# Model Predictive Control of Grid Forming Converters with Enhanced Power Quality
## 4 Results and Discussion
### Spectrum Analysis  
The spectrum analysis is shown in this work in order to validate the functionality of the proposed FCS-MPC algorithms, where several points have been observed during the tests as follows:  
\(\square\) In Figure 9, the switching frequency fixed behaviour is obtained successfully by the periodic control technique. In case of having no control over the switching frequency, both conventional and improved FCS-MPC have high switching fluctuations. Thus, the output voltage and current harmonics are spread to a wide range of frequencies, as shown in Figure 10.  
\(\square\) Figure 11 shows the output current spectrum on phase (a) following a reference frequency of 2 kHz using P-CMPC strategy. Here, it can be seen clearly that the output spectrum presents  
Figure 8: A bode plot shows the frequency response of the LC, which is used in the experimental setup. Figure 7: Experimental setup. a similar behaviour as the one achieved with using a modulator. In Figure 12, P-IMPC has a magnitude's reduction in the output spectrum, which is resulting in a higher power quality than the P-CMPC as it is shown in the time between 0.26 s and 0.36 s.
* A series of tests were performed on all algorithms to compare the spectrum performance of each method using the experimental setup. That can be verified in Figures 13 and 14. It can be concluded from the figures that N-IMPC and N-CMPC have higher spectrum magnitude than the P-CMPC and P-IMPC. It can be seen also that it is difficult to keep the spectrum magnitude at the desired frequency in case of using SP-IMPC. Bearing in mind that the SP-CMPC can not be operating at exactly 2 kHz. All these findings make P-IMPC the best algorithm, among the discussed ones in this paper, in terms of fixed switching frequency while providing high power quality. In addition, it is easy to obtain the reference switching frequency and follow it accurately. Table 2 summarizes the THDv for each method utilizing the same LC filter design. It can be concluded that periodic control has a better THDv in both the conventional and improved FCS-MPC. * Figure 15 shows the measured switching frequency in cases where using the P-CMPC and P-IMPC as discussed in Equation (29). It depicts that in P-IMPC, the deviation from the reference is a little higher compared to the conventional P-CMPC, and the reason is that the weighting factors for both tests, in this case, were kept constant. That was to illustrate the effect of using the same weighting factors for both algorithms. * Figure 16a,b show two important aspects. Firstly, they show how the periodic control strategy follows the different references resulting in a fixed switching frequency. Secondly, they show the effect of samplings, which indicates that P-CMPC and P-IMPC are using high sampling frequency to give better fixed switching frequency performance. Figure 10: The spectrum of the conventional CF (CMPC). Figure 9: Different frequency concentrations using periodic control with conventional CMPC. (a) P-CMPC at 1 kHz; (b) P-CMPC at 2 kHz; and (c) P-CMPC at 4 kHz. Figure 11: Experimental results of output load current (phase a) with its corresponding spectrum utilizing periodic control (P-CMPC). Figure 12: Obtained experimental voltage and spectrum results using the conventional and improved CFs. \(F_{sw}\) = 2 kHz, \(C_{f}\) = 60 \(\mu\)F, \(L_{f}\) = 5 mH. Figure 14: Obtained experimental spectrum results using three different frequency control methodologies with conventional CF (CMPC). (**a**) Notch control; (**b**) periodic control; and (**c**) simple penalization control. Figure 13: Obtained experimental spectrum results using three different frequency control methodologies with improved CF (IMPC). (**a**) Notch control; (**b**) periodic control; and (**c**) simple penalization control.