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This paper describes photovoltaic (PV) module architectures with parallel-connected submodule-integrated dc-dc converters (subMICs) that improve efficiency of energy capture in the presence of partial shading or other mismatch conditions. The subMICs are bidirectional isolated dc-dc converters capable of injecting or subtracting currents to balance the module substring voltages. When no mismatches are present, the subMICs are simply shut down, resulting in zero insertion losses. It is shown that the objective of minimum subMIC power processing can be solved as a linear programming problem. A simple close-to-optimal distributed control approach is presented that allows autonomous subMIC control without the need for a central controller or any communication among the subMICs. Furthermore, the proposed control approach is well suited for an isolated-port architecture, which yields additional practical advantages including reduced subMIC power and voltage ratings. The architectures and the control approach are validated by simulations and experimental results using three bidirectional flyback subMICs attached to a standard 180-W, 72-cell PV module, yielding greater than 98% module-level power processing efficiency for a mismatch less than 25%.