With proliferation of distributed energy resources (DERs) and advent of advanced measurement devices in modern distribution grids, an advanced distribution management system (ADMS) is needed to be developed in order to maintain reliability and efficiency of modern distribution systems. However, the numbers of sensors and measurement devices in distribution networks are limited, and communication links between switch devices, sensors, and ADMS are not well-established. Moreover, the fast voltage fluctuation and violation issues caused by high penetration levels of DERs cannot be easily coped with traditional Volt-VAr control (VVC) devices. In this regard, this Dissertation report proposes an ADMS tool including all core components, i.e., topology processor, state estimation, outage detection, DERs scheduling, and Volt-VAr optimization of DERs, for smart distribution networks with DERs, smart meters, and micro-phasor measurement units (micro-PMUs). In order to execute the ADMS tool’s components in an unbalanced distribution system, novel nonlinear and convex AC optimal power flow models based on current-voltage (IVACOPF) formulation are proposed for an unbalanced distribution system with DERs. Applications of the proposed convex IVACOPF model on key parts of ADMS and DERs management system (DERMS), i.e., (i) simultaneous state estimation, topology processor, and outage detection, (ii) DERs scheduling, and (iii) Volt-VAr optimization of DERs, are presented in this report. In this regard, an efficient MIQP-based optimization model based on IVACOPF is proposed to simultaneously identify real-time network topology, estimate system state, and detect outages of unbalanced distribution systems. The proposed model copes with challenges of a real distribution network including: (1) limited locations of measurement devices and unsynchronized measurement data as well as missing and bad data, and (2) complicated mixed-phase switch actions and mutual impedances and shunt admittances. For the Volt-VAr optimization component of ADMS and DERs scheduling, an operational scheduling model of DERs and PV smart inverters with Volt-VAr controllers is proposed using IVACOPF in an unbalanced distribution network. The setpoints of controller setting of each individual PV smart inverter are optimized within the allowable range of the IEEE 1547-2018 standard to improve local as well as system-level voltage regulation in an unbalanced distribution system.