A Inverter Dead-time Compensation Method Based on Phase current Polarity Determination and Voltage Partitioning

The introduction of the dead time of the inverter solves the straight-arm conduction problem of the upper and lower power devices of the inverter, but also leads to the deviation of the actual output voltage of the inverter from the given voltage. Dead time increases the harmonic components of phase voltage and phase current, which is also an important factor leading to motor torque ripple. In this paper, the mechanism of the deviation of phase voltage and phase current caused by the dead time of voltage space vector modulation is analyzed, and the effect of dead time on phase voltage and phase current harmonic components is studied. A simple and effective dead time compensation method based on phase voltage division and phase current polarity determination is proposed to directly compensate the dead time. This method can suppress the current harmonic and torque ripple in the running state of the motor, and can greatly simplify the calculation process of the traditional dead time compensation method. Through the system modeling and simulation, it is verified that the method can significantly improve the current waveform distortion, and has good practical value.


Introduction
Permanent magnet synchronous motor has been widely used in industrial control because of its high power density, high efficiency, and high reliability.When the three-phase voltage source bridge inverter is used to drive the permanent magnet synchronous motor, it is necessary to add a certain dead time in order to avoid the direct connection between the upper and lower bridge arms of the inverter [1].The inverter nonlinearity caused by the dead time will cause the phase current and voltage harmonic components to increase, and then cause the current harmonics and torque ripple during the motor operation [2].Therefore, many scholars have carried out relevant research on the compensation of dead time.
There are two methods commonly used to compensate the dead time effect: voltage feedback and current feedback.The voltage feedback method can compensate the bad effect caused by the dead zone, but it needs to add the hardware circuit to detect the voltage value of each phase, and the structure is more complex [3].The current feedback mode has some ambiguity in the zero-crossing of the current and it is difficult to determine directly and accurately [4].In addition to the above two methods, there is also a large body of literature that proposes different dead-zone compensation schemes.In reference [5], the dead-zone is compensated by the method of current direction detection and volt second balance.In reference [6], current closed-loop and dead-time compensation are combined by detecting the current error of the orthogonal axis.This method does not need additional hardware circuit, but the compensation effect is affected by the current controller.In reference [7], the fuzzy compensation algorithm was used to calculate the error voltage caused by the dead zone in real time, and the feed-forward control was applied to the error voltage compensation.The reference [8] proposes a compensation method of disturbance observer, which takes the error voltage caused by the dead-time effect as the system disturbance.This method uses disturbance observer to estimate the compensation signal, but it needs a large number of tests to obtain the appropriate control parameters.In this paper, the mechanism of the deviation of the dead time of voltage space vector modulation on the phase voltage and phase current of the motor is first analyzed.Then, the influence of the dead time effect on the harmonic components of the phase voltage and phase current is studied.Combined with the traditional dead-time direct compensation method, a dead-time compensation method based on phase voltage division and phase current polarity determination is proposed.The method compensates the voltage vector by directly calculating the conduction time of the adjacent voltage vector after the compensation dead zone using the voltage neutral point, the polarity of the phase current and the three-phase reference voltage value in different partitions.This method solves the computational complexity of the traditional dead-zone direct compensation.Finally, the system modeling and simulation analysis were carried out to verify the feasibility and effectiveness of the proposed method to reduce torque ripple.

Dead-time Effect of Voltage Space Vector Modulation
In order to understand the influence of dead-time on voltage space vector PWM modulation of inverter, the mechanism of voltage deviation caused by dead-time is analyzed theoretically.The relationship between the actual output voltage and the given voltage is derived, and the deviation between the voltage and the current is calculated.The topology of the three-phase universal PWM inverter is shown in Fig. 1, and a typical space-vector gate trigger signal is shown in Fig. 2.  In order to clearly show the effect of dead time, the tube voltage drop and parasitic capacitance of power devices are not considered.The switch trigger signal with the added dead zone and the actual output voltage are shown in Fig. 2. Since the analysis method of the bridge arm is the same for each phase, phase A is taken as an example here to analyze the dead zone effect.The waveform in Fig. 2(a) is a typical ideal IGBT gate trigger waveform with no dead zone added.Fig. 2(b) shows the ideal IGBT gate trigger signal after adding the dead zone.The Fig. 2 (d) shows the waveform of the inverter output voltage when the current is less than zero.
According to the analysis in the figure above, it can be known that the disturbance voltage generated by the dead zone is related to the current direction, so the following formula can be obtained: Where, T s is current sampling period, t ON is turn-on time of power device, t ON is turn-off time of power device.
The relationship between the three-phase average voltage disturbance and the current direction can be written as follows.

Working Principle of Voltage Neutral Point Phase Current Polarity Determination Method
The Fig. 3 depicts the waveform of the voltage at a given value for each phase of the three-phase voltage source inverter.Vas*, Vbs* and Vcs* are the voltage reference values for each phase.After comparing the three phase voltages, there are maximum, minimum and intermediate values of voltage at any time.They are denoted as Vmax*, Vmin* and Vmid*.Analysis of Fig. 3 shows that the maximum value of the voltage is the voltage of phase A, the intermediate value is the voltage of phase C, and the minimum value is the voltage of phase B in the time period ① and ②.In the time period ③ and ④, the voltage of phase A is the maximum value, the voltage of phase B is the intermediate value, and the voltage of phase C is the minimum value.The polarity of the intermediate voltage is always changing.However, the actual situation does not output the voltage according to the ideal output mode, and there are many factors that affect the voltage accuracy in the circuit.These factors are dead time, delay of switch tube actuation, and tube voltage drop of power devices.In order to analyze the influence of these factors on the actual output voltage more accurately, it is necessary to analyze the model nonlinearity in more detail.Fig. 4 depicts the trigger signals of the actual switching devices and the actual inverter output voltage after the dead-time is added to the three-phase voltage source inverter when the voltage mid-phase current is greater than zero.The output voltage error can be divided into two parts, one is the tube voltage drop of the power switching device and the free flowing diode, and the other is the tube voltage drop due to the delay time.The equivalent circuit diagram in each time period is shown in Fig. 5.The magnitude of the voltage error depends on the characteristics of the power devices as well as the magnitude of the current.It is generally considered that the current in the phase with the maximum command voltage is positive.The phase current with the minimum command voltage is in reverse phase conduction.The intermediate phase current direction may be positive or negative.During time period t0-t1 and t6-t7, it is the action time of voltage vector (000), and the current polarity of the phase with the intermediate voltage value is positive.The actual operation of the circuit is equivalent to the Fig. 5(a).The formula can be derived as follows:       max min 1 3   00 max(00) max   00 m (00) m   00 min(00) min Where, VCE(i) is voltage drop of switch tube, VDF(i) is voltage drop of freewheeling diode.The equivalent circuit of the four is assumed to be the maximum voltage in phase A and the minimum voltage in phase C in the Fig. 5.
When the current polarity of the intermediate voltage phase is positive, the actual effective conduction time of this voltage vector in time period T1 is as follows.
Where, tdr is the rise delay time of the gate driver circuit of the power device.
In the time period T2, the effective time of the actual voltage vector is: The According to the previous calculation method, the per-phase voltage in time periods t2-t3 and t4-t5 can be calculated, denoted as VN, Vmax(2), Vmid(2), and Vmin(2).
In the time period t3-t4 (111), the effective time of the actual voltage vector is: According to the previous calculation method, the per-phase voltage in time periods t 3 -t 4 can be calculated, denoted as V N , V max(01) , V mid(01), and V min(01) .

Dead-time Compensation Method for Computation of Action Time of Voltage Vectors
Due to the inherent characteristics of semiconductors, the tube voltage drop of power devices shows a high degree of nonlinearity with respect to the magnitude of current.It is difficult to measure or calculate the voltage error caused by the voltage drop of the power device in the actual drive system.However, compared with the influence of dead time on the voltage error, the influence of tube voltage drop on the actual output voltage error of the inverter is relatively small.So the voltage error is mainly caused by the dead time, and the whole analysis will be simplified.It is considered that the tube voltage drop of either switching device or freewheeling diode is expressed as follows: Although the above three values are not equal, but most of these values are relatively small, when converted to the voltage source inverter will further reduce the error, so this simplification is reasonable.
From the subsection analysis of each stage of a PWM cycle in the previous section, it can be obtained that when the current in the intermediate voltage phase is greater than zero, the three-phase voltage can be written as follows: Similarly, the three-phase voltage can also be obtained when the current of the intermediate voltage phase is less than zero and the value of T 1 and T 2 can be obtained by simplification.
Therefore, the flow of the whole compensation process is shown in Fig. 6.

Simulation Analysis of Dead-time Compensation Method
In this section, the simulation analysis of the compensation strategy proposed in this paper is carried out, and the stator phase resistance of the motor is 0.11Ω, the quadrature axis inductance is 2.54mH, and the number of poles is 4. The DC-side bus voltage of the inverter is 270V and the dead time is set to 6us.The PWM switching frequency is 10kHz.The simulation analysis of the permanent magnet synchronous motor running at 750rpm is carried out.Motor external characteristics are mainly the motor current and output torque characteristics.Fig. 7 and Fig. 8 show the current waveforms when the motor is running at 750rpm with dead zone and using compensation control strategy.Due to the existence of the inverter dead zone, the current waveform will produce a relatively large distortion.In Figure 7, the phase current is greatly distorted at the current zero-crossing point.The current waveform after compensating the model by the compensation method is shown in Figure 8.The current waveform in this figure has been well improved, and the overall waveform sinicity is good.Figure 9 shows that due to the existence of the dead zone, the torque presents a torque ripple with obvious periodicity, and the torque range is expanded to more than 0.5N.m.Because the large number of harmonics in the current lead to torque instability, the torque ripple becomes larger.When the deadtime compensation is added, the torque ripple obviously decreases, the torque waveform is relatively stable, and the torque change is basically controlled at about 0.25N.m,as shown in Figure 10.By analyzing the phase current harmonics, it can be seen that the dead zone produces more obvious harmonics of 5, 7, 11 and 13, and the harmonic components are very well suppressed when the compensation strategy is used.The harmonic analysis of the torque is also basically the same, and the harmonics generated by the current distortion will generate 6n torque ripples in the motor torque.Due to the influence of the dead zone, the sixth torque harmonic of the motor is more obvious.This is consistent with the sixth torque ripple of the motor caused by the fifth and seventh harmonics of the current caused by the dead zone.

Conclusions
In this paper, the mechanism of voltage deviation after adding dead time in the inverter is analyzed in detail.Secondly, the average voltage method is used to calculate the deviation voltage of each phase in different intervals of the symmetrical three-phase current.Thirdly, in order to suppress the harmonics caused by the dead-time deviation voltage, a simple and effective dead-time compensation method based on phase voltage division and phase current polarity determination is proposed to directly compensate the dead-time.This method solves the actual output phase voltage of the inverter through the current direction of the intermediate voltage phase and the three-phase output voltage reference value.It directly calculates the action time of adjacent voltage vector with dead-time compensation method by three-phase actual output voltage equation.The voltage vector calculation time is directly

Figure 3 .
Figure 3. Waveform of the given three-phase voltage.

Figure 4 .
Figure 4. Power tube actual trigger signal and output voltage waveform.

Figure 5 .
Equivalent circuit of each period when the i mid >0.

Figure 6 .
Figure 6.Block diagram of the dead-time compensation control strategy.

Figure
Figure 10.Torque waveform after compensation.
The values of T 1 and T 2 can be obtained by simplifying them as follows: 6