# Data-Efficient Strategies for Probabilistic Voltage Envelopes under Network Contingencies

arXiv: https://arxiv.org/abs/2310.00763 · HTML: https://mlsanity.com/paper/2310.00763/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 32 references that are in the map.
- First posted on arXiv 1 Oct 2023.

## Builds on (most cited first, 3 of 3)

- [The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms](https://mlsanity.com/paper/1908.02788/) (2019)
- [Transfer Learning with Gaussian Processes for Bayesian Optimization](https://mlsanity.com/paper/2111.11223/) (2021)
- [Learning Power Flow with Confidence: A Probabilistic Guarantee Framework for Voltage Risk](https://mlsanity.com/paper/2308.07867/) (2023)

## Abstract (arXiv)

This work presents an efficient data-driven method to construct probabilistic voltage envelopes (PVE) using power flow learning in grids with network contingencies. First, a network-aware Gaussian process (GP) termed Vertex-Degree Kernel (VDK-GP), developed in prior work, is used to estimate voltage-power functions for a few network configurations. The paper introduces a novel multi-task vertex degree kernel (MT-VDK) that amalgamates the learned VDK-GPs to determine power flows for unseen networks, with a significant reduction in the computational complexity and hyperparameter requirements compared to alternate approaches. Simulations on the IEEE 30-Bus network demonstrate the retention and transfer of power flow knowledge in both N-1 and N-2 contingency scenarios. The MT-VDK-GP approach achieves over 50% reduction in mean prediction error for novel N-1 contingency network configurations in low training data regimes (50-250 samples) over VDK-GP. Additionally, MT-VDK-GP outperforms a hyper-parameter based transfer learning approach in over 75% of N-2 contingency network structures, even without historical N-2 outage data. The proposed method demonstrates the ability to achieve PVEs using sixteen times fewer power flow solutions compared to Monte-Carlo sampling-based methods.