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For the conservativeness and computational delay of the traditional finite control set model predictive control (FCS-MPC), a multi-step model predictive voltage control method based on finite control set (FCS-MMPVC) with delay compensation method is proposed in this paper, and the proposed method is validated on a three-level three-phase voltage source PV inverter. In each control cycle, the 27 voltage vectors for inverters are evaluated on line based on predictive model to obtain the optimal and suboptimal switching state. The selected switching state is optimal in two control cycle with the proposed method. Considering that the time spent in the actual sampling and calculation process cannot be ignored, the delay compensation is added in FCS-MMPVC algorithm. The simulation and experimental results show that the proposed method has good stability and reliability. Compared with the traditional FCS-MPC algorithm, the proposed method can reduce the difference significantly between the output voltage and the reference under the unbalanced and non-linear load, and the output voltage quality of the inverter is improved. [ABSTRACT FROM AUTHOR]