient to obtain the third intermediate wave of phase i. The third amplitude limiting submodule 506 is used to perform amplitude limiting processing on the third intermediate wave of phase i to obtain the third modulation wave of phase i. .

[0058] To verify the effectiveness of the control method and system for the three-battery energy storage air conditioning regulated converter described in this application, a simulation model was built in Matlab / Simulink. It should be noted that, to simplify the control loop of the three-battery energy storage air conditioning regulated converter, the simulation model adjusts the three-phase modulation wave command voltage. , , and three-phase grid voltage E a E b E c The amplitude and phase are used to obtain the desired current.

[0059] In the simulation model, the DC bus capacitance C1=C2=C3=1000μF, and the filter inductance L a =L b =L c =3mH. Three-phase modulated wave command voltage. , , The phases are 35.61°, -84.39°, and 155.61°, with a frequency of 50Hz and an amplitude of 0.95. The three-phase grid voltage E... a E b E c The phases are 40.11°, -79.89°, and 160.11°, with a frequency of 50Hz and an amplitude of 311V. The DC-side battery voltages E1, E2, and E3 are all set to 200V. Carrier m z The frequency is 10kHz, with a minimum and maximum value of 0 and 1 respectively. The load resistance R of the simulated air conditioner inverter and compressor is set to 150Ω.

[0060] Figures 9 to 11 The image shows the waveform of a three-phase split-modulation wave. Figures 9 to 11 It can be seen that the modulated wave m ij The shape of (i=a, b, c, j=1, 2, 3) has a clear clamping range. Within the clamping range, the SiC MOSFET does not perform switching operations, which can effectively reduce switching losses and improve efficiency.

[0061] Figure 12The figure shows the three-phase grid current waveforms using the three-battery energy storage air conditioning regulated current control method and system described in this application. The total harmonic distortion (THD) of the three-phase grid currents a, b, and c are 1.33%, 1.57%, and 1.62%, respectively, all below the 5% requirement of the national grid connection standard.

[0062] Figure 13 The diagram shows the three-phase grid voltage and current waveforms using the three-battery energy storage air conditioning regulated current control method and system described in this application. It can be seen that the three-phase AC voltage and three-phase AC current are in opposite phase, achieving unity power factor operation.

[0063] The simulation results above demonstrate the correctness and effectiveness of the three-battery energy storage air conditioning regulator control method and system described in this application.

[0064] The above embodiments are used to explain this application, not to limit it. Any modifications and changes made to this application within the spirit and scope of the claims shall fall within the protection scope of this application.

Claims

1. A control method for a three-battery energy storage air conditioning regulator, characterized in that, include: Acquisition steps: Acquire the three-phase command current and three-phase modulation wave command voltage of the three-battery energy storage air conditioning regulated current unit; The superimposed signal generation steps are as follows: Take the maximum and minimum current values ​​from the three-phase command currents, add them together to obtain a first intermediate value, generate a second intermediate value k0 based on the magnitude of the first intermediate value, multiply the second intermediate value k0 by a first set coefficient and add a first constant to obtain a first signal; Take the maximum and minimum voltage values ​​from the three-phase modulation wave command voltages, subtract the second intermediate value k0 from the first constant, multiply the difference by the minimum voltage value to obtain a second signal, multiply the second intermediate value k0 by the maximum voltage value to obtain a third signal; Multiply the sum of the first, second, and third signals by a second set coefficient to obtain the superimposed signal; Modulation wave generation steps: Generate a three-phase initial modulation wave based on the three-phase modulation wave command voltage and the superimposed signal; Modulation wave splitting step: Multiply the difference obtained by subtracting the first constant from the initial modulation wave of phase i by the third set coefficient, and then perform amplitude limiting to obtain the first modulation wave of phase i. , i = a, b, c; The sum of the initial modulation wave of phase i and the first constant is multiplied by the third set coefficient, and then subjected to amplitude limiting processing to obtain the second modulation wave of phase i. ; The sum of the initial modulation wave of phase i and the second constant is multiplied by the third set coefficient, and then subjected to amplitude limiting to obtain the third modulation wave of phase i. ; Drive signal generation steps: Based on the first modulation wave of phase i With carrier The size generates the i-phase drive signal S i1 and i-phase drive signal S i2 According to the second modulation wave of phase i With carrier The size generates the i-phase drive signal S i3 and i-phase drive signal S i4 According to the third modulation wave of phase i With carrier The size generates the i-phase drive signal S i5 and i-phase drive signal S i6 ; Drive control steps: Discard the i-phase drive signal S i1 and i-phase drive signal S i6 Driven by i-phase signal S i3 Drive i-phase SiC MOSFET power switching device Q i1 Driven by i-phase signal S i2 Drive i-phase SiC MOSFET power switching device Q i2 Driven by i-phase signal S i5 Drive i-phase SiC MOSFET power switching device Q i3 Driven by i-phase signal S i4 Drive i-phase SiCMOSFET power switching device Q i4 .

2. The control method for a three-battery energy storage air conditioning regulator as described in claim 1, characterized in that, In the signal superposition generation step, the method for generating the second intermediate value k0 based on the magnitude of the first intermediate value includes: Determine if the first intermediate value is greater than 0; If yes, assign 1 to the second intermediate value k0; otherwise, assign 2 to the second intermediate value k0.

3. The control method for a three-battery energy storage air conditioning regulator as described in claim 1, characterized in that, In the modulation wave generation step, the method for generating the three-phase initial modulation wave includes: adding the i-phase modulation wave command voltage and the superimposed signal, and then multiplying by the fourth set coefficient to obtain the i-phase initial modulation wave.

4. The control method for a three-battery energy storage air conditioning regulator as described in claim 1, characterized in that, In the modulation wave splitting step, the amplitude limiting process uses an amplitude limiting module with a limiting range of 0 to 1 for amplitude limiting.

5. The control method for a three-battery energy storage air conditioning regulator as described in claim 1, characterized in that, In the drive signal generation step, the i-phase drive signal S is generated. i1 and i-phase drive signal S i2 The methods include: Compare the first modulation wave of phase i With carrier Size; If the first modulation wave of phase i Greater than or equal to carrier Then the i-phase drive signal S is obtained. i1 It is high level; if the first modulation wave of phase i is high. Less than carrier Then the i-phase drive signal S is obtained. i1 Low level; for i-phase drive signal S i1 Inverting the signal yields the i-phase drive signal S. i2 .

6. The control method for a three-battery energy storage air conditioning regulator as described in claim 1, characterized in that, In the drive signal generation step, the i-phase drive signal S is generated. i3 and i-phase drive signal S i4 The methods include: Compare the second modulation wave of phase i With carrier Size; If the second modulation wave of phase i Greater than or equal to carrier Then the i-phase drive signal S is obtained. i3 It is high level; if the second modulation wave of phase i is high. Less than carrier Then the i-phase drive signal S is obtained. i3 Low level; for i-phase drive signal S i3 Inverting the signal yields the i-phase drive signal S. i4 .

7. The control method for a three-battery energy storage air conditioning regulator as described in claim 1, characterized in that, In the drive signal generation step, the i-phase drive signal S is generated. i5 and i-phase drive signal S i6 The methods include: Compare the third modulation wave of phase i With carrier Size; If the third modulation wave of phase i Greater than or equal to carrier Then the i-phase drive signal S is obtained. i5 It is high level; if the third modulation wave of phase i is high. Less than carrier Then the i-phase drive signal S is obtained. i5 Low level; for i-phase drive signal S i5 Inverting the signal yields the i-phase drive signal S. i6 .

8. A control system for a three-battery energy storage air conditioning regulator, used to implement the control method for a three-battery energy storage air conditioning regulator as described in any one of claims 1 to 7, characterized in that, include: The acquisition module is used to acquire the three-phase command current and three-phase modulated wave command voltage of the three-battery energy storage air conditioning regulated current device; The setting module is used to set the carrier wave, the first setting coefficient, the second setting coefficient, the third setting coefficient, and the fourth setting coefficient. The superimposed signal generation module takes the maximum and minimum current values ​​from the three-phase command currents, adds them together to obtain a first intermediate value, generates a second intermediate value k0 based on the magnitude of the first intermediate value, multiplies the second intermediate value k0 by a first set coefficient and adds a first constant to obtain a first signal; it takes the maximum and minimum voltage values ​​from the three-phase modulation wave command voltages, subtracts the second intermediate value k0 from the first constant, multiplies the difference by the minimum voltage value to obtain a second signal, multiplies the second intermediate value k0 by the maximum voltage value to obtain a third signal; and multiplies the sum of the first, second, and third signals by a second set coefficient to obtain a superimposed signal. The modulation wave generation module generates a three-phase initial modulation wave based on the three-phase modulation wave command voltage and the superimposed signal. The modulation wave splitting module multiplies the difference between the initial modulation wave of phase i and the first constant by a third set coefficient, and then performs amplitude limiting to obtain the first modulation wave of phase i. , i = a, b, c; The sum of the initial modulation wave of phase i and the first constant is multiplied by the third set coefficient, and then subjected to amplitude limiting processing to obtain the second modulation wave of phase i. ; The sum of the initial modulation wave of phase i and the second constant is multiplied by the third set coefficient, and then subjected to amplitude limiting to obtain the third modulation wave of phase i. ; The drive signal generation module, based on the i-phase first modulation wave With carrier The size generates the i-phase drive signal S i1 and i-phase drive signal S i2 According to the second modulation wave of phase i With carrier The size generates the i-phase drive signal S i3 and i-phase drive signal S i4 According to the third modulation wave of phase i With carrier The size generates the i-phase drive signal S i5 and i-phase drive signal S i6 ; The control module is configured to: drive the i-phase signal S i3 Drive i-phase SiC MOSFET power switching device Q i1 Driven by i-phase signal S i2 Drive i-phase SiC MOSFET power switching device Q i2 Driven by i-phase signal S i5 Drive i-phase SiCMOSFET power switching device Q i3 Driven by i-phase signal S i4 Drive i-phase SiC MOSFET power switching device Q i4 .

9. The three-battery energy storage air conditioning regulator control system as described in claim 8, characterized in that, The superimposed signal generation module includes: The first comparison submodule is used to compare the magnitudes of the three-phase command currents to obtain the maximum and minimum current values. The second comparison submodule is used to compare the magnitudes of the three-phase modulated wave command voltages to obtain the maximum and minimum voltage values. The first adder is used to add the maximum current value and the minimum current value to obtain the first intermediate value; A selector is used to generate a second intermediate value k0 based on the size of a first intermediate value; The first calculation submodule is used to multiply the second intermediate value k0 by the first set coefficient and add the first constant to obtain the first signal; The second calculation submodule is used to multiply the difference obtained by subtracting the second intermediate value k0 from the first constant by the minimum voltage value to obtain the second signal. The first multiplier multiplies the second intermediate value k0 by the maximum voltage value to obtain the third signal; The third calculation submodule adds the first signal, the second signal, and the third signal together, multiplies the sum by a second set coefficient to obtain the superimposed signal.

10. The three-battery energy storage air conditioning regulator control system as described in claim 8, characterized in that, The modulation wave splitting module includes: The fourth calculation submodule is used to multiply the difference obtained by subtracting the first constant from the initial modulation wave of phase i by the third set coefficient to obtain the first intermediate wave of phase i. The first amplitude limiting submodule is used to perform amplitude limiting processing on the first intermediate wave of phase i to obtain the first modulated wave of phase i. ; The fifth calculation submodule is used to multiply the sum of the initial modulation wave of phase i and the first constant by the third set coefficient to obtain the second intermediate wave of phase i; The second amplitude limiting submodule is used to perform amplitude limiting processing on the second intermediate wave of phase i to obtain the second modulated wave of phase i. ; The sixth calculation submodule is used to multiply the sum of the initial modulation wave of phase i and the second constant by the third set coefficient to obtain the third intermediate wave of phase i; The third amplitude limiting submodule is used to perform amplitude limiting processing on the third intermediate wave of phase i to obtain the third modulation wave of phase i. .