Bi-level stochastic optimization model of smart distribution grids considering the transmission network to reduce vulnerability

This paper presents a novel optimization framework for integrating transmission and distribution networks. The proposed framework consists of a bi-level optimization model, which comprises an upper-level problem and a lower-level problem. The upper-level problem addresses unit commitment (UC) in the transmission network, aiming to minimize operating costs and load shedding. It is formulated as a mixed-integer linear programming model (MILP). Meanwhile, the lower-level problem focuses on the optimal operation of the distribution network, considering both renewable and non-renewable resources, as well as electric vehicle charging stations (EVCS). This problem is formulated as a linear model with the objectives of reducing power purchase costs from the transmission network and maximizing the utilization of renewable energy and EVCS charging power. The literature review highlights three main research gaps. Firstly, it is crucial to develop a convex model that ensures globally optimal solutions. Secondly, considering the problem-solving time, it is important to devise a method that can achieve globally optimal solutions in the shortest possible time, accounting for the dimensions, number of variables, and parameters involved in coordinating the transmission and distribution networks. Lastly, there is a need to develop a modeling approach that allows the integration of any number of distribution networks with the transmission network. To address these research gaps, we propose a solution methodology that involves rewriting the optimization problems using reformulation and decomposition methods. This approach enables the modeling of globally optimal solutions while ensuring faster solution times and the ability to incorporate numerous distribution networks into the transmission network. We validate the proposed model and methodology using various networks, and the results demonstrate the efficiency of our approach in coordinating the operation of transmission and smart distribution networks. The simulation results indicate that our proposed method outperforms alternative approaches. Specifically, the results show that the proposed approach effectively mitigates load interruptions in the distribution networks when renewable and non-renewable resources experience interruptions in each system. As a direct consequence, the vulnerability of the distribution networks has significantly diminished, showcasing the robustness and resilience of our approach to handling resource interruptions. Notably, the proposed approach is 40% faster than the KKT method and 20% faster than the evolutionary method, with approximately 8% more optimal results than the evolutionary method, demonstrating its superior coordination for integrated transmission and distribution networks.