1. Introduction

An inverter is a power conversion device that generates variable-frequency and variable-voltage AC power from a DC source. It utilizes switching power devices and gate drivers to control and drive permanent magnet synchronous motors (PMSMs). PMSMs are driven using inverters. Depending on the application, either two-level inverters or multilevel inverters are employed. Multilevel inverters are typically utilized in high-voltage or grid-connected systems where high current quality and superior control performance are required. However, two-level inverters are more widely adopted due to their relatively lower implementation cost and reduced control complexity.

Techniques such as pulse width modulation (PWM) and space vector pulse width modulation (SVPWM) are generally employed in inverter to produce AC power^[1]. In inverter design, it is crucial to consider power losses, particularly switching and conduction losses, as these factors influence the performance and overall efficiency of inverters^[2]. To reduce switching losses, the discontinuous pulse width modulation(DPWM) technique has been proposed^[3-5]. The DPWM technique enhances efficiency in PMSM drive system by maintaining the power semiconductor in either an on or off state over specified intervals, offering advantages over the SVPWM technique^[6].

The DPWM technique includes a discontinuous region within one fundamental cycle, during which a specific switching devices remain in either the on or off state for 120°. This approach reduces the number of switching events to two-thirds compared to continuous pulse width modulation techniques, thus achieving an average reduction in switching losses of 33%^{[7, 8]}. In driving a balanced load with the DPWM technique, the discontinuous region is configured based on the phase voltage. This setup reduces switching events when the absolute value of the phase current reaches its maximum. However, when driving an inductive load such as a PMSM, the phase difference between voltage and current limits the effectiveness of setting the discontinuous region solely based on phase voltage. This method does not sufficiently minimize switching events during the interval when phase current is at its maximum^[9]. When driving a PMSM, a phase current-based DPWM technique can be applied to set the discontinuous region according to the phase current. This approach improves the effectiveness of switching loss reduction achieved by DPWM.

Two series-connected switching devices within a leg of an inverter cause a short circuit when operated simultaneously. The excessive current flow resulting from the short circuit can damage switching devices. Therefore, the switches are configured to operate in a complementary manner. Since the turn-off time of an actual switching device is always longer than its turn-on time, there is a risk of a momentary short circuit in switching devices configured to operate complementary in series^[10-16]. To prevent this, dead time is commonly applied by inserting a sufficient period during which both switching devices are off

A Discontinuous Pulse Width Modulation Method Based on a Current Angle for Driving Interior Permanent Magnet Synchronous Motor with Dead Time Compensation between their on/off signals. During dead time, the output voltage of the inverter is passively determined based on the current flow direction through the switching devices, meaning the inverter cannot actively control its output voltage. Consequently, an error arises between the reference voltage and the output voltage, distorting the output voltage^[17-19]. This voltage distortion introduces harmonic components into the current flowing through the PMSM, which increases the total harmonic distortion (THD) of the current. Therefore, a compensation method is required to address the voltage distortion induced by dead time.

This paper proposes a method to reduce switching losses and decrease the THD of the current in an interior permanent magnet synchronous motor (IPMSM) drive systems through a phase current-based DPWM technique combined with a dead time compensation component. To reduce switching losses in IPMSM drive systems, the phase current-based DPWM technique is applied by setting the offset voltage according to the phase angle of current so that the switching device is clamped in the region where the absolute value of the phase current is at its maximum. The polarity of current is identified using the phase angle, and the dead time compensation voltage is set according to the polarity of current. By applying the dead time compensation voltage, the THD of the current is improved, reducing torque ripple and enhancing the efficiency of the IPMSM drive system. In this paper, a two-level inverter is utilized as the topology for motor drives since it is more widely applied across various motor drive applications. The validity of the proposed method is verified through simulations and experiments.

2. Modeling of a Two-Level Inverter for Driving IPMSM

2.1 Modeling of IPMSM

Fig. 1 depicts the circuit diagram of IPMSM drive system using a two-level inverter. VDC and iabc represent DC-link voltage and three-phase current. Fig. 2 illustrates the interior structure of the IPMSM. In Fig. 2, the three- phase windings are simplified for representation, and the air gap length varies depending on the rotor position. This characteristic creates differences in inductance in the rotor reference d-q frame, which generates reluctance torque. The stator voltage equation of an IPMSM is expressed in the d-q frame, as shown in equation (1).

(1)

$\left[\begin{aligned}v_{d}\\v_{q}\end{aligned}\right]=\left[\begin{matrix}R_{s}+p L_{d}&-\omega_{r}L_{q}\\\omega_{r}L_{d}&R_{s}+p L_{q}\end{matrix}\right]\left[\begin{aligned}i_{d}\\i_{q}\end{aligned}\right]+\left[\begin{aligned}0\\\lambda_{f}\end{aligned}\right] $

where the subscripts d and q refer to the d-axis and q-axis in the rotor reference frame. vd and vq represent the stator voltages, and id and iq denote the stator currents. Ld and Lq are the inductances on the d-q frame, respectively, p is the differential operator, Rs is the stator resistance, and ωr and λf denote the rotor electrical angular speed and the flux linkage of the permanent magnet, respectively.

The output torque Te of the IPMSM is generated by both the d-axis and q-axis currents, and the torque equation is given by equation (2).

(2)

$T_{e}=\dfrac{P}{2}\dfrac{3}{2}(\lambda_{f}+(L_{d}-L_{q})i_{d})i_{q}$

where P represents the number of poles. Generally, the q-axis current is the primary component responsible for torque generation, as it interacts with the magnetic flux produced by the permanent magnets to generate torque, contributing to the majority of the output torque of the IPMSM.

Fig. 1. Circuit diagram of IPMSM drive system using two-level inverter

Fig. 2. Interior structure of the IPMSM

3. Proposed IPMSM Drive Method for a Two-Level Inverter

3.1 DPWM Operation of Inverter

The phase voltage-based DPWM technique cannot minimize switching losses when the power factor of the load is not in unity. Such effects occur even when the discontinuous region is set within the region of the maximum phase voltage. This difficulty occurs as the phase current lags or leads due to the phase difference when using phase voltage as the reference. Switching losses increase with higher current magnitudes, so switching in regions where the absolute value of the current is high results in even greater losses.

Fig. 3 illustrates the waveforms of phase voltage and phase current for an inductive load. When driving an inductive load such as an IPMSM, the phase current lags behind the phase voltage. Setting the discontinuous region based on the phase voltage leads to frequent switching during high-current periods. This switching method reduces the effectiveness of switching loss reduction achieved by DPWM. For this reason, a DPWM technique based on phase current rather than phase voltage is necessary. Setting the discontinuous region in the region where the absolute value of the phase current is at its peak facilitates a reduction in switching losses.

Fig. 3. Waveforms of the phase voltage and the phase current under the inductive load condition

3.2 Phase Current-Based DPWM Method

As previously described, the conventional phase voltage-based method for setting the discontinuous region reduces the effectiveness of switching loss reduction. To address this drawback, the discontinuous region is set at the point where the absolute value of the current is maximized based on the current phase angle. While driving an IPMSM, switching losses across the entire system can be reduced by minimizing switching at the point where the phase current is highest. This approach enables efficient IPMSM operation by adjusting the discontinuous region to reflect the phase of the current.

Fig. 4 illustrates the discontinuous region in the phase current-based DPWM technique. Ipeak and Sa represent the peak value of current and switching function of a-phase. For a-phase, the inverter is clamped to State 1 during the 60° interval where the a-phase current reaches its maximum, and clamped to state 0 during the 60° interval where the a-phase current is at its most negative. The same approach is applied to b-phases and c-phase to implement the phase current-based DPWM.

The phase current-based DPWM technique can be implemented by equations (5) to (7) with offset voltages.

(5)

$\theta_{d}=\theta_{current}-\theta_{volt}$

(6)

$v_{di}^{*}=v_{d}^{*}\cos\theta_{d}-v_{q}^{*}\sin\theta_{d}\\ v_{qi}^{*}=v_{d}^{*}\sin\theta_{d}+v_{q}^{*}\cos\theta_{d}$

(7)

$v_{off}=\left\{\begin{matrix}\dfrac{V_{DC}}{2}-v_{\max}&(v_{\max}^{*}+v_{\min}^{*}\ge 0)\\\dfrac{V_{DC}}{2}-v_{\max}&(v_{\max}^{*}+v_{\min}^{*}<0)\end{matrix}\right\}$

Equation (5) represents the difference θd between the phase of the phase current θcurrent and the phase of the phase voltage θvolt. Equation (6) illustrates the process of transforming the phase of the reference voltage to align with the phase of the phase current. In equation (6), vdi* and vqi* denote the reference voltages on the d-q frame in the rotor reference frame based on phase current, vd* and vq* represent the reference voltages on the d-q frame. When the range of the offset voltage voff is set as shown in equation (7), the discontinuous region of DPWM is defined based on the phase angle of the phase current. vmax* and vmin* denote the maximum and minimum values of the phase current-based reference voltage, and vmax and vmin represent the maximum and minimum values of the reference voltage, respectively.

Fig. 4. Discontinuous region of the phase current-based DPWM method

4. Simulation Results

The performance of the proposed DPWM method with dead time compensation was verified throughsimulation results. The simulations were conducted with PSIM software. To analyze the effect of dead time, a dead time of 2μs was applied. Table 1 show the simulation parameters of the IPMSM used in the simulations.

Fig. 5 shows the waveform comparing SVPWM and DPWM during speed control of the IPMSM. Initially, the IPMSM was driven using SVPWM, and from 1 second in the simulation waveform, it switched to a phase voltage-based conventional DPWM. The THD of the waveform was measured using the features provided by the PSIM tool. The load torque of IPMSM was 1.1Nm (10% of rated torque) and the speed of IPMSM was 450rpm (10% of rated speed). The THD was 4.0% in SVPWM, but after switching to DPWM, the THD increased to 5.3%.

Fig. 6 shows the waveform comparing the proposed phase current-based dead time compensation DPWM technique with the conventional DPWM technique. This simulation was also conducted under a load torque of 1.1Nm and a speed of 450rpm, with both techniques performing DPWM, resulting in switch clamping. In this case, the THD decreased from 5.3% to 4.2%. The compensated dead time applied was 2μs.

Fig. 5. Simulation results of SVPWM and conventional DPWM

Fig. 6. Simulation results of conventional DPWM and proposed DPWM

Fig. 7. Experimental setup used for validating the proposed method

5. Experimental Results

The performance and validity of the switching loss and THD reduction techniques were verified through experiments. Fig. 7 shows the experimental setup used for validating the proposed method. The experimental setup consists of a control board, a two-level inverter, and an IPMSM with a load motor. The control board utilizes a DSP (TMS320F28377), and the parameters of the IPMSM used in the experiment are the same as those listed in Table 1.

Fig. 8 shows the experimental results of the phase current-based DPWM technique across different speed ranges. The load torque was set to 3.3Nm, the dead time to 2μs, and dead time voltage compensation was not applied. The speed of IPMSM was 1000rpm in Fig. 8(a) and 1800 rpm in Fig. 8(b). The modulation index (MI) of the inverter was 0.5 and 0.9, respectively, for each case. In Fig. 8, the reference voltage was clamped to 0.5 times the VDC in the 60° interval where each phase current reached its maximum, and clamped to -0.5 times the DC input voltage in the 60° interval where each phase current reached its minimum.

Additionally, there was an improvement in switching loss reduction with the phase current-based DPWM technique across speed ranges. Under the conditions of Fig. 8(a), applying the phase current-based DPWM technique reduced inverter losses from 81W to 77W with the SVPWM technique. Under the conditions of Fig. 8(b), inverter losses decreased from 128W to 120W. Since the RMS values of the phase current remained the same before and after applying the DPWM technique in both conditions, the conduction losses of the inverter remained consistent. Typically, inverter losses consist of the sum of switching and conduction losses, indicating that the phase current-based DPWM technique effectively reduces switching losses. However, since the dead time compensation technique was not applied, ripple appeared in the phase current where the pole voltage reference was clamped.

Fig. 9 presents the experimental results of the phase current-based DPWM technique with dead time voltage compensation across different speed ranges. In Fig. 9, the load torque was set as 3.3Nm, and a dead time was set as 2μs. The speed range was 1000 rpm in Fig. 9(a) and 1800 rpm in Fig. 9(b), with MI of 0.5 and 0.9, respectively. Compared to the waveforms in Fig. 8, where the dead time voltage compensation was not applied, the current ripple in the waveforms of Fig. 9 was reduced. When measuring the THD of the phase current, it was found that for an MI of 0.5 the THD decreased from 8.1% to 7.5%, reducing by approximately 0.6% after applying the dead time voltage compensation technique. For the case when MI was 0.9, the THD decreased from 6.56% to 6.12%, a reduction of approximately 0.44%. With the dead time voltage compensation technique applied, the distortion of the output voltage of inverter was compensated. As a result, the THD of the phase current was decreased.

Fig. 8. Experimental results of the phase current-based DPWM technique according to speed (a) 1000rpm condition (b) 1800rpm condition

Fig. 9. Experimental results of the phase current-based DPWM technique with dead time voltage compensation (a) 1000rpm condition (b) 1800rpm condition

6. Conclusion

This paper proposed a method to reduce switching losses and lower the THD of current in an IPMSM drive system by combining a phase current-based DPWM technique with dead time compensation. A phase current-based DPWM was employed to determine the offset voltage based on the phase angle of current. In this method, the switch is clamped when the absolute value of the phase current reaches its peak to reduce switching losses. The compensation voltage was applied according to the current polarity to reduce the THD of the stator current. The application of the phase current-based DPWM and dead time compensation techniques improved the efficiency of the IPMSM drive system. The validity of the proposed method was confirmed through simulation and experimental results.