This paper proposes an 𝑁-step ahead model predictive controller for a multilevel asymmetric cascade gridconnected inverter. To this goal, a predictive function controller has been designed based on the Lyapunov theory. First, the equations of the 𝑁-step ahead predictive sequence have been derived for the reference current as well as the reference voltage using first-order linear interpolation considering the mean of previous values. Second, the current, voltage, current error, and Lyapunov function have been calculated for the N-samples ahead. Then, the switching scenario has been determined such that it minimizes the derivation of the Lyapunov function. Moreover, the effect of the number of prediction steps on the unwanted harmonic reduction, switching average, grid power injection, and inverter efficiency has been investigated. Finally, The proposed controller is implemented on a 19-level asymmetric cascaded inverter. The results show that by increasing the prediction steps from 1 to 5, the harmonic distortion and the number of switches are reduced.
