Simulation Study on Carrier PWM Control Method of Multilevel Inverter-EEWORLD

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Abstract: The carrier PWM control methods of multi-level inverters are discussed and their principles are introduced. In order to compare their control effects, a simulation study is carried out using Matlab software. Finally, based on the simulation results and analysis, conclusions are drawn and suggestions for future research are put forward.

Keywords: carrier PWM; multi-level inverter; simulation

1 Introduction

In recent years, multi-level converters have become a hot topic in the field of high voltage and high power, mainly because it can achieve high voltage and high power output with low voltage devices, without the need for dynamic voltage balancing circuits and transformers; the increase in the number of levels improves the output voltage waveform. At present, there are three topological structures of multi-level inverters: diode-clamped inverter, flying-capacitor inverter and cascaded-inverters with separate DC sources. Among these three circuit structures, the diode-clamped type is the most widely used. The circuit topology of the diode-clamped five-level inverter is shown in Figure 1. This article mainly discusses the PWM control method of the diode-clamped multi-level inverter.

Figure 1 Main circuit of diode-clamped five-level inverter

The PWM control technology of multilevel inverter is a key technology in the research of multilevel inverter. It is symbiotic with the proposal of multilevel inverter topology because it not only determines whether multilevel inverter can be realized, but also has a direct impact on the quality of voltage output waveform of multilevel inverter, the stress of active and passive components in the circuit, the reduction of system loss and the improvement of efficiency. So far, a large number of multilevel converter PWM control methods have been proposed ^[1][2] , including carrier PWM control method and space voltage vector method (SVPWM), which are both extensions of two-level PWM method in multilevel. The SVPWM method has attracted wide attention and application due to its advantages such as high voltage utilization, low harmonic content and simple hardware circuit. However, when this method is applied to circuits with more than five levels, its control algorithm becomes very complicated. Therefore, for multilevel circuits with more than five levels, the control method of triangle carrier PWM is a more feasible solution.

2 Subharmonics PWM (SHPWM)

The carrier-based PWM control method of the multi-level inverter is an extension of the two-level PWM method in multi-level. Their principles are that each phase of the circuit uses a sinusoidal modulation wave to compare with several triangular carriers.

2.1 Principle of SHPWM method ^[4]

For an N-level converter, each phase uses _N - ₁ triangular carriers with the same frequency fc and the same peak-to-peak value Ac to compare with a sine wave with a frequency of _fm_and an amplitude of Am. In order to make the area occupied by the N -1 triangular carriers continuous, they are closely connected in space and the entire carrier set is symmetrically distributed on the positive and negative sides of the zero reference. At the moment when the sine wave and the triangular wave intersect, if the amplitude of the modulated wave is greater than the amplitude of a certain triangular wave, the corresponding switching device is turned on. Conversely, if the amplitude of the modulated wave is less than the amplitude of a certain triangular wave, the device is turned off. The principle of this method is shown in Figure 2. For an N -level converter, the modulation index _ma and _the carrier ratio mf are defined as follows:

ma ₌ (1)

mf ₌ (2)

Figure 2 SHPWM principle

2.2 SHPWM method simulation results and analysis

According to the phase of the triangular carrier, SHPWM can be divided into three typical cases:

1) All carriers have the same phase (PD type);

2) All carriers above the zero reference are in phase, and all carriers below the zero reference have opposite phases (POD type);

3) All carriers are from top to bottom, alternating in phase and out of phase (APOD type).

Aiming at these three multi-level PWM methods, simulation research was carried out using Matlab simulation software, and a five-level diode clamped inverter was established. Figures 3, 4, and 5 are the simulation waveforms obtained when the modulation index is 0.8, the carrier ratio is 21, and the output voltage fundamental frequency is 50Hz.

(a) Carrier and modulating wave waveforms

(b) Phase voltage waveform

(d) Line voltage waveform

(e) Line voltage spectrum

Figure 3 PD type SHPWM method simulation waveform

(a) Carrier and modulating wave waveforms

(b) Phase voltage waveform

(d) Line voltage waveform

(e) Line voltage spectrum

Figure 4 POD type SHPWM method simulation waveform

(a) Carrier and modulating wave waveforms

(b) Phase voltage waveform

(d) Line voltage waveform

(e) Line voltage spectrum

Figure 5 APOD type SHPWM method simulation waveform

Figure 6 SFOPWM schematic diagram

Parts (b) and (d) of each figure correspond to the waveform diagrams of the phase voltage and the line voltage, and parts (c) and (e) correspond to the frequency spectrum diagrams of the phase voltage and the line voltage.

From the simulation results, it can be seen that for the PD type system, from the spectrum diagram in the output phase voltage, it can be seen that the harmonic energy is mainly concentrated at the carrier frequency, where the harmonic amplitude is large, so that the THD of the phase voltage (calculating harmonics within 50 times) reaches 23.94%, and the other harmonic components are mainly sideband harmonics centered on the integer multiple frequency of the carrier, with a small amplitude. In the output line voltage of the three-phase system, since each triangular carrier is in phase, the harmonics at the carrier cancel each other, reducing the THD of the line voltage to 12.76%.

For the POD type system, there are no carrier harmonics in the phase voltage and line voltage, but there are sideband harmonics centered on integer multiples of the carrier frequency, and their amplitudes are larger than the corresponding amplitudes in the PD type system. Therefore, the THD of the phase voltage and line voltage finally obtained by this method are 22.5% and 19.71% respectively.

For the APOD system, its spectrum distribution is very similar to that of the POD system. All harmonics are basically located on the sidebands centered on the integer multiple frequency of the carrier. The only difference is that the harmonic energy in the POD type is mainly concentrated in the sidebands on both sides of the carrier frequency, while the harmonic distribution in the APOD system is more uniform. The final THD of the phase voltage and line voltage are 22.13% and 22.56% respectively.

Obviously, in the APOD type system, the corresponding harmonics in the three-phase system not only cannot cancel each other, but some even superimpose each other, resulting in the line voltage THD being greater than the phase voltage THD. From the simulation results of the above three multi-level harmonic elimination PWM methods, it can be seen that for the output phase voltage, the THD of the three methods is not much different, but for the output line voltage, the PD type system has the smallest THD, which has obvious advantages and is most commonly used in practical applications. From this perspective, the PD type system is the best in the three-phase system. In addition, from the simulation results, it can be found that in the output phase voltage and line voltage of the three forms of SHPWM methods, from PD type to POD type and then to APOD type, the harmonic content in the bandwidth increases successively, that is, the APOD type has the largest number of residual harmonics in the transmission bandwidth, which brings difficulties to the output filtering. This phenomenon will be more obvious when the frequency modulation ratio is higher and the number of levels is larger.

3 Switch frequency optimized PWM (SFOPWM)

3.1 Principle of SFOPWM method ^[4]

The switching frequency optimization PWM method ^[2] is another triangular carrier PWM method. This method is similar to the SHPWM method. Their carrier requirements are the same, but the zero-sequence component is injected into the sine modulation wave of the SFOPWM. For a three-phase system, this zero-sequence component is the average value of the maximum and minimum transient values of the three-phase sine wave. Therefore, the modulation wave of the SFOPWM method is the waveform obtained by subtracting the zero-sequence component from the usual three-phase sine wave. The calculation formula of the zero-sequence component and the three-phase modulation wave is as follows:

V _zero =(3)

V _a^＊ = V _a － V _zero (4)

V _b^＊ = V _b － V _zero (5)

V _c^＊ = V _c － V _zero (6)

This method can only be used in three-phase systems, because the injected zero-sequence components cannot cancel each other out in a single-phase system, resulting in the presence of third harmonics in the output waveform. This does not happen in a three-phase system, which will be clearly reflected in the simulation results later.

3.2 Simulation results and analysis of SFOPWM method

For the switching frequency optimal PWM method (SFOPWM) given above, the carrier waveform is arranged according to the PD type system of the harmonic elimination PWM method, and the other simulation parameters are exactly the same. The obtained simulation waveform is shown in Figure 7. It can be seen from the figure that in the output phase voltage of this PWM method, the harmonic energy is mainly distributed at the carrier frequency. At the same time, due to the injection of the zero-sequence component in the modulation wave, there is an obvious third harmonic in the output phase voltage. This harmonic will offset each other in the line voltage of the three-phase system, and the final output phase voltage and line voltage THD are 36.26% and 14.40% respectively. It can be seen that the THD of the output line voltage of this PWM method is close to that of the PD type SHPWM method, and its most significant advantage is that the voltage modulation ratio of the output voltage can reach 1.15, so this method is most suitable for three-phase motor speed control systems that want high voltage utilization.

(a) Carrier and modulating wave waveforms

(b) Phase voltage waveform

(d) Line voltage waveform

(e) Line voltage spectrum

Figure 7 Simulation results of SFOPWM method

4 Conclusion

From the above analysis of the principles and simulation results of several typical multi-level carrier PWM methods, it can be seen that they each have their own advantages and disadvantages, and these methods are derived from the combination of different control degrees of freedom in the multi-level inverter PWM method. Due to the increase in the control degrees of freedom of the multi-level inverter, the number of corresponding PWM methods will be very large. Specifically, in terms of carrier, the multi-level inverter often has more than one carrier, and its shape can be a common triangle wave or other waveforms such as a sawtooth wave. For the same waveform, each carrier has at least multiple degrees of freedom such as frequency, amplitude, phase, offset, etc.; and the multi-level modulation wave can be not only a sine wave, but also a trapezoidal wave. For the same waveform, there are at least multiple degrees of freedom such as frequency, amplitude, superimposed zero-sequence component, etc. The combination of the above control degrees of freedom, and further combined with the basic topologies of various multi-level inverters, will produce a large number of multi-level PWM control methods.

Reference address：Simulation Study on Carrier PWM Control Method of Multilevel Inverter

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