## 1 Introduction  
Voltage source inverters (VSIs) are a common interface in modern power electronic systems, facilitating the conversion between direct-current (DC) and alternating-current (AC) domains [1, 2]. These devices are widely used in various technological applications, such as advanced motor drive systems [3, 4], renewable energy systems, and distributed energy resources (DERs) [5]. Figure 1 presents a generic representation of the VSI control system. The energy resource (ER) typically consists of sources such as photovoltaic panels (PV) [6], battery energy storage systems (BESS) [7], or wind energy systems (WES) [8]. The inverter converts the ER's DC voltage into AC and is connected through an LC filter to attenuate high-frequency harmonics. An isolation transformer is used to connect to the point of coupling (PC), facilitating the connection to the microgrid or local loads. This system is equipped with sensors to measure the voltages and currents required for the VSI controller. The control objective of the VSI is to achieve reference tracking of the LC filter's output voltage with robustness and low distortion. The control action is sent to a pulse-width modulation (PWM) to generate the inverter's triggering pulses [9, 10]. The voltage control of the LC filter requires advanced strategies compared to current control in grid-connected converters [9]. Typically, proportional-integral (PI) cascaded control strategies are employed [11; 12]. These strategies have the advantage of imposing restrictions on the converter current by imposing limits on its reference; however, they result in limited dynamic performance [13]. Multiple-input multiple-output (MIMO) control strategies have been proposed [12] for VSI control. Nevertheless, these approaches often preserve the cascaded control structure. State feedback control with disturbance compensation has also been proposed [14], satisfying the dynamic performance objectives. However, this strategy does not allow for imposing the converter's physical constraint. The control of VSIs can be formulated using Model Predictive Control (MPC) to achieve a dynamic performance consistent with MIMO optimal control when operational constraints are not violated. Furthermore, MPC offers the distinctive advantage of directly incorporating operational and physical constraints into the control design process [15], effectively overcoming the performance limitations of hierarchical control structures. This topic has gained significant attention in recent years, prompting researchers to propose various MPC strategies for VSIs [16; 17; 18]. In [16], an implicit MPC is proposed, using a custom active set method to solve the optimization problem. The estimated computational complexity of the algorithm is five times lower than explicit MPC formulations, but only for a prediction horizon of one, and only simulation results are presented. In [18], simulation results using MATLAB / Simulink show the use of finite control set model predictive control (FCS-MPC) with horizon one for voltage control of VSIs in a droop-controlled standalone AC microgrid. None of the two previous works incorporate integration for voltage regulation. In [19], an FCS-MPC strategy is proposed again with a prediction horizon of one, but with delay compensation, incorporating an observer that provides integration to the control. This mitigates the effects of uncertainties in voltage regulation. Experimental results obtained in a laboratory setup validate the proposal. However, tuning the bandwidth of an FCS-MPC controlled system is not possible; it has stringent requirements on sampling time and produces a spread switching harmonics spectra, which is undesirable. In general, the MPC strategy can be formulated as a quadratic programming (QP) problem, minimizing a quadratic cost function subject to linear constraints [20; 21]. Several solvers are available for QP problems, such as MOSEK [22], GUROBI [23], ECOS [24], and OSQP [25].