Probabilistic modelling of power systems operation and planning processes
depends on data-driven methods, which require sufficiently large datasets. When
historical data lacks this, it is desired to model the underlying data
generation mechanism as a probability distribution to assess the data quality
and generate more data, if needed. Kernel density estimation (KDE) based models
are popular choices for this task, but they fail to adapt to data regions with
varying densities. In this paper, an adaptive KDE model is employed to
circumvent this, where each kernel in the model has an individual bandwidth.
The leave-one-out maximum log-likelihood (LOO-MLL) criterion is proposed to
prevent the singular solutions that the regular MLL criterion gives rise to,
and it is proven that LOO-MLL prevents these. Relying on this guaranteed
robustness, the model is extended by assigning learnable weights to the
kernels. In addition, a modified expectation-maximization algorithm is employed
to accelerate the optimization speed reliably. The performance of the proposed
method and models are exhibited on two power systems datasets using different
statistical tests and by comparison with Gaussian mixture models. Results show
that the proposed models have promising performance, in addition to their
singularity prevention guarantees.

基于数据驱动方法的概率建模用于电力系统运行和规划过程，需要充足的大型数据集。本文提出一种自适应的核密度估计模型，通过分配可学习的权重给核心实现了该模型的性能改进，同时使用修正的期望最大化算法加快优化速度，并通过和高斯混合模型的比较，表明所提出的模型具有良好的性能。