In recent years, the adoption of Distributed Energy Resources (DERs) in power systems has been increasing, driven by technological advancements, development of monitoring and control techniques, policy guidance among various countries, and the benefits DERs bring to the power system. These benefits include low-cost energy production, environmental sustainability promotion, and enhanced operational efficiency of the power system. For instance, demand response (DR) can alleviate pressure during peak load periods, while solar PV units and wind turbines with smart inverters can improve grid reliability through grid regulation based on IEEE Standard 1547. Despite the opportunities DERs present, their adoption also poses challenges. The growing reliance on renewable sources introduces uncertainty, variability, and intermittency, directly impacting system stability and efficiency. Addressing these challenges necessitates comprehensive research to enhance stability, improve system operations, and maximize resource utilization. This dissertation concentrates on two primary research areas: analyzing prosumer (consumers and producers, as one) consumption behavior and developing AC optimal power flow (ACOPF) models. Firstly, understanding prosumer consumption behavior is important for reducing DERs' uncertainty, particularly DR programs. This study employs a proposed probabilistic algorithm to analyze the causal relationships between prosumer consumption behavior and other factors. Two causal-oriented approaches are utilized to establish accurate prediction models and assess demand flexibility. Causal artificial intelligence facilitates intervention and counterfactual analyses of prosumers’ DR participation and consumption behavior. Finally, a Conditional Hidden Semi-Markov Model (CHSMM) is applied to model and predict household appliance electricity consumption, further enhancing understanding of prosumer behavior. Secondly, the dissertation investigates optimization models for efficient, cost-effective power system operation and resource utilization maximization. A convex two-stage socially-aware and risk-aware Second-Order Cone Programming (SOCP)-based ACOPF model is introduced to mitigate DER uncertainty, enhance PV energy utilization, and reduce operational costs. Additionally, a convex SOCP-based ACOPF model is presented for three-phase unbalanced distribution systems, incorporating the Q-V characteristics of PV units with smart inverters based on IEEE Standard 1547. This model enables the participation of PV units with smart inverters in grid voltage regulation, enhancing power system stability and achieving efficient, cost-effective operation.

The grand transition of electric grids from conventional fossil fuel resources to intermittent bulk renewable resources and distributed energy resources (DERs) has initiated a paradigm shift in power system operation. Distributed energy resources (i.e. rooftop solar photovoltaic, battery storage, electric vehicles, and demand response), communication infrastructures, and smart measurement devices provide the opportunity for electric utility customers to play an active role in power system operation and even benefit financially from this opportunity. However, new operational challenges have been introduced due to the intrinsic characteristics of DERs such as intermittency of renewable resources, distributed nature of these resources, variety of DERs technologies and human-in-the-loop effect. Demand response (DR) is one of DERs and is highly influenced by human-in-the-loop effect. A data-driven based analysis is implemented to analyze and reveal the customers price responsiveness, and human-in-the-loop effect. The results confirm the critical impact of demographic characteristics of customers on their interaction with smart grid and their quality of service (QoS). The proposed framework is also applicable to other types of DERs. A chance-constraint based second-order-cone programming AC optimal power flow (SOCP-ACOPF) is utilized to dispatch DERs in distribution grid with knowing customers price responsiveness and energy output distribution. The simulation shows that the reliability of distribution gird can be improved by using chance-constraint.