By using single molecule fluorescence spectroscopy we have investigated the excitation energy migration processes occurring in a series of cyclic porphyrin arrays bearing a close proximity in overall architectures to the LH2 complexes in purple bacterial photosynthetic systems. We have revealed that the conformational heterogeneity induced by the structural flexibility in large cyclic porphyrin arrays, which provides the nonradiative deactivation channels as an energy sink or trap, reduces significantly the energy migration efficiency. Our study provides detailed information on the energy migration efficiency of the artificial light-harvesting arrays at the single molecule level, which will be a guideline for future applications in single molecular photonic devices in the solid state.