## 1 Introduction
Similarly, to minimize the switching frequency to optimize power converter performance, fewer commutations are needed. This can be achieved by adding a term to the cost function (\(g\)) that specifies the allowable switch transitions between states \(S(k)\) and \(S(k-1)\). This term, combined with other control goals via a weighting factor, is detailed in Equation (12) of [47]. As before, a higher weighting factor negatively affects the controller's primary control goal, as noted in [47]. Inclusion of terms in the cost function to penalize the switching effort or the number of commutations is a common strategy to reduce the average switching frequency [17; 19; 51]. This term typically quantifies the number of commutations between the previous applied state and the candidate state being evaluated [19]. Although increasing the weighting factor for this term can effectively reduce the average switching frequency and associated losses, it often introduces a trade-off, potentially degrading current tracking performance and increasing harmonic distortion [19; 36]. Another approach, Model Predictive Direct Current Control (MPDCC), distinguishes between transient and steady-state operation; in steady-state operation, it optimizes VSI switching behavior to reduce switching frequency, potentially by up to 70%, by selecting voltage vectors using a graph algorithm and an optimization criterion that prioritizes minimal state changes when the current error is small [52]. Furthermore, simply penalizing switching transitions may not guarantee a strictly fixed switching frequency or a clean harmonic spectrum [17; 19; 37]. However, simply penalizing switching transitions may not guarantee a strictly fixed switching frequency or a clean harmonic spectrum and often involves a trade-off with current ripple or tracking accuracy [17; 37]. Most academic literature on adding terms to the cost function in model predictive control (MPC) and using weighting factors for control objectives relies on simulations and experiments [53]. This paper emphasizes that before experimenting with technologies like power converters with control strategies, it is crucial to simulate both the plant and controller. Achieving realistic results requires real-time simulation, which is vital for research in power electronics and control systems. The OPAL-RT real-time simulator (RTS) serves as a key tool for experimental platforms in power systems due to its high-fidelity modeling, simulation, and hardware-in-the-loop (HIL) capabilities [54]. OPAL-RT RTS integrates MATLAB/Simulink for modeling and algorithm application, offers various I/O extension capabilities, and supports complex algorithms [55]. An essential finding of this study is evidence that an FCS-MPC strategy incorporating an explicit objective to minimize the switching frequency demonstrates superior performance compared to the operation of a conventional fixed-frequency controller at a lower frequency. Although operating at a low fixed switching frequency can reduce losses, it typically compromises dynamic response and results in a static trade-off between efficiency and waveform quality. In contrast, the proposed MPC controller achieves a low average switching frequency by systematically penalizing commutations within the cost function at each sampling interval [56]. This approach prevents unnecessary switching during steady-state conditions while maintaining the inherent capability of MPC to react rapidly during transients to correct errors, thereby preserving a rapid dynamic response. This study confirms, through the use of a real-time platform, that this optimized state-dependent control methodology provides a more effective and adaptable balance between switching losses and control performance than traditional fixed-frequency techniques. This paper evaluates the performance of finite-control-set model predictive control (FCS-MPC) strategies in scenarios with and without constraints, like switching frequency minimization.