# A Multivariate Density Forecast Approach for Online Power System Security Assessment

arXiv: https://arxiv.org/abs/2105.03047 · HTML: https://mlsanity.com/paper/2105.03047/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 24 references that are in the map.
- First posted on arXiv 7 May 2021.

## Builds on (most cited first, 5 of 5)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [LSTM: A Search Space Odyssey](https://mlsanity.com/paper/1503.04069/) (2015)
- [A Data-Driven Sparse Polynomial Chaos Expansion Method to Assess Probabilistic Total Transfer Capability for Power Systems with Renewables](https://mlsanity.com/paper/2010.14358/) (2020)

## Abstract (arXiv)

A multivariate density forecast model based on deep learning is designed in this paper to forecast the joint cumulative distribution functions (JCDFs) of multiple security margins in power systems. Differing from existing multivariate density forecast models, the proposed method requires no a priori hypotheses on the distribution of forecasting targets. In addition, based on the universal approximation capability of neural networks, the value domain of the proposed approach has been proven to include all continuous JCDFs. The forecasted JCDF is further employed to calculate the deterministic security assessment index evaluating the security level of future power system operations. Numerical tests verify the superiority of the proposed method over current multivariate density forecast models. The deterministic security assessment index is demonstrated to be more informative for operators than security margins as well.