The future smart grid is envisioned as a large scale cyber-physical system encompassing advanced power, computing, communications and control technologies. This work provides comprehensive accounts of the application with optimization methods, probability theory, commitment and dispatching technologies for addressing open problems in three emerging areas that pertain to the smart grid: unit commitment, service restoration problems in microgrid systems, and charging services for the plug-in hybrid electric vehicle (PHEV) markets. The work on the short-term scheduling problem in renewable-powered islanded microgrids is to determine the least-cost unit commitment (UC) and the associated dispatch, while meeting electricity load, environmental and system operating requirements. A novel probability-based concept, {\em probability of self-sufficiency}, is introduced to indicate the probability that the microgrid is capable of meeting local demand in a self-sufficient manner. Furthermore, we make the first attempt in approaching the mixed-integer UC problem from a convex optimization perspective, which leads to an analytical closed-form characterization of the optimal commitment and dispatch solutions. The extended research of the renewable-powered microgrid in the connection mode is the second part of this work. In this situation, the role of microgrid is changed to be either an electricity provider selling energy to the main grid or a consumer purchasing energy from the main grid. This interaction with the main grid completes work on the scheduling schemes. Third, a microgrid should be connected with the main grid most of the time. However, when a blackout of the main grid occurs, how to guarantee reliability in a microgrid as much as possible becomes an immediate question, which motivates us to investigate the service restoration in a microgrid, driven islanded by an unscheduled breakdown from the main grid. The objective is to determine the maximum of the expected restorative loads by choosing the best arrangement of the power network configurations immediately from the beginning of the breakdown all the way to the end of the island mode. Lastly, the work investigating the pricing strategy in future PHEV markets considers a monopoly market with two typical service classes. The unique characteristics of battery charging result in a piecewise linear quality of service model. Resorting to the concept of subdifferential, some theoretical results, including the existence and uniqueness of the subscriber equilibrium as well as the convergence of the corresponding subscriber dynamics are established. In the course of developing revenue-maximizing pricing strategies for both service classes, a general tradeoff has been identi ed between monetization and customer acquisition. / Graduate