Distributed energy resources (DER) are integrated into a microgrid through dc-dc power electronic converters. The bidirectional dc-dc converter regulates charging and discharging operations of ESS. Model predictive control (MPC), is a high-performance control technique for these converters, but it is limited in robustness to parameter mismatch, model uncertainties and sensor measurement noise. Therefore, in this paper, an improved hybrid cascade-parallel extended state observer (CP-ESO) is proposed, for model-free predictive control, to guarantee both robustness to parameter/model uncertainties and measurement noise suppression. A novel structurally-adaptive ESO scheme is also proposed to improve the disturbance rejection of CP-ESO during transient response. These results are supported by analysis and design guidelines for the selection of optimal sub-frequencies. Experimental results, for a bidirectional dc-dc boost converter, validate the effectiveness of the proposed methods against model uncertainties, external disturbances from variable input voltage and load, as well as measurement noise.