This paper presents a generalized multilevel direct power control (ML-DPC) scheme for grid-connected multilevel power converters. The proposed method extends the original DPC operating principle by considering only the closest subset of two-level voltage vectors to the present switching state. The implementation of this principle requires the power derivatives for feedback, which can present numerical problems when applied experimentally, mainly due to high measurement noise sensitivity. Therefore, a derivative estimator is proposed based on the converter-grid model in the synchronous reference frame. In addition, a virtual flux observer is developed to achieve synchronization and improve robustness in the presence of grid voltage harmonics. The proposed method is applicable to any multilevel converter topology of any number of levels. In this paper, simulations and experimental results are presented for a seven-level cascaded H-bridge converter.