Accurate optimal power flow for active distribution networks via floating tangent surface

Decarbonization legislated the risen integration of renewable energy sources (RESs) in the presence of energy storage systems (ESS) in distribution networks. Nonetheless, these resources may impose substantial costs to the utilities for managing frequency. In the present era, the concept of active distribution networks (ADNs) has been taken into consideration in the study of grid penetration of RESs and ESSs. Accordingly, ADN requires a so-phisticated AC optimal power flow (OPF) to solve such a complex decision-making process. This paper aims to develop an accurate and effective OPF in ADNs. To this end, this paper contributes to developing a highly efficient tool to operate ADNs under uncertainties in load and renewables. Firstly, a highly accurate and dynamic linear load flow is presented to compensate for the restrictions of nonlinear OPF, such as scalability and robustness. In more detail, the floating tangent surface method is utilized to approximate better the nonlinear and nonconvex equations in the OPF formula. For the iterative process of the dynamic linear approximation, its local convergence can be derived. Then, to make the model much more realistic, the uncertainty of RESs, load, and price is accounted for in a robust approach which alleviates their vulnerability in decisions. The proposed approach is finally formulated as a mixed integer linear problem and implemented in various case studies. After assessing the proposed strategy under different circumstances, the average error of different case studies is 3.30E-06 and 6.24E-02, respectively, for the proposed method and another approach in the literature, which means the proposed method has less error than other methods. From the results, it can be observed that the presented OPF solving method is vastly superior to other prior approaches in terms of more accurate results.