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We formulate a comprehensive theoretical description of excitation harvesting in molecular aggregates photoexcited by weak incoherent radiation. An efficient numerical scheme that respects the continuity equation for excitation fluxes is developed to compute the nonequilibrium steady state (NESS) arising from the interplay between excitation generation, excitation relaxation, dephasing, trapping at the load, and recombination. The NESS is most conveniently described in the so-called preferred basis in which the steady-state excitonic de