The proposed dissertation research investigates Optimization and Control for Microgrid and Power Electronic Converters. The research has two major parts: i- Microgrid Operation and Control, ii- Power Electronic Converter Control and Optimization. In the first part, three focuses are investigated. First, a completely distributed algorithm is developed for dc optimal power flow problem for power distribution systems as one of the necessary functions considered in unit-commitment problem in day-ahead markets. This method is derived based upon the partial primal-dual representation of the economic dispatch problem, which is finally translated to DC-OPF problem. Second, the optimal interaction between the utility and communities will be studied, due to its improtance in real-time markets. The objective of this section will be to develop an iterative agent-based algorithm for optimal utility-community control. The algorithm will consider the AC power system constraints to maintain power system stability. In this algorithm, a simplified model of microgrid is considered. In the third focus, a comprehensive model of microgrid is taken into account. The optimal operation of the microgrid considering energy storage systems and renewable energy resources is investigated. The interaction of such microgrids with the main grid to define the optimal operation of the entire embedded system is studied through two iterative methods. In the microgrid's internal problem, a moving-horizon algorithm is considered to define the optimal dispatch of all distributed energy resources while considering the time-correlated constraints of energy storage systems. A thorough analysis of the effects of the size of storage systems on energy and reserve market parameters are also performed. In the second part, the focus of research is to develop optimal control strategies for Power Electronic Converters. A Model Predictive Control (MPC) switching method is proposed for Modular Multilevel Converters (MMC). The optimal solution of MPC problem is then represented as an optimization problem. Due to lack of efficient algorithms to seek the optimal solution, a fast algorithm will be proposed in this research. The method proposed reduces the number of possible solutions and computation efforts dramatically.