Nonparametric Probabilistic Pseudo-Measurement Model for Unbalanced Active Distribution Networks

In this paper, a multi-variant and probabilistic pseudo-measurement model is proposed for unbalanced active distribution networks. This model can establish a different set of pseudo-measurements at forecasting and process levels. The least-square density estimator (LSCDE) is developed to model pseudo-measurements as a conditional probability density function (PDF) to provide full statistics of measurable parameters without the knowledge of the PDF model. The proposed model performs well at the forecasting level for load consumption and renewable power generation, and at the process level for signals measured by advanced measuring systems for buses and lines. It requires a limited number of data and shows robust performance in the presence of noises. Its effectiveness is validated by the IEEE 123-bus test system, which is a large-scale and highly unbalanced network, and by comparing with the performance of the neighbor kernel density estimator (NKDE) and conditional kernel density estimator (CKDE).