Data-Efficient Strategies for Probabilistic Voltage Envelopes under Network Contingencies

TL;DR

This paper introduces a data-efficient, transfer learning-based Gaussian process method for constructing probabilistic voltage envelopes in power grids with network contingencies, significantly reducing computational effort and data requirements.

Contribution

It proposes a novel multi-task vertex degree kernel that effectively transfers knowledge across network configurations, outperforming existing methods in accuracy and efficiency.

Findings

Over 50% reduction in prediction error for N-1 contingencies.

Achieves PVEs with sixteen times fewer power flow solutions.

Outperforms hyper-parameter transfer learning in most N-2 scenarios.

Abstract

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.