## 8 Conclusions  
This work proposed an MPC technique with integral action for the control of voltage source inverters with LC filters in grid-connected applications and validated it in an experimental VSI setup. The control design enabled accurate reference tracking of the output voltage within the model predictive control framework while achieving a suitable transient response to load current disturbances. Furthermore, the method integrates operational constraints on the filter current and modulated voltage, providing effective protection for the power converter during grid faults or significant network transients. Simulation results conducted in MATLAB demonstrate the dynamic performance of the  
Figure 11: Experimental results when the \(3A\) current limit is activated by connecting an additional load resistance bank of \(23\)\(\Omega\) at \(t=2.66\) s.  
proposed MPC algorithm and its capability to protect critical power electronics assets in the grid, making it a superior alternative to traditional hierarchical PI controllers. Furthermore, the experimental implementation achieved resolution times for the resulting QP problem of less than 70 \(\,\upmu\)s using the readily available OSQP solver, appropriately configured and tuned. This validates the feasibility of the proposed method for practical implementation in VSIs with LC filters for grid-connected applications. Finally, the experimental offset-free MPC could be explored for extension to higher closed-loop levels in the microgrid hierarchy that require integration, such as secondary control, to enhance stability, incorporate operational constraints, and ensure accurate voltage and frequency tracking.  
Conceptualization, R.L.A., C.A.S. and J.C.A.; methodology, R.L.A., C.A.S. and J.C.A.; software, R.L.A., D.F. and C.A.S.; validation, R.L.A. and D.F.; formal analysis, R.L.A., C.A.S. and J.C.A.; investigation, R.L.A., C.A.S. and J.C.A.; resources, R.L.A., D.F. and C.A.S.; writing--original draft preparation, R.L.A., D.F. and C.A.S.; writing--review and editing, R.L.A., D.F. and C.A.S.; visualization, R.L.A., D.F. and C.A.S.; supervision, J.C.A. and C.A.S.; project administration, C.A.S. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the Chilean National Agency for Research and Development (ANID) Scholarship Program/doctorado nacional 2021-21211446, in part by the PIIC program of DGP at Universidad Tecnica Federico Santa Maria No 061/2023, and in part by the grants ANID-Fondecyt 1211630 and 1211676, ANID-Basal Project FB0008 (AC3E) and ANID-PIA/Apoyo AFB180002 (CCTVal).  
Not applicable.  
No new data were created or analyzed in this study. Data sharing is not applicable to this article.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
ADC Analog to Digital Converter  
ADMM Alternating Directions Method of Multipliers  
DER Distributed Energy Resources  
ER Energy Resource  
HMI Human-Machine Interface  
LQI Linear Quadratic Regulator with Integral Action  
MPC Model Predictive Control  
MIMO Multiple Input Multiple Output  
OSQP Operator Splitting Quadratic Programs  
QP Quadratic Programming  
SVPWM Space Vector Pulse-Width Modulator  
VSI Voltage Source Inverter