High-power multi-level digital waveform generator and multi-stage cooperative control method thereof

Abstract

The invention discloses a high-power multi-level digital waveform generator and a multi-stage cooperative control method thereof, and belongs to the technical field of power electronic waveform generators. The generator system is formed by connecting a plurality of power units in series, each power unit comprises an isolated DC-DC converter and an H-bridge module, outputs are cascaded to form a multi-level DC-AC converter, and after high-frequency harmonics are filtered out through a filter, an amplified instruction signal is generated to be used by a load. According to the invention, the requirement of high-fidelity output in a wide-amplitude range is met by dynamically and cooperatively adjusting the output voltage of the front-stage DC-DC converter and the modulation degree of the rear-stage DC-AC converter, the multi-level technology is applied to the high-power digital waveform generator, and the equivalent switching frequency of the system is greatly improved in a module cascading manner; the problem that the output fidelity of a traditional two-level digital waveform generator is limited by the switching performance of a device is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of power electronic waveform generators, and in particular relates to a high-power multi-level digital waveform generator and a multi-level coordinated control method thereof. Background Art

[0002] A waveform generator is an electronic device that can generate arbitrary waveforms, frequencies, and amplitudes. It can be used to measure the amplitude-frequency characteristics or transmission characteristics of various systems, and can also be used in actual production, including industrial scenarios such as pulse excitation sources, medical scenarios such as pacemakers, and communication scenarios for radio frequency signal generation. The output accuracy of a signal generator is its most critical parameter. In some specific high-precision systems, waveform generators are usually required to have high-precision tracking and output performance in a wide range and wide frequency range. However, due to the limitations of topology, control strategy, and modulation mechanism, digital waveform generators composed of traditional two-level converters are difficult to maintain high-precision output in a wide output range, especially at low modulation, and cannot achieve the output performance requirements within the full bandwidth of the system. In particular, when the output system requires the waveform generator to output with high fidelity when the modulation index of the input reference signal is very low, and when using traditional topology and control, the output voltage equivalent level number of the digital waveform generator will be significantly reduced, that is, the ability of the output voltage to approach the input signal will decrease, and the THD will increase rapidly as the modulation index decreases, making it difficult to meet the system's high-precision output requirements within a wide amplitude range. Summary of the invention

[0003] In order to solve the above-mentioned problems, the present invention proposes: a high-power multi-level digital waveform generator, the topology of which adopts a cascade of low-voltage modules to achieve high-voltage output; the generator system is composed of a plurality of power units connected in series, each power unit includes an isolated DC-DC converter and an H-bridge module, and the output is cascaded to form a multi-level DC-AC converter. After the high-frequency harmonics are filtered out by a filter, an amplified command signal is generated for use by the load.

[0004] A multi-level cooperative control method for a high-power multi-level digital waveform generator as described above comprises the following steps: a DC-DC converter provides a stable DC voltage, and n DC-AC converters are cascaded to convert it into a multi-level AC output, and after filtering out high-frequency harmonics through a filter, an amplified command signal is generated for use by the load; a high-fidelity output with a wide amplitude range is achieved by dynamically and cooperatively adjusting the output voltage of the front-stage converter and the modulation degree of the rear-stage converter; this topology introduces multi-levels into the high-power digital waveform generator, and improves the system equivalent switching frequency in a module cascade manner.

[0005] Furthermore, the front-stage control process of the front-stage DC-DC converter includes the following steps:

[0006] (1) First, for the front stage of the high-power multi-level digital waveform generator, let the output voltage of the n modules on the input side be V in , its input power is shared by n parallel DC-DC converters, that is, n DC-DC converters are connected in parallel, thus, the input power of the previous n DC-DC converters can be obtained as:

[0007]

[0008] Among them, P i1 ,P i2 ,…,P in are the input side powers of the 1st to the nth preceding DC-DC converters, i i1 ,i i2 ,…,i in are the input side currents of the 1st to the nth preceding DC-DC converters respectively;

[0009] (2) Ignoring the losses of the converter, the input power and output power of the DC-DC converter are equal, and the load power will be evenly distributed among the modules, thus obtaining:

[0010] P i1 :P i2 :…:P in =P o1 :P o2 :…:P on =1:1:…:1 (2)

[0011] Among them, P o1 ,P o2 ,…,P on Respectively represent the output power of the first to nth subsequent DC-AC converters, control the output voltages of n DC-DC submodules to be equal, and ensure that the output power of each module is equal;

[0012] (3) The control strategy of the front-stage DC-DC converter includes three control links, namely: the system output voltage control loop, the sub-module voltage equalization control loop and the current control loop; the system output voltage control loop adjusts the output of the front-stage DC-DC converter to reach the specified DC voltage value; on this basis, the sub-module voltage equalization control loop is inserted to achieve dynamic balance of the sub-module output voltage; finally, in order to meet the needs of the high-power waveform generator to output fast tracking reference instructions within a wide frequency conversion range, a current control loop is added to improve the dynamic response speed of the system.

[0013] Furthermore, the control strategy of the subsequent DC-AC converter includes the following steps:

[0014] (1) First, since the output side of each DC-AC converter in the rear stage of the high-power multi-level digital waveform generator is cascaded, the output voltage of the i-th unit is expressed as (S Ai -S Bi ) dci , since the current of all submodules is proportional to the output inductor current i L equal, therefore, the output power of each submodule is obtained as:

[0015]

[0016] Among them, u dc1 ,u dc2 ,…,u dcn Respectively represent the input voltages of the 1st to nth DC-AC converters;

[0017] (2) In order to reduce the size of the filter, the cascaded DC-AC converter adopts single-pole frequency multiplication modulation. Therefore, the output voltage of the i-th DC-AC converter can be expressed as:

[0018]

[0019] (3) Since the modulation signal of each DC-AC converter unit in the subsequent stage is the same, ignoring the influence of higher harmonics, it can be obtained that the output power of the first to nth DC-DC converters satisfies the following formula:

[0020]

[0021] (4) Since the output fundamental voltage amplitude u of the DC-AC converter abi With the previous DC voltage u dci Proportional to each other, let the ratio be the modulation index M. The rear-stage DC-AC converter can be equivalent to a series output load relative to the front-stage DC-DC converter.

[0022] Furthermore, the control idea of ​​the subsequent DC-AC converter is to achieve equivalent high modulation index output and dynamic compensation of low-order harmonics by dynamically adjusting the modulation index M'. Dynamic adjustment of the modulation index M' can suppress the double frequency ripple of the DC voltage and improve the waveform quality of the output AC voltage. By adjusting the equivalent output modulation index, the system can be kept running at a high modulation index.

[0023] Furthermore, the control part of the post-stage DC-AC converter includes three parts: a modulation index dynamic adjustment part, a dead zone compensation part and a carrier phase shift modulation part;

[0024] (1) The dynamic adjustment process of modulation index is as follows: when the output voltage required by the load is low, the invented method reduces the DC bus voltage command value to keep the inverter running at an equivalent high modulation index. In addition, by real-time detection of the DC bus voltage value, the modulation index M' is dynamically adjusted in a small range. In order to minimize the impact of the DC side double frequency ripple on the AC side output, it is necessary to extract the amplitude information of the amplified signal source signal |u s | and phase information sin(ω s t) to obtain the dynamic modulation degree M';

[0025] (2) Dead zone compensation control is: sampling the load current and superimposing a rectangular compensation voltage with the same amplitude and opposite phase as the dead zone error wave according to its direction, and superimposing it on the modulation signal;

[0026] (3) Carrier phase-shift PWM modulation part: 2N triangular carriers with a phase difference of π / N are constructed through FPGA and compared with the modulation signal, thereby realizing unipolar frequency-doubled carrier phase-shift PWM modulation.

[0027] Furthermore, where M0 is less than 1 but close to 1, the DC side voltage command value U of the DC-DC converter can be obtained. r ' ef for:

[0028]

[0029] When the AC output command of the high-power multi-level digital waveform generator changes, the DC side command of the DC-DC converter will also be adjusted accordingly, thereby ensuring that the subsequent DC-AC converter maintains the output under the high modulation index M0; in addition, in order to keep the adjusted system output waveform unaffected, it is necessary to meet the following conditions:

[0030]

[0031] Then the dynamic modulation degree M' expression superimposed with the previous stage signal is obtained:

[0032]

[0033] Real-time detection of the sum of the output voltages of the preceding DC-DC converters Then the dynamic modulation index M' is calculated; dynamic compensation of modulation index is realized, which can suppress the double frequency fluctuation of the DC side bus, reduce the impact on the output AC voltage quality, and keep the system running at an equivalent high modulation index; then the expression of the output u of the high-power multi-level digital waveform generator under the coordinated control of the present invention is derived as follows:

[0034]

[0035] According to the above, the waveform generator can maintain high-fidelity output characteristics under any load condition.

[0036] The beneficial effects of the present invention are as follows: the present invention is a high-power multi-level digital waveform generator, the power unit is input by three-phase AC mains, after diode rectification, stable DC is obtained by DC-DC converter, and finally multi-level output is obtained by cascading H-bridge converters. After passing through the LC filter, the switching high-order harmonics can be filtered out to obtain the amplified command signal and connect to the load. Under the working condition of output amplitude variation, high-fidelity output with a wide amplitude range is achieved by dynamically adjusting the output voltage of the front-stage DC-DC converter and the modulation index of the rear-stage DC-AC converter. This topology applies multi-level technology to high-power digital waveform generators, and improves the equivalent switching frequency of the system by means of module cascading, solving the problem that the output fidelity of the traditional two-level digital waveform generator is limited by the switching performance of the device, and has the advantages of wide range regulation, low voltage stress, low electromagnetic interference, low switching loss and high-quality output. The specific advantages are as follows:

[0037] 1) Dynamically adjust the DC bus voltage, improve the equivalent output modulation, and reduce the high-order harmonic content of the system when the output is low;

[0038] 2) Dynamically adjust the modulation index to offset the low-order harmonics caused by the double frequency ripple on the DC side, greatly improving the output fidelity of the system; BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a topological diagram of a high-power multi-level digital waveform generator;

[0040] Figure 2 It is a schematic diagram of multi-level coordinated control of a high-power multi-level digital waveform generator;

[0041] Figure 3 This is the control block diagram of the DC-AC converter at the back end of a high-power multi-level digital waveform generator. DETAILED DESCRIPTION

[0042] In order to make the technical means and objectives of the present invention easy to understand, the present invention is further described below in conjunction with specific implementation methods. A high-power multi-level digital waveform generator, such as Figure 1As shown, the topology device adopts a modular structure of low-voltage cascade high-voltage output, which is composed of N power units cascaded, and each power unit module consists of a front-stage DC-DC converter and a rear-stage DC-AC converter. The front stage is composed of an isolated DC-DC converter, and the rear stage is composed of N H-bridge converters cascaded to form a multi-level converter. The power unit obtains stable DC from the DC-DC converter, and finally obtains a multi-level output through the cascade of H-bridge converters. After passing through the filter, the switching high-order harmonics can be filtered out, and the amplified command signal is obtained and connected to the load. Under the condition of output amplitude changes, high-fidelity output with a wide amplitude range is achieved by dynamically adjusting the output voltage of the front-stage DC-DC converter and the modulation degree of the rear-stage DC-AC converter. This topology applies multi-level technology to high-power digital waveform generators, improves the equivalent switching frequency of the system by module cascading, and solves the problem that the output fidelity of the traditional two-level digital waveform generator is limited by the switching performance of the device. It has the advantages of wide range adjustment, low voltage stress, low electromagnetic interference, low switching loss and high-quality output.

[0043] Typically, the output system requires a high-power multi-level digital waveform generator to output with high fidelity over a wide range of amplitudes. When the modulation index of the input reference signal is very low, the number of equivalent levels of the output voltage under traditional control will be significantly reduced, that is, the ability of the output voltage to approach the input signal decreases, and the THD will increase rapidly as the modulation index decreases. To this end, based on the multi-level digital waveform generator topology structure proposed in the present invention, a multi-level collaborative control strategy is proposed. By dynamically adjusting the DC side voltage of the front-stage DC-DC converter and the modulation index of the rear-stage DC-AC converter, the waveform generator is kept running at an equivalent high modulation index to reduce high-order harmonics, while suppressing the output low-order harmonics caused by the double frequency ripple on the DC side, thereby achieving high-fidelity output of the system over a wide range of amplitudes. The overall control structure of the proposed multi-level collaborative control strategy is as follows: Figure 2 As shown in the figure, it includes two parts: the front-stage control and the rear-stage control. The following is a detailed introduction to the control of the two parts.

[0044] For the front stage of a high-power multi-level digital waveform generator, the voltage of n modules can be expressed as V in , its input power is shared by n DC-DC converters, that is, n DC-DC converters are connected in parallel. It can be obtained that the input power of n DC-DC converters is:

[0045]

[0046] Among them, P i1 ,P i2 ,…,P in are the input power of the previous DC-DC converter, i i1 ,i i2 ,…,iin They are the input currents of the previous DC-DC converter respectively.

[0047] The loss of the converter is not considered here, that is, the input power of the DC-DC converter is equal to the output power, so the power between the modules can be evenly distributed, and we can get:

[0048] P i1 :P i2 :…:P in =P o1 :P o2 :…:P on =1:1:…:1 (2)

[0049] Among them, P o1 ,P o2 ,...,P on They respectively represent the output power of the subsequent DC-AC converter.

[0050] Therefore, by controlling the voltage balance between submodules, the output power balance between modules can be achieved. For the back stage of the high-power multi-level digital waveform generator, the output side of each DC-AC converter is connected in series. The output voltage of each unit i can be expressed as (S Ai -S Bi ) dci The current flowing through all submodules is the same output inductor current i L , the output power of each submodule can be obtained as:

[0051]

[0052] Among them, u dc1 ,u dc2 ,...,u dcn Respectively represent the input voltage of the DC-AC converter.

[0053] Taking unipolar frequency multiplication modulation as an example, the output voltage expression of each DC-AC converter can be obtained as follows:

[0054]

[0055] Since the modulation signal of each module of the subsequent DC-AC converter unit is the same, ignoring the higher harmonics, the power output of each DC-DC converter submodule can be obtained as follows:

[0056]

[0057] The output fundamental voltage amplitude u of the DC-AC converter abi With the previous DC voltage u dciThe ratio is the modulation index M. Therefore, the rear-stage DC-AC converter can be equivalent to a series output load for the front-stage DC-DC converter.

[0058] In order to better ensure the consistency of the DC side bus voltage of each module, reduce the DC side ripple to improve the output accuracy of the high-power multi-level digital waveform generator. The overall control system of the front-stage DC-DC converter includes three control loops: system output voltage control loop, sub-module voltage balancing control loop and current control loop. Among them, the system output voltage control loop is used to control the front-stage DC-DC converter to reach the specified DC voltage value. In actual engineering applications, the parameters of multiple modules cannot be guaranteed to be completely consistent, which will cause the total output DC side voltage to fluctuate, and then cause low-order harmonics in the output voltage of the digital waveform generator, affecting the output distortion. Therefore, a sub-module voltage balancing control loop is added to ensure the dynamic balance of the sub-module output voltage. In addition, in order to meet the needs of the waveform generator to quickly and dynamically adjust the DC side voltage under alternating output conditions, a current control loop is added to improve the dynamic response speed of the system.

[0059] The idea of ​​high-precision output tracking control is to achieve equivalent high modulation index output and low-order harmonic dynamic compensation by dynamically adjusting the modulation index M'. The dynamic modulation index M' can achieve two functions. On the one hand, it is used to compensate for the impact of the DC voltage double frequency ripple on the output AC voltage. On the other hand, it is used to adjust the equivalent output modulation index so that the system can operate at a high modulation index.

[0060] The control block diagram of the rear stage DC-AC converter is as follows: Figure 3 As shown, it includes three parts: dynamic modulation adjustment part, dead zone compensation part, and carrier phase shift PWM modulation. The idea of ​​dynamic modulation adjustment is: when the output is externally displayed as a low-frequency modulation, the DC bus voltage command is correspondingly reduced, so that the inverter remains in operation under an equivalent high modulation. And by real-time detection of the DC bus voltage value, the value of the modulation M' is dynamically adjusted in a small range, so that the system can compensate for the impact of the DC side double frequency ripple on the AC side output to the maximum extent. In the specific implementation, it is necessary to extract the amplitude information of the signal source to be amplified |u s | and phase information sin(ω s t) to obtain the value of dynamic modulation. The dead zone compensation part is realized by detecting the direction of the load current to superimpose a rectangular compensation voltage with the same amplitude and opposite phase as the dead zone error wave to the modulation wave signal. The carrier phase shift PWM part uses 2N triangular carriers with a phase difference of π / N to form a unipolar frequency-doubled CPS-SPWM modulation.

[0061] In order to prevent overshoot, this chapter sets M0 to a value less than 1 but close to 1 (such as 0.9). The DC-DC converter DC side command voltage U r 'ef as follows:

[0062]

[0063] When the AC output command of the high-power multi-level digital waveform generator changes, the DC-DC converter's DC side command will also change accordingly, so that the DC-AC converter can maintain output at a high modulation index M0. And in order to keep the adjusted system output waveform unaffected, the following formula needs to be maintained:

[0064]

[0065] Therefore, the dynamic modulation degree M' with the previous stage signal superimposed can be expressed as follows:

[0066]

[0067] By real-time detection of the sum of the output voltages of the preceding DC-DC converter The dynamic modulation index M' can be obtained. Through dynamic compensation of the modulation index, the influence of the double frequency fluctuation of the DC bus can be offset, and the system can be kept running at a high modulation index. In order to verify the effectiveness of the proposed control, the expression of the output u of the high-power multi-level digital waveform generator under the proposed coordinated control is derived as follows:

[0068]

[0069] It can be seen that the fundamental amplitude under the proposed control is consistent with the ideal situation when the DC side is fixed. The dynamic modulation can offset the third harmonic caused by the double frequency ripple and improve the output performance of the system. However, there are still a small amount of carrier and its sideband harmonics caused by the double frequency of the DC side in the system, and the amplitude of this part of the harmonics is related to the output power, DC side capacitance value and output frequency. Considering that the harmonic content of this part is relatively small, and the switching harmonics are easily filtered out, they can be ignored.

[0070] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical solutions and concepts of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A high-power multi-level digital waveform generator, characterized in that: The topology adopts low-voltage module cascade to achieve high-voltage output; the generator system is composed of multiple power units in series, each power unit contains an isolated DC-DC converter and an H-bridge module, and the output is cascaded to form a multi-level DC-AC converter. After the high-frequency harmonics are filtered out by the filter, an amplified command signal is generated for the load to use.

2. A multi-level coordinated control method for a high-power multi-level digital waveform generator as claimed in claim 1, characterized in that: The method comprises the following steps: a DC-DC converter provides a stable DC voltage, and n DC-AC converters are cascaded to convert it into a multi-level AC output. After filtering out high-frequency harmonics, an amplified command signal is generated for use by the load; a high-fidelity output with a wide amplitude range is achieved by dynamically and cooperatively adjusting the output voltage of the preceding converter and the modulation index of the succeeding converter; the topology introduces multi-levels into a high-power digital waveform generator, and improves the system equivalent switching frequency in a module cascade manner.

3. The multi-level coordinated control method of a high-power multi-level digital waveform generator according to claim 2, characterized in that: The front-stage control process of the front-stage DC-DC converter comprises the following steps: (1) First, for the front stage of the high-power multi-level digital waveform generator, let the output voltage of the n modules on the input side be V in , its input power is shared by n parallel DC-DC converters, that is, n DC-DC converters are connected in parallel, thus, the input power of the previous n DC-DC converters can be obtained as: Among them, P i1 ,P i2 ,…,P in are the input side powers of the 1st to the nth preceding DC-DC converters, i i1 ,i i2 ,…,i in are the input side currents of the 1st to the nth preceding DC-DC converters respectively; (2) Ignoring the losses of the converter, the input power and output power of the DC-DC converter are equal, and the load power will be evenly distributed among the modules, thus obtaining: P i1 :P i2 :…:P in =P o1 :P o2 :…:P on =1:1:…:1 (2) Among them, P o1 ,P o2 ,…,P on Respectively represent the output power of the 1st to the nth subsequent DC-AC converters, control the output voltages of the n DC-DC submodules to be equal, and ensure that the output power between each module is equal; (3) The control strategy of the front-stage DC-DC converter includes three control links, namely: the system output voltage control loop, the sub-module voltage equalization control loop and the current control loop; the system output voltage control loop adjusts the output of the front-stage DC-DC converter to reach the specified DC voltage value; on this basis, the sub-module voltage equalization control loop is inserted to achieve dynamic balance of the sub-module output voltage; finally, in order to meet the needs of the high-power waveform generator to output fast tracking reference instructions within a wide frequency conversion range, a current control loop is added to improve the dynamic response speed of the system.

4. The multi-level coordinated control method of a high-power multi-level digital waveform generator according to claim 3, characterized in that: The control strategy of the subsequent DC-AC converter includes the following steps: (1) First, since the output side of each DC-AC converter in the rear stage of the high-power multi-level digital waveform generator is cascaded, the output voltage of the i-th unit is expressed as (S Ai -S Bi ) dci , since the current of all submodules is proportional to the output inductor current i L equal, therefore, the output power of each submodule is obtained as: Among them, u dc1 ,u dc2 ,…,u dcn Respectively represent the input voltages of the 1st to nth DC-AC converters; (2) In order to reduce the size of the filter, the cascaded DC-AC converter adopts single-pole frequency multiplication modulation. Therefore, the output voltage of the i-th DC-AC converter can be expressed as: (3) Since the modulation signal of each DC-AC converter unit in the subsequent stage is the same, ignoring the influence of higher harmonics, it can be obtained that the output power of the first to nth DC-DC converters satisfies the following formula: (4) Since the output fundamental voltage amplitude u of the DC-AC converter abi With the previous DC voltage u dci Proportional to each other, let the ratio be the modulation index M. The rear-stage DC-AC converter can be equivalent to a series output load relative to the front-stage DC-DC converter.

5. The multi-level coordinated control method of a high-power multi-level digital waveform generator according to claim 4, characterized in that: The control idea of ​​the post-stage DC-AC converter is to achieve equivalent high modulation index output and dynamic compensation of low-order harmonics by dynamically adjusting the modulation index M'. Dynamic adjustment of the modulation index M' can suppress the double frequency ripple of the DC voltage and improve the waveform quality of the output AC voltage. By adjusting the equivalent output modulation index, the system can be kept running at a high modulation index.

6. The multi-level coordinated control method of a high-power multi-level digital waveform generator according to claim 5, characterized in that: The control part of the post-stage DC-AC converter includes three parts: dynamic modulation adjustment part, dead zone compensation part and carrier phase shift modulation part; (1) The dynamic adjustment process of modulation index is as follows: when the output voltage required by the load is low, the invented method reduces the DC bus voltage command value to keep the inverter running at an equivalent high modulation index. In addition, by real-time detection of the DC bus voltage value, the modulation index M' is dynamically adjusted in a small range. In order to minimize the impact of the DC side double frequency ripple on the AC side output, it is necessary to extract the amplitude information of the amplified signal source signal |u s | and phase information sin(ω s t) to obtain the dynamic modulation degree M'; (2) Dead zone compensation control is: sampling the load current and superimposing a rectangular compensation voltage with the same amplitude and opposite phase as the dead zone error wave according to its direction, and superimposing it on the modulation signal; (3) Carrier phase-shift PWM modulation part: 2N triangular carriers with a phase difference of π / N are constructed through FPGA and compared with the modulation signal, thereby realizing unipolar frequency-doubled carrier phase-shift PWM modulation.

7. The multi-level coordinated control method of a high-power multi-level digital waveform generator according to claim 6, characterized in that: Where M0 is less than 1, but close to 1, the DC side voltage command value U of the DC-DC converter can be obtained. r ' ef for: When the AC output command of the high-power multi-level digital waveform generator changes, the DC side command of the DC-DC converter will also be adjusted accordingly, thereby ensuring that the subsequent DC-AC converter maintains the output under the high modulation index M0; in addition, in order to keep the adjusted system output waveform unaffected, it is necessary to meet the following conditions: Then the dynamic modulation degree M' expression superimposed with the previous stage signal is obtained: Real-time detection of the sum of the output voltages of the preceding DC-DC converters Then calculate the dynamic modulation degree M'; The dynamic compensation of modulation index can suppress the double frequency fluctuation of the DC side bus, reduce the impact on the quality of the output AC voltage, and keep the system running at an equivalent high modulation index. The expression of the output u of the high-power multi-level digital waveform generator under the coordinated control of the present invention is derived as follows:

Images