Abstract: Multi-carrier PWM technology is a commonly used switching modulation technique in multilevel converters, characterized by its simple principle, convenient implementation, and widespread applicability to various multilevel converters. Based on the phase of each triangular carrier, multi-carrier PWM technology can be divided into three specific modulation schemes. This paper compares the advantages and disadvantages of various schemes from the perspective of harmonic quality, and determines the optimal modulation scheme for different situations. CPS-SPWM technology is an organic combination of multiplexing technology and SPWM technology. This technology can achieve a higher equivalent switching frequency at a lower device switching frequency by canceling out lower harmonics, thus improving the equivalent switching frequency rather than simply shifting harmonics to higher orders, resulting in good harmonic characteristics. Time-shifted sampling space vector modulation is a novel switching modulation strategy that can achieve a higher equivalent switching frequency at a lower device switching frequency, exhibiting good harmonic characteristics. Theoretically, this technology can significantly improve the equivalent switching frequency of the device without fundamental frequency loss; this conclusion is universally applicable to various carrier pulse width modulation techniques. Keywords: multi-carrier PWM, multi-level frequency converter, carrier phase shift SPWM, space vector modulation, time-staggered sampling SVM MODULATION TECHNIQUE FOR HIGH POWER CONVERTET Li jianlin Xuhongfei Panlei Wangliqiao Zhangzhongchao [1]Institute of Electrical Engineering, Chinese Academy of Sciences [2]Institute of hydraulic sciences [3] Yanshan University [4]Zhejiang University Abstracts: Multi-carrier PWM technique is a kind of switch modulation strategy for multi-level converters in common use, which is of such advantages as explicit principle, easy realization and suitability for any multi-level converters. According to the phases of each triangle carrier, there are three modulated methods. the relative merits of each method are analyzed and compared from the viewpoint of harmonic quality. The operation principal of carrier phase-shifted SPWM (abbreviated as CPS-SPWM) has been analyzed in this paper. The key idea of ​​this approach is the combination of multi-modular technique and SPWM technique. The high equivalent switching frequency can be obtained with low Switching frequency devices. This technique improves the equivalent switching frequency by counteracting lower-order harmonics, not simply by processing the harmonics from lower to higher order, thus achieving perfect performance on the harmonic feature. Time-staggered space vector modulation is deduced. Therefore, the advantages of this technique are theoretically demonstrated, allowing it to significantly improve the equivalent switching frequency without fundamental frequency losses. Keywords: Multi-carrier PWM, Multi-level converters, carrier phase-shifted SPWM, SVM, STS-SVM 1. Introduction The choice of switching modulation strategy is crucial for frequency converters. For the high-power power electronic devices discussed in the previous section, the following switching modulation strategies are currently available: stepped-wave pulse width modulation, carrier group-based PWM technology, multi-level voltage space vector modulation, carrier phase-shifted sinusoidal pulse width modulation (CPS-SPWM), and sample time-staggered space vector modulation (STS-SVM), etc. 2. Stepped Wave Pulse Width Modulation Stepped wave pulse width modulation is to approximate a sine wave with a stepped wave[1]. The advantage of this strategy is that it is simple to implement and has a low switching frequency (equal to the fundamental frequency). The main disadvantage is that the output voltage regulation depends on the DC bus voltage or phase shift angle. In stepped wave modulation, the elimination and suppression of low-order harmonics can be achieved by selecting the duration of each level. Reference [2] proposes an optimized modulation wave width technique, which introduces the selected harmonic elimination PWM[3] (Selected Harmonic Elimination PWM) originally applied to ordinary two-level frequency converters into cascaded multi-level frequency converters. The selected harmonic components can be eliminated by calculating the switching angle through the optimization algorithm. However, in this modulation method, it is necessary to use optimization algorithms (such as the Newton-Raphson method) to solve high-order nonlinear equations. Even with high-speed computing chips such as DSPs, it is difficult to achieve real-time control. Generally, control is completed by offline lookup table method. Therefore, this modulation strategy is mainly used in some situations where the output voltage regulation requirements are not high, such as static var compensators. 3. Multi-carrier PWM method In an N-level inverter, N-1 triangular carriers with the same frequency and amplitude are placed side by side to form a carrier group. The horizontal center line of the carrier group is used as the reference zero line, and the common modulation wave intersects with it [4]. According to the phase of the triangular carriers, PWM control can be in three forms as shown in Figure 1: The phases of each triangular carrier are consistent, as shown in Figure 1(a), which is called type A. Above the reference zero line, the phases of the triangular carriers are consistent; below the reference zero line, the phases of the triangular carriers are opposite to the former, as shown in Figure 11(b), which is called type B. The triangular carriers are opposite from top to bottom, as shown in Figure 11(c), which is called type C. When the frequency modulation is relatively low, the outputs of the three PWM modulations are different. In type A PWM modulation, the harmonic amplitude is large at the carrier harmonics, while the sideband harmonic amplitude is significantly smaller than the latter two. For odd-level inverters, type B and type C PWM outputs do not contain carrier harmonics. When carrier harmonics are not considered, the THD of type A PWM modulation output is smaller. In a single-phase system, the C-type modulation scheme is optimal; while in a three-phase balanced system without a neutral line, the A-type scheme is more suitable. In terms of the distribution and content of the low-order dominant harmonics, regardless of whether the number of levels is odd or even, scheme C is the best. In terms of modulation principle, scheme C is completely consistent with the modulation effect of carrier CPS-SPWM technology [4], 5]. In situations where the requirements for the characteristics of low-order harmonics are relatively high, such as unity power factor correction devices, scheme C is more suitable. 4. PWM technology based on carrier groups This control method is suitable for diode-clamped multilevel inverters. The basic principle is: in an N-level inverter, N-1 triangular carriers with the same frequency and amplitude are placed side by side to form a carrier group; the horizontal neutral line of the carrier group is used as the reference zero line, and the common modulation wave intersects with it to obtain the corresponding switching signal. According to the phase of the triangular carrier, this control method can have three different forms. Under this control method, the inverter has good output characteristics, the switching frequency of the devices is low while the equivalent switching frequency is high, the input and output are linearly related, and a certain bandwidth can be output; however, the conduction load of the devices is inconsistent, especially under deep modulation, the power devices on the periphery of the inverter are almost non-conducting, while the internal power devices have a high switching frequency. To solve this problem under deep modulation, some improved control methods have emerged. As for the modulation wave, a standard sine wave or a harmonic-injected sine wave can be used. 5. Multilevel voltage space vector modulation (1) This is an extension of the conventional two-level voltage space vector modulation (SVM) technology to multilevel inverters. The conventional two-level SVM technology generates eight voltage space vectors according to different switching combinations, of which six are non-zero vectors and two are zero vectors; in the spatial rotating coordinate system, the vector at any time is synthesized by two adjacent non-zero vectors. By optimizing the action time of the two non-zero vectors and the zero vector within a modulation cycle, the PWM output waveform is obtained. For multilevel SVM technology, its basic principle is similar to that of two-level SVM technology, except that the switching combination method increases with the increase of the number of levels; the rule is that for m-level frequency converters, the number of voltage space vectors is m3, and of course some of these levels overlap in space. For example, for three-level frequency converters, the number of voltage space vectors is 27, of which there are 19 independent voltage space vectors, one zero vector, and 18 non-zero vectors; similarly, in the spatial rotating coordinate, the vector at any time is synthesized by three adjacent non-zero vectors, and the action time of the three non-zero vectors and the zero vector are optimized in one switching modulation cycle to obtain the PWM output waveform [4-6]. Since the relationship between the number of levels and the number of voltage space vectors is cubic, multilevel SVM technology is greatly limited when the number of levels is high [7]; therefore, the current research on multilevel SVM technology is generally limited to five levels and below. ⑵ The phase voltage modulation wave of MSL-SVM can also be obtained as an explicit function of the phase voltage modulation wave in the above way. Based on the mathematical expression of the modulation wave, the phase voltage modulation wave waveform of SVM can be plotted. The modulation wave waveforms of methods one to four are shown in Figure 2 (amplitude modulation ratio is 1). The thin solid line represents phase A, the dashed line represents phase B, the dotted line represents phase C, and the thick solid line represents the line voltage. As shown in Figure 2, although the modulation algorithms of the four methods are different, and their phase voltage waveforms are also different, the line voltage waveforms are completely consistent, being standard sine waves of the same amplitude. From the phase voltage modulation wave waveforms and modulation principles of various methods, the following two conclusions can be qualitatively drawn: (3) In terms of shape, the phase voltage modulation wave waveforms of methods one and two are completely opposite. Vertically flipping the phase voltage modulation wave waveform of method two by 180° yields a waveform that is exactly the same in shape as the phase voltage modulation wave of method one; however, there is a difference in phase. From the properties of Fourier transform, it can be seen that waveform flipping and phase shifting only affect the phase of each harmonic, not their amplitude. In other words, under the same modulation ratio, the effects of Method 1 and Method 2 are completely consistent in terms of harmonic distribution and amplitude of the output voltage. (4) From the perspective of the modulation waveform, the modulation wave of the alternating zero-vector modulation method has anti-symmetric properties of positive and negative half-cycles, belonging to symmetrical modulation; while the modulation wave of the single zero-vector modulation method does not have anti-symmetric properties of positive and negative half-cycles, belonging to asymmetrical modulation. The harmonic characteristics of symmetrical modulation are obviously better than those of asymmetrical modulation, that is, the harmonic characteristics of the alternating zero-vector modulation method are better than those of the single zero-vector modulation method. The modulation waveform of Method 4 has the best symmetry among the four methods, therefore its harmonic characteristics are also the best. To verify the above two conclusions, a voltage-type three-phase six-switch inverter was constructed using Matlab, and simulation studies were conducted using the above four methods respectively. Figure 3 shows the spectrum of the output line voltage when modulated by the four methods respectively (amplitude modulation ratio is 0.9, frequency modulation ratio is 27); the THD (total harmonic loss) of the output line voltage are 61.66%, 61.66%, 61.04%, and 59.52% respectively. Comparing the four modulation methods, from the perspective of THD and spectrum distribution, method four is the best; while the THD and spectrum of method one and method two are exactly the same. This shows that the conclusions obtained above are correct. 6. CPS-SPWM CPS-SPWM technology can greatly improve the output waveform and reduce the output harmonics in high-power applications, thereby reducing the capacity of the filter and reducing the cost. At the same time, due to its high equivalent switching frequency and wide transmission bandwidth, various advanced control strategies can be introduced to optimize the performance indicators of the entire system [10]. From this perspective, this is also a breakthrough in control methods in ultra-high power applications. When implementing CPS-SPWM technology, the complexity of the main power circuit does not increase. CPS-SPWM is a switching modulation strategy suitable for high-power power electronic devices. It can be applied to combined frequency converters and multi-level frequency converters. The basic idea of ​​CPS-SPWM technology is: in a voltage-type combined frequency converter with a number of frequency converter units, each frequency converter unit adopts a common modulation wave signal M(t), the frequency of which is . The triangular carrier frequency of each inverter unit is , and the phase of each triangular carrier is staggered from the triangular carrier period, i.e.: , as shown in Figure 4(a) (number of inverter units, frequency modulation ratio kc/km = 5, amplitude modulation ratio m = 0.8). The waveforms shown in Figure 4(b) are the outputs of the inverter units respectively. The AC outputs of the inverter units are superimposed to form the output waveform of the entire combined inverter device as shown in Figure 4(c). It can be seen from the figure that the total output waveform of the combined inverter is closer to the sine wave than the output waveform of the inverter unit, or in other words, the harmonic components are smaller and the waveform is better. In addition to SPWM technology, the carrier phase shift PWM technology also adopts the following modulation strategies. ⑴ Phase-shifted Selected Harmonic Elimination PWM (Phase-shifted Selected Harmonic Elimination PWM) [42] This control method is based on the traditional fixed harmonic elimination method PWM. A preset phase shift amount is added in the switching angle calculation. The switching angles with different phase shift amounts are used for different inverter units, so that the superimposed AC side voltage and current reach the optimal harmonics. (2) Sample Time Staggered SVM (hereinafter referred to as STS-SVM) [6][7] The modulation method of STS-SVM technology in combined frequency converters is simply to stagger the sampling time of each frequency converter unit. Specifically, in a combined frequency converter, N frequency converter units perform SVM modulation under the same frequency modulation ratio k and amplitude modulation ratio mr; the sampling time of each frequency converter unit has a phase difference of 2π/(N•k). Compared with carrier phase shift SPWM technology, STS-SVM technology has the characteristics of high voltage utilization, low switching frequency, and easy digital implementation. In addition, other modulation strategies, such as hysteresis current control [43][44], single-cycle control [45][46][47], etc., can be applied to carrier phase shift PWM technology, which has certain research prospects. Carrier phase shift PWM technology has the following characteristics: (1) The switching frequency of each frequency converter unit is low, and high-power power electronic devices such as GTO can be used to form a high-power converter device, and the switching loss of the device is reduced. (2) The output harmonics are small, which can greatly reduce the volume and size of the filter. (3) The equivalent switching frequency is high and the transmission bandwidth is wide; the transmission linearity is good and it is easy to introduce some excellent control methods. (4) The circuit structure of each inverter unit is exactly the same, which is easy to implement in a modular way. 7. STS-SVM voltage space vector modulation technology (SVM technology) is a modulation strategy based on the theory of AC asynchronous motor magnetic field, but now its application scope is no longer limited to motor application, but is a PWM technology that can be widely used. Compared with SPWM technology, SVM technology has the following advantages: (1) The utilization rate of DC voltage is 15% higher than that of SPWM; (2) When using the minimum switching loss modulation method, the switching loss of the switching device is reduced by 1/3; (3) The modulation method is easy to implement digitally. STS-SVM is inspired by CPS-SPWM technology and integrates SVM modulation method to obtain a space vector modulation method suitable for multi-level inverters [33]. In short, it is to stagger the sampling time of each inverter unit. Specifically, in the combined frequency converter, each frequency converter unit performs SVM modulation under the same frequency modulation ratio and amplitude modulation ratio m; the sampling time of each frequency converter unit has a phase difference of . Compared with carrier CPS-SPWM technology, STS-SVM technology has the advantages of high voltage utilization, low switching frequency, and easy digital implementation. Flexible and diverse modulation techniques combined with rich circuit topologies form converter devices with unique characteristics [11-20]. Currently, the diode clamping frequency converter based on multi-level SVM and the CPS-SPWM cascaded H-type frequency converter proposed in this paper have entered the research stage. In addition, there are some promising research directions, such as phase shift single-cycle control combined frequency converters. 8. Simulation and experimental verification To verify the above conclusions, this paper constructs a three-phase voltage-type six-switch inverter using Matlab, with a frequency modulation ratio of 27 and an amplitude modulation ratio of 0.9. Using modulation method four, the line voltage output is shown in Figure 5(a) and the theoretical spectrum is shown in Figure 5(b). It can be seen that the two are basically the same. Table 1 lists the relative amplitudes of the main harmonics in the two sets of spectra (with the fundamental amplitude as the unit amplitude). The mean square error of the two sets of spectrum data is calculated to be 0.71%. This paper constructs a three-phase AC/DC/AC frequency converter and drives an asynchronous motor for speed regulation experiments. The inverter section adopts a voltage-type three-phase six-switch circuit, and uses Method 1 as the switching modulation strategy. The sampling frequency is set to 1050Hz. The main switching device uses IRFP460 from IR Corporation, and the control circuit uses ADI's motor-specific DSP chip ADMCF328. When the rated frequency (50Hz) is reached, the amplitude modulation ratio is calculated to be 0.8 according to the control principle. The output line voltage waveform of the frequency converter is shown in Figure 2.21(a). The experimental waveform data is acquired by a Tektronix TDS240 oscilloscope and sent to a computer. The spectrum of Figure 2.21(a) can be calculated by FFT, as shown in Figure 2.21(b); and the theoretical spectrum can be calculated according to Equation (2-25), as shown in Figure 2.21(c). Comparing Figure 2.21(b) and Figure 2.21(c), it can be seen that they are very close, but there is a certain error; after calculation, the mean square error of the two sets of spectrum data is 1.73%. The main reasons for the error between the experimental spectrum and the theoretical spectrum are: (1) the accuracy of the data collected by the oscilloscope is not high enough, (2) a dead time is set to prevent short circuit of the bridge arm, which causes waveform distortion. 9. Conclusion Based on reading and analyzing domestic and foreign literature, this paper compares the advantages and disadvantages of several typical modulation strategies of multilevel converters. CPS-SPWM technology can effectively suppress and eliminate low-order harmonics at a lower switching frequency and has a wider transmission bandwidth. It is an excellent switching modulation strategy suitable for high-power power electronic devices. The cascaded H-bridge multilevel converter requires the fewest components among various multilevel converters; due to the use of independent DC structure, the voltage equalization problem on the DC side is relatively easy to solve; the circuit structure of each basic unit is completely consistent, which is more conducive to modular design. In parallel active filter systems, since the DC side does not need to provide active power, the advantages of cascaded H-bridge multilevel converters can be fully utilized; the excellent harmonic transmission characteristics of CPS-SPWM technology can also be well taken advantage of. References [1] HS Patel, et. al. 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About the authors: Li Jianlin (1976–), male, postdoctoral researcher at the Institute of Electrical Engineering, Chinese Academy of Sciences, specializing in active power filters and variable-speed constant-frequency wind power generation technology. Xu Hongfei (1974–), female, engineer at the Shanxi Provincial Institute of Water Resources Science. Pan Lei (1981–), male, assistant engineer at the Institute of Electrical Engineering, Chinese Academy of Sciences, specializing in variable-speed constant-frequency wind power generation technology.