# Model Predictive Control of Grid Forming Converters with Enhanced Power Quality
## 4 Results and Discussion
### Factor weights  
Three optimization criteria have been employed in this paper in order to choose the best factor values and maintain system stability. Mainly, the tuning process was based on the relative importance between the objectives and in this work, the tuning processes of P-CMPC and P-IMPC schemes are shown as an example. Normally, there are no specific guidelines to determine the exact tuning factors of any multi-objective function. In this paper, the relative importance between objectives was determined by defining the priority of each objective. As shown in Figure 21, different tuning of P-IMPC gives somehow a reduced switching frequency until the fixed switching behaviour is reached at 0.8 s and at 1 s for P-CMPC. The importance which is given to the periodic objective determines how the output performance is, in terms of the fixed switching frequency. It worth to mention that power quality is greatly maintained. Figure 22 demonstrates the performance of P-CMPC and P-IMPC during the selection of weighting factors for all three cases, which are defined in Table 2. It can be seen that both equal and higher importance criterion give very good results in terms of switching frequency and THDv for P-IMPC. In the end, Table 3 summarizes the characteristics of all eight algorithms to have an overview of their features. The Table includes THDv, stability assessment, implementation, computational burden, and switching behaviour.  
Figure 20: Sampling effect: a comparison between the switching frequency and currents response of the 40 kHz and 80 kHz samplings. (**a**) A step response from 2.2 kW to 5.2 kW when Ts = 25 μs; and (**b**) a step response from 2.2 kW to 5.2 kW when Ts = 12.5 μs. (**a**) Experimental results: the dynamic response for a VSC using a periodic control strategy having a 40 kHz sampling; (**b**) Simulated dynamic response for VSC using periodic control strategy having an 80 kHz sampling frequency.  
Figure 21: Weighting factors drifting based on the relative importance: average switching frequency and THDv of the \(V_{\alpha}\) for the three criteria; (black line) the derivative term is higher importance than the periodic term; (red line) the derivative term is lower importance than the periodic term; and (grey line) the derivative term is equal importance to the periodic term. (**a**) Average switching frequency for the three criteria; and (**b**) THDv of \(V_{\alpha}\) for the three criteria.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Relative Importanace** & **Frequency Control Methods** & **Improved MPC (IMPC)** \\ \hline Case I & High importance & Low importance \\ Case II & Equal importance & Equal importance \\ Case III & Low importance & High importance \\ \hline \hline \end{tabular}
\end{table}
Table 2: Relative Importance between Objectives  
Figure 21: Weighting factors drifting based on the relative importance: average switching frequency and THDv of the \(V_{\alpha}\) for the three criteria; (black line) the derivative term is higher importance than the periodic term; (red line) the derivative term is lower importance than the periodic term; and (grey line) the derivative term is equal importance to the periodic term. (**a**) Average switching frequency for the three criteria; and (**b**) THDv of \(V_{\alpha}\) for the three criteria.  
Figure 22: Measured switching frequencies and THDV for the three criteria at 1 kW (**a**) the drift of the weights, where the derivative weighting factor \(\lambda_{d}\) is equal to the periodic weighting factor \(\lambda_{p}\); (**b**) the drift of the weights, where the derivative weighting factor \(\lambda_{d}\) is lower than the periodic weighting factor \(\lambda_{p}\); and (**c**) the drift of the weights, where the derivative weighting factor \(\lambda_{d}\) is higher than the periodic weighting factor \(\lambda_{p}\). (**a**) Equal importance case; (**b**) Lower importance case; (**c**) Higher importance case.