Flexible Shifted-Frequency analysis for Multi-Timescale simulations of active distribution networks

The growing proportion of distributed generators in active distribution networks highlights the importance of multi-timescale system dynamics. The electromagnetic transient simulators with detailed modeling have been widely used for high-fidelity simulations, which leads to a contradiction between the efficiency and accuracy in the studies of the multi-timescale property of the ADNs. The shifted-frequency analysis method integrated with state-space based exponential integration is introduced in this paper, which possesses both high accuracy of exponential integration and the advantage of system-level modeling. It accurately simulates the networks considering the nonlinearities with the advantage that allows large time-steps in the simulations wherein the signals have a small bandwidth around the fundamental frequency. A model-switching method based on the integral transformation of the shifted-frequency models is designed to address the inefficiency of multi-timescale simulations. In addition, a flexible discontinuity treatment in the shifted-frequency domain is introduced for the reduction of the errors brought by the detections and interpolations of discontinuities in the time-domain. Numerical studies are conducted considering the distributed generations, the shifted-frequency models are generated integrally from the original time-domain models. The results of the multi-timescale simulations with model-switching in different domains show the high efficiency of the proposed method, and the discontinuity treatment presents higher accuracy compared with the time-domain solution. Those combined advantages compose the flexible shifted-frequency analysis for the multi-timescale simulations of active distribution networks.