CN110138250B - Switched capacitor N-level inverter and modulation method thereof - Google Patents

Switched capacitor N-level inverter and modulation method thereof Download PDF

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CN110138250B
CN110138250B CN201910398262.0A CN201910398262A CN110138250B CN 110138250 B CN110138250 B CN 110138250B CN 201910398262 A CN201910398262 A CN 201910398262A CN 110138250 B CN110138250 B CN 110138250B
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capacitor
inverter
switch
switch tube
switched capacitor
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CN110138250A (en
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王要强
周成龙
李忠文
海德伦
王金凤
章健
梁军
王凯歌
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Zhengzhou University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/483—Converters with outputs that each can have more than two voltages levels
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/483—Converters with outputs that each can have more than two voltages levels
    • H02M7/4835—Converters with outputs that each can have more than two voltages levels comprising two or more cells, each including a switchable capacitor, the capacitors having a nominal charge voltage which corresponds to a given fraction of the input voltage, and the capacitors being selectively connected in series to determine the instantaneous output voltage
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/53—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/537—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
    • H02M7/5387—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration
    • H02M7/53871—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration with automatic control of output voltage or current
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/0067—Converter structures employing plural converter units, other than for parallel operation of the units on a single load
    • H02M1/007—Plural converter units in cascade

Abstract

The invention provides a switched capacitor N-level inverter and a modulation method thereof, wherein the inverter comprises a single direct current input power supply, a switched capacitor unit and a full-bridge unit; the switched capacitor unit is connected in parallel with the single direct current input power supply and is used for performing series-parallel conversion between the single direct current input power supply and a capacitor of the switched capacitor unit and outputting multi-step voltage; and the full-bridge unit is connected with the switched capacitor unit in parallel and is used for outputting the multi-step voltage output by the switched capacitor unit after positive and negative polarity conversion. The modulation strategy adopts a step wave specific harmonic elimination modulation mode based on the combination of specific harmonic elimination and step wave modulation. The inverter outputs any level by expanding the modular structure of the switch capacitor submodule, and the quantity of power devices of the inverter is greatly reduced by a simpler modular structure.

Description

Switched capacitor N-level inverter and modulation method thereof
Technical Field
The invention relates to the field of electric energy conversion and new energy distributed grid-connected power generation, in particular to a switched capacitor N-level inverter and a modulation method thereof.
Background
Energy is an important resource on which humans live. However, as people continue to exploit and utilize fossil energy, traditional fossil energy is depleted due to limited reserves, global energy crisis is being demonstrated, and the large exploitation and utilization of fossil energy also causes serious environmental pollution problems. Therefore, the development and utilization of abundant, clean and pollution-free renewable energy resources are receiving worldwide attention.
In a renewable energy power generation system, a power electronic inverter is a key link of electric energy conversion and transmission of the system, and the power electronic inverter has important influence on the working performance, the inversion efficiency, the system reliability and the like of the whole system. The multilevel inverter has the advantages of low harmonic content of output voltage, high quality of output electric energy, low voltage stress of a switching device, smaller output filter requirement and the like, and has important application prospect in a renewable energy combined power generation system.
In recent years, switched capacitor technology has been widely used in multilevel inverters. The switched capacitor technology is applied to the multi-level inverter, and the method has important research significance for improving the voltage regulation capacity of the multi-level inverter, widening the application range of the inverter and realizing the miniaturization, integration and high-efficiency development of the inverter. However, the traditional switched capacitor multi-level inverter has a fixed topological structure, single conversion, no structural expansion and few output levels; the existing extensible switched capacitor multi-level inverter needs more devices and has large voltage stress, so that the application range of the inverter is limited, and therefore, the novel inverter which is flexible in extension, small in device quantity and low in voltage stress is significant to find.
In order to solve the above problems, people are always seeking an ideal technical solution.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a switched capacitor N-level inverter and a modulation method of the switched capacitor N-level inverter.
In order to achieve the purpose, the invention adopts the technical scheme that: a switched capacitor N-level inverter comprises a single direct current input power supply, a switched capacitor unit and a full bridge unit;
the switched capacitor unit is connected in parallel with the single direct current input power supply and is used for performing series-parallel conversion between the single direct current input power supply and a capacitor of the switched capacitor unit and outputting multi-step voltage;
and the full-bridge unit is connected with the switched capacitor unit in parallel and is used for outputting the multi-step voltage output by the switched capacitor unit after positive and negative polarity conversion.
Based on the above, the switched capacitor unit includes a switched capacitor base module and a plurality of switched capacitor sub-modules connected in series;
the switch capacitor basic module comprises a switch tube S1.1、S1.2、S1.3、S1.4Capacitor C1Diode D0；
The switched capacitor submodule comprises a capacitor CiAnd two switching tubes Si.1、Si.2，i≥2；
The switch tube Si.1Input end and switch tube S of preceding stage switch capacitor submodule(i-1).1And a switch tube S of a rear-stage switch capacitor submodule(i+1).1Is connected with the input end of the switch tube Si.1And said capacitor CiAnode and switch tube S of post-stage switch capacitor submodule(i+1).2Is connected to the input terminal of the capacitor CiAnd the switching tube Si.2Is connected with the output end of the switch tube Si.2Input terminal and switching tube S of preceding stage switch capacitor submodule(i-1).1Output terminal of and capacitor C of preceding stage switch capacitor submodulei-1The anode of the anode is connected;
the anode of the single direct current input power supply and the switch tube S1.3、S1.2Is connected with the input end of the single direct current input power supply, and the negative electrode of the single direct current input power supply is connected with the switch tube S1.4Is connected with the output end of the switch tube S1.3Is connected with the diode D0The anode of (2), the diode D0Negative pole of (2) is connected with the switch tube S1.1Of the switching tube S1.4Respectively with the switching tube S1.2And said capacitor C1Are connected with each other.
A modulation method of the switched capacitor N-level inverter, wherein control signals of all switching devices in the inverter are determined according to the output level number of the inverter, and the control signals are determined by 2N square waves, and the modulation method comprises the following steps:
output voltage waveform Vout2n positive and negative symmetrical square waves VoiThe components are superposed, namely:
Figure GDA0002630430800000031
the amplitude and the initial conduction angle of each square wave are respectively +/-VdcN and thetaiAnd 0 < theta1＜…＜θi＜…＜θ2n＜π/2；
Square wave VoiThe fourier expansion of (a) is expressed as:
Figure GDA0002630430800000032
output voltage VoutThe fourier expansion of (a) is expressed as:
Figure GDA0002630430800000033
fundamental wave amplitude modulation degree MofComprises the following steps:
Figure GDA0002630430800000034
the Total Harmonic Distortion (THD) of the output waveform is:
Figure GDA0002630430800000035
eliminating the harmonic wave of a specific order in the step wave by adopting a specific harmonic elimination method, and calculating the initial conduction angle of the step wave, wherein the initial conduction angle calculation equation set comprises:
Figure GDA0002630430800000036
Figure GDA0002630430800000037
compared with the prior art, the invention has outstanding substantive characteristics and obvious progress, and particularly provides the switched capacitor N level inverter and the modulation method thereof.
Drawings
Fig. 1 is a block diagram of a topology of an inverter according to an embodiment of the present invention.
Fig. 2(a) is a schematic diagram of the operating current path of mode 1 when the inverter outputs 13 levels according to the embodiment of the present invention.
Fig. 2(b) is a schematic diagram of the operating current path of mode 2 when the inverter outputs 13 levels according to the embodiment of the present invention.
Fig. 2(c) is a schematic diagram of the operating current path of mode 3 when the inverter outputs 13 levels according to the embodiment of the present invention.
Fig. 2(d) is a schematic diagram of the operating current path of mode 4 when the inverter outputs 13 levels according to the embodiment of the present invention.
Fig. 2(e) is a schematic diagram of the operating current path of the mode 5 when the inverter outputs 13 levels according to the embodiment of the present invention.
Fig. 2(f) is a schematic diagram of the operating current path of the mode 6 when the inverter outputs 13 levels according to the embodiment of the present invention.
Fig. 2(g) is a schematic diagram of the operating current path of the mode 7 when the inverter outputs 13 levels according to the embodiment of the present invention.
Fig. 3 is a schematic diagram of a modulation strategy of an inverter according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of the control signal of the switching tube and the output level of the inverter according to the embodiment of the invention.
Fig. 5(a) is a waveform diagram of an inverter output voltage according to an embodiment of the present invention.
Fig. 5(b) is a waveform diagram of the inverter load current according to the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the following describes the technical solutions of the embodiments of the present invention clearly and completely, but the present invention is not limited to these embodiments:
a switched capacitor N-level inverter, the topology of which is shown in figure 1, comprises a single DC input power supply VdcA switched capacitor unit 1 and a full bridge unit 2;
the switched capacitor unit 1 and the single DC input power supply VdcConnected in parallel for carrying out said single DC input power supply VdcThe series-parallel conversion with the capacitor of the switched capacitor unit 1 is performed, and a multi-step voltage is output;
and the full-bridge unit 2 is connected in parallel with the switched capacitor unit 1 and is used for outputting the multi-step voltage output by the switched capacitor unit 1 after positive and negative polarity conversion.
Specifically, the switched capacitor unit comprises a plurality of switched capacitor sub-modules 11 connected in series;
the switch capacitor basic module comprises a switch tube S1.1、S1.2、S1.3、S1.4Capacitor C1Diode D0；
The switched capacitor submodule 11 comprises a capacitor CiAnd two switching tubes Si.1、Si.2，i≥2；
The switch tube Si.1Input end and switch tube S of preceding stage switch capacitor submodule(i-1).1And a switch tube S of a rear-stage switch capacitor submodule(i+1).1Is connected with the input end of the switch tube Si.1And said capacitor CiAnode and switch tube S of post-stage switch capacitor submodule(i+1).2Is connected to the input terminal of the capacitor CiAnd the switching tube Si.2Is connected with the output end of the switch tube Si.2Input terminal and switching tube S of preceding stage switch capacitor submodule(i-1).1Output terminal and capacitor of preceding stage switch capacitor submoduleCi-1The anode of the anode is connected;
the anode of the single direct current input power supply and the switch tube S1.3、S1.2Is connected with the input end of the single direct current input power supply, and the negative electrode of the single direct current input power supply is connected with the switch tube S1.4Is connected with the output end of the switch tube S1.3Is connected with the diode D0The anode of (2), the diode D0Negative pole of (2) is connected with the switch tube S1.1Of the switching tube S1.4Respectively with the switching tube S1.2And said capacitor C1Are connected with each other.
By expanding the switched capacitor submodule 11, the inverter structure of the present embodiment can output any level: 0. v + Vdc/n、…±iVdc/n、…±2Vdc(i ═ 1,2, … n); the relationship between the number of inverter output levels and the capacitance is: n is a radical oflevel＝4n+1。
For convenience of analysis, fig. 2 shows a specific example of the inverter operating state when the inverter output 13 of the present embodiment is at the level, and fig. 2(a) to (g) are schematic diagrams of the operating current paths of the positive half cycle when the inverter output 13 of the present embodiment is at the level. In the figure, the solid line indicates the current flow path in the forward direction of the current, and the broken line indicates the current flow path in the reverse direction of the current. The operation principle analysis of each operation state of the inverter is as follows:
mode 1: as shown in fig. 2 (a). In the structure of the switched capacitor, the switch tube S7、S9、S11、S12The other switching tubes are switched off, and the single direct current input power supply V is connecteddcSeries capacitor C1、C2、C3Generating 2VdcPositive step voltage of (d); switch tube S in full bridge circuit1、S4Conduction, S2、S3Cut off, the output level of the inverter is +2Vdc。
Mode 2: as shown in fig. 2 (b). In the structure of the switched capacitor, the switch tube S7、S9、S10The other switching tubes are switched off, and the single direct current input power supply V is connecteddcSeries capacitor C1、C2Generating 5VdcA forward step voltage of/3; switch tube S in full bridge circuit1、S4Conduction, S2、S3Cut off, the output level of the inverter is +5Vdc/3。
Modality 3: as shown in fig. 2 (c). In the structure of the switched capacitor, the switch tube S6、S7The other switching tubes are switched off, and the single direct current input power supply V is connecteddcSeries capacitor C1Generating 4VdcA forward step voltage of/3; switch tube S in full bridge circuit1、S4Conduction, S2、S3Cut off, the output level of the inverter is +4Vdc/3。
Modality 4: as shown in fig. 2 (d). In the structure of the switched capacitor, the switch tube S5、S8、S12The other switching tubes are switched off, and the single direct current input power supply V is connecteddcTo the capacitors C connected in series1、C2、C3Charging; on the other hand, the DC input power passes through the switch tube S of the full bridge circuit1、S4Supplying power to the load, the output level of the inverter is + Vdc。
Mode 5: as shown in fig. 2 (e). In the structure of the switched capacitor, the switch tube S8、S9、S10The other switch tubes are turned off, and the capacitor C is turned on1And C2Series discharge to produce 2VdcA forward step voltage of/3; switch tube S in full bridge circuit1、S4Conduction, S2、S3Cut off, the output level of the inverter is +2Vdc/3。
Modality 6: as shown in fig. 2 (f). In the structure of the switched capacitor, the switch tube S6、S8The other switch tubes are turned off, and the capacitor C is turned on1Discharge to produce VdcA forward step voltage of/3; switch tube S in full bridge circuit1、S4Conduction, S2、S3Cut off, inverter output level is + Vdc/3。
Modality 7: as shown in fig. 2 (g). In the structure of the switched capacitor, the switch tube S5、S8、S12The other switch tubes are turned offSaid single DC input power supply VdcTo the capacitors C connected in series1、C2、C3Charging; switch tube S in full bridge circuit2、S4And the conduction forms a closed follow current loop, and the output level of the inverter is 0.
When the inverter works in the modes 8, 9, 10, 11, 12 and 13, the working states of the inverter switched capacitor structure are respectively corresponding to the same working states as the modes 6, 5, 4, 3, 2 and 1. Switch tube S in full bridge circuit2、S3Conduction, S1、S4Turn-off, inverter output negative half cycle level-Vdc/3、-2Vdc/3、-Vdc、-4Vdc/3、-5Vdc/3、-2Vdc。
As the number of output levels increases, the maximum voltage stress borne by any switching tube in the inverter is always twice of the input voltage, and the voltage stress of the switching tube is low.
All working modes of the inverter are provided with reverse follow current loops corresponding to forward current paths of the inverter, and the inverter can be independently applied to inductive loads to provide reactive power.
Fig. 3 shows a schematic diagram of a modulation strategy when the inverter outputs 13 levels, and in each operating mode of the inverter, a modulation strategy is selected for each switching tube, so as to obtain a control signal of each switching tube, and each switching tube is controlled according to the control signal, so as to realize the output of the inverter. Fig. 4 is a graph showing the relationship between the control signal of each switching tube and the output level of the inverter in one working cycle.
The modulation strategy of the inverter adopts a step wave specific harmonic elimination modulation mode based on the combination of specific harmonic elimination and step wave modulation. The step wave modulation is based on a waveform synthesis principle, a plurality of square waves are superposed to form step waves, and the switching frequency of an inverter switching device always works at the fundamental frequency; the specific harmonic elimination method eliminates the output harmonic of a specific order by controlling the conduction time of the switching device, reduces the harmonic content of the output voltage and improves the output waveform quality. Based on the combination of specific harmonic elimination and step wave modulation, the step wave specific harmonic elimination modulation scheme can effectively reduce the harmonic content of the output voltage of the inverter and the switching frequency of a switching device, and improve the working performance of the inverter.
For the N-level inverter, based on the waveform synthesis principle, outputting a voltage waveform VoutCan be seen as 2n positive and negative symmetrical square waves VoiThe components are superposed, namely:
Figure GDA0002630430800000081
the amplitude and the initial conduction angle of each square wave are respectively +/-VdcN and thetaiAnd 0 < theta1＜…＜θi＜…＜θ2n＜π/2。
Square wave VoiThe fourier expansion of (a) can be expressed as:
Figure GDA0002630430800000082
output voltage VoutThe fourier expansion of (a) can be expressed as:
Figure GDA0002630430800000083
fundamental wave amplitude modulation degree MofComprises the following steps:
Figure GDA0002630430800000084
the Total Harmonic Distortion (THD) of the output waveform is:
Figure GDA0002630430800000085
the harmonic wave of specific order in the step wave is eliminated by adopting a specific harmonic elimination method, the initial conduction angle of the step wave is calculated, the harmonic content of the output step wave can be reduced, and the initial conduction angle calculation equation set is as follows:
Figure GDA0002630430800000086
Figure GDA0002630430800000087
fig. 5(a) and (b) show example waveforms of the output voltage and the load current of the inverter when the inverter outputs 13 levels according to the present invention, where the inverter output voltage in fig. 5(a) is an ideal 13-level step wave, and the load current in fig. 5(b) is a smooth sinusoidal waveform.
Finally, it should be noted that the above examples are only used to illustrate the technical solutions of the present invention and not to limit the same; although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art will understand that: modifications to the specific embodiments of the invention or equivalent substitutions for parts of the technical features may be made; without departing from the spirit of the present invention, it is intended to cover all aspects of the invention as defined by the appended claims.

Claims (5)

1. A switched capacitor N-level inverter, characterized in that: the single direct current input power supply, the switched capacitor unit and the full-bridge unit are included;
the switched capacitor unit is connected in parallel with the single direct current input power supply and is used for performing series-parallel conversion between the single direct current input power supply and a capacitor of the switched capacitor unit and outputting multi-step voltage;
the full-bridge unit is connected with the switched capacitor unit in parallel and is used for outputting the multi-step voltage output by the switched capacitor unit after positive and negative polarity conversion;
the switch capacitor unit comprises a switch capacitor basic module and a plurality of switch capacitor sub-modules which are connected in series;
the switch capacitor basic module comprises a switch tube S1.1、S1.2、S1.3、S1.4Capacitor C1Diode D0；
The switched capacitor submodule comprises a capacitor CiAnd two switching tubes Si.1、Si.2，i≥2；
The switch tube Si.1Input end and switch tube S of preceding stage switch capacitor submodule(i-1).1And a switch tube S of a rear-stage switch capacitor submodule(i+1).1Is connected with the input end of the switch tube Si.1And said capacitor CiAnode and switch tube S of post-stage switch capacitor submodule(i+1).2Is connected to the input terminal of the capacitor CiAnd the switching tube Si.2Is connected with the output end of the switch tube Si.2Input terminal and switching tube S of preceding stage switch capacitor submodule(i-1).1Output terminal of and capacitor C of preceding stage switch capacitor submodulei-1The anode of the anode is connected;
the anode of the single direct current input power supply and the switch tube S1.3、S1.2Is connected with the input end of the single direct current input power supply, and the negative electrode of the single direct current input power supply is connected with the switch tube S1.4Is connected with the output end of the switch tube S1.3Is connected with the diode D0The anode of (2), the diode D0Negative pole of (2) is connected with the switch tube S1.1Of the switching tube S1.4Respectively with the switching tube S1.2And said capacitor C1Are connected with each other.
2. The switched-capacitor N-level inverter of claim 1, wherein: the full-bridge unit comprises a switch tube S1、S2、S3And S4Said switch tube S1And S3And a switching tube S of the switched capacitor unitn.1Are connected, the switch tube S2And S4And the output end of the switch tube S1.4Connection, the switching tube S1And the switching tube S2Is connected with the anode as the output end of the inverter, and the switching tube S3Output terminal andthe switch tube S4Is connected as the negative pole of the inverter output.
3. The switched-capacitor N-level inverter according to claim 2, characterized in that: each switching tube is connected with a fly-wheel diode in parallel in a reverse direction.
4. The switched-capacitor N-level inverter of claim 3, wherein: the switch capacitor N level inverter outputs any level of 0 +/-Vdc/n、…±iVdc/n、…±2Vdc(i ═ 1,2, … n), where the relationship between the number of inverter output levels and the capacitance is: n is a radical oflevelN is the number of capacitors, V, 4n +1dcThe supply voltage is input for direct current.
5. A modulation method of the switched capacitor N-level inverter as claimed in claim 4, characterized in that: determining control signals of each switching device in the inverter according to the output level number of the inverter, wherein the control signals are determined by 2n square waves, and the method comprises the following steps:
output voltage waveform Vout2n positive and negative symmetrical square waves VoiThe components are superposed, namely:
Figure FDA0002630430790000021
the amplitude and the initial conduction angle of each square wave are respectively +/-VdcN and thetaiAnd is and
0＜θ1＜…＜θi＜…＜θ2n＜π/2；
square wave VoiThe fourier expansion of (a) is expressed as:
Figure FDA0002630430790000022
output voltage VoutThe fourier expansion of (a) is expressed as:
Figure FDA0002630430790000023
fundamental wave amplitude modulation degree MofComprises the following steps:
Figure FDA0002630430790000024
the Total Harmonic Distortion (THD) of the output waveform is:
Figure FDA0002630430790000031
eliminating the harmonic wave of a specific order in the step wave by adopting a specific harmonic elimination method, and calculating the initial conduction angle of the step wave, wherein the initial conduction angle calculation equation set comprises:
Figure FDA0002630430790000032
Figure FDA0002630430790000033
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