Discrete/continuous-time online algorithm application for time-varying optimal power flow in active distribution networks.

• Four discrete/continuous-time online optimal power flow algorithms are designed. • The proposed algorithms are suitable for active distribution network optimization. • The proposed algorithms are fully evaluated and compared via detailed case studies. • The proposed discrete-time prediction-correction algorithm is the most recommended. This paper discusses and analyzes the latest online algorithm applications for time-varying optimal power flow problems in active distribution networks with numerous power-electronics-interfaced distributed energy resources, which bring significant time-varying characteristics to the optimal operation of active distribution networks. Conventional offline optimization algorithms are time-consuming and unable to track time-varying optimal solutions in highly variable environments. In contrast, online algorithms are characterized by fast calculation speeds and the ability to continuously track optimal solutions, thus having great potential in solving optimization problems that vary rapidly over time. In this paper, we design online time-varying optimal power flow algorithms based on the latest online algorithms, including three discrete-time algorithms (i.e., correction-only, prediction-correction, and correction-extra correction algorithms) and one continuous-time algorithm (i.e., prediction-correction interior-point method). According to our survey of the current applications of online algorithms, this study represents the first time that discrete-time prediction-correction and correction-extra correction algorithms have been applied in solving time-varying optimal power flow problems in active distribution networks. Detailed case studies, including correctness, validity, and sensitivity analysis, are carried out on a modified IEEE 33-node system. The numerical results reveal the advantages, disadvantages, and applicability of the proposed algorithms. Moreover, the characteristics of the discrete-time and continuous-time algorithms are compared intuitively. Finally, based on the numerical results, a guide for how to select an appropriate online time-varying optimal power flow algorithm for active distribution network optimization is provided, wherein the discrete-time prediction-correction optimal power flow algorithm is the most frequently recommended choice. [ABSTRACT FROM AUTHOR]