Non-convexity of Optimal Power Flow (OPF) problem in power systems poses difficulties in reaching optimal solutions which can adversely affect the overall solution efficiency, convergence and appropriate scheduling of generators. Dynamic convex OPF approaches aims to provide optimal generation scheduling and determine appropriate control action across operational time frames for different components of active power systems. In this work, an approach based on convex Optimal Power Flow (OPF) formulation integrated within Receding Horizon Control (RHC) method using second order conic programming (SOCP) suitable for active power distribution system is proposed. The main advantages of the RHC-Convex OPF approach are that, it can; a) integrate dynamic models and uncertain energy resources and, b) reach global optimal scheduling with faster computation time. An architecture for real-time implementation is also presented. Also, a new voltage stability constrained convex optimal power flow (VSC-OPF) approach is proposed using semi-definite programming (SDP). Methods within this approach provide optimal dispatch solution considering a) maximum stability margin, b) minimum operating cost constrained by stability margin and c) an intermediate function that can define a trade-off between cost and enhancing stability. Further, these methodologies are extended for optimal scheduling of integrated AC-DC system. The proposed methods address some limitations of AC-DC OPF methods due to non-convexity, separate scheduling of AC and DC networks or using equivalent of DC network. The advantages of the proposed approach are that it can; a) find the optimal operating point, b) find the maximum loadablility point and c) assess voltage security cost.