A three-phase trinary-asymmetric cascaded H-bridge multilevel inverter topology with single dc source per phase is presented in this paper. Only one of the H-bridges (called Main bridge) is fed from a dc source and all others (called auxiliary bridges) derive their dc links from floating capacitors. Existing literature mostly depend on closed loop control schemes to stabilize the dc link voltage. This paper proposes a new open loop control strategy for balancing of voltage across floating capacitors naturally. DC bus voltages of the auxiliary bridges are converged to maintain a trinary asymmetric ratio with the main-bridge by selecting the right set of space-vectors. Modulation of the inverter is carried out by exploring the space-vector redundancies that will help in achieving natural balancing of capacitor voltages. Selection of number bridges to be cascaded depends on criteria such as the allowable time of convergence, number of switching devices, acceptable power quality indices etc. Considering such constraints, a system with three cascaded cells per phase is found to exhibit satisfactory performances. Hence in this paper, simulation results obtained in MATLAB/ Simulink based model corresponding to such a system are presented. Experimental results observed on a laboratory prototype matched well with the simulation.