Conformalized Prediction of Post-Fault Voltage Trajectories Using Pre-trained and Finetuned Attention-Driven Neural Operators

TL;DR

The proposed operator regression model maps the observed portion of the voltage trajectory to its unobserved post-fault trajectory, and integrates conformal prediction into the fine-tuned model to ensure coverage guarantees for the predicted intervals.

Abstract

This paper proposes a new data-driven methodology for predicting intervals of post-fault voltage trajectories in power systems. We begin by introducing the Quantile Attention-Fourier Deep Operator Network (QAF-DeepONet), designed to capture the complex dynamics of voltage trajectories and reliably estimate quantiles of the target trajectory without any distributional assumptions. The proposed operator regression model maps the observed portion of the voltage trajectory to its unobserved post-fault trajectory. Our methodology employs a pre-training and fine-tuning process to address the challenge of limited data availability. To ensure data privacy in learning the pre-trained model, we use merging via federated learning with data from neighboring buses, enabling the model to learn the underlying voltage dynamics from such buses without directly sharing their data. After pre-training, we fine-tune the model with data from the target bus, allowing it to adapt to unique dynamics and operating conditions. Finally, we integrate conformal prediction into the fine-tuned model to ensure coverage guarantees for the predicted intervals. We evaluated the performance of the proposed methodology using the New England 39-bus test system considering detailed models of voltage and frequency controllers. Two metrics, Prediction Interval Coverage Probability (PICP) and Prediction Interval Normalized Average Width (PINAW), are used to numerically assess the model's performance in predicting intervals. The results show that the proposed approach offers practical and reliable uncertainty quantification in predicting the interval of post-fault voltage trajectories.

Figures (10)

• Figure 1: Temporal domains $\mathcal{T}_u$ and $\mathcal{T}_v$ for a sample voltage trajectory. The input function $u$ is defined over $\mathcal{T}_u$, and the output function $v$ is defined over $\mathcal{T}_v$. $\Delta t_{\text{obs}}$ is an adjustable hyperparameter that determines the duration of observable part of the post-fault stage, directly influencing the performance of the mapping $\mathcal{G}$.
• Figure 2: A schematic representation of the DeepONet architecture. The figure illustrates the two main components: the branch network, which encodes the input function $u \in \mathcal{U}$, and the trunk network, which processes the evaluation points $t \in \mathcal{T}_v$. The outputs of these networks are merged through an inner product to approximate the target operator $\mathcal{G} \approx \mathcal{G}^{\theta}.$
• Figure 3: Schematic representation of the Attention-Fourier Deep Operator Network (AF-DeepONet).
• Figure 4: Schematic representation of the Quantile Attention-Fourier Deep Operator Network (QAF-DeepONet).
• Figure 5: New England 39-bus test system.