Finite control-set model predictive control (FCS-MPC) has been found as a promising alternative in the control of power converters and motor drives, albeit with model dependence issues. This inherent defect of the FCS-MPC controller triggered the widespread of model-free or data-driven control schemes in recent decades. This article, at hand, presents a data-enabled finite set predictive control solution subject to model dependence issues from the dynamic modeling point of view. In this regard, a dynamic-linearization data model is utilized to equivalently reformulate the governed power converter at each operation point. In pursuit of the accurate modeling of the plant, the time-varying parameters of the data model are updated online by an adaptive linear neural network, rendering a favorable influence on implementation. Additionally, an improved capacitance-less voltage balancing method is proposed to regulate the neutral point potential. Since the parameterless prediction process for both load currents and capacitor voltage relies solely on measured and historical input- output data of the plant, the destructive effect of parameter variations can be circumvented. To evaluate the correctness of the proposed solution, the comparative simulation and experimentation with the conventional method and state-of- the-art solutions are examined on a classic three-level neutral-point-clamped inverter.