# A performance comparison between different PWM techniques for the Hybrid Inverter Drive

Daniel Lendi, Reiko Raute, Cedric Caruana

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Daniel Lendi, Reiko Raute, Cedric Caruana. A performance comparison between different PWM techniques for the Hybrid Inverter Drive. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0046. hal-05077100

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Submitted on 21 May 2025

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# A performance comparison between different PWM techniques for the Hybrid Inverter Drive

Daniel Lendi, Reiko Raute, Cedric Caruana

University of Malta

E-Mail: Daniel.Lendi@um.edu.mt, Reiko.Raute@um.edu.mt, Cedric.Caruana@um.edu.mt

## Acknowledgements

Project "Hybrid Inverter Drive (HID)" financed by the Malta Council for Science & Technology, for and on behalf of the Foundation for Science and Technology.

## Keywords

Variable speed drive (VSD), Voltage source inverter (VSI), Pulse Width Modulation (PWM), Space vector PWM (SVPWM), Hybrid inverter drive (HID).

## Abstract

Variable Speed Drives (VSDs) allow energy savings for loads where operation below the grid frequency may be required. However, when operating the motor load at the grid frequency, they introduce, compared to grid-connected operation, energy losses and Electromagnetic Interference (EMI). The Hybrid Inverter Drive (HID) offers maximum efficiency at either mode of operation. With the HID the motor load is operated in inverter-driven mode for motor frequencies below grid frequency and operated in direct grid-connected mode for operation at grid frequency. This eliminates inverter losses and EMI at the grid frequency. In previous work [5], the HID and its semi-closed transitions were introduced. A performance comparison of the HID operation using pure Sinusoidal PWM (SPWM), Space Vector PWM (SVPWM) and the injection of the DC-link mid-point voltage into the SPWM reference signals during semi-closed transitions is presented in this paper. The HID is modelled in MATLAB Simulink.

## Introduction

In VSDs, the most widely used PWM techniques are SPWM and SVPWM [1]. The injection of a third harmonic common-mode component into the inverter output voltage reference signals is the basic principle behind the improved DC-link

voltage utilization in both, SPWM and SVPWM. However, SVPWM was found to be the superior modulation technique due to additional benefits such as reduced harmonic current ripple and optimized switching sequences [2]. While the choice of modulation techniques can improve the performance of the VSD at all frequencies, the drawback that the VSD introduces additional energy losses [3] and undesired EMI signals [4] still remains. When operating the motor load at the grid frequency, these drawbacks could be avoided if the motor load is directly grid-connected. The HID introduced in [5] presents a drive system capable of operating a motor in two distinct modes of operation. The motor load is operated in inverter-connected mode for frequencies less than the grid frequency, but if operation at the grid frequency is required, the motor load is transitioned to direct grid-connected mode. Semi-closed transitions were carried out using SVPWM in [5], where the motor supply phases are transitioned sequentially, ensuring the motor supply remains uninterrupted during the transition. The motor load is supplied partially by the grid and inverter legs during such a semi-closed transition between the operating modes. Figure 1 shows an overview of the HID system structure. The inverter module is controlled by a microcontroller µC in Figure 1. The bypass module consists of thyristors, whose gate signals are also controlled by the microcontroller. The system measures both grid and inverter output voltage vectors and adjusts the frequency of the latter until synchronization is achieved. This paper presents the synchronization procedure of the HID patented in [6]. Once synchronized, the microcontroller changes between the inverter-and grid-connected modes of operation.
<figure><img src="image_2.png" /><figcaption>Figure 1: HID system structure</figcaption></figure>

A performance comparison between pure SPWM, SVPWM and SPWM with the injection of the DC-link mid-point voltage into the SPWM reference signals is carried out in this paper for semi-closed transitions. This DC-link mid-point voltage injection aims to compensate for a mismatch in reference potentials during transitions between the two modes of operation and is further explained in the following section.

# Methodology

## Used PWM modulation techniques

In a Voltage Source Inverter (VSI), the input source may consist of an AC grid voltage $v_G$. This is then rectified by a six-pulse diode input rectifier as shown in Figure 2.

<figure><img src="image_3.png" /><figcaption>Figure 2: VSI input rectifier</figcaption></figure>

It is a common practice to implement the DC-link capacitor as two separate capacitors $C_{DC+}$ and $C_{DC-}$ for the positive and negative DC-link rails respectively. The input rectifier converts the grid voltage to a DC-link voltage $V_{DC}$ defined in its amplitude by (1) assuming a grid voltage of 400Vrms/50Hz.

$$V_{DC} = \sqrt{2}v_G = 565.69V \quad (1)$$

It is well-known that for pure SPWM, without entering into overmodulation, the maximum achievable inverter phase output voltage magnitude is limited to $V_{DC}/2$ for a two-level

inverter [7]. This occurs due to the switching nature of the inverter, which connects the inverter output to either the positive or negative DC-link rail. This output voltage limit may be increased through overmodulation for pure SPWM. However, this is undesirable as overmodulation is known to produce low-frequency baseband distortion [7]. It was found through research started by Buja and Indri in 1975 [8] that the injection of a common-mode third harmonic term into the reference signals or duty cycles leads to an increase in the DC-link utilization [9] [10]. This third harmonic common-mode component is cancelled out between the inverter phase legs and hence does not affect the fundamental line output voltage [7]. Figure 3 shows an example of injecting a third harmonic sinusoidal signal into the phase voltage reference signal for a single phase leg. Using pure SPWM and a modulation index of $M = 1$, a sinusoidal inverter output phase voltage reference signal is obtained in the yellow waveform. A sinusoidal third harmonic voltage, having an amplitude of 1/6 of the original phase voltage reference waveform, is shown in the blue waveform of Figure 3. These two added together give the red waveform, whose peak amplitude is now reduced. Hence, the addition of a third harmonic signal can increase the modulation index, which increases the DC-link voltage utilization. More precisely, using a 1/6 third harmonic component, the modulation index may be increased by approximately 15% to $M = 1.15$. This resulting reference waveform is represented by the purple waveform. This ratio of the third harmonic injection has been found to be the optimum injection level [7].

Space vector modulation also utilizes the injection of a third harmonic common-mode component into the inverter phase output voltage reference signals. This allows for an increased inverter output voltage of approximately 15% when compared to pure SPWM without third harmonic injection and overmodulation [7]. SVPWM also offers reduced harmonic distortion compared to SPWM with a third harmonic common-mode component injection [7]. Figure 4 shows the range of possible inverter output voltage space vectors for both pure SPWM and SVPWM, assuming that the SPWM does not reach overmodulation and no third harmonic component is injected into the reference signals. In this paper, it is proposed that a third harmonic found at the DC-link mid-point $DC_M$ is injected into the inverter output reference signals. As
previously explained, this is known to increase the inverter output voltage level and also aims to eliminate the difference in reference potentials between the DC-link mid-point and the grid neutral point.

<figure><img src="image_4.png" /><figcaption>Figure 3: Third harmonic injection in SPWM</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 4: Pure SPWM and SVPWM inverter voltages</figcaption></figure>

An inverter output voltage matching the grid voltage both in phase and amplitude as closely as possible results in a smoother transition from the inverter- to grid-connected operating mode and vice versa. The third harmonic voltage found at the DC-link mid-point is chosen as this represents the difference in reference potentials seen by the motor windings during transitions. During transitions, at least one motor winding is connected to a different voltage source. For example, two motor windings may be already connected to the grid, while the third winding is still connected to the inverter. Consider Figure 5, which shows the circuit diagram of the HID. When the motor is operated in inverter-connected mode, the DC-link mid-point DC<sub>M</sub> acts as a reference potential for the voltages present at the motor windings. However, when the motor is

operated in grid-connected mode, the grid's neutral acts as the reference potential. Normally this does not present any problem as long as all motor windings have the same reference potential. However, during the HID transitions between modes of operation, the three motor windings will not be connected to the same reference potential, which will introduce a voltage disturbance during the motor supply changeover.

<figure><img src="image_6.png" /><figcaption>Figure 5: Principal HID circuit diagram</figcaption></figure>

Figure 6 shows the three-phase grid voltages and the resulting DC-link voltage without a DC-link capacitor. All voltages are measured with reference to the grid neutral point N in Figure 5. Only the most positive and most negative grid phase voltages are connected to the DC-link through the diode rectifier. This results in the DC-link voltage's envelope shown in Figure 6, defined by v<sub>DC+</sub> and v<sub>DC-</sub>, which follow the peaks of the most positive and negative grid voltage phases. Furthermore, Figure 6 also shows the resulting DC-link mid-point voltage v<sub>DCM</sub>. The voltage v<sub>DCM</sub> is present at the DC-link mid-point due to the moving envelope of the DC-link voltage and is mathematically represented by (2).

$$v_{DCM} = \frac{v_{DC+} + v_{DC-}}{2} \quad (2)$$

This DC-link mid-point voltage with respect to the grid voltage neutral point N can be measured. Subtracting v<sub>DCM</sub> from the inverter output voltage reference signals removes the difference in reference potentials between the DC-link mid-point and the grid neutral point. This shall provide improved transition results, especially when moving from grid- to inverter-connected mode of operation, as this takes place over a 120° period of the grid frequency. The resulting reference
duty cycle for each inverter phase leg may be expressed by (3) for SPWM with injection of the DC-link mid-point voltage.

$$d_{ABC} = 0.5 + \frac{1}{V_{DC}} [v_{ABCref} - v_{DCM}] \quad (3)$$

<figure><img src="image_7.png" /><figcaption>Figure 6: Three-phase grid supply 400V/50Hz and DC-link voltages</figcaption></figure>

## Simulation model and parameters

The HID shown in Figure 1 was modelled in MATLAB Simulink for this paper. The microcontroller is simulated using a 4kHz s-function, which controls the gate signals of the bypass thyristors and the duty cycles for the IGBTs. It also measures both grid and inverter output voltages to achieve synchronization for the transitions between modes of operation. Table 1 provides a summary of the simulation parameters for the used squirrel cage induction motor and grid supply.

<table><caption>Table I: Simulation model parameters</caption><thead><tr><th>Grid Parameters</th><th>Symbol</th><th>Value</th></tr></thead><tbody><tr><td>Grid resistance</td><td>R<sub>T</sub></td><td>30mΩ</td></tr><tr><td>Grid inductance</td><td>L<sub>T</sub></td><td>100μH</td></tr><tr><td>DC-link capacitance</td><td>C<sub>DC</sub></td><td>2x1600μF</td></tr><tr><th>Motor Parameters</th><th>Symbol</th><th>Value</th></tr><tr><td>Nominal power</td><td>P<sub>n</sub></td><td>15kW</td></tr><tr><td>Nominal line-line voltage</td><td>V<sub>n</sub></td><td>400V</td></tr><tr><td>Nominal frequency</td><td>f<sub>n</sub></td><td>50Hz</td></tr><tr><td>Stator resistance</td><td>R<sub>s</sub></td><td>0.2147Ω</td></tr><tr><td>Stator leakage inductance</td><td>L<sub>ls</sub></td><td>0.991mH</td></tr><tr><td>Rotor resistance</td><td>R<sub>r</sub></td><td>0.2205Ω</td></tr><tr><td>Rotor leakage inductance</td><td>L<sub>lr</sub></td><td>0.991mH</td></tr><tr><td>Mutual inductance</td><td>L<sub>m</sub></td><td>64.19mH</td></tr><tr><td>Inertia</td><td>J</td><td>0.502kgm<sup>2</sup></td></tr><tr><td>Friction factor</td><td>F</td><td>0.0595Nms</td></tr></tbody></table>

## Grid voltage phase tracking

In the simulation case study the induction motor is started using scalar V/f voltage control under full-load conditions. Once the motor reaches the grid frequency of 50Hz, the micro-controller measures both the grid and inverter output voltage vectors through Phase Locked Loops (PLLs) as explained in [5]. The phase error between the voltage vectors is reduced by deviating the inverter output frequency from the 50Hz grid frequency. This deviation from the grid frequency remains small to approach the grid phase gradually. Once both vectors are synchronized by reducing their phase error to 0.01rad, the inverter output frequency is set to the 50Hz grid frequency again. This change in frequency causes a small disturbance in the motor currents and torque and hence a 100ms settling period is implemented. Such a settling period ensures that the disturbance resulting from the change in frequency does not affect the transition performance. Figure 7 shows an example of when the inverter output frequency is increasing to 50.6Hz to synchronize with the grid voltage vector. Both voltage vector phases are shown in the figure.

<figure><img src="image_8.png" /><figcaption>Figure 7: Inverter frequency and vector phases</figcaption></figure>

For this paper, the semi-closed transitions developed in [5] were tested for the following modulation techniques:

1. Pure SPWM

2. SPWM + injection of DC-link third harmonic

3. SVPWM

For pure SPWM to produce the same magnitude in the inverter output voltage as the grid voltage without a third harmonic injection, it must enter into overmodulation. This results in an increased
harmonic distortion in the inverter output voltage. The resulting motor currents will also show non-sinusoidal distortions. To improve on the drawbacks of pure SPWM, the third harmonic measured at the DC-link mid-point is injected into the inverter output phase voltage reference signals. This not only achieves a greater output voltage vector magnitude, but it also results in more sinusoidal motor currents. It is also expected that during the transition from grid- to inverter-connected mode of operation, a lower torque disturbance is observed compared to SVPWM. The DC-link mid-point voltage of the inverter was measured with respect to the grid neutral. The resulting waveform of vDCM and the grid supply current pulses through the input diode rectifier iSA, iSB and iSC are shown in Figure 8.

<figure><img src="image_9.png" /><figcaption>Figure 8: Grid supply currents and vDCM</figcaption></figure>

The measured DC-link mid-point voltage vDCM can be seen to consist of a different shape than the waveform previously shown in Figure 6. The shape of this waveform is dependent on the DC-link capacitor charging behaviour and is difficult to predict, particularly under different load conditions. It is hence preferable to directly measure this voltage for the subtraction from the inverter phase output voltage reference signals as given in (3). Preceding a transition, the inverter must be in voltage control and allow the disabling of individual inverter leg IGBT switching signals. All transitions were carried out starting from sector I. The sectors defined by the three-phase grid voltages, are shown in Figure 9.

<figure><img src="image_10.png" /><figcaption>Figure 9: Grid phase voltages and corresponding sectors</figcaption></figure>

## Simulation results of transitions of motor between inverter operation and direct grid connection

### Transitions with pure SPWM

Figure 10 shows the motor stator currents and the electromagnetic torque during a transition from inverter- to grid-connected operation using pure SPWM and commutating only one phase per voltage sector. Thus, the total 3-phase current commutation period is 120 electrical degrees of the grid frequency as explained in [5]. In Figure 10 the motor is first operated by the inverter using voltage control following the grid voltage. As explained before, due to the limited maximum inverter output voltage amplitude in pure SPWM, overmodulation is required leading to non-sinusoidal currents and a large ripple in the torque. During the transition, each phase is sequentially commutated from the inverter to the grid. The arrows in Figure 10 point to the individual phase current commutation instances. The current commutation of iMA occurs in sector I, 60 electrical degrees later iMC is switched over in sector II and iMB is finally commutated in sector III. When the transition is complete and the motor is directly connected to the grid, the currents become sinusoidal and the torque no longer contains a ripple. The motor torque can be seen dropping to 46.71Nm and peaking at 165Nm during the transition disturbance. With respect to the nominal torque of 104Nm, these represent deviations of 55.09% and 58.65% respectively.
<figure><img src="image_11.png" /><figcaption>Figure 10: Inverter to grid transition with pure SPWM and one phase per voltage sector commutation</figcaption></figure>

Figure 11 shows the transition from inverter- to grid-connected mode using pure SPWM but with commutating initial two phases in one sector and the third phase one sector later. The sequential voltage sector commutation sequence is in detail explained in [5]. As indicated by the arrows, phases A and B are transitioned together in sector I, followed by phase C in the following sector II. This commutation is completed in only 60 electrical degrees of the grid voltage frequency. The motor torque is shown to peak at 158.4Nm and drop to 89.15Nm or 52.31% and 14.28% respectively.

<figure><img src="image_12.png" /><figcaption>Figure 11: Inverter to grid transition with pure SPWM and initial two phases per voltage sector commutation</figcaption></figure>

Figure 12 shows the motor transition back from grid connected to inverter driven mode. As established in [5], the individual phase transitions may only be carried out one phase at a time due to the turn-off characteristics of the bypass

thyristors. The thyristor gate signals are disabled and the thyristors are considered to be turned off once their current drops to 0A.

<figure><img src="image_13.png" /><figcaption>Figure 12: Grid to inverter transition pure SPWM</figcaption></figure>

The motor currents, as indicated by the arrows in Figure 12 remain at 0A for a short period of 0.5-1ms before the referring inverter leg PWM switching is enabled again. This transition creates a visible current distortion for approximately three 50Hz cycles. The torque is shown to peak at under- and overshoots of 12.44Nm and 170Nm or 88.04% and 63.46% respectively during the transient disturbance.

## Transitions with SPWM and DC-link mid-point voltage injection

The same transition conditions were repeated with SPWM and the additional injection of the third harmonic measured between the DC-link mid-point and neutral point of the grid $v_{DCM}$. Figure 13 shows the transition from inverter- to grid-connected mode of operation transitioning by switching over only one phase per voltage sector. Comparing to the results shown in Figure 10 the motor current is more sinusoidal during the inverter-connected operation. Also the total current and torque distortion distortions have been improved compared to the results of Figure 10. The motor torque peaks at 124.7Nm and drops to 87.85Nm or 19.90% and 15.53% respectively during the transient disturbance.
<figure><img src="image_14.png" /><figcaption>Figure 13: Inverter to grid transition SPWM and DC-link mid-point injection and one phase per voltage sector commutation</figcaption></figure>

Figure 14 shows the resulting motor currents and torque when transitioning two phases in the first grid voltage sector and the remaining phase 60 electrical degrees later in the second grid voltage sector. While the torque overshoot is slightly larger than that seen in Figure 13, the undershoot is improved greatly. These are shown to be 126.6Nm and 95.45Nm or 21.73% and 8.22% compared to the motor nominal torque value.

<figure><img src="image_15.png" /><figcaption>Figure 14: Inverter to grid transition SPWM and DC-link mid-point injection and initial two phases per voltage sector commutation</figcaption></figure>

Figure 15 shows the transition back from grid- to inverter-connected motor operation with SPWM and DC-link mid-point injection. The single phase commutations are done again 60 electrical degrees apart as in Figure 12 due to the fact that the bypass thyristor currents have to reach zero to disable the thyristor conduction. It can be seen in Figure 15. that the motor currents remain at 0A

for a short period of 0.5 to 1ms before the inverter phase legs PWM switching is enabled. The inverter legs are then enabled one phase at a time 60 electrical degrees apart, starting from phase A, followed by phases C and B. The resulting torque transient shown in Figure 15 shows a dip to 44Nm and peaks afterwards at 159Nm which is a dip of 57.69% and a peak of 52.88% from the nominal torque value. This is a significant improvement over pure SPWM without the DC-link mid-point injection shown in Figure 12.

<figure><img src="image_16.png" /><figcaption>Figure 15: Grid to inverter transition SPWM and DC-link mid-point injection</figcaption></figure>

## Transitions with SVPWM

Figure 16 shows a transition from inverter- to grid-connected motor operation and commutation of each single phase per grid voltage sector using SVPWM. Each phase current commutation is indicated by the arrows in the Figure 16.

<figure><img src="image_17.png" /><figcaption>Figure 16: Inverter to grid transition with SVPWM and one phase per voltage sector commutation</figcaption></figure>
Comparing the results with Figure 10 and Figure 13 shows that the current and torque disturbances are less than with pure SPWM (Figure 10) but slightly bigger than with SPWM and DC-link mid-point voltage injection (Figure 13). The resulting torque transient in Figure 16 shows a drop to 62.95Nm, followed by an overshoot to 122.9Nm which is 39.47% and 18.17% compared to the nominal motor torque.

Figure 17 shows the transition from inverter- to grid-connected mode transitioning with SVPWM and commutating two phases in voltage sector I and the third phase during voltage sector II similar as Figure 11 and Figure 14. The current and torque disturbances seen in Figure 17 are similar to the results of Figure 14 which uses SPWM with DC-link mid-point injection. The resulting motor torque transition in Figure 17 shows a drop to 93Nm and a following peak of 125.5Nm which are an undershoot of 20.67% and a peak overshoot of 10.58% compared to the motor nominal torque value.

<figure><img src="image_18.png" /><figcaption>Figure 17: Inverter to grid transition SVPWM and initial two phases per voltage sector commutation</figcaption></figure>

Figure 18 shows the motor supply transition from direct grid connection to inverter-driven operation with SVPWM. The result should be compared to Figure 12 and 15. It can be seen that the results in Figure 18 show less current and torque disturbances during the transition than the results in Figure 12 which uses pure SPWM. However, comparing Figure 18 to Figure 15 shows that SPWM and DC-link mid-point injection still performs slightly better than SVPWM and introduces less current and torque disturbances. The torque plot in Figure 18 shows that during the transition a drop to 33.04Nm and following peak to 154.9Nm occur during the

transient. This results to a relative motor torque drop of 68.23% and an overshoot of 48.94%.

<figure><img src="image_19.png" /><figcaption>Figure 18: Grid to inverter transition SVPWM</figcaption></figure>

## Final result comparison

Table II shows a summary of the different PWM modulation techniques used for the transitions from inverter operation to direct grid connection. As already concluded in [5], for all PWM modulation schemes, transitions from inverter to grid-connected motor operation results in a reduced torque disturbance when transitioning two phases in sector I, followed by the third phase in sector II. When using SPWM and injecting the DC-link mid-point voltage into the inverter phase output voltages, a significant improvement is observed for all transitions. In comparison to SVPWM, using SPWM and injecting the DC-link mid-point voltage into the inverter phase output voltages performs better when transitioning a single phase per grid voltage sector. However, both modulation techniques perform similarly well when transitioning initially two phases in sector I and the third phase in sector II.

Table III summarises the torque transient under- and overshoot during the direct grid connection to inverter-driven commutation of the motor. The injection of the DC-link mid-point voltage into the SPWM duty cycles shows an improvement over pure SPWM and SVPWM when transitioning from grid- to inverter-connected mode. In practice, the measurement of $v_{DCM}$ can be implemented at a very low cost as $v_{DCM}$ may be measured directly through a simple voltage divider connected to the microcontroller ADC.
<table><caption>**Table II: Summary of results of transitions from inverter to direct grid-connected operation**</caption><thead><tr><td>Transition</td><td>Torque over- and undershoot</td></tr></thead><tbody><tr><td>Pure SPWM and one phase per voltage sector commutation (Figure 10)</td><td>58.65%, 55.09%</td></tr><tr><td>Pure SPWM and initially 2 phase commutation (Figure 11)</td><td>52.31%, 14.28%</td></tr><tr><td>SPWM and DC-link mid- point injection and one phase per voltage sector commutation (Figure 13)</td><td>19.9%, 15.53%</td></tr><tr><td>SPWM and DC-link mid- point injection and initial two phases per voltage sector commutation (Figure 14)</td><td>21.73%, 8.22%</td></tr><tr><td>SVPWM and one phase per voltage sector commutation (Figure 16)</td><td>18.17%, 39.47%</td></tr><tr><td>SVPWM and initial two phases per voltage sector commutation (Figure 17)</td><td>20.67%, 10.58%</td></tr></tbody></table>

<table><caption>**Table III: Summary of transition results of direct grid-connected operation to inverter operation**</caption><thead><tr><td>Transition</td><td>Torque over- and undershoot</td></tr></thead><tbody><tr><td>Pure SPWM (Figure 12)</td><td>63.46%, 88.04%</td></tr><tr><td>SPWM and DC-link mid- point injection (Figure 15)</td><td>52.88%, 57.69%</td></tr><tr><td>SVPWM (Figure 18)</td><td>48.94%, 68.23%</td></tr></tbody></table>

**Conclusion**

In this paper, the advantages of a third harmonic common mode voltage injection in SPWM and SVPWM was shown for the application in the Hybrid Inverter Drive (HID). A technique was developed, where the DC-link mid-point voltage was measured with respect to the grid supply neutral and injected into the phase output voltage reference signals. This was proposed as during grid- to inverter-connected transitions, the motor windings experience a mismatch in their reference potentials. From the transition results presented in this paper, it can be concluded that

all modulation techniques result in transient disturbances that decay within 100ms. However, pure SPWM without any third harmonic injection results in the most significant motor torque disturbances in all transitions. The injection of the DC-link mid-point voltage $v_{DCM}$ into the reference signals of SPWM yielded similar results compared to SVPWM when transitioning from inverter- to grid-connected operation. However, when transitioning from grid- to inverter-connected operation, as expected, the injection of $v_{DCM}$ results in a reduced disturbance when compared to SVPWM. As mentioned, this voltage may be measured and injected into the inverter reference signals at a very low cost.

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