Model-predictive control is a constrained optimization control method with superior performance than linear methods for multivariable and multiobjective control of power converters. Nonetheless, its performance is limited by model uncertainties and measurement noise. This study tackles this challenge by proposing a new hybrid parallel-cascade extended state observer (PC-ESO) with two key advantages: 1) higher disturbance rejection than the conventional linear ESO and cascade ESO (CESO) at low bandwidth and 2) better noise suppression than the conventional ESO. PC-ESO's time-domain structure and comprehensive frequency-domain analysis are presented. Furthermore, PC-ESO is applied to improve the transient disturbance rejection of CESO through a novel structurally adaptive ESO (SAESO) algorithm. The proposed SAESO provides both high-frequency noise suppression and better disturbance rejection than CESO and cascade-parallel ESO. Finally, the proposed methods are experimentally validated by the model-free predictive control of a grid-connected power converter.