## 5 Conclusions  
This paper explores the application of finite-control-set model predictive control (FCS-MPC) to a three-phase, two-level voltage source inverter (VSI) connected to an isolated load. The analysis considers both linear (\(RL\)) and non-linear loads, with the power converter interfaced through an \(LC\) filter. FCS-MPC stands out for its remarkable flexibility in managing complex non-linear dynamics and seamlessly integrating multiple control objectives. By incorporating secondary objectives such as operational constraints, this control paradigm enables a sophisticated regulation of power converters. However, embedding additional constraints, as described in Equation (15), can significantly increase computational complexity. Despite advancements in microcontroller technologies that mitigate this challenge, the added complexity can detract from the achievement of primary control objectives, particularly when dealing with highly non-linear systems. Even under significant disturbances, such as large variations in the amplitude and frequency of capacitor voltage references, the three-phase, two-level VSI demonstrates a robust capability to accurately track reference waveforms for both capacitor voltages and load currents. This resilience underscores the superior engineering of the system, ensuring reliable performance, even in challenging conditions. A higher sampling rate in the FCS-MPC scheme was shown to significantly improve the total harmonic distortion (THD) of the capacitor voltage, which is crucial for effective power converter control. Sampling rates of 10 and 11.5 kHz proved insufficient for the algorithm to properly track references, whereas higher rates yielded lower total harmonic distortion (THD) and improved dynamic response. This study explored the addition of switching frequency minimization to the cost function. Its impact depends on the load type: non-linear loads complicate capacitor voltage stabilization, while linear loads exhibit slower waveform quality degradation. This analysis of capacitor voltage and load currents highlights the trade-offs in this control strategy. An essential finding of this study is the significant superiority of the proposed FCS-MPC with the minimization of the switching frequency compared to a conventional fixed-frequency controller operating at low frequencies. Although both methods aim to minimize switching losses, the fixed-frequency method constrains the system to a fixed, slow switching pattern, which inherently compromises dynamic performance during transients. In contrast, the proposed predictive controller attains a low average switching frequency through intelligent, state-dependent decision-making. It avoids superfluous commutations in steady-state conditions to enhance efficiency but maintains the ability to switch as rapidly as the sampling rate permits during variations in load or reference, thereby preserving the exceptional dynamic response characteristic of MPC. The weighting factor \((\lambda_{\text{min}})\) serves as a direct and effective mechanism to adjust the optimized balance between efficiency and waveform quality, providing a degree of flexibility and performance not achievable with simple fixed-frequency methods [56]. Real-time analysis, especially using OPAL-RT platforms, is proven superior to software-based methods, offering greater precision in control output waveforms. This precision, achieved even with MATLAB/Simulink modeling, is crucial for improving predictive control strategies for the three-phase, two-level VSI, highlighting the importance of real-time platforms in power electronics research. Conceptualization, A.V., C.B.-M. and M.R. ; methodology, A.V., R.Z., H.L. and C.B.-M.; software, A.V., R.Z., H.L. and C.B.-M.; validation, M.R., P.W. and C.B.-M.; formal analysis, A.V. and C.B.-M.; investigation, A.V., H.L. and R.Z. ; resources, A.V., L.Y.G. and M.R. ; data curation, A.V. and C.B.-M.; writing--original draft preparation, A.V. ; writing--review and editing, A.V., C.B.-M., P.W. and M.R. ; visualization, A.V.