"The integration of higher shares of renewable generation is essential for decarbonizing electricity generation. However, the main challenge of integrating renewable energy sources into a power system is the management of the increased disturbances in power balancing. These disturbances are caused by the inherent variability and uncertainty of renewable energy sources, which can put significant stress on reserve requirements in the system. Traditional power system operation paradigms are becoming less capable of handling this challenge, and this has spurred interest in studying the concept of power system flexibility. Flexibility-based operational planning algorithms typically rely on robust optimization to offer guarantees on the ability of the operator to meet a wide array of possible scenarios. The main downside of these approaches is their conservative results whose operating costs and/or carbon footprint may be sub-economical. Such results come by because these approaches immunize their solutions for the required level of security against realizations of potential events within their uncertainty set. Moreover, these approaches also often ignore the inherent time and spatial couplings of wind and solar generation variability. To tackle this issue, this thesis proposes a modeling technique for uncertainty sets which is called the spatio-temporal flexibility requirement envelope. It reduces the over-conservatism of the robust solution by comprehensively capturing and representing the temporal trends and spatial correlation of multisite renewable generation and load demand. A mathematical program is also developed for applying this envelope to power system unit commitment and dynamic dispatch through projections of the spatio-temporal envelopes, where we mainly focus on microgrid type power systems. We illustrate the effectiveness of the spatio-temporal flexibility requirement envelopes through several case studies. Furthermore, flexibility-based operational planning approaches are usually formulated based on model predictive control paradigms, which requires the online solution of a mixed-integer optimization problem at each sampling time. Such approaches are not amenable to most remote microgrid and practical field microgrid implementations, where controls are typically implemented by industrial controllers with limited computational power and the dispatch algorithm faces stringent execution time for real time operation. To tackle this challenge, in this thesis we also develop rigorous machine learning approaches for simplifying and accelerating the flexibility-based microgrid dispatch algorithms, so that they can be implemented in practical settings for real time operation. The proposed machine learning approaches are able to preserve as much as possible the control performance obtained by full mixed-integer optimization. At the same time, they can provide feasible dispatch decisions. We conduct comprehensive performance evaluations to demonstrate the effectiveness of the proposed machine learning approaches"--