The risk warning for steady-state power quality in the power grid is essential for its prevention and management. However, current risk warning methods fall short in predicting the power quality trend while accounting for potential risks. Consequently, this study introduces a novel steady-state power quality risk warning method utilizing VMD-LSTM and a fuzzy model. Firstly, a power quality index prediction method based on variational mode decomposition (VMD) and long short-term memory (LSTM) is proposed. This approach significantly enhances prediction accuracy. Secondly, a power quality risk warning method incorporating kernel density estimation (KDE) and a fuzzy model is proposed, which systematically addresses the uncertainty associated with power quality risks. To validate the effectiveness and practicality of the proposed method, experiments are conducted using field monitoring data from a residential load in southern China. The results affirm the reliability and applicability of the proposed method. The simulation results show that the median error of prediction of power quality indexes by the proposed method is 5.03 % during the evaluated time period, and the prediction accuracy is mostly maintained above 90 %.
In response to the growing demand for economic and social development, there has been a significant increase in the integration of distributed generation (DG) into distribution networks. This paper proposes a dynamic risk assessment method for voltage violations in distribution networks with DG. Firstly, considering the characteristics of random variables such as load and DG, a probability density function estimation method based on boundary kernel density estimation is proposed. This method accurately models the probability of random variables under different time and external environmental conditions, such as wind speed and global horizontal radiation. Secondly, to address the issue of correlated DG in the same region, an independent transformation method based on the Rosenblatt inverse transform is proposed, which enhances the accuracy of probabilistic load flow. Thirdly, a voltage violation severity index based on the utility function is proposed. This index, in combination with probabilistic load flow results, facilitates the quantitative assessment of voltage violation risks. Finally, the accuracy of the proposed method is verified on the IEEE-33 system.
It is a highly significant area of research to investigate how to effectively enhance the focusing ability of abruptly auto-focusing beams (AAFBs) while extending the focal length. We introduce a dual-region parabolic trajectory offset modulation to auto-focusing ring Pearcey beams (RPBs), presenting a novel, to the best of our knowlege, approach to extend the focal length while greatly enhancing their auto-focusing capabilities. Unlike directly introducing a linear chirp, which inevitably shortens the focal length to enhance the auto-focusing ability and allows only single focusing in the RPBs, our scheme can achieve a multi-focusing effect. Furthermore, we have experimentally generated such a beam, verifying our theoretical predictions. Our findings offer promising possibilities for generating optical bottles, trapping multiple particles periodically, and enhancing free-space optical communication capabilities.
A virtual source (VS) is a hypothetical source instead of an actual physical entity, but provides a distinctive perspective to understand physical fields in a source-free area. In this work, we generalize the VS theory to structured partially coherent light fields (PCLFs) by establishing the partially coherent inhomogeneous Helmholtz equation, then demonstrate that PCLFs can be generated from the incoherent extended VS in imaginary space. Especially, we put forward an understanding of the Gaussian Schell-model beam, which consists of a group of partially coherent paraxial complex rays. The mutual coherence between these rays depends on the included angle between them. In previous studies, the analytical solution of the partially coherent Airy beam was obtained with difficulty by the Huygens-Fresnel integral; however, by applying the VS, we put forward, to our knowledge, an unprecedented analytical solution for a partially coherent Airy beam. We believe this example will qualify the VS as an important perspective to understand structured PCLFs.
The group velocity in the free space of space-time wave packets (STWPs) and light bullets can be flexibly regulated by many advanced strategies; however, these regulations are restricted to only the longitudinal group velocity. In this work, a computational model based on catastrophe theory is proposed, to devise STWPs with both arbitrary transverse and longitudinal accelerations. In particular, we investigate the attenuation-free Pearcey-Gauss STWP, which enriches the family of non-diffracting STWPs. This work may advance the development of space-time structured light fields.
We introduce the propagation of Pearcey Gaussian (PG) beams in a strongly nonlocal nonlinear medium (SNNM) analytically. Our results show that PG beams propagating in the SNNM have two different focusing positions. The intensity peak appears at different focusing positions depending on the selection of the nonlinear parameters. In addition, the effects of the nonlinear parameters and the scaling factor on the trajectory, the position of the intensity focusing, the intensity evolution between focus locations, and the radiation force are studied.
