## 1 Introduction
This leads to a variable switching frequency and a spread current harmonic spectrum, which can be undesirable [36; 37], particularly for applications that require a clean and predictable harmonic profile and a simplified filter design [21; 22]. Another critical issue in inverter-driven systems is the generation of common-mode voltage (CMV), defined as the voltage difference between the neutral point of the stator and the midpoint of the DC bus. This CMV can induce bearing currents in AC motors, leading to potential damage and increased common-mode currents, which, in turn, cause electromagnetic interference (EMI) [38]. Several modulation strategies aim to reduce or eliminate CMV. For instance, in three-level neutral-point clamped (3L-NPC) inverters, specific modulation schemes can select voltage vectors that generate zero CMV, but this often comes at the cost of reduced DC-bus utilization and increased voltage harmonic distortion [38]. An alternative is the use of active common-mode elimination (ACME) methods, which employ an external power circuit, such as a common-mode transformer with an H bridge, to inject a compensating voltage. This approach can eliminate CMV without compromising DC bus utilization or increasing distortion [38]. Several strategies have been proposed to achieve a fixed switching frequency in FCS-MPC, aiming to combine the fast dynamic response of MPC with the predictable harmonic spectrum of the modulator-based scheme, thereby addressing the drawbacks of a variable switching frequency [21,22]. Another approach involves incorporating an implicit modulator in which the switching patterns mimic those of carrier-based PWM (CB-PWM) or space vector modulation (SVM), with optimal switching instants determined by solving an optimization problem [37]. For example, [PERSON] et al. [37] proposed direct model predictive control (MPC) with an implicit modulator that utilizes the gradient of the system output, thereby formulating the problem as a constrained quadratic program (QP) to ensure a fixed switching frequency and zero current ripple at discrete time instants. [PERSON] et al. [39] presented an alternative FCS-MPC scheme that uses the analogy of a PWM carrier to construct a concatenated sequence of prediction regions, limiting switching choices to predetermined sequences to achieve a fixed switching frequency and enable a higher sampling rate over long prediction horizons. Another technique involves selecting an optimal set of precalculated and stored concatenated voltage vectors, which are applied at optimal switching times computed by solving an optimization problem, thereby achieving a fixed switching frequency and concentrated current harmonic spectra [40]. [PERSON] et al. [17] proposed a hybrid FCS-MPC that uses a linear controller with integral action to impose a PWM switching pattern through an input restriction in the FCS-MPC cost function, achieving zero steady-state error and a well-defined harmonic spectrum. Similarly, [PERSON] et al. [18] introduced an optimal switching time-modulated model predictive control (OST-M2 PC) in which optimal switching times are calculated using a cost function, resulting in a fixed switching frequency and improved power quality compared to conventional FCS-MPC. These fixed-switching-frequency schemes aim to produce a discrete output harmonic spectrum, often with harmonics concentrated at predictable multiples of the fundamental or switching frequency [36,37], which is crucial for meeting grid codes and simplifying filter design [21,22]. The concept of an optimal switching sequence (OSS) has been introduced to multivector MPC schemes to reduce output ripples further and achieve a constant switching frequency [20,21,40,41]. Essentially, the OSS provides an optimal method for selecting the vector-switching sequence to be applied [20]. [PERSON] et al. (2016) extended the OSS concept to control single-phase NPC converters, demonstrating fixed switching behavior and fast dynamic response [40]. [PERSON] et al.