## 4 Experimental Results  
The proposed method was tested with a prototype of the single-phase three-level NPC converter circuit. The peak value of the source line voltage was 110 V, the dc-link voltage was set to 150 V, and \(R_{L}\) was 100 \(\Omega\). The proposed method and the conventional method for comparison were implemented on a digital signal processor (DSP) board TMS320F28335 (Texas Instruments Incorporated, Dallas, TX, USA). The sampling period \(T_{s}\) was set to 50 \(\upmu\)s to generate a sinusoidal ac source current with a unity power factor. Figure 7 shows the performance of the conventional MPC method as a function of different weighting factors. From Figure 7, the conventional MPC method in the experiment in this paper used the value 0.5 for the weighting factor. Figure 6: A flow chart of the proposed MPC method. Figure 7: The THD of the source current and peak-to-peak value of the capacitor ripple voltage obtained by the conventional MPC method vs. weighting factor (\(\lambda_{c}\)). The source voltage, source current, frequency spectra of the source current, line-to-line converter voltage, and the two capacitor voltages obtained by the conventional and proposed methods are shown in Figures 8 and 9. It can be seen that the source currents are sinusoidal in phase with the source voltages and that the two capacitor voltages are well balanced for both methods. The frequency spectra of the source currents obtained from the conventional and proposed methods are also shown where it is evident that the total harmonic distortion (THD) of the proposed method is slightly lower than that of the conventional method. The converter input voltage and the two capacitor voltage waveforms obtained by the two methods are almost similar, as shown in Figures 8 and 9. For the purposes of comparison, experimental results obtained by using only the difference-mode reference voltage without adding the common-mode voltage term are shown in Figure 10. It can be seen that the difference-mode reference voltage can synthesize sinusoidal source current even with a higher THD value as well as maintain the two capacitor voltages. In addition, the line-to-line converter input voltage exhibits only a three-level waveform with \(\pm\)\(V_{dc}\) and zero, as shown in Figure 10c. It can be seen that the model predictive control method with only the difference-mode voltage to control the grid currents can increase the current ripples, as shown in Figures 8 and 10, because the limited number of the switching states are used. However, the proposed algorithm with both the difference-mode and the common-mode voltages results in reduced current ripples in comparison with the conventional method, as shown in Figures 8 and 9. Figure 8: Experimental results from the conventional method: (**a**) source voltage (\(v_{s}\)), source current (\(i_{s}\)), capacitor voltages (\(v_{c1}\) and \(v_{c2}\)); (**b**) fast Fourier transform (FFT) spectrum of source current (\(i_{s}\)); and (**c**) line-to-line converter voltage (\(v_{ab}\)) and ac component of capacitor voltages (\(v_{c1}\) and \(v_{c2}\)). In Figure 10(a),b, experimental waveforms of the two capacitor voltages resulting from the conventional and the proposed methods are shown when intentionally imbalanced capacitor voltages occur. Both the conventional and proposed methods can balance the capacitor voltages with the  
Figure 10: Experimental results using only the difference-mode reference voltage without the common-mode voltage terms: (**a**) source voltage (\(v_{s}\)), source current (\(i_{s}\)), capacitor voltages (\(v_{c1}\) and \(v_{c2}\)); (**b**) FFT spectrum of source current (\(i_{s}\)); and (**c**) line-to-line converter voltage (\(v_{ab}\)) and ac component of capacitor voltages (\(v_{c1}\) and \(v_{c2}\)).