#### 5.1. Theoretical Results

Theoretical results relevant for the current ripple in single-2L and dual-2L (3L) inverters are given here. Analysis and comparison of the output current ripple for the two inverters are made with reference to the schemes presented in

Figure 1, and based on the analytical developments presented in the previous section.

In

Figure 4 the normalized function

r(

m, ϑ) defined by Equation (15) is shown, considering various modulation indexes (

m = 1/3, 2/3, and 1), in case of 2L and dual-2L inverters. As expected, the current ripple in dual-2L inverter is generally lower than the ripple of single-2L inverter, valid for the whole phase angle range. In the same figure, the maximum normalized current ripple (

r^{max}) is emphasized with dots. From the figure can be noted that

r^{max} in case of dual-2L inverter has a reduced variability with

m, almost close to the value 0.2 (dashed line), whereas

r^{max} in the case of 2L inverter is increasing almost proportionally with

m [

14]. This is due to the lower distance between the reference vector

**v*** and the available voltage vectors in the case of dual-2L inverter, as consequence of applying the NTV modulation.

**Figure 4.**
Normalized peak-to-peak current ripple amplitude r(m, ϑ) for single- and dual-2L inverters in the range ϑ = [0, 90°] for different modulation indexes.

**Figure 4.**
Normalized peak-to-peak current ripple amplitude r(m, ϑ) for single- and dual-2L inverters in the range ϑ = [0, 90°] for different modulation indexes.

In

Figure 5 the average of normalized current ripple,

r_{avg}, is shown as a function of the modulation index. The goal was to summarize the current ripple amplitude in the whole fundamental period for the two inverters, considering the same output voltage capabilities. It can be noticed that single-2L inverter has almost the double of the average normalized ripple compared to dual-2L inverter, except for low modulation indexes,

i.e., less than 0.4.

**Figure 5.**
Average normalized current ripple vs. modulation index for single-2L and dual-2L (3L) inverters.

**Figure 5.**
Average normalized current ripple vs. modulation index for single-2L and dual-2L (3L) inverters.

Figure 5 also shows that

r_{avg} has a reduced excursion range in the case of dual-2L inverter, ranging between 0.075 and 0.15 for

m = [0.1, 1.15], whereas it is a monotonic increasing function of

m in the case of 2L inverter, ranging between 0.075 and 0.31 (

i.e., almost the double) [

14]. Note that the average current ripple amplitude can be related to the acoustic noise emission from the motor in case of switching frequencies within the audible frequencies.

#### 5.2. Experimental Results

Experimental results are carried out to verify the peak-to-peak current ripple amplitude calculated by the proposed analytical developments, considering both single- and dual-2L inverters. The experimental setup including the custom-made inverters and the Arduino Due microcontroller board, based on the 84 MHz Atmel SAM3X8E ARM Cortex-M3 CPU, is presented in

Figure 6.

**Figure 6.**
Experimental setup. (**a**) Single-2L inverter feeding the star-connected three-phase induction motor; (**b**) dual-2L inverter feeding the same motor in the open-end windings configuration; (**c**) microcontroller board with optic link fibers (up and bottom sides).

**Figure 6.**
Experimental setup. (**a**) Single-2L inverter feeding the star-connected three-phase induction motor; (**b**) dual-2L inverter feeding the same motor in the open-end windings configuration; (**c**) microcontroller board with optic link fibers (up and bottom sides).

The three-phase Mitsubishi PS22A76 intelligent power modules (1200 V, 25 A) have been used for the implementation of single- and dual-2L inverters. The experiments have been carried out by a three-phase induction motor load, in star and open winding configuration, considering single- and dual-2L inverters, respectively. The main rated motor parameters are: P_{n} = 0.55 kW, V_{n} = 380 V (star connected), f_{n} = 50 Hz, ω_{n} = 1400 rpm, two pole pairs. According to the model of induction motor for higher order harmonics, the total equivalent leakage inductance L ≈ 60 mH has been experimentally determined and considered for the ripple evaluation.

The single-2L inverter was supplied with 2

V_{dc} = 420 V, while each inverter in the dual-2L configuration was supplied with

V_{dc} = 210 V. Switching frequency was set to 2.1 kHz and fundamental frequency was kept at 50 Hz for easier comparison with analytical developments. A relatively low switching frequency was chosen in order to keep the current ripple well visible within one fundamental period. The nearly-optimal centered carrier-based PWM is implemented leading to equally share the application times of pivot vectors, as described in

Section 3.2.

A Yokogawa DLM2024 oscilloscope with a PICO TA057 differential voltage probe and LEM PR30 current probe were used for measurements, and the built-in noise filter (cut-off frequency f_{c} = 16 kHz) was applied to the current signal. Instantaneous current ripple is evaluated by post processing the experimental data with numerical high-pass filter in Matlab (cut-off frequency 0.5 kHz, essentially to remove the fundamental current component).

As in the previous sections, the 1st phase is selected for further analysis and different values of

m are investigated. In

Figure 7,

Figure 8 and

Figure 9 are shown the experimental results for three different modulation indexes,

m = 1/3, 2/3, and 1, respectively. Left side diagrams correspond to single-2L inverter, right side diagrams correspond to dual-2L inverter. The same y-axis range has been selected for easier comparison.

**Figure 7.**
Experimental results: details of the output voltage and current waveforms from the oscilloscope, instantaneous output current with calculated peak-to-peak amplitude envelopes, and detail of current ripple with envelopes for m = 1/3: (**a**) single-2L inverter; (**b**) dual-2L (3L) inverter.

**Figure 7.**
Experimental results: details of the output voltage and current waveforms from the oscilloscope, instantaneous output current with calculated peak-to-peak amplitude envelopes, and detail of current ripple with envelopes for m = 1/3: (**a**) single-2L inverter; (**b**) dual-2L (3L) inverter.

**Figure 8.**
Experimental results: details of the output voltage and current waveforms from the oscilloscope, instantaneous output current with calculated peak-to-peak amplitude envelopes, and detail of current ripple with envelopes for m = 2/3: (**a**) single-2L inverter; (**b**) dual-2L (3L) inverter.

**Figure 8.**
Experimental results: details of the output voltage and current waveforms from the oscilloscope, instantaneous output current with calculated peak-to-peak amplitude envelopes, and detail of current ripple with envelopes for m = 2/3: (**a**) single-2L inverter; (**b**) dual-2L (3L) inverter.

**Figure 9.**
Experimental results: details of the output voltage and current waveforms from the oscilloscope, instantaneous output current with calculated peak-to-peak amplitude envelopes, and detail of current ripple with envelopes for m = 1: (**a**) single-2L inverter; (**b**) dual-2L (3L) inverter.

**Figure 9.**
Experimental results: details of the output voltage and current waveforms from the oscilloscope, instantaneous output current with calculated peak-to-peak amplitude envelopes, and detail of current ripple with envelopes for m = 1: (**a**) single-2L inverter; (**b**) dual-2L (3L) inverter.

In the upper diagrams are shown the oscilloscope screenshots with voltage and current waveforms for both single- and dual-2L inverter configurations (voltage across the 1st phase winding and corresponding phase motor current). It can easily be noted that voltages have the same maximum level (4/3V_{dc} = 280 V) in the two configurations, whereas the current ripple is higher in the case of the single-2L inverter, as expected.

For all figures, the middle and lower diagrams are obtained by post processing in Matlab the experimental current data shown in the upper diagrams. In the middle diagrams are shown the instantaneous phase currents (purple traces) together with the calculated peak-to-peak current ripple absolute envelopes (blue traces). In the lower diagrams are shown the current ripples evaluated by high-pass filtering the instantaneous currents (purple traces) together with the peak-to-peak current ripple envelopes (blue traces).

It can be noted that the experimental results are in very good agreement with the calculated current ripple envelopes, for all the considered cases, proving the effectiveness of the proposed analytical developments for practical and realistic applications. In general, the amplitude of the current ripple is well recognizable and the ripple reduction in the case of the dual-2L inverter compared to the single-2L inverter is evident, according to the summarizing diagram shown in

Figure 5.