This work presents an efficient data-driven method to learn power flows in
grids with network contingencies and to estimate corresponding probabilistic
voltage envelopes (PVE). 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.

通过数据驱动方法，本研究提出了一种高效的电网潮流学习方法，用于处理带有网络事故的电网系统，并估算相应的概率电压包络。该方法利用网络感知高斯过程预测电压功率函数，提出了一种多任务顶点度核方法，将学习到的核函数推广到未知的电网系统，同时降低了计算复杂度和超参数需求。通过在 IEEE 30-Bus 电网上进行的模拟实验，证明了该方法在 N-1 和 N-2 事故情景下保留和传递潮流知识的能力。对于低训练数据量（50-250 个样本）的 N-1 事故网络结构，与 VDK-GP 相比，多任务顶点度核方法的平均预测误差减少了 50% 以上。此外，即使没有历史 N-2 事故数据，多任务顶点度核方法在超过 75% 的 N-2 事故网络结构中也优于基于超参数的迁移学习方法。该方法相比基于蒙特卡洛采样的方法，仅需十六分之一的潮流解决方案即可实现概率电压包络。