Hybrid Modulation Strategy for Common-mode Voltage Suppression in Three-level Inverters

A hybrid modulation strategy is proposed to suppress the common-mode voltage (V com) of the three-level PWM inverter on the strength of the SVPWM modulation algorithm (space vector pulse width modulation) for V com generated during the run of the three-level inverter. The three-level space vector is classified as two different modulation areas by modulation ratios. In the low modulation ratio region, according to the nearest three vectors principle, the spatial voltage vector is obtained by combining the small vector with the medium vector, which suppresses V com and ensures that only one bridge arm is switched for any voltage vector. In the high modulation ratio region, the vector with large common-mode voltage is discarded, and the zero-vector, medium-vector, and large-vector are selected to synthesize the space voltage vector, which suppresses V com and ensures the good output current waveform of the PWM inverter. From the simulation results, we can see the hybrid modulation strategy of dividing the region by modulation ratio reduces the magnitude of V com to 1/6 of the dc bus voltage, and at the same time, a good current waveform is obtained at the output of the three-level inverter.


Introduction
Due to the rapid promotion of the SVPWM algorithm, three-level inverters are frequently used in permanent magnet synchronous motor drive systems.The com V generated during the SVPWM control process acts on the stator-rotor parasitic capacitance and generates a shaft voltage between the motor bearing and the housing, which may break the oil film and generate shaft current when the shaft voltage amplitude is too high [1].Therefore, it is indispensable to study how to suppress the com V of the inverter.
For the com V suppression strategy, many experts and scholars have done a lot of work, and the main methods are to apply passive filters or active filters, optimize the SVPWM control strategy and change the inverter topology [2].In [3], the inverter common-mode voltage is suppressed by adding feedforward active filters.In [4], an active common-mode noise voltage option is designed, which can effectively dispel the com V of inverter output.Adding filters or changing the inverter topology increases the difficulty of designing the system.Therefore, modulation algorithms without zero vector were gradually developed [5][6][7], which suppressed the common-mode voltage to some extent, but did not achieve the expected suppression effect due to the switching tube deadband effect.In [8], a zero-vector-free modulation algorithm is introduced, but it is only suitable for high modulation ratio regions.
In response to the shortcomings in the com V suppression process of the three-level inverter, this paper proposes a hybrid modulation strategy by analyzing the mechanism of the

V
produced by the inverter to 1/6 of the DC-side bus voltage.The total harmonic distortion of the inverter output current waveform is kept below 6%.We simulate the open and the closed loop system based on vector control and use the MATLAB/SIMULINK tool to simulate.After verification, the strategy is proven to be correct and effective.

Traditional three-level SVPWM working principle
The topology of a T-type three-level inverter can be seen in Figure 1.In this figure, the busbar voltage is expressed in U dc , C 1 and C 2 are DC side capacitance, Point O is the midpoint of DC side capacitance, and n is the load neutral point.Since each of its phases has three level states P, O, and N, it corresponds to 27 combinations, that's the 27 basic voltage vectors [9]. Figure 2 shows the three-level vector diagram.
The traditional SVPWM arithmetic is mainly divided into three steps: sector judgment, time calculation, and time allocation.The traditional SVPWM algorithm has been studied more, and due to the limitation of space, this paper will not go into too much detail.

Mechanism of common mode voltage generation
The topology of the PMSM three-level three-box inverter drive system is shown in Figure 1.The voltage between point O and load neutral n in the DC-side capacitor is the common mode voltage of this inverter [10] .
Table 1 illustrates the connection between switching states and com V .

Hybrid modulation strategy for common mode voltage suppression
This paper re-divides the modulation area of the three-level inverter on the strength of the zoning idea of the traditional SVPWM algorithm, dividing the modulation area into high modulation ratio and low modulation ratio areas according to the modulation ratio.The low modulation ratio area is divided into six sectors, small vectors and medium vectors that generate smaller common-mode voltages that are selected to synthesize reference vectors.The high modulation ratio area is divided into twelve sectors, zero vectors, medium vectors, and large vectors that generate smaller common-mode voltages that are selected to synthesize reference vectors V ref .
The modulation ratio in the three-level SVPWM modulation strategy is k a =√3V ref /U dc , where V ref is the reference voltage vector amplitude.Bounded by the interior regular hexagon in Figure 3, at this point, the modulation ratio k 0 ≈0.577.When the modulation ratio k≤ k 0 , V ref is located in the low modulation ratio region (blue area); When k>k 0 , it is located in the high modulation ratio region (red region).

Low modulation ratio area
The low modulation ratio region is divided into six sectors, with 60° counterclockwise as one sector, and sectors I~VI are shown in Figure 3.When the V ref is located in the position shown in Figure 4(a), the com V produced by the middle vector PON is zero, and the com V produced by the small vector OON and POO is of amplitude U dc /6.The conduction sequence of the voltage vector is rationalized to avoid excessive losses in its switching process, and the vector action sequence in sectorⅠis: OON-PON-POO-PON-OON.

High modulation ratio area
When the V ref is in the high modulation ratio region shown in Figure 4(b), it can infer from Table 1 that, to suppress the com V , the switching state that generates U dc /3 is discarded, and zero vectors OOO, medium vectors PON, and large vectors PNN that generate common-mode voltage amplitudes of U dc /6 are selected.
A sector of 30°counterclockwise can divide the high modulation ratio region into 12 sectors, as shown in Figure 3.When V ref is located in sector 1 of the high modulation ratio region of Figure 4, V ref is synthesized from the voltage vector V 0 , V 1 , and V 2 .Its duration of action is: (2)

Open-loop systems
To verify the correctness of the above hybrid modulation strategy, the T-shaped three-level inverter circuit shown in Figure 1    Analysis of the simulation results shows that the hybrid modulation strategy can decrease the amplitude of the common-mode voltage to 1/6 of the busbar voltage in both high and low modulation ratio regions, which is half of the traditional SVPWM algorithm.Due to the effective utilization of various voltage vectors by three-phase voltage source type PWM inverters, the output waveform of PWM inverters contains fewer harmonic components.The inverter output voltage and current waveform are similar to a sinusoidal waveform under the traditional SVPWM algorithm, and the total harmonic distortion rate (THD) of the inverter output voltage waveform is increased under the hybrid modulation strategy that divides the high and low modulation ratio regions, but the THD of the current waveform is controlled to less than 6%.

FOC closed-loop system
To demonstrate the stability of the hybrid modulation strategy to the speed control system, a permanent magnet synchronous motor vector control simulation diagram is built, as shown in Figure 9.The correctness of the algorithm is verified by comparing the motor speed, electromagnetic torque, and other parameters under the traditional SVPWM algorithm and hybrid modulation strategy.In Figure 9, the space vector modulation module adopts the traditional SVPWM modulation algorithm and the hybrid modulation strategy proposed in this paper.
When the traditional SVPWM algorithm is used, the motor is started at no load and 10 Nm load torque is added in 0.1 seconds, at which time the motor stator current, electromagnetic torque, speed, and common mode voltage are shown in Figure 10   The waveform obtained by simulation is visible that the motor stator current waveform is close to a sinusoidal waveform, and the speed drops when the load is added at 0.1 s and follows the given value soon after, and the com V amplitude is 1/3 of the busbar voltage.
When the hybrid modulation strategy is used, the motor stator current, electromagnetic torque, speed, and common mode voltage are shown in Figures 11(a  Figure 11 shows that the motor stator current waveform is good, and the speed quickly follows the given value after decreasing when a load is added at 0.1 s.The com V amplitude is 1/6 of the busbar voltage.By contrasting Figure 8 and Figure 9, it follows that compared to the traditional SVPWM algorithm, the hybrid modulation strategy proposed in this paper can reduce the amplitude of the common-mode voltage to 1/6 of the DC busbar voltage amplitude while maintaining a good three-phase current waveform, with smaller motor output torque fluctuations and faster response to the given value.

Conclusion
By analyzing the working principle of SVPWM for three-level inverters and the cause of the com V generation, this essay obtains the common-mode voltages corresponding to different voltage vectors of the three-level inverter.A hybrid modulation strategy is proposed to divide the high and low modulation ratio areas by modulation ratio.On the basis of vector control, the open loop and closed loop systems are simulated, and the following conclusions are obtained: (1) Different from the traditional SVPWM strategy, the hybrid modulation strategy decreases the amplitude of the com V produced by the inverter to 1/6 of the busbar voltage.(2) Compared with other common-mode voltage suppression algorithms, the hybrid modulation strategy makes reasonable use of various voltage vectors to ensure that the THD of the inverter output current waveform is below 6%.
(3) The hybrid modulation strategy only allows one-phase leg switch action in both high and low modulation ratio areas, reducing switching losses while achieving common-mode voltage suppression effects.
(4) In the closed-loop vector control method utilizing the hybrid modulation strategy discussed in this study, the motor's three-phase current exhibits minimal harmonic distortion.This results in reduced torque ripple, allowing the motor to quickly respond to set values.Consequently, the hybrid modulation approach holds practical significance.
com V voltage produced by the T-type three-level inverter.This strategy uses different voltage vectors to synthesize reference voltage vectors in different modulation ratio regions.It reduces the com

Figure 1 T
Figure 1 T-type three-level inverter topological structure

Figure 2
Figure 2 Three-level vector diagram

8 Figure 3 Figure 4 3 ) 3 )
Figure 3 Three-level spatial voltage vector distribution in different regions is established in SIMULINK for simulation and analysis.The permanent magnet synchronous motor can be viewed as three star-connected loads.The inverter parameters are as follows: DC bus voltage: 700 V, base wave frequency: 314 Hz, carrier frequency: 50000 Hz, resistance: 10 Ω.When the traditional SVPWM algorithm and the hybrid modulation strategy are used respectively, the T-inverter output A-phase voltage and current waveforms, at the same time the com V waveforms are shown in Figure5~Figure7.

Figure 8
Figure 8 Inverter output A-phase current FFT (a) to (d).

Figure 9
Figure 9 Vector control diagram.

Figure 11
Figure 11 Hybrid modulation strategy

Table 1
Common Mode Voltage Versus Switching State