Research on Multi-carrier PWM Technology Based on Modular Multilevel Inverter

The modular multilevel inverter circuit structure is introduced, three traditional multi-carrier PWM modulation strategies for modular multilevel inverter circuits are studied and analyzed, and the inverter-side output voltage spectrum is analyzed by simulation. Based on the traditional multi-carrier PWM modulation strategy, this paper uses the PWM technology combining multi-reference wave and multi-carrier to analyze and simulate, and builds a modulation model and a circuit model of the modular multilevel inverter circuit in the Matlab/Simulink environment. Compared with the simulation results of the traditional multi-carrier PWM strategy, the multi-carrier modulation algorithm of the multi-reference wave can slightly reduce the total harmonic distortion rate. At the same time, the multi-carrier modulation algorithm of multiple reference waves can ensure that the capacitor voltage values of each submodule of the modular multilevel inverter circuit are equal so that there is no circulation phenomenon between each phase. Finally, a physical platform is built to verify the authenticity of the simulation experiment.


Introduction
MMC is a relatively advanced multilevel converter, which has attracted extensive attention from many scholars at home and abroad [1] .Its low switching frequency and high output voltage waveform quality can effectively reduce the content of high-order harmonics [2] .The main feature of this new topology multilevel converter is that it has the characteristics of cascading, which consists of a series of low-withstand voltage and topologically identical submodules in series.By controlling the switching state of the sub-modules on the bridge arm, the number of output levels can be easily changed, and the output voltage quality can be effectively guaranteed.With the above advantages, MMC can be widely used in active power filters, static reactive generators, and many other fields [3] .
Currently, the commonly used modulation strategies of MMC mainly include PWM control technology modulation and step wave modulation.PWM can force the desired sine wave by controlling the on-off of semiconductor switching devices, converting the output DC voltage into a series of voltage pulse trains, and controlling the width of the voltage pulses.Literature [4] adopts the carrier phase-shift modulation strategy, which has good harmonic characteristics, but the loss of switching devices is relatively high.The literature [5] studies the performance of recent level approximation modulation strategies under different control trigger conditions.The literature [6] adopts a carrier stacking modulation strategy, although the modulation strategy of this method is easy to implement and relatively simple.However, the voltage quality of the output is not very high, and it needs to be further improved.
This paper proposes a modular multilevel inverter circuit applied to permanent magnet synchronous motors, introduces the output waveform under three multi-carrier PWM modulation methods: noninverting stacking method, alternating inverting stacking method, and positive and negative inverting stacking method, and compares it with the new multi-reference wave multi-carrier modulation algorithm, and analyzes its advantages over the traditional method: the new multi-reference wave multi-carrier modulation algorithm can improve the output voltage spectrum with a small reduction in the total harmonic distortion rate.And it can ensure that the capacitor voltage of each submodule on each phase bridge arm is equal and that there is no circulating phenomenon in the circuit to ensure its safety of the circuit.

Modular multilevel inverter circuit principle analysis
The topology of the modular multilevel inverter circuit is shown in Figure 1 [6] .Each phase of the three-phase boom has two legs, the upper and lower arms, and on each arm, there is 1 inductor and N identical submodules.The structural model of the submodule is in the upper right corner of Figure 1.As can be seen from the figure, in the submodule model, there are two switch tubes in series on the left and a capacitor in parallel on the right side.To avoid short circuits in the circuit, the upper and lower legs are complementary, and different output voltages can be changed by controlling the number of submodules put into the upper and lower legs [8] .

Figure 1. The modular multilevel inverter circuit topology
According to the topology shown in Figure 1, the single-phase output voltage equation and the circulation equation can be obtained as follows: In the formula: uo v is the U phase voltage value; Nu v is the sum of the voltages of the submodules connected to the bridge leg under the U phase; Pu v is the sum of the voltages of the submodules connected to the bridge arm on the U phase; u i is the U-phase current; L is a bridge leg inductor; d r is the equivalent DC resistance of the bridge arm; zu i is the circulating current; d V is the DC voltage.
It can be seen from equations ( 1) and ( 2): The difference between the number of voltage sources (number of open modules) connected to the upper and lower bridge arms determines the output voltage, and the sum of its numbers will cause changes in the system circulation.To allow the output voltage of the circuit to contain zero voltage, the number of neutron modules in the bridge leg is usually even.
The article will be simulated at 2 N = .Taking the U-phase bridge arm of the modular multilevel inverter circuit as an example, according to the submodule equivalent circuit diagram of Figure 1, it can be seen that when VT 1 is on, VT 2 is in the off state, so only one IGBT power device is still on in the submodule.
To ensure the stable operation of the modular multilevel inverter circuit, it is necessary to ensure that the number of submodules required on the phase unit at any time is always equal to 2. When submodules SM 1 and SM 2 are turned on.Currently, the voltage between the midpoint of the U phase and the O point is .In summary, the number of output levels per phase bridge arm is 3 when 2 N = .

Typical multi-carrier modulation algorithm
Multi-carrier PWM technology [9] uses natural sampling to compare a reference wave (usually a sine wave) with a carrier wave (usually a triangle wave or sawtooth wave) to produce a drive signal for a switching device.
(1) In-phase cascading method As a basic carrier PWM modulation method, the inverting stacking method, the PD-PWM modulation algorithm compares a single reference wave with a carrier of the same phase to produce a PWM waveform (all carriers are arranged up and down in the same phase).
(2) Alternately reversed cascading method The alternating inverting stacking method (APOD-PWM) also requires multiple carrier signals and a single reference wave to compare the resulting multilevel output voltage, unlike the noninverting stacking method, which requires all adjacent carriers to be in opposite phases.
(3) Positive and negative inverting cascading methods The positive and negative inverting stacking method (POD-PWM) is to make the carrier phase above the zero axis, and the carrier phase below the zero line differ by 180°, but keep the carrier phase above the zero axis and below the zero axis equal, respectively.Similarly, this method uses multiple triangular carriers compared to a single reference sine wave to generate a switching drive signal.

Multi-reference wave multi-carrier modulation algorithm
Based on the traditional multi-carrier modulation method, a new three-level output modulation method is used.The difference between this method and the above modulation methods is that it requires only two carriers and two reference waves.Figure 2 shows that r 1 and r 2 are the reference waves; C 1 and C 2 are triangular carriers, and the control signal waveform is generated by comparing the reference wave and carrier separately.Since r 1 and r 2 are two reference waves with a difference of 180, the theoretical analysis can be analyzed according to r 1 , and according to the definition of the double Fourier series, the following formula can be obtained: where A and B are constants, n represents the number of output levels, and m is the integer of n.
When the three phases are modulated with symmetrical sine waves, it can be calculated that sin( ) sin( 2 / 3) sin( 2 / 3) Where: U as , U bs , U cs is expressed as a sine wave.Therefore, it can be calculated that the output phase voltage waveform is sinusoidal.

Figure 2 Multi-fundamental multi-reference wave modulation algorithm
The main circuit simulation is built based on the Matlab/Simulink environment: the new PWM module is packaged for the IGBT control signal generation module, and the driving signal shows that the two signals on each bridge arm are complementary states so that the two switch transistors on each bridge arm will not be turned on at the same time, which avoids the occurrence of short circuit phenomenon.As shown in Figure 2, set the carrier ratio to 20, the modulation ratio to 0.9, and the fundamental frequency to 50 Hz to obtain the gate input signal waveform shown in Figure 3.

Experimental simulation and physical verification
To verify the effectiveness of space-vector pulse-width modulation for modular multilevel inverter circuits and the stability of capacitor voltage control algorithms, this paper builds a modular three-level inverter circuit model on the Matlab/Simulink simulation platform and the specific parameters of modular three-level inverter circuits will be referenced [10] and literature [11] .The detailed values are shown in Table 1.Under the above parameters, using the multi-carrier modulation algorithm proposed in this paper, the analysis plots of the U-phase midpoint output voltage and FFT of the modular multilevel inverter circuit are shown in Figure 4 and Figure 5.It can be seen from Figure 4 that the output voltage waveform is stable, in line with the midpoint output waveform of the modular three-level inverter circuit, and the shape of the waveform is close to the sinusoidal trapezoidal wave, which shows that the modular multilevel inverter circuit has a certain effectiveness in the output characteristics of the circuit.The output voltage THD value of the noninverting stacking method used in the literature [12] is 33.56%, the output voltage THD value of the alternating inverting stacking method is 37.33% in the literature [13] , and the output voltage THD of the positive and negative inverting stacking method is 37.17% in the literature [14] .From Figure 5, it can be seen that the output voltage THD value of the multi-carrier modulation algorithm using the article is 25.45%.The lower the THD value of the output voltage than the three modulation algorithms described above, the smaller the THD value, the closer the waveform is to the sine wave, and it verifies that the output voltage waveform of Figure 4 is close to the sinusoidal trapezoidal wave.
Given the capacitance problem of each submodule of the modular multilevel inverter circuit, to avoid the circulating phenomenon of the circuit, the voltage value of each capacitor is observed as shown in Figure 6 and Figure 7 below.It can be seen that the capacitance value of the four submodules on the single-bridge arm of the U phase is equal.The capacitance value between each phase and each phase is also equal, so there is no circulating phenomenon in the circuit.Therefore, it can be seen that the multi-carrier modulation algorithm in this paper can ensure the safety of the circuit in the modular multilevel inverter circuit., the switching frequency of the switching device is 12 kHz, the initial value of the capacitor voltage is 24 V, and the remaining parameter sizes refer to Table 1 to obtain the output voltage waveform of the midpoint of the U phase as shown in Figure 9, where the voltage size of each cell is 7 V. Figure 9 shows that the output voltage waveform at the midpoint of the U phase is similar to the simulation verification, which verifies the feasibility of the modulation algorithm used in this paper.Since signal interference is considered, an RC filter circuit can be added, where filter circuit 50 R = Ω , 2200 C F μ = .The filter circuit processes the sinusoidal waveform shown in Figure 10, where each cell of the oscilloscope graph represents a voltage size of 10 V. From Figure 10, it can be seen that the output voltage waveform of the modular multilevel inverter circuit after the filter circuit is similar to a sine wave, and the glitch occurs because the switching frequency is too high, which is a normal phenomenon, which just verifies the simulation results of the article, and the output voltage waveform at the midpoint of the inverter circuit is similar to a sine wave.At the same time, the capacitor voltage value of each submodule was measured with an oscilloscope.The capacitor voltage value waveform of the submodule was obtained as shown in Figure 11, where the amplitude size of each cell was 8 V.The capacitor voltage value of the remaining submodules was the same as Figure 11, and the waveforms were shown in Figure 11, which can be obtained from Figure 11.The modulation algorithm used in the article can ensure that the capacitor voltage waveform of each sub-module is the same.There is no circulation phenomenon, thus verifying the authenticity of the simulation.

Conclusion
This paper analyzes the common multi-carrier modulation algorithms for modular multilevel inverter circuits and describes in detail a PWM modulation strategy using a combination of multiple reference waves and multiple carriers.Through analysis and simulation research, the following conclusions are obtained: In the modular multilevel inverter circuit, the THD value of the midpoint output voltage of the PWM modulation strategy combined with a multi-reference wave and multi-carrier proposed in this paper is lower than that of the traditional multi-carrier modulation algorithm, which improves the spectrum of the output voltage.At the same time, the modular multilevel inverter circuit can ensure that the capacitor voltage values of each submodule are equal, the circuit will not circulate current, and the authenticity of the article simulation is verified by building a physical verification platform.
and SM 3 are on, the voltage between the midpoint of the U phase and the O point is 0. When SM 3 and SM 4 are on, the voltage at the midpoint and O point is / 2 dc U −

Figure 3
Figure 3 Gate-level input signals of submodules

Figure 4 Figure 5
Figure 4 Output voltage at the midpoint of the U phase

Figure 6 6 Figure 7
Figure 6 Capacitor voltage values of the four submodules of the U-phase bridge arm

Figure 8
Figure 8 Physical simulation platform Figure 9 Output voltage waveform at the midpoint of the U phase

Table 1
Modular multilevel inverter circuit parameters