The rapid growth of Distributed Energy Resources (DERs), electrification, and the push for decarbonization are transforming the operational landscape of power distribution systems, creating new challenges and opportunities. This thesis presents novel contributions to advance distribution system modeling and energy scheduling methodologies, focusing on improving efficiency, reliability, and scalability. The key contributions are categorized into three main areas: (i) development of a standardized distribution modeling framework, (ii) proposing and enhancing energy scheduling formulations, and (iii) applications to critical operational problems. A generalized modeling framework based on primitive admittance matrices is proposed, offering seamless translation between standard and per-unit representations. Based on this framework, we extend the traditional forward-backward sweep iterative technique for solving the nonlinear power flow equations. The enhancements to traditional energy scheduling formulations incorporate realistic distribution system features, including three-phase networks, loss penalties, reactive power considerations, and a branch constraint screening algorithm. A novel scheduling approach is proposed using the custom forward-backward sweep equations for providing a sequential linearization approach to the exact nonlinear optimization model. Empirically, we demonstrate that the proposed formulation obtains near-optimal primal solutions while reducing computation times by an order of magnitude. Some of the considered Applications include dynamic pricing for Electric Vehicle (EV) smart charging, scheduling-based operating envelopes for DERs, and a web-based interactive visualization interface for supporting sense making when analyzing operations planning results. The EV charging model illustrates how smart strategies can defer infrastructure upgrades, while operating envelopes dynamically manage DER uncertainty by computing in-advance maximum power injection limits. Additionally, a web-based interface was developed to analyze and support sense-making of operations planning results. Together, these advancements support the integration of DERs, enhance grid flexibility, and provide tools for modern distribution network management in a rapidly evolving energy ecosystem.