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This article presents a hierarchical finite-set model predictive control (MPC) scheme to enable autonomous operation and self-balancing cascaded multilevel inverter. The proposed approach is an alternative to MPC scheme based on a generic cost function, which in some applications is ill fit or challenging to design. The proposed controller has a hierarchical framework to eliminate the overall cost function optimization and associated weight factor design stage of the control objectives. The control formulation approach allows for multiobjective optimization with a cost-tolerance framework. The concept is well suited to simplify the control design stage of cascaded H-bridge inverters at the grid-edge with advanced functionality. The control scheme achieves active and reactive power control with switching event reduction while equalizing power draw from the independent voltage sources. The latter of these objectives is made possible by the proposed hierarchical approach to the control objective tracking. The control is modularized for each phase, making the system robust to unbalanced grid conditions. The concept is explained in depth in simulation, and then tested experimentally on hardware.