This paper proposes a new cascaded multilevel converter topology based on three-phase H bridge cells with a common DC-link structure. The proposed multilevel converter topology main advantages, compared with literature renowned multilevel converters topologies, are discussed in the paper, such as modularity, construction, implementation cost, and DC voltage ripple mitigation. Despite presenting an elementary structure and easy implementation, the use of classic PWM switching strategies is not feasible for this topology, causing the appearance of several short-circuit states between its capacitors. Thus, a graph theory algorithm combined with a model predictive control is also proposed in this work to identify and avoid the new cascaded multilevel converter short-circuit switching states and, concomitantly, guaranteeing the converter output power quality. In order to validate the presented topology applicability, a low voltage synchronous static compensators (STATCOM) with an optimal switching vector model predictive control (OSV-MPC) is implemented in a hardware-in-the-loop platform. The real-time experimental results prove the proposed multilevel topology and the OSV-MPC control strategy effectiveness.