The transition to a sustainable and resilient power grid is essential for addressing the environmental and socio-economic challenges posed by climate change. While the integration of renewable energy resources offers significant benefits, it also introduces complexities in grid management due to their non-dispatchable nature and the need for advanced energy storage solutions. This dissertation focuses on optimizing grid operations, managing renewable integration, and ensuring reliability under various conditions, presenting novel methodologies and insights into our future energy infrastructure. Grid decarbonization is a primary goal, driven by the need to reduce greenhouse gas emissions, mitigate climate change, and promote public health. It also fosters economic benefits such as green job creation and energy independence. However, the shift to a cleaner energy grid presents challenges, including the increased penetration of non-dispatchable resources like wind and solar, the necessity for advanced energy storage solutions, and the requirement for economic analyses to evaluate new technologies and policies. Additionally, upgrading the existing grid infrastructure to accommodate renewable energy sources is crucial to ensure reliability and resilience. Enhancing grid resilience is vital for mitigating the impacts of natural disasters, improving power system reliability and security, and ensuring continuity of supply to customers and critical loads. Achieving resilience involves modeling and incorporating risk into grid operations, preparing for natural disasters, and addressing the exponential complexity of optimization problems. This research introduces wildfire risk-aware planning and the strategic relocation of electric vehicles (EVs) for resilient grid operation as key components of a robust resilience framework. To further improve grid operations, this dissertation proposes an agile decision-support system that accelerates power grid optimization. Enhanced grid resilience is achieved by making the system more robust against disruptions, and improved decision-making is facilitated through faster and more accurate analyses. Real-time optimization becomes feasible, allowing for immediate adjustments to changing conditions, reducing costs, increasing grid flexibility, and improving the accuracy of predictions and planning. This leads to more effective utilization of renewable energy sources. This dissertation presents comprehensive strategies to enhance the resilience and sustainability of a decarbonized power grid. By leveraging advanced optimization techniques and incorporating dynamic models of natural gas and renewable energy interactions, it addresses the critical need for real-time optimization, improved decision-making, and effective renewable energy utilization, ultimately contributing to a more resilient and sustainable energy future.

Emerging sustainable solutions in smart grids such as Distributed Energy Resources(DERs), Vertical Farms (VFs), and Electric Vehicles (EV s) enhances the resilience of the Active Distribution Networks (ADNs). We propose an operational framework to integrate emerging technologies into ADN under solar and demand uncertainty to reduce the operation cost, carbon emissions, and power quality issues of the smart communities. We primarily focus on enhancing the reliability and efficiency of power systems through advanced optimization techniques. A key contribution of this work is the development of a second-order cone programming (SOCP) relaxation approach that addresses cycle constraints in the optimal xxi power flow (OPF) problem. We demonstrate how this method improves the tightness of solutions and reduces computation burdens compared to traditional convex relaxation methods. Additionally, we introduced a strategic bidding framework in electricity markets based on the convexified AC market clearing problem (MCP) for market participants to optimize their bids under various market conditions. Our results demonstrate that the proposed framework renders 52.3% more profit for the market participants. The increase in utilization of solar generation units and EV s in past decades, especially in California, lead to power quality and uncertainty issues in the grid. We proposed the model of Smart Inverters (SI s) to leverage the potential of DERs to offer grid services through reactive power compensation. The results show that solar dispatchability increases by 12% and voltage violation is mitigated when the proposed volt/VAR model is utilized for IEEE 33-bus system. Furthermore, we propose the model of various systems in VFs as an emerging sustainable demand responsive asset in ADNs to mitigate the carbon emissions of the smart communities and increase the resiliency of ADNs against uncertainties in demand and solar generation. To quantify the uncertainties more accurate based on the real data and decrease the conservatism of the robust optimization (RO) method, we propose the data-driven mean robust optimization (MRO) approach for the vertical farming expansion planning problem in ADNs. It is shown that the proposed MRO method can mitigate the carbon emissions of the smart city by up to 10% and decrease the total operation and planning cost of the system compared to utilizing the more conservative RO method.