Nowadays, a high penetration level of distributed energy resources (DERs), such as renewables, energy storage, and electric vehicles, are integrated into modern electric power grids, especially power distribution sections, through inverter-based interfaces. Depending on the interfacing technologies and capacities of different DERs, the power distribution networks with inverter-based DERs feature different characteristics, which motivates this dissertation to investigate the modeling, design, and control of heterogeneous inverter-based power distribution networks. First, an example of a DER power distribution network, a PV system, is studied and an optimal design framework for PV systems is proposed considering two objectives, levelized cost of energy (LCOE) and power density (PD). Second, to further improve the performance of the inverter-based distribution networks, the harmonic characteristics of a generic grid-interactive inverter is investigated. A holistic mathematical harmonic state space (M-HSS) model of a grid-interactive inverter is derived to calculate each order of harmonics of grid-connected current. Moreover, to further reduce the computation burden caused by repetitive usage of the mathematical HSS model during the optimal design process, a data-driven HSS (D-HSS) modeling method is proposed by incorporating the data-driven techniques into the aforementioned M-HSS modeling. Based on the M- and D-HSS models, an effective optimal design framework is proposed to determine the closed-loop inverter system parameters. Furthermore, due to the increasing deployment of power electronic devices and nonlinear loads, power grids in the distribution network typically present certain degrees of low and/or high order harmonics. Thus, a harmonic compensation control (HCC) scheme is proposed to ensure that the inverter-based distribution network could provide high-quality grid current injection under distorted grid voltage conditions. Additionally, an energy-stored quasi-Z source converter (qZSC) based interlink converter is proposed for hybrid AC/DC microgrids in the distribution networks. The proposed system not only interlinks both AC and DC sub-microgrids but also incorporates energy storage. The operating principle, operating states as well as control schemes are presented in detail. Finally, another DER power distribution network, a medium voltage DC (MVDC) distribution network, is investigated in the study. First, the dissertation proposes an effective fault management scheme for MVDC networks, which includes a virtual-impedance-based fault current limiter (VI-FCL) on the DC side and a positive-negative-sequence (PNS) control scheme on the AC side. Finally, another DER power distribution network, a medium voltage DC (MVDC) distribution network, is investigated in the study. First, the dissertation proposes an effective fault management scheme for MVDC networks, which includes a virtualimpedance-based fault current limiter (VI-FCL) on the DC side and a positive-negativesequence (PNS) control scheme on the AC side. Then, a detailed 2ω mathematical model of the MVDC network under unbalanced AC voltage conditions is derived to investigate how the 2ω ripple propagates across the network and the corresponding control scheme is investigated to mitigate the 2ω ripple. / Electrical and Computer Engineering